Interim report on. Algorithms to derive BRDF-normalised reflectance and spectral albedo from AVHRR timeseries

Transcription

1 Interim report on Algorithms to derie BRDF-normalised reflectance and spectral albedo from AVHRR timeseries A product of EOC Task 3.3: BRDF of typical Australian landcoer types I. F. Grant CSIRO Atmospheric Research PMB 1 Aspendale VIC 3195 Australia June 29, 2001 This is a draft document not to be distributed outside CSIRO. 1

2 Contents 0 Comments on the interim report 3 1 Introduction 3 2 Outline of Method 4 3 Preparation Selection of sites and creation of AVHRR timeseries POLDER timeseries POLDER-to-AVHRR conersion BRDF models examined BRDF normalisation of AVHRR Choice of standard geometry Results

3 0 Comments on the interim report This interim report documents work done to date. Specifically, this includes the preparation of test AVHRR and POLDER datasets, the deelopment of the POLDER-band to AVHRR-band conersion required to intercompare those datasets, and initial comparisons of twele linear kernel-based models in terms of their performance in the BRDF-normalisation of AVHRR timeseries as alidated with POLDER data. The work to be completed is as follows. The cases when AVHRR itself happens to obsere at the standard geometry proide another source of alidation of the BRDF-normalisation of AVHRR. The set of models examined will be extended to include nonlinear models such as the RPV and Staylor and Suttles models. The models will also be compared in terms of their goodness of fit to the AVHRR multiangular data. The spectral albedos predicted by inerting the BRDF models on the AVHRR data will be assessed against spectral albedos calculated from POLDER measurements. Finally, the performance of an adaptie window length, such as deeloped by O Brien et al. will be inestigated. The final ersion of this report will add detail to some sections included here, reiew the literature on preious approaches to BRDF-normalisation and albedo retrieal, and hae improed consistent in presentation aspects such as Figure formatting and placement. 1 Introduction The archie of daily 1-km resolution obserations of Australia from the Adanced Very High Resolution Radiometer (AVHRR) series of sensors on the NOAA polar-orbiting satellites stretches back to 1992 and is a aluable record of the dynamics of the continent s land coer. Howeer, the measured reflectance of the surface aries with both the direction from which it is iewed, which aries during an NOAA 10-day orbital repeat cycle, and with the illumination direction, which aries with season. Thus the full realisation of the AVHRR archie for land surface monitoring requires that the AVHRR obserations be normalised to a standard iew-illumination geometry. Correction for angular effects is a recent innoation in the processing of AVHRR data. Some schemes derie the correction from the data itself [Cihlar et al. (1994), Ba et al. (1995), Cabot and Dedieu (1997), ] but some select the BRDF to be applied on the basis of land coer class (see references in [Cihlar (2000)]. For instance, [Strugnell and Lucht (2000)] hae deeloped an approach to the correction of data from wide-swath sensors like AVHRR for iew angle effects that assigns an archetypal BRDF shape to each land coer type and deries the BRDF amplitude from the data. The dependence of the surface reflectance on the iew and illumination directions is quantified by the bidirectional distribution function (BRDF) of the surface. One approach to the normalisation of multiangular measurements is to inert a BRDF model on the cloud-free obserations within a temporal window near the time of interest, then use the model to predict the reflectance at the standard geometry. There is a need to compare the performance of seeral BRDF models and to inestigate the effect of the choice of window length. The accuracy of the normalised AVHRR reflectance could be assessed if it could be compared with an actual measurement of the reflectance made with iew and illumination directions near the standard alues. The POlarization and Directionality of the Earth s Reflectances (POLDER) sensor on the ADanced Earth Obseration Satellite (ADEOS) was the first satellite sensor to measure the angular reflectance signatures of the Earth s surface with good angular sampling and global coerage. In this work we first demonstrate that POLDER data can sere as a standard-geometry spectral reflectance and so be used to measure the accuracy of the AVHRR normalisation. 3

4 2 Outline of Method The AVHRR is a cross-track scanner. It has two shortwae bands, spanning waelength ranges of approximately nm and nm. The spatial resolution ranges from 1 km at nadir iews to km at extreme scan angles. A 10-month timeseries of AVHRR LAC (local area coerage) spanning the POLDER period of operation was extracted at each site, and the Common AVHRR Processing System (CAPS) software package was used to naigate and calibrate the data, reproject it to a longitude-latitude grid, and generate a cloud mask using the CLAVR-1 algorithm. Means of the reflectances oer the central km of each site were used in the subsequent analysis. No atmospheric correction was performed; the comparison of AVHRR with POLDER was done with top-of-atmosphere reflectances. The POLDER sensor operated from Noember 1996 to June It took two-dimensional images with a CCD through a filter wheel. A gien surface point was imaged from up to fourteen directions during a single oerpass, with a spatial resolution of km that was roughly constant with iew direction. The spectral bands included bands at 443, 555, 670, 765 and 865 nm. For each site, the data from a single pixel of the POLDER Leel 1 product was used, which was calibrated top-of-atmosphere (TOA) reflectances. AVHRR and POLDER measure at local times approximately 2 hours after and before noon, respectiely. Thus although the solar azimuths are different for the two sensors, the solar zenith angles will be similar and the bidirectional reflectances should be comparable at similar iew zenith angles and relatie azimuths, proided that the surface is azimuthally symmetric. The approach adopted here is to test arious methods of modelling the angular effects in the AVHRR timeseries against the POLDER reflectances as truth. The benefits of using this approach with actual timeseries of clear AVHRR measurements oer Australia, compared with some other approaches, are the geometry sampling is naturally that pertaining to AVHRR; the temporal sparseness due to cloudiness is automatically that applicable to (conseratiely cloud masked) Australian AVHRR data; the 6-km resolution of POLDER is comparable to the 1-km or greater resolution of AVHRR; the ranking of BRDF models and error quantification are applicable to Australian land coer types. 3 Preparation The AVHRR data were extracted from the tape archie at CAR. During the POLDER period, only afternoon passes of NOAA-14 were archied, and so this study is restricted to those. 3.1 Selection of sites and creation of AVHRR timeseries Comparison of AVHRR and POLDER reflectance measurements is most straightforward if the two measurements are made for identical surface patches. Also, the algorithms deeloped here should be applicable to the full range of Australian land coer types. Thus study sites were selected that were each spatially uniform areas of uniform egetation type, and taken together spanned a large range of Australian egetation types. The egetation classification was Graetz s 32-class aggregation of the AUSLIG (1990) Present Vegetation map. The AVHRR pixel size (pixel separation) aries from km ( km) (acrosstrack along-track) at nadir to km ( km) at the swath edge [Prata et al. (1990)], and multiiew AVHRR datasets can include mixtures of pixels from anywhere in this range. The 4

5 # # # POLDER Leel 1 data are supplied on a grid with (1/18) 7 km resolution, with each pixel being interpolated from a set of raw measurements. Thus 7 km is a natural resolution at which to intercompare AVHRR and POLDER reflectances, and will minimise the effect of the ariation of AVHRR pixel size with scan angle. We will compare POLDER Leel 1 reflectances in single cells of the POLDER grid with colocated aerages of cells of AVHRR reflectances mapped to a! longitude-latitude ( km) grid. The deriation of a mean oer a " km region requires interpolation from neighbouring regions for both AVHRR (nearest neighbour) and POLDER (cubic interpolation in the generation of Leel 1 data). The nearest neighbour can be up to 3.5 km away for both AVHRR and POLDER. Furthermore, geolocation errors will cause a relatie displacement of the AVHRR and POLDER regions. The effect of these issues on the mean reflectances will be reduced if the surface is uniform oer the target patch and a buffer margin around the patch which is taken to be 7 km wide. Thus we seek uniform # $# km patches, where the uniformity criterion is that the mean oer any included % km patch should ary little with its position within the # # km patch. AVHRR passes in the CAR archie gie complete angular coerage for sites east of approximately longitude 140 E. To measure landscape uniformity, a montage coering eastern Australia to longitude 138 E (the Queensland-NT border) was created from the mostly cloud-free and generally near-nadir areas of four passes in December 1996 (Figure 1). The uniformity in the box centred on each POLDER grid cell was measured by the coefficient of ariation (CV, defined as the standard deiation normalised by the mean) of the aerages oer all 225 included subareas of &! &. From the cells associated with each of 32 egetation classes, were selected up to three cells that were among the most uniform in both bands, and for which the surrounding # ' area was of one egetation type throughout, with the proision that no two cells could be separated by less than 100 km. This yielded 72 cells on the POLDER grid that spanned all egetation types, had icinities that were amongst the most uniform (in December 1996) for their egetation type, and had complete or nearly complete angular sampling by the AVHRR passes in the CAR archie. Another 80 cells were selected at random locations across eastern Australia for assessment of the BRDF modelling at typical sites. Finally, 19 cells at the sites of recent field or airborne data collections were selected. Thus AVHRR data were extracted for a total of 171 cells, but most of this report considers only cells from the uniform set. Data for these sites oer ten months spanning the POLDER period ( to ) were extracted from the CAR AVHRR archie. At the time of POLDER s operation, the AVHRR reception facility at Aspendale was nearing the end of its operational life and its reliability was decreasing. Only NOAA-14 afternoon passes were being archied, and there are a few small gaps in the period extracted. Oerpasses were read from 38 Exabyte tapes in DISIMP format and CAPS was used to naigate, calibrate and remap each one to a longitude-latitude grid. Bands 1 and 2 were calibrated to yield CAPS s reflectance factor because this corresponds to the normalised radiance of POLDER Leel 1 product. Because CAPS could not access the naigation information it required in the DISIMP files, the CAPS naigation had errors which were typically a few km but could exceed 10 km. Thus the naigation of each pass was nudged by a global shift in longitude and latitude that was determined from the correlations of small image patches at regular 1 spacings in longitude and latitude with a mostly clear, near-nadir reference image. The naigation of the reference image was itself (*) adjusted by comparison with maps of seeral prominent coastal features. A + (*) region centred on each target POLDER cell was extracted from eery AVHRR oerpass using CAPS, in all fie bands along with sun and iew angles. A cloud mask was generated by an implementation of CLAVR-1 in CAPS and the data for the region saed. The cloud mask was erified to be ery reliable, and een conseratie, in identifying clear regions, by inspecting timeseries of the means and standard deiations oer the region of the band 5

6 LL M2 M3 L3 T4 H2 LL L2M2 M2 T4 L2-20 H2 L3 G4 H1 M1 G4-25 M3 G1 F1-30 H2 S1 SL F1H1 G1 H1 G1 SL Z1 G2 Z1S1 Z1 G2 Z2 M1 M1 M3 LL -T3-35 G3 Z2 S2 G3 F3S S2 Z3 F3F1 F2 L3 F4F2 L2 S2 Z2 G3 F3S G2F4 F3S F4 T3 F2 T3 F3 F3 U -40 T4 S , 155, Figure 1: Locations of the test sites shown on a mosaic of December 1996 AVHRR images of eastern Australia. Uniform sites are in blue and labelled with their egetation codes. Random sites are in red. Field sites are in green; some are west of the region and not shown. 6

7 1 and 2 reflectances and the band 4 brightness temperature, and the ratio of bands 1 and 2, at seeral sites. Subsequently, these regions were processed to gie the band 1 and 2 aerages oer the central /0/21&354 /0/21&3 region, the coefficient of ariation of the aerage as the /0/21&364 /0/21&3 region moed within a / / box, and cloud statistics. BRDF modelling of the surface can only make use of cloud-free satellite obserations, so only those cases with the central /0/ /0/21 3 region cloud-free are used further. The spatial CVs of all the clear obserations for each nominally uniform site were examined for nonuniformity at times different from that of the December 1996 image on which the sites selection was based. Also, while some land coer types will tend to be less inhomogeneous than others, excluding sites that are markedly more inhomogeneous than the rest will simplify later analysis. In iew of these two considerations, sites were rejected if the median CV exceeded 0.05 or if the 90th percentile CV exceeded 0.10, in either band 1 or band 2. This reduced the original 72 uniform sites to a set of 59 sites with median CVs of in bands 1 and 2. These timeseries of clear-sky band 1 and 2 obserations, aeraged oer /0/21 3 4$/0/21 3 corresponding to a POLDER grid cell, at 59 sites across eastern Australia that span a wide range of land coer types, constitute the data set to be used for assessing the BRDF normalisation of, and deriation of albedo from, AVHRR data. 3.2 POLDER timeseries The Leel 1 POLDER data product consists of calibrated geolocated TOA reflectances in all POLDER spectral and polarisation bands, along with the sun and iew angles and ancillary information, on the POLDER fine resolution reference grid. A subset coering the Australian region was ordered and is approximately 150 Gbyte in size, occupying 33 Exabyte tapes. The data for a single POLDER cell at each of the 171 sites was extracted from all oerpasses. The geolocation accuracy of POLDER products was expected before launch to be better than one pixel. We independently checked the geolocation accuracy by correlation with reference AVHRR images at distinctly shaped coastal features for seeral dozen POLDER passes, and found it to be nearly always better than in longitude and latitude. The Leel 1 product includes only a rough cloud indicator, which is unreliable for selecting cloud-free land pixels (Hautecœur, priate communication). A more reliable cloud flag is generated during the production of Leel 2 Surface Reflectances, and so the Leel 2 cloud mask was used to flag the Leel 1 data. Both the AVHRR and POLDER radiances were diided by the cosine of the SZA and normalised by the solar irradiance to conert them to the reflectances used in BRDF modelling. Figures 2 and 3 show the POLDER and AVHRR time series of reflectances and angles for one site. A strong angular signature is obious in the AVHRR reflectances as large cyclic ariations that are coordinated with the cycles in the angles oer the NOAA 10-day orbital repeat cycle. The POLDER reflectances ary strongly through each oerpass as the iew direction changes. 3.3 POLDER-to-AVHRR conersion The spectral bands of POLDER and AVHRR are not the same, and both sensors lack onboard calibration systems and so hae been calibrated indirectly. So a relation to predict AVHRR-band reflectances from POLDER reflectances must be determined. It is assumed that a linear combination of POLDER bands will be adequate, and this will be justified by the results below. All pairs of cloud-free AVHRR and POLDER obserations in the dataset were identified that were acquired: for the same site; on the same date; with solar zenith angles differing my less than 103 ; and with iew directions differing by less than 103. Pairs with one of the iew directions within 303 of the antisolar direction were excluded to aoid strong BRDF effects near the hot spot. The AVHRR measurements were linearly regressed against POLDER measurements in two bands, both bands 7

8 ? R1 R2 VZA SZA RAZ : -80 ; -60 < -40 = -20 Day number of 1997 > 0: Clear Cloudy Figure 2: Part of the timeseries of AVHRR obserations at a uniform site of sparse open herbfield (type F1) at @ E, 26.53@ S. The panels show the reflectances in bands 1 and 2, the iew and solar zenith angles and the relatie azimuth. Bars on the reflectances indicate ACBED spatial standard deiations (of FGF2H&@9IFGF2H&@ means within FG JBK@9IFG JBK@ ), and are generally much smaller for the clear obserations. 8

9 L M? R670 R VZA SZA RAZ < -40 = -20 Day number of 1997 > 0: 20 Clear Cloudy Figure 3: Part of the timeseries of POLDER obserations for the same site as in Figure 2. A shorter period than for AVHRR is shown at a stretched scale to more clearly show the multiple obserations on each oerpass, which are shown slightly staggered in time here despite being acquired within 5 minutes. The panels are reflectances in the 670-nm and 865-nm bands, the iew and solar zenith angles, and the relatie azimuth. 9

10 together and also one band at a time: AVHRR band 1 against the POLDER 565-nm and 670-nm bands; AVHRR band 2 against the POLDER 765-nm and 865-nm bands. Two regressions were performed for each case, with the regression line forced to pass through the origin or not forced. Figures 4 and 5 show the results. The relations chosen are: NPORQ STS*SVUXW!Y"ST ZV[W2\']_^aà^bY"STc[XSVU*U']_èdgf (1) N hiq STS jes2[ykj&tsvl*mxw] dgà^&n where N and ] are the AVHRR and POLDER reflectances. Including the 865-nm band makes a negligible reduction in the error in predicting AVHRR band 2. Figures 6 and 7 show that the fit residuals do not ary systematically by a significant amount with the following parameters: 1. site index (and, indirectly, egetation type) 2. difference between the AVHRR and POLDER solar zenith angles 3. angle between the AVHRR and POLDER iew directions, each relatie to the solar azimuth 4. minimum of the angular separation of each of the AVHRR and POLDER iew directions from the hot spot 5. AVHRR solar zenith angle 6. POLDER solar zenith angle 7. reflectance in the first POLDER band in the regressions 8. reflectance in the second POLDER band in the regressions 9. ratio between the POLDER reflectances 10. NDVI formed from AVHRR bands 1 and 2 Figure 8 shows the actual AVHRR reflectances and those predicted from the matching POLDER obserations for all of the 320 points used in the regression. The rms prediction error is 65 and for bands 1 and 2 respectiely. Reducing the tolerance on the match in sun-iew geometries did not substantially reduce this error (see statistics noted at top-left of Figures 6 and 7). 3.4 BRDF models examined The Ambrals code distributed by the MODIS BRDF group in the Department of Geography at Boston Uniersity (BU) seres as a ready tool-kit for the inersion of linear kernel-based BRDF models on multiiew data sets, and for the forward modelling of reflectance at specified geometries using such models. Version 3.2 of Ambrals was installed. Described by the BU team as research grade, this code lacks the extensie error checking and quality flags of the operational MODIS code. IDL code was written to read and write the ASCII data files that Ambrals uses for input and output. In deeloping the set of linear models to be examined, we note that an early ersion of the MODIS algorithm [Wanner et al. (1997)] inerted the four models formed by combining RossThick or RossThin for the olume kernel, with LiThick or LiSparse for the geometric kernel, and an isotropic kernel. The original forms of the LiThick/Sparse kernels are not reciprocal with respect to interchange of the illumination and iew directions, and reciprocal forms were deeloped for the MODIS processing [Lucht et al. (2000)]. The early MODIS algorithm selected the best 10

11 Figure 4: Linear regressions of AVHRR band-1 reflectances against arious one-band and two-band combinations of POLDER 565-nm and 670-nm reflectances, where the AVHRR and POLDER obserations match, within tolerances, in location, date, and iew and sun geometries. 11

12 Figure 5: The same as Figure 4 for AVHRR band-2 reflectances and POLDER 765-nm and 865- nm reflectances. 12

13 Figure 6: The residuals of the chosen regression relation between AVHRR band 1 and the POLDER 565-nm and 670-nm bands, plotted against each of the parameters listed in the text (panels going left-to-right then top-to-bottom). All of the points hae the difference between AVHRR and POLDER iew directions less than 10 and difference between the solar zenith angles less than 10. The red points are the subset for which both of these differences are less than 5. The red and green points together are the subset with iew difference less than 10 and solar zenith angle difference less than 5. These characteristics and some statistics for these nested subsets of residuals are written at the top left. o o o o 13 o

14 Figure 7: The same as Figure 6 but for AVHRR band 2 and the POLDER 765-nm and 865-nm bands. 14

15 t u POLDER combination p 0.10 q 0.20 r 0.30 s 0.40 AVHRR Band POLDER combination p 0.10 q 0.20 r 0.30 s 0.40 t 0.50 AVHRR Band 2 Figure 8: Comparison of AVHRR TOA reflectances with predictions from POLDER obserations at near identical iew-illumination geometries. The rms difference between the AVHRR and POLDER alues is 65 (0.0103) for AVHRR band 1 (band 2). 15

16 of the four models at each pixel, but this approach was replaced by fitting just the RossThick- LiSparseReciprocal (RTLSR) model, which was considered the best of the four oerall. The MODIS processing also inerts the Walthall model. The Walthall model is not based on physics but is purely empirical, but was regarded as a flexible model that performed reasonably well on a large ariety of surfaces, and was originally included to proide a BRDF product based on a model that was the same at all pixels. More recently, the (nonreciprocal) LiTransit kernel has been deeloped to switch between the LiSparse and LiDense kernels across the boundary in angular space where they match. The semiempirical model deeloped by [Roujean et al. (1992)] combines the isotropic, Roujean geometric and RossThick kernels, and was the model chosen for the POLDER Leel 3 Directional Signatures product, which comprises the coefficients of a BRDF model inerted on multiangular surface reflectances. The full list of linear models studied is RossThick-LiSparseRModis RossThick-LiDenseRModis RossThick-LiSparseNModis RossThick-LiDenseNModis RossThick-LiTransitNModis RossThin-LiSparseRModis RossThin-LiDenseRModis RossThin-LiSparseNModis RossThin-LiDenseNModis RossThin-LiTransitNModis Walthall RossThick-Roujean. 4 BRDF normalisation of AVHRR Modelling of BRDF effects in AVHRR data can fulfill seeral objecties: BRDF-normalisation of reflectance in near-real time in an operational setting BRDF-normalisation of historical data estimation of spectral albedo, usually from historical datasets for use in, for example, climate modelling. We now consider the first of these. 16

17 x { z w y Latitude w 100 w 200 w 300 Day of Figure 9: Solar zenith angle at 1430 local time as a function of latitude and day of year. The thick contour is at solar zenith angle Choice of standard geometry We must select the standard iew-illumination geometry to which the AVHRR time series will be normalised. Nadir is the natural choice of standard iew direction: AVHRR samples that direction, it has its best spatial resolution there, the atmospheric effects are least, and the need to specify a iew azimuth or relatie azimuth is aoided. A standard solar zenith angle of 45 is a common choice. Figure 9 shows the SZA at 1430 LT through the year oer latitudes -45 to -10. The SZA ranges from about 30 to about 75. Howeer, at all latitudes the 1430 LT SZA is 45 on some date (within 50 days of the equinoxes). Also, at the equinoxes, when the sun is at the middle of its declination range, at all latitudes the 1430 LT SZA differs from 45 by no more than 10. So 45 seres as a single middle solar zenith angle for all of Australia, and will be be adopted as the standard for BRDF normalisation. 4.2 Results In a real-time operational enironment, the goal of BRDF normalisation is to predict the normalised clear-sky reflectance at each pixel from AVHRR data collected on the day of interest and on preious days, despite the fact that in the single image acquired on the day of interest some pixels will be cloudy or obsered at non-standard iew directions or solar zenith angles. First, the POLDER obserations taken near the standard geometry were identified, using a tolerance of 10 17

18 on both the iew and sun directions. There are 477 such cases, and next AVHRR reflectances will be predicted for the site and date of each case. A temporal window was placed on the AVHRR timeseries at a site, and if there were more than four clear measurements within the window the suite of BRDF models was inerted on the measurement set. The resulting model parameters were then used with the BRDF models in a forward mode to predict the reflectance at the standard geometry. The predictions were made with each of twele BRDF models. All window lengths from 4 to 30 days were trialled, in each case the window finishing on the day of interest. The BRDF model inersions and the forward BRDF modelling to predict reflectances were both done with the Ambrals. Figure 10 shows the errors in normalising AVHRR to a standard iew-illumination geometry, using the POLDER predictions as the reference. For all models, the error drops rapidly as the window length increases to the NOAA repeat period of 10 days, then decreases more slowly as the window lengthens further. Longer windows are more likely to capture a sufficient number of clear obserations to perform an inersion, but shorter windows will better capture changes in the land surface that would be manifested as changes in the normalised reflectance. Howeer, windows shorter than the 10-day NOAA repeat cycle risk inadequately sampling the full range of iew directions. All models appear to tend towards a bias (nonzero error) that aries in magnitude and sign between models. The RossThick-LiSparseRModis (RTLSR) model, compared to the other models in Fig. 10, has a small bias and achiees close to the optimum error with a short window: 9 or 10 days, which is the NOAA orbit repeat cycle. The rms error of 65 in the prediction of AVHRR band 1 from POLDER at a near-identical geometry sets a limit on how closely the two datasets can agree. The median bias of the RTLSR model in Figure 10 is not significantly greater than this, being around 4 to 0.010, which suggests that the normalisation is accurate to around 0.01 or better, on reflectances of typically For band 2, the RTLSR model has median biases of 0.01 for windows of 10 days or longer, compared with an rms error in the POLDER prediction of AVHRR of These results are preliminary. Acknowledgments We thank Wolfgang Lucht, Crystal Schaaf and others at Boston Uniersity for making the AM- BRALS code aailable. The results presented in this paper were obtained using measurements from the Centre National d Etudes Spatiales (CNES) POLDER instrument on board the National Space Deelopment Agency (NASDA) ADEOS platform. References [Ba et al. (1995)] Ba, M. B., P.-V. Deschamps, and R. Frouin, reduction in NOAA satellite monitoring of the land surface during FIFE, J. Geophys. Res., 100, 25,537 25,548, [Cabot and Dedieu (1997)] Cabot, F., and G. Dedieu, Surface albedo from space: Coupling bidirectional models and remotely sensed measurements, J. Geophys. Res., 102, 19,645 19,663, [Cihlar (2000)] Cihlar, J., Land coer mapping of large areas from satellites: status and research priorities, Int. J. Remote Sensing, 21, , [Cihlar et al. (1994)] Cihlar, J., D. Manak, and N. Voisin, AVHRR bidirectional reflectance effects and compositing, Remote Sens. Eniron., 48, 77 88,

19 } RossThick-LiSparseRModis } RossThick-LiDenseRModis RossThick-LiSparseNModis } RossThick-LiDenseNModis RossThick-LiTransitNModis RossThin-LiSparseRModis RossThin-LiDenseRModis RossThin-LiSparseNModis RossThin-LiDenseNModis RossThin-LiTransitNModis Walthall RossThick-Roujean Figure 10: s in the normalisation of AVHRR band 1 timeseries compared for twele linear kernel-based BRDF models, for window lengths of up to 30 days. The solid line is the median error and the dashed lines are the upper and lower quartiles, where the statistics are oer the subset of cases that could be processed for any particular window length. 19

20 [Lucht et al. (2000)] Lucht, W., C. B. Schaaf, and A. H. Strahler, An algorithm for the retrieal of albedo from space using semiempirical BRDF models, IEEE Trans. Geosci. Remote Sens., 38, , [Prata et al. (1990)] Prata, A. J., R. P. Cechet, I. J. Barton, and D. T. Llewellyn-Jones, The Along Track Scanning Radiometer for ERS-1 scan geometry and data simulation, IEEE Trans. Geosci. Remote Sens., 28, 3 13??, [Priette et al. (1997)] Priette, J. L., T. F. Eck, and D. W. Deering, Estimating spectral albedo and nadir reflectance through inersion of simple BRDF models with AVHRR/MODIS-like data, J. Geophys. Res., 102, 29,529 29,542, [Roujean et al. (1992)] Roujean, J.-L., M. Leroy, and P.-V. Deschamps, A bidirectional model of the Earth s surface for the correction of remote sensing data, J. Geophys. Res., 97, 20,455 20,468, [Strugnell and Lucht (2000)] Strugnell, N., and W. Lucht, Continental-scale albedo inferred from AVHRR data, land coer class and field obserations of typical BRDFs, J. Climate, p. in press, [Wanner et al. (1997)] Wanner, W., A. H. Strahler, B. Hu, P. Lewis, J.-P. Muller, X. Li, C. L. B. Schaaf, and M. J. Barnsley, Global retrieal of bidirectional reflectance and albedo oer land from EOS MODIS and MISR data: Theory and algorithm, J. Geophys. Res., 102, 17,143 17,161,