Tomographic Imaging of the Tropical Forest in P-Band · 2014-01-26 · BIOMASS of the European Space Agency. This satellite would host a P-band radar with 6 MHz bandwidth for the

Politecnico di MilanoDipartimento di Elettronica e Informazione

DOTTORATO DI RICERCA IN INGEGNERIA DELL’INFORMAZIONE

Tomographic Imaging of the TropicalForest in P-Band

Doctor dissertation of

Ho Tong Minh Dinh

AdvisorProf. Fabio Rocca

2013-XXV

“All truths are easy to understand once they are discovered;the point is to discover them.” [Galileo Galilei]

Contents

Abstract 1

1. Introduction 31.1. Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2. Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2. BIOMASS mission 92.1. The need for global biomass information . . . . . . . . . . . . . . . . 92.2. BIOMASS mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1. Main objective . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2. Mission characteristics . . . . . . . . . . . . . . . . . . . . . . 12

2.3. BIOMASS Tomography Phase : orbital constraint . . . . . . . . . . . 15

3. Multi-Baseline SAR Tomography: Biomass Estimation 173.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2. Tomography processing . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2.1. Phase calibration and baseline interpolation . . . . . . . . . . 203.2.2. Tomographic imaging . . . . . . . . . . . . . . . . . . . . . . . 213.2.3. Terrain topography estimation . . . . . . . . . . . . . . . . . . 213.2.4. Topographic compensation . . . . . . . . . . . . . . . . . . . 223.2.5. Geocoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3. TropiSAR Paracou data-sets . . . . . . . . . . . . . . . . . . . . . . . 243.3.1. Paracou test site . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.2. SAR data-sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.3. Above-ground biomass data-sets . . . . . . . . . . . . . . . . 25

3.4. Results from tomography . . . . . . . . . . . . . . . . . . . . . . . . 263.4.1. Multi-layer images . . . . . . . . . . . . . . . . . . . . . . . . 263.4.2. Topographic compensation . . . . . . . . . . . . . . . . . . . 293.4.3. Tomographic profiles . . . . . . . . . . . . . . . . . . . . . . . 293.4.4. Ground-trunk scattering . . . . . . . . . . . . . . . . . . . . . 32

3.5. Relation to forest biomass . . . . . . . . . . . . . . . . . . . . . . . . 323.5.1. Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . 323.5.2. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.5.3. Biomass inversion . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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Contents Contents

4. Ground Based Array for Tomographic Imaging 434.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2. TropiScat experiment overview . . . . . . . . . . . . . . . . . . . . . 44

4.2.1. The Paracou field station . . . . . . . . . . . . . . . . . . . . . 444.2.2. System architecture . . . . . . . . . . . . . . . . . . . . . . . . 454.2.3. Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.4. Vector Network Analyzer . . . . . . . . . . . . . . . . . . . . 46

4.3. Mathematical data model . . . . . . . . . . . . . . . . . . . . . . . . 464.3.1. Scattering model . . . . . . . . . . . . . . . . . . . . . . . . . 474.3.2. Antenna field model . . . . . . . . . . . . . . . . . . . . . . . 484.3.3. Received signal model . . . . . . . . . . . . . . . . . . . . . . 49

4.4. TropiScat tomographic array design . . . . . . . . . . . . . . . . . . . 494.4.1. Tomographic array design . . . . . . . . . . . . . . . . . . . . 504.4.2. Tomographic coherent focusing . . . . . . . . . . . . . . . . . 534.4.3. Numerical simulations . . . . . . . . . . . . . . . . . . . . . . 544.4.4. Bistatic effects . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.5.1. System pulse response . . . . . . . . . . . . . . . . . . . . . . 564.5.2. System stability . . . . . . . . . . . . . . . . . . . . . . . . . . 584.5.3. Multi polarization tomograms . . . . . . . . . . . . . . . . . . 624.5.4. Multi frequency tomograms . . . . . . . . . . . . . . . . . . . 63

4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5. Multi-Temporal Multi-Polarimetric Tomographic Imaging 655.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2. TropiScat tomographic mode . . . . . . . . . . . . . . . . . . . . . . 65

5.2.1. Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2.2. Tomographic system array . . . . . . . . . . . . . . . . . . . 66

5.3. Tomographic movie . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.3.1. Terrain flattening . . . . . . . . . . . . . . . . . . . . . . . . . 675.3.2. Tomographic movie . . . . . . . . . . . . . . . . . . . . . . . . 68

5.4. Short term temporal decorrelation . . . . . . . . . . . . . . . . . . . 705.4.1. Coherency matrix . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.2. 1 full day coherency matrix . . . . . . . . . . . . . . . . . . . 725.4.3. Multi-temporal multi-polarization decomposition . . . . . . . 72

5.5. Long term temporal decorrelation . . . . . . . . . . . . . . . . . . . 775.5.1. Coherency matrix at night time . . . . . . . . . . . . . . . . . 775.5.2. Temporal coherence estimation . . . . . . . . . . . . . . . . . 825.5.3. Temporal decorrelation modelling . . . . . . . . . . . . . . . . 84

5.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6. BIOMASS Tomography Phase Performances 876.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

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Contents

6.2. BIOMASS SAR reconstruction . . . . . . . . . . . . . . . . . . . . . 886.2.1. SAR Data model . . . . . . . . . . . . . . . . . . . . . . . . . 886.2.2. Impulse response function . . . . . . . . . . . . . . . . . . . . 906.2.3. BIOMASS parameters . . . . . . . . . . . . . . . . . . . . . . 90

6.3. Tomographic processing . . . . . . . . . . . . . . . . . . . . . . . . . 916.3.1. Phase flattening . . . . . . . . . . . . . . . . . . . . . . . . . . 916.3.2. Common Band Filtering . . . . . . . . . . . . . . . . . . . . . 926.3.3. Spectral density estimation . . . . . . . . . . . . . . . . . . . 94

6.4. Reduce of bandwidth: ideal scenario . . . . . . . . . . . . . . . . . . 956.5. Ionospheric disturbances . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.5.1. Phase disturbances . . . . . . . . . . . . . . . . . . . . . . . . 986.5.2. Faraday rotation . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.6. Temporal decorrelation . . . . . . . . . . . . . . . . . . . . . . . . . 1026.6.1. Simulation of temporally decorrelated data . . . . . . . . . . . 1026.6.2. Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . 1046.6.3. Other configurations . . . . . . . . . . . . . . . . . . . . . . . 107

6.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7. Summary 113

Publications 117

Acknowledgments 119

A. Polarimetry independent SAR tomography for tropical forest biomass 121A.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121A.2. Paracou and Nouragues forests result . . . . . . . . . . . . . . . . . . 122A.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

B. P-band SAR tomography imaging at 6 MHz bandwidth 125B.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125B.2. Reducing 6 Mhz data-sets . . . . . . . . . . . . . . . . . . . . . . . . 126B.3. Tomography profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126B.4. Tropical forest biomass relation . . . . . . . . . . . . . . . . . . . . . 126B.5. Forest height estimation . . . . . . . . . . . . . . . . . . . . . . . . . 131B.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Bibliography 135

iii

Abstract

The scope of this dissertation is to provide a discussion about the potentials andperformances of the Tomographic Phase of the candidate future radar satelliteBIOMASS of the European Space Agency. This satellite would host a P-bandradar with 6 MHz bandwidth for the remote sensing of natural scenarios, such asagricultural fields, soil surfaces, mountain areas and forests. In the case of forestedareas, the object under analysis corresponds to the vertical structure of the trees,to be explored by tomographic techniques. This work can be divided in three partsas follows.The first part of the dissertation focuses on the problem of biomass estimation intropical forests. The retrieval of biomass in dense tropical forests using SyntheticAperture Radar (SAR) images is widely recognized as a challenging task. Thisis mainly due to the backscatter saturation effect at high biomass values and theground topography effect. The study presented in this part is an attempt to over-come these problems based on direct three-dimensional imaging of the forest volume,which is possible through multi-baseline SAR tomography.The second part is dedicated to the ground based array system to complementtomographic airborne data-set. We proposed an array design which is well suitedto study the vertical distribution of forest parameters and their temporal changes.This design has been successfully implemented in October 2011 in Paracou, FrenchGuiana. Concerning short term temporal decorrelation, results indicate that duringthe day-time the motion of the forest is strong due to wind and temperature changes,whereas it appears to be definitively more stable during night hours. This resultsuggests that BIOMASS mission performance over tropical forest could be optimizedby gathering acquisitions at dawn or dusk time. The coherence values at differentforest heights are observed to stay high even after 27 days. This result is criticalfor the BIOMASS mission because the high temporal coherence after a 27 day is aprerequisite for SAR Polarimetric Interferometry and Tomographic applications ina single satellite configuration.The final part is to provide performance assessments on the BIOMASS TomographicPhase. We discuss the impact of temporal decorrelation and ionospheric distur-bances affecting SAR images on the quality of BIOMASS tomographic measure-ments. It is shown that temporal decorrelation has a more significant impact thanionosphere disturbance. Concerning the temporal decorrelation, the results fromstudies show that, providing that the revisit times for the tomographic campaignsbe 3-4 days as predicted, the problem does not becomes critical.

1

Lo scopo della dissertazione è discutere il potenziale e le prestazioni derivanti dallaFase Tomografica del sistema Radar satellitare BIOMASS, attualmente in fase di va-lutazione presso l’Agenzia Spaziale Europea (ESA) in qualità di futura missione perl’osservazione della Terra. Tale sistema sarebbe costituito da un Radar ad AperturaSintetica (SAR) operante in banda-P dedicato al telerilevamento di scenari naturali,quali ad esempio i campi agricoli, zone montagnose e soprattutto foreste. Questeultime verrebbero analizzate tramite BIOMASS per mezzo di tecniche tomografiche,permettendo di ricostruire l’informazione sulla struttura verticale della vegetazione.Questo lavoro è diviso in tre parti.La prima parte della dissertazione è focalizzata sulla stima della biomassa nelleforeste tropicali. Tale problema è stato considerato in un gran numero di lavori inletteratura, nei quali la biomassa viene stimata a partire da misure SAR di intensitào polarimetriche. È stato tuttavia largamente riconosciuto che tali metodi offronoprestazioni limitate, a causa degli effetti di saturazione dell’intensità del segnalead alti valori di biomassa e delle interazioni con la topografia del territorio. Lostudio in oggetto si propone di risolvere questi problemi mediante la formazionedi immagini tridimensionali del volume delle foreste, ottenute combinando passaggimultipli tramite tecniche SAR tomografiche.La seconda parte della dissertazione è dedicata ad illustrare il progetto, l’implementazionee i risultati di una campagna Radar di terra volta a raccogliere informazioni sullevariazioni temporali in una foresta tropicale. La strumentazione è costituita da unaschiera di antenne, configurate in modo tale da produrre immagini della strutturaverticale della foresta ogni 15 minuti per un tempo totale di vari mesi. Il sistemaè stato realizzato con successo nell’Ottobre 2011 a Paracou, in Guiana Francese. Irisultati indicano una forte decorrelazione a breve termine durante il giorno, a causadel cambiamento di vento e temperatura, mentre le ore serali e notturne appaionoessere più stabili. Questo risultato suggerisce che le prestazioni di BIOMASS nelleforeste tropicali possano essere ottimizzate acquisendo all’alba o al tramonto. Lacoerenza a differenti altezze nelle foreste si osserva essere alta persino dopo 27 giorni.Questo risultato è essenziale per la missione BIOMASS perché l’alta coerenza tem-porale a 27 giorni è un prerequisito per l’applicazione di tecniche interferometriche.L’ultima parte della dissertazione è dedicata alla valutazione delle prestazioni dellaFase Tomografica di BIOMASS sulla base degli sviluppi descritti nelle prime dueparti. Verrà dimostrato come la decorrelazione temporale sia il principale elementodi criticità. Verrà inoltre dimostrata sperimentalmente, sulla base delle misure ot-tenute, la possibilità di ottenere misure tomografiche tramite BIOMASS utilizzandoun tempo di rivisita di 3-4 giorni.

2

1. Introduction

Synthetic Aperture Radar (SAR) imaging has become a powerful remote sensingmean for observing the Earth’s surface since the late 1970’s. Airborne and space-borne SAR systems are able to image immense portions of the Earth’s surface witha spatial resolution in the order of tens of meters to tens of centimeters [1], [2], [3].SAR systems utilize active sensors operating in microwave regimes, typically in P-,L-, C-, and X- bands. This results in the capability to acquire data independently onsun illumination and weather conditions, hence constituting a significant advantageover traditional optical imaging techniques. As a consequence, in the last thirtyyears spaceborne SARs provided a continuous coverage of almost the whole Earth’ssurface, resulting in data for many applications over sea, ice, urban, forest, volcano,and mountain areas [4], [5], [6], [7], [8].Tropical forest biomass plays a key role in the global carbon cycle, and hence inthe global climate [9], [10], [11], [12]. Despite their importance, however, tropicalforests remain poorly characterized compared to other ecosystems on the planet [13],[14]. Unfortunately, up to now spaceborne SAR data are still limited in dense forestsbecause they are only available at three different frequency bands: L-, C- and X-band[15], [16], [17]. A foreseen, a significant attempt to fill this gap is represented by thecandidate Earth Explorer Core Mission BIOMASS [18], [19]. The BIOMASS missionwould employ the first spaceborne SAR operated at long wavelength P-band (435MHz), therefore providing unprecedented capabilities concerning the investigationof densely forested areas.The BIOMASS mission was selected for Feasibility Study (Phase A) in March 2009[19],[18]. If selected, this would be the first ever SAR P-band (435 MHz) sensorin space. BIOMASS certainly appears to be a sensor capable of providing the ur-gently needed global knowledge about biomass. It seizes the new opportunity fromthe allocation of a P-band frequency band for remote sensing by the InternationalTelecommunications Union (ITU) in 2003. It will be a major addition to currentefforts to build a global carbon data assimilation system that will harness the ca-pabilities of a range of satellites and in situ data [20]. It is within this context thatBIOMASS will find its most important application, both gaining from and comple-menting what can be learnt from other satellite systems, ground data, and carboncycle models [19].The biomass retrieval algorithms developed for BIOMASS are mainly based on theuse of backscatter measurements derived from intensity, polarimetry and interfer-ometry [21], [22]. For tropical forests with very high biomass density (more than

3

Chapter 1 Introduction

300 t.ha−1), for which intensity inversion provides biomass values with low accu-racy [23], the polarimetric interferometric SAR (PolInSAR) and tomographic SAR(TomoSAR) measurements are expected to become the key measurements [19]. How-erver, this argument has not been proved so far and therefore it is necessary to haveexperimental demonstrations.TomoSAR has often been employed in recent years to retrieve information aboutthe vertical structure of the observed scene, based on its capability to resolve mul-tiple targets within a single resolution cell [24], [25], [26], [27], [28]. The BIOMASSis foreseen to be operated in a Tomographic Phase during approximately the firsttwo months of mission lifetime. During this phase the system will orbit in sucha way to be able to gather multiple acquisitions characterized by small baselines,i.e: the distance between two repeat orbits, and a repeat pass time in the order offew days, i.e: 3-4 days, therefore allowing tomographic imaging of the vegetationlayer. This phase is expected to result in an important reference data set providinginformation on the forest vertical structures. This will potentially lead to usefulinputs and recommendations for improving single baseline PolInSAR inversion dur-ing the Operational Phase, as well as giving a better understanding of how longwavelength radar signals interact with forests. However, in a repeat-pass system,the time between the acquisitions allows changes due not only to the wind inducedmotions but also to other events, i.e., rainfall precipitations, soil moisture, break-ing branches, etc. Such changes lead to temporal decorrelation of the InSAR data.Temporal decorrelation is probably the most critical factor against a successful im-plementation of PolInSAR and TomoSAR techniques. As a result, evaluating theimpact of temporal decorrelation in forested areas becomes a crucial issue. Thetemporal decorrelation in spaceborne L-band InSAR from forested areas was firstreported for SEASAT data [29]. More recently, with JERS-1 and PALSAR data,it had been shown that the loss of temporal coherence (i.e: after repeat intervalof 45 days) prevented recovery of forest height by polarimetric SAR interferometry.Therefore, studying temporal decorrelation at P-band seems to be the most urgenttask to be accomplished nowadays. This will then provide input for the quantita-tive assessment of PolInSAR and specially TomoSAR results achievable through theexploitation of multi pass BIOMASS surveys on tropical forests.

1.1. Contributions

There are three main focuses of this work. First, we describe a novel method thatdemonstrates our ability to image tropical forest biomass using airborne P-bandSAR tomography. Second, we propose and present a ground based radar systemfor vertical temporal decorrelation studies in forests. Third, we combine the air-borne and ground based data measurements to study the performances of temporaldecorrelation, in order to answer the fundamental questions about BIOMASS To-mography Phase.

4

1.1 Contributions

Although the candidate is the first author of all contributions in this dissertation, itis certainly the results of working closely with research colleagues. We summarizethe main contributions of this dissertation as below:

1. We propose and implement a novel approach to obtain TomoSAR informationrelevant to the retrieval of forest biomass.

2. We demonstrate this approach to retrieve forest biomass in Paracou andNouragues.

3. We find that volume scattering is significantly related to the high range biomass.Double bounces from ground-trunk interactions in flat terrain topography arevisible everywhere and are a significant noise source for forest biomass retrieval.

4. We find that for both test-sites, the backscattered power associated with thevolume layer (about 30 m above the ground) is observed to exhibit the high-est sensitivity to forest biomass, even for high biomass values (250-500 t/ha).Furthermore, this result appears to be loosely dependent on the employedpolarization, as a similar behavior is observed in both linear and circular po-larization.

5. We find that in tropical forests not only in the cross-polar HV channel, butalso in the co-pol HH and VV channels, the contributions from the canopy isimportant. However, relevant contributions from the ground level beneath theforest are also observed.

6. We design and implement a ground based tomographic array for vertical imag-ing of tropical forests based on a virtual array concept.

7. We produce the first tomographic movie capturing the forest daily reflectivity.8. We find that there is a diurnal vertical motion of the forest center of mass and

this phenomenon is strongly related to daily temperature variations, whichsuggests a connection with forest evapotranspiration phenomena.

9. We find that the temporal coherence daily drops during daytime and there-fore it suggests that performance over tropical forest could be optimized bygathering acquisitions at dawn or dusk time.

10. We propose the sum of Kronecker products as a model to represent and providea reasonable description of the structure of the covariance matrix of the multi-polarimetric and multi-temporal data.

11. We find that temporal coherence in the HV channel after 27 days has beenobserved to be about 0.8 at the ground level and 0.65 in the middle of thevegetation layer, therefore witnessing coherence sensitivity to height.

12. We demonstrate that the reduction of the bandwidth to BIOMASS 6 MHz from150 MHz causes the losses in vertical resolution but it is not really damaging.

13. We find that for ionosphere disturbances in BIOMASS, using 6 or more passes,no relevant performance loss is expected to arise from the Faraday rotation

5

Chapter 1 Introduction

within an accuracy of 5 degrees and from phase screens with standard deviationup to 10 degrees.

14. We find that temporal decorrelation has a more significant impact than iono-sphere disturbance. However, the results from the studies show that the revisittimes for the tomographic campaigns at 4 days as predicted should not be crit-ical.

15. We propose that in BIOMASS acquisitions, the total aperture does not needto be greater than about 1.5 time the critical baseline. Moreover, the spatialbaseline can be designed in such a way to parallel the temporal baseline, thussimplifying the data acquisition strategy.

1.2. Thesis outline

This thesis is organized as follows. Chapter 2 will be devoted to highlight theopportunity of the BIOMASS SAR P-band satellite system. The aim of this chapteris to introduce the work.The original contributions of this dissertation will be presented in chapters from 3 to6. These chapters are written as independent works based on manuscripts that arein preparation for submission to scientific journals, or have already been submitted.Therefore, the reader can read each chapter independently without the necessityof reading any previous chapter. For each work associated manuscript there aremultiple authors. However, the author of this dissertation is the key researcher andauthor in each case.In chapter 3, the problem of the biomass estimation in tropical forest areas will beconsidered by multi-baseline TomoSAR. Then, this chapter will report the resultsrelative to the tomographic analysis of the forest site of Paracou, French Guiana,carried out on the basis of a multi-baseline and multi polarimetric data acquired byONERA’s SETHI in the frame of TropiSAR campaign. This chapter was submittedto the IEEE Transactions on Geoscience and Remote Sensing in March 2012.In chapter 4, a ground based experiment TropiScat is introduced for forest study.The chapter is dedicated to reporting the results relative to the design of the sys-tem to be located at the Guyfalux tower, Paracou, French Guiana. To improveour understanding of the scattering mechanisms in time via temporal inteferometriccoherence behaviour, necessary for the development of robust retrieval algorithms, aground based experiment is proposed, designed and implemented. Such experimentover the same site of the airborne TropiSAR campaign in tropical forest completessignificantly airborne experiments by providing detailed and continuous data andground truth for various seasonal and weather conditions. This chapter was submit-ted to the IEEE Transactions on Geoscience and Remote Sensing in June 2012.Chapter 5 will describe the processing of the multi-temporal multi-polarimetric to-mographic data from the system design in the chapter 4. The behaviour of short

6

1.2 Thesis outline

term and long term temporal interferometric complex coherence as a function ofheight and polarization will be dicussed directly using the TropiScat data. A modelfor temporal contributions to the total backscatter power associated to the stableand to the varying component can be defined. For long term temporal coherenceinvestigation, an exponential model can depict the behaviour of amplitude temporalcoherence as a function of height and time. This chapter will be submitted to theIEEE Transactions on Geoscience and Remote Sensing.In Chapter 6, TropiSAR and TropiScat experiments will be combined for the val-idation of the concepts Tomographic Phase in BIOMASS system. A simulation ispresented to study the satellite performances as a function of temporal decorrelationphenomena, ionospheric disturbances and acquisition strategies. This chapter willbe submitted to the IEEE Transactions on Geoscience and Remote Sensing.Conclusive remarks will be drawn in Chapter 7.

7

2. BIOMASS mission

2.1. The need for global biomass information

The global carbon cycle

The continual and accelerating growth of carbon dioxide (CO2) in the atmospherehas been considered to be one of the most unequivocal indications of man’s effecton our planet. The climate-change implication of increasing atmospheric CO2 isthought to be a central concern. The key contributions to this growth are emissionsfrom fossil fuel burning 6.4 ± 0.4GtCyr−1. The rate of growth is substantially lessand much more variable than these emissions as it depends on the net flux of CO2 tothe atmosphere for the Earth’s surface. This flux can be divided into atmosphere-ocean and atmosphere-land components, whose average values for the 1990s are2.2± 0.4GtCyr−1 and 1.0± 0.6GtCyr−1 respectively [30].

It has observed that more than 98% of the land-use-change flux is caused by trop-ical deforestation, which converts carbon stored as woody biomass (which is ap-proximately 50% carbon [10]) into emissions. The calculation of this flux is usuallycompromised due to lack of reliable information on the levels of biomass actuallybeing lost in deforestation [31], [32], [33]. However, this uncertainty alone accountsfor a spread of values of about 1GtCyr−1 in different estimates of carbon emissionsdue to tropical deforestation [34].

The residual land flux has major significance for climate because of reducing thebuild-up of CO2 in the atmosphere. If we assume a land use change flux of 1.6GtCyr−1,the total anthropogenic flux to the atmosphere in the 1990s was 8GtCyr−1. As aresult, around 32.5% was absorbed by the land, but this value has very large un-certainties arising from the uncertainties in the land use change flux. The action ishighly variable from year to year, for reasons that are poorly understood [35]. Aprimary question is how much of this residual sink is due to fixing of carbon in forestbiomass [19].

Biomass product

Biomass has been identified by the United Nations Framework Convention on Cli-mate Change (UNFCCC) as an Essential Climate Variable (ECV). Reduction of its

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Chapter 2 BIOMASS mission

uncertainty is needed to improve our knowledge of the climate system [36], [13]. Fur-ther strong motivations to improve methods for measuring global biomass come fromthe Reduction of Emissions due to Deforestation and Forest Degradation (REDD)mechanism, which was introduced in the UNFCCC Committee of the Parties (COP-13) Bali Action Plan. Its implementation relies fundamentally on systems to monitorcarbon emissions due to loss of biomass from deforestation and forest degradation.

Regarding climate change, this mechanism provides a compelling reason for acquir-ing improved information on biomass, but biomass is also profoundly important asa source of energy and materials for human use. It is a major energy source insubsistence economies, contributing around 9–13% of the global supply of energy(i.e. 35–55 × 1018Jyr−1 in [37]). The FAO provides the most widely used infor-mation source on biomass harvest [38], [39] but other studies differ from the FAOestimates of the wood-fuel harvest and forest energy potential by a factor 2 or more[40], [41]. Reducing these large uncertainties requires frequently updated informa-tion, i.e. from satellite, on woody biomass stocks and their change over time, to becombined with other data on human populations and socio-economic indicators.

Moreover, biomass and biomass change also act as indicators of other ecosystemservices. Field studies have shown how large-scale and rapid change in the dynamicsand biomass of tropical forests lead to forest fragmentation and increase in thevulnerability of plants and animals to fires [42]. It is also showed that above-groundbiomass was strongly related to biodiversity [43]. Regional to global information onhuman impacts on biodiversity therefore requires accurate determination of foreststructure and forest degradation, especially in areas of fragmented forest cover. Thisis also fundamental for ecological conservation. The provision of regular, consistent,high-resolution mapping of biomass and its changes would be a major step towardsmeeting this information need.

Biomass mapping

Despite the obvious need for biomass information, and in contrast with most ofthe other terrestrial ECVs for which programmes are advanced or evolving, there iscurrently no global observation programme for biomass [14].

At global scale, the global biomass map has a very coarse spatial resolutions (0.5to 1°) based largely on ground data of unknown accuracy [44], [45], [46]. Recentsresult are achieved in about 30% at 1000-m pixels level [12]. At regional scale, variousapproaches have been used to produce biomass maps. Seven biomass maps of theBrazilian Amazon forest produced by different methods, including interpolation of insitu field measurements, modelled relationships between above-ground biomass andenvironmental parameters, and the use of optical satellite data to guide biomassestimates, were compared [47]. In these maps, estimates of the total amount ofcarbon in the Brazilian Amazon forests varied from 39 to 93 GtC, and the correlation

10

2.1 The need for global biomass information

between the spatial distributions of biomass in the various maps was only slightlybetter than what would be expected by chance.

Remote sensing approaches are recognized as one of the solutions for a large-scalesystematic vegetation monitoring. However, there are severe limitations on the useof this method to measure biomass. Optical data are not physically related tobiomass, although estimates of biomass have been obtained from Leaf Area Index(LAI) derived from optical greenness indices. However, these are neither robust normeaningful above a low value of LAI. For example, by using optical data from theAdvanced Very High Resolution Radiometer (AVHRR) sensors, it had been inferredthat biomass changed in northern forests over the period 1981–1999, and concludedthat Eurasia was a large sink [48]. However, both field data and vegetation modelsindicate that the Eurasian sink is much weaker [49]. Radar measurements, resultingfrom the interaction of the radar waves with tree scattering elements, are more phys-ically related to biomass, but their sensitivity to forest biomass depends on the radarfrequency. C-band (ERS, Radarsat and ENVISAT ASAR) backscatter in generalshows little dependence on forest biomass. C-band interferometric measurements dobetter; for example, ERS Tandem data were combined with JERS-1 L-band data togenerate a map of biomass up to 40–50 t.ha−1, with 50 m pixels covering 800,000km2 of central Siberia [50]. In boreal forests, C- and L-band repeat-pass InSARcan provide biomass estimates with accuracies similar to those of standard in-situmeasurements [51]. In 2006, JAXA launched the Advanced Land Observing Satel-lite (ALOS) mission, providing Phased Array L-band SAR (PALSAR) data beingsystematically collected to cover the major forest biomes [15]. Results have shownPALSAR’s ability to map forest (e.g. in the Amazon and Siberia) but retrieval offorest biomass is still typically limited to values less than 50 t.ha−1, which excludesmost temperate and tropical forests. Furthermore, loss of temporal coherence overthe PALSAR repeat interval of 45 days prevents recovery of forest height by polari-metric SAR interferometry. In other words, the need for better penetration reachingwoody elements of large size which are the main constituent of biomass has beenthe reason to push towards longer wavelengths SARs [52], [53].

Therefore, there is the urgent need for greatly improved mapping of global biomass.In response to this, the BIOMASS mission was proposed in the Call for Ideas re-leased in March 2005 by the ESA for the third cycle of Earth Explorer Core missions.BIOMASS was selected in May 2006 for Assessment Study (phase 0) and in March2009 for Feasibility Study (phase A). In the next section, we will summarize themission inluding its specific research objectives and specify the observational re-quirements within the context of the scientific objectives, particularly its uniquetomography phase.

11


2.2. BIOMASS mission

An official ESA report for BIOMASS mission was presented in [18] and [19], whichthe reader is referred to for details. In this section, the description is then just brieflyrecalled for sake of completeness.

2.2.1. Main objective

The primary scientific objectives and characteristics of the BIOMASS mission arereported in Table 2.1. It will carry a polarimetric P-band SAR sensor that willprovide:

• Measurements of the full range of the world’s above-ground biomass, by com-bining several complementary SAR measurement techniques;

• Geophysical products whose accuracy and spatial resolution are compatiblewith the needs of national scale inventory and carbon flux calculations;

• Repeated global forest coverage, enabling mapping of forest biomass and forestbiomass change.

Over the proposed five year mission lifetime, a unique archive of measurement infor-mation about the world’s forests and their dynamics will be built up, which will havelasting value well beyond the end of the mission. The P-band frequency was chosenbecause of its unique capabilities for forest biomass and height measurement. Sen-sitivity to forest biomass and biomass change increases with wavelength [54], [21],[23], [22]. In addition, longer wavelength SAR exhibits greater temporal coherence,allowing canopy height to be retrieved by polarimetric interferometry and tomog-raphy; this is a crucial complement to methods that recover biomass by invertingSAR intensity data. Both considerations strongly support the use of P-band, sinceit is the longest wavelength available for spaceborne application. The opportunity touse P-band arose only when the ITU designated the frequency range 432–438 MHzas a secondary allocation to remote sensing at the World Radio CommunicationsConference in 2003 [55]. The BIOMASS will therefore operate at a centre frequencyof 435 MHz (i.e., a wavelength of around 69 cm) and with a bandwidth of 6 MHz.

2.2.2. Mission characteristics

2.2.2.1. Polarimetry

A fully polarimetric system capacity will be available in order to support PolInSARinversion. Direct methods of measuring forest biomass benefit from using intensitymeasurements at diversity polarizations, and correction of Faraday rotation causedby ionosphere disturbances requires fully polarimetric data [56], [57], [58].

12

2.2 BIOMASS mission

Primary scienceobjectives

Measurement requirements Instrument requirements

Quantify magnitude anddistribution of forestbiomass globally toimprove resourceassessment, carbon

accounting and carbonmodels

Above-ground forestbiomass from 70° N to 56°S with accuracy notexceeding ± 20% (or ± 10t.ha−1 in forest regrowth)at spatial scale of 100–200m;Forest height with accuracyof ± 4 m;Forest mapping at spatialscales of 100–200 m;Biomass loss due todeforestation and forestdegradation, annually orbetter, at spatial scales of100–200 m;Biomass accumulation fromforest growth, at spatialscale of 100–200 m;1 estimate per yr intropical forests, 1 estimateover 5 yr in other forests;Changes in forest heightcaused by deforestation;Changes in forest area atspatial scales of 100–200 m,annually or better.

P-band SAR (432–438MHz);Polarimetry for biomassretrieval and ionosphericcorrection;PolInSAR capability tomeasure forest height;Tomography capabilityto measure forestvertical structure;Constant incidence angle(in the range of 25°–35°)25–45 day repeat cyclefor interferometry;Dawn-dusk orbit toreduce ionosphericeffects;1 dB absolute accuracyin intensitymeasurements;0.5 dB relative accuracyin intensitymeasurements;5 yr mission lifetime.

Monitor and quantifychanges in terrestrial

forest biomass globally,leading to improved

estimates of:(a) terrestrial carbon

sources (primarily fromdeforestation) usingaccounting methods;(b) terrestrial carbonsinks due to forest

regrowth andafforestation

Table 2.1.: BIOMASS primary science objectives and mission requirements [19].

13


2.2.2.2. Resolution

It is envisaged that BIOMASS will provide level-1 products with around 50 m×50m resolution at 4 looks. By applying optimal multichannel filtering techniques toa time-series of HH, HV and VV intensity data, the speckle in each image can besignificantly reduced without biasing the radiometric information in each image. Forexample, a multi-temporal set of six such triplets of intensity data would yield 40equivalent looks or more at each pixel, so averaging 2×2 blocks of pixels would yieldaround 150 looks at a scale of 1 ha, after allowing for interpixel correlation [59].This yields a radiometric accuracy better than 1 dB, which is sufficient to meet thescience objectives.

2.2.2.3. Incidence angle

Airborne experiments have been carried out for incidence angles ranging from 25°to 60°, and most indicate that the preferred incidence angle is in the range 40–45°.However system considerations are expected to favour steeper incidence angles. Cur-rently, the incidence angle is set to be about 25°.

2.2.2.4. Revisit time

Forest height recovery using PolInSAR inversion requires a revisit time small enoughto maintain high temporal coherence between successive SAR acquisitions. Althoughthis issue is still being investigated, preliminary results suggest that a revisit timeof 12-22 days is predicted for the Operational Phase.

2.2.2.5. Orbit

A sun-synchronous dawn-dusk orbit will minimise ionospheric disturbances [60].This argument will be strongly supported in section section 5.4, as it shows thatinterferometric coherences drop in daytime.

2.2.2.6. Mission duration

A 5 year mission is planned in order to obtain repeated measurements of the world’sforests. This will lead to reduced uncertainties in measurements of the biomassof undisturbed forests and will allow measurement of forest dynamics by detectingchanges in biomass and forest cover. Although the regrowth of fast-growing tropicalforests may be detectable even with measurements spaced one or two years apart,measurement of regrowth in temperate forests requires as long a mission as possible.BIOMASS will have very limited capability for measuring regrowth in the slowly-growing boreal forests.

14

2.3 BIOMASS Tomography Phase : orbital constraint

2.2.2.7. Tomography

The mission is expected to include a short tomographic phase during which mea-surements with 10 spatial baselines and a revisit time of 4 days will be collected. Inthe next section, the detail introduction about this capability will be presented.

2.3. BIOMASS Tomography Phase : orbitalconstraint

BIOMASS Tomographic Phase

Elevation

Slant range

θ

π/2

Cross range

Heig

ht

[m]

Capon spectrum - HH channel

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR heightH

eig

ht

[m]

Capon spectrum - HV channel

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Heig

ht

[m]

Capon spectrum - VV channel

Slant range [m]

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Figure 2.1.: BIOMASS Tomography Phase concept

During the mission, it is proposed to provide TomoSAR capability by including ashort experimental phase (approximately two months). This phase is refered to asTomography Phase. During this phase the system will be able to gather multipleacquisitions characterized by small baselines and a repeat pass time of 4 days, thusallowing tomographic imaging of the vegetation layer. This phase is expected toresult in an important reference data set providing information about: i) the mainscattering mechanisms (SMs) at forest and ground level; ii) how the SMs vary asa function of polarization; iii) how the SMs vary over the global forest biomes. Inparticular, the BIOMASS Tomographic Phase is expected to provide important in-formation about the extent of temporal decorrelation associated with ground andvolume scattering separately. This will potentially result in useful inputs and rec-ommendations for improving height retrieval from single baseline PolInSAR during

15


the Operational Phase. Figure 2.1 depicts the concept of tomography configura-tion and an example of potential results, which are reconstructed from the AirborneTropiSAR data, see section 6.2.However, there is a main factor expected to have significant impact on the qualityof the tomographic results. This is the one related to temporal decorrelation, i.e.instantaneous (quick), short term and long term decorrelation mechanisms. Toreduce the influence of the temporal decorrelation, future BIOMASS missions shouldaim for shorter orbit repeat-cycles. In principle, the shorter the revisit time isthe better the performance. However, it is impossible to provide simultaneouslyacquisition of the same area in a single satellite configuration; the revisit time isat least 1 day. Therefore, the question is whether a tomographic processing canoperate with 4 days revisit time.

16

3. Multi-Baseline SAR Tomography:Biomass Estimation

3.1. Introduction

The use of remote sensing for investigating forested areas has been the object ofgrowing interest in the last years. Concerning the use of Synthetic Aperture Radars(SARs), much work has been done aiming at correlating forest above-ground biomass(AGB) with backscattered power measurements [21]. The need for better penetra-tion reaching woody elements of large size which are the main constituent of AGBhas been the reason to push towards longer wavelengths SARs [53]. However, evenat P-band (450 MHz) the backscatter was found to saturate for biomass values lowerthan that of dense tropical forests in literature (e.g. [23]). Another limiting factor isassociated with the topographic variations, as they can affect significantly the mag-nitude of returns from trunk-ground or branch-ground double-bounce interactions[61], [62], [63], [64]. Accordingly, terrain topography is likely to determine variationsof the observed signal that are not correlated with forest biomass 1. The issues out-lined above make the retrieval of biomass from tropical dense forests (e.g. > 300tons/ha), which are often over terrains with significant topography, a challengingtask for SAR remote sensing.Forest biomass estimation has also been proposed by means of allometric relation-ships between AGB and forest height [65]. The forest height measurement by remotesensing has been reported based on methods such as airborne light detection andranging (LiDAR) [11], [66], space-borne LiDAR [12] or polarimetric interferometrySAR (PolInSAR) [67]. Still, the retrieval is not yet demonstrated for forest biomasshigher than 300 tons/ha (t.ha−1) using SAR measurements. In this chapter, weshow the possibility to estimate tropical forest AGB by accessing into the forestvertical structure from P-band multi-baseline SAR tomography.SAR tomography (TomoSAR) generalizes SAR interferometry (InSAR) to the mul-tiple baseline case, the imaged scene being illuminated from a number of slightlydifferent look angles [24], [26], [27], [28]. In such a context the response of a pointscatterer to the multi-baseline array can be modeled as a complex sinusoid whose

1It is certainly a lot of other factors such as soil, canopy moisture and forest structure varyingcan be contributed [53]. However, in this work we assume it is not significant as topographyeffects.

17

Chapter 3 Multi-Baseline SAR Tomography: Biomass Estimation

frequency is proportional to the scatterer’s height with respect to a reference plane.This relation between height and frequency allows the separation of the contributionsof scatterers displaced along the vertical direction by means of spectral estimationtechniques [24], resulting in the possibility to generate a new stack of SAR images,each of which associated with scatterers within a layer at a certain height with re-spect to the ground [68], [69], [64]. The question addressed in this chapter is to whatextent this new source of information can be used to derive forest parameters, themost important of them being forest biomass. In particular, the aim of the studyreported in this chapter is 1) to propose a methodology for obtaining SAR tomog-raphy information relevant to the retrieval of forest biomass and 2) to demonstratethe use of this tomographic information to retrieve forest biomass.

The chapter is organized as follows: section 3.2 presents the SAR tomographymethodology; in section 3.3 the study site is introduced; in section 3.4 the P-bandSAR tomography results are shown; in section 3.5 the relationship between radarmeasurements and AGB is evaluated and discussed, the inversion results are pre-sented ; conclusions are drawn in section 3.6.

3.2. Tomography processing

Tomography processing is aimed to convert the multi-baseline stack of SAR imagesinto a multi-layer stack of SAR images, where each image represents the complexreflectivity associated with a layer at a certain height above the ground. The ba-sic principle of tomographic processing can be stated in relatively simple terms asfollows. We consider a multi-baseline data-set of single look complex (SLC) SARimages acquired by flying the sensor along N parallel tracks, and let yn(r, x) denotesthe complex valued pixel at slant range, azimuth location (r, x) in the n− th image.Assuming that each image within the data stack has been resampled on a commonmaster grid, and that phase terms due to platform motion and terrain topographyhave been compensated for, the following model holds [70], [24], [27]:

yn (r, x) =ˆS (ξ, r, x) exp

(j

4πλrbnξ

)dξ (3.1)

where: bn is the normal baseline relative to the n−th image with respect to a commonmaster image; λ is the carrier wavelength; ξ is the cross range coordinate, defined bythe direction orthogonal to the Radar Line of Sight (LOS) and the platform track;S (ξ, r, x) is the average scene complex reflectivity within the slant range, azimuth,cross range resolution cell [27]. Equation 3.1 states that SAR multi-baseline dataand the cross range distribution of the scene reflectivity constitute a Fourier pair.Hence, the latter can be retrieved by taking the Fourier Transform of the dataalong the baseline direction. The final conversion from cross range to height is then

18

3.2 Tomography processing

obtained through straightforward geometrical arguments. The resulting verticalresolution is approximately [24]:

∆z ' λ

2rsinθ

bmax(3.2)

where θ is the radar look angle and bmax the overall normal baseline span. Equation 3.2defines the so called Rayleigh limit, well-known in the field of array processing andtomography. A common issue of SAR tomographic surveys is that the resolutionallowed by the Rayleigh limit is often too coarse if compared to the vertical extentof the observed scene. For this reason, tomographic processing is usually carried outby employing super-resolution techniques, see for example [71], [72]. Although suchtechniques allow to recover details not accessible otherwise, they result in poor ra-diometric accuracy in the case of distributed targets, which limits their applicationto the aim of yielding quantitative measurements in a completely model-free fash-ion. This task, however, becomes possible whenever the available baseline set allowsit, resulting in the possibility to carry out model-free, unbiased measurements ofthe vertical distribution of the backscattered power. This is the case of the P-banddata-set analyzed in this paper, as it will be discussed in the remainder. For thisreason the image formation along the vertical direction has been carried out in thiswork simply by coherent focusing, that is by Fourier transforming the data withrespect to the normal baseline. This way of processing does not optimize verticalresolution. Yet, it grants radiometric accuracy along the vertical direction.

Prior to applying the simple approach described above it is usually necessary totake a number of factors into account. In the first place, blurring phenomena af-fecting the quality of tomographic focusing can arise due to: i) phase disturbancesresulting from uncompensated platform motion [73], [74], [75]; ii) irregular base-lines sampling, the effective baseline set being determined by the actual trajectoriesalong which the sensor has been flown. These two factors need to be carefullytaken care of to provide accurate measurements of the vertical distribution of thebackscattered power. Terrain topography has to be considered as well, as it playsa three-fold role in tomographic measurements. Firstly, in tomographic analyses offorested areas, the interest is in the vertical backscattered power distribution withinthe vegetation layer. Accordingly, terrain topography has to be removed, in sucha way as to reference each image within the multi-layer stack produced by the to-mographic processing to a certain height above the ground, rather than to heightwith respect to a fixed reference. Furthermore, topography determines a variationof the backscattered power that is not correlated to vegetation, and thus it mayproduce a significant change in the backscattered power [61]. Finally, knowledgeof terrain topography is required to geocode the measurements. The implementedprocessing chain is depicted in Figure 3.1. A description of each block is providedin the following.

19


Figure 3.1.: The proposed SAR tomography processing chain.

3.2.1. Phase calibration and baseline interpolation

A complete procedure for phase calibrating the data stack and resampling the multi-baseline array on a regular grid was already discussed and validated against the samedata-set analyzed in this paper in [64], which the reader is referred to for details.The procedure is then just briefly recalled here for sake of completeness.Phase calibration was carried out according to the two-step procedure proposed in[74]. In the first step the Algebraic Synthesis technique is used to recover the matrixof interferometric coherences associated with ground-only contributions [76]. In thesecond step the Phase Linking algorithm is used to retrieve the best estimate of theground phases [77]. Phase calibration is then performed by removing the retrievedground phases from the SLC data stack, which corresponds to the block referred toas Phase flattening in Figure 3.1. It is important to note that the retrieved groundphases are directly related to the optical paths from the ground layer to the N sensorpositions, and are therefore determined not only by terrain topography, but also bythe phase disturbances deriving from platform motion. Accordingly, removing theground phases brings two advantages. The first is the removal of the propagationdisturbances, which allows a correct focusing along the vertical direction. The secondis the removal of terrain topography, resulting in the contributions from the terrainto be automatically focused at 0 m, independently of the actual topography.Vertical focusing from irregularly sampled data is a well-known problem in literature

20


about SAR tomography, resulting in several approaches for its treatment [72], [71],[73]. In this work a simple, yet quite fast and robust solution was chosen. In order tosimulate a null displacement from the ideal regularly spaced trajectories, the imagestack has been interpolated at each slant range, azimuth location on a regularlysampled baseline grid [64]. The interpolator has been implemented by employing alinear kernel, properly adjusted in phase so as to guarantee a maximal flat responsebetween 0 m and 40 m, consistent with the vertical extent of the vegetation layer[64]. Based on numerical simulations, the residual error with respect to the idealcase of regularly sampled baselines has been assessed to be less than 0.2 dB over thewhole imaged scene.

3.2.2. Tomographic imaging

After phase calibration and baseline interpolation have been carried out, tomo-graphic imaging has been performed simply by taking the Fourier Transform (withrespect to the normal baseline) of the multi-baseline SLC data set at every slantrange, azimuth location. The focused imaged in 3D space can expressed as:

S (ξ, r, x) =N∑n=1

yn (r, x) exp(−j 4π

λrbnξ

)(3.3)

The result of this operation is a multi-layer SLC set, where each layer is referredto a fixed height above the terrain. We will hereinafter refer to each image withinthe multi-layer data stack simply by the associated height (i.e.: 10 m layer, 20 mlayer...), or as ground layer for the image focused at 0 m.

3.2.3. Terrain topography estimation

Knowledge of terrain topography is required for compensating the backscatteredpower measurements for the local terrain slope, as well as for mapping the multi-layer data stack onto ground geometry. In this work terrain topography has beenobtained by analyzing the ground phases, which are available as a by-product of thephase calibration procedure described in subsection 3.2.1. More in detail, neglectingestimation noise the retrieved ground phase in the n − th image can be expressedas a the sum of two contributions, one relative to topography and the other topropagation disturbances. In formula:

ϕn = 4πλrsinθ

bnzg + ηn (3.4)

where zg is the local terrain height and ηn the phase disturbance in the n− th im-age. Terrain height can then be retrieved at each slant range, azimuth location by

21


linear fitting the (unwrapped) ground phases in eq. (Equation 3.4) with respect tothe normal baseline, as customary in multi-baseline InSAR, see for example [78].Of course, the presence of phase disturbances results in a residual error about ter-rain height. Such an error impacts mostly on the lowest spatial frequencies of theretrieved terrain height, due to the fact the phase disturbances exhibit a low passbehaviour. Accordingly, the residual error can be corrected by imposing furtherconstraints about the low frequency components of terrain topography, that areeasily derived from available Digital Elevation Models (DEMs) [79]. The approachfollowed in this work is the one depicted in [79], that provides a formal algebraicframework for imposing external constraints. A DEM of the area from the ShuttleRadar Topographic Mission (SRTM) [80], has been used to derive the mean topo-graphic slopes along azimuth and range, which have been employed to constraintopography retrieval. A comparison with LiDAR DEM available analysis has beenobserved with no significant bias greater than 4 m and standard deviation less than3 m.

3.2.4. Topographic compensation

As outlined above, topographic slopes determine a variation of the backscatteredpower that is not related to vegetation [61], and thus it has to be properly com-pensated for in order to relate backscatter measurements to forest biomass. LetS (z, r, x) denote a complex valued pixel from the image corresponding to the layerat height z within the multi-layer data stack produced by the tomography process-ing. The topographic compensation has been performed as in [81]:

P (z, r, x) = |S (z, r, x)|2 · sin(θ − α) (3.5)

where P (z, r, x) is the signal backscattered power, α is the local ground slope andθ is the radar look angle. However, in general, it would be preferable to normalizelayers differently as it will be discussed in subsection 3.4.2.

3.2.5. Geocoding

Being able to link precisely one pixel in the slant range geometry image to the pixelin ground range geometry is essential, especially for studying the relation betweenSAR and in-situ measurement. Once the vertical distribution of the backscatteredpower has been retrieved in radar geometry, an interpolation step is required inorder to convert to ground geometry. The difference of these geometries is depictedin Figure 3.2.This operation is conceptually not different from standard geocoding of SAR images[82], with the only exception that the elevation location of the targets has to be

22


Figure 3.2.: Left panel (a), the forest tomographic resolution cells in slant range(radar) geometry. Righ panel (b), the forest tomographic resolution cells in groundrange geometry.

accounted for, resulting in an increase of dimensionality in the interpolation step.Accordingly, the correct implementation of such an interpolation step requires theknowledge of terrain topography, analogously to conventional geocoding.

Tomogram focusing

Slant range [m]

heig

ht [

m]

4500 4600 4700 4800 49000

20

40

Tomogram focusing

Ground range [m]

heig

ht [

m]

2100 2200 2300 2400 2500 2600 2700 2800 29000

20

40

True forest height Tomogram geocoding

Ground range [m]

heig

ht [

m]

2100 2200 2300 2400 2500 2600 2700 2800 29000

20

40

0 0.2 0.4 0.6 0.8 1

4500 4600 4700 4800 49000

10

20

Slant DEM

Slant range [m]

heig

ht [m

]

2200 2400 2600 28000

10

20

Ground DEM

Ground range [m]

heig

ht [m

]

2200 2400 2600 2800-10

0

10Local slope

Ground range [m]

degr

ee

Figure 3.3.: Left panels: simulated DEM in slant range coordinate (a), groundrange coordinate (b), and the corresponding local slope in ground range coordinate(c). Right panels: tomogram focused in radar geometry (d), tomogram focusedin ground geometry (e), and geocoded tomogram (f).

To illustrate the result of this processing step, we simulate tomograms from a forestscene over a terrain with a given DEM. The simulated system geometry is the same asthe actual TropiSAR data-set. The simulated scene consists of a single phase centerrepresenting the tree tops, placed at a constant height of 20 m above the groundfrom near to far range. The left panel of Figure 3.3 shows the simulated DEM in(radar) slant range geometry (a), ground range geometry (b), and the correspondinglocal slope (c). The top right and middle right panels of the same figure report the

23


outcome of the tomographic processing as performed in slant range geometry (d), ordirectly in ground geometry (e). In both cases the tomogram has been flattened byremoving the ground phase, in such a way that the terrain always corresponds to 0m. The undulation visible in the slant range tomogram (d) is due to the bias abouttarget height induced by local slope [83]. This phenomenon is no longer present inthe ground geometry (e), which was focused with accounting for terrain topography.Finally, it is reported in the bottom right panel of Figure 3.3 (f) the ground geometrytomogram obtained by geocoding the one focused in radar geometry. It is worthremarking that except few samples at the boundaries, the tomograms in panel (e)and (f) are identical, indicating the validity of the implemented geocoding procedure.

3.3. TropiSAR Paracou data-sets

The TropiSAR campaign was conducted in French Guiana in the summer 2009 in theframework of the Phase A studies pertaining to the BIOMASS mission, one of thethree for Earth Explorer candidates [18], [19]. The main campaign objectives werethe evaluation of P-band radar imaging over tropical forests for biomass and forestheight estimation [84]. Two main forest sites have been studied: Nouragues andParacou. For both, an extensive in-situ database was available. Seven SAR flightswere conducted with the SETHI system from ONERA both at P-Band and L-Band,a number of which suitable for tomographic processing. The data-set analyzed inthis paper is the P-band data relative to the Paracou test site.

3.3.1. Paracou test site

The Paracou experimental site is located in a lowland tropical rain forest near Sinna-mary, French Guiana (5018′

N , 52055′W ) [85]. Elevation is between 5 and 50 m, andmean annual temperature is 260C, with an annual range of 1–1.50C. Rainfall aver-ages 2980mm/yr (30- year period) with a 3-month dry season (< 100mm/month)from mid-August to mid-November [86]. The landscape is characterized by a patch-work of hills (100–300 m wide and 20–35 m high) separated by narrow streams.Slopes range from 25% to 50%. The forest in Paracou is classified as a low landmoist forest with 140− 200 species per ha, specified in the forest census of all treeswith diameter at breast height (DBH) > 10 cm.To analyze the relationship between tomographic data and forest biomass, we usein-situ forest measurements on 16 permanent plots established starting 1984 in theParacou primary forest. These are 15 plots of 250 × 250 m (6.25ha) each and oneplot of 500× 500 m (25ha) in which all stems of DBH ≥ 10 cm were mapped andregularly surveyed since 1986. For the Paracou primary forests, the number of treeswith DBH > 10 cm ranges between 400 to 700 stems per ha. The range of AGBand mean height depends on the spatial resolution. At 1ha the mean AGB rangesfrom 370 to 430t.ha−1.

24

3.3 TropiSAR Paracou data-sets

From 1986 to 1988, nine of these 6.25ha 15 plots underwent three different loggingtreatments ranging from mild to severe for a study of the forest responses to log-ging intensities. In Treatment 1, selected timbers were extracted, with an averageof 10 trees 50 or 60 cm DBH removed per hectare. Treatment 2 was logged as inTreatment 1, followed by timber stand improvement by poison girdling of selectednon-commercial species, with about 30 trees 40 cm DBH removed per hectare. Treat-ment 3 was logged as in Treatment 2 for an expanded list of commercial species,with about 45 trees 40 cm DBH removed per hectare. In 2009, the degraded plotshad the AGB at 1 ha resolution ranging between 250 to 392t.ha−1, depending onthe initial logging intensity [87].

3.3.2. SAR data-sets

The SAR system used in the TropiSAR campaign is the ONERA airborne systemSETHI [84]. The P-band SAR has a bandwidth of 335−460MHz and the resolutionis about 1 m in slant range and 1.245 m in azimuth direction [84]. The wholeTropiSAR data-sets including in-situ data, are available through the archive of theEuropean Space Agency (ESA). Details on access to campaign data can be foundat the ESA EOPI portal (http://eopi.esa.int), under the campaigns link.In this paper, we use the Paracou tomographic data-sets which consists of 6 fullypolarimetric SLC images at P-band acquired on 24 August 2009. The baselines havebeen spaced vertically with a spacing about 15 m (50ft). The trajectory flown islower than the reference line (13000ft/ 3962m) with a vertical shift of 50ft, 100ft,150ft, 200ft and 250ft respectively.Since the tomographic flight lines are in a vertical plane rather than in a horizontalplane, the phase to height factor has a small variation across the scene swath, andsimilarly for the height of ambiguity (ranging between 102 m and 185 m) well abovethe vegetation height [84]. The resulting Fourier vertical resolution is about 20 m(±10 m at −3.5 dB), whereas forest height ranges from 20 m to 40 m. These featuresmake it possible to map the 3-D distribution of the scene complex reflectivity by acoherent focusing, i.e. without assuming any physical model or employing super-resolution techniques.

3.3.3. Above-ground biomass data-sets

The AGB data were estimated based on forestry censuses, making use of allometricequations to convert measured dimensions (DBH, total tree height and wood density)into AGB for each tree. Within the 16 experimental plots, all individual trees withdiameter > 10 cm have been measured. In order to increase the number of plots forstatistical analysis of the relationships between biomass and backscatter power, theplots have been subdivided into subplots. In this paper, plots 1 to 15 are subdividedinto 4 subplots of 125× 125 m (1.5ha), while plot 16 is divided into 25 subplots of

25


100 × 100 m (1ha), resulting in independent 85 subplots for which the AGB dataare reconstructed (see top right panel in Figure 3.4). The size of the plots of 1haand 1.5ha is chosen for reducing speckle effect and uncertainties in AGB estimates(< 9% at 1ha [88]). For the 85 plots, the mean AGB ranges from 250 to 450t.ha−1,and the tree top height varies from 20 m to 40 m with the average value being about28 m.

3.4. Results from tomography

The tomographic focusing has been carried out for all polarizations according to theprocessing chain discussed in section 3.2, resulting in three (HH, HV, VV) multi-layer SLC data stacks. We recall that we refer to each image within a multi-layerdata stack simply by the associated height (i.e.: 10 m layer, 20 m layer...), or asground layer for the image focused at 0 m. It is also worth remarking that theimplemented phase calibration procedure automatically steers ground contributionsat 0 m, so that the height of each layer is always to be intended as being relative toterrain elevation.

3.4.1. Multi-layer images

First of all, to clarify how the terrain topographic contribution can be handledby SAR tomography, we do not include the topographic compensation step (seesubsection 3.2.4) in the processing chain. Figure 3.4 shows the HV backscatteredpower for layers at 0 m (ground layer), 15 m, 30 m and 45 m. The backscatteredpower relative to one image from the original multi-baseline data-stack (i.e. non-tomographic) is shown in the top left panel of Figure 3.4 to provide a comparisonand the terrain topography is shown as well in the top right panel.

The four tomographic layers are observed to be different in their information content.In particular, the ground and the top (45 m) layers show strong topographic effect,whereas the middle layer images appear much less affected by topography. Thisphenomenon may easily be interpreted by taking a closer look at the distributionof the scatterers within the tomographic resolution cell in both geometries of slantand ground range, see Figure 3.5.

In the bottom resolution cell, the tomographic layer SAR signal is affected by terrainslope the same way as in traditional SAR images of bare surfaces with slope. Inthe resolution cell corresponding to tree top height the signal can also be affectedby topography, although more weakly, because in general the top height of naturalforests follows terrain slope. Finally, cells inside the canopy are always filled up bytrunk and woody branches irrespective of the ground slope, resulting in topographicslope to have a minor effect on signal power.

26

3.4 Results from tomography

Terrain topography [m]

500 1000 1500 2000 2500 3000 3500

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und r

ange [m

]

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und r

ange [m

]

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Backscattered power HV - original image G

round r

ange [m

]

500 1000 1500 2000 2500 3000 3500

2000

2500

3000

3500

4000

4500

A

A’

Figure 3.4.: Tomographic results over the Paracou study site: HV backscatteredpower for four tomographic layers associated with four different heights above theground 0 m (ground layer), 15 m, 30 m and 45 m. The top left panel presentsthe original HV image. The top right panel is the terrain topography with circlesrelative to center areas where in-situ AGB measurments are available.

27


Figure 3.5.: Schematic view of the tomographic resolution cells in a forest locatedon a terrain slope. This illustration depicts an interpretation the high correlationbetween the backscattered power of the outermost cell and the ground topographyslope. It can be observed that the intermediary cells are always filled up by trunkand woody branches irrespective of the slope.

28


3.4.2. Topographic compensation

Based on the interpretation of the previous section, it is possible to classify the to-mographic layers as surface layers, i.e. the ground (0 m) and the upmost layers, andvolume layers, i.e. the middle height ones. In order to relate the tomographic datato in-situ measurements, such as forest biomass, it is required that the backscatteredpower is normalized with respect to a surface for surface layers and to a volume forvolume layers. We propose to use a geometric projection law [81], for the normal-ization both of surface and volume layers. Results are reported in Figure 3.6. Fromleft panels in Figure 3.6, it is possible, in some cases, to observe a reduction of thenon-normalized backscattered power with increasing look angle. The surface layers,namely the ground and the top layer (45 m) show the trend visibly, whereas themiddle layers look less sensitive. The right panels in Figure 3.6 show the backscat-tered power normalized by the factor sin(θ − α). We note that the change of thebackscattered power from near to far range is reduced, for the surface layers. For themiddle (volume) layers, a normalization with respect to the volume size would bepreferable. However, the TropiSAR data analyzed in this paper are characterized bya small variation with range of the vertical resolution, while slant range and azimuthresolution are constant. So, this last normalization has not been carried out.

3.4.3. Tomographic profiles

A convenient way to observe the forest vertical structure at a local scale is providedby taking a tomographic profile, namely a slice of the multi-layer data stack cor-responding to a constant ground range or azimuth value. Figure 3.7 presents thetomographic profile of a constant azimuth section AA’ (x = 2270 m, see Figure 3.6)at HH, HV and VV. All panels have been normalized in such a way that the sumalong height is unitary, in order to help visualization. The white line denotes foresttop height derived from LiDAR measurements.

The first observation is that for all polarizations the total backscattered power resultsfrom the interaction with all layers, including the ground layer. The contributionof the vegetation is important. Yet, relevant contributions from the ground levelbeneath the forest are observed. In HH and VV, the ground contribution is moreimportant than the contribution of vegetation layers, indicating double bounce scat-tering from either trunk-ground or branch-ground interactions dominating volumescattering. In HV, instead, the contribution of the ground layer appears to be lessimportant than that of the vegetation layers. These results show that the scatter-ing mechanisms in tropical forest are quite different from boreal forests, where thedominating contribution was observed to be associated with the ground level in allpolarizations [68], [28], [89]. Finally, it is worth noting that the spatial distributionof the backscatter over the analyzed transect in the upper layers (20 m - 40 m) isquite similar in all polarizations.

29


(Before) HV - original image : P

Sla

nt

ran

ge [

m]

1000 2000 3000

4600

5000

5400

5800

(After) HV - original image : P.sin( q - a )

1000 2000 3000

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Sla

nt

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ge [

m]

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ge [

m]

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nt

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ge [

m]

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ge [

m]

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1000 2000 3000

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4600

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Azimuth [m]

1000 2000 3000

4600

5000

5400

5800

-20 -15 -10 -5 0 5

A

A’

Figure 3.6.: Left panels : before topographic compensation. Right panels : aftertopographic compensation. HV backscattered power for four tomographic layersassociated with four different heights above the ground 0 m (ground layer), 15 m,30 m and 45 m. Two top panels present the original HV image.

30


A A’

A A’

A A’

HH channel

Heig

ht

[m]

4600 4800 5000 5200 5400 5600 5800

0

20

40

60

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HV channel

Heig

ht

[m]

4600 4800 5000 5200 5400 5600 5800

0

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60

LiDAR height

VV channel

Heig

ht

[m]

Slant range [m]

4600 4800 5000 5200 5400 5600 5800

0

20

40

60

LiDAR height

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 3.7.: Tomographic reconstruction along the same azimuth cut AA’ (seeFigure 3.4 and Figure 3.6) in all polarizations, from top to bottom: HH, HVand VV. The while line denotes the LiDAR height measurements. All panelshave been normalized in such a way that the sum along height is unitary.

31


3.4.4. Ground-trunk scattering

Figure 3.8 shows the co-polar phase, defined as ϕco−polar = ∠HH · V V ∗, joint dis-tribution between backscattered power (without topographic compensation and theco-polar channel HH) and co-polar phase, joint distribution between co-polar phaseand ground slope, respectively, in the original image and in the 0 m ground layer.Comparing the left column and the right column panels, it is important to note thatthe ground layer image is characterized by a better contrast information compared tothe original data. This can be explained that the signal at ground level is focused bythe tomography processing, thus rejecting contributions from the upper vegetationand allowing a better characterization of the polarimetric signature of ground scat-tering. The following interpretation focuses on the results of tomographic groundlayer.

The double bounce scattering from ground-trunk interactions is visible everywhereby examining the co-polar phase value closed to -180° [90]. The ground-trunk in-teractions result in stronger backscattered power and are the dominant scatteringmechanism, as shown in the joint distribution between backscattered power andco-polar phase. By examining the joint distribution between co-polar phase andground slope, it is clearly visible that double bounce scatterings are found wheneverterrain topography is flat and they tend to vanish whenever the topographic groundslope increases. The width of the main lobe of the variation of the co-polar phase isobserved to be about 10° as the radar look angle increases ranging from 30° to 50°.

In summary, ground-trunk scatterings will be a significant noise source for forestbiomass retrieval.

3.5. Relation to forest biomass

3.5.1. Linear regression

Prior to analyzing the correlation it is worth remarking that it is necessary to takethe topographic compensation procedure (see subsection 3.2.4) into account. To ap-preciate the effectiveness of this step, we report here both the results of i) no topo-graphic compensation in Figure 3.9 and ii) topographic compensation in Figure 3.10.These figures display the backscattered power in HV and HH of the 85 plots as afunction of in-situ AGB, for 9 layers varying from 0 m to 40 m, at 5 m interval. Asobserved in subsection 3.4.1 layers corresponding to different heights provide differ-ent information content, so that correlation of backscatter power with AGB is alsoexpected to differ among layers. These graphs indicate that linear regression canbe used to quantify the relationship between the backscattered power and AGB. A

32

3.5 Relation to forest biomass

Azimuth [m]

Sla

nt

range [

m]

1000 1500 2000 2500 3000

4600

4800

5000

5200

5400

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5800

Ground phase [°]

Co-p

ola

r phase [

°]

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Sla

nt

range [

m]

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Co-p

ola

r phase [

°]

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Co-polar phase [°]

Backscatt

ere

d p

ow

er

[dB

]

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Backscatt

ere

d p

ow

er

[dB

]

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Backscattered power vs co-polar phase

Co-polar phase vs ground phase

Co-polar phase Co-polar phase

Original image Ground layer

Figure 3.8.: The variation of polarimetric signature with respect to topographicterrain ground slope. Left column panels: co-polar phase, joint distribution be-tween backscattered power and co-polar phase, joint distribution between co-polarphase and ground slope for the original images. Right column panels: co-polarphase, joint distribution between backscattered power and co-polar phase, jointdistribution between co-polar phase and ground slope for the ground layers only.Two histograms on the bottom have been normalized such that the maximumalong each column is one.

33


linear fit has then been performed by assuming a classical log law [21]:

B = a · log10(P ) + b (3.6)

where B is the above-ground biomass; P is the backscattered power; a and b arefactors defining a linear trend. The quality of the linear fit is assessed using thePearson linear correlation rP [91], which measures the degree of association betweenthe in-situ AGB and backscattered power. The full sets of 85 plots is considered,for which the significance level for the Pearson correlation at 1% and 5% risk isrespectively about 0.27 and 0.21 [91]. For example, given |rP | > 0.27, the confidencelevel for having significant correlation is 99%.Although there is no topographic compensation in the data, we can see that the up-per layers (i.e, 30 m and 35 m ) have strong correlation with the biomass as shownin Figure 3.9. The correlation is further improved by normalizing the backscatteredpower by the factor sin(θ − α). Figure 3.10 reports this result. Applying the topo-graphic compensation, the dispersion is reduced in all layers and the correlation ofupper layers with biomass is enhanced say from rP = 0.7 to rP = 0.84 in HV 30 mlayer.The following interpretation focuses on the results after properly topographic com-pensation. The Pearson correlation coefficients for all layers in all polarizations aresummarized in Table 3.1. The best correlation (rP = 0.84) is found for the 30 mlayer in HV, for which the backscattered power increases by about 4.3 dB as AGBchanges from 250t.ha−1 to 450t.ha−1 (about 1.1dB for 50t.ha−1). For the 35 m layerthe backscatter dynamic range is larger but the correlation is reduced and the dis-persion is increased. For the 40 m layer, the correlation decreases and the dispersionincreases despite that the dynamic range is the same as the 30 m layer. These anal-yses results are in agreement with the observations in the previous subsection 3.4.1.It is worth noting that the 30 m layer exhibits a noticeable correlation with AGBnot only in HV, but also in HH and VV, indicating that the co-polar channels maybe used as well for biomass estimation. This is consistent with the tomographicprofiles discussed in section 3.4, whose spatial distribution was observed to showpoor sensitivity to polarization in the upper layers.In order to provide a comparison, the same sensitivity analysis has been carried outconsidering the backscattered power of the original (i.e.: non-tomographic) data. Re-sults are reported in Figure 3.11. It is immediate to observe that non-tomographicdata exhibit a much lower sensitivity to forest biomass than tomographic data,resulting in the Pearson linear correlation to drop from rP = 0.84 to rP = 0.18(see right panel of Figure 3.11). This low sensitivity to biomass of the backscat-tered power for high biomass values requires more elaborate topographic correctionand development of suitable biomass indicator from polarimetric SAR intensity forbiomass retrieval [92].

34


2 3 4 5-15

-10

-5

0

5

0 m layer, rP = -0.23, Slope = -0.698

PH

H [dB

]

2 3 4 5-15

-10

-5

0

5

5 m layer, rP = -0.26, Slope = -0.692

2 3 4 5-15

-10

-5

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5

10 m layer, rP = -0.31, Slope = -0.618

2 3 4 5-15

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PH

H [dB

]

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20 m layer, rP = 0.1, Slope = 0.172

2 3 4 5-15

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25 m layer, rP = 0.42, Slope = 0.829

2 3 4 5-15

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30 m layer, rP = 0.54, Slope = 1.332

PH

H [dB

]

Above-ground biomass (100t.ha-1)

2 3 4 5-15

-10

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5

35 m layer, rP = 0.47, Slope = 1.481


2 3 4 5-15

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-5

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2 3 4 5-15

-10

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PH

V [

dB]

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5

5 m layer, rP = -0.4, Slope = -1.038

2 3 4 5-15

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2 3 4 5-15

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PH

V [

dB]

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2 3 4 5-15

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25 m layer, rP = 0.61, Slope = 1.101

2 3 4 5-15

-10

-5

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PH

V [

dB]


2 3 4 5-15

-10

-5

0

5

35 m layer, rP = 0.64, Slope = 2.017


2 3 4 5-15

-10

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5

40 m layer, rP = 0.49, Slope = 1.637


No topographic compensation

No topographic compensation

Figure 3.9.: Sensitivity of backscattered power at different layers to above-groundbiomass. (a) HV channel, (b) HH channel. rP is the Pearson correlation coeffi-cient. Slope is referred to the angular coefficient of the resulting linear fit.

35


2 3 4 5-20

-15

-10

-5

0

0 m layer, rP = -0.3, Slope = -0.617

PH

V [

dB]

2 3 4 5-20

-15

-10

-5

0

5 m layer, rP = -0.35, Slope = -0.563

2 3 4 5-20

-15

-10

-5

0

10 m layer, rP = -0.27, Slope = -0.314

2 3 4 5-20

-15

-10

-5

0

15 m layer, rP = 0.14, Slope = 0.162

PH

V [

dB]

2 3 4 5-20

-15

-10

-5

0

20 m layer, rP = 0.61, Slope = 0.848

2 3 4 5-20

-15

-10

-5

0

25 m layer, rP = 0.81, Slope = 1.571

2 3 4 5-20

-15

-10

-5

0

30 m layer, rP = 0.84, Slope = 2.167

PH

V [

dB]


2 3 4 5-20

-15

-10

-5

0

35 m layer, rP = 0.8, Slope = 2.452


2 3 4 5-20

-15

-10

-5

0

40 m layer, rP = 0.68, Slope = 2.064


2 3 4 5-20

-15

-10

-5

0

0 m layer, rP = -0.09, Slope = -0.216

PH

H [dB

]

2 3 4 5-20

-15

-10

-5

0

5 m layer, rP = -0.1, Slope = -0.212

2 3 4 5-20

-15

-10

-5

0

10 m layer, rP = -0.11, Slope = -0.145

2 3 4 5-20

-15

-10

-5

0

15 m layer, rP = 0.1, Slope = 0.108

PH

H [dB

]

2 3 4 5-20

-15

-10

-5

0

20 m layer, rP = 0.49, Slope = 0.642

2 3 4 5-20

-15

-10

-5

0

25 m layer, rP = 0.74, Slope = 1.296

2 3 4 5-20

-15

-10

-5

0

30 m layer, rP = 0.79, Slope = 1.789

PH

H [dB

]


2 3 4 5-20

-15

-10

-5

0

35 m layer, rP = 0.7, Slope = 1.92


2 3 4 5-20

-15

-10

-5

0

40 m layer, rP = 0.51, Slope = 1.433


With topographic compensation

With topographic compensation

Figure 3.10.: Sensitivity of backscattered power at different layers to above-groundbiomass. (a) HV channel, (b) HH channel. rP is the Pearson correlation coeffi-cient. Slope is referred to the angular coefficient of the resulting linear fit.

36


2 2.5 3 3.5 4 4.5 5-16

-14

-12

-10

-8

-6

-4No topographic compensation, rP = -0.09, Slope = -0.231

PH

V -

ori

gina

l im

age

[dB

]


2 2.5 3 3.5 4 4.5 5-16

-14

-12

-10

-8

-6

-4With topographic compensation, rP = 0.18, Slope = 0.248

PH

V -

ori

gina

l im

age

[dB

]


Figure 3.11.: Left panel shows the sensitivity of the HV backscattered power of theoriginal (non-tomographic) data to above-ground biomass without topographiccompensation. Right panel is the same one with topographic compensation. rPis the Pearson correlation coefficient. Slope is referred to the angular coefficientof the resulting linear fit.

Layer HH HV VV0 m -0.09 -0.30 -0 .105 m -0.10 -0.35 -0.2310 m -0.11 -0.27 -0.3615 m 0.10 0.14 -0.1520 m 0.49 0.61 0.3525 m 0.74 0.81 0.7330 m 0.79 0.84 0.8235 m 0.70 0.80 0.7640 m 0.51 0.68 0.63

Table 3.1.: Pearson correlation coefficients between backscattered power layeringin 3 polarizations and in-situ AGB.

37


3.5.2. Discussion

Based on the results shown in the previous section, we deem there are two findingsthat need be highlighted, namely:

• The ground layer is poorly or negatively correlated to forest biomass, andstrongly varying with topographic slopes.

• The 30 m layer is significantly correlated to forest biomass.The aim of this section is to provide an interpretation of the results highlightedabove. In order to do this, it is firstly required a brief discussion about the physicsof radar scattering from forested areas, in order to recall what are the expectedproperties of TomoSAR imaging of forested areas. As shown in many works in liter-ature, forested areas can be characterized as the ensemble over the ground of trunksand crown, to be described as a volume of random scatterers representing leavesand branches [93], [94], [25]. According to this general model, the interaction ofradar waves with a forest can be described by modeling the ground as a half spacedielectric and using image theory [95], [96], [93]. Four scattering mechanisms result[93], [95]: ground backscattering; double bounce scattering from ground-trunk andvegetation-ground interactions; volume scattering; multiple scattering (triple andmore bounces) interactions. Ground backscattering is clearly associated with theground level. As such, these contributions are captured in TomoSAR imaging bythe ground layer. Concerning double bounce contributions from ground-trunk andvegetation-ground interactions, through simple geometric arguments and assumingflat terrain it is possible to see that the distance covered by the wave as it under-goes the two consecutive specular reflections on the ground and on the target, orviceversa, is equal to the distance between the sensor and the projection of the tar-get onto the ground [27]. It follows that under the assumption of flat terrain everydouble bounce mechanism is located at the ground level. Accordingly, it will be cap-tured in TomoSAR imaging by the ground layer. However, this conclusion does nothold in topographic areas, in which case the contributions of double bounces rapidlyvanish as terrain slope increases [61], [95], [93], [64]. In particular, in [64], whichis specific to the test site analyzed in this paper, it was found that trunk-groundcontributions vanish as terrain slope approaches 6° (see subsection 3.4.4). Concern-ing third order scattering (triple bounces), it makes sense to retain that ground totarget to ground contributions may be neglected, by virtue of the higher attenua-tion, with respect to the double bounce case, undergone by the wave in the furtherreflection on the ground and in the subsequent propagation through the trunk layerand the canopy layer of adjacent trees. Accordingly, higher order multiple scatter-ing will be neglected as well. Vegetation backscattering is then the sole scatteringmechanism that can give rise to backscattered power contributions from above theground. As such, it is captured in TomoSAR imaging by layers focused above theground. Based on this simple, yet largely retained, model, we will assume in thefollowing that: i) the ground layer captures backscattering contributions from thesoil and from lower vegetation, and double bounce contributions from trunk-ground

38


and vegetation-ground double bounce interactions; ii) each layer above the groundcaptures backscattering contributions associated only with the portion of vegeta-tion at the layer height. It is also important to note that no action is taken bythe TomoSAR processor to compensate for wave extinction. This means that thebackscattered power level sensed in each layer is sensitive to forest density in thelayer above, which certainly is particularly important when considering the groundlayer. With this in mind, we suggest the following interpretation for the results.For the layers below 20 m, the correlation between the backscattered power and AGBis very weak (and with negative trend, especially for HV). This can be explainedby: i) the trend is negative because of extinction, in that the higher the trees, theweaker the signal penetrating down to the ground; and ii) the scatter plots aredispersed since dominant scattering mechanisms may change drastically when theground surface is tilted relative to the horizontal.For layers between 20 m and 40 m, the correlation between backscatter and AGBbecomes highly significant, implying that: i) the perturbing effect of the groundcontribution is minimized (i.e.: TomoSAR focusing allows a very good rejection ofground contributions); ii) there is a strong correlation between the biomass containedin this layer and the total above ground biomass.To evaluate the correlation between biomass within the 20-40 m layer and the totalAGB, Monte-Carlo simulations have been performed based on the TROLL model[97], a spatially explicit forest growth model, designed to study structural, succes-sional and spatial patterns in natural forests with special emphasis on neotropicalrainforests as in French Guiana. In this model, because of the high number of speciesin the forest, species have been grouped into functional type groups (light demand-ing, shade tolerant and intermediary), and into 4 height classes (0-5 m, 6-15 m, 15-25m and 25-50 m). The parameters of the model for each of the species groups havebeen determined using field data in French Guiana. For our simulations, 3 classes ofDBH have been considered with their corresponding number of trees per ha [97]. AGaussian dispersion around these mean DBH is then governed by the Monte-Carloprocess, from which the other characteristics (total height and crowns shape) arededuced using the TROLL tree architecture allometry. Considering a surface extentof 400x400 m2 and 4 different random seeds for the Monte-Carlo process, 8x8x4samples of 50 m2 have been generated from which the biomass between 20 an 40 mcan be extracted from the total AGB. Figure 3.12 shows the model derived propor-tion of biomass contained in the 20-40 m layer in the total AGB. The simulationresult shows that for the tropical forest, there is a strong relationship (rP = 0.92)between the biomass within 20-40 m canopy volume and the total AGB.

3.5.3. Biomass inversion

Based the results and the discussion provided above, in this section an estimator isintroduced to retrieve AGB based on the backscattered power in HV for the 30 m

39


200 300 400 500 600 700 8000

50

100

150

200

250

300

350

400

Above-ground biomass (t.ha-1)

Bio

mas

s of

the

20-

40m

laye

r (t

.ha-1

)

rP = 0.92

Figure 3.12.: The correlation between the proportion of biomass contained in the20− 40 m layer and the total AGB using TROLL model. The linear relationshipcan be established, as confirmed by a 0.92 correlation coefficient.

layer. AGB estimation is carried out according to the log linear law expressed inEquation 3.6. The estimator parameters have been set by using 10 training samplesout of 85 plots. The retrieved AGB values are then validated with the remained75 samples. Performance are assessed by evaluating the Root Mean Square Error(RMSE) between in-situ measurements and estimated AGB values. Results arereported in Figure 3.13. The Pearson correlation is found to be rP = 0.84, whereasthe RMSE turned out to be lower than 10% .

3.6. Conclusion

In this work SAR tomography has been exploited for the retrieval of biomass indense tropical forests based on TropiSAR 2009 data-sets.

The tomography methodology to derive the biomass information has been described.The processing chain for multi-layer imaging, i.e. for deriving a synthetic image ata specific height above the ground has been presented. Airborne SAR tomographyallows to accurately map the vertical distribution of the backscattered power ineach polarization, providing a new tool to investigate forest biomass from radarmeasurements. The methodology and the results apply to the tropical forest, evenover hilly terrain. The results provide a novel approach to understand the scatteringmechanisms at P-band in a tropical forest, leading to the development of appropriatemethods to derive forest biomass information using SAR intensity and PolInSAR.Ground scattering is strongly visible and double bounces in flat terrain topographyare visible everywhere. Volume scattering is significantly related to the high rangebiomass.

40

3.6 Conclusion

0 100 200 300 400 500 6000

100

200

300

400

500

600

Above-ground biomass (t.ha-1)

Ret

rieve

d bi

omas

s (t

.ha-1

)

RMSE = 34.5 (t.ha-1)= 9.41 (%)

rP

= 0.84

Figure 3.13.: Comparison between in-situ biomass and biomass derived from in-version of the P-band HV 30 m layer. The RMSE in retrieved AGB is about 9.4%,indicating the very good performance for the AGB estimation from tomographydata from this high range of tropical forest biomass.

We have shown the similarity of the results of HH, HV and VV polarizations intropical forest in terms of their sensitivity to biomass, and we have derived indica-tions about the relative contribution of the ground scattering and the forest volumescattering in each of the vertical layers inside the forest canopy. For the lower levellayers (below 20 m), the correlation between the backscattered power and AGB isvery weak. The forest layer where SAR backscatter is the most sensitive to biomassand the least sensitive to ground contribution has been identified. In particular, weobserved that the log-backscattered power in HV at 30 m above the ground exhibitsan almost linear relationship (rP = 0.84) with forest biomass for the 85 plots of 1ha and 1.5 ha (60 plots at 1.5 ha and 25 plots at 1ha), having biomass ranging from250t.ha−1 to 450t.ha−1. The inversion using P-band HV backscattered power at 30m layer has provided mapping results with RMSE of about 9.4%.For the BIOMASS P-band space-borne mission [19], a tomographic phase is sched-uled at the beginning of the mission. Current work is dedicated to the assessmentof the method when the P-band bandwidth for space-borne mission is reduced to 6MHz, see more detail in Appendix B.

41

4. Ground Based Array forTomographic Imaging

4.1. Introduction

Four airborne campaigns have so far been carried out in the frame of Phase-ABIOMASS activities [98], [99], [100], [101], resulting in a number of studies aboutforest scattering and biomass retrieval at P-band [102], [68], [28], [92], [103]. Roughlyspeaking these studies can be grouped in two classes, depending on whether the in-formation from multiple passes is processed incoherently, involving intensity basedmethods using amplitude and polarimetric signature [21], [23], [22], or coherently,involving techniques such as Polarimetric SAR Interferometry (PolInSAR) and SARTomography (TomoSAR) [104], [105], [24], [27]. Concerning tropical forest areas,the TropiSAR campaign was carried out in 2009 in the area of Paracou, FrenchGuiana [100]. Data from this campaign have been analyzed by means of TomoSARtechniques in a number of recent studies, which showed that the forest vertical struc-ture represents a key element to characterize scattering from a tropical forest, andprovides a more direct link to forest biomass than the intensity based methods [64],[106], [69], [103]. Clearly, the availability of multiple passes is a necessary conditionfor TomoSAR, after which it follows that the replicability of the results above basedon spaceborne data is strictly connected to the stability of forest scattering overtime.The TropiScat ground based experiment has been planned to give an answer to thisquestion, by investigating temporal coherence at short and long term in all polar-izations and at different heights within the vegetation layer. The experiment waschosen to be set up at the Paracou field station, which is the same site investigatedduring the TropiSAR campaign. The equipment was installed on top of the Guyafluxtower (55m), to radiate P to L-band signals to the forest below. A preliminary testwas carried out in October 2010 using a Vector Network Analyzer (VNA) connectedto 2 P-band antennas [107]. The vertical aperture for tomographical imaging wasthen formed by progressively moving downwards the couple of antennas. The firstsuccessful test results provided input to the implementation of a stable configura-tion, designed to ensure the quality of the results of the experiments over a oneyear acquisition campaign. The aim of the study reported in this chapter is to:i) illustrate the leading design concepts that made it possible to achieve verticalimaging capabilities; ii) discuss system calibration and validation; iii) comment on

43

Chapter 4 Ground Based Array for Tomographic Imaging

the experiment capability to produce reliable coherence measurements at short andlong temporal lags.This chapter is organized as follows. The TropiScat experiment is briefly introducedin section 4.2; in section 4.3 a mathematical model for the received signal is intro-duced; the design of the tomographic array is illustrated in section 4.4; results fromreal data are presented in section 4.5; in section 4.6 conclusions are drawn.

4.2. TropiScat experiment overview

The major objectives of the experiment are the temporal survey of the variationof the measurements in time scales ranging from diurnal, weekly, monthly, up to 9months of observation and possibly beyond [107]. The observables which have to betracked are:

• the interferometric complex coherence in HH, VV and HV, at a very short ratein the order of 15 minutes, covering daily and monthly scale;

• intensity in all scales of time;• 2D vertical imaging through tomographic focusing;• the vertical distribution of temporal coherence, as obtained by comparing to-

mographic data taken at different times, covering time scales of minutes, days,and months.

Complementary to electromagnetic scattering measurements, ancillary in-situ dataare collected on the same area, including air temperature and humidity, rainfall,wind direction and speed, incident and reflected photosynthetic photon flux densityand atmospheric pressure.

4.2.1. The Paracou field station

The 55 m high Guyaflux tower in the locality of Paracou, French Guiana, has beenselected to support this experiment. The Paracou site is located in a lowland tropicalrain forest near Sinnamary, French Guiana. The forest in Paracou is classified aslow land moist forest with 140-200 species per ha, specified in the forest census ofall trees with diameter at breast height (DBH) > 10 cm. In 2003, the metallic towerwas built in the westernmost part of the Guyaflux area in an existing natural 100m2

gap, thus with a minimum of disturbance to the upper canopy. This location wasselected to cover a range of more than 1 km of undisturbed forest in the directionof the prevailing winds. The top of the tower is about 20 m higher than the overallcanopy and meteorological and eddy flux sensors were mounted 3 m above the tower.The distance from the base of the tower to the nearest trunks of the forest is about7 m. The ground slope is close to 0° in the NS directions and approximately 7°

44

4.2 TropiScat experiment overview

in the EW directions. The radar instruments are decidedly set up within onlyavailable space from EW directions. It is important to note that due to slopingterrain this set up results in the absence of scattering contributions from groundtrunk interactions [108], [61]. This constitutes a relevant difference with respect tothe TropiSAR airborne data-set, which was observed to be characterized by relevantdouble bounce scattering contributions on all flat areas [64].

4.2.2. System architecture

The TropiScat architecture is depicted in Figure 4.1. The main TropiScat hardwareis composed of a VNA, a tropicalized industrial computer PC, a set of wide-bandantennas, a radar frequency (RF) switching box and a command unit. The PC isprogramed in such a way as to manage all instruments in a fully automatic fashion.The VNA and PC are situated in a shelter at the tower foot. The VNA is connectedto the transmitting and receiving antennas with four 70 m low loss cables. Lossesin each cable are approximately 3 dB at 400 MHz and 5 dB at 1 GHz. The RFswitch box allows RF signal to be routed between the VNA and the antennas.For measurements, each pair of antennas is automatically selected before startingRF acquisition as well as the calibration loop. Due to the long duration of theTropiSCAT experiment, an internal calibration of the VNA is made before everymeasurement.

RF switchbox

Vector Network Analyzer

Tropicalized PC

Guyaflux tower

Antennas (20)

Forest

RF Transmit

RF Receive

Power line (24V)

Control line

Command unit

Figure 4.1.: Schematic view of the TropiScat system architecture

45


4.2.3. Antenna

20 wide-band antennas, four of which have been tested from field trial experimentsin October 2010 [107], have been chosen. In detail, the antennas are log periodicalantennas, useable from 400 MHz to 1000 MHz, SATIMO LP 400 model. They havethe property of relatively similar radiation pattern in both H and E planes, with a3dB aperture of 65° in H plane, and 50° in E plane. The polarization isolation isbetter than 20 dB, with very low side lobes and backward radiation less than -23dB. Moreover, the antennas weight about 1kg are easy to fix in any polarization andincidence angle.

4.2.4. Vector Network Analyzer

The radar instrument based on a stepped frequency continuous wave VNA, AgilentA5061B model, is used for the experiment. This VNA has a dynamic range of 120dB in frequency domain, between 1MHz to 3 GHz, with an Intermediate FrequencyBand Width (IFBW) equal to 10Hz. The output power of the VNA is from -45 to+10 dB.An IFBW of 10 kHz and a number of 1601 points in each ramp are selected, so thatthe final dynamic range is worth approximately 105 dB, with a sweep time close to1s. As a result, frequency resolution is 0.375 MHz. Unambiguous range is found as400 m if one covers the full bandwidth (i.e. 400 MHz-1000 MHz), and as 1200 mif one covers only 200 MHz bandwidth (i.e. 400 MHz-600 MHz). One convenientoption is to cover separately the bandwidth 400-600 MHz (Band 1), then 600-800MHz (Band 2), and at last 800-1000 MHz (Band 3). So, Band 1 will correspond toP-band, Band 3 will be representative of L-band, and aggregation of the 3 bandwidthwill obtain ultra-bandwidth data. For the 200 MHz and 600 MHz bandwidth, thetheoretical range resolutions are 0.75 m and 0.25 m, respectively.The fundamental requirement is that the frequency band has to cover the 432-438MHz band of BIOMASS, providing input for the mission assessment. Therefore,the experiment has to be performing at P-band which is the top priority. Yet, thepossibility for it to work at L-band is also very valuable. Moreover, to get a goodresolution in range and obtain independent samples of forest, one needs to use abroader bandwidth while maintaining good SNR. A 200 MHz bandwidth appearsto be a reasonable number, and allows enough independent samples.

4.3. Mathematical data model

In this section we derive the mathematical data model for a signal at a receivedantenna from a transmitted antenna by using the general concept of DiffractionTomography, widely exploited in seismic processing [109].

46

4.3 Mathematical data model

4.3.1. Scattering model

We consider a plane wave incident on an object in a homogeneous, infinite medium.Suppose the receiver is far from the object so that the scattered wave from theobject can be treated as a plane wave at the receiving point. Considering scatteringfrom stationary targets, we derive the signal model at a receiver from a waveformtransmitted by an antenna.For further simplification, we consider the case of the wave equation with constantdensity. The object is described by the velocity distribution c(r), where r is theposition vector. The host medium has a velocity c0, which is the speed of light invacuum. In the time domain, the scalar wave equation in the source-free region is[109]:

∇2εtot(t, r) + ω2

c2(r)εtot(t, r) = 0 (4.1)

where εtot(t, r) is the a scalar quantity of the field such as total electric field, ω isthe angular frequency, and ∇2 is the Laplacian operator.When a scatterer is present, the wave speed is no longer constant and it will changewhen the wave interacts with the object. We may refer to this as a perturbation inthe wave speed. In formula

S(r) = 1− c20

c2(r) (4.2)

where S(r) is known as the reflectivity function or the object function.Substituting c(r) into Equation 4.1 results in the following expression

∇2εtot(t, r) + k2εtot(t, r) = k2S(r)εtot(t, r) (4.3)

where k = ω/c0 is the wavenumber of the field in the host medium. Let

εtot = εin + εsc (4.4)

where εin and εscare the incident and scattered field respectively. Substituting inEquation 4.3, we have

∇2εsc(t, r) + k2εsc(t, r) = k2S(r)εtot(t, r). (4.5)

47


By using the free-space Green’s function g(t, r) solution [110], we obtain εsc(t, r)from Equation 4.5 :

εsc(t, r) = −¨

g(t− τ, r− r′)k2S(r′)εtot(τ, r′)dτdr′ (4.6)

where :

g(t, r) = δ(t− |r|/c0)4π|r| . (4.7)

In the frequency domain the corresponding to Equation 4.7 is

G(ω, r) = exp(jk|r|)4π|r| . (4.8)

Assuming the object is a weak inhomogeneity, the Born approximation (εtot ' εin)applies [111] and Equation 4.6 becomes

εsc(t, r) ' εB(t, r) = −¨

g(t− τ, r− r′)k2S(r′)εin(τ, r′)dτdr′. (4.9)

Taking the Fourier transform of Equation 4.9, we obtain the frequency domain

EB(ω, r) = −ˆG(ω, |r− r′|)ω2S(r′)Ein(ω, r′)dr′. (4.10)

4.3.2. Antenna field model

Assuming the incident wave is a plane wave with a waveform transmitted by anantenna at a location rTx, we have [110]

Ein(ω, r′) ' exp(jk|r′ − rTx|)4π|r′ − rTx|

Fpattern(k, r′ − rTx) (4.11)

where Fpattern is the scalar analogue of the radiation vector, representing for antennabeam patterns and transmitted waveform and r′ − rTx is the unit vector in thedirection of r′ − rTx. In formula

Fpattern(k, r) =êxp(−jkr)Jl(ω, r)dr

where Jl is the current density of the antenna.

48

4.4 TropiScat tomographic array design

4.3.3. Received signal model

Assuming the same antenna is used for transmission and reception, to obtain theexpression for the data received in a location rRx, we substitute Equation 4.8 andEquation 4.11 into Equation 4.10 and include a second factor corresponding to theradiation vector of receiver. In formula

Y (ω, rTx, rRx) =êxp(jk(|rTx−r′|+ |rRx−r′|))A(rTx, rRx, r′, ω)S(r′)dr′ (4.12)

where

A(rTx, rRx, r′, ω) = ω2Fpattern(k, r′ − rTx)Fpattern(k, r′ − rRx)(4π)2 |rTx − r′| |rRx − r′|

(4.13)

incorporates the geometrical spreading factors, transmitted waveform and antennabeam patterns.Finally, in time domain we have

y(t, rTx, rRx) =êxp(−jω(t−Rr′/c0)) A(rTx, rRx, r′, ω)S(r′)dr′ (4.14)

where

Rr′ = |rTx − r′|+ |rRx − r′| (4.15)

is the bistatic distance of the transmitter - receiver pair at target position r′.

4.4. TropiScat tomographic array design

The system is intended to accomplish three requirements as following:Requirement 1: provide fully polarimetric vertical resolution capabilities, while

ensuring unambiguous imaging of the whole vegetation layer,Requirement 2: gather data continuously for about a year with a conveniently

short time, so as to study both the short term temporal coherence andits seasonal variations,

49


Requirement 3: provide a sufficient number of looks to allow reliable coherenceevaluation at every fixed height by averaging independent and homoge-neous samples.

It follows after Requirement 1 that the system needs to have sufficient aperture alongthe vertical direction. On the other hand, the antennas have to be closely spacedalong the vertical direction to ensure unambiguous imaging. Requirement 2 entailsthat the system is capable of acquiring data of the same scene for an extended periodof time. Requirement 3 can be fulfilled by using a large bandwidth system and/orby exploiting time averages. As an alternative, Requirement 3 could also be fulfilledby forming a further aperture along the azimuth direction. This option, however,would entail the usage of an either very large number of antennas or the capabilityto move the array horizontally, and hence it has been discarded. Finally, the systemhas to be able to operate at wavelengths compatible with those commonly used forinvestigations of vegetated scenarios through space borne SAR’s, namely P-bandand L-band. However, studying temporal decorrelation at P-band seems to be themost urgent task to be accomplished nowadays, in order to provide input for thequantitative assessment of TomoSAR and PolInSAR results achievable through theexploitation of multi-pass BIOMASS surveys on tropical forests.The following constraints have been established:Constraint 1: employment of 20 antennas,Constraint 2: each antenna has to be operated either as transmitter or a receiver,Constraint 3: the physical separation between any two antennas has to be equal

or larger than 0.8 m.Constraint 1 is intended to limit experiment costs. Constraint 2 allows simplify-ing system installation and improving the overall SNR by operating a simpler RFswitchbox. Constraint 3 has been established in order to minimize electromagneticcoupling effects due to the interaction among different antennas. The value of 0.8 mhas been deemed to be a sufficiently safe distance to operate the equipment correctly,as resulted from field trial experiments in October 2010 [107].

4.4.1. Tomographic array design

To conjugate requirements and constraints above we considered a multistatic arrayconfiguration, obtained by placing a transmitting and receiving antenna pair in suchpositions as to illuminate, at least theoretically, the same wavenumbers of the in-vestigated object as a single monostatic (i.e. transmitting and receiving) antennaplaced in the middle. In the remainder of the chapter we will refer to such an equiv-alent monostatic array as a virtual array. The leading concept in the design of thevirtual array is to achieve the same imaging performance as a vertical array consti-tuted by closely spaced antennas, even though the physical separation is actuallyconsistent with Constraint 3.

50


-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5

Azimuth [m]

Real array

Heig

ht

[m]

H - Rx

H - Tx

V - Rx

V - Tx

Figure 4.2.: Antenna positions for tomographic measurements

The best solution among those we considered encompasses one vertical array of 5antennas for each polarization (i.e. horizontal or vertical) and for each operatingmode (i.e. transmit or receive). This simplifies not only the switch boxes but alsothe system operation. This design has been optimized for a central frequency of500 MHz. However, the system is expected to provide imaging capabilities at 700MHz and 900 MHz, so as to cover all cases to be investigated within TropiScat. Thesystem main dimensions are summarized as follows: overall horizontal extent: <2.5m; overall vertical extent: <4.5 m; minimum distance between antennas: 0.8 m.The physical antenna positions are shown in Figure 4.2, whereas Figure 4.3 reportsthe physical and virtual antenna positions for each polarization. Each virtual arrayis formed by N = 15 positions, corresponding to 15 transmitting and receivingantenna pairs. The virtual arrays for HH and VV are found at the same positions,whereas the virtual arrays for HV and VH are 0.8 m apart, yielding two looks. Theposition of each virtual antenna along the vertical direction is the same in all cases,which entails the same imaging properties in all four polarizations. In particular,the resulting virtual array aperture and spacing are, respectively: Az = 2.8 m; 4z= 0.2 m. As a first approximation the vertical resolution can be assessed as:

ρz = λ

2AzR (4.16)

where λ is the carrier wavelength and R is the distance from the antenna to the

51


(a) Transmitter : H Receiver: H

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5

Azimuth [m]

Real array

Hei

ght

[m]

H - Rx

H - Tx

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5Virtual array

Hei

ght

[m]

Azimuth [m]

Tx-Rx

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5

Azimuth [m]

Real array

Hei

ght

[m]

V - Rx

V - Tx

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5Virtual array

Hei

ght

[m]

Azimuth [m]

Tx-Rx

(b) Transmitter : V Receiver: V

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

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55

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Hei

ght

[m]

H - Tx

V - Rx

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

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55

55.5Virtual array

Hei

ght

[m]

Azimuth [m]

Tx-Rx

(c) Transmitter : H Receiver: V

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5

Azimuth [m]

Real array

Hei

ght

[m]

V - Tx

H - Rx

-2 -1 0 1 250

50.5

51

51.5

52

52.5

53

53.5

54

54.5

55

55.5Virtual array

Hei

ght

[m]

Azimuth [m]

Tx-Rx

(d) Transmitter : V Receiver: H

Figure 4.3.: Lelf panels: real arrays; right panels: virtual arrays; from top tobottom: HH, VV, VH and HV operational mode.

52


target. For example, vertical resolution at R = 70 m is readily obtained as: ρz =7.5 m at 500 MHz; ρz = 5.3 m at 700 MHz; ρz = 4.1 m at 900 MHz.Ambiguities can arise depending on the vertical spacing between two nearby posi-tions along the array, 4z. Again as a first approximation, the height of ambiguitycan be assessed as:

zamb = λ

24zR (4.17)

It turns out to be higher than 40 m for R > 50 m even at 900 MHz.

4.4.2. Tomographic coherent focusing

Despite the array design having been based on the concept of the virtual array,the focusing algorithm implemented for data processing fully takes into account themultistatic nature of the antenna array. To form the image at a certain point in thespatial domain, we aim to invert Equation 4.14 by applying an imaging backprojec-tion operator to the collected data. The imaging operator takes on the form

I(p) =N∑n=1

êxp(jω(t−Rn

p/c0)) y(t, rTxn , rRxn )dt (4.18)

where y(t, rTxn , rRxn ) is the data of the transmitter-receiver pair n, N is total numberof transmitter-receiver pairs, p represents a certain point in the ground (or slant)range and height plane, and

Rnp = |rTxn − p|+ |rRxn − p| (4.19)

is the bistatic distance of the transmitter-receiver pair n at target position p.We can carry out the t integration in the Equation 4.18 to obtain :

I(p) =N∑n=1

y(τnp , rTxn , rRxn ) (4.20)

where τnp = Rnp/c0 is the bistatic time delay of the transmitter-receiver pair n at

target position p.

53


The target I(p) is then focalized by superposition of all the back projected datafrom all transmitter-receiver pairs.Such a focusing approach provides resolution capabilities consistent with the wellknown Rayleigh limit [24], [112]. Another approach would be to resort to super-resolution algorithms such as MUSIC, CAPON filtering, RELAX, or even Com-pressive sensing algorithms [112], [72], [71]. Such algorithms, however, are mostlysuited for the problem of detecting and localizing a collection of few point targets,whereas they could easily produce processing artifacts in presence in the imaging ofdistributed media.

4.4.3. Numerical simulations

Detailed information about the tomographic imaging performance is displayed inFigure 4.4 and Figure 4.5. All panels have been obtained by simulating the presenceof random scatterers on the tower and at the ground layer. Scattering from theforest has intentionally not being included, so as to allow evaluation of ambiguouscontributions within the vegetation layer. The ground terrain is flat, resulting in notargets appearing at negative height values.. The same bandwidth 50 MHz is usedfor three different center frequencies, i.e. 500 MHz, 700 MHz and 900 MHz. Weconsidered four scenarios, one corresponding to the case of isotropic antennas and theothers to the cases of directional antennas pointing at a look angle θ = 30°, 40°, 50°.The latter three cases were simulated using the radiation pattern of antenna LPSATIMO 400 [113].In all cases the array ensures rejection of spurious contributions well beyond 20 dB.The situation is clearly improved by accounting for the elevation antenna pattern.The best imaging quality is found, as expected, at 500 MHz. At higher frequencies,especially at 900 MHz, spurious contributions appear that might jeopardize theoverall imaging quality at near ranges, where ambiguities from the tower and terrainare likely to appear within the forest.

4.4.4. Bistatic effects

No artifacts are expected to arise from bistatic effects as long as signal focusing isconcerned, since the focusing processor explicitely takes into account the multistaticnature of the antenna array. On the other hand, bistatic effects could be relevantin presence of a strong anisotropic behavior of particular targets within the forestvolume. It has to be kept in mind, however, that the TropiScat system has noazimuth resolution, meaning that vertical profiles are relative to an average over anazimuth angular sector. We deem to be reasonable to assume this angular averagemake anisotropy phenomena negligible. Finally, bistatic effects are expected to resultin an azimuth-dependent intensity unbalance between different polarizations, due tothe fact that transmission and reception antennas are placed at different physical

54


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55


positions. This effect is, however, a systematic bias, which does not impact onthe temporal variation of forest scattering as sensed by the TropiScat tomographicsystem.

4.5. Experimental results

The TropiScat tomographic mode has been implemented in October 2011, by in-stalling the 20 antennas on top of the Guyaflux tower, see Figure 4.6.The temporal sampling for tomographic imaging at P-band is 15 minutes (96 samplesper day), thus allowing the study of both the short term and long term temporalcoherence variations within the forest.The format for the acquisition name assumed in this section is the following: Year– Month (1-12) – Day (1-31) Acquisition time (H-min) Frequency band (1,2,3),Polarization (HH,HV,VH,VV).

Figure 4.6.: Tomographic array on the top of the Guyaflux tower, Paracou, FrenchGuiana.

4.5.1. System pulse response

The tomographic responses of a 2 m trihedral and a (rotated) dihedral reflectorhave been derived by taking the difference between the signals acquired with andwithout the reflectors, so as to remove forest contributions through coherent can-cellation. The pulse responses for the trihedral reflector at 500 MHz of HH and VVpolarizations are reported in Figure 4.7. The trihedral is observed to be very wellvisible in HH. The corner is visible in VV polarization as well, even though signalintensity is about 10 dB lower than in HH. Such a discrepancy appears to be dueto the different antenna patterns for HH and VV at very steep incidence angles. Incross-pol HV and VH (not shown here), the trihedral reflector is partially visible.Instead, the pulse response for cross-pol is well recovered by exploiting the rotateddihedral reflector, for which the signal intensity is observed to be significantly higherthan uncompensated forest contributions, see Figure 4.8.

56

4.5 Experimental results

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57


4.5.2. System stability

Tower stability is a fundamental parameter to achieve the aim of this experiment, asunwanted oscillations of the antenna equipment on top of the Guyaflux tower couldbe confused with motions within the vegetation layer. The stability analysis reportedhereinafter is based on data collected in October 2011, when the corner reflectorin front of the Guyaflux tower was available. The area surrounding the tower isnot very windy (wind speed < 5 m/s). However the wind pressure can generatesmall oscillating movements of the tower top. The amplitude of such movementsis expected to be less than ±5 centimeters at worse with a temporal frequency ofabout 0.5 Hz. Another possible source of errors is represented by changes in theelectromagnetic response of the equipment, for example due to rainfall events.

To assess system stability we considered the time series obtained by taking the pix-els in the focused tomograms corresponding to the three targets. These are thetomographic array itself, the trihedral corner on the ground (H = 1m,R = 61m)and a point within the forest canopy (H = 30m,R = 85m). The analysis is carriedout based on P-band data, as they provide the finest temporal sampling. Figure 4.9shows intensity and apparent Line Of Sight (LOS) displacement for the three con-sidered targets over 35 hours, starting from midnight Y2011-M10-D07 00H00. Ap-parent LOS displacement has been obtained as dr = 4λϕ/π, where ϕ is the phasew.r.t. the first acquisition and λ = 0.6m. It is important to note that an abruptchange took place at slightly before 6:00 in the morning on day 8, corresponding to30 hours lag from the starting time. Such an event is readily found to be associatedwith a heavy morning rain, see Figure 4.10. The impact of rainfall is even betterobserved by considering the change of the interferometric phase over time, as shownin Figure 4.11.

The fact that the phase is modified by rain both at the corner and at the array in-dicates that rainfall affects the electromagnetic response of the equipment. Accord-ingly, data acquired during rainfalls should be neglected in evaluating the temporalbehavior of the forest.

Excluding the rainfall event, in Figure 4.9 and Figure 4.12, three different phasebehaviours are observed concerning the time series associated with the corner andthe array:

• From 4 to 6 in the morning there are two phase peaks both at the cornerand at the array. The observed trend is about 2 mm in LOS motion, but nooscillations are observed.

• From 9 to 16 the corner phase is observed to have a trend of about 8 mmplus a number of phase oscillations (< 1 mm). No relevant change is observedconcerning the array phase.

• During most night hours, from dusk to dawn, the phase histories at both thearray and the corner exhibit an excellent stability.

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60


Concerning the motion of the antenna array under the action of the wind, two effectsare expected. The first is a rigid translation due to a slight leaning of the towertop under the effect of a constant wind. This motion has no effect on the quality oftomographic imaging, as it would just result in a very slight image translation. Theother effect is associated with random horizontal oscillations due to varying windspeed. This kind of motion can potentially degrade image quality due to the factthat tomographic focusing is carried out by processing data acquired by 15 differentantenna pairs, the time duration for the entire acquisition being about 30 seconds.Assuming the observed oscillations of the corner phase history are entirely due tohorizontal motions of the tower, the standard deviation of the latter can be upperbounded as:

σx = σrsinθ√

15 (4.21)

where σr is the standard deviation of LOS motion, θ is the incidence angle at thecorner position, and the factor

√15 accounts for the fact that 15 antenna pairs are

used in the tomographic focusing in the late afternoon or at night. As a result, apeak value on the order of 4 cm is found during day time, when wind speed is atits maximum (5 m/s), whereas the average value during night time is 1 cm or less.To demonstrate that such a motion does not jeopardize image quality we simulatedthe effect of random motion errors about the sensor positions on data focusing. Todo this we consider a real HH data acquired at midnight (Y2011-M12-D15 00H00)and produce two synthetic raw data by injecting a Gaussian random displacementwith zero mean and standard deviation equal to 2.5 cm and 5 cm, respectively. Theraw data are then focused in all cases assuming the tower is perfectly still. Singlerealization imaging results under perturbed conditions are presented in Figure 4.13.

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Figure 4.13.: The effects of tower motion to the tomographic imagings.

It is important to observe that image quality is fully preserved, even in the worst casescenario where the tower moves randomly by 5 cm. As discussed above this valuewas derived by assuming that the observed corner phase variations are entirely dueto tower motions, therefore providing a worst case scenario upper bound for towermotions. It is also worth noting that in the rare case of such a strong wind asto induce very large tower motions (> 5 cm) the forest would be heavily shakentoo, giving unavoidably rise to relevant temporal decorrelation phenomena. Basedon this analysis, we then conclude that the defocusing phenomena observed during

61


daytime (see section 5.3) can be safely imputed to forest motion under the actionof wind. Moreover, the excellent tower stability during night hours confirms thefeasibility of yielding accurate measurements of the forest temporal decorrelation,with the one precaution to exclude rainfalls from the analysis.

4.5.3. Multi polarization tomograms

P-band tomograms for all polarimetric channels are shown in Figure 4.14. It shouldbe noted that the terrain slopes down moving away from the tower, which is whytargets appear at negative height values. Up to about 50-70 m away from thetower the tomographic imaging shows scattering from the ground and from about30 m above, which clearly reveals the structure of the vegetation in that area. Itis interesting to note a substantial gap between the top and the bottom of thescattering layers, which suggest the most dense canopy layer is on top. Fartheraway from the VNA at about 200 m, the imaging is not as certain, due to both theincreased distance and the vertical resolution loss.

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Figure 4.14.: Multi polarization tomograms are shown at 500 MHz. Data is atY2011-M10-D15_00H00.

Accordingly, the near range area (i.e. up to 120 m away from the array) is certainlythe most interesting for present and future analysis. In this area, vertical resolutionis on the order of 6-12 m, which allows us to separate different vertical layers withinthe forest volume. On the contrary, physical interpretation becomes uncertain at far

62

4.6 Conclusion

ranges, as vertical resolution increases with range. Furthermore, in the near rangearea the incidence angle varies from 20°-60°, allowing to combine and investigatethe temporal backscatter of Airborne or Spaceborne P-band SAR data.

4.5.4. Multi frequency tomograms

Figure 4.15 reports multi frequency tomograms at VV and also shows the exploita-tion of the ultra-bandwidth from 400 MHz to 1000 Mhz. The best imaging quality isexpected at 500 MHz. As expected, at higher frequencies volume contributions aredominant even at near range, due to reduced wave penetration. The best verticalresolution is achieved at 900 MHz due to the shortest wavelength.The ultra-bandwidth tomogram, see the right bottom panel in Figure 4.15, is ob-served to produce the highest range resolution thanks to 600 MHz bandwidth, wit-nessing that different bands are properly combined.

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Figure 4.15.: Multi frequency tomograms are shown at VV. Right bottom panelis tomogram with ultra bandwidth 600 MHz. Data is at Y2011-M12-D15 00H00.

4.6. Conclusion

In this chapter we discussed the design and performance of the 20 element multistaticarray employed in the TropiScat campaign, whose main aim is to produce reliable

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information about temporal coherence in tropical forests at P-band, considering timelags ranging from hours to months. The multistatic array has been designed so as toform an equivalent monostatic array consisting of 15 closely spaced phase centers,which enables unambiguous imaging of the forest volume while granting a sufficientlylarge distance between nearby antennas to minimize coupling effects. Nevertheless,the implemented focusing algorithm fully takes into account the multistatic natureof the array. The TropiScat tomographic mode was implemented in October 2011by installing the designed array on the top of the Guyaflux tower at the Paracoufield station, French Guyana.The analysis so far focused on instrument calibration and validation. Image qualitywas checked by using a trihedral and a rotated dihedral reflector, which allowed us toobserve that the system pulse response is consistent with the design at all polariza-tions. Tower and system stability has been discussed based on time series collectedover 35 hours with a temporal sampling of 15 minutes. Rainfall events have beenobserved to affect the electromagnetic response of the equipment. Accordingly, dataacquired during rainfall should be disregarded in evaluating the temporal behaviorof the forest. Random motion of the tower due to the action of the wind have beenobserved to be about 4 cm at most in the case when wind speed approaches 5 m/s.Tower motions of such an extent have been shown not to affect image quality in anynoticeable way at P-band. We can then conclude that the perturbation phenomenaobserved during daytime can be safely imputed to forest motion under the actionof wind. This conclusion already appears to provide a very useful input concerningthe BIOMASS mission, as it suggests that performance over tropical forest couldbe optimized by gathering acquisitions at dawn or dusk time. The excellent towerstability (1 cm at most) observed during night hours fully confirms the feasibilityof yielding accurate measurements of the forest temporal decorrelation, with theone precaution to exclude rainfalls from the analysis. Next chapter is focused oninvestigating forest changes concerning temporal coherence at short and long terms,seasonal variations, and on providing physical interpretations of the observed phe-nomena.

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5. Multi-Temporal Multi-PolarimetricTomographic Imaging

5.1. Introduction

The TropiScat ground based experiment will be the one giving an response to thisquestion, by investigating temporal coherence at short and long term in all polariza-tions and at different heights within the vegetation layer. In order to illuminate theforest from the top, a set of 20 antennas was installed on top of the Guyaflux tower(55 m high) at the Paracou test-site, to radiate P to L band signals to the forestbelow [114], [115]. Such an equipment is intended to provide 2D (ground range -height) resolution capabilities through the coherent combination of the signal fromdifferent antennas via tomographic techniques [116]. By comparing, again coher-ently, tomographic images taken at different times it is possible to gain access tothe variation of temporal coherence with respect to forest height. The aim of thestudy reported in this chapter is to present the analysis results related to both ofshort term and long term temporal decorrelation.This chapter is organized as follows: section section 5.2 presents the brief intro-duction of the TropiScat tomographic mode, in section 5.3 the tomographic movieis presented, in section 5.4 the tomographic array is proposed, in section 5.5 theexperiment results are shown and in section 5.6 conclusions are drawn.

5.2. TropiScat tomographic mode

5.2.1. Objective

The TropiScat tomographic mode system aims to provide fully polarimetric verticalresolution capabilities, gather data continuously for about a year, and provide asufficient number of looks for reliable coherence evaluation at several height levels[116].The system is able to operate at wavelengths compatible with those commonly usedfor investigations of vegetated scenarios through space borne SAR’s, namely P-bandand L-band. However, studying temporal decorrelation at P-band seems to be themost urgent task to be accomplished nowadays, in order to provide input for the

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Chapter 5 Multi-Temporal Multi-Polarimetric Tomographic Imaging

quantitative assessment of Tomographic and PolInSAR results achievable throughthe exploitation of multi-pass BIOMASS surveys on tropical forests.

5.2.2. Tomographic system array

The TropiScat tomographic array has been designed and implemented in Octocber2011 as shown in Figure 5.1. The system is characterized by 20 antennas, each ofwhich is operated either as a transmitter or a receiver. The array extent is 2.4 x4.4 m in the horizontal and vertical direction, respectively. The minimum distancebetween antennas equals 0.8 m, which ensures reduction of coupling effects.

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Figure 5.1.: Antenna positions for TropiScat tomographic system in Guyafluxtower. The design encompasses one vertical array of 5 antennas for each po-larization (i.e: horizontal or vertical) and for each operating mode (i.e.: transmitor receive).

Figure 5.1 shows that the vertical locations of the real array antenna is irregular.However, by employing multiple transmitting–receiving pairs, a uniform equivalentmonostatic array is formed along the vertical direction for each polarimetric chan-nels, resulting in the same tomographic imaging properties in all four channels [116].This design has been optimized for a central frequency of 500 MHz. The resultingvirtual array aperture and spacing are, respectively, Az = 2.8 m; dz =0.2 m. Thisvertical spacing yields at P-band (500 MHz) an ambiguous return appearing at anangle close to 135° from the target, well distinguished from the forest. Furthermore,the virtual array aperture results in the vertical resolution in far range (70m) beingabout 7.5m in P-band and proportionally higher at higher frequencies. The tem-poral sampling for tomographic imaging at P-Band is 15 minutes, resulting in 96

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5.3 Tomographic movie

samples per day. This allows to study both the short term temporal coherence andits seasonal variations within the forest.

5.3. Tomographic movie

5.3.1. Terrain flattening

Tomograms are sensitive to fast motion of the forest induced by gusts of wind [116].A simple way to mitigate the side-lobe impact is to average a number of acquisitionsgathered at nearby times, i.e.: 4 acquisitions. Furthermore, we would like to moveto range domain rather than ground domain [115]. By working in range domain, it isnot only producing better imaging but also reducing the vertical resolution varyingfrom 2D to 1D as shown in the top of Figure 5.2.

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Figure 5.2.: Top panel:intensity HH; Bottom panel: Temporal coherence;

It is possible to see the terrain slopes down when moving far away from the tower. Itsuggests a way to extract the ground surface. By using the maximal coherence, wecan extract the ground surface information as shown in bottom of Figure 5.2. Thisthen can be used in focusing procedure to flatten the terrain, referring the groundsurface as 0 m. By processing this way, this allows us to investigate the interestingparameters as a certain height above the ground.In Figure 5.3 full polarization tomograms are shown. In near range, we can seethe ground and the canopy separately. While in the far range, the imaging is not

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Figure 5.3.: All polarization at 500 MHz

certain, due to the vertical resolution loss. In HH and VV, the ground contributionis more visible as expected. There is a gap between the ground and the canopy atthe elevation about 10m. This can be explained by the fact that not only the canopylayer is very dense but also the vegetation at this layer generally consists of shrubsand small trees.

5.3.2. Tomographic movie

Figure 5.4 reports a few snapshots from the “tomographic movie” obtained over timeat P-Band. Each panel has been generated in slant range - height coordinates, andflattened so as to bring terrain level at 0 m, so as to help visualization and inter-pretation of the results. It is however important to note that terrain topography inthe illuminated area is characterized by a strong back-slope (i.e. the terrain is tiltedaway from the tower) [115]. This results in the absence of scattering contributionsfrom ground-trunk interactions, differently from other areas within the TropiSARdata-set [64]. As visible, acquisitions collected during day time are often character-ized by a lower intensity with respect to night hours. This phenomenon is due to thefact that data have been acquired by 15 different antenna pairs, the time durationfor the entire acquisition being about 30 seconds, which makes the imaging qualitysensitive to wind gusts [116].Another interesting finding resulting from the tomograms is that the location of theforest center of mass is observed to go up and down by more than 1 m during day

68

5.3 Tomographic movie

(a) – 00H day 1 (b) – 09H day 1

(c) – 18H day 1 (d) – 03H day 2

(e) – 12H day 2 (f) – 21H day 2

Figure 5.4.: Polarimetric tomogram stability as a function of acquisition time atP-band (500 MHz).

69


0 5 10 15 20 2522

23

24

25

26

27

28

29

Tem

pera

ture

[0C

]

Time lag [h]

Average temperature [0C]

0 5 10 15 20 25-2

-1.5

-1

-0.5

0

0.5

Time lag [h]

Heig

ht

[m]

Center of mass as a function of time (from midnight)

HH

HV

VH

VV

Figure 5.5.: Upper panel: the diurnal change of the forest center of mass. Bottompanel: temperature variation over one day.

hours, as shown in Figure 5.5.The strong correlation with temperature variation over one day seems to suggest thisphenomenon may be connected to the water content within the vegetation layer. Onepossible explanation considers evapotranspiration phenomena [117]. There is heatand mass transfer between forest organisms and their surroundings. With changingtemperature, the exchange of oxygen and carbon dioxide between leaves and theatmosphere varies. This leads to changes of the water content inside the trunks. Theforest stores water inside them overnight; in the morning, with higher temperaturesand in the afternoon when the temperature goes down again, the center of massshifts.

5.4. Short term temporal decorrelation

5.4.1. Coherency matrix

For forests, signals coming from such distributed targets may be described as real-izations of a zero mean complex normal random variable. In order to study suchtargets, an estimation of the covariance matrix which characterizes their probabilitydensity function, is needed.

70

5.4 Short term temporal decorrelation

Since there is no geometrical decorrelation in this kind of data, the impact is mainlydependent on temporal decorrelation [118]. Let us indicate with yn(x) the nthcomplex speckle signal out of a stack of N , with n = 1, ..., N . Each signal will be adelayed version of a corresponding unknown not delayed signal ξn(x). We can write[119]

yn(x) = ξn(x− dn), (5.1)

where the d′ns are the various delays or shifts, one per signal or acquisition. Notethat the ξn(x)′s are not identical, though aligned to one another. This is because ofsignal decorrelation, which includes also the effects of additive noise. The coherenceproperties of the various signals are expressed by the N × N covariance matrix Wwhose elements are:

[W ]n,k = E[ξn(x)ξ∗k(x)] (5.2)

whereas the spectral properties of each signal are given by the autocorrelation func-tion

E[yn(x)y∗n(x′)] = E[ξn(x)ξ∗n(x′)] = sinc(x− x′) (5.3)

By using the normalized cardinal sine, it is equivalent to having unitary bandwidth.One important problem in the application is how to retrieve a reliable measurementof the data covariance matrix. In absence of a-priori information, the solution isto compute the sample covariance matrix with discrete signals. Then, the covari-ance matrix W is obtained by assuming and exploiting statistical stationarity in aregion surrounding the analyzed pixel. In order to operate with discrete signals weintroduce the N vectors yn which collect the available samples of yn(x), sampledaccording to Nyquist’s limit. For example, x = 1, 2, ..., L, assuming that L inde-pendent samples are available then yn = [yn(1), yn(2), . . . , yn(L)] and the estimatedcoherency matrix W whose elements can be written:

[W]n,k

= 1L

∑yny

∗k (5.4)

Let us also assume that the vectors yn are circular-Gaussian distributed, and thatthe coherency matrix is a complete statistical description. Then, we can safelyconfuse coherency and covariance matrices.In summary, in coherency matrix, the coherence values can be arranged in a squarematrix having the number of rows and columns equal to the number of signals Nand their elements on the main diagonal equal to one.

71


H = 0 m

Tim

e la

g [

h]

0 5 10 15 200

5

10

15

20

H = 10 m

0 5 10 15 200

5

10

15

20

H = 20 m

0 5 10 15 200

5

10

15

20

0

0.2

0.4

0.6

0.8

1

Figure 5.6.: HV coherency matrix over one day.

5.4.2. 1 full day coherency matrix

Figure 5.6 shows HV coherency matrices over one day at the ground layer (0 m),and at 10 m and 20 m above the ground. Each entry in the three matrices has beenobtained by taking the interferometric coherence between two different acquisitiontimes at one particular location within the forest. Coherence evaluation has beencarried out by employing an averaging window of 5m x 40m (height-range), corre-sponding to about 50 looks. We notice a regular decline of coherence moving awayfrom the main diagonal, which corresponds to increasing time lag. However, themost relevant phenomenon is the coherence drop during daytime, which confirmsthe effect of the wind moving the forest canopy observed in the previous section. Itis worth noting that this phenomenon is partly observed at the ground level as aresulting of defocused contributions from the rest of the vegetation layer.

5.4.3. Multi-temporal multi-polarization decomposition

Multi-baseline multi-polarimetric data allows to identify the sources of forest scatterthrough the assumption of the Sum of Kronecker Products (SKP) structure [76],[28]. The same principle can be developed with multi-temporal multi-polarimetric(MTMP) data.

5.4.3.1. Methodology

We assume that there are 2 main scattering contributions in the forest, i.e. from thestable and varying mechanism scatterings (SM). It is possible to describe each maincontribution from a polarimetric and temporal point of view. This section presentsan Algebraic Synthesis (AS) technique to be used to separate and recognize theinformation associated with each contribution, resulting in the stable and varyingmechanism information.

72


Considering the case of a MTMP data-set of data images acquired in N acquisitions,a data vector gathers all measurements associated with a single resolution cell andit can be expressed by :

y = [yT (w1) yT (w2) yT (w3) yT (w4)]T (5.5)

where y(wi) = [y1(w1) . . . yN(wi)]T and w1,w2,w3,w4 are four projection vectorswhich represent the polarimetric information. yn(wi) is a complex value in a singleresolution cell, where the subscript n refers to the acquisition index.

Three general hypotheses for temporal coherence are here assumed: i) it is obtainedas the weighted sum of few components (statistical independence among differentSMs); ii) loss of each component alone is invariant to polarization of structural pa-rameters; iii) data stationarity across different acquisitions, which may be expectedto hold if events such as fires, frosts, deforestation do not occur during the acquisitionperiod.

Under such hypotheses, a MTMP covariance matrix WK of the data may be ex-pressed as a SKP. The decomposition of the second order moments of the MTMPdata WK gives the best least square solution WK [120]:

WK = E[yyH ] =K∑k=1

Ck(a)⊗ Tk(a) (5.6)

Where Ck and Tk referred to as polarimetric and temporal signatures matrices. K isthe number of scattering mechanisms contributing to the data. ⊗ is the Kroneckerproduct.

The key is finding a matrix a such that Ck(a) and Tk(a) are physically meaningfulwhich means they must be combined in such a way to characterize polarimetric andtemporal information. This can be attained by exploiting the fact that both Ck(a)and Tk(a) are Hermitian, semi-positive definite matrices for every k.

Since we assume 2 main SMs model which implies the rank 2 of WK , it means thatthe first two terms of the SKP decomposition of the covariance matrix WK yield thebest approximation of the data covariance matrix W in the Least Square sense. Informula, the matrix W2 is described by :

W2 = λ1C1 ⊗ T1 + λ2C2 ⊗ T2 = CS ⊗ TS + CV ⊗ TV (5.7)

where subscripts S and T refer to the stable and varying backscattering mechanism.

73


It follows that any solution of the stable-varying decomposition problem is deter-mined by just 2 real numbers, say (a, b), the general form of the solution beingwritten as:

TS = aT1 + (1− a)T2 (5.8)TV = bT1 + (1− b)T2

CS = 1a− b

((1− b)C1 − bC2)

CV = 1a− b

(−(1− a)C1 + aC2).

The two parameters (a,b) represent the model space. The polarimetric behaviors andtemporal signatures associated with the stable and varying component do changeby varying (a,b).

So far, the AS technique becomes an operational tool for the separation of stableand varying scattering even in absence of a physical model, while ensuring thephysical validity of the solution and yielding the best Least Square solution giventhe hypothesis of two SMs. The procedure can be summarized as follows:

1. Truncate the SKP decomposition of the sample covariance matrix of the databy retaining the first two terms. This operation ensures the best Least Squarefit given the hypothesis of two SMs, independently on the choice of the pa-rameters (a, b).

2. Determine the range of values for the parameters (a, b) that yields positivedefinite solutions for Ti, Cii=T,V . This operation ensures the physical validityof the solutions.

3. Optimize some criterion in order to pick an unique solution among the set ofall the physically valid ones.

A trivial solution is based on their entropy values from a polarimetric analysis [121].The stable component can then be assigned to the minimum entropy solution.

5.4.3.2. Experimental results

We consider on the full day data as in subsection 5.4.2 for a demonstration the con-cept. From the SKP decomposition, we have two matrices, one temporal signatureand the other for the polarimetric color signature.

First of all, for model validation, we evaluate of the error εerror between the samplecovariance matrix W and its best approximation with two Kronecker products W2.

74


In formula [120]

εerror =

∥∥∥W − W2

∥∥∥F∥∥∥W∥∥∥

F

(5.9)

where ‖·‖F is Frobenius norm.The error has turned out to be lower than 10%, after which it follows that theassumption of two SMs is well justified, see Figure 5.7.

0 10 20 300.85

0.9

0.95

1

Height [m]

1 -

e

rro

r

Percent of information

Figure 5.7.: The information can be represented by the sum of just two Kroneckerproducts

In the first part of the Kronecker product, Figure 5.8 shows the coherency matrix for1 full day as a function of height associated with temporal signature. The principaldiagonal is always unitary because every image is perfectly coherent with itself. Wenotice a regular decline of coherence moving away from the main diagonal, whichcorresponds to increasing time lag. The same behaviour can be seen with bothstable and varying part. However, the varying part shows much more changes.The second part of the Kronecker product, namely the product of the 4x4 polari-metric color matrix is shown in Figure 5.9.It will be interesting to find the interferometric phases of the SKP (one stable, theother changing). What would be very important is the interferometric phase historyof each KP. In Figure 5.10, all polarizations are shown, as well as the stable andvarying components. The temporal interferometric coherence amplitude and phasevariation during day and night as a function of height can thus be observed. At theground layer, the coherence amplitude and phase are the most stable.In summary, night hours are observed to be preferable for data acquisition due tothe high coherence, which is also very consistent with the phenomena center of masschanging in forest as discussed in section 5.3.

75


Stable part: H = 0m

Tim

e lag [

h]

0 5 10 15 20

0

5

10

15

20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Varying part: H = 0m

Tim

e lag [

h]

0 5 10 15 20

0

5

10

15

20

H = 10m

Tim

e lag [

h]

0 5 10 15 20

0

5

10

15

20

H = 10m

Tim

e lag [

h]

0 5 10 15 20

0

5

10

15

20

H = 20m

Tim

e lag [

h]

0 5 10 15 20

0

5

10

15

20

H = 20m

Tim

e lag [

h]

0 5 10 15 20

0

5

10

15

20

Figure 5.8.: Full day stable and varying temporal structure matrices

HH

HV

VH

VV

HH

HV

VH

VV

HH HV VH VV

Stable part: H = 0m

Varying part: H = 0m

0

0.1

0.2

0.3

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0.6

0.7

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1

H = 10m

H = 10m

0

0.1

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1

H = 20m

H = 20m

0

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0.7

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1

0

0.1

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1

0

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1

0

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0

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1

0

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1

0

0.1

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0.4

0.5

0.6

0.7

0.8

0.9

1

HH HV VH VV HH HV VH VV

Figure 5.9.: Stable and varying polarimetric structure matrices

76

5.5 Long term temporal decorrelation

0 5 10 15 20 25

-20

-10

0

10

20

Time lag [h]

Inte

rfero

metr

ic p

hase [

degre

e]

H = 0m

0 5 10 15 20 25

-20

-10

0

10

20

Time lag [h]

H = 10m

0 5 10 15 20 25

-20

-10

0

10

20

Time lag [h]

H = 20m

0 5 10 15 20 250.5

0.6

0.7

0.8

0.9

1

Time lag [h]

Tem

pora

l in

terf

ero

metr

ic c

ohere

nce

H = 0m

0 5 10 15 20 250.5

0.6

0.7

0.8

0.9

1

Time lag [h]

H = 10m

0 5 10 15 20 250.5

0.6

0.7

0.8

0.9

1

Time lag [h]

H = 20m

HH

HV

VH

VV

Stable

Varying

Figure 5.10.: Temporal interferometric coherence amplitude and phase as a func-tion of time and polarizations.

5.5. Long term temporal decorrelation

5.5.1. Coherency matrix at night time

How much is the temporal decorrelation in forest at P-band such as after 3-4 daysfor SAR tomography and 17-27 days for PolInSAR analysis? This part is dedicatedto answer such a question. We now are going to show the complete coherency matrixfor 35 days (dusk-dusk or dawn-dawn).

Dusk-dusk

Figure 5.11 shows the coherency matrix of the HV channel as a function of forestheight at 0m - 10m – 20m and 30m. This is 35 days matrix with the beginning dayis Y2011-M12-D07. The dusk time is selected at 19:00. One column is 1 day.We again notice a regular decline of coherence moving away from the main diago-nal which corresponds to increasing time lag. However, the coherency matrix is abit noisy. We found that the weather, specially the rainfall, plays a key role. InFigure 5.12, we plot the same matrix with excluding the rainy day.The gradually decreasing coherence in Figure 5.12 is very visible. The rain impact issignificant for radar measurements but fortunately the target remains coherent over

77


H = 0 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

H = 10 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35

0

0.1

0.2

0.3

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0.5

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0.7

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0.9

1

H = 20 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35 0

0.1

0.2

0.3

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0.5

0.6

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1

H = 30 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.11.: HV coherency matrices for 35 day at dusk-dusk time as a functionof height

78


H = 0 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35

0

0.1

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H = 10 m

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e lag [

day]

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30

35

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1

H = 20 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35 0

0.1

0.2

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1

H = 30 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.12.: HV coherency matrices for 35 day at dusk-dusk time as a functionof height with dry days.

79


time. We can see how the temporal coherence changes after 3 days or 27 days. Wenotice that after 27 days the coherence value is pretty good, which is also consistentwith the TropiSAR results [100].

HH HV VH VV

HH

HV

VH

VV

HH HV VH VV

HH

HV

VH

VV

HH HV VH VV

HH

HV

VH

VV

HH HV VH VV

HH

HV

VH

VV

H = 0 m

0

0.1

0.2

0.3

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0.5

0.6

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1

H = 10 m

0

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0

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1

H = 30 m

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.13.: Coherency matrices for 35 day at dusk-dusk time as a function ofheight at full polarization

Figure 5.13 shows the full picture with all polarizations. The same behavior is foundwith other three channels. In the next, we would like to concern on dawn-dawn time.

Dawn-dawn

Again, we start with HV at the same range. Figure 5.14 shows the dawn-dawnresults. The same behavior can be found. However, in dusk-dusk, the averagecoherence is a bit higher.

Regarding the best time for data acquisitions, ionospheric disturbances will be ananother noise source besides the temporal coherence [60].

80


H = 0 m

Tim

e lag [

day]

10 20 30

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10

15

20

25

30

35

0

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e lag [

day]

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H = 20 m

Tim

e lag [

day]

10 20 30

5

10

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20

25

30

35 0

0.1

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1

H = 30 m

Tim

e lag [

day]

10 20 30

5

10

15

20

25

30

35 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5.14.: HV coherency matrices for 35 day at dawn-dawn time as a functionof height

81


5.5.2. Temporal coherence estimation

5.5.2.1. Space varying coherence estimation

As the vertical resolution is space varying, we resort to use a space varying windowfor coherence estimation to have the same confidence level in the whole area. Weexploit samples in the range direction rather than in the height one. Figure 5.15gives an example of such processing.

Range [m]

Heig

ht

[m]

Space varying window for coherence estimation

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Figure 5.15.: Space varying window for coherence estimation

Since we have multi-temporal data, this allows us to increase the number of looksby employing many tomographic snapshots to obtain the coherence as a functionof time separation. In detail, we firstly take all the pairs in the data set, spanningthe same interval nT . This represents the interval between two consecutive pointsat which the signal is defined (for example, all the pairs with a temporal baselineof 4 days or 17 days), and n = Z. Then, we average their coherence to make theestimates more robust, i.e.,

γ(nT ) =∑t(k2)−t(k1)=nT γ(k1, k2)∑

t(k2)−t(k1)=nT 1 (5.10)

where t(k) is the time of the k th acquisition, and γ(nT ) is the coherence estimatedat the instant nT time lag.We note here, for example, we have 13 sample snapshots and use L = 20 Numberof looks to minimize issues related to coherence bias and dispersion. The coherence

82


estimated at each image with 20 number of looks, and with 13 sample snapshots,results in a number > 20 but 260 looks due to the high correlation of nearbysamples.

5.5.2.2. Temporal coherence map

We study dawn-dawn measurements at 6:00 local time to minimize ionospheric dis-turbances. Figure 5.16.a shows the temporal coherence map after 4 days. After 4days, as we can see, the average coherence is remarkable high. This allows SARTomography analyses as it is addressed in the next chapter work.

Range [m]

Heig

ht

[m]

Time lag: 4days 06H-06H BAND1 HH

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Time lag: 4days 06H-06H BAND1 HV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Time lag: 4days 06H-06H BAND1 VV

50 60 70 80 90 100 110 120-20

-10

0

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20

30

40

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Time lag: 17days 06H-06H BAND1 HH

50 60 70 80 90 100 110 120-20

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30

40

50

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Heig

ht

[m]

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50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Time lag: 17days 06H-06H BAND1 VV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

0

0.2

0.4

0.6

0.8

1

(a) 4 day lag

(b) 17 day lag

Figure 5.16.: (a) Temporal coherence after 4 days lag; (b) Temporal coherenceafter 17 days lag

In middle forest layers, i.e. 10m, the coherence is bit lower. After 17 days, as wecan see in Figure 5.16.b, the average coherence is still good. Temporal coherencein HV at dawn time is observed to be about > 0.8 at the ground level and > 0.7in the middle of the vegetation layer, therefore witnessing coherence sensitivity toheight. The picture is more clear now with their results. As we would like moreinformation about forest structure for robust biomass retrieval, we have shown thatas the coherence after repeat 17 days is still high, good results from the PolInSARprocessing can be expected as well.

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5.5.3. Temporal decorrelation modelling

Long term temporal decorrelation has been analyzed so far by considering dawn timeacquisitions from December 2011 to March 2012. Rainy days have been excludedfrom the analysis, as rainfalls have been observed to affect the electromagnetic re-sponse of the tomographic array until a few hours (about 4-5 hours) after the rainstops. The temporal coherence has been characterized by assuming an initial valueγ0 and a time constant τ0, as well discussed in [122]. The model simply writes asfollows:

γ(nT ) = γ0e−nT/τ0 (5.11)

The nugget term γ0 in Equation 5.11 can range from 1 to 0 and represents thefraction of the scatterers that did not suffer from a “quick decorrelation” mechanism.For the parameter identification, by using estimates of coherence, the parametersof the exponential models can be found. The sampled coherence estimate has usedsuch as an estimation window to minimize the bias of the estimate. The result is aseries of matrices, each of them representing the correlation properties in a particularplace in the scene (actually, the estimation window). The parameters of the modelthat can best justify the observations can then be found. In detail, the identificationprocess consists of trying many combinations of the parameters and choosing thebest one according to some figure of merit. In this case, the L1 norm is minimized,i.e.,

F (γ0, τ) =∑nT

∣∣∣γ(nT )− γ0e−nT/τ

∣∣∣ (5.12)

The sum is extended to all nTs for which an estimate γ(nT ) is available. The outputof the identification step is the triple γ0,τ , F (γ0, τ) and for each processed point.Figure 5.17 shows the initial coherence, which is quite uniform and pretty high. Thetime constant is much more varying as shown in Figure 5.18. It is easy to recognizetwo key separate moments in the scatterer’s “life.” It is possible to see the groundlevel is the most stable due to the long time constant.In Figure 5.19, the model fitting quality value, which is the average absolute differ-ence between the coherence model identified and the coherence samples is less than0.01. It shows the fit is pretty good. We can estimate the expectation temporal co-herence at each layer by taking the average along range 60 m – 75 m correspondentwith incident angle varied from 20° to 40°, as shown in Figure 5.20.In detail results, for instance, we can figure out the coherence as a function of heightas shown in Table 5.1:

84


Range [m]

Heig

ht

[m]

Initial coherence map (0), BAND1 HH

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Initial coherence map (0), BAND1 HV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Initial coherence map (0), BAND1 VV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

0

0.2

0.4

0.6

0.8

1

Figure 5.17.: Initial coherence map

Range [m]

Heig

ht

[m]

Time constant map (0) [days], BAND1 HH

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Time constant map (0) [days], BAND1 HV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

Range [m]

Heig

ht

[m]

Time constant map (0) [days], BAND1 VV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

0

50

100

150

200

250

Figure 5.18.: Time constant map

Range [m]

Heig

ht

[m]

Model fitting quality, BAND1 HH

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

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Range [m]

Heig

ht

[m]

Model fitting quality, BAND1 HV

50 60 70 80 90 100 110 120-20

-10

0

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20

30

40

50

Range [m]

Heig

ht

[m]

Model fitting quality, BAND1 VV

50 60 70 80 90 100 110 120-20

-10

0

10

20

30

40

50

0

0.05

0.1

0.15

0.2

Figure 5.19.: Model fitting quality map

Layer HH HV VV4 days 27 days 4 days 27 days 4 days 27 days

0 m 0.93±0.03 0.81±0.04 0.91±0.02 0.80±0.02 0.95±0.02 0.84±0.0210 m 0.89±0.02 0.71±0.04 0.84±0.02 0.67±0.03 0.86±0.02 0.70±0.0620 m 0.80±0.04 0.62±0.07 0.77±0.02 0.63±0.03 0.76±0.04 0.59±0.0530 m 0.80±0.06 0.66±0.08 0.77±0.04 0.64±0.05 0.74±0.08 0.61±0.09

Table 5.1.: Quantitative expectation of temporal coherence as a function of forestheight after 4 and 27 days.

85


5 10 15 20 25 300.5

0.6

0.7

0.8

0.9

1 Temporal coherence E[], HH

Time lag [day]

Expecta

tion c

ohere

nce |E

[ ]|

5 10 15 20 25 300.5

0.6

0.7

0.8

0.9

1 Temporal coherence E[], HV

Time lag [day]

Expecta

tion c

ohere

nce |E

[ ]|

Layer H = 0 m

Layer H = 10 m

Layer H = 20 m

Layer H = 30 m

5 10 15 20 25 300.5

0.6

0.7

0.8

0.9

1 Temporal coherence E[], VV

Time lag [day]

Expecta

tion c

ohere

nce |E

[ ]|

SAR Tomography

PolInSAR

Figure 5.20.: Dawn-dawn temporal coherence at P band (excluding rainfalls). Theblack and green vertical lines indicate the 4 and 27 day repeat pass time foreseenfor the BIOMASS mission.

5.6. Conclusion

A successful TropiScat ground based radar experiment for tomographic imaging hasbeen presented. Thanks to the fine time sampling, the daily temporal interferometriccoherence amplitude and phase variation of the Paracou tropical forest as a functionof height could be observed. The first ever tomographic movie capturing the forestdaily change has been produced, at least to our knowledge. Tomogram analysesrevealed a diurnal vertical motion of the forest center of mass. This phenomenon isstrongly related to daily temperature variations, which suggests a connection withforest evapotranspiration phenomena.Concerning the short time temporal coherence, the most relevant phenomenon isthe coherence drop during daytime, due to the effect of the wind moving the forestcanopy. The sum of Kronecker products has been proposed as a model to representand provide a reasonable description of the structure of the covariance matrix ofthe multi-polarimetric and multi-temporal data. Accordingly, all the complexity inmodeling the data may be concentrated in the expression of the structure matrices,which rule the coherence loss of the targets as a function of time. This resultalready appears to provide a very useful input concerning the BIOMASS mission,as it suggests that performance over tropical forest could be optimized by gatheringacquisitions at dusk or dawn time.The coherence values are observed to stay high even after 27 days. Indeed, theexpectation of temporal coherence in HV at 27 days has so far been observed tobe about 0.8 at the ground level and 0.65 in the middle of the vegetation layer,therefore witnessing coherence sensitivity to height. Further studies can be devotedto investigate the coherence behavior over the whole duration of the TropiScat ex-periment.Furthermore, the outcome of the temporal deccorrelation model will provide inputfor assessment the BIOMASS SAR Tomographic Phase performance, which will betreated in next chapter.

86

6. BIOMASS Tomography PhasePerformances

6.1. Introduction

The candidate Earth Explorer Core Mission BIOMASS is actually foreseen to be op-erated in a Tomographic Phase during approximately the first two months of missionlifetime [19]. During this phase the system will be able to gather multiple acqui-sitions characterized by small baselines and a repeat pass time in the order of fewdays, thus allowing SAR tomography (TomoSAR) imaging of the vegetation layer.This will potentially lead to useful inputs and recommendations for improving singlebaseline polarimetric interferometric SAR (PolInSAR) inversion during the Opera-tional Phase, as well as giving a better understanding of how long wavelength radarsignals interact with forests. However, there are three main factors expected to havesignificant impact on the quality of the results. One is the 6 MHz limit allowed forpulse bandwidth due to frequency unavailability for remote sensing at P-band, re-sulting in a severe limit to vertical resolution if not properly accounted for. Secondis the interaction with the ionosphere. Ionosphere can affect significantly the qualityof focused single look complex (SLC) images, resulting in disturbances such as Fara-day rotation, residual phase screens, image shifts, and even defocusing [123], [60].Finally, the most important factor is the one related to temporal decorrelation, i.e.instantaneous (quick), short term and long term decorrelation mechanisms [124].The presence of temporal decorrelation has been shown to constitute a crucial issueas well in multi-baseline applications, either interferometric and tomographic. Tem-poral decorrelation can make InSAR measurements with X-band or C-band almostunfeasible over vegetated areas because of the changes of the electromagnetic pro-files and/or the positions of the scatterers with time within the resolution cell [29].Long wavelength at P-band is expected to have a better measurement. However, toreduce the influence of the temporal decorrelation, the future mission should aimfor shorter repeat-cycles. In principle, the shorter the repeat-cycle is, the better theperformance achieves. However, since it is impossible to simultaneously capture thesame area in a single satellite configuration, the repeat-cycle is at least of one day.What would become very important is the question whether that can a tomographicprocessing be carried out with revisit times such as 1, 3, 4 or even 27 days.In this context, the TropiSAR 2009 and TropiScat 2011 experiments have beenconducted over the tropical rain forest in Paracou, French Guiana [100], [107].

87

Chapter 6 BIOMASS Tomography Phase Performances

TropiSAR allowed to study the vertical structure of the vegetation by means ofTomoSAR, which is one of the key elements for the assessment of the forest biomass[69], [103]. In order to complement the airborne TropiSAR dataset in producinga well-controlled dataset in various seasons and weather conditions, the TropiScatground based experiment acquires intensity and complex coherence in quad polar-ization, together with a vertical imaging capability [114], [115]. Such an equipmentprovides 2D (ground range - height) resolution capabilities through the coherentcombination of the signal from different antennas via tomographic techniques [116].By comparing, again coherently, tomographic images taken at different times it ispossible to gain access to the variation of temporal coherence with respect to forestheight.The aim of this chapter is to assess the impact of temporal decorrelation and ofresidual ionospheric disturbances affecting SLC images on the tomographic perfor-mance of BIOMASS, with reference to a tomographic processor explicitly designedfor a 6 MHz bandwidth system. The airborne TropiSAR and ground based TropiS-cat data will numerically complement to advocate for the feasibility of providingaccurate tomographic measurements.The chapter is organized as follows: section 6.2 presents the BIOMASS SAR datamodel; in section 6.3 the basic SAR tomography methodology is shown; in section 6.5the ionospheric disturbance assessment is evaluated; in section 6.6 the temporaldecorrelation performance is discussed; conclusions are drawn in section 6.7.

6.2. BIOMASS SAR reconstruction

6.2.1. SAR Data model

The BIOMASS SAR tomographic polarimetric data has been simulated in such away as to synthesize SLC SAR images in radar slant range geometry, taking as inputthe parameters of the acquisition system (carrier frequency, pulse bandwidth, reso-lution, look angle etc.), the platform orbits, and the scene to be imaged. The inputscene, the key of this simulation, is the TropiSAR SAR reconstruction. Structuraland polarimetric scattering mechanism features are preserved as shown in Figure 6.1.Then, the scene is simulated by synthesizing each pixel in each SAR image accordingexactly to the well-known forward model [70]:

yn (r, x, AB) =ˆf(r− r′, x−x′)S (r′, x′, ξ;AB) exp

(j

4πλRn(r′, x′, ξ)

)dξ (6.1)

where:(r, x, ξ) are the slant range, azimuth and cross range coordinates with respect to afixed master image,

88

6.2 BIOMASS SAR reconstruction

AB =HH,HV, V H, V V indicates the polarization,

yn(r, x, AB) is the complex valued pixel at slant range, azimuth location (r, x), inthe SLC SAR image corresponding to track n, polarization AB,

S(r, x, ξ;AB) is the wide-band complex reflectivity, i.e. the complex reflectivity ofthe elementary scatterer at location (r, x, ξ) in polarization AB,

Rn(r, x, ξ) is the zero-Doppler distance between the orbit of the n-th acquisition andthe elementary scatterer at location (r, x, ξ),

f(r, x) is the end to end impulse response function of the BIOMASS system.

The wide-band complex reflectivity corresponds to the tomographic multilayer TropiSARdata, see [103]. The statistics of each of those terms are such as to emulate both thevertical structure and the polarimetric behaviour of forest scattering. As a result,the simulation is consistent with real data.

For simplifying, we have neglected system noise and clutter. Scattering symmetryassumptions about the distribution of the scatterers are made in this simulation,namely SHV = SV H .

For temporal decorrelation simulation, the TropiScat output product acts as aninput, see [125].

Data

HH HV VV

Elementary Scatterers at time tN

HH

HV

VV H

H HV

VV H

H HV

VV H

H HV

VV

Elementary Scatterers at time t2

HH HV VV

Elementary Scatterers at time t1

hei

ght

azimuth

hei

ght

azimuth

System

Orbit 1

Orbit 2

Orbit N

Simulated Orbits

TropiSAR Scene

Impulse Response Function

2D Convolution

SLC multi-baseline, multi-pol and multi-temp data stack

Figure 6.1.: BIOMASS SAR simulation

89


6.2.2. Impulse response function

The impulse response function is simulated through a separable model with respectto the azimuth and range axes, i.e.:

f(r, x) = fr(r) · fa(x) (6.2)

The range impulse response function fr and the azimuth fa, both belonging to theraised-cosine function family, are shown in Figure 6.2. Range pulse envelope hasbeen modeled so as to ensure an attenuation of 40 dB at ± 3 MHz. A roll-off factorof 0.75 has been assigned to the range impulse function because of the strict 6 MHzband range requirement. This operation was done in order to mitigate as muchas possible side-lobes exceeding the portion of the frequency spectrum allowed toBIOMASS, though at the price of a resolution loss. A more relaxed roll-off factor(0.5) has been instead adopted for the azimuth system response.

-5 0 5-40

-30

-20

-10

0

Frequency [MHz]

Range filter

-0.1 -0.05 0 0.05 0.1-40

-30

-20

-10

0

Spatial frequency [m-1]

Azimuth filter

-100 -50 0 50 100

0

0.5

1

Range [m]

Range filter

-50 0 50

0

0.5

1

Azimuth [m]

Azimuth filter

Figure 6.2.: Range and azimuth IRF for BIOMASS SAR simulation

In order to avoid problems due to spectral aliasing, each image has been oversampledby a factor 2 in both the slant range and the azimuth directions.

6.2.3. BIOMASS parameters

The vertical resolution depends not only on baseline aperture but also on bandwidth.Projecting the slant range and cross range extent of the resolution cell along the

90

6.3 Tomographic processing

vertical direction, one easily gets that the vertical resolution is limited as:

4z(bandwidth) = c

2Bcosθ (6.3)

4z(baseline) = λr

2Azsinθ (6.4)

Equating the two limits to vertical resolution (4z(bandwidth) = 4z(baseline)), it isreadily obtained that:

Az = B

fcrtanθ = bcrit (6.5)

Therefore, we get the result that the finer vertical resolution is obtained by lettingthe overall baseline aperture equal the critical baseline. Baseline spacing determinesthe height of ambiguity, according to the well-known relation:

zamb = λ

2rsinθ

4b(6.6)

The height of ambiguity due to the vertical sampling has to be designed to belarger than the expected forest height, to avoid superposition of the replicas. Asafe choice is typically to set the height of ambiguity equal to at least twice theforest height. Assuming a vegetation layer 50 m top high, the resulting numberof passages for tomographic imaging can be assessed in about 6 tracks (height ofambiguity 110 m) per site with the baseline aperture equaling the critical baseline.As widely addressed in the remainder, more passages can be exploited to enhancesystem robustness versus ionospheric disturbances.The BIOMASS parameter specifics, collected in Table 6.1, claim an available 6 MHzbandwidth in range. This parameter, when related to the 25° satellite look angle,is responsible for limiting both the ground-range resolution (about 60 m for a flatterrain) and in particular the tomographic height resolution at 23 m approximately.

6.3. Tomographic processing

6.3.1. Phase flattening

First of all, the terrain topography is flattened so that the height has to be intendedas the height from the local surface, to help visualization and interpretation of the

91


Item CharacteristicsSatellite altitude 650 kmIncidence angle 25°Carrier frequency 435 MHz

Bandwidth 6 MHzCritical baseline 4610 mRange resolution > 25 m

Azimuth resolution > 12.5 mTable 6.1.: BIOMASS parameters for simulation

results. This can be done by removing the ground phases ϕgroundn which directlyrelate to the optical paths from the ground surface to the N sensors. In formula:

yn (r, x) = yn (r, x) exp(−jϕgroundnm

)(6.7)

ϕgroundnm = ϕgroundn − ϕgroundm = 4πλrsinθ

bnzg (6.8)

After phase flattening, at a given azimuth plane x and slant range r, in the n− thSLC SAR image, the complex valued pixel yn(r, x) can be expressed through [70]:

yn (r, x) =ˆS (ξ, r, x) exp

(+j 4π

λrbnξ

)dξ (6.9)

Where: ξ is cross range coordinate, S (ξ, r, x) is the target reflectivity functionprojection along the cross range and bn is the normal baseline relative to the n− thimage.

6.3.2. Common Band Filtering

As discussed above the 6 MHz pulse bandwidth allowed for the BIOMASS systemlimits the vertical resolution to about 23 m, independently on baseline aperture. Forthis reason, the Common Band Filtering (CBF) based approach has been considered[126]. The CBF technique can be employed for the estimation of the normalized ver-tical distribution of backscattered power only, whereas it does not help the verticalfocusing of the complex reflectivity, see subsection 6.3.3. Halving the vertical res-olution is obtained at the expense of side lobes and potential algorithm instability[126]. Operationally, the CBF operator is embedded in the tomographic processing

92

6.3 Tomographic processing

by taking the complex interferometric coherence between any two acquisitions asobtained after filtering both pairwise in such a way as to retain only their commonspectral components [127], [128], [129]. We remark that the step phase flattening isincluded in this procedure. In formula:

yCBFn = FCBFyn (6.10)

FCBF = ΦHHCBFΦ (6.11)

Where Φ is the ground phase matrix and HCBF is a low-pass filter.When there is no CBF operator, considering only spatial decorrelation, we can writethe interferometric coherence γ(b) at baseline b in the product of two terms, one as-sociated with volumetric decorrelation and the other with flat terrain decorrelation,[29]:

γ(b) = γv(b) · tri(b

bcrit) (6.12)

where bcrit is the critical baseline and tri() is the triangular pulse function.Under the assumption of data stationarity, the vertical backscattered power can beobtained by the Fourier spectrum estimation of γ(b) [28]:

S(z) = Sv(z) ∗ sinc2(2Bc

z

cosθ) (6.13)

where: Sv(z) is the true volume vertical backscattered power distribution; ∗ denoteslinear convolution; sinc() is the cardinal sine function; B is the pulse bandwidth, andθ the radar look angle. The latter term in Equation 6.13 represents the tomographicpoint spread function (PSF) arising from pulse bandwidth as in Equation 6.3.Meanwhile, with CBF operator using Equation 6.11, Equation 6.12 modifies to:

γCBF (b) = γv(b) · rect(b

bcrit) (6.14)

where rect() is the rectangular pulse function. The spectrum of γCBF (b) can bewritten:

SCBF (z) = Sv(z) ∗ sinc(4Bc

z

cosθ) (6.15)

By comparing Equation 6.13 and Equation 6.15, at least theoretically it is expectedthat the vertical resolution has an enhancement after CBF operator.

93


6.3.3. Spectral density estimation

Vertical focusing

A simple way to implement SAR tomography is by coherent focusing, resulting inmulti-layer SLC associated with specific heights, see [103]. We consider Equation 6.9again. This is well known in SAR tomography and it stated that the multi-baselineSAR data and the target projection form a Fourier pair. Therefore, the targetprojection can be retrieved by Fourier transforming the data with respect to thenormal baseline. The focused imaged in 3D space can expressed as:

S (z) =N∑n=1

ynexp(−j 4π

λrsinθbnz

)(6.16)

We refer this simple beamforming as Fourier transform method. The main advantageassociated with the conventional Fourier analysis is the radiometric accuracy, whichis the most important for physically matching with quantitative measurements, see[103]. The main drawback is that if data are no longer uniformly sampled then thebeamforming may give poor reconstruction performances in terms of sidelobes [130].

Fourier and Capon spectrum

Alternatively, we can resort to use super resolution methods. It allows data de-pendent sidelobe cancellation by rejecting interference coming from other elevationdirections than the selected, as sensed through the information in the spatial covari-ance matrix [24]. This method can be understood as partially model free as it doesnot rely on any a-priori information, exception that it has to be cast in a coherentmultilook framework to allow reliable covariance estimation in terms of bias andvariance. In detail, the sample covariance matrix can be computed by averaging allthe interferograms over the estimation window, namely:

[R]nm = yHn ym (6.17)

where yn is a vector corresponding to the pixels of the n − th image within theestimation window.The steering vector is defined as:

a(z) = [1 exp(j 4πλ

bn2

sinθz) . . . exp(j 4π

λ

bnN

sinθz)]H (6.18)

94

6.4 Reduce of bandwidth: ideal scenario

Then the Fourier spectrum can be estimated through :

SF (z) = a(z)HRa(z) (6.19)

The Capon spectrum can be estimated through :

SC(z) = 1a(z)HR−1a(z)

(6.20)

6.4. Reduce of bandwidth: ideal scenario

The need to estimate the covariance matrix from sample data typically requiresthe exploitation of many independent looks, in order to avoid well known problemsrelated to coherence bias and dispersion [131]. On the other hand, to use a largeaveraging window may result in a loss of target homogeneity, as well as spatialresolution of the final product. As a trade-off between the two aspects above it hasbeen chosen to implement covariance estimation by exploiting an averaging windowas large as 100 x 100 m (slant range, azimuth). With 6 MHz bandwidth, this choiceallows about 32 independent looks for covariance estimation.

Tomographical campaigns have been carried out in tropical areas using the full band-width of 150 MHz within the TropiSAR experiment, see section 3.3. Using 6 flights,5 m layers were created, providing the input scene for the simulation. The sensorparameters employed by the simulation have been set in order to ensure compatibil-ity with BIOMASS, see section 6.2. A transect of the survey at 25° incidence anglewas then reconstructed, and a comparison among bandwidth 150 MHz, 30Mhz, 12MHz and BIOMASS bandwidth 6 MHz results can be made. The overall baselinespan has been fixed to the critical value of BIOMASS and 7 passes are used.

The results from the simulation are shown from Figure 6.3 to Figure 6.6. Theseshow the vertical backscattered power at height z in ideal conditions. It is possible toobserve how information is loosely correspondent even if the bandwidth is decreasing.The reduction of the bandwidth to 6 MHz from 150 MHz is evident in the loss ofhorizontal resolution; however, the loss in vertical resolution, even if present andvisible, is not really damaging. In the simulation, neither ionospheric disturbancesnor temporal decorrelation has been considered. In a generic P-band acquisitionscenario, it must be considered that the ionosphere indeed introduces different kindsof distortion effects which degrade the tomographic quality. In the next section, weare going to show these impacts.

95


0

0.1

0.2

0.3

0.4

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0.8

0.9

1

150 MHz

Heig

ht

[m]


200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Heig

ht

[m]


200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Heig

ht

[m]


Slant range [m]

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Figure 6.3.: Tomographic profile with 150 MHz bandwidth

0

0.1

0.2

0.3

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1

30 MHz

Heig

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ht

[m]


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ht

[m]


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LiDAR height


96

6.4 Reduce of bandwidth: ideal scenario

0

0.1

0.2

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1

12 MHz

Heig

ht

[m]


200 400 600 800 1000 1200 1400 1600 1800 2000

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Heig

ht

[m]


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[m]


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0.1

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ht

[m]


200 400 600 800 1000 1200 1400 1600 1800 2000

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ht

[m]


200 400 600 800 1000 1200 1400 1600 1800 2000

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Heig

ht

[m]


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200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height


97


6.5. Ionospheric disturbances

The criterion for evaluating the quality of tomographic measurements is based ona direct comparison of the tomograms resulting from data generated by the tomo-graphic simulation under ideal or perturbed conditions. The following metric, here-after referred to as tomographic accuracy, has been adopted for evaluating imagingquality:

Γ(z) =

√E[(S(z)− Sd(z))2]

E(S(z)) (6.21)

where S(z) and Sd(z) are the estimated vertical backscattered power distributionsat height z in ideal conditions and in the presence of disturbances, respectively; andE(·) is the expectation operator. The metric in Equation 6.21 provides then therelative accuracy in the estimate of the backscattered power associated with eachvertical layer.Note that the HH and VV channels are useful estimating both ground and vol-ume (though with low height resolution the ground sidelobes tend to polarize theestimated volume), whereas the HV is dominated by the canopy’s layer returns.Therefore, we can expect the tomography accuracy as shown in Figure 6.7.

Volume spectrum Ground spectrum Volume disturbance

Ground disturbance Expected tomographic accuracy

HH channel

Hei

ght

Better accuracy

HV channel

Hei

ght

Better accuracy

Figure 6.7.: The expectation tomography accuracy at HH and HV

6.5.1. Phase disturbances

Uncompensated phase terms affect vertical focusing by introducing random side-lobes, resulting in the tomographic imaging to be blurred [74]. In formula, phase

98

6.5 Ionospheric disturbances

screens are accounted for as:

M(P, n) = M(P, n) · exp(jαn) (6.22)

where M is the ideal scattering matrix of the target P in the image n− th, M is theperturbed observation and alpha is the phase screen residual, modeled as the zero-mean, stationary process αn ∼ N(0, σ2

α). The accuracy resulting from simulationruns is shown in Figure 6.8 for HV channel and Figure 6.9 for HH channel. Theleft panels show the accuracy of the configuration with a fixed number of tracks(NI = 7). The upper panels show the results from Fourier transform and the bottompanels one is Fourier spectrum. The Capon spectrum results are found to be worsethan the Fourier spectrum. However, both Fourier and Capon spectrum results arebetter than Fourier transform. This is mainly because the covariance matrix wasestimated by exploiting an averaging window. The following interpretation focuseson the Fourier spectrum results.As expected, the worst accuracy is found at canopy level in HH and at groundlevel in HV. This is due to the fact that blurred contributions from the strongestscattering mechanism affect those from the weakest, resulting in different ground tovolume ratios to determine different vertical profiles for the tomographic accuracy.A different representation is provided in the right panels, where critical areas (i.e.:canopy level for HH and ground level for HV) are investigated as a function ofthe number of tracks. Tomographic accuracy is observed to stay about -10 dB forphase screens with standard deviation σα < 10°, provided that at least 6 passes areavailable. The accuracy is increased when more passes are available.

6.5.2. Faraday rotation

Faraday rotation has the effect of coupling backscattering contributions from differ-ent channels. The model of the distorted observation M is:

M(P, n) = RF (4Ω) ·M(P, n) ·RF (4Ω) (6.23)

RF (4Ω) =[

cos4Ω sin4Ω−sin4Ω cos4Ω

](6.24)

MHH(P, n) = MHH(P, n)cos24Ω(n)−MV V (P, n)sin24Ω(n) (6.25)MHV (P, n) = MHV (P, n)− [MHH(P, n) +MV V (P, n)]cos4Ω(n)sin4Ω(n)MV H(P, n) = MV H(P, n) + [MHH(P, n) +MV V (P, n)]cos4Ω(n)sin4Ω(n)MV V (P, n) = −MHH(P, n)sin24Ω(n) +MV V (P, n)cos24Ω(n)

99


Fourier transform

Fourier spectrum (with CBF)

-14 -12 -10 -8 -6-5

0

5

10

15

20

25

30

35

Tomographic accuracy [dB]

Heig

ht

[m]

= 5

0

= 10

0

= 15

0

= 20

0

Phase screen disturbance

6 8 10 12 14-16

-14

-12

-10

-8

-6

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 5

0

= 10

0

= 15

0

= 20

0


-20 -15 -10 -5-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 5

0

= 10

0

= 15

0

= 20

0


6 8 10 12 14-20

-15

-10

-5

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 5

0

= 10

0

= 15

0

= 20

0


7 pass 0 m

7 pass 0 m

HV

Figure 6.8.: Phase disturbances in HV channel

Fourier transform


7 pass 30 m

7 pass 30 m

HH -14 -12 -10 -8 -6

-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 5

0

= 10

0

= 15

0

= 20

0


6 8 10 12 14-16

-14

-12

-10

-8

-6

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 5

0

= 10

0

= 15

0

= 20

0


6 8 10 12 14-20

-15

-10

-5

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 5

0

= 10

0

= 15

0

= 20

0


-20 -15 -10 -5-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 5

0

= 10

0

= 15

0

= 20

0


Figure 6.9.: Phase disturbances in HH channel

100

6.5 Ionospheric disturbances

where RF is the Faraday rotation matrix and 4Ω is the residual Faraday rotationangle.In Equation 6.25, it can be argued that the rotation affects with different strengththe four polarimetric channels: the HV and VH channel, in particular, should bethe one suffering the most for the mixing of the stronger HH and VV channel. Suchhypothesis is indeed confirmed by the simulation results shown in Figure 6.10 forHV channel and Figure 6.11 for HH channel, where Faraday residuals have beengenerated in accordance to the zero-mean normal distribution 4Ω ∼ N(0, σ2

4Ω).Again, the upper panels show the results from Fourier transform and the bottompanels one is Fourier spectrum. We found that the Capon spectrum results are worsethan the Fourier spectrum and both of Fourier and Capon spectrum results are bet-ter than Fourier transform, with a similar behaviour as that for phase disturbances.The following interpretation focuses on the Fourier spectrum results.Results show that with a residual Faraday rotation angle of a few degrees (up to5°) the effects on tomography are acceptable even with 6 tracks, both for the co-polHH channel and for the cross-pol HV channel.

Fourier transform


7 pass 0 m

7 pass 0 m

HV -15 -10 -5 0

-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 10

= 30

= 50

= 70

= 100

Faraday rotation

6 8 10 12 14-16

-14

-12

-10

-8

-6

-4

-2

0

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 10

= 30

= 50

= 70

= 100

Faraday rotation

-30 -25 -20 -15 -10 -5-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 10

= 30

= 50

= 70

= 100

Faraday rotation

6 8 10 12 14-30

-25

-20

-15

-10

-5

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 10

= 30

= 50

= 70

= 100

Faraday rotation

Figure 6.10.: Fraday rotation disturbances in HV channel

It is important to note that phase screens can be removed based on a sufficientlydense grid of reliable targets, to be used as calibration points in InSAR processing[78], [132], [133]. However, in the absence of a sufficient density of targets, as it may

101


Fourier transform


7 pass 30 m

7 pass 30 m

HH -15 -10 -5 0

-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 10

= 30

= 50

= 70

= 100

Faraday rotation

6 8 10 12 14-16

-14

-12

-10

-8

-6

-4

-2

0

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 10

= 30

= 50

= 70

= 100

Faraday rotation

-30 -25 -20 -15 -10 -5-5

0

5

10

15

20

25

30

35


Heig

ht

[m]

= 10

= 30

= 50

= 70

= 100

Faraday rotation

6 8 10 12 14-30

-25

-20

-15

-10

-5

Tom

ogra

phic

accura

cy [

dB

]

Number of passes

= 10

= 30

= 50

= 70

= 100

Faraday rotation

Figure 6.11.: Faraday rotation disturbances in HH channel

occur in forested areas, one has to resort to a different strategy. A viable approach isto extract the signal relative to ground components beneath the forest, and use theseto carry out a continuous calibration of the data stack by removing the estimatedground phases [74].

6.6. Temporal decorrelation

6.6.1. Simulation of temporally decorrelated data

In this section, it is required to simulate temporal SAR data for specified covarianceor coherency matrix R. Given a single-look SAR data, the real and imaginary partsof y0 SAR returns are Gaussian distributed with its mean zero and its variance =0.5. For a covariance matrix R = E[yyH ] with y = [y0 y1 . . . yn]H and y0 ∼ N(0, I),we need to simulate single-look data y1, .., yn.We have to simulate a complex random vector v ∼ N(0, I) that is complex normaldistributed with zero mean and identity covariance matrix I. This can be accom-plished by independently generate the real and imaginary parts of each componentof v that are statistical independent from a normal distribution with zero mean and0.5 variance.

102

6.6 Temporal decorrelation

In formula, the simulation can be carried out by solving the following equation:

y =

y0y1...yn

=

1 0 . . . 0 0

A

y0v1...vn

(6.26)

where y0, y1, ...yn correspond to the values of the reflectivity in the n + 1 compleximages and v1, v2, ...vn are complex random vectors.

The problem is to find the transform matrix A.

By definition covariance matrix R, we can denote R and m as following:

R =[

1 mT

m R

]. (6.27)

We have :

R = E[yyH ] =[eT1A

]E[ddH ][ e1 AT ] =

[eT1 e1 eT1AAe1 AAT

](6.28)

where e1 =

10...0

, and d =

y0v1...vn

.From Equation 6.27 and Equation 6.28, we have :

Ae1 = m. (6.29)

We then immediately know the first column of A should be m. In formula

A = [ m U ]. (6.30)

The problem now resorts to find the matrix U .

Again, from Equation 6.27 and Equation 6.28, we have:

103


AAT = R

⇒ [ m U ]

mT

UT

= R

⇒ mmT + UUT = R.

Therefore

UUT = R−mmT = R. (6.31)

The matrix U is then obtained by using either Cholesky decomposition of R or aunitary transform Z to diagonalize R [134].This simulation algorithm can then apply to simulate for HH, HV, VV multi-layermulti-baseline and multi-temporal SAR data.It has been observed that the temporal stability of the forest scene is rather good forall polarimetric channels, indicating the presence of stable scattering mechanisms.Most of the volume layer is varying its as in the layer 10 m and layer 30 m. Indeed,it is possible to decompose stable part and varying part, see [125] and section 5.5.However, these components are almost colocated, making it difficult to separatetheir location. Therefore, we simulate the temporal decorrelation in such a way thatall layers are in progressive decay according to their exponential law.

6.6.2. Numerical results

The principal concept is that the vegetation decorrelation time has to be significantlylonger than revisit time to preserve structural information. The shorter will bethe revisit time, the better performance we can expect. Such hypothesis is indeedconfirmed by the following simulation.The same transect of the survey, which is shown in Figure 6.6, is reconstructed anda comparison between revisit times 1 day, 3 days, 4 days and 27 days results can bemade. The overall baseline span has been fixed to the critical value of BIOMASS, 7passes are used and the temporal baselines grow proportionally to the spatial normalbaselines.The results from the simulation are shown from Figure 6.12. It is possible to observehow information losses correspond to increased revisit times. With 1, 3 and 4 daysscenario, the results are quite acceptable. If the revisit time is 27 days, which can

104


Heig

ht [m

]

Revisit time = 27 days, HV

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Heig

ht [m

]


200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Heig

ht [m

]


200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Slant range [m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Heig

ht [m

]

Revisit time = 1 day, HV

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Heig

ht [m

]

Revisit time = 0 day, HV

200 400 600 800 1000 1200 1400 1600 1800 2000

0

20

40

60

LiDAR height

Figure 6.12.: From top to down, tomographic profile stability as a function ofrevisit time

105


-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 3 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 1 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 27 day

HH

HV

VV

Figure 6.13.: Temporal decorrelation at 7 passes

106


be the Operational Phase of BIOMASS, the loss of vertical resolution is evident andslide lobes appear. However, the vertical structure is still visible.In Figure 6.13, the tomographic accuracy Γ(z) ' -4 dB, the useful signal is dom-inant, and the structural information is still retrievable. Temporal decorrelationappears to have a more significant impact than ionospheric disturbance.

6.6.3. Other configurations

Parallel or interposition

There are 2 basic scenarios for multi-temporal multi-baseline data acquisitions. Thefirst one is that the temporal baselines grow with the spatial normal baselines, i.e.:b = [ 0 250 500 750 . . . ] , t = [0 T 2T 3T . . . ]. This is realistic due to a simplerrealization. Another one is the interposition between spatial and temporal baselines.Figure 6.14 shows an example of two configurations with 15 passes.

0 2 4 6 8 10 12 140

10

20

30

40

50

60

Spatial baseline [1000 m]

Tem

pora

l baselin

e [

days]

Strategic acquisition

Parallel

Interposition

Figure 6.14.: Two strategic acquisitions with 15 passes configuration

Total aperture baseline

As discussed above the 6 MHz pulse bandwidth allowed for the BIOMASS systemlimits the vertical resolution to about 23 m, independently on baseline aperture.Therefore, we selected the overall baseline aperture equaling the critical baseline.Beyond this value vertical resolution is limited by pulse bandwidth. However, with

107


CBF, we consider the complex interferometric coherence between pairwise acquisi-tions. It means that, the overall baseline aperture can be allowed to be larger thecritical baseline. In the sense of wavenumbers [127], for a certain target, the bettera wavenumber is illuminated within the target, the better the target reconstructioncan be achieved. Based on this concept, we can expect the improvement of thetomographic accuracy by going beyond the critical baseline.

For justification of this concept, we firstly simulate a simple scenario without tem-poral decorrelation. Scattering at the ground layer 0 m and at the forest 25 m havebeen included. The true profile is reconstructed by 12 MHz bandwidth with thebaseline aperture btot = 2× bcrit = 9220 m. Four 6 MHz bandwidth scenarios corre-sponding to increase of the aperture baseline are considered. The result is reportedin Figure 6.15. When the aperture baseline is greater than the critical baseline, itshows an improvement. This is due to the fact that it tries to have a best fit to thetrue one. However, it becomes worse when it is greater than about 1.5 times thecritical baseline.

-20 -10 0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

Height [m]

Norm

aliz

ed s

ignal pow

er

True profile - 12 MHz

1 bcritical

- 6 MHz

1.3 bcritical

- 6 MHz

1.5 bcritical

- 6 MHz

2 bcritical

- 6 MHz

1 bcritical

2 bcritical

Figure 6.15.: Tomographic profile impacts as a function of the baseline aperture.

Moving to the TropiSAR data, we again run the simulations with 15 passes andwithout temporal decorrelation. The true profile is reconstructed by 12 MHz band-width with the baseline aperture btot = 2× bcrit = 9220 m. This profile will be usedto evaluate the distortion in the remainder. The results are shown in Figure 6.16for HH channel. The improvement is gradually increased from 1.0 bcrit to 1.5 bcrit,after which it becomes unstable.

Concerning the temporal decorrelation of the TropiSAR data, the simulations arecarried out with 15 passes and 4 days revisit time. The results are shown inFigure 6.17 for parallel and Figure 6.18 for interposition configuration. When thebaseline aperture increases, the tomographic accuracy is improved but then it be-comes worse. It is possible to have an optimal choice for the total aperture baselinefor BIOMASS, with a value exceeding (say 50%) the critical baseline. Moreover,

108

6.7 Conclusion

-15 -10 -5 0 5-10

-5

0

5

10

15

20

25

30

35

40


Heig

ht

[m]

1.0 b

critical

1.3 bcritical

1.5 bcritical

2.0 bcritical

2.5 bcritical

3.0 bcritical

-10 -5 0 5 10

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Height [m]

Cross correlation

Autocorrelation truth-truth

3 bcritical

1 bcritical

1 bcritical

3 bcritical

Figure 6.16.: Tomographic accuracy and cross correlation as a function of the base-line aperture.

by comparing between the parallel and interposition configuration, it is possibleto observe that two configurations have quite similar performances. This resultsuggests the parallel configuration because it ensures the same performance of theinterposition configuration, while simplifying the mission design.Assuming the baseline aperture btot = 1.5 × bcrit = 6920m and the height of ambi-guity > 100 m, we will get the minimum number of track is 8.

6.7. Conclusion

In this chapter, we discussed the impact of temporal decorrelation and ionosphericdisturbances affecting SLC images on the quality of BIOMASS tomographic mea-surements. The following conclusions are drawn.Temporal decorrelation has a more significant impact than ionosphere disturbances.Ionospheric fringes on focused SLC images cause the tomographic imaging to beblurred, depending on the number tracks employed. A tomographic accuracy (Γ '−10 dB) is achieved for phase screens with standard deviation up to 10 degreeswith 6 passes. Using 6 or more passes, no relevant performance loss is expected toarise from Faraday rotation provided it can be corrected to within an accuracy of5 degrees, which appears to be achievable by current Faraday rotation correctionmethods.Concerning the temporal decorrelation, the results from studies show that, providedthat the revisit times for the tomographic campaigns be 3-4 days as predicted, it isnot critical. Having a total aperture less than about 1.5 times the critical baselineshould be fine. Finally, to let the spatial baseline parallel to the temporal baselineto simplify the data acquisition strategic is also acceptable.

109


btotal = 1.0*bcritical






Parallel configuration

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

Figure 6.17.: Parallel configuration : from up and down, left to right, temporaldecorrelation impacts as a function of the baseline aperture.

110

6.7 Conclusion







Interposition configuration

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

-6 -4 -2 0 2-10

0

10

20

30

40


Heig

ht

[m]

Time interval 4 day

HH

HV

VV

Figure 6.18.: Interposition configuration : from up and down, left to right, tem-poral decorrelation impacts as a function of the baseline aperture.

111

7. SummaryThis dissertation has considered the problem of the remote sensing of natural sce-narios through multiple SAR acquisitions, especially for BIOMASS. A basic choicewithin this work has consisted in considering tomographic imaging as a tool to studythe vertical structure of forests.The first part of the work focused on the problem of biomass estimation in tropicalforest areas. The processing chain for multi-layer imaging, i.e. for deriving a syn-thetic image at a specific height above the ground has been presented. Airborne SARtomography allows to accurately map the vertical distribution of the backscatteredpower in each polarization, providing a new tool to investigate forest biomass fromradar measurements. The methodology and the results apply to the tropical forest,even over hilly terrain. The results provide a novel approach to understanding thescattering mechanisms at P-band in a tropical forest, leading to the development ofappropriate methods to derive forest biomass information using SAR intensity andPolInSAR. Ground scattering is strongly visible and double bounces in flat terraintopography are visible everywhere. Volume scattering is significantly related to thehigh range biomass. Moving to the results relative to the Paracou site, they indicatethat not only in the cross-polar HV channel, but also in the co-pol HH and VV thecontributions from the canopy is important. Yet, relevant contributions from theground level beneath the forest are observed. It is worth noting that the spatial dis-tribution of the backscatter in the upper layers (20 m - 40 m) is quite similar in allpolarizations. As a result, we have shown the similarity of the results of HH, HV andVV polarizations in tropical forest in terms of their sensitivity to biomass, and wehave derived indications about the relative contribution of the ground scattering andthe forest volume scattering in each of the vertical layers inside the forest canopy.For the lower level layers (below 20 m), the correlation between the backscatteredpower and AGB is very weak and negative. The forest layer where SAR backscatteris most sensitive to biomass and the least sensitive to ground contribution has beenidentified. In particular, we observed that the log-backscattered power in HV at30 m above the ground exhibits an almost linear relationship with forest biomassranging from 250t.ha−1 to 450t.ha−1. In general, however, we certainly do not meanto claim that such approach is robust for all kind of forests. Low biomass areasare usually well treated by SAR intensity-based methods. Tomography should beprimarily intended to treat high biomass areas, i.e. where intensity saturation mayturn out to be critical. In this sense, we believe that the most important contribu-tions within this part, is that the tomography is able to separate different scatteringmechanisms in a model-free fashion, i.e. without the choice of the model of the

113

Chapter 7 Summary

forest, providing the possibility to retrieve biomass.

The second part presents the TropiScat ground based radar experiment for tomo-graphic imaging, which is dedicated to temporal decorrelation investigation. In thiscontext, we proposed a tomographic array design which is well suited to study thevertical distribution of forest parameters, providing the feasibility of the experi-ment. This design has been successfully implemented in October 2011 in Paracou,French Guiana. The TropiScat equipment allows to gather the signal with thetomographic array within few minutes, resulting in the possibility to produce a to-mographic image of the forest with a temporal sampling of 15 minutes. Thanks tofine time sampling, the daily coherence variation of the tropical forest is well observ-able and the first ever tomographic movie, capturing the forest daily change, hasbeen produced. Tomography revealed a diurnal vertical motion of the forest cen-ter of mass. This phenomenon is strongly related to daily temperature variations,which suggests a connection with forest evapotranspiration phenomena. Regardingthe short time temporal coherence, the most relevant phenomenon is the coherencedrop during daytime, due to the effect of the wind moving the forest canopy. In thistheme, the sum of Kronecker products has been proposed as a model to representand provide a reasonable description of the structure of the covariance matrix ofthe multi-polarimetric and multi-temporal data. Accordingly, all the complexity inmodeling the data may be concentrated in the expression of the structure matrices,which rule the coherence loss of the targets as a function of time. These resultalready appears to provide a very useful input concerning the BIOMASS mission,as it suggests that performance over tropical forest could be optimized by gatheringacquisitions in the early morning or night hours. For this reason long term temporaldecorrelation has been evaluated considering dusk-dusk and dawn-dawn time. Longterm temporal decorrelation has been analyzed by considering dawn time acquisi-tions from November 2011 to February 2012. Rainy days have been excluded fromthe analysis, as rainfalls have been observed to affect the electromagnetic responseof the tomographic array until a few hours (about 4-5 hours) after the rain stops.The expectation of the temporal coherence at different heights in HV after 27 dayshas so far been observed to be about 0.8 at the ground level and 0.65 in the middleof the vegetation layer, therefore witnessing coherence sensitivity to height.

The final part is an assessment to what extent the BIOMASS tomographic phase canoperate. This is based on the combination of the back projected SAR data in partone and temporal decorrelation information in part two. The vertical separationbetween the ground and the tree canopies is often well below the vertical resolution.The role of pulse bandwidth has been widely discussed, taking into account its role indetermining the vertical resolution capabilities of tomography and the implicationsof performing Common Band Filtering in a multi-baseline framework. Based on thespectral analysis of radar backscattering from forested areas, it has been shown thatthe retrieval of the vertical structure of forested areas may be carried out on the basisof a single polarimetric channel even with 6 MHz bandwidth, if a sufficient numberof acquisitions is available. Concerning ionosphere disturbances, a tomographic

114

Summary

accuracy (Γ ' −10 dB) is achieved for phase screens with standard deviation up to10 degrees with 6 passes. Using 6 or more passes, no relevant performance loss isexpected to arise from Faraday rotation provided it can be corrected to within anaccuracy of 5 degrees, which appears to be achievable by current Faraday rotationcorrection methods. A sun-synchronous dawn-dusk orbit will minimize not onlyionosphere disturbances but also temporal decorrelation. Temporal decorrelationhas a more significant impact than ionosphere disturbance. However, the resultsfrom studies show that the revisit times for the tomographic campaigns at 3-4 daysas predicted should not be critical. Finally, going beyond the critical baseline canimprove tomographic accuracy; it has been shown that the total aperture does notneed go further than about 1.5 times the critical baseline. Moreover, the spatialbaseline can be designed in such a way to be parallel to the temporal baseline tosimplify the data acquisition.

115

Publications on the topic

Journals

1. D. Ho Tong Minh, S. Tebaldini, F. Rocca, T. Le Toan, and L.Villard, “P-bandTomography imaging of a Tropical Forest at 6 MHz bandwidth: capabilities forforest biomass and height estimation,” Geoscience and Remote Sensing, IEEETransactions on, in prepration.

2. D. Ho Tong Minh, S. Tebaldini, F. Rocca, T. Le Toan, P. Borderies, T. Koleck,C. Albinet, L. Villard and A. Hamadi, “Temporal Decorrelation in a TropicalForest: Results from TropiScat and Implications for Repeat Pass Tomography,”Geoscience and Remote Sensing, IEEE Transactions on, in prepration.

3. D. Ho Tong Minh, T. Le Toan, F. Rocca, S. Tebaldini, M. Mariotti d’Alessandro,and L. Villard, “Relating P-Band SAR tomography to tropical forest biomass,”Geoscience and Remote Sensing, IEEE Transactions on, under revision.

4. D. Ho Tong Minh, S. Tebaldini, F. Rocca, T. Koleck, P. Borderies, C. Albinet,L. Villard, A. Hamadi, and T. Le Toan, “Ground based array for tomographicimaging of the tropical forest in P-band,” Geoscience and Remote Sensing,IEEE Transactions on, under revision.

5. T. Koleck, P. Borderies, F. Rocca, C. Albinet, D. Ho Tong Minh, S. Tebaldini,A. Hamadi, L.Villard and T. Le Toan, “TropiScat: A Polarimetric And Tomo-graphic Scatterometer Experiment In French Guiana Forests”, IEEE Journalof Selected Topics in Applied Earth Observations and Remote Sensing, underrevision.

6. C. Albinet, P. Borderies, T. Koleck, F. Rocca, S. Tebaldini, L. Villard, T.Le Toan, A. Hamadi, and D. Ho Tong Minh, “TropiScat: A ground basedpolarimetric scatterometer experiment in tropical forests”, IEEE Journal ofSelected Topics in Applied Earth Observations and Remote Sensing, No. 99,pp. 1 -7, Jun. 2012.

Conferences

1. D. Ho Tong Minh, S. Tebaldini, F. Rocca and T. Le Toan, “P-band Tomographyimaging of tropical forest at 6 MHz bandwidth: capabilities for forest biomassestimation”, in PolInSAR 2013, 2013.

2. D. Ho Tong Minh, Tebaldini S., Rocca F., Albinet C., Borderies P., KoleckT., Le Toan T., Villard L., "TropiScat: Multi-temporal multi-polarimetric to-

117

Acknowledgments

mographic imaging of tropical forest", Geoscience and Remote Sensing Sym-posium (IGARSS), 2012 IEEE International , vol., no., pp.7051-7054, 22-27July 2012.

3. D. Ho Tong Minh, Rocca F., Tebaldini S., Mariotti d’Alessandro M., Le ToanT., Villard L., "Relating tropical forest biomass to P-band SAR tomography,"Geoscience and Remote Sensing Symposium (IGARSS), 2012 IEEE Interna-tional , vol., no., pp.7589-7592, 22-27 July 2012.

4. T. Koleck, Borderies P., Rocca F., Albinet C., Ho Tong Minh D., Tebaldini S.,Hamadi A., Villard L., Le Toan T., "TropiSCAT: A polarimetric and tomo-graphic scatterometer experiment in French Guiana forests," Geoscience andRemote Sensing Symposium (IGARSS), 2012 IEEE International, vol., no.,pp.7597-7600, 22-27 July 2012.

5. D. Ho Tong Minh, T. Le Toan, F. Rocca, M. Réjou-Méchain, J. Chave, HoTong Phuong Que, S. Tebaldini, T. Koleck, P. Borderies, C. Albinet, L. Villard,A. Hamadi, “Day-Night Tropical Forest Phenomenology through TomographicImaging: Paracou results”, in Selper 2012, 2012.

6. T. Koleck, Borderies P., Albinet C., Hamadi A., Ho Tong Minh D., TebaldiniS., Rocca F., Villard L., Le Toan T., “TropiScat: a polarimetric tomographicscatterometer experiment in French Guiana forests”, in Selper 2012, 2012.

7. D. Ho Tong Minh, S. Tebaldini, F. Rocca and T. Le Toan, “BIOMASS : P-bandtomography imaging at 6 MHz bandwidth”, in CeTeM-AIT 2012, 2012.

8. D. Ho Tong Minh, F. Rocca, S. Tebaldini, M. Mariotti d’Alessandro, andT. Le Toan, “Linear and circular polarization P band SAR tomography fortropical forest biomass study,” Synthetic Aperture Radar, 2012. EUSAR. 9thEuropean Conference on, pp. 489 –492, april 2012.

9. D. Ho Tong Minh, S. Tebaldini, and F. Rocca, “Design of the ground basedarray for tomographic imaging in the TropiScat experiment,” Synthetic Aper-ture Radar, 2012. EUSAR. 9th European Conference on, pp. 661 –664, april2012.

10. D. Ho Tong Minh and T. Le Toan, “Tropical Forest Top Height Retrieval”,Proceeding of the 12th Conference on Science & Technology, HCMUT, Oct.2011.

11. D. Ho Tong Minh, S. Tebaldini, and F. Rocca, “Design of the ground basedarray for the Tropiscat experiment,” in FRINGE 2011, 2011.

12. S. Tebaldini, M. Mariotti d’Alessandro, D. Ho Tong Minh, and F. Rocca, “Pband penetration in tropical and boreal forests: Tomographical results,” in Geo-science and Remote Sensing Symposium (IGARSS), 2011 IEEE International,july 2011, pp. 4241 –4244.

118

Acknowledgments

First of all I would like to thank Prof. Fabio Rocca, my helpful “hero” advisor,and Dr. Stefano Tebaldini for so many hours of exciting, clarifying and motivatingdiscussion about everything to do with SAR. There is probably no better place toobtain motivation and for studying SAR than here. Particular thanks also go toMauro Mariotti d’Alessandro, Lorenzo Iannini and Francesco Banda for many hoursof pleasure not only dedicated to SAR activities but also to living life. I would liketo thank Nadia Prada, Silvia Scirpoli, Guido Gatti, Prof. Claudio Prati and Prof.Andrea Monti-Guarnieri for much help in my first year.I wish to thank Dr. Thuy Le Toan and Prof. Lars Ulander for accepting the roleof external reviewers of my thesis. It is certain that any error within this work isexclusively my own.Concerning chapter 3, I would like to thank Dr. Ludovic Villard and Dr. Thuy LeToan for the results of our discussions. Special thanks for Thuy’s support when I wasin Toulouse during my research period abroad. I would like to thank the TropiSARteam for the excellent quality of the SAR data-sets they provided. Particular ac-knowledgement goes to Dr. Pascale Dubois-Fernandez. I wish to acknowledge Prof.Jerome Chave and Dr. Maxime Réjou-Méchain for suggestions on biomass interpre-tation.I would like to acknowledge Dr. Thierry Koleck, Dr. Pierre Borderies, ClementAlbinet, Dr. Alia Hamadi, Dr. Stephane Mermoz, Dr. Yannick Lasne and Dr.Remo Bianchi, with whom I was able to discuss the concepts and results withinchapter 4 and 5 of this thesis during the ESA project TropiScat. I would also like tothank Lilian Blanc, Benoit Burban and Damien Bonal, for their welcome and helpat the Paracou station.To conclude, I would like to thank Politecnico di Milano for the PhD scholarshipaward to support my research. In this context, I also would like to thank Prof.Ramon Hanssen (Delft University of Technology), Dr. Andrew Sowter (Universityof Nottingham), Dr. Francesco Sarti (ESA) and Dr. Steffen Dransfeld (ESA) fortheir hard work in helping me obtain a PhD position.Moving to non-SAR people, I wish to thank my parents, brothers and sisters for theirunconditional support offered to me. Special thanks to my sister Ho Tong PhuongQue for suggestions on the connection with forest evapotranspiration phenomenainterpretation. Big thanks also go to my friend Alan Murray for so many correctionsto my English writing.

119

Acknowledgments

Finally, a huge thank you goes to my sweetheart, Incung.

120

A. Polarimetry independent SARtomography for tropical forestbiomass

A.1. Introduction

This appendix aims at investigating the potential of P-band SAR tomography inestimating biomass in tropical rain forests. The analysis here presented is based onmulti-baseline data acquired by ONERA at the test sites of Paracou and Nourages,French Guyana, in the frame of the ESA campaign TropiSAR. The favorable baselinedistribution of this data set results in a tomographic vertical resolution of about 20- 25m, whereas forest height ranges from 20 to 40 m. These features result in thepossibility to map the vertical distribution of the backscattered power in aboutthree independent layers, without assuming any a-priori model of the forest. Forboth test-sites, the backscattered power associated with the volume layer (about 30m above the ground) is observed to exhibit the highest sensitivity to forest biomass,even for high biomass values (250-500 t/ha). Furthermore, this result appears to beloosely dependent on the employed polarization, as a similar behavior is observedin both linear and circular polarization.

The SAR system used in the TROPISAR campaign is the ONERA airborne systemSETHI [84]. 6 and 5 P-band fully polarimetric SLC images were acquired at twotest sites of Paracou and Nouragues. The resolution is about 1m and 1.245m inslant range and azimuth directions. The baselines have been spaced vertically witha spacing about 15m (50ft). The tomographic lines for TropiSAR were flown in avertical plane rather than in the conventional horizontal plane, resulting in the phaseto height factor to have a small variation across the imaged swath. The resultingFourier vertical resolution is about 20 m and 25 m in the whole investigated area ofParacou and Nouragues, respectively. Thanks to this favorable condition, image for-mation along the vertical direction has been carried out through coherent focusing,without resorting to super-resolution techniques nor model based approaches.

For in-situ biomass data-sets, the TropiSAR data include field estimated of AGB fora number of experimental plots. For the Paracou site, we use 60 subplots of 125 mx 125 m, and 25 subplots of 100 m x100 m, resulting in 85 independent data points.For the Nouragues site, 20 subplots of 100 m x 100 m are used. Terrain topography

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Chapter A Polarimetry independent SAR tomography for tropical forest biomass

is hilly for both sites, but especially in Nouragues, as it can be shown on the figureFigure A.1. The thickness of vegetation layer in Paracou is about 40m and slightlyhigher in Nouragues.

234 5678 91011121314 16171819202122

23

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4800

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6200 -10

-5

0

5

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15

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Figure A.1.: Topographic maps of Paracou and Nouragues. The circle shows thecenter position of the plots where in situ AGB measurements are available.

A.2. Paracou and Nouragues forests result

Tomographic processing has been applied for all polarizations in order to convertthe multi-baseline SLC data stack into a multi-layer SLC data stack, where eachimage represents the complex scene reflectivity associated with a certain layer alongthe vertical direction. A slice of the multi-layer data stack corresponding to a con-stant ground range or azimuth value has been selected to display the vertical foreststructure. Figure Figure A.2 presents a tomographic section of an azimuth sectionlocated at 2270m P azimuth bin and 1770m N azimuth bin at LL and HV polariza-tions in Paracou and Nouragues, respectively. The white line denotes the LIDARcanopy height measurement, indicating the validity of the tomographic processingat both sites. It is worth noting that contributions from the whole vegetation layerare well visible both in the LL and VV polarizations.We investigate the relationships between AGB and HH, HV, VV, LL, RR and LRpolarizations at different layers for both sites. We found that good correlation al-ways comes up with volume layer (30 m above the ground) independently of theemployed polarization. The linear correlation and robustness for both of Paracouand Nouragues are found in all polarization. Scatter plots showing the sensitiv-ity of the volume layer to biomass are reported in figure Figure A.3 (VV and HVpolarizations) and figure Figure A.4 (LL polarization).In all the considered polarizations the volume backscattered power is observed to in-crease by over 3.4 dB (dRR = 3.6, dLL = 3.8, dLR = 3.4, dHH = 3.4, dV V = 3.6, dHV =

122

A.2 Paracou and Nouragues forests result

Paracou: azimuth at P bin Nouragues: azimuth at N bin LL channel

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vation [

m]

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LL channel

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vation [

m]

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VV channel

Ele

vation [

m]

Slant range [m]

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500

0

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VV channel

Ele

vation [

m]

Slant range [m]

4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500

0

20

40

60

Lidar height

Figure A.2.: Tomographic reconstruction of an azimuth section in LL and VVpolarization in the Paracou and Nouragues images. The power level ranges from0 to 1.

2 2.5 3 3.5 4 4.5 5-14

-12

-10

-8

-6

-4

-2

0

VV and HV linear polarization intensity vs forest biomass

Forest biomass [100 t.ha-1]

Backscatt

ere

d inte

nsity [

dB

]

VV-Paracou

VV-Nouragues

HV-Paracou

HV-Nouragues

Figure A.3.: The sensitivity of VV and HV backscattered intensity at the volumelayer to AGB.

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Chapter A Polarimetry independent SAR tomography for tropical forest biomass

2 2.5 3 3.5 4 4.5 5

-10

-8

-6

-4

-2

LL circular polarization intensity vs forest biomass

Forest biomass [100 t.ha-1]

Backscatt

ere

d inte

nsity [

dB

]

LL-Paracou

LL-Nouragues

Figure A.4.: The sensitivity of LL backscattered intensity at the volume layer toAGB.

4.0) as AGB increases from 250 t/ha up to 450 t/h, resulting in a dynamic rangegreater than 1.2 dB than that resulting from the SAR intensity approach [92, 87].The largest dynamic range is found at HV (4 dB). The resulting linear correlation co-efficients are RRR = 0.76, RLL = 0.78, RLR = 0.76, RHH = 0.76, RV V = 0.75, RHV =0.78.

A.3. Conclusion

In this appendix we investigated the sensitivity of different tomographic layers toAGB in tropical rain forests. For the two investigated test site it was observed thatthe backscattered intensity associated with the volume layer, about 30 m above theground, is sensitive to biomass values in the range between 250 t/ha and 500 t/ha.The linear correlation coefficient has been found to be better than 0.75. This resulthas been observed to be substantially invariant to the the employed polarization,since a similar behavior has been observed in all polarizations. The cross-polarHV would be the best candidate for the development of methods aiming at AGBretrieval. Circular polarizations also appear as a very important indicators as theyare not affected by Faraday rotation.

124

B. P-band SAR tomography imagingat 6 MHz bandwidth

B.1. Introduction

SAR Tomography (TomoSAR) imaging allows to retrieve the vertical structure ofthe vegetation, which would be one of the key elements for the assessment of theforest biomass [103]. However, a major contributor to the error budget is the limitedbandwidth allowed for the BIOMASS system by ITU regulations to 6 MHz [55].Bandwidth reduction causes the SAR resolution cell to spread along the Line of Sight(LOS). At the proposed incidence angle of 23° this translates into an appreciableresolution loss not only in the ground range direction, but in the vertical direction aswell [126]. As a result, BIOMASS tomography is hindered by two different factorscompared to airborne tomography, that is: i) A significant reduction of the numberof looks to be used for coherence evaluation, ii) A significant vertical resolution loss.The analysis presented in this appendix is carried out on airborne data acquiredby ONERA over the site of Paracou, French Guyana, during the ESA campaignTropiSAR [100]. Those data have been reprocessed in order to generate a new datastack consistent with BIOMASS as for bandwidth and carrier frequency. To dothis, two different processing approaches have been considered. One consisted indegrading the resolution of airborne data through linear filtering. This approachhas the main advantage of being fast, although it does not allow to have the sameLOS as the emulated spaceborne system along the whole imaged swath. The otherapproach consisted in recovering the 3D distribution of the scatterers at high res-olution, which was then reprojected onto BIOMASS geometry accounting for theavailable radiofrequency bandwidth. This procedure allows to obtain a data stackthat is consistent with BIOMASS concerning not only spatial resolution, but alsogeometrical features, i.e.: system LOS. Accordingly, the data stack obtained by re-projection exhibits the same vertical resolution along the swath, resulting in a faith-ful emulation of BIOMASS imaging capabilities. The connection to forest biomasshas been examined in both cases, by investigating the correlation between backscat-tered power at different forest heights and above ground biomass (AGB) values fromin-situ data.The aim of the study reported in this appendix is to provide a better understandingof BIOMASS capabilities concerning the estimation of forest biomass and height bymeans of tomographic techniques.

125

Chapter B P-band SAR tomography imaging at 6 MHz bandwidth

B.2. Reducing 6 Mhz data-sets

To generate 6 MHz SAR data sets, two different processing approaches can be carriedout.The first one is simply done by a linear filtering from the airborne SAR data set.This is also provided by ONERA.The other approach will be dedicated in such a way to have a data stack which isconsistent with BIOMASS concerning not only spatial resolution, but also geomet-rical features, i.e.: system LOS. A simulator has been implemented able to generatemulti-baseline and multi-polarimetric SLC data stacks consistent with BIOMASSspecifics, see detail in section 6.2.We will hereinafter refer to the reducing bandwidth results associated with a filteringairborne data simply by airborne geometry and the other one is spaceborne geometry.

B.3. Tomography profile

For sake of simplicity we will hereinafter refer to a SLC image associated with acertain height above the ground simply through the layer height.Figure B.1 shows the HH backscattered power for the layer at the four levels inairborne geometry. The ground layer (0 m) and top layer (45 m) shows strong topo-graphic effect, whereas the layer 30 m is observed to be less affected by topography.Figure B.2 reports a tomographic profile of an azimuth section in HV polarizationat 125 MHz and 6 MHz in both geometries. The white line denotes the LiDARheight measurements, for comparison with the tomography profile.The reduction of the bandwidth to 6 MHz from 125 MHz is evident in the loss ofhorizontal resolution; however, the loss in vertical resolution, even if present andvisible, is not really damaging. In the result, neither ionospheric disturbances nortemporal decorrelation has been considered.

B.4. Tropical forest biomass relation

The analysis in this section is focused on relationship between the backscatteredpower associated with layers at different height and in-situ AGB measurements fromthe 16 and 85 plots described above. Figure B.3 displays the backscatter power inHV plots as a function of 16 plots in-situ AGB, considering 9 layers varying from 0m to 40 m, at 5 m interval.Similarities between two geometries can be made. For the layers under 20 m, thePearson linear correlation rP between the backscatter intensity and AGB is very

126

B.4 Tropical forest biomass relation

h = 0m

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Layer 0 m

Layer 30 m

Layer 15 m

Layer 45 m

Figure B.1.: HH backscattered power for the layer at the four levels in airbornegeometry

weak (and negative). For layers from 20 m 40 m the correlation between backscatterand AGB becomes instead highly significant.

Layer 30 m exhibites a correlation at the highest value with in-situ data and nobias phenomena over AGB values ranging from 250 t/ha to 450 t/ha. At the 35 mlayer, the backscatter dynamic range is larger but the correlation is reduced and thedispersion is increased. For the top layer (40 m), the correlation decreases and thedispersion increases as well. This result indicates that the 30 m layer appears to bethe most suited for tropical forest biomass retrieval, by virtue of its high correlationwith AGB. This is consistent with 125 MHz observed results [103].

Based the results and the discussion provided above, an estimator is introduced toretrieve AGB based on the backscattered power in HV for the 30 m layer. Per-formance is assessed by evaluating the Root Mean Square Error (RMSE) betweenin-situ measurements and estimated AGB values. Results are reported in Figure B.4.The RMSE turned out to be lower than 10% in very large plot (6 ha), whereas inhigher resolution the RMSE is lower than 20% .

127


H

eig

ht [m

]

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2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000

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Heig

ht [m

]

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Heig

ht [m

]

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2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000

0

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Ground range [m]

Figure B.2.: Tomographic reconstruction along the same azimuth cut in HV po-larizations at 125 MHz and 6 MHz in both geometries. The while line denotesthe LiDAR height measurements. All panels have been normalized in such a waythat the sum along height is unitary.

128

B.4 Tropical forest biomass relation

2 3 4 5-20

-15

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0

0 m layer, rP = -0.26, Slope = -0.36

PH

V [

dB]

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PH

V [

dB]


-20

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-20

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40 m layer, rP = 0.8, Slope = 2.24

Above-ground biomass (100 t/ha)

Figure B.3.: Sensitivity of backscatter power at different layers to above-groundbiomass in HV channel in both geometries. rP is the Pearson correlation coeffi-cient. Slope is referred to the angular coefficient of the linear regression.

129


6 ha : 250m x 250m 1.5ha : 125m x 125m

0 100 200 300 400 500 6000

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Re

trie

ve

d fo

rest b

iom

ass (

t/h

a)

RMSD = 35.39 (t/ha)

= 9.97 (%)

MPE = 0.27 (%)

rP = 0.83

rS = 0.83

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trie

ve

d fo

rest b

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ass (

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= 19.87 (%)

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rS = 0.56

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trie

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ass (

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= 19.14 (%)

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trie

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ass (

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RMSD = 35.02 (t/ha)

= 9.86 (%)

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rP = 0.84

rS = 0.79

Airborne geometry – HV

Spaceborne geometry - HV 6 ha : 250m x 250m 1.5ha : 125m x 125m

(a)

(b)

Figure B.4.: Comparison between in-situ biomass and biomass derived from inver-sion of the P-band HV 30 m layer in both geometries.

130

B.5 Forest height estimation

B.5. Forest height estimation

The retrieval of forest height has been assessed through a direct investigation of theshape of the 3D backscattered power distributions from the multi-layer SLC at eachlocation in HV.The LiDAR forest height available is shown in Figure B.5a to facilitate the interpre-tation of the results. In Figure B.5b and Figure B.5c, an agreement of tomographicforest height with the LiDAR measurements is shown for airborne and spacebornegeometry respectively. Both LiDAR and tomographic forest height are filtered byan average window of 100 x 100 m. The average relative error is 0.13 (13%) and0.10 (10%) for airborne and spaceborne geometry respectively.The joint distribution of forest height is shown in Figure B.6. The joint distributionhas been normalized such that the maximum is unitary along each column. Theestimation appears to be reliable for vegetation layers ranging from 21 m to 31 m.For this range height, standard deviation has been assessed in about 4 m.

B.6. Conclusion

This appendix has demonstrated the ability of the P-band SAR tomography at6 MHz to retrieve biomass and height in tropical forest. Two approaches havebeen considered through airborne and spaceborne geometry. The loss of verticalresolution from both approaches due to reducing bandwidth is evident but it is notcritical. The sensitivity between biomass and tomographic volume scattering fromboth approaches is clear and similar. With HV channel, we can achieve less than20% relative accuracy with 1.5 ha resolution and less than 10% relative accuracywith 6 ha resolution. From both approaches, the forest height estimation appearsto be reliable for vegetation layers ranging from 21 m to 31 m, which is consistentwith the relative high forest height in tropical forest areas. For this range height,standard deviation has been assessed in less than 4 m.

131


Relative error

0 10 20 30 40 0 0.2 0.4 0.6 0.8 1

|Htomogaphy – HLiDAR|/HLiDAR

(b)

(a)

(c)

Airborne geometry

Spaceborne geometry

LiDAR

Figure B.5.: Comparison between LiDAR and tomography retrieval of forestheight in both geometries.

132

B.6 Conclusion

Spaceborne geometry Airborne geometry

LIDAR (m)

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s (

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(m

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(a) (b)

Figure B.6.: Joint distribution between LiDAR and tomography retrieval of forestheight in both geometries.

133

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