LAND surface broad-band albedo is a critical land

Transcription

1 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER Retrieval of Surface Albedo on a Daily Basis: Application to MODIS Data Belen Franch, Eric F. Vermote, José A. Sobrino, and Yves Julien Abstract In this paper, we will evaluate the Vermote et al. method, hereafter referred to as VJB, in comparison to the MCD43 MODerate Resolution Imaging Spectroradiometer (MODIS) product, focusing on the white sky albedo parameter. We also present and study three different methods based on the VJB assumption, the 4param, 5param Rsqr, and 5param Vsqr. We use daily MODIS Climate Modeling Grid data both from Terra and Aqua platforms from 2002 to 2011 for all the pixels over Europe. We obtain an overall root-mean-square error of 5% when using the VJB method and 6.1%, 5.1%, and 5.3% for the 4param, 5param Rsqr, and 5param Vsqr methods, respectively. The main differences between the methods are located in areas where only few cloud-free snow-free samples were available that correspond mainly to mountainous areas during the winter. We finally conclude that the VJB method has an equivalent performance in deriving the white sky albedo results to the MODIS product with the advantage of daily temporal resolution. Additionally, we propose the 5param Rsqr method as an alternative to the VJB method due to its decreased data processing time. Index Terms Albedo, bidirectional reflectance distribution function (BRDF) inversion, MODerate Resolution Imaging Spectroradiometer (MODIS), VJB method. I. INTRODUCTION LAND surface broad-band albedo is a critical land physical parameter affecting the Earth s climate. It has been well recognized that surface albedo is among the main radiative uncertainties in current climate modeling. In fact, an accuracy requirement of 5% is suggested by the Global Climate Observing System [7] for albedo characterization at spatial and temporal scales compatible with climate studies. Modern climate models are now attaining the ability to incorporate global surface albedo spatial features. Satellite remote sensing provides the only practical way of producing highquality global albedo data sets with high spatial and temporal resolutions. Manuscript received May 29, 2013; revised October 28, 2013 and January 22, 2014; accepted March 15, This work was supported in part by the Spanish Ministerio de Economia y Competitividad (EODIX, project AYA C04-01; CEOS-SPAIN, project AYA C02-01) and in part by the European Union (CEOP-AEGIS, project FP7-ENV proposal No ; WATCH, project ). B. Franch is with the Department of Geographical Sciences, University of Maryland, College Park, MD USA. E. F. Vermote is with NASA Goddard Space Flight Center, Greenbelt, MD USA. J. A. Sobrino and Y. Julien are with the Global Change Unit, Image Processing Laboratory (UCG-IPL), Parque Cientifico, Universitat de Valencia, Valencia, Spain. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TGRS Albedo is highly variable in space and time, both as a result of changes in surface properties (e.g., snow deposition or seaice growth and melting, changes in soil moisture and vegetation cover, etc.) and as a function of changes in the illumination conditions (solar angular position, atmospheric and cloud properties, etc.). Consequently, a daily temporal resolution is required by the Global Climate Observing System (GCOS) [7]. For view-illumination geometries typical of medium-resolution sensors such as the MODerate Resolution Imaging Spectroradiometer (MODIS) onboard the Terra and Aqua satellites, in order to obtain enough bidirectional observations to retrieve the bidirectional reflectance distribution function (BRDF) free parameters, a period of sequential measurement is usually needed to accumulate sufficient observations. During this temporal window, the model parameters are assumed to be constant. This method is currently used to derive the MODIS BRDF/albedo product, MCD43 [19], which combines registered multidate multiband atmospherically corrected surface reflectance data from Terra and Aqua data to fit a BRDF in seven spectral bands over a composite period of 16 days, although MCD43 is produced every eight days. Several studies have evaluated the MODIS MCD43 product accuracy using in situ data [5], [8], [11], [12], [16]. They found a high correlation between in situ and satellite albedos for almost all cases, concluding that the MODIS albedo product met an absolute accuracy requirement of However, in some cases, the studies observed negative mean biases [8], [16] in which the magnitude increased as the solar zenith angle increased [12]. Cescatti et al. [4] compared MODIS albedo retrievals with surface measurements taken at 53 FLUXNET sites that met strict conditions of land cover homogeneity, and they observed a good agreement for forest sites. However, in case of nonforest sites with larger albedo values (grasslands and croplands), MODIS generally underestimated in situ measurements across the seasonal cycle. Nevertheless, one limitation of the method employed in the MODIS BRDF/albedo product is the assumption of the stability of the target over the temporal compositing period. Another limitation is that it requires several cloud-free measurements of the target during the compositing period. Additionally, the observation geometry of these measurements may not be suitable to properly constrain the BRDF model. Looking for an improvement in the albedo temporal resolution that mitigated the assumption of a stable target, Vermote et al. [20] presented the VJB method that assumes that the BRDF shape variations throughout a year are limited and linked to the Normalized Difference Vegetation Index (NDVI). This method permits more accurate tracking of events such as IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 7550 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014 snow melt and vegetation phenology. Additionally, it retains the highest temporal resolution (daily, cloud cover permitting) without the noise generated by the day-to-day changes in observation geometry. Bréon and Vermote [3] compared this method with the MCD43 MODIS product for the correction of the surface reflectance time series. They worked with MODIS Climate Modeling Grid (CMG) data along 2003, analyzing a representative set of +100 targets selected on the basis of the location of Aerosol Robotic Network (AERONET) sites. Their results showed that the performances of the two approaches are very similar, demonstrating that a simple four-parameter NDVI-scaled model performs as well as a more complex model with many more degrees of freedom. Abelleyra and Verón [1] supported recently these conclusions at higher spatial resolution by comparing (at 250-m spatial resolution) the surface reflectance corrected for the BRDF using the VJB method to the BRDF correction using the MCD43 product. Although they found similar results, the VJB showed slightly better general statistics (lower noise median values) and, at pixel-by-pixel level, presented the highest differences with the MCD43 that are a function of crop type and differing time series lengths. The purpose of this paper is to complete the Bréon and Vermote [3] study comparing the MCD43 product with the VJB method through the white sky albedo parameter. Additionally, we propose three methods in order to improve the time processing of the VJB method. In this paper, we focus our analysis on MODIS CMG Collection 6 data from both Aqua and Terra satellites over Europe from 2002 to We used coarse resolution in order to work at global scale. This enabled us to study several different classes of surfaces. Moreover, the CMG product has been well established as an official MODIS product for the global modeling community. In fact, Gao et al. [6] discuss the implications for the representation of albedo at coarser spatial resolution in climate models. Although they worked with Collection 4 data, they concluded that global albedos at this resolution have spatial and temporal patterns appropriate for the underlying land cover classes. II. DATA AND METHODS A. Satellite Data This study used the MODIS CMG surface reflectance Collection 6 data (M{OY}DCMG) which are gridded in the linear latitude longitude projection at 0.05 resolution. Science data sets provided for this product include surface reflectance values for bands 1 7, brightness temperatures for bands 20, 21, 31, and 32, solar and view zenith angles, relative azimuth angle, ozone, granule time, quality assessment, cloud mask, aerosol optical thickness at 550 nm, and water vapor content. We analyzed daily data from both Aqua and Terra platforms over Europe from 2002 to Additionally, we used the land cover type yearly CMG that provides the dominant land cover type and also the subgrid frequency distribution of land cover classes and has the same spatial resolution (0.05 ) as the surface reflectance product. The CMG product (MCD12C1) is derived using the same algorithm that produces the V005 Global 500-m land cover type product (MCD12Q1). It contains three classification schemes, which describe the land cover properties derived from observations spanning a year s input of Terra and Aqua MODIS data. The primary land cover scheme, which we consider in this paper, identifies 17 land cover classes defined by the International Geosphere Biosphere Programme, which includes 11 natural vegetation classes, 3 developed and mosaicked land classes, and 3 nonvegetated land classes. The study is centered in the analysis of the MCD43 BRDF/albedo snow-free quality product (MCD43C2). It contains the weighting parameters for the models used to derive the albedo and nadir BRDF-adjusted reflectance products (MCD43C3 and MCD43C4) describing only snow-free conditions. The models support the spatial relationship and parameter characterization best describing the differences in radiation due to the scattering (anisotropy) of each pixel, relying on multidate atmospherically corrected cloud-cleared input data measured over 16-day periods. Both Terra and Aqua data are used in the generation of this product, providing the highest probability for quality input data and designating it as an MCD, meaning combined, product. The MCD43 MODIS product is estimated using a kernelbased BRDF model [19], [18]. The theoretical basis of this semiempirical model is that the land surface reflectance is modeled as a sum of three kernels (1) representing basic scattering types: isotropic scattering, radiative transfer-type volumetric scattering as from horizontally homogeneous leaf canopies, and geometric-optical surface scattering as from scenes containing 3-D objects that cast shadows and are mutually obscured from view at off-nadir angles. Following the Vermote et al. [20] notation, the surface reflectance (ρ) is written as [ ρ(θ s,θ v,φ)=k 0 1+ k 1 F 1 (θ s,θ v,φ)+ k ] 2 F 2 (θ s,θ v,φ) (1) k 0 k 0 where θ s is the sun zenith angle, θ v is the view zenith angle, ϕ is the relative azimuth angle, F 1 is the volume scattering kernel, based on the Ross-Thick function derived by Roujean et al. [17], and F 2 is the geometric kernel, based on the Li-sparse model [9] but considering the reciprocal form given by Lucht [13]. Although these are the models used in the MCD43 product, in order to derive the BRDF with the VJB method and the proposed methods, we consider the same models but corrected for the Hot-Spot process proposed by Maignan et al. [14]. F 1 and F 2 are fixed functions of the observation geometry, but k 0, k 1, and k 2 are free parameters. Following this notation, we use V as k 1 /k 0 (since it is linked to the Volume kernel) and R for k 2 /k 0 (since it is linked to the geometric kernel and represents the surface Roughness). These parameters (V and R) represent the shape of the BRDF, while k 0 is the amplitude. In this paper, we analyze the white sky albedo, which was estimated from the BRDF parameters following Strahler et al. [19]. The spectral to broad-band albedo conversion was achieved following Liang [10]. B. MODIS MCD43 BRDF Inversion For view-illumination geometries typical of mediumresolution sensors such as Terra and Aqua MODIS, in order to obtain enough bidirectional observations to retrieve the

3 FRANCH et al.: RETRIEVAL OF SURFACE ALBEDO ON DAILY BASIS: APPLICATION TO MODIS DATA 7551 BRDF free parameters, a period of sequential measurement is usually needed to accumulate sufficient observations. During this temporal window, the model parameters are assumed to be constant. This method is currently used to derive the MODIS BRDF/albedo product (MCD43), which combines Terra and Aqua data to invert the BRDF model parameters over a composite period of 16 days, although it provides images every eight days. Additional information about the method can be found in [19]. C. VJB Method Vermote et al. [20] proposed the VJB method for the inversion of the BRDF model with less constraint on the stability of the target. This method accounts for the fact that the target reflectance changes during the year, but assumes that the BRDF shape variations are limited. Another way of presenting the hypothesis is that k 0, k 1, and k 2 vary in time but k 1 and k 2 stay proportional to k 0. Additionally, the difference between the successive observations is mainly attributed to directional effects while the variation of k 0 (t) is supposed small. Therefore, V and R can be derived through the minimization of the day-to-day variations of k 0 (t) ρ(t i ) 1+VF1 i+1 +RF2 i+1 ρ(ti+1 ) 1+VF1 i +RF2 i. (2) This leads to a system of equations that can only be solved through iteration. The objective is to minimize the merit function N 1( [ [ ρi+1 1+VF i M = 1 +RF2] i ρi 1+VF i+1 1 +RF i+1 ]) 2 2 day i+1 day i. +1 (3) Therefore, R and V are solved by the classic derivation of the merit function which leads to Δ i ρf 1 Δ i ρf 1 Δ i ρf 1 Δ i ρf 2 ( ) V Δ i ρf 1 Δ i ρf 2 Δ i ρf 2 Δ i R ρf 2 where N 1 Δ i ρδ i ρf 1 = (4) Δ i ρδ i ρf 2 Δ i d = day i+1 day i +1 Δ i ρ = (ρ i+1 ρ i ) Δi d ( Δ i ρi+1 F1 i ρ i F i+1 ) 1 ρf 1 = Δi d ( Δ i ρi+1 F2 i ρ i F i+1 ) 2 ρf 2 =. (5) Δi d In order to estimate V and R to apply (4), each year of the data set considered is segmented into five different classes of NDVI with equal population. The reason of assuming a dependence of V and R with the NDVI over a year is that BRDF has been shown to be significantly different for bare soil and vegetated surfaces because vegetated surfaces show higher anisotropy than bare soil [2]. Also, the NDVI is sensitive to the presence of vegetation and is easy to derive, and as a ratio, the NDVI implicitly contains a directional correction because the effects are similar in the two bands [20]. Then, R and V are inverted for each of these classes and bands. After that, one can generate a linear function (two coefficients) that represents V and R as a function of the NDVI. However, this fitting must be weighted by each NDVI class error bar in order to minimize outlier influence. The error bars are estimated by running the inversion ten times, each time removing 10% of the data set at random. Finally, these functions can be applied to each NDVI image, obtaining instantaneous BRDF parameters. This method, in contrast to the MODIS BRDF/albedo product inversion, can generate a product with the same frequency as the observations, which is particularly useful for monitoring rapid changes of vegetation cover, e.g., for agricultural areas. However, with the aim of improving the processing time of the VJB method, we will present three different methods based on the original algorithm. D. 4parameter Method The 4parameter method consists of considering that R and V are represented by a linear function of the NDVI (that coincides with the assumption of the VJB method). That is V = V 0 + V 1 NDVI (6) R = R 0 + R 1 NDVI. (7) However, compared to the VJB method, we include this assumption into the merit function, which leads to A V 0 V 1 R 0 R 1 = Δ i ρδ i ρf 1 Δ i ρδ i ρf 1 NDVI Δ i ρδ i ρf 2 Δ i ρδ i ρf 2 NDVI where A is defined as (9), shown at the bottom of the next page. We have used the same notation described in (5). In this way, each parameter will be estimated by inverting this matrix over each year of the data set but avoiding the classification depending on the NDVI. This method, as well as the VJB method, provides a product with the same frequency as the observations. (8)

4 7552 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014 E. 5parameter Rsqr Method Next, we will consider that the V parameter depends linearly on the NDVI but the R parameter presents a second-degree dependence. The R parameter is linked to the geometrical kernel which models the surface roughness. A quadratic dependence of R with the NDVI should describe adequately, for instance, agricultural areas. Along these surfaces, low NDVI values describe bare soils where R should be low. The first stages of vegetation growth should increase R (increase the roughness of the surface) until a maximum value. Finally, as crops get denser, one may expect R to decrease. Therefore, this method assumption can be written as V = V 0 + V 1 NDVI (10) R = R 0 + R 1 NDVI + R 2 NDVI 2. (11) Now, the derivation of the merit function is C V 0 V 1 R 0 R 1 R 2 = Δ i ρδ i ρf 1 Δ i ρδ i ρf 1 NDVI Δ i ρδ i ρf 2 Δ i ρδ i ρf 2 NDVI Δ i ρδ i ρf 2 NDVI 2 where C is defined as (13), shown at the bottom of the page. (12) F. 5parameter Vsqr Method Finally, we consider that R depends linearly on the NDVI but V presents a second-degree dependence. The V parameter is linked to the volume kernel which models a collection of randomly located facets absorbing and scattering radiation which represent mainly leaves of canopies and can also model the behavior of dust, fine structures, and porosity of bare soils [17]. As the vegetation grows and the NDVI gets higher values, one may expect V to increase. In this case, the assumption is written as V = V 0 + V 1 NDVI + V 2 NDVI 2 (14) R = R 0 + R 1 NDVI. (15) Aside from the 5parameter Rsqr method, we have included another parameter to the VJB model. Following the same scheme as the previous method, now, the derivation of the merit function is V 0 B V 1 V 2 = R 0 R 1 Δ i ρδ i ρf 1 Δ i ρδ i ρf 1 NDVI Δ i ρδ i ρf 1 NDVI 2 Δ i ρδ i ρf 2 Δ i ρδ i ρf 2 NDVI N 1 (16) where B is defined as (17), shown at the bottom of the next page. (Δ i ρf 1 ) 2 (Δ i ρf 1 ) 2 NDV I Δ i ρf 1 Δ i ρf 2 Δ i ρf 1 Δ i ρf 2 NDV I (Δ i ρf 1 ) 2 NDV I (Δ i ρf 1 ) 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 A = N 1 Δ i ρf 1 Δ i ρf 2 Δ i ρf 1 Δ i ρf 2 NDV I (Δ i ρf 2 ) 2 (Δ i ρf 2 ) 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 (Δ i ρf 2 ) 2 NDV I (Δ i ρf 2 ) 2 NDV I 2 (9) (Δ i ρf 1 ) 2 (Δ i ρf 1 ) 2 NDV I Δ i ρf 1 Δ i ρf 2 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 (Δ i ρf 1 ) 2 NDV I (Δ i ρf 1 ) 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 NDV I 3 N 1 C = Δ i ρf 1 Δ i ρf 2 Δ i ρf 1 Δ i ρf 2 NDV I (Δ i ρf 2 ) 2 (Δ i ρf 2 ) 2 NDV I (Δ i ρf 2 ) 2 NDV I 2 (13) N 1 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 (Δ i ρf 2 ) 2 NDV I (Δ i ρf 2 ) 2 NDV I 2 (Δ i ρf 2 ) 2 NDV I 3 N 1 Δ i ρf 1 Δ i ρf 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 NDV I 3 (Δ i ρf 2 ) 2 NDV I 2 (Δ i ρf 2 ) 2 NDV I 3 (Δ i ρf 2 ) 2 NDV I 4

5 FRANCH et al.: RETRIEVAL OF SURFACE ALBEDO ON DAILY BASIS: APPLICATION TO MODIS DATA 7553 In this paper, we will compare the MCD43 product with the results obtained from the VJB method and the three improvements proposed. For this purpose, we will focus on the white sky albedo or bihemispherical-reflectance analysis. It is defined as albedo in the absence of a direct component when the diffuse component is isotropic. Thus, it is a constant and does not depend on the view zenith angle like the blue sky albedo or black sky albedo does where α ws (λ) = 2 k i (λ)h i (λ) (18) i=0 H i (λ) =2 h i (θ s,λ)= π/2 0 2π 0 h i (θ s,λ)sinθ s cos θ s dθ s (19) π/2 0 F i (θ s,θ v,φ; λ)sinθ v cos θ v dθ v dφ. (20) Finally, the spectral to broad-band conversion is achieved following Liang [10]. Since the temporal resolution of the MODIS product is eight days while the other methods provide daily albedo estimation, during the whole study, we averaged each eight-day product, for a total of 16 days, in order to be sure that we were comparing equivalent results. In this paper, we estimate the root-mean-square error (RMSE) for each day (D) of an average year, which can be expressed as where stddev D defined as stddev D = 1 n RMSE D = bias 2 D + stddev2 D (21) is the standard deviation of the day D 2011 i=2002 ( αd,i(v JB,prop meth) α D,i(MCD43) ) 2 (22) Fig. 1. Temporal evolution of the broad-band white sky albedo derived with the different methodologies at the Ispra site. and bias D is the bias of the day D 2011 i=2002 ( αd,i(v JB,prop meth) α D,i(MCD43) ) bias D = (23) n where α is the broad-band white sky albedo for the day D along the years and n is the total of the data considered. Note that we estimate the relative RMSE to compare the VJB and the proposed methods with the MCD43 official product, not the absolute RMSE that would be estimated using in situ data. III. RESULTS First of all, we processed all the data. The MCD43 was filtered following the quality flag labels for best quality (75% or more with best full inversion). All the data considered in this work corresponded to clear snow-free land pixels following the cloud/snow/land mask. Comparing the proposed algorithms to the VJB method, we detected a decrease in the time processing of 44%. We did not observe any significant difference in the time processing of the three proposed methods. In order to compare the methodologies, we analyzed in detail a particular pixel centered in the AERONET site in Ispra, Italy (45.5 N, 8.5 E) which is a mixed forest/urban pixel. Fig. 1 presents the temporal evolution of the broad-band white sky albedo derived with the different methodologies. The plot (Δ i ρf 1 ) 2 (Δ i ρf 1 ) 2 NDV I (Δ i ρf 1 ) 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 Δ i ρf 1 Δ i ρf 2 NDV I (Δ i ρf 1 ) 2 NDV I (Δ i ρf 1 ) 2 NDV I 2 (Δ i ρf 1 ) 2 NDV I 3 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 N 1 B = (Δ i ρf 1 ) 2 NDV I 2 (Δ i ρf 1 ) 2 NDV I 3 (Δ i ρf 1 ) 2 NDV I 4 Δ i ρf 1 Δ i ρf 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 NDV I 3 N 1 Δ i ρf 1 Δ i ρf 2 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 (Δ i ρf 2 ) 2 (Δ i ρf 2 ) 2 NDV I N 1 Δ i ρf 1 Δ i ρf 2 NDV I Δ i ρf 1 Δ i ρf 2 NDV I 2 Δ i ρf 1 Δ i ρf 2 NDV I 3 (Δ i ρf 2 ) 2 NDV I (Δ i ρf 2 ) 2 NDV I 2 (17)

6 7554 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014 Fig. 2. Plot of the broad-band white sky albedo of the proposed methods and the VJB method versus the MCD43 product. shows that the VJB method provides similar results as that of the proposed methods, and we did not observe significant differences between the proposed methods. In 2004, VJB presents slightly lower values than the proposed methodologies, while for 2007 and 2009, it shows slightly higher albedo values. The 5parameter Rsqr method showed similar results as that of the 4parameter method while it showed slightly lower values during 2005 and 2010 and higher values during 2007 and 2008 when compared to the 5parameter Vsqr method. Moreover, the MCD43 product temporal evolution exhibits greater variability than the other methodologies mainly during the summer, which leads to greater difference with the other methods. Both the VJB and the proposed methods provided data continuously, while the MCD43 product did not provided values during some periods of winter or spring. Comparing the number of data provided by the VJB and the proposed methods with the total data provided by the MCD43 product, the fraction of data provided by the MCD43 product was 70%. Fig. 2 presents the white sky broad-band albedo estimated from the VJB method and the proposed methods versus the MCD43 product along the time series considered at the Ispra site. The plot shows that larger difference with the original product corresponds to the highest values of albedo. The VJB method provides slightly better results than the proposed methods with the highest correlation coefficient. The total RMSE of each method against the MCD43 product in this site was in case of the VJB method and in case of the proposed methods, which suggests a relative error of 5% 6%. This range of errors meets the required accuracy proposed by thegcos[7]. Fig. 3 shows the behavior of V and R (band 2) with the NDVI for the five NDVI classes of the Ispra pixel considered in the VJB method in In these graphs, we represented the VJB method as well as the three proposed method fittings. Although the proposed methods consider every data to compute V and R (not five-ndvi-class linear fitting), Fig. 3 provides the V and R approached behavior with the NDVI. At first glance, V is more linear than R when represented versus the NDVI, so a seconddegree fitting is more appropriate in case of the R parameter. Therefore, the 5parameter Rsqr method fits well the R data while it seems to slightly underestimate the V data. On the Fig. 3. R and V parameters (band 2) versus the five NDVI classes of the Ispra pixel considered in the VJB method in the particular case of contrary, the 5parameter Vsqr method does not fit the V data, underestimating them, while it provides the same fitting as that of the VJB method in case of the R parameter. Fig. 3 shows that the 4parameter linear fit provides slightly higher R values than the VJB method (in Fig. 3(a), it is coincident to the 5parameter Vsqr fitting) and lower V values than the VJB method [in Fig. 3(b), it is coincident to the 5parameter Rsqr fitting]. In fact, although both methods assume V and R linear dependence with the NDVI, each one of them solves the problem differently. Since the volume kernel is mostly positive and the geometric kernel is always negative, the 4parameter method provides lower albedo values than the VJB method in this particular case. In order to see the spatial variability of the methods versus the MODIS product, we proceed to analyze the whole Europe scene considering all the data to analyze the error through the time series. Fig. 4 shows the percentage of the total RMSE of the VJB method [see Fig. 4(a)] and the proposed methods [see Fig. 4(b) (d)] against the MCD43 product. The images display that southern latitudes present lower errors with values lower than 5% while they increase for northern latitudes with values that can reach 10% along Great Britain, Ireland, and the Scandinavian Peninsula. Also, we obtain the highest errors for mountainous areas with errors that can reach 20%. Comparing VJB to the proposed methods, the VJB presents errors higher than 15% in 8.2% of total land pixels while these errors comprise 7.3%, 6.9%, and 7.8% of pixels when using the 4param, 5param Rsqr, and 5param Vsqr, respectively. The results show

7 FRANCH et al.: RETRIEVAL OF SURFACE ALBEDO ON DAILY BASIS: APPLICATION TO MODIS DATA 7555 Fig. 5. Histogram of Fig. 4 images. Fig. 4. Percentage RMSE of the (a) VJB method, (b) 4param method, (c) 5param Rsqr method, and (d) 5param Vsqr method against the MCD43 product. additional differences comparing the methods errors along other areas. In northern Africa, eastern Spain, Germany, Italy, or southern Sweden, the 4param provides higher errors than the VJB. However, the 5param Rqr and 5param Vsqr provide better results in these areas than the 4param which got similar results as that of the VJB. Overall, the total RMSE through the Europe scene was 5.0% in case of the VJB method and 6.1%, 5.1% and 5.3% in case of the 4param, 5param Rsqr, and 5param Vsqr methods, respectively. Fig. 5 shows the histogram of Fig. 4 images, and it shows two peaks. The first one is the highest one for every method and corresponds to 1.5% RMSE in case of VJB (which presents the highest number of pixels), 5param Rsqr, and 5param Vsqr. However, the 4param first peak is located around 2% RMSE and shows the lowest number of pixels. The second peak that represents a similar number of pixels in every method is centered around 6% RMSE for VJB and around 7% for the other methods. From this plot, the conclusion is that most pixels present an RMSE around 1.5% or 2% depending on the model, although there are other significant numbers of pixels that present an RMSE around 6% or 7%. The best results of this histogram corresponded to the VJB method, although 5param Rsqr and 5param Vsqr showed similar profiles. Finally, we analyzed the difference between each method, dividing the study into different classes extracted from the MCD12C1 MODIS product. Fig. 6 displays the spatial distribution of each class through the Europe scene. In this paper, we will consider only the most representative classes of the considered scene. Table I shows the land cover classification types. Fig. 7 shows the RMSE of the average year for each class for each method against the MCD43 product. The RMSE of an average year is defined as the RMSE of each day of the year (DOY) through every year studied (from 2002 Fig. 6. Land cover type yearly CMG (MCD12C1 MODIS product) and the classes considered in this study. TABLE I LAND COVER CLASSIFICATION TYPES CONSIDERED IN THIS STUDY to 2011) and quantifies the difference of the tested methods throughout the year. The plots show that the highest errors were obtained for classes 1 and 5 (the classes that represent forests) during the winter. Looking at Fig. 6, those classes (mostly class 1) are located along the northern latitudes or along rugged mountainous areas that, during the winter, are covered by snow. Since the snow pixels were masked along both the MCD43 product and the MODIS reflectance data (from which we obtained the albedo with the other inversion methods),

8 7556 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014 Fig. 7. Average year RMSE for each class of the Europe scene between the proposed methods and the VJB method regarding the MCD43 product. during the winter, the RMSE was estimated considering much less data than during the rest of the year. Previous studies that validated the surface albedo of the MCD43 product with in situ measurements also found larger differences in the winter season [8], [4]. Jin et al. [8] suggested that this was the result of the increased heterogeneity of surface reflectivity due to the presence of residual snow and canopy heterogeneity. The greatest difference between the methods was observed in these cases. The highest errors for classes 1 and 5 during the winter were provided by the 4param method followed by the 5param Vsqr method while 5param Rsqr led to similar RMSE as compared to the VJB method. Leaving aside the winter season, the RMSE of classes 1 and 5 from DOY 20 to 305 changed from 0.01 to 0.02, obtaining the poor results with the 5param Vsqr method during the spring and similar results with the other methods. Regarding the other classes, the RMSE generally presented values between 0.01 and These classes that describe mainly stable surfaces along the year suppose most of the surface

9 FRANCH et al.: RETRIEVAL OF SURFACE ALBEDO ON DAILY BASIS: APPLICATION TO MODIS DATA 7557 in the central and southern latitudes. The lowest errors were obtained for class 16 (barren or sparsely vegetated), where the errors decreased below Comparing the VJB method with the other methods, they provided similar results with the VJB method. The larger differences between the proposed methods and VJB (leaving classes 1 and 5 aside) were detected for classes 7 (open shrublands), 8 (woody savannas), and 10 (grasslands). In case of classes 7 and 8, VJB led to slightly lower RMSE than the other methods from DOY 100 to 150 (spring). However, for classes 7 and 10, the other methods provided slightly better results from DOY 200 to 300 (end of summer and fall). Locating these classes in Fig. 6, class 7 is placed along Norway, east of Spain, and the Mediterranean coast of Africa, class 8 is located in the east of Norway and the center of Spain, and class 10 is found in the east of the United Kingdom, Ireland, and Turkey. Most of these regions different errors among methods were detected in Fig. 4. Finally, in this analysis, we did not see significant differences between the proposed methods (from class 7 to 16) showing similar RMSEs. This must be a consequence of including several pixels (not just every pixel of the same class but also the temporal evolution of each pixel for the same DOY through the years) into the RMSE estimation. IV. DISCUSSION AND CONCLUSIONS In this paper, we have compared the MCD43 MODIS product with different BRDF inversion methods through the white sky albedo analysis. Moreover, we presented and studied three methods that strengthen the VJB method and improve its time processing. The results show that both the VJB and the proposed methods present good agreement with the MCD43 MODIS product, obtaining errors lower than 5% 6% for most cases. The main discrepancies with the MODIS product were detected along mountainous areas in the winter season. As commented in the Results section, the reason must be due to the lack of data which may lead to insufficient angular sampling. Therefore, in these cases, the difficulty of obtaining the BRDF leads to higher errors regardless of the method considered. In the case of the MODIS product, these situations are solved by using a backup algorithm which constrains the BRDF shape from prior information but adjusts it to match the observations made [19]. In the case of the VJB method and the proposed methods, they are based on V and R dependence on the NDVI over a year. The VJB method particularly divides the NDVI into five classes with equal population. Considering the lack of data during the winter in these pixels, they must be less represented by the V and R fitting. In the same way, the proposed methods consider all the data through a year to invert the BRDF, which gives less weight to less frequent data. Comparing the results provided by the methods proposed with the VJB method, we obtain similar values, although the VJB method led to the highest proportion of pixels (8.2%) with errors higher than 15% in mountainous areas, obtaining the lowest proportion of these pixels (6.9%) with the 5param Rsqr method. Overall, considering every pixel and all the data, the VJB method RMSE was 5.0%, while it was 6.1%, 5.1%, and 5.3% for the 4param, 5param Rsqr, and 5param Vsqr methods, respectively. Consequently, the VJB and the 5param Rsqr methods provide the lowest error. The results therefore lead to the same conclusion as that by Breon and Vermote [3] (although they analyzed the normalized reflectance) that the VJB method (as well as the three methods proposed) provides equivalent albedo results as the MDC43 MODIS product with the advantage of daily versus 16-day temporal resolution. Regarding the methods proposed, we also obtained equivalent results as that of the VJB method with the advantage of using more robust algorithms that avoided the NDVI classification into five different classes and speeded up the time processing, reducing it by 44%. Among the three methods, including a fifth parameter (5param Rsqr and 5param Vsqr versus 4param) supposes an additional parameter in the system equation (which did not change the time processing), but it improves 4param results from 6.1% to 5.1% when using 5param Rsqr. 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P. d Entremont, B. Hu, S. Liang, J. L. Privette, and D. Roy, Proc. 1st Oper. BRDF, Albedo Nadir Reflectance Products MODIS, Remote Sens Environ, vol. 83, no. 1 2, pp , Nov [19] NASA EOS-MODIS Doc., V5.0 A. H. Strahler, W. Lucht, C. B. Schaaf, T. Tsang, F. Gao, X. Li, J.-P. Muller, P. Lewis, and M. J. Barnsley, MODIS BRDF Albedo Product: Algorithm Theoretical Basis Document 1999, NASA EOS-MODIS Doc., V5.0. [20] E. F. Vermote, C. Justice, and F. M. Bréon, Towards a generalized approach for correction of the BRDF effect in MODIS directional reflectances, IEEE Trans. Geosci. Remote Sens., vol. 47, no. 3, pp , Mar Belen Franch received the Ph.D. degree in physics from the University of Valencia, Valencia, Spain, in She is currently a Research Assistant Professor with the Department of Geographical Sciences, University of Maryland, College Park, MD, USA, and a Science Collaborator in the NASA Goddard Space Flight Center. Her research interests include atmospheric correction in the solar spectral range, the study and application of BRDF inversion methods and land surface albedo estimation and analysis. Eric F. Vermote received the Ph.D. degree from the Laboratoire d Optique Atmospherique, University of Lille, Lille, France. Since 2009, he has been a Research Professor with the Department of Geographical Sciences, University of Maryland, College Park, MD, USA. He is a team member of the NASA Moderate Resolution Imaging Spectroradiometer Science Team and is responsible for the surface reflectance product and monitoring instrument calibration and performance for the MODLAND Team. He is also a member of the NASA NPP Science Team responsible for VIIRS atmospheric correction and EDR evaluation. He was also leading the development of the atmospheric correction algorithm of TM/ETM+ data for the LEDAPS project, in and was a Landsat Science Member in , responsible for the development of the surface reflectance product. In 2012, he was selected as a Landsat Data Continuity Mission Science Team member. José A. Sobrino is a Professor of physics and remote sensing, the President of the Spanish Association of Remote Sensing, and the Head of the Global Change Unit at the University of Valencia, Valencia, Spain. He is the author of more than 150 papers and the Coordinator of the European projects WATERMED and EAGLE. His research interest include atmospheric correction in visible and infrared domains, the retrieval of emissivity and surface temperature from satellite images, and the development of remote sensing methods for land cover dynamic monitoring. Dr. Sobrino has been a member of the Earth Science Advisory Committee of the European Space Agency since November of He is the Chairperson of the series of International Symposiums on Recent Advances in Quantitative Remote Sensing. Yves Julien received the Ph.D. degree in earth physics and thermodynamics from the University of Valencia, Valencia, Spain, in 2008 and the Ph.D. degree in electronics, electrotechnics, and automatics (specialized in remote sensing) from the University of Strasbourg, France. He is a Researcher at the Global Change Unit at the University of Valencia. He is the author of more than 23 international papers ( publications.htm). His research interests include temperature and vegetation index interactions as well as time series analysis for land cover dynamic monitoring.