Remote Sensing of Environment 115 (2011) 44–54

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Remote Sensing of Environment

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Remote sensing retrieval of suspended sediment concentration in shallow waters

V. Volpe a, S. Silvestri b, M. Marani a,⁎a Department of Hydraulic, Maritime, Environmental and Geotechnical Engineering, University of Padua, via Loredan 20, Padua, Italyb Servizio Informativo, Magistrato alle Acque di Venezia, via Asconio Pediano 6, 35127 Padova, Italy

⁎ Corresponding author.E-mail addresses: valeria.volpe@unipd.it (V. Volpe),

(S. Silvestri), marani@idra.unipd.it (M. Marani).

0034-4257/$ – see front matter © 2010 Elsevier Inc. Aldoi:10.1016/j.rse.2010.07.013

a b s t r a c t

a r t i c l e i n f o

Article history:Received 29 September 2009Received in revised form 27 April 2010Accepted 30 July 2010

Keywords:Water turbiditySuspended sedimentRemote sensingRadiative transfer model

The dynamics of coastal lagoons and estuarine areas is characterized by a delicate balance between biologicaland physical processes and the comprehension and monitoring of such processes require observations over awide range of temporal and spatial scales. Remote sensing techniques in this context are very advantageousand potentially allow overcoming the spatial limitations of traditional in situ point observations, providingnew opportunities for a better understanding of the relevant bio-geomorphological processes and for thecalibration and validation of spatially-distributed hydrodynamic and transport models. Remote sensing ofsuspended particulate matter (SPM) concentration in shallow waters must, however, overcome thedifficulties associated with i) the influence of bottom reflection, which may interfere with an accurateretrieval; ii) the necessity of accurately knowing the optical properties of the suspended matter, and iii) theimportance of providing an assessment of the uncertainty associated with the estimates produced. This workpresents a method to estimate SPM concentration in lagoon/estuarine waters by use of a simplified radiativetransfer model. We use a calibration/validation method based on cross-validation and bootstrap techniquesto provide a statistically sound determination of model parameters and an evaluation of the uncertaintyinduced by their inaccurate determination as well as by the uncertain knowledge of the bottom sedimentreflectance. The method is applied to the Venice lagoon, using observations from a network of turbiditysensors and from several multispectral satellite sensors (LANDSAT, ASTER and ALOS AVNIR). The bootstrapand cross-validation procedures employed show that consistent estimates of SPM concentration can indeedbe retrieved from satellite remote sensing, provided that sufficient in situ ancillary information forappropriate calibration is available. The quantification of the estimation uncertainty shows that retrievalsobtained from remote sensing are accurate, robust and repeatable. The SPM concentration maps producedshow a general coherence with known features in the Venice lagoon and, together with suitable biologicalinformation, point to the role played by benthic vegetation in the stabilization of the bottom sediment.

sonia.silvestri@magisacque.it

l rights reserved.

© 2010 Elsevier Inc. All rights reserved.

1. Introduction

The geomorphic dynamics of shallow coastal areas, such as lagoonsand estuaries, is crucially dependent on a subtle balance betweensediment inflow from inland waters or the sea and sediment outfloworiginated by wind-wave erosion and tidal currents. From a broaderperspective the entire bio-physical evolution of a tidal environment islargely controlled by the transport of sediment, organic matter andother suspended or dissolved substances (Fagherazzi et al., 2004,2007; Marani et al., 2007; Perillo et al., 2009).

Suspended particulate matter (SPM) dynamics, in particular, playsa major role in erosion/deposition processes, biomass primaryproduction, the transport of nutrients, micropollutants, and heavymetals. It is thus of great importance to acquire reliable and space-distributed observations of SPM concentration in order to advance our

understanding of the biogeomorphic dynamics of estuarine andlagoon systems and to develop effective and quantitative monitoringschemes. Ideally, observations of SPM would be required with a highspatial and temporal resolution (order of tens of meters and of tens ofminutes respectively). In practice, while turbidity observations can beacquired at a high temporal resolution (e.g. hourly) observationnetworks are typically sparse (spacings of several kilometers) ascompared to the intrinsic scale of variability of SPM, which is inducedby morphological features having a typical size ranging from a fewmeters to kilometers.

Remote sensing can be used to obtain information about severalwater quality parameters, including SPM concentration, and it hasindeed been applied to several test sites. SPM retrievals in lagoon andestuarine waters (Case II waters, (Mobley, 2004)) are particularlydifficult due to the presence of a variety of suspended and dissolvedmaterials and to the potentially large contribution of the bottomsediment to the detected remote sensing signal, which becloud theidentification and accurate measurement of the contribution comingfrom sediments in the water column. Additionally, the literature on

Table 1List of symbols.

Symbol Description Unit

rrs Subsurface remote sensing reflectance sr−1

Rrs Above-surface remote sensing reflectance sr−1

ρ Surface reflectance –

ρb Bottom albedo –

r rsdp rrs value for optically deep waters sr−1

Kd Vertically averaged diffuse attenuationcoefficient for downwelling irradiance

–

KuC Vertically averaged diffuse attenuation

coefficient for upwelling radiance fromwater-column scattering

–

KuB Vertically averaged diffuse attenuation

coefficient for upwelling radiance frombottom reflectance

–

θw Subsurface solar zenith angle radaw Absorption coefficient of pure water m−1

aNAP Absorption coefficient of non algal particles m−1

aph Absorption coefficient of phytoplankton pigments m−1

aCDOM Absorption coefficient of yellow substances m−1

a Absorption coefficient of the total:a=aw+aNAP+aph+aCDOM

m−1

bb Backscattering coefficient m−1

bw Scattering coefficient of pure water m−1

bph Scattering coefficient of phytoplankton pigments m−1

bNAP Scattering coefficient of suspended particles m−1

b Scattering coefficient of the total: b=bw+bph+bNAP m−1

45V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

the estimation of SPM concentration from remote sensing is quitedeveloped but it mostly concerns oceanic or relatively deep marinecoastal waters (Ferrari & Tassan, 1991; Babin et al., 2003a,b; Bindinget al., 2005; Giardino et al., 2007) and, often, low-resolution sensorsunsuitable for applications in estuaries and lagoons (e.g. Chen et al.,2007). Finally, much of the existing literature concerns empiricalapproaches, which attempt to link, through an assumed algebraicrelation, observed turbidity to the observed remote sensing signal(Östlund et al., 2001; Zhang et al., 2002; Ekercin, 2007; Chen et al.,2007). These approaches, which have the merit of demonstrating theexistence of a clear and detectable relation between water compo-sition and remote sensing observations and are certainly useful forspecific study sites, are not suitable for general applications toestuarine/lagoon studies because they fundamentally depend on thespecific data and conditions under which they are calibrated. Thismeans that any application to a new site or any change of sensor orresolution requires a new calibration, leaving little room forgeneralization. A more general approach should be based ontheoretical models of radiative transfer in turbid waters, which,with varying degrees of approximation, provide a representationwhich is consistent with the governing physical processes, possiblyallowing insights in the processes themselves and applications to awider range of conditions than afforded by empirical approaches (e.g.Dekker et al., 2001; Mobley, 2004; Giardino et al., 2007; Brando et al.,2009). Here we follow a theoretically- and physically-based approachusing a simple radiative transfer model (Lee et al., 1998, 1999) torelate at-satellite radiance measurements and in situ turbidityobservations with application to the Venice lagoon (Italy).

Previous contributions to the literature usually lack an assessmentof the uncertainties involved in the estimation of suspended sedimentconcentration (or, more generally, of the water quality parameters ofinterest). This information, on the contrary, is extremely importantwhen estimates are to be compared with in situ observations or withresults from numerical models. The main sources of uncertainty in analgorithm for the retrieval of SPM concentration from remote sensing(but generalizations to otherwater parameters are quite straightforward)can be identified as i) uncertainties in the measurement of at-sensorradiances (the ‘input’ of the retrieval algorithm), ii) uncertainties in themodel structure (e.g. due to simplifying assumptions and/or neglectedprocesses), and iii) uncertainties in the determination of the parametersappearing in the model. Interestingly, even though statistical methodsallowing a formal quantification of uncertainty are widely used in otherdisciplines (e.g. Montanari, 2007), they are seldom applied to remotesensing retrieval methods.

We focus in the following on the quantitative assessment of thetotal estimation uncertainty (sum of i) through iii)) through cross-validation techniques, and of the error induced in SPM concentrationretrievals by the uncertain determination of model parameters(source iii)), often the dominant contribution to the overalluncertainty. This latter quantification is obtained by estimating theprobability distribution of model parameters and of the associateduncertainty in SPM concentration retrievals using bootstrap proce-dures. The Matlab codes implementing the model introduced aremade available as supplementary online material.

2. Methods

2.1. The radiative transfer model

The remote sensing reflectance of a ‘water pixel’ is a function of thewater depth, of the properties of thematter suspended in it, and of theoptical properties of the bottom. In order to obtain a physically-basedestimation of SPM concentration we invert a simple radiative transfermodel (Lee et al., 1998, 1999), which links the directional remotesensing reflectance in the nadir direction (at a fixed wavelength ofinterest, λ, which is omitted here to simplify the notation) to the

controlling physical factors in a direct and controllable manner. Thebelow-surface remote sensing reflectance rrs (sr−1) is defined as theratio between upwelling (directional) radiance and downwellingirradiance (Table 1). In this framework, it is modeled as:

rrs = rdprs 1−e− Kd + KCuð ÞH

� �+

ρbπe− Kd + KB

uð ÞH ð1Þ

where:

– H=water depth (m);– ρb=bottom albedo (assuming bottom as a Lambertian reflector);– r rs

dp=subsurface remote sensing reflectance for an infinitely deepwater column 1 = srð Þ = 0;084 + 0;17uð Þu (Lee et al., 1999);

– u=bb /(a+bb), with bb backscattering coefficient (1/m) and aabsorption coefficient (1/m);

– Kd=Ddα=downwelling diffusive attenuation coefficient;– Ku

C=DuCα=upwelling diffusive attenuation coefficient due to the

water column;– Ku

B=DuBα=upwelling diffusive attenuation due to the bottom

reflectance;– α=a+bb;– Dd=1/cos Θw,Θw=subsurface solar zenith angle (rad);– Du

C=1,03(1+2,4u)0,5 (Lee et al., 1999);– Du

B=1,04(1+5,4u)0, 5 (Lee et al., 1999).

A complete list of symbols is provided in Table 1. The above-surface remote sensing reflectance Rrs (sr−1), defined as the ratiobetween water-leaving radiance and downwelling irradiance, may beexpressed, for the nadir direction, by the following approximaterelationship (Lee et al., 1999):

Rrs =0:5rrs

1−1:5rrs: ð2Þ

Eqs. (1) and (2) together constitute a model relating the surfacedirectional remote sensing reflectance Rrs, which can be obtained fromremote sensing observations upon proper atmospheric correction,with the quantity and type of matter suspended in the water column.In fact, the absorption and backscattering coefficients are influencedby suspended sediments (organic or inorganic), dissolved solids and

46 V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

suspended phytoplankton. These coefficients may have a significantvariation because of the specific properties of the sediments (e.g. thegrain size distribution) and are in the following determined bycalibration. However, physically meaningful values of these para-meters fall within somewhat limited intervals, allowing additionalconstraints and control on the formulation of the model, as well as thepossibility of assigning parameter values on the basis of sedimentcharacteristics or by analogy with similar sites.

The influence of the different components of the total solids in thewater column (suspended inorganic and organic matter, dissolvedorganic matter, etc.) on its optical properties strongly depends on thewavelength considered. Here we choose, consistently with previousliterature (e.g. Petzold, 1972; Gallegos & Correl, 1990; Ferrari &Tassan, 1991; Li et al., 2003; Babin et al., 2003a,b; Binding et al., 2005;Bowers & Binding, 2006), to focus on the value of remote sensingreflectance at λ=650nm, where the sensitivity to suspendedsediment concentration is high, while effects e.g. by chlorophyll andorganic particles are limited (e.g. Mobley, 2004).

The total absorption coefficient, a, is expressed as the sum of theabsorption coefficients of pure water aw (aw(λ=650nm)=0.3594m−1,Pope& Fry, 1997), inorganic particles aNAP, phytoplankton aph, andorganicparticles aCDOM:

a = aw + aNAP + aph + aCDOM : ð3Þ

aNAP may be assumed to be a linear function of the SPMconcentration (in g/m3), as proposed in Babin et al. (2003b) forλ=443nm:

aNAP λ = 443nmð Þ = γ⋅SPM ð4Þ

Previous studies allow the computation of possible values for γ(e.g. parameter values given in Babin et al. (2003b) yieldγ=0.041m2/g in the northern Adriatic Sea) but, because of itsdependence on local sediment characteristics, we choose to deter-mine γ by calibration. In what follows we then use the relation aNAP(λ)=aNAP(λ=443nm)0.75e−0.0128(λ−443) (Babin et al., 2003b) toobtain aNAP(λ=650nm).

The phytoplankton absorption coefficient can be linearly related tothe chlorophyll-a concentration, Ca, as aph(λ=650nm)=aph

* ⋅Ca, withaph* =0.0077m2/mgChla, the specific phytoplankton absorption coef-

ficient (Gallegos & Correl, 1990). Knowledge of the chlorophyll-aconcentration (e.g. from reflectance information in other spectralbands) can be used to eliminate Ca from the absorption model. Inorder to quantify the advantage of accounting for chlorophyll effects,we used chlorophyll concentrations observed simultaneously withSPM concentrations and found that the associated correction to theabsorption term was not significant for the estimation of SPMconcentrations. We thus choose to fix chlorophyll-a concentrationto a nominal value in subsequent analyses (3mg/l, the summeraverage in the Venice lagoon).

Similarly, we assume aCDOM(λ)=aCDOM(λ=375nm)e−0.0192(λ−375)

(Babin et al., 2003b) (aCDOM(λ=375nm)=1.25m−1 consistently withparameter values derived from Ferrari & Tassan (1991) for theNorthernAdriatic Sea). Tests with different assumptions for aCDOM(λ=375nm)show little sensitivity on its specific value in a relatively largerange.

The backscattering coefficient bb is the fraction of the total scatteringcoefficient, b, determined by photons scattered at an angle greater than90°. Here we adopt a fixed value of the ratio bb/b=0.019 determinedobservationally (Petzold, 1972; Binding et al., 2005; Bowers & Binding,2006). The total scattering coefficient b is expressed as the sum ofcontributions by pure water bw, phytoplankton bph, and inorganicparticles bNAP:

b = bw + bph + bNAP : ð5Þ

Scattering by inorganic particles dominates other scatteringsources, such that bw and bph may be neglected with respect to bNAP(Pope & Fry, 1997; Binding et al., 2005; Bowers & Binding, 2006).Following Babin et al. (2003a) we set:

bNAP λ = 650nmð Þ = η⋅SPM ð6Þ

(based on bNAP(λ=650nm)=η1 ⋅bNAP(λ=555nm) and bNAP λ =ð555nmÞ = η2⋅SPM, η=η1 ⋅η2).

η is here determined by calibration, due to its dependence onsediment properties. Previous studies (Babin et al., 2003a) allow thecomputation of the value η=0.405m2/g, which may be used as aterm of comparison for calibration results.

The bottom albedo is a function of the type of bottom sedimentand of the possible presence of vegetation or of benthic organisms. Inthe following, we perform a sensitivity analysis of the SPMconcentration retrieved by the use of Eq. (1) on the basis of valuesof ρb within a range consistent with observations.

2.2. Study site and observations

The Venice lagoon (Fig. 1) has an area of about 550 km2, a meanwater depth of about 1.1 m, and is characterized by a tidal range ofabout 1.3 m, with a main periodicity of about 12 h.

Water quality and sediment transport are very important issues inthe Venice lagoon due to the high water residence times, particularlyin the inner parts of the lagoon, and to the large net outgoingsediment flux associated with a diffuse erosion of tidal morphologies(Fagherazzi et al., 2007; Marani et al., 2007).

A network of multi-parametric probes (currently 10, see Fig. 1)monitors with a half-hourly temporal resolution several key waterquality parameters, among which are turbidity and chlorophyll-aconcentration (the network is managed by the Venice WaterAuthority, see http://www.magisacque.it/sama/sama_monitoraggi1.htm). Water turbidity is measured through a backscattering opticalprobe (Seapoint turbidity meter, operating at 880 nm) and isexpressed in Formazine Turbidity Units (FTU), 179 which may bedirectly related to the suspended sediment concentration (Old et al.,2001). Pressure measurements at the probe allow the determinationof the local instantaneous water depth. In fact, because the tidalamplitude is comparable to the mean water depth, the localinstantaneous water depth varies significantly over time and thismust be properly accounted for in the radiative modelling and SPMconcentration retrieval scheme.

A set of 13 multispectral satellite acquisitions was used to matchfield observations for the calibration and validation of the SPMconcentration retrieval scheme. In the search through archivedremote sensing data only cloud-free acquisitions were selected inorder to minimize uncertainties due to possibly heterogeneousatmospheric conditions. We purposely chose to use data fromdifferent sensors in order to explore the possible impacts of specificsensor characteristics and spatial resolution. In particular we useddata from the Landsat TM5, Landsat ETM7, ASTER and ALOS AVNIRsensors. These are all nadir-viewing sensors, with a narrow field ofview (FOV) (FOV=5° for ASTER and ALOS, FOV=15° for Landsat),consistently with the narrow field of view assumption embedded inthe radiative transfer model for the water column (Section 2.1). Thekey technical characteristics of the satellite sensors/data involved inthe study are summarized in Table 2.

We note that resolution is an important issue when comparingremote sensing data from different sensors (which provide an integralmeasure of surface optical properties) and in situ point observations.However, the distribution of SPM concentration is generated by theinteraction of wind waves with the bottom sediment and ismodulated by the lagoon morphology. The typical spatial correlationscales of wind fields and of the bathymetry of the tidal flats where the

Fig. 1. Map of the Venice lagoon with the 10 in situ observation stations.

47V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

turbidity sensors are located are larger than the resolutions of the dataconsidered here and the suspended sediment concentration may thusbe assumed to be homogeneous within each pixel. Hence, it isreasonable to ‘mix’ remote sensing data with the different resolutionsconsidered here, and to compare the information retrieved with pointin situ observations.

In order to retrieve the at-surface reflectance information, theremote sensing data have been radiometrically calibrated andatmospherically corrected by use of MODTRAN 4.1 (as implementedin ATCOR 2/3, see Richter, 2009). The radiometric calibration, ie. theconversion of digital numbers into radiances, was performed usingimage-specific information provided in each imagemetafile.MODTRANallows the determination of the downwelling spectral irradiance and ofthe at-surface upwelling spectral radiance in the nadir direction frommeasured radiances (all sensors used are nadir-viewing and the in-scene variation of the view angle has been neglected), the observationgeometry for each image (sun azimuth and elevation), and theatmospheric parameters, thereby allowing the estimation of thespectral directional reflectance for the nadir direction, R̂rs. Atmosphericproperties were defined in terms of aerosol type, water vapour andvisibility. The specification of the aerosol type determines theabsorption and scattering properties of the particles and the wave-

Table 2Technical characteristics of the satellite sensors/data used in the study.

Sensor Spectral band used (μm) Pixel size (m) Number of images

LANDSAT 5TM B3 0.63−0.69 30 2LANDSAT 7ETM B3 0.63−0.69 30 2ASTER VNIR B2 0.63−0.69 15 8ALOS AVNIR2 B3 0.61−0.69 10 1

length dependence of the optical properties. We assumed here themaritime aerosol type (see Richter, 2009; Cattrall & Thome, 2003),which produced the best match with available reference spectra. Thewater vapour content has been estimated on the basis of season(midlatitude summer or winter according to the acquisition period, seeRichter, 2009 for definitions). The visibility, assumed to be constantwithin each scene, was computed from the aerosol optical thickness at550nm obtained from a CIMEL CE-318-2 sun photometer from theAERONET network (http://aeronet.gsfc.nasa.gov). The computed visi-bility values range between 30 km and 70 km.

The images have finally been georeferenced with a typical RMSEsmaller than 1 pixel size and a maximum RMSE smaller than 1.5 pixelsize, thus ensuring an accurate matching between remote sensing andfield observations.

The value of the nadir directional reflectance at the surfaceretrieved from remote sensing, R̂rs, may now be used on the left-hand side of Eq. (2), which allows, upon consideration of Eq. (1)and proper calibration, the estimation of SPM, the only remainingunknown.

After geocoding, the remote sensing reflectance values relative tothe pixel containing each observation station was extracted andpaired to the measurement performed at the time closest to theacquisition time. The data selection procedure and the variablenumber of stations active at any time resulted in a data set consistingof 53 data pairs, to be used for calibration and validation.

Observations of bottom reflectance (mean of 0.027sr− 1 atλ=644nm), were available from just one site in the lagoon, withina shallow area with silty-sand bottom sediment (MAV, 2004). Bottomreflectance estimates were derived from simultaneous upwellingand downwelling radiance and irradiance observations (SeaPRISMradiometer, see Zibordi et al., 2004). Data were collected with an

Fig. 2. Calibration of the relation Rrs SPM;Hð Þ of the full set of 53 observations. Notice thatRrs SPM;Hð Þ is here represented by ‘projecting’ the dependence on H onto the SPM;Rrsð Þplane.

48 V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

azimuth angle of 90° with respect to the sun plane, and with a nadirview angle of 40° (S95 protocol (Mueller & Austin, 1995)).

3. Results

3.1. Model calibration and validation

A possible limitation to the application of Eq. (1) to the retrieval ofSPM concentration lies in the term on the right-hand-side of Eq. (1)involving the bottom albedo, ρb. This term tends to become importantwhen the water depth is low and/or when the turbidity is low. ρb isnot usually known in a spatially-distributedmanner andmay be time-dependent (e.g. due to vegetation, algal, and microphytobenthosdynamics). Attempts can be made to estimate the bottom reflectancefrom remote sensing data collected under clear-water conditions.However, it is in practice impossible to identify situations in whichSPM is nearly zero everywhere. This circumstance makes theestimation of ρb rather uncertain, because relatively small changesin the assumed SPM, particularly when the suspended concentrationis low, can induce significant differences in the estimated values. Inthe following we will thus use a single bottom reflectance valuederived from the point observations described above and, in order tolimit the inaccuracies involved in this assumption, wewill identify theconditions under which the specific value assumed significantlyaffects the retrieved SPM concentration.

Once the bottom reflectance has been specified, Eq. (1) onlycontains the unknown SPM concentration and the yet-undeterminedparameters describing absorption and scattering processes as afunction of SPM (Eqs. (4) and (6)). Because of their impact on thecomputed reflectance and their potential dependence on site-specificsediment properties, such as the grain size distribution, we choosehere to calibrate them on the basis of the available field observationsrather than to use generic literature values. The estimation of SPMconcentration thus first requires the calibration of the parameters γand η in Eqs. (4) and (6) respectively, using the concurrent remotesensing and in situ observations available.

A calibration procedure requires the minimization of a scalar errordefining the departure of the model from observations in the planeSPM;Rrsð Þ. Because both the observed SPM and R̂rs values are affectedby relevant observation errors, a reasonable definition of distancebetween the model curve and the data points is the sum of thedistances between curve and experimental points in the directionorthogonal to the curve itself. This involves using an OrthogonalDistance Regression (ODR, see Boggs et al., 1989, 1992; Zwolak et al.,2007). However, there is some degree of subjectivity as to how thedistance components along the two axes (SPM and Rrs, which havedifferent units and represent different physical quantities) should berescaled in order to compute the point to curve distance. In particular,rescaling the observed reflectance and SPM values to the [0,1]interval, typical in the ODR literature, is not necessarily justified. Infact, because we are interested in estimating the SPM concentration, asecond reasonable choice is minimizing the Root Mean Square Error(RMSE) in the direction of the SPM-axis. We have implemented bothprocedures and found that the results are similar and that theminimization of distances in the SPM direction produces smallerprediction errors in the validation phase. We thus only describe theresults from the latter procedure in what follows. The minimization ofRMSE in the SPM direction produces the results represented in Fig. 2,with parameters η=0.4695m2/g and γ=0.2044m2/g. It is importantto emphasise here that Fig. 2 provides, for the sake of a more effectiveillustration, a cross-sectional representation in the SPM;Rrsð Þ plane of arelationship involving three quantities SPM, Rrs, and H. In fact,reflectance is a function of both SPM concentration and waterdepth, as seen in Eqs. (1) and (2).

After having calibrated the absorption and backscattering para-meters of the retrieval procedure, we now address the sensitivity of

the retrieval scheme to different assumptions for the bottomreflectance value. As noted above, the bottom sediment reflectance(at the chosen wavelength λ=644nm) is here assumed to beρb=0.027 π=0.08 (assuming the bottom sediment is a Lambertianreflector), based on in situ observations.

Observed reflectance values in the literature range from 0.04 to0.22 for silt and from 0.38 to 0.53 for sandy sediments (Durand et al.,2000; Albert & Mobley, 2003; Mobley, 2004). Because of the typicallysilty nature of the bottom sediment in the Venice lagoon we will hereexplore possible values in the range 0.04–0.25 and determine underwhat conditions important variations in the estimated SPM concen-trations arise. It is seen (Fig. 3), that variations in ρb induce differencesin the retrieved values of SPM concentrations for relatively smallwater depths and turbidity. In particular, for a depth of 1.3 m, therange of bottom sediment reflectance values considered producesmaximum deviations in the retrieved SPM concentration of about15 FTU. Estimates of SPM concentration for intermediate values ofSPM are moderately unaffected by the uncertainty in the bottomsediment reflectance (e.g. for SPM=20 FTU the maximum deviationin the retrieved SPM concentration is about 30% depending on theassumed bottom reflectance). For high SPM concentrations theinfluence of the bottom reflectance vanishes.

In the following we will thus exclude from the calibration/validation process the data corresponding to a water depth smallerthan 1.3 m, for which the contribution of the bottom reflectance to thetotal reflectance would be greater than 10% (fora reference SPMconcentration of 20 FTU).

Validation is a fundamental phase in the development of anestimation procedure in order to provide an evaluation of the overallreliability of the retrieval scheme and a characterization of theuncertainty which should be associated with the estimated values.The model performance must be evaluated on independent observa-tions, i.e. observations which have not been used in the calibrationphase. In order to obtain such an independent evaluation of theestimation error (i.e. the sum of errors i) to iii) discussed in theIntroduction) we adopted a leave-one-out cross-validation procedure(Wilks, 2006). In this procedure all but one observed SPM;Rrsð Þ pairsare used to calibrate the parameters of the retrieval model. Anestimation error (observed SPM — estimated SPM) is then computedfrom the excluded SPM;Rrsð Þ pair. The procedure is repeated byexcluding, in turn, all N available pairs (N=53 in this case). Thescatterplot comparing estimated and observed turbidity values fromthe leave-one-out procedure (Fig. 4) shows the absence of a

Fig. 3. Sensitivity of the model to different bottom reflectance values for different waterdepths: (a) 1 m, (b) 1.3 m and (c) 2 m. The sensitivity of the retrieved SPMconcentration values on the bottom albedo decreases rapidly with depth, such thatits contribution to the total reflectance is down to about 10% for H=1.3 m a referenceSPM concentration of 20 FTU.

Fig. 4. Scatterplot of estimated and observed turbidity values obtained from the leave-one-out procedure.

Fig. 5. Confidence intervals for estimated turbidity values obtained from the bootstrapprocedure. The dashed lines bound the 65% confidence interval. Only point observa-tions for depths in the range 1.5–1.7 m are reported for comparison.

49V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

significant estimation bias (the average estimation error is about−1.1 FTU) and the relatively modest scatter between predicted andobserved values (the error standard deviation is 14.3 FTU).

A cross-validation procedure was also applied to the estimationmodel obtained from the ODR regression scheme described above.The results (not shown here for brevity) yield an average estimationerror of−24.0 FTU and a standard deviation of 79.6 FTU, showing thatindeed the minimization of errors along the ‘turbidity axis’ providesmore accurate SPM concentration predictions.

Leave-one-out cross-validation is useful to provide an overallassessment of the model accuracy. However, it does not allow anevaluation of the dependence of the estimation error on the turbidityvalue. Such an evaluation, for the estimation error associated with theuncertainmodel parameters, can be achieved through a non parametricbootstrapmethod (Efron, 1979). Herewe adopt a bootstrap resamplingmethod, inwhich the observed set of SPM;Rrsð Þ pairs is re-sampledwithre-substitution (i.e. a pair that has been extracted is available forpossible subsequent sampling). In the present case the observed setwasre-sampled 10,000 times, a number determined by making sure that afurther increase in the number of pairs considered does not produceappreciably different results. This procedure essentially constructs alarge number of samples from the same empirical distribution. Themodel is then calibrated on each of the re-sampled SPM;Rrsð Þ sets toobtain a sample of (10,000) parameter values and a set of correspondingcurves (which yield the shaded area in Fig. 5).

Fig. 6. Frequency distributions of the calibrated parameters obtained via bootstrap. Thestandard deviations are 0.062m2/g for γ and 0.081m2/g for η and the calibrated valueslie close to the mean.

50 V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

Fig. 6 represents the estimated probability density functions of theestimators ofγ and η, obtainedwith thebootstrapmethod. The standarddeviation is 0.062m2/g for γ and 0.081m2/g for η. For both theestimators, themean value of the distribution is very close to the valuesobtained in the calibration using all the 53 experimental values. In thecase of γ the mean value of the distribution is 0.188m2/g, whilecalibration on the entire experimental dataset gives 0.204m2/g. For η,themean value of the distribution is 0.446m2/g and the result of modelcalibration is 0.469m2/g. This is a further confirmation of the robustnessof the model calibration. Furthermore, we note that the literature valuefor the backscattering coefficient (η=0.405m2/g (Babin et al., 2003a))also falls well within a standard deviation from the estimationmean. Asfor the absorption coefficient, we obtain a calibrated value which isgreater than literature values from comparable sites (γ=0.041m2/g(Babin et al., 2003b)). However, the literature value takenhere as a termof comparison corresponds to a secondary relative maximum in theestimated probability density function of this parameter.

Table 3Standard deviation of estimated turbidity via bootstrap (FTU), for different reflectance and

Rrs 0 0.003 0.006 0.010 0.01

h=1.30 m 6.32E−12 1.52E−11 0.79 1.68 2.33h=1.60 m 2.00E−11 1.43E−10 1.00 1.76 2.33h=1.90 m 1.70E−12 0.21 1.12 1.80 2.33h=10 m 4.86E−09 0.71 1.33 1.85 2.28

The confidence intervals for SPM estimates are then obtained bythe percentile method, by identifying the empirical 17.5% and 82.5%quantiles as a function of reflectance, as shown by the dashed lines inFig. 5. We have calculated these confidence intervals by inverting themodel (1) for each pair of the bootstrap-estimated parameters. Due tothe important influence of water depth this procedure was repeatedfor different values of H of applicative interest. Fig. 5 shows a sampleresult for H=1.60m. As discussed above, upper and lower bounds inFig. 5 express the uncertainty induced in SPM concentration estimatesby the uncertainty in parameter estimation as characterized by thedifferent samples originated by the bootstrap procedure. It is importantto note that other factors contribute to the observed differencesbetween measured and estimated SPM concentrations. In particular,turbidimetric observations are also affected by significant uncertainty,which explains the spread of observational points beyond the boundsdefined by parameter uncertainty.

Results for other values of the water depth, not shown for brevity,are all very similar as indicated by the standard deviation values listedin Table 3 for a wide set reflectance and depth values.We note that theestimation standard deviation increases with reflectance (Table 3)and with turbidity (Fig. 5).

3.2. Mapping SPM concentration

The calibrated and validated radiative transfer model was used toproduce maps of turbidity for the satellite images available. In thiscase, the water depth, necessary for the SPM concentration retrieval,was obtained from a recent bathymetry and a detailed finite-elementhydrodynamic model (Carniello et al., 2005). Fig. 7 shows a sampleturbidity map produced using the ASTER data acquired on 24 June2007. This information is complemented by the distribution ofestimation accuracy (Fig. 8), as represented by the estimation errorstandard deviation, which allows an immediate appreciation of theareas in which estimates are most reliable. The error standarddeviation is quite small in the central and southern parts of theVenice lagoon (values are between 0.2 and 3 FTU), while themaximum values (about 34 FTU) are observed in the northern andlandward parts of the lagoon.

We notice that turbidity values are, as expected, lower in thecentral part of the lagoon, characterized by deeper waters, and in themain channels. This feature is consistently observed in all theacquisitions analyzed, as shown in Fig. 9, which shows the spatialdistribution of mean turbidity as computed from the set of imagesavailable. It is interesting to note that the particularly low turbidityvalues observed in the southern part of the lagoon may be connectedto the presence of bottom vegetation. The red line in Fig. 9 bounds thearea where phanerogams occur (mainly zostera marina and cymodo-cea nodosa) as indicated by in situ mapping for 2004 (MAV, 2004). It isseen that most of the areas with low average turbidity are indeedcolonized by bottom vegetation, providing compelling evidence of thestabilizing effect exerted by macrophytes in tidal areas.

4. Discussion and conclusions

We have developed a new SPM concentration retrieval algorithmbased on a simple, and yet physically-based, radiative transfer modelapplied to satellite-measured reflectance at λ=650nm. The model

depth values.

3 0.016 0.019 0.022 0.025 0.029 0.032

2.82 3.17 3.63 5.31 11.24 34.022.76 3.07 3.56 5.43 11.57 34.352.72 3.01 3.54 5.53 11.76 34.512.61 2.90 3.54 5.69 11.97 34.66

Fig. 7. Map of estimated turbidity for the ASTER image acquired on 24 June 2007. The inset shows the day tidal oscillation and the tidal level at the moment of acquisition.

51V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

was calibrated and validated using in situ turbidity observations. TheSPM concentration retrieval algorithm performs well according to theleave-one-out cross-validation procedure applied, with negligible biasand an overall error standard deviation of about 14 FTU. The formalbootstrap method applied allowed the determination of estimationconfidence intervals quantifying the uncertainty associated withmodel parameters. The confidence interval defined is, as expected,wider for larger FTU values.

The statistical distributions of absorption and backscatteringparameters obtained from the bootstrap procedure yield coeffi-cients which are coherent with those from the existing literatureon coastal areas in the Adriatic Sea. This is not an obvious result, asthe optical properties of suspended sediments depend (at least) onthe grain size distribution, which is expected to be significantlydifferent in lagoons (where fines are typically abundant) withrespect to coastal seas.

Fig. 8. Map of the estimation error standard deviation for the ASTER image acquired on 24 June 2007 computed on the basis of the values in Table 3.

52 V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

A distinct advantage of the proposed methodology, because itmakes use of a bootstrap technique, is the possibility to producesediment concentration maps along with the associated uncer-tainty maps. This immediately allows the identification of theareas where remote sensing estimates may be considered to bereliable.

The inversion of the radiative transfer model allows concludingthat the bottom albedo does not significantly affect the SPMconcentration estimates for the turbidity values of typical interest insediment transport studies, i.e. for moderate to large turbidity valuesand greater water depths. This is for example important whenattempting to identify erosion hotspots and areas where sediment

Fig. 9. Map of mean turbidity as computed from the set of available images. The red shape represents the area where macrophytes plants are present.

53V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

fluxes are relatively large, thus giving the largest contribution to theoverall sediment budget.

The retrieval method was here developed and applied on the basisof satellite observations from different sensors. The sensors exploredhere yield retrievals which are quite consistent, implying that theatmospheric correction scheme applied allows an accurate determi-

nation of surface reflectance. The possibility of using differentplatforms with homogeneous results significantly indicates thatmonitoring and analysis procedures based on remote sensing canexploit the full range of existing sensors. While satellite data allowone to draw from a large existing database of past observations,interesting applications of the proposed algorithm can be envisioned

54 V. Volpe et al. / Remote Sensing of Environment 115 (2011) 44–54

using airborne and proximal sensors. Airborne sensors can be used toperform targeted and high-resolution surveys during intense re-suspension events, which play a dominant role in determining themorphodynamic evolution of estuaries and lagoons. Proximal sensors,e.g. mounted on fixed and tall structures, could be used to provide acontinuous monitoring of suspended sediment in areas of particularinterest (e.g. tidal inlets, where the overall sediment budget can becomputed), with accuracies rivaling those obtainable from turbiditysensors (particularly if uncalibrated) and acoustic devices (e.g.ADCP's) and with a much wider areal coverage. In these settings themethod developed here to assess the uncertainty associated with theestimations is of particular importance, in order to provide a measureof the accuracy with which the sediment budget can be described.

The algorithms for the estimation of the suspended sedimentconcentration and of the associated uncertainty are thus shown toallow reliable and repeatable SPM concentration estimates even inshallow intertidal areas, where remote sensing methods werepreviously applied with limited success and where alternativemethods of observation can only provide point measurements oflimited use in closing the sediment budget.

Acknowledgements

This work was supported by the Ministero delle Infrastrutturee dei Trasporti — Magistrato alle Acque di Venezia and by thePRIN research project “Eco-morfodinamica di ambienti a marea ecambiamenti climatici”. We thank the Consorzio Venezia Nuova –

Servizio Ambiente – for providing data and reports of MELa2Projects. We thank Dr. Alberotanza and Dr. Zibordi for providingCIMEL data as a part of the NASA AERONET Project. We also thankAndrea Defina and Luca Carniello for kindly providing thedistribution of water levels derived from a numerical hydrodynamicmodel of the Venice lagoon.

Appendix A. Supplementary data

Supplementary data to this article can be found online atdoi:10.1016/j.rse.2010.07.013.

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