Retrieval of Surface Albedo on a Daily Basis: Application ...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014 7549

Retrieval of Surface Albedo on a DailyBasis: 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 tothe MCD43 MODerate Resolution Imaging Spectroradiometer(MODIS) product, focusing on the white sky albedo parameter.We also present and study three different methods based on theVJB assumption, the 4param, 5param Rsqr, and 5param Vsqr. Weuse daily MODIS Climate Modeling Grid data both from Terraand Aqua platforms from 2002 to 2011 for all the pixels overEurope. We obtain an overall root-mean-square error of 5% whenusing the VJB method and 6.1%, 5.1%, and 5.3% for the 4param,5param Rsqr, and 5param Vsqr methods, respectively. The maindifferences between the methods are located in areas where onlyfew cloud-free snow-free samples were available that correspondmainly to mountainous areas during the winter. We finally con-clude that the VJB method has an equivalent performance inderiving the white sky albedo results to the MODIS productwith the advantage of daily temporal resolution. Additionally, wepropose the 5param Rsqr method as an alternative to the VJBmethod due to its decreased data processing time.

Index Terms—Albedo, bidirectional reflectance distributionfunction (BRDF) inversion, MODerate Resolution Imaging Spec-troradiometer (MODIS), VJB method.

I. INTRODUCTION

LAND surface broad-band albedo is a critical landphysical parameter affecting the Earth’s climate. It has

been well recognized that surface albedo is among the mainradiative uncertainties in current climate modeling. In fact,an accuracy requirement of 5% is suggested by the GlobalClimate Observing System [7] for albedo characterization atspatial and temporal scales compatible with climate studies.Modern climate models are now attaining the ability to incor-porate global surface albedo spatial features. Satellite remotesensing provides the only practical way of producing high-quality global albedo data sets with high spatial and temporalresolutions.

Manuscript received May 29, 2013; revised October 28, 2013 and January22, 2014; accepted March 15, 2014. This work was supported in part by theSpanish Ministerio de Economia y Competitividad (EODIX, project AYA2008-0595-C04-01; CEOS-SPAIN, project AYA2011-29334-C02-01) and in part bythe European Union (CEOP-AEGIS, project FP7-ENV-2007-1 proposal No.212921; WATCH, project 036946).

B. Franch is with the Department of Geographical Sciences, University ofMaryland, College Park, MD 20742 USA.

E. F. Vermote is with NASA Goddard Space Flight Center, Greenbelt, MD20771 USA.

J. A. Sobrino and Y. Julien are with the Global Change Unit, ImageProcessing Laboratory (UCG-IPL), Parque Cientifico, Universitat de Valencia,46100 Valencia, Spain.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2014.2313842

Albedo is highly variable in space and time, both as a resultof changes in surface properties (e.g., snow deposition or sea-ice growth and melting, changes in soil moisture and vegetationcover, etc.) and as a function of changes in the illumina-tion conditions (solar angular position, atmospheric and cloudproperties, etc.). Consequently, a daily temporal resolution isrequired by the Global Climate Observing System (GCOS) [7].For view-illumination geometries typical of medium-resolutionsensors such as the MODerate Resolution Imaging Spectrora-diometer (MODIS) onboard the Terra and Aqua satellites, inorder to obtain enough bidirectional observations to retrieve thebidirectional reflectance distribution function (BRDF) free pa-rameters, a period of sequential measurement is usually neededto accumulate sufficient observations. During this temporalwindow, the model parameters are assumed to be constant. Thismethod is currently used to derive the MODIS BRDF/albedoproduct, MCD43 [19], which combines registered multidatemultiband atmospherically corrected surface reflectance datafrom Terra and Aqua data to fit a BRDF in seven spectralbands over a composite period of 16 days, although MCD43is produced every eight days.

Several studies have evaluated the MODIS MCD43 productaccuracy using in situ data [5], [8], [11], [12], [16]. They founda high correlation between in situ and satellite albedos foralmost all cases, concluding that the MODIS albedo productmet an absolute accuracy requirement of 0.05. However, insome cases, the studies observed negative mean biases [8], [16]in which the magnitude increased as the solar zenith angleincreased [12]. Cescatti et al. [4] compared MODIS albedoretrievals with surface measurements taken at 53 FLUXNETsites that met strict conditions of land cover homogeneity, andthey observed a good agreement for forest sites. However, incase of nonforest sites with larger albedo values (grasslands andcroplands), MODIS generally underestimated in situ measure-ments across the seasonal cycle.

Nevertheless, one limitation of the method employed in theMODIS BRDF/albedo product is the assumption of the stabilityof the target over the temporal compositing period. Anotherlimitation is that it requires several cloud-free measurements ofthe target during the compositing period. Additionally, the ob-servation geometry of these measurements may not be suitableto properly constrain the BRDF model.

Looking for an improvement in the albedo temporal res-olution that mitigated the assumption of a stable target,Vermote et al. [20] presented the VJB method that assumes thatthe BRDF shape variations throughout a year are limited andlinked to the Normalized Difference Vegetation Index (NDVI).This method permits more accurate tracking of events such as

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7550 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 12, DECEMBER 2014

snow melt and vegetation phenology. Additionally, it retainsthe highest temporal resolution (daily, cloud cover permitting)without the noise generated by the day-to-day changes inobservation geometry. Bréon and Vermote [3] compared thismethod with the MCD43 MODIS product for the correction ofthe surface reflectance time series. They worked with MODISClimate Modeling Grid (CMG) data along 2003, analyzing arepresentative set of +100 targets selected on the basis of thelocation of Aerosol Robotic Network (AERONET) sites. Theirresults showed that the performances of the two approachesare very similar, demonstrating that a simple four-parameterNDVI-scaled model performs as well as a more complex modelwith many more degrees of freedom. Abelleyra and Verón [1]supported recently these conclusions at higher spatial resolu-tion by comparing (at 250-m spatial resolution) the surfacereflectance corrected for the BRDF using the VJB method tothe BRDF correction using the MCD43 product. Although theyfound similar results, the VJB showed slightly better generalstatistics (lower noise median values) and, at pixel-by-pixellevel, presented the highest differences with the MCD43 thatare a function of crop type and differing time series lengths.

The purpose of this paper is to complete the Bréon andVermote [3] study comparing the MCD43 product with theVJB method through the white sky albedo parameter. Addition-ally, we propose three methods in order to improve the timeprocessing of the VJB method. In this paper, we focus ouranalysis on MODIS CMG Collection 6 data from both Aquaand Terra satellites over Europe from 2002 to 2011. We usedcoarse resolution in order to work at global scale. This enabledus to study several different classes of surfaces. Moreover, theCMG product has been well established as an official MODISproduct for the global modeling community. In fact, Gao et al.[6] discuss the implications for the representation of albedoat coarser spatial resolution in climate models. Although theyworked with Collection 4 data, they concluded that globalalbedos at this resolution have spatial and temporal patternsappropriate for the underlying land cover classes.

II. DATA AND METHODS

A. Satellite Data

This study used the MODIS CMG surface reflectance Col-lection 6 data (M{OY}DCMG) which are gridded in the linearlatitude–longitude projection at 0.05◦ resolution. Science datasets provided for this product include surface reflectance valuesfor bands 1–7, brightness temperatures for bands 20, 21, 31, and32, solar and view zenith angles, relative azimuth angle, ozone,granule time, quality assessment, cloud mask, aerosol opticalthickness at 550 nm, and water vapor content. We analyzeddaily data from both Aqua and Terra platforms over Europefrom 2002 to 2011.

Additionally, we used the land cover type yearly CMG thatprovides the dominant land cover type and also the subgridfrequency distribution of land cover classes and has the samespatial resolution (0.05◦) as the surface reflectance product. TheCMG product (MCD12C1) is derived using the same algorithmthat produces the V005 Global 500-m land cover type product(MCD12Q1). It contains three classification schemes, which

describe the land cover properties derived from observationsspanning a year’s input of Terra and Aqua MODIS data. Theprimary land cover scheme, which we consider in this paper,identifies 17 land cover classes defined by the InternationalGeosphere Biosphere Programme, which includes 11 naturalvegetation classes, 3 developed and mosaicked land classes, and3 nonvegetated land classes.

The study is centered in the analysis of the MCD43BRDF/albedo snow-free quality product (MCD43C2). It con-tains the weighting parameters for the models used to de-rive the albedo and nadir BRDF-adjusted reflectance products(MCD43C3 and MCD43C4) describing only snow-free condi-tions. The models support the spatial relationship and parametercharacterization best describing the differences in radiation dueto the scattering (anisotropy) of each pixel, relying on multidateatmospherically corrected cloud-cleared input data measuredover 16-day periods. Both Terra and Aqua data are used in thegeneration of this product, providing the highest probability forquality input data and designating it as an “MCD,” meaning“combined,” product.

The MCD43 MODIS product is estimated using a kernel-based BRDF model [19], [18]. The theoretical basis of thissemiempirical model is that the land surface reflectance is mod-eled as a sum of three kernels (1) representing basic scatteringtypes: isotropic scattering, radiative transfer-type volumetricscattering as from horizontally homogeneous leaf canopies, andgeometric-optical surface scattering as from scenes containing3-D objects that cast shadows and are mutually obscured fromview at off-nadir angles. Following the Vermote et al. [20]notation, the surface reflectance (ρ) is written as

ρ(θs, θv, φ)=k0

[1+

k1k0

F1(θs, θv, φ)+k2k0

F2(θs, θv, φ)

](1)

where θs is the sun zenith angle, θv is the view zenith angle, ϕis the relative azimuth angle, F1 is the volume scattering kernel,based on the Ross-Thick function derived by Roujean et al.[17], and F2 is the geometric kernel, based on the Li-sparsemodel [9] but considering the reciprocal form given by Lucht[13]. Although these are the models used in the MCD43 prod-uct, in order to derive the BRDF with the VJB method and theproposed methods, we consider the same models but correctedfor the Hot-Spot process proposed by Maignan et al. [14]. F1

and F2 are fixed functions of the observation geometry, but k0,k1, and k2 are free parameters. Following this notation, we useV as k1/k0 (since it is linked to the Volume kernel) and R fork2/k0 (since it is linked to the geometric kernel and representsthe surface Roughness). These parameters (V and R) representthe shape of the BRDF, while k0 is the amplitude.

In this paper, we analyze the white sky albedo, whichwas estimated from the BRDF parameters following Strahleret al. [19]. The spectral to broad-band albedo conversion wasachieved following Liang [10].

B. MODIS MCD43 BRDF Inversion

For view-illumination geometries typical of medium-resolution sensors such as Terra and Aqua MODIS, in orderto obtain enough bidirectional observations to retrieve the

FRANCH et al.: RETRIEVAL OF SURFACE ALBEDO ON DAILY BASIS: APPLICATION TO MODIS DATA 7551

BRDF free parameters, a period of sequential measurement isusually needed to accumulate sufficient observations. Duringthis temporal window, the model parameters are assumed to beconstant. This method is currently used to derive the MODISBRDF/albedo product (MCD43), which combines Terra andAqua data to invert the BRDF model parameters over a com-posite period of 16 days, although it provides images everyeight days. Additional information about the method can befound in [19].

C. VJB Method

Vermote et al. [20] proposed the VJB method for the inver-sion of the BRDF model with less constraint on the stabilityof the target. This method accounts for the fact that the targetreflectance changes during the year, but assumes that the BRDFshape variations are limited. Another way of presenting thehypothesis is that k0, k1, and k2 vary in time but k1 and k2stay proportional to k0. Additionally, the difference betweenthe successive observations is mainly attributed to directionaleffects while the variation of k0(t) is supposed small. There-fore, V and R can be derived through the minimization of theday-to-day variations of k0(t)

ρ(ti)⌊1+V F i+1

1 +RF i+12

⌋≈ρ(ti+1)

⌊1+V F i

1+RF i2

⌋. (2)

This leads to a system of equations that can only be solvedthrough iteration. The objective is to minimize the meritfunction

M=

N−1∑i=1

(ρi+1

[1+V F i

1+RF i2

]−ρi

[1+V F i+1

1 +RF i+12

])2dayi+1 − dayi + 1

.

(3)

Therefore, R and V are solved by the classic derivation of themerit function which leads to

⎛⎜⎜⎝

N−1∑i=1

ΔiρF1ΔiρF1

N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1

ΔiρF2ΔiρF2

⎞⎟⎟⎠

⊗(VR

)

=

⎛⎜⎜⎝

−N−1∑i=1

ΔiρΔiρF1

−N−1∑i=1

ΔiρΔiρF2

⎞⎟⎟⎠ (4)

where

Δid = dayi+1 − dayi + 1

Δiρ =(ρi+1 − ρi)√

Δid

ΔiρF1 =

(ρi+1F

i1 − ρiF

i+11

)√Δid

ΔiρF2 =

(ρi+1F

i2 − ρiF

i+12

)√Δid

. (5)

In order to estimate V and R to apply (4), each year of thedata set considered is segmented into five different classesof NDVI with equal population. The reason of assuming adependence of V and R with the NDVI over a year is thatBRDF has been shown to be significantly different for baresoil and vegetated surfaces because vegetated surfaces showhigher anisotropy than bare soil [2]. Also, the NDVI is sensitiveto the presence of vegetation and is easy to derive, and asa ratio, the NDVI implicitly contains a directional correctionbecause 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 inorder to minimize outlier influence. The error bars are estimatedby running the inversion ten times, each time removing 10%of the data set at random. Finally, these functions can beapplied to each NDVI image, obtaining instantaneous BRDFparameters.

This method, in contrast to the MODIS BRDF/albedo prod-uct inversion, can generate a product with the same frequencyas the observations, which is particularly useful for monitoringrapid changes of vegetation cover, e.g., for agricultural areas.However, with the aim of improving the processing time of theVJB method, we will present three different methods based onthe original algorithm.

D. 4parameter Method

The 4parameter method consists of considering that R and Vare represented by a linear function of the NDVI (that coincideswith the assumption of the VJB method). That is

V =V0 + V1NDV I (6)

R =R0 +R1NDV I. (7)

However, compared to the VJB method, we include this as-sumption into the merit function, which leads to

A⊗

⎛⎜⎝

V0

V1

R0

R1

⎞⎟⎠ =

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

−N−1∑i=1

ΔiρΔiρF1

−N−1∑i=1

ΔiρΔiρF1NDV I

−N−1∑i=1

ΔiρΔiρF2

−N−1∑i=1

ΔiρΔiρF2NDV I

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(8)

where A is defined as (9), shown at the bottom of the nextpage. We have used the same notation described in (5). In thisway, each parameter will be estimated by inverting this matrixover each year of the data set but avoiding the classificationdepending on the NDVI. This method, as well as the VJBmethod, provides a product with the same frequency as theobservations.


E. 5parameter Rsqr Method

Next, we will consider that the V parameter depends linearlyon the NDVI but the R parameter presents a second-degreedependence. The R parameter is linked to the geometricalkernel which models the surface roughness. A quadratic de-pendence of R with the NDVI should describe adequately, forinstance, agricultural areas. Along these surfaces, low NDVIvalues describe bare soils where R should be low. The firststages of vegetation growth should increase R (increase theroughness of the surface) until a maximum value. Finally, ascrops get denser, one may expect R to decrease. Therefore, thismethod assumption can be written as

V =V0 + V1NDV I (10)

R =R0 +R1NDV I +R2NDV I2. (11)

Now, the derivation of the merit function is

C⊗

⎛⎜⎜⎜⎝

V0

V1

R0

R1

R2

⎞⎟⎟⎟⎠ =

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

−N−1∑i=1

ΔiρΔiρF1

−N−1∑i=1

ΔiρΔiρF1NDV I

−N−1∑i=1

ΔiρΔiρF2

−N−1∑i=1

ΔiρΔiρF2NDV I

−N−1∑i=1

ΔiρΔiρF2NDV I2

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(12)

where C is defined as (13), shown at the bottom of the page.

F. 5parameter Vsqr Method

Finally, we consider that R depends linearly on the NDVIbut V presents a second-degree dependence. The V parameteris linked to the volume kernel which models a collectionof randomly located facets absorbing and scattering radiationwhich represent mainly leaves of canopies and can also modelthe 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 iswritten as

V =V0 + V1NDV I + V2NDV I2 (14)

R =R0 +R1NDV I. (15)

Aside from the 5parameter Rsqr method, we have includedanother parameter to the VJB model. Following the samescheme as the previous method, now, the derivation of the meritfunction is

B⊗

⎛⎜⎜⎜⎝

V0

V1

V2

R0

R1

⎞⎟⎟⎟⎠ =

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

−N−1∑i=1

ΔiρΔiρF1

−N−1∑i=1

ΔiρΔiρF1NDV I

−N−1∑i=1

ΔiρΔiρF1NDV I2

−N−1∑i=1

ΔiρΔiρF2

−N−1∑i=1

ΔiρΔiρF2NDV I

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(16)

where B is defined as (17), shown at the bottom of the next page.

A =

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

N−1∑i=1

(ΔiρF1)2

N−1∑i=1

(ΔiρF1)2NDV I

N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1

ΔiρF1ΔiρF2NDV I

N−1∑i=1

(ΔiρF1)2NDV I

N−1∑i=1

(ΔiρF1)2NDV I2

N−1∑i=1

ΔiρF1ΔiρF2NDV IN−1∑i=1

ΔiρF1ΔiρF2NDV I2

N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1


(ΔiρF2)2

N−1∑i=1

(ΔiρF2)2NDV I

N−1∑i=1


ΔiρF1ΔiρF2NDV I2N−1∑i=1

(ΔiρF2)2NDV I

N−1∑i=1

(ΔiρF2)2NDV I2

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(9)

C=

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

N−1∑i=1

(ΔiρF1)2

N−1∑i=1

(ΔiρF1)2NDV I

N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1



N−1∑i=1

(ΔiρF1)2NDV I

N−1∑i=1

(ΔiρF1)2NDV I2

N−1∑i=1




N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1


(ΔiρF2)2

N−1∑i=1

(ΔiρF2)2NDV I

N−1∑i=1

(ΔiρF2)2NDV I2

N−1∑i=1



(ΔiρF2)2NDV I

N−1∑i=1

(ΔiρF2)2NDV I2

N−1∑i=1

(ΔiρF2)2NDV I3

N−1∑i=1



(ΔiρF2)2NDV I2

N−1∑i=1

(ΔiρF2)2NDV I3

N−1∑i=1

(ΔiρF2)2NDV I4

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(13)


In this paper, we will compare the MCD43 product with theresults obtained from the VJB method and the three improve-ments proposed. For this purpose, we will focus on the whitesky albedo or bihemispherical-reflectance analysis. It is definedas albedo in the absence of a direct component when the diffusecomponent is isotropic. Thus, it is a constant and does notdepend on the view zenith angle like the blue sky albedo orblack sky albedo does

αws(λ) =

2∑i=0

ki(λ)Hi(λ) (18)

where

Hi(λ) = 2

π/2∫0

hi(θs, λ) sin θs cos θsdθs (19)

hi(θs, λ) =

2π∫0

π/2∫0

Fi(θs, θv, φ;λ) sin θv cos θvdθvdφ. (20)

Finally, the spectral to broad-band conversion is achieved fol-lowing Liang [10].

Since the temporal resolution of the MODIS product is eightdays while the other methods provide daily albedo estimation,during the whole study, we averaged each eight-day product, fora total of 16 days, in order to be sure that we were comparingequivalent results.

In this paper, we estimate the root-mean-square error(RMSE) for each day (D) of an average year, which can beexpressed as

RMSED =√

bias2D + stddev2D (21)

where stddevD is the standard deviation of the day Ddefined as

stddevD=

√√√√ 1

n

2011∑i=2002

(αD,i(V JB,prop meth)−αD,i(MCD43)

)2(22)

Fig. 1. Temporal evolution of the broad-band white sky albedo derived withthe different methodologies at the Ispra site.

and biasD is the bias of the day D

biasD=

2011∑i=2002

(αD,i(V JB,prop meth)−αD,i(MCD43)

)n

(23)

where α is the broad-band white sky albedo for the day D alongthe years and n is the total of the data considered. Note thatwe estimate the relative RMSE to compare the VJB and theproposed methods with the MCD43 official product, not theabsolute RMSE that would be estimated using in situ data.

III. RESULTS

First of all, we processed all the data. The MCD43 wasfiltered following the quality flag labels for best quality (75%or more with best full inversion). All the data considered in thiswork corresponded to clear snow-free land pixels following thecloud/snow/land mask. Comparing the proposed algorithms tothe VJB method, we detected a decrease in the time processingof 44%. We did not observe any significant difference in thetime processing of the three proposed methods.

In order to compare the methodologies, we analyzed in detaila 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 whitesky albedo derived with the different methodologies. The plot

B=

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

N−1∑i=1

(ΔiρF1)2

N−1∑i=1

(ΔiρF1)2NDV I

N−1∑i=1

(ΔiρF1)2NDV I2

N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1

ΔiρF1ΔiρF2NDV I

N−1∑i=1

(ΔiρF1)2NDV I

N−1∑i=1

(ΔiρF1)2NDV I2

N−1∑i=1

(ΔiρF1)2NDV I3

N−1∑i=1



N−1∑i=1

(ΔiρF1)2NDV I2

N−1∑i=1

(ΔiρF1)2NDV I3

N−1∑i=1

(ΔiρF1)2NDV I4

N−1∑i=1



N−1∑i=1

ΔiρF1ΔiρF2

N−1∑i=1



(ΔiρF2)2

N−1∑i=1

(ΔiρF2)2NDV I

N−1∑i=1




(ΔiρF2)2NDV I

N−1∑i=1

(ΔiρF2)2NDV I2

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

(17)


Fig. 2. Plot of the broad-band white sky albedo of the proposed methods andthe VJB method versus the MCD43 product.

shows that the VJB method provides similar results as that ofthe proposed methods, and we did not observe significant dif-ferences between the proposed methods. In 2004, VJB presentsslightly lower values than the proposed methodologies, whilefor 2007 and 2009, it shows slightly higher albedo values.The 5parameter Rsqr method showed similar results as that ofthe 4parameter method while it showed slightly lower valuesduring 2005 and 2010 and higher values during 2007 and 2008when compared to the 5parameter Vsqr method. Moreover, theMCD43 product temporal evolution exhibits greater variabilitythan the other methodologies mainly during the summer, whichleads to greater difference with the other methods. Both theVJB and the proposed methods provided data continuously,while the MCD43 product did not provided values during someperiods of winter or spring. Comparing the number of dataprovided by the VJB and the proposed methods with the totaldata provided by the MCD43 product, the fraction of dataprovided by the MCD43 product was 70%.

Fig. 2 presents the white sky broad-band albedo estimatedfrom the VJB method and the proposed methods versus theMCD43 product along the time series considered at the Isprasite. The plot shows that larger difference with the originalproduct corresponds to the highest values of albedo. TheVJB method provides slightly better results than the proposedmethods with the highest correlation coefficient. The totalRMSE of each method against the MCD43 product in this sitewas 0.008 in case of the VJB method and 0.009 in case of theproposed methods, which suggests a relative error of 5%–6%.This range of errors meets the required accuracy proposed bythe GCOS [7].

Fig. 3 shows the behavior of V and R (band 2) with the NDVIfor the five NDVI classes of the Ispra pixel considered in theVJB method in 2007. In these graphs, we represented the VJBmethod as well as the three proposed method fittings. Althoughthe proposed methods consider every data to compute V and R(not five-NDVI-class linear fitting), Fig. 3 provides the V and Rapproached behavior with the NDVI. At first glance, V is morelinear than R when represented versus the NDVI, so a second-degree fitting is more appropriate in case of the R parameter.Therefore, the 5parameter Rsqr method fits well the R datawhile 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 Isprapixel considered in the VJB method in the particular case of 2007.

contrary, the 5parameter Vsqr method does not fit the V data,underestimating them, while it provides the same fitting as thatof the VJB method in case of the R parameter. Fig. 3 shows thatthe 4parameter linear fit provides slightly higher R values thanthe VJB method (in Fig. 3(a), it is coincident to the 5parameterVsqr fitting) and lower V values than the VJB method [inFig. 3(b), it is coincident to the 5parameter Rsqr fitting]. In fact,although both methods assume V and R linear dependence withthe NDVI, each one of them solves the problem differently.Since the volume kernel is mostly positive and the geometrickernel is always negative, the 4parameter method provideslower albedo values than the VJB method in this particular case.

In order to see the spatial variability of the methods versusthe MODIS product, we proceed to analyze the whole Europescene considering all the data to analyze the error through thetime series. Fig. 4 shows the percentage of the total RMSEof the VJB method [see Fig. 4(a)] and the proposed methods[see Fig. 4(b)–(d)] against the MCD43 product. The imagesdisplay that southern latitudes present lower errors with valueslower than 5% while they increase for northern latitudes withvalues that can reach 10% along Great Britain, Ireland, and theScandinavian Peninsula. Also, we obtain the highest errors formountainous areas with errors that can reach 20%. ComparingVJB to the proposed methods, the VJB presents errors higherthan 15% in 8.2% of total land pixels while these errors com-prise 7.3%, 6.9%, and 7.8% of pixels when using the 4param,5param Rsqr, and 5param Vsqr, respectively. The results show


Fig. 4. Percentage RMSE of the (a) VJB method, (b) 4param method,(c) 5param Rsqr method, and (d) 5param Vsqr method against the MCD43product.

additional differences comparing the methods’ errors alongother areas. In northern Africa, eastern Spain, Germany, Italy,or southern Sweden, the 4param provides higher errors than theVJB. However, the 5param Rqr and 5param Vsqr provide betterresults in these areas than the 4param which got similar resultsas that of the VJB. Overall, the total RMSE through the Europescene was 5.0% in case of the VJB method and 6.1%, 5.1% and5.3% in case of the 4param, 5param Rsqr, and 5param Vsqrmethods, respectively.

Fig. 5 shows the histogram of Fig. 4 images, and it showstwo peaks. The first one is the highest one for every methodand corresponds to 1.5% RMSE in case of VJB (which presentsthe highest number of pixels), 5param Rsqr, and 5param Vsqr.However, the 4param first peak is located around 2% RMSEand shows the lowest number of pixels. The second peakthat represents a similar number of pixels in every methodis centered around 6% RMSE for VJB and around 7% forthe other methods. From this plot, the conclusion is that mostpixels present an RMSE around 1.5% or 2% depending on themodel, although there are other significant numbers of pixelsthat present an RMSE around 6% or 7%. The best results of thishistogram corresponded to the VJB method, although 5paramRsqr and 5param Vsqr showed similar profiles.

Finally, we analyzed the difference between each method,dividing the study into different classes extracted from theMCD12C1 MODIS product. Fig. 6 displays the spatial distri-bution of each class through the Europe scene. In this paper,we will consider only the most representative classes of theconsidered scene. Table I shows the land cover classificationtypes. Fig. 7 shows the RMSE of the average year for eachclass for each method against the MCD43 product. The RMSEof an average year is defined as the RMSE of each dayof the year (DOY) through every year studied (from 2002

Fig. 5. Histogram of Fig. 4 images.

Fig. 6. Land cover type yearly CMG (MCD12C1 MODIS product) and theclasses considered in this study.

TABLE ILAND COVER CLASSIFICATION TYPES CONSIDERED IN THIS STUDY

to 2011) and quantifies the difference of the tested methodsthroughout the year. The plots show that the highest errorswere obtained for classes 1 and 5 (the classes that representforests) during the winter. Looking at Fig. 6, those classes(mostly class 1) are located along the northern latitudes or alongrugged mountainous areas that, during the winter, are coveredby snow. Since the snow pixels were masked along both theMCD43 product and the MODIS reflectance data (from whichwe obtained the albedo with the other inversion methods),


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 muchless data than during the rest of the year. Previous studies thatvalidated the surface albedo of the MCD43 product with in situmeasurements also found larger differences in the winter season[8], [4]. Jin et al. [8] suggested that this was the result of theincreased heterogeneity of surface reflectivity due to the pres-ence of residual snow and canopy heterogeneity. The greatestdifference 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 Vsqrmethod while 5param Rsqr led to similar RMSE as comparedto the VJB method. Leaving aside the winter season, the RMSEof classes 1 and 5 from DOY 20 to 305 changed from 0.01 to0.02, obtaining the poor results with the 5param Vsqr methodduring the spring and similar results with the other methods.Regarding the other classes, the RMSE generally presented val-ues between 0.01 and 0.02. These classes that describe mainlystable surfaces along the year suppose most of the surface


in the central and southern latitudes. The lowest errors wereobtained for class 16 (barren or sparsely vegetated), where theerrors decreased below 0.01. Comparing the VJB method withthe other methods, they provided similar results with the VJBmethod. The larger differences between the proposed methodsand VJB (leaving classes 1 and 5 aside) were detected forclasses 7 (open shrublands), 8 (woody savannas), and 10 (grass-lands). In case of classes 7 and 8, VJB led to slightly lowerRMSE than the other methods from DOY 100 to 150 (spring).However, for classes 7 and 10, the other methods providedslightly better results from DOY 200 to 300 (end of summerand fall). Locating these classes in Fig. 6, class 7 is placed alongNorway, 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 amongmethods were detected in Fig. 4. Finally, in this analysis, we didnot see significant differences between the proposed methods(from class 7 to 16) showing similar RMSEs. This must be aconsequence of including several pixels (not just every pixel ofthe same class but also the temporal evolution of each pixel forthe same DOY through the years) into the RMSE estimation.

IV. DISCUSSION AND CONCLUSIONS

In this paper, we have compared the MCD43 MODIS productwith different BRDF inversion methods through the white skyalbedo analysis. Moreover, we presented and studied threemethods that strengthen the VJB method and improve its timeprocessing.

The results show that both the VJB and the proposed methodspresent good agreement with the MCD43 MODIS product,obtaining errors lower than 5%–6% for most cases. The maindiscrepancies with the MODIS product were detected alongmountainous areas in the winter season. As commented in theResults section, the reason must be due to the lack of datawhich may lead to insufficient angular sampling. Therefore,in these cases, the difficulty of obtaining the BRDF leads tohigher errors regardless of the method considered. In the caseof the MODIS product, these situations are solved by using abackup algorithm which constrains the BRDF shape from priorinformation but adjusts it to match the observations made [19].In the case of the VJB method and the proposed methods, theyare based on V and R dependence on the NDVI over a year.The VJB method particularly divides the NDVI into five classeswith equal population. Considering the lack of data during thewinter in these pixels, they must be less represented by the Vand R fitting. In the same way, the proposed methods considerall the data through a year to invert the BRDF, which gives lessweight to less frequent data. Comparing the results provided bythe methods proposed with the VJB method, we obtain similarvalues, although the VJB method led to the highest proportionof pixels (8.2%) with errors higher than 15% in mountainousareas, obtaining the lowest proportion of these pixels (6.9%)with the 5param Rsqr method. Overall, considering every pixeland all the data, the VJB method RMSE was 5.0%, whileit 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 byBreon and Vermote [3] (although they analyzed the normalizedreflectance) that the VJB method (as well as the three methodsproposed) provides equivalent albedo results as the MDC43MODIS product with the advantage of daily versus 16-daytemporal resolution.

Regarding the methods proposed, we also obtained equiva-lent results as that of the VJB method with the advantage of us-ing more robust algorithms that avoided the NDVI classificationinto five different classes and speeded up the time processing,reducing it by 44%. Among the three methods, including afifth parameter (5param Rsqr and 5param Vsqr versus 4param)supposes an additional parameter in the system equation (whichdid not change the time processing), but it improves 4paramresults from 6.1% to 5.1% when using 5param Rsqr. Finally, wepropose the 5param Rsqr method as an alternative to the VJBmethod as it provides the best results mainly in mountainousregions during the winter season.

Note that the main scope of this paper is the intercomparisonof the VJB and the proposed methods with the MCD43 officialproduct, considering it as a well-established method that hasbeen already validated in previous works. Future work willfocus on validating the results of the different methods within situ data in order to develop a more extensive study. Thecollection 6 MCD43 algorithm will generate daily albedo, andthe start of the processing is scheduled early this year. Futurework will compare both approaches on a daily basis.

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Belen Franch received the Ph.D. degree in physicsfrom the University of Valencia, Valencia, Spain,in 2013.

She is currently a Research Assistant Professorwith the Department of Geographical Sciences, Uni-versity of Maryland, College Park, MD, USA, anda Science Collaborator in the NASA Goddard SpaceFlight Center. Her research interests include atmo-spheric correction in the solar spectral range, thestudy and application of BRDF inversion methodsand land surface albedo estimation and analysis.

Eric F. Vermote received the Ph.D. degree from theLaboratoire d’Optique Atmospherique, University ofLille, Lille, France.

Since 2009, he has been a Research Professorwith the Department of Geographical Sciences, Uni-versity of Maryland, College Park, MD, USA. Heis a team member of the NASA Moderate Resolu-tion Imaging Spectroradiometer Science Team andis responsible for the surface reflectance product andmonitoring instrument calibration and performancefor the MODLAND Team. He is also a member of

the NASA NPP Science Team responsible for VIIRS atmospheric correctionand EDR evaluation. He was also leading the development of the atmosphericcorrection algorithm of TM/ETM+ data for the LEDAPS project, in 2003–2006and was a Landsat Science Member in 2006–2011, responsible for the develop-ment of the surface reflectance product. In 2012, he was selected as a LandsatData Continuity Mission Science Team member.

José A. Sobrino is a Professor of physics and remotesensing, the President of the Spanish Association ofRemote Sensing, and the Head of the Global ChangeUnit at the University of Valencia, Valencia, Spain.He is the author of more than 150 papers and theCoordinator of the European projects WATERMEDand EAGLE. His research interest include atmo-spheric correction in visible and infrared domains,the retrieval of emissivity and surface temperaturefrom satellite images, and the development of remotesensing methods for land cover dynamic monitoring.

Dr. Sobrino has been a member of the Earth Science Advisory Committeeof the European Space Agency since November of 2003. He is the Chairpersonof the series of International Symposiums on Recent Advances in QuantitativeRemote Sensing.

Yves Julien received the Ph.D. degree in earth physics and thermodynamicsfrom the University of Valencia, Valencia, Spain, in 2008 and the Ph.D. degreein 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 (http://www.uv.es/juy/publications.htm). His research interests include temperature and vegetationindex interactions as well as time series analysis for land cover dynamicmonitoring.

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