RESEARCH ARTICLE

Inversion of PROSAIL Model for Retrieval of PlantBiophysical Parameters

Rahul Tripathi & Rabi N. Sahoo & Vinay K. Sehgal &R. K. Tomar & Debashish Chakraborty &

S. Nagarajan

Received: 14 December 2010 /Accepted: 24 May 2011 /Published online: 25 June 2011# Indian Society of Remote Sensing 2011

Abstract The current development of satellite technol-ogy particularly in the sensors like POLDER andMISR,has emphasized more on directional reflectance meas-urements (i.e. spectral reflectance of the target measuredfrom different view zenith and azimuth angles) of theearth surface features mainly the vegetation for retrievalof biophysical parameters at regional scale usingradiative transfer models. This approach being physicalprocess based and uses directional reflectance measure-ment has been found to better and more reliablecompared to the conventional statistical approach usedtill date and takes care of anisotropic nature (i.e.reflectance from the target is different if measured fromdifferent view angles) of the target. Keeping this in viewa field experiment was conducted in mustard crop toevaluate the radiative transfer model for biophysicalparameter retrieval through its inversion with theobjectives set as (i) to relate canopy biophysicalparameters and geometry to its bidirectional reflectance,(ii) to evaluate a canopy reflectance model to bestrepresent the radiative transfer within the canopy for itsinversion and (iii) to retrieve crop biophysical parame-ters through inversion of the model. Two varieties of the

mustard crop (Brassica juncea L) were grown with twonitrogen treatments. The bidirectional reflectance dataobtained at 5 nm interval for a range of 400–1100 nmwere integrated to IRS LISS–II sensor’s four band valuesusing Newton Cotes Integration technique. Biophysicalparameters like leaf area index, leaf chlorophyll content,leaf length, plant height and average leaf inclinationangle, biomass etc were estimated synchronizing withthe bi-directional reflectance measurements. Radiativetransfer model PROSAIL model was validated and itsinversion was done to retrieve LAI and ALA. Look UpTable (LUT) of Bidirectional reflectance distributionfunction (BRDF) was prepared simulating throughPROSAIL model varying only LAI (0.2 interval from1.2 to 5.4 ) and ALA (5° interval from 40° to 55°)parameters and inversion was done using a meritfunction and numerical optimization technique givenby Press et al. (1986). The derived LAI and ALAvaluesfrom inversion were well matched with observed onewith RMSE 0.521 and 5.57, respectively.

Keywords BRDF. PROSAIL . Hotspot effect .Modelinversion . Numerical optimization . LAD . LAI .

Mustard

Introduction

The knowledge of canopy biophysical variables is ofprime interest in many applications including cropfunction modeling, evapotranspiration and crop growthmodeling and yield prediction. Moreover, establishing

J Indian Soc Remote Sens (March 2012) 40(1):19–28DOI 10.1007/s12524-011-0129-8

R. Tripathi (*)Central Rice Research Institute,Cuttack, Orissa, Indiae-mail: rahulcrri@gmail.com

R. N. Sahoo :V. K. Sehgal : R. K. Tomar :D. Chakraborty : S. NagarajanIndian Agricultural Research Institute,New Delhi, India

maps of biophysical characteristics is necessary forpredicting the soil-vegetation- atmosphere energy trans-fers. There are mainly two methods to estimate bio-physical variables from reflectance data such as empiricalapproaches and physical modeling approaches.Empirical or statistical approaches are only based onobservations of the spectral contrasts of reflectance andconsist of fitting a relationship between reflectance andsome biophysical variables, mainly by the use ofvegetation indices (Asrar et al. 1984). Physical model-ing approaches are based on the inversion of canopyreflectance models, which physically relate canopybiophysical variables to reflectance data (Jacquemoud1993; Bicheron and Leroy 1999). The empiricalmethods are usually sensitive to the soil background,crop chlorophyll content, or to the orientation andspatial distribution of the leaves in the canopy. Thereliability of these methods, although they bear uponmost operational applications, is intrinsically limited bythe fact that they poorly account for the anisotropicproperties of these surfaces. Moreover, since earthsurface features reflect radiation anisotropically, satel-lite measurements strongly depend on both position ofsun and position of the observer relative to the sun,hence the term ‘bidirectional reflectance’. The bidirec-tional reflectance is not only a function of relativegeometry of illumination and observation, but alsophysical and morphological properties of the observedsurface. Since late 80’s, the anisotropy properties ofearth surface features came out for the assessment ofkey characteristics of plant canopies (Kimes andSellers 1985). Inversion of bidirectional canopy reflec-tance (CR) models emerged as a promising alternativefor retrieval issues (Goel 1987, 1988, 1989; Myneniand Ross 1991). The new generation of space borneinstruments like POLDER, ADEOS, MISR, TERRA,etc are designed to study both the spectral anddirectional characteristics of the earth surfaces. Thistrend depicts one of the scientific stakes to come inremote sensing, which is to take advantage of both thespectral and the directional signatures of vegetation inorder to retrieve the biophysical parameters that revealits functioning. Keeping this in back ground, anexperiment was conducted to relate canopy biophysicalparameters and geometry to its bidirectional reflec-tance, to evaluate the canopy reflectance model to bestrepresent the radiative transfer within the canopy for itsinversion and to retrieve crop biophysical parametersthrough inversion of the model.

Materials and Methods

In order to achieve the objectives, a field experimentwas conducted in the experimental farm of IndianAgricultural Research Institute, New Delhi, located at28.40° N latitude, 78.10° East longitude. Two varieties(Pusa Agrani and Pusa Jaikisan) of mustard (Brassicajuncea L.) crop having contrasting plant architecturewere raised during Rabi season (2005–2006) with twonitrogen treatments each. The field was divided intotwo equal parts, for sowing with different nitrogentreatment (i.e. 40 and 80 kg N ha−1) in each part inparallel direction. Each half was then divided into 4plots of size (6×6 m2). Two nitrogen treatments wereimposed in each half in order to achieve a wide rangeof values for the biophysical parameters mainly leafarea index and chlorophyll content. The layout ofexperimental plot was made having four sides alignedwith four directions respectively. The spectral reflec-tance observations of the crop canopy were taken byportable spectroradiometer (LICOR-1800). Solar zenithand azimuthal positions were computed during mustardcrop growing period i.e. Oct, 2005 to Feb, 2006 at10 days interval and during 10–15 hrs of a day at halfan hour interval. Ranges of solar zenith and azimuthwere found be 45° to 60° and 145° to 240°respectively. This was used to decide the range forview zenith and azimuth values for spectral observa-tion. To have different view zenith and azimuthpositions, a hemispherical structure with a strong basemade up of galvanized iron rectangular structure wasfabricated. The hemispherical sensor was modified tohave a FOV of 15°. Taking true north direction as 0°,the six azimuthal angles for A, B, C, D, E, F werecalculated as 0°, 90°, 135°, 180°, 225° and 270°respectively. The bidirectional spectral observation wasrecorded at 0°, 20°, 40°, 50° and 60° view zenithangles for each azimuthal position making a total of 25and one hemispherical scanning for each plot . Thedesign of the set up ensures that the sensor receivedreflected radiation from the same area of vegetation atthe centre of the structure for different view azimuthand zenith angles throughout growth period. A 4′×6′size wooden board coated with barium sulphatepowder was used as reference panel for collecting bothhemispherical and bidirectional spectral reflectancewhich was used to calculate the reflectance percentagefrom both hemispherical and bi-directional measure-ments (Fig. 1). Spectral observations were taken on

20 J Indian Soc Remote Sens (March 2012) 40(1):19–28

clear sunny days i.e. on 52, 58, 69, 78, 87, 98, 105 and121 days after sowing (DAS). A programme waswritten in IDL (6.1) environment to compute thereflectance at 5 nm interval and integrate it to fourband widths corresponding to of IRS LISS II sensorsuch as 450–520 nm (B1), 520–590 nm (B2), 620–680 nm (B3) and 770–860 nm (B4) using five pointNewton-Cotes integration technique (Mikkawy andMoawwad 2003). The bidirectional reflectance valueswere plotted with different azimuth and view anglestaken in Y and X-axis using geostatistical softwareSurfer (ver. 8.0). Different plant parameters like canopyheight, Leaf Area Index (LAI), specific leaf area,Average Leaf Angle (ALA), leaf chlorophyll content,leaf length and dry biomass were recorded at weeklyinterval synchronizing with the spectral observationsstarting from 52 to 121 DAS. Equivalent leaf moisturethickness was calculated and Leaf chlorophyll contentwas measured by DMSO method given by Arnon(1949). The radiative transfer model PROSAIL wasused for simulation of bi-directional reflectance and itsvalidation was done. The PROSAIL model wasdeveloped (Jacquemoud 1993) combining PROSPECTand SAIL model. It considers the detailed informationon leaf optical properties and also accounts for hotspoteffect. The PROSAIL model computes canopy reflec-tance in a particular wavelength band as a function of(1) canopy structural parameters such as leaf area index(LAI), leaf mesophyll structure parameter (N), meanleaf inclination angle (tl), leaf size/crop height (sl); (2)biochemical parameters like chlorophyll-a+b concen-tration (Cab) and water content (Cw); (3) viewinggeometry parameters- solar zenith, view zenith and

relative azimuth angle; and (4) soil reflectance. Themodel is given by the expression as R ¼ f isat; ihot;ðqs;Φs; tl; l; vai;Cab;Cw;Cm; sl; vis; qv;Φv; rsoil; naÞ

Where,

isat sensor parameterihot hotspot parametertl mean leaf inclination (degree)l leaf area indexVai leaf internal structure parameterCab chlorophyll a and b (μg/cm2)Cw leaf equivalent water thickness (cm)Cm leaf dry matter content (g/cm2)sl leaf size/crop heightvis horizontal visibilityθs, θv solar and view zenithФs, Фv solar and view azimuthrsoil soil hemispherical reflectancena Total no of view azimuth X

view zenith angles considered.

Results and Discussion

Relationship Between BRDF and Plant BiophysicalParameters

The two mustard varieties Pusa jaikisan and Pusa Agranistudied for bi-directional reflectance were different inphenology, canopy geometry and leaf properties. LAIvaried from 1.27 and 1.37 to higher values 4.84 and 5.20for Pusa agrani and Pusa jaikisan varieties respectively.

Fig. 1 Metallic hemispheri-cal structure to set differentview geometries of sensorand barium sulfate referencepanel at the centre. Insetshows modified sensorattached to the arc ofhemisphere for particularview geometry

J Indian Soc Remote Sens (March 2012) 40(1):19–28 21

Irrespective of nitrogen treatment, LAI for Pusa jaikisanwas higher compared to that of Pusa agrani. Average leafangle (ALA) for Pusa jaikisan varied from 47° to 53° and39° to 46° in Pusa agrani. Figure 2 shows bi directionalreflectance at different view zenith angles plotted at aparticular view azimuth angle. This graph clearlyindicates the difference in reflectance pattern at differentangles and hence the anisotropic nature of the mustardcrop. Plotting of NDVI having view azimuth in x-direction and view zenith in y-direction, revealed that itsvalues was highest at around 180° view azimuth and60° view zenith positions for both the varieties havingcorresponding azimuth and zenith positions of sun as

167.7°, 57.75°, 176.46° and 55.63° and 195.8° and52.83° for 52, 78 and 105 DAS, respectively. This wasmainly due to hot spot effect (Suits 1972) i.e. when sunis just behind the sensor position. One such example for105 DAS is given in Fig. 3.

It was also observed that NDVI values for both thevarieties increased with increase in view zenith from 20°to 60° at a fixed azimuth (i.e. 180°) on all eight days ofobservation. At lower zenith angle (i.e near nadir) thesensor was looking at the top of the canopy i.e. theupper surface of the leaves. Since the lower surfacereflects more than the upper surface with increase inzenith angle, lower surface of the plant leaves were

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Fig. 2 Bidirectional reflectance of mustard crop at different azimuth angles (0°,90°,135°,180°,225° and 270°). Four colour shades inreflectance curve represent reflectance at view zenith angles 20°, 40°, 50° and 60°

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exposed more to the sensor and we got higherreflectance. At higher zenith angle, also the sensor wasexposed to more diffused radiation and hence gave riseto higher reflectance values. The finding obtained here

is supported by the work done by Kimes and Sellers(1985).

With the increase in zenith angle from 20° to 60°,the difference between NDVI values of two varieties

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Fig. 3 Pattern of NDVIderived from bidirectionalreflectance at different viewgeometry (Azimuth 0°–270°and zenith 20°–60°)for (a)Pusa agrani and (b) Pusajaikisan at 105 DAS(Sun geometry Va=195.80,Vz=52.83)

Table 1 Coefficient of determination (R2) of NDVI with Leaf Area Index (LAI) and leaf chlorophyll content at different view azimuthand view zenith angles for Pusa Agrani and Pusa Jaikisan 105 DAS

View Azimuth View Zenith R2 (NDVI vs Chl) R2 (NDVI vs LAI)

jaikisan agrani jaikisan agrani

0 20 0.6553 0.4853 0.5231 0.4311

40 0.7700 0.5700 0.6762 0.5762

50 0.7951 0.6951 0.7451 0.5451

60 0.8336 0.7136 0.8617 0.6177

90 20 0.6823 0.6924 0.5826 0.4826

40 0.7329 0.7329 0.6736 0.5736

50 0.8228 0.7938 0.7971 0.7297

60 0.8412 0.8312 0.8434 0.8334

135 20 0.7504 0.7504 0.6807 0.5807

40 0.8365 0.7835 0.7581 0.6881

50 0.7846 0.7984 0.7528 0.7528

60 0.7999 0.8299 0.7941 0.7941

180 20 0.7333 0.7833 0.8364 0.7664

40 0.8215 0.7921 0.8628 0.8528

50 0.8841 0.8840 0.8906 0.8806

60 0.8982 0.8980 0.9432 0.9232

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40 0.6564 0.7564 0.7841 0.8341

50 0.7199 0.8199 0.8645 0.8825

60 0.8696 0.8696 0.8883 0.8928

270 20 0.6121 0.6121 0.6976 0.5976

40 0.7375 0.7375 0.7634 0.6634

50 0.7881 0.8381 0.7905 0.7905

60 0.8656 0.8623 0.8321 0.8321

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increased and were found to be the highest at 60°zenith positions. Also Pusa jaikisan was havinghigher NDVI compared to that of Pusa agranithroughout the growth period. Same trend was alsofound with respect to their leaf length, plant heightand ALA. Therefore, at hot spot position, not onlydiscrimination of both varieties was much better, butalso plant geometry defined by leaf length and plantheight found to be well depicted through NDVIvalues. The biophysical parameters were reported tobe highly correlated with NDVI (Asrar et al. 1984).Regression analysis for relationship between NDVIand LAI, NDVI and biomass and NDVI andchlorophyll content for both varieties revealed thatBRDF derived NDVI was highly correlated withLAI, biomass and chlorophyll content and highestR2 values (0.92, 0.89 and 0.89 respectively) werefound at hot spot position i.e. at 180° azimuth and60° zenith positions. R2 values for regressionbetween NDVI and LAI and Chlorophyll content ispresented in Table 1.

Validation of PROSAIL Model

PROSAIL model was evaluated at three stages ofcrop growth period i.e. 52, 78 and 105 DAS to best

represent the radiative transfer within the canopy forits inversion. Model generated BRDF were found tobe under-estimated compared to measured one.However, better fitting of simulated BRDF withmeasured one was found at NIR region comparedto visible range (400–700 nm) at hot spot positionfor all the dates of observation (Figs. 4 and 5) andRMSE for visible and NIR range for 52,78 and 105DAS were 0.048 and 0.234, 0.036 and 0.192 and0.028 and 0.198 respectively. Possible reason may bedue to (i) assumption taken in the model that soilalbedo was taken as input considering its surface asLambertian which is not true and (ii) the BaSO4

coated reference panel coated with does not repre-sent truly a Lambertian surface. NDVI values werecomputed from NIR and red bands integrated fromsimulated BRDF.

Comparison of simulated NDVI with observedone for different zenith and azimuthal combinationsrevealed that maximum NDVI value was obtainedboth for observed and simulated at hot spotpositions (Fig. 6). In conclusion, we can say thatPROSAIL model can give a good estimation of non-isotropic reflectance behaviour of plant canopyprovided the standard reflectance reading should beflawless.

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Fig. 4 Comparison between observed and PROSAIL model simulated reflectance at a fixed view azimuth (180°) and different viewzenith positions

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Biophysical Parameter Retrieval Through ModelInversion

An attempt was made to retrieve two biophysicalparameters i.e. LAI and ALA through inversion of thePROSAIL model. Its suitability for this use is due to thereduced number of parameters and to the speed ofsimulation of multiangular spectra (Casa and Jones2004). BRDFs values were simulated through PRO-SAIL model at varying LAI (0.2 interval from 1.2 to5.4) and ALA (5° interval from 40° to 55°) valueskeeping other parameters fixed. Values of other inputparameters for the model are given in Table 2. Look UpTable (LUT) was prepared for simulated BRDFs

(ranging from 400–1100 nm at 5 nm) with correspondingLAI and ALAvalues. To carry out the inversion, a meritfunction was defined and numerical optimizing routinewas chosen in order to find the minimum of that function.The merit function F used here was given by Nilson andKuusk (1989) and defined as

F ¼Xn

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Fig. 5 Comparison between observed and PROSAIL model simulated reflectance at a fixed view zenith (60°) and different viewazimuth positions

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The method chosen for the iterative minimizationof the merit function was the downhill simplexmethod of Neldar and Mead (1965) (sub routineAMOEBA). Inversion was carried out using multi-angular hyperspectral data. Spectra for the waveband400–1100 nm at 5 nm interval (i.e. 141 hyperbands)were generated for 24 (6 azimuth × 4 zenith) possibleview geometry conditions. Therefore, merit functionwas computed using the differences between 3384(141 hyperbands by 24 view geometry conditions)modeled and measured BRDFs. The LAI, ALA valuecorresponding to optimized value of merit function isthe derived value of the inversion (Fig. 7). Thesevalues were compared with observed one and predic-tive accuracy was evaluated with RMSE values.Results revealed that LAI and ALA very wellretrieved and comparable with observed values withRMSE error 0.521 and 5.57 respectively.

Conclusions

The surface of a crop canopy behaves like a non-lambertian surface that is anisotropic, and hence itsgeometry must be considered while studying thecanopy reflectance measurement. The bi-directionalreflectance contains more information than the hemi-

spherical reflectance as almost all the surface featuresare non-isotropic. The reflectance increases with theincrease in view zenith angle irrespective of thesensor azimuth position. Therefore, view zenithposition is an important parameter while consideringsensor geometry. BRDF-NDVI was found to bemaximum at hot spot position (180° view azimuthand 60° view zenith in this study) and yielded betterdiscrimination of varieties having contrasting geom-etry parameters. The biophysical parameters are bestcorrelated with the bidirectional NDVI at the hot spotposition. PROSAIL model was found to be simpleand easy having few and measurable parameters asinputs and could simulate spectral values well fittingwith the observed one in NIR region at hot spotposition. Inversion of the model using numericaloptimization technique could find to give reliableestimates of LAI and ALA. Similarly, other parame-ters like leaf dry biomass, chlorophyll content may beretrieved and compared with the measured one.However, leaf moisture content can’t be estimated asit requires spectral range 1100 to 2500 nm which isnot available with the spectroradiometer used for thestudy. However, The absolute determination of cano-py biochemical properties-chlorophyll and water butalso carotenoids, starch, lignin, nitrogen, etc., whichare not yet included into the PROSAIL model and is a

Fig. 6 Reflectance vs viewzenith and view azimuthangle for jaikisan variety ofmustard: (a) measured (b)simulated

26 J Indian Soc Remote Sens (March 2012) 40(1):19–28

challenge for further research. The precision is goodfor high LAI values corresponding to a dense canopy,or for low values when soil background effects are notnegligible. The hypothesis of a known soil is realisticin field experiments, but it rarely happens withairborne data. It will be necessary, in future works,to take into account parameters characterizing soiloptical properties while inverting the reflectancemodel. The approach in this study which has been

validated at a local scale, generally provides accurateinformation on canopy morphology, since sufficientdirections of observation are available (here 24different combinations). At a larger scale, except theairborne experimental instruments such as ASAS(Advanced Solid-State Array) or POLDER (Polariza-tion and Directionality of the Earth's Reflectances),there are limited ways to acquire so many bidirec-tional reflectances.

Average Leaf Angle

Merit function error

LAI

Fig. 7 Model Inversion re-sult showing optimizedmerit function error and itscorresponding LAI andALA values

Table 2 Input parameters of PROSAIL model for validation for two varieties of mustard (105 DAS)

PROSAIL Model Input Parameters A1 A2 J1 J2

isat (spectroradiometer, 400–1100 nm,5 nm interval)

0 0 0 0

ihot 1 1 1 1

theta_s, phi_s (sun position) 48.9, 193 49.9, 199 48.6, 169 49.8, 161

tl (mean leaf inclination) 43 42 51 52

l (Leaf Area Index) 3.71 4.10 4.50 4.83

vai (leaf internal structure) 1.5 1.5 1.5 1.5

Cab (Leaf chlorophyll content, μgcm-2) 41.46 41.77 38.5 39.2

Cw (Equivalent water thickness) 0.026 0.025 0.032 0.034

Cm ,Leaf dry matter content (g/cm2) 0.0049 0.0046 0.0042 0.0041

Sl Leaf length/crop height 0.068 0.075 0.095 0.094

vis (Horizontal visibility) 50 50 50 50

na (Total no of azimuth*view angles considered) 24 24 24 24

A1: Pusa agrani with 40 kg Nha−1 , A2 : Pusa agrani with 80 kg Nha−1

J1: Pusa jaikisan with 40 kg Nha−1 ,J2 : Pusa jaikisan with 80 kg Nha−1

J Indian Soc Remote Sens (March 2012) 40(1):19–28 27

Acknowledgements First author thanks Indian AgriculturalResearch Institute, New Delhi for providing Junior ResearchFellowship for this study.

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