Albedo estimation from PolDER data

Transcription

1 Albedo estimation from PolDER data F. Jacob 1, M. Weiss 1, A. Olioso 1, O. Hautecoeur 2, C. François 3, M. Leroy 2, and C. Ottlé 3 1 INRA Bioclimatologie, Domaine St Paul, Avignon Cedex 9, France 2 CESBio, 18 avenue E.Belin, BP 2801, Toulouse Cedex 4, France 3 CETP / IPSL / CNRS, avenue de l Europe, Velizy, France Camera-ready Copy for Physics and Chemistry of the Earth Manuscript-No.??? Offset requests to: F. Jacob INRA-Bioclimatologie Domaine St Paul, Site Agroparc Avignon Cedex 9 France

2 First author: Jacob 1 Albedo estimation from PolDER data F. Jacob 1, M. Weiss 1, A. Olioso 1, O. Hautecoeur 2, C. François 3, M. Leroy 2, and C. Ottlé 3 1 INRA Bioclimatologie, Domaine St Paul, Avignon Cedex 9, France 2 CESBio, 18 avenue E.Belin, BP 2801, Toulouse Cedex 4, France 3 CETP / IPSL / CNRS, avenue de l Europe, Velizy, France Received??? Accepted??? Abstract. Multi-spectral and multi-directional data acquired during the ReSeDA experiment thanks to the airborne Pol- DER sensor were used to retrieve surface albedo over the experimental site, for 16 days over the year The data were available in four wave-bands (10 or 20 nm width) centered at 443 nm, 550 nm, 670 nm, and 865 nm. Zenith view angles ranged from 0 to 50 o. This study aimed at evaluate a procedure based on the use of multi-directional and multi-spectral information to retrieve surface albedo. Multidirectional information was extracted thanks to BRDF kerneldriven models. We compared the performances of three models (Walthall, Roujean and MRPV) in the four PolDER channels. The spectrally integrated value of the albedo was then derived from the of the hemispherical reflectance estimates in the four wave-bands, thanks to the linear regressions proposed by Weiss et al. (1999). 20 m resolution albedo maps were computed, and then compared to field measurements over several crop fields considering all days of the experiment. Results showed that PolDER retrievals overestimated ground measurements. This might be explained, at least partially, by inappropriate linear combinations used for the spectral extrapolation. 1 Introduction Surface albedo is defined as the fraction of incident solar energy over the whole solar spectrum reflected in all directions (Pinty and Verstraete, 1992). It is especially important for the global climate modeling (Dickinson, 1983), as well as for surface fluxes estimation (Kustas et al., 1994; Olioso et al., 1999). Generally, a relative accuracy of ±5% is required (Henderson-Sellers and Wilson, 1983). In this study, we map surface albedo using multi-directional and multi-spectral remotely sensed data acquired with the airborne PolDER sensor during the ReSeDA experiment. The determination of albedo from remote sensing depends on two Correspondence to: F. JACOB aspects: i) the anisotropic behavior of natural surfaces requires the characterization of the angular distribution of the reflected solar radiation (expressed as BRDF for Bidirectional Reflectance Distribution Function) from the available directional measurements in a given wave-band; ii) the determination of the reflected energy over the whole solar spectrum from the wave-band estimates requires a spectral extrapolation. Several methods have been developed to characterize the BRDF from satellite data. Two classes may be distinguished: the inversion of radiative transfer models, and the inversion of kernel-driven models. As the first one is mathematically complex and time consuming, we have chosen to consider the second one, which has been validated by several authors (see the review by Wanner et al. (1997)). Generally, the spectral extrapolation is performed thanks to linear combinations. Several coefficient sets have been proposed and validated in the literature (e.g. Tucker and Sellers (1986); Brest and Goward (1987); Song and Gao (1999)). In this study, we have chosen to use the coefficients proposed by Weiss et al. (1999). The ReSeDA experiment provided a framework with two interesting aspects for the validation of the proposed approach: i) it covered the whole cycles of different types of crops including winter (wheat) and summer crops (sunflower, corn); ii) the high spatial resolution remote sensing data reduced problems related to mixed pixels. 2 Data acquisition and preprocessing 2.1 The ReSeDA Field Experiment The ReSeDA experiment lasted from December 1996 to December 1997, in the South East of France (N 43 o 47, E 4 o 45 ). The experimental site was a small agricultural region (5 5km 2 ) with sunflower, wheat, corn, grassland and alfalfa fields with a mean size of m 2 (Prévot et al., 1998; Olioso et al., 1998).

3 First author: Jacob Airborne data Airborne PolDER data were acquired approximately one or two times per month, on clear sky days and at a 3000 m altitude involving a 20 m nadir spatial resolution. Four flight lines were parallel to the solar plan, and one perpendicular. These five lines were completed within 45 minutes centered at the solar noon. The data were available in four wave-bands (10 or 20 nm width) centered at 443 nm, 550 nm, 670 nm, and 865 nm. Zenith view angles ranged from 0 to 50 o. Sensor calibration was performed by the L.O.A. (Laboratoire d Optique Atmosphérique, Lille, France) with a 3 month frequency. The procedure accounted for ambient temperature, dark current, and inter-calibration of CCD matrix detector. Its accuracy was about 5%. Atmospheric effects were corrected thanks to the SMAC algorithm (Rahman and Dedieu, 1994) based on the inversion of the atmospheric radiative transfer model 6S (Vermote et al., 1997). The required information consisted in aerosol optical thickness, water vapor content, both estimated from field sunphotometer measurements, and ozone atmospheric concentration obtained from TOMS climatic daily data. Each image was registered thanks to a Global Positioning System and an inertial central data, according to a Lambert II projection. This projection provided a spatial sampling of the site corresponding to a grid of pixels with a 20 m resolution. All these pre-processing are described in details by Leroy et al. (2000). They allowed to derive BRDF samplings that depended on both the location on the site and the flight line configuration. 2.3 Field data Field measurements of albedo were performed on seven locations corresponding to alfalfa, wheat, and sunflower crops. Albedo was deduced from measurements of incident radiation using a Kipp pyranometer located on the meteorological site, and measurements of reflected radiation using Kipp pyranometers or Skye silicon sensors looking to the ground surface. The data set corresponded to 20 minutes mean values having a circular footprint between 1000 and 3000 m 2. The spectral ranges of Kipp and Skye sensors were different, corresponding respectively to [ ] nm and [ ] nm. For the latter, it was necessary to consider the spectral behavior of the observed surface, in order to extrapolate the estimates over the whole solar spectrum. This has been performed thanks to a formulation of the actual albedo as a function of the measured one. The formulation was calibrated over simulations of the radiative transfer model SAIL (Verhoef, 1984, 1985) performed by François et al. (2000). Model input variables were soil and leaf optical properties, incident solar radiation from simulations of the atmospheric radiative transfer model 6S (Vermote et al., 1997) that took account for numerous atmospheric situations, and measurements of Leaf Area Index (LAI). Simulations of actual albedo and Skye estimates are described in details by François et al. (2000). The calibrated formulation had a linear shape, inducing a residual error of 0.003: Albedo actual =0:781 Albedo Skye +0:022 (1) 3 Methodology 3.1 Position of the problem From the definition given in Sect. 1, the instantaneous albedo a( s ;' s ) is expressed as following ( s and ' s are respectively the solar zenith and azimuth angles): a( s ;' s )= R 3000nm ρ h; ( s ;' s ) R g; d 300nm 3000nm R R g; d 300nm where is the wavelength. The spectral albedo or hemispherical reflectance ρ h; ( s ;' s ) represents the fraction of the spectral incoming solar radiation R g; reflected in the whole hemisphere. It is expressed through the bidirectional reflectance ρ ( s ;' s ; v ;' v ) ( v and ' v are respectively the view zenith and azimuth angles): ρ h; ( s ;' s )= R 0 2ß ß=2 R 0 ρ ( s ;' s ; v ;' v )cos v sin v d v d' v PolDER provided measurements of bidirectional reflectances ρ ( s ;' s ; v ;' v ) in the four considered channels. From these directional samplings, we estimated hemispherical reflectances ρ h; ( s ;' s ) by inverting BRDF kernel-driven models, and then the instantaneous albedo using a simple spectral extrapolation procedure. Both aspects are presented below. 3.2 Retrieving hemispherical reflectance using BRDF kerneldriven models The philosophy of a BRDF kernel-driven model is to express the bidirectional reflectance ρ ( s ; v ;' s ;' v ) thanks to a linear combination of n kernels N i (a kernel is a predefined function of view and solar angles): nx ρ ( s ; v ;' s ;' v )= ff i; N i ( s ; v ;' s ;' v ) (4) i=1 where ff i; are the weighting coefficients. The number and the formulation of the kernels N i differ from one model to another. Among the large number of kernel-driven models that were developed these last years, we have chosen to test three of them: Walthall (Walthall et al., 1985), Roujean (Roujean et al., 1992) and MRPV (Engelsen et al., 1996). Several studies showed that MRPV was the most accurate model both for the accuracy of the fitting and the extrapolation capabilities, while Walthall and Roujean were often presented as robust models (Baret et al., 1997; Wanner et al., 1997; Weiss (2) (3)

4 First author: Jacob 3 Coefficient Blue Green Red Near Infra-Red Set (445 nm) (560 nm) (665 nm) (865 nm) Set n o Set n o Set n o Table 1. Sets of coefficients for the computation of the albedo as a linear combination of wave-band hemispherical reflectances. et al., 2000). We should notice that Roujean and Walthall are linear models, while MRPV is a semi-linear one. The weighting coefficients ff i; might be obtained by inverting the model from the multi-angular data set. This was performed for each pixel and each PolDER channel using the procedure described by Weiss et al. (2000). The retrieved BRDF through these coefficients were then integrated to obtain the hemispherical reflectances ρ h;j in the PolDER channels (j =1;:::;4). 3.3 Spectral extrapolation from PolDER channels The spectral extrapolation was based on the assumption that for a given wavelength 2 [ ] nm, the hemispherical reflectance ρ h; ( s ;' s ) is a linear combination of the hemispherical reflectance ρ h;j ( s ;' s ) estimated in the four channels PolDER. Then, it was possible to express the albedo as: 4X a( s ;' s )= fi j :ρ h;j ( s ;' s ) (5) j=1 Several studies have been devoted to the determination of the coefficients fi j, but there is not at the present time any proposition for the PolDER sensor. In this context, we have chosen to test three sets of coefficients proposed by Weiss et al. (1999) when considering blue, green, red and near infrared channels (corresponding to 445, 560, 665 and 865 nm). These coefficients were obtained from a linear regression calculated over numerous soil coverage situations by the radiative transfer model DISORD (Myneni et al., 1992), between 400 and 2500 nm. These simulations were representative of several kinds of canopies at three different latitudes and for three days corresponding to different seasons. Coefficient sets are given in Table 1. The relative accuracy of these linear regressions was estimated as the Root Mean Square Error (RMSE) between simulated and retrieved albedo: it was about 7%. 4 Results and validation 4.1 Performances of BRDF kernel-driven models We evaluated the BRDF retrieval performances of the kerneldriven models by calculating for each pixel the absolute RMSE and the relative RMSE (RRMSE) between observed (ρ obs j ) Model Error Blue Green Red NIR MRPV Roujean Walthall RMSE RRMSE 24.6% 11.0% 11.8% 08.3% RMSE RRMSE 20.1% 11.6% 12.7% 08.6% RMSE RRMSE 20.8% 12.8% 13.6% 09.0% Table 2. Absolute and relative RMSE between observed and retrieved BRDF through the three kernel-driven models for the 10 April and retrieved (ρ ret j ) bidirectional reflectances: RMSE = vu u P RRMSE = RMSE <ρ obs j > t k=m k=1 (ρobs j (k) ρ ret 2 j (k)) where <ρ obs j > is the mean value of the m observed bidirectional reflectances. Results showed that the greatest errors occurred for pixels located on both the Alpilles mountain chain and field edges. In the first case, this might be explained by the inadequacy of BRDF models when they are applied to mountainous areas. In the second case, it might be explained by the combination of registration inaccuracy and spatial variability. Table 2 presents the RMSE and the RRMSE over the whole site for a representative day. The errors in the blue channel were more important whatever was the model, and maybe induced by the perturbations occurring in this channel such as the inaccuracy of the sensor calibration or the residual noise due to atmospheric diffusion by aerosols. The BRDF retrieval performances of the three models were very similar and slightly better for MRPV at 550, 670 and 865 nm. However, this model presented a great sensitivity to the perturbations mentioned previously. This high sensitivity could be explained by the semi-linear model formulation. When considering BRDF retrieval performances without pixels located on both the mountain chain and field edges, the models gave slightly better results, with a lower RRMSE about 3 to 5%. On the other hand, these performances were quite better when considering only pixels located on the field measurements, with a RRMSE divided by 2. We explained this by the homogeneity around field measurements locations, inducing small perturbations due to the combination of image registration inaccuracy and spatial variability. The comparison of the hemispherical reflectance estimates over the whole site showed differences between MRPV and the two others models. These differences were more important in the blue channel, for which MRPV provided numerous unrealistic values such as hemispherical reflectances close to one. Moreover, we observed that differences between models decreased with respect to the wave-band. There- m (6) (7)

5 First author: Jacob Channel 865nm 0.35 ρ h from Walthall s model ρ from Roujean model h Fig. 1. Comparison of hemispherical reflectance estimates from Walthall s and Roujean s models for the channel 865 nm when considering pixels located on field measurements. The solid line represents the linear regression between the estimates from the two models. fore, the hemispherical reflectance retrieval through kerneldriven BRDF models should be more stable with an increase of the wavelength. This observation was in agreement with the conclusions of Baret et al. (1997). When considering only pixels located on field measurements, Roujean overestimated the hemispherical reflectance as compared to the others models (see an example with Fig. 1), while the underestimation was observed for MRPV at 443 and 670 nm, and for Walthall at 550 and 865 nm. 4.2 Validation of albedo estimates Albedo calculations have been performed considering the three BRDF kernel-driven models and the three sets of coefficients. Therefore, nine albedo maps were computed for each day of the experiment (see for example Fig. 2). These maps depicted albedo values between 0.1 and 0.4. This important variability was explained by the simultaneous presence on the site of vegetative surfaces and bare soils. As expected, the lowest values corresponded to well vegetated fields or wet bare soils, while the highest ones corresponded to dry bare soils or very sparse vegetation. Since the field data and PolDER pixels had different footprints (Sect. 2), we assessed the impact of the spatial variability on the airborne albedo estimates by computing the relative standard deviation (standard deviation / mean value) inside both 3 3 and 5 5 PolDER pixel windows. The results, between 1 and 2%, underlined the negligible effect of the spatial variability around field measurement locations as much as the window size was smaller than the field one. Therefore, we decided to perform the validation by extracting PolDER estimates through 3 3 pixels windows. An example of comparison between field and airborne estimates of the albedo is given in Fig.3 for one kernel-driven Fig. 2. Albedo map for the 29 July 1997 using the MRPV model and the coefficient set n o 3. The Alpilles mountain chain has been removed. model and one set of coefficients. These comparisons showed that were no differences between Kipp and Skye estimates after the corrections of the latter (Sect.2). For each of the nine possibilities, we computed the absolute RMSE as in eq.6 and relative RMSE (RRMSE) as in eq.7, as well as the absolute bias (Bias) and relative bias (RBias) calculated as: k=m P k=1 (apolder (k) a in situ (k)) Bias = (8) M Bias RBias = (9) <a in situ > where a PolDER is the albedo estimated from PolDER data, a in situ is the albedo measured in-situ, and < a in situ > is the mean value of the M field data. The results are given in Table 3. Airborne retrievals were systematically higher than field estimates. Considering each model, an important overestimation occurred with the first coefficient set that cor- BRDF Model & Coefficient set RMSE RRMSE Bias RBias MRPV & set % % MRPV & set % % MRPV & set % % Roujean & set % % Roujean & set % % Roujean & set % % Walthall & set % % Walthall & set % % Walthall & set % % Table 3. Absolute and relative RMSE and Bias between airborne and field estimates of the albedo. The solid line represents the linear regression between the in-situ and airborne estimates.

6 First author: Jacob 5 Airborne estimates Field estimates from Kipp sensors Field estimates from Skye sensors In situ estimates BRDF Model & Coefficient set a b RMSE U RRMSE U MRPV & set % MRPV & set % MRPV & set % Roujean & set % Roujean & set % Roujean & set % Walthall & set % Walthall & set % Walthall & set % Table 4. Coefficient of the linear regression between field and airborne estimates of the albedo (a: slope, b: offset), and RMSE between PolDER estimate and the linear regression (RMSE U ). Fig. 3. Comparison between field and airborne albedo for the whole Re- SeDA experiment, considering the MRPV model and the coefficient set n 0 3. responded to the contributions of the red and NIR channels, while this overestimation decreased with a decrease in the red and NIR channels contributions. The comparison from a model to another with the same set of coefficient showed that the highest estimates were obtained with Roujean, while the lowest ones corresponded to Walthall. These observations were explained as following: Roujean provided the highest hemispherical reflectances whatever was the channel, and therefore the highest albedo values; since the absolute value of the bias between Walthall and MRPV hemispherical reflectances was lower in the red (0.0004) than in the NIR ( ), Walthall yielded the lowest albedo values with the set of coefficient n o 1; Walthall provided the lowest albedo values with the sets of coefficients n o 2 and n o 3 because it yielded the lowest hemispherical reflectances in the green and NIR channels. These results showed that the albedo retrieval strongly depends on the hemispherical estimates, and then requires accurate ones. Besides, the RMSE and bias were generally close from a model to another, while the high RMSE values were partially induced by the bias. At the present time, we think that this general overestimation could result from either the hemispherical reflectance estimates or the assumptions used when calibrating the linear combination (Sect.3). Indeed, the simulations performed by Weiss et al. (1999) to estimate the coefficients corresponded to the spectral interval [ ] nm, while the whole solar spectrum ranges between 300 and 3000 nm. Therefore, the incident solar radiation were lower than the actual one, by 6-8% referring to the works of Avaste et al. (1962). At a lower extent, the accuracy of these sets of coefficients was affected by the spectral difference between the radiative transfer model simulations and the PolDER wave-bands, as well as by the residual noises due to instrumental and atmospheric effects. In order to assess the accuracy that it would be possible to achieve, we calculated the coefficients of the linear regression between predicted (or airborne) and observed (or insitu) estimates, as well as the absolute and relative unsystematic RMSE (RMSE U and RRMSE U ) (see the Table 4). The RMSE U computes the scattering around the linear regression as the RMSE between the predicted values corrected from this regression and the actual ones (Kustas et al., 1996). The coefficients of the linear regression suggested that considering only hemispherical reflectances in red and NIR induced mainly an offset, while using more wave-bands seemed to provide an overestimation of low albedo values and an underestimation of high ones. Finally, the RMSE U computations showed that it would be possible to achieve an absolute accuracy between and for albedo values ranging from 0.1 to 0.25 after the removal of slopes and offsets. This would correspond to a relative accuracy ranging between 7 and 9%. We should notice that in this case, the result corresponding to the lower discrepancy would be obtained with the Roujean model when considering the hemispherical reflectances in the red and the NIR channels. 5 Conclusions The objective of this study was to map albedo on the Re- SeDA experiment site, using the airborne multi-spectral and multi-directional Vis-Near Infra-Red PolDER remote sensing data. Moreover, these high spatial resolution and multitemporal data allowed to perform a validation with less problems related to mixed pixels and over cycles of several crops. The multi-directional information was extracted through BRDF kernel-driven models. We tested three models (MRPV, Roujean and Walthall) that gave similar results for both the BRDF retrieval and the hemispherical reflectance estimation. However, results showed that the data set acquired in the blue channel have to be considered with care; and that the MRPV

7 First author: Jacob 6 model was the most sensitive to inaccuracy of both radiometric processing and image registration. The multi-spectral information was used by computing the albedo as a linear combination of the hemispherical reflectances in PolDER channels. We tested three sets of coefficients previously proposed as generic ones by Weiss et al. (1999). The validation thanks to field measurements underlined an overestimation whatever were the BRDF model and the set of coefficients. This could be explained by either the hemispherical reflectance estimates or the assumptions used for the calibration of the linear combination. The first point could results from the PolDER measurements or the kerneldriven model retrievals. The second point could result from the underestimation of the incident solar radiation. This could be improved by considering the whole solar spectrum when calibrating the linear regression. We observed that the removal of this overestimation should yield an absolute accuracy between and for albedo values ranging from 0.1 to 0.25 (which corresponds to a relative accuracy between 7 and 9%). Another possibility could be to take into account surface properties through the NDVI when calibrating the linear combination, as proposed by Song and Gao (1999). In the future, these maps could be used as a reference for validation at larger scale considering sensors such as NOAA / AVHRR for instance, and as inputs for surface energy balance calculation models (Jacob et al., 2000). However, one should note that for pixels far from the site center, the Pol- DER directional sampling quality was very poor and therefore that these results must be considered with care. References Avaste, O., Moldau, H., and Shifrin, K., Distribution spectrale des rayonnements directs et diffus, Instrumental and Physical Astronomy, 3, 44 57, Baret, F., Weiss, M., Leroy, M., Hautecoeur, O., Santer, R., and Bégué, A., Impact of surface anisotropies on the observation of optical imaging sensors, final report, Esa contract 11341/95/nl/cn, ESA, ESTEC, the Netherlands, Brest, C. and Goward, S., Deriving surface albedo measurements from narrow band satellite data, International Journal of Remote Sensing, 8, , Dickinson, R., Land surface processes and climate-surface albedos and energy balance, Advances in Geophysics, 25, , Engelsen, O., Pinty, B., Verstraete, M., and Martonchik, J., Parametric bidirectional reflectance factor models : evaluation, improvements and applications, Report eur16426en, European Commission, Joint Researches Center, Space Application Institute, ISPRA, Italy, François, C., Ottlé, C., and Olioso, A., Correction of silicon sensors albedo measurements using a canopy radiative transfer model, in Physics and Chemistry of the Earth, EGS symposium, special ReSeDA session, submitted, Henderson-Sellers, A. and Wilson, M., Surface albedo data for climatic modelling, Reviews on Geophysics, 23, , Jacob, F., Olioso, A., Gu, X., Hanocq, O., Hautecoeur, O., and Leroy, M., Mapping surface fluxes using Visible - Near Infra-Red and Thermal Infra-Red data with the SEBAL algorithm, in Physics and Chemistry of the Earth, EGS symposium, special ReSeDA session, submitted, Kustas, W., Moran, M., Humes, K., Stannard, D., Pinter, P., Hipps, L., Swiatek, E., and Goodrich, D., Surface energy balance estimates at local and regional scales using optical remote sensing from an aircraft platform and atmospheric data collected over semiarid rangelands, Water Resources Research, 30, , Kustas, W., Humes, K., Norman, J., and Moran, M., Single and dual source modeling of surface energy fluxes with radiometric surface temperature, Journal of Applied Meteorology, 35, , Leroy, M., Hautecoeur, O., Berthelot, B., and Gu, X., The airborne polder data during the reseda experiment, in Physics and Chemistry of the Earth, EGS symposium, special ReSeDA session, submitted, Myneni, R., Asrar, G., and Hall, F., A three-dimensional radiative transfer method for optical remote sensing of vegetated land surfaces, Remote Sensing of Environment, 41, , Olioso, A., Prévot, L., Baret, F., Chanzy, A., and et al., Spatial aspects in the alpilles-reseda project, in Scaling and modeling in forestry: application in remote sensing and GIS, Ed. D.Marceau, Université de Montréal, Québec, pp , Olioso, A., Chauki, H., Courault, D., and Wigneron, J., Estimation of evapotranspiration and photosynthesis by assimilation of remote sensing data into svat models, Remote Sensing of Environment, 68, , Pinty, B. and Verstraete, M., On the design and validation of surface bidirectional reflectance and albedo model, Remote Sensing of Environment, 41, , Prévot, L., Baret, F., Chanzy, A., Olioso, A., and et al., Assimilation of multi-sensor and multi-temporal remote sensing data to monitor vegetation and soil: the Alpilles ReSeDA project, in IGARSS 98 (Seattle, WA, USA), International Geoscience and Remote Sensing Symposium, Ed. L. Tsang, pp , Rahman, H. and Dedieu, G., Smac : a simplified method for the atmospheric correction of satellite measurements in the solar spectrum, International Journal of Remote Sensing, 16, , Roujean, J.-L., Leroy, M., and Deschamps, P., A bidirectional reflectance model of the earth s surface for the correction of remote sensing data, Journal of Geophysical Research, 97, , Song, J. and Gao, W., An improved method to derive surface albedo from narrowband avhrr satellite data: narrowband to broadband conversion, Journal of Applied Meteorology, 38, , Tucker, C. and Sellers, P., Satellite remote sensing of primary production, International Journal of Remote Sensing, 7, , Verhoef, W., Light scattering by leaf layers with application to canopy reflectance modeling : the sail model, Remote Sensing of Environment, 16, , Verhoef, W., Earth observation modelling based on layer scattering matrices., Remote Sensing of Environment, 17, , Vermote, E., Tanré, D., Deuzé, J., and Morcrette, J., Second simulation of the satellite signal in the solar spectrum: an overview, IEEE Transactions on Geosciences and Remote Sensing, 35, , Walthall, C., Norman, J., Welles, G., Campbell, G., and Blad, G., Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces, Applied Optics, 24, , Wanner, W., Strahler, A., Hu, B., Lewis, P., Muller, J.-P., Li, X., Barker Schaaf, C., and Barnsley, M., Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: theory and algorithm., Journal of Geophysical Research, 102, , Weiss, M., Baret, F., Leroy, M., Bégué, A., Hautecoeur, O., and Santer, R., Hemispherical reflectance and albedo estimate from the accumulation of across-track sun-synchronous satellite data, Journal of Geophysical Research, 104, , Weiss, M., Jacob, F., Baret, F., Pragnère, A., Leroy, M., Hautecoeur, O., Prévot, L., and Bruguier, N., Evaluation of kernel-driven brdf models for the normalization of alpilles/reseda polder data, in Physics and Chemistry of the Earth, EGS symposium, special ReSeDA session, 2000.