Albedo estimation from PolDER data
F. Jacob1 , M. Weiss1 , A. Olioso1, O. Hautecoeur2 ,
C. Franc¸ois3 , M. Leroy2 , and C. Ottl´e 3
1

INRA Bioclimatologie, Domaine St Paul, 84914 Avignon Cedex 9, France
2
CESBio, 18 avenue E.Belin, BP 2801, 31041 Toulouse Cedex 4, France
3
CETP / IPSL / CNRS, 10-12 avenue de l’Europe, 78140 Velizy, France

Camera-ready Copy for
Physics and Chemistry of the Earth
Manuscript-No. ???
Offset requests to:
F. Jacob
INRA-Bioclimatologie
Domaine St Paul, Site Agroparc
84914 Avignon Cedex 9 France


Journal: Physics and Chemistry of the Earth
MS No.: ???
First author: Jacob

1

Albedo estimation from PolDER data
F. Jacob1 , M. Weiss1 , A. Olioso1 , O. Hautecoeur 2,
C. Franc¸ois3 , M. Leroy2 , and C. Ottl´e 3
1

INRA Bioclimatologie, Domaine St Paul, 84914 Avignon Cedex 9, France
CESBio, 18 avenue E.Belin, BP 2801, 31041 Toulouse Cedex 4, France
3
CETP / IPSL / CNRS, 10-12 avenue de l’Europe, 78140 Velizy, France
2

Received ??? – Accepted ???

Abstract. Multi-spectral and multi-directional data acquired
during the ReSeDA experiment thanks to the airborne PolDER sensor were used to retrieve surface albedo over the
experimental site, for 16 days over the year 1997. The data
were available in four wave-bands (10 or 20 nm width) centered at 443 nm, 550 nm, 670 nm, and 865 nm. Zenith view
angles ranged from 0 to 50 o . This study aimed at evaluate a procedure based on the use of multi-directional and
multi-spectral information to retrieve surface albedo. Multidirectional information was extracted thanks to BRDF kerneldriven models. We compared the performances of three models (Walthall, Roujean and MRPV) in the four PolDER channels. The spectrally integrated value of the albedo was then
derived from the of the hemispherical reflectance estimates
in the four wave-bands, thanks to the linear regressions proposed by Weiss et al. (1999). 20 m resolution albedo maps
were computed, and then compared to field measurements
over several crop fields considering all days of the experiment. Results showed that PolDER retrievals overestimated
ground measurements. This might be explained, at least partially, by inappropriate linear combinations used for the spectral extrapolation.

1 Introduction
Surface albedo is defined as the fraction of incident solar
energy over the whole solar spectrum reflected in all directions (Pinty and Verstraete, 1992). It is especially important
for the global climate modeling (Dickinson, 1983), as well
as for surface fluxes estimation (Kustas et al., 1994; Olioso
et al., 1999). Generally, a relative accuracy of ¦ % is required (Henderson-Sellers and Wilson, 1983).
In this study, we map surface albedo using multi-directional
and multi-spectral remotely sensed data acquired with the
airborne PolDER sensor during the ReSeDA experiment. The

determination of albedo from remote sensing depends on two
Correspondence to: F. JACOB

aspects: i) the anisotropic behavior of natural surfaces requires the characterization of the angular distribution of the
reflected solar radiation (expressed as BRDF for Bidirectional
Reflectance Distribution Function) from the available directional measurements in a given wave-band; ii) the determination of the reflected energy over the whole solar spectrum
from the wave-band estimates requires a spectral extrapolation. Several methods have been developed to characterize
the BRDF from satellite data. Two classes may be distinguished: the inversion of radiative transfer models, and the
inversion of kernel-driven models. As the first one is mathematically complex and time consuming, we have chosen to
consider the second one, which has been validated by several
authors (see the review by Wanner et al. (1997)). Generally,
the spectral extrapolation is performed thanks to linear combinations. Several coefficient sets have been proposed and
validated in the literature (e.g. Tucker and Sellers (1986);
Brest and Goward (1987); Song and Gao (1999)). In this
study, we have chosen to use the coefficients proposed by
Weiss et al. (1999).
The ReSeDA experiment provided a framework with two
interesting aspects for the validation of the proposed approach:
i) it covered the whole cycles of different types of crops including winter (wheat) and summer crops (sunflower, corn);
ii) the high spatial resolution remote sensing data reduced
problems related to mixed pixels.

2 Data acquisition and preprocessing
2.1 The ReSeDA Field Experiment
The ReSeDA experiment lasted from December 1996 to
December 1997, in the South East of France (N 43 o 47’, E 4o
45’). The experimental site was a small agricultural region
(5¢5 km¾ ) with sunflower, wheat, corn, grassland and alfalfa
fields with a mean size of 200¢200 m ¾ (Pr´evot et al., 1998;
Olioso et al., 1998).



Journal: Physics and Chemistry of the Earth
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First author: Jacob

2

2.2 Airborne data

Francáois et al. (2000). The calibrated formulation had a linear shape, inducing a residual error of 0.003:

Airborne PolDER data were acquired approximately one
or two times per month, on clear sky days and at a 3000 m
altitude involving a 20 m nadir spatial resolution. Four flight
lines were parallel to the solar plan, and one perpendicular.
These five lines were completed within 45 minutes centered
at the solar noon. The data were available in four wave-bands
(10 or 20 nm width) centered at 443 nm, 550 nm, 670 nm,
and 865 nm. Zenith view angles ranged from 0 to 50 o .
Sensor calibration was performed by the L.O.A. (Laboratoire dOptique Atmospherique, Lille, France) with a 3 month
frequency. The procedure accounted for ambient temperature, dark current, and inter-calibration of CCD matrix detector. Its accuracy was about 5%.
Atmospheric effects were corrected thanks to the SMAC
algorithm (Rahman and Dedieu, 1994) based on the inversion of the atmospheric radiative transfer model 6S (Vermote
et al., 1997). The required information consisted in aerosol
optical thickness, water vapor content, both estimated from
field sunphotometer measurements, and ozone atmospheric
concentration obtained from TOMS climatic daily data.
Each image was registered thanks to a Global Positioning
System and an inertial central data, according to a Lambert II

projection. This projection provided a spatial sampling of the
site corresponding to a grid of 250Â250 pixels with a 20 m
resolution.
All these pre-processing are described in details by Leroy
et al. (2000). They allowed to derive BRDF samplings that
depended on both the location on the site and the flight line
configuration.
2.3 Field data
Field measurements of albedo were performed on seven
locations corresponding to alfalfa, wheat, and sunflower crops.
Albedo was deduced from measurements of incident radiation using a Kipp pyranometer located on the meteorological site, and measurements of reflected radiation using Kipp
pyranometers or Skye silicon sensors looking to the ground
surface. The data set corresponded to 20 minutes mean values having a circular footprint between 1000 and 3000 m ắ .
The spectral ranges of Kipp and Skye sensors were different, corresponding respectively to [300-3000] nm and [4001100] nm. For the latter, it was necessary to consider the
spectral behavior of the observed surface, in order to extrapolate the estimates over the whole solar spectrum. This
has been performed thanks to a formulation of the actual
albedo as a function of the measured one. The formulation was calibrated over simulations of the radiative transfer
model SAIL (Verhoef, 1984, 1985) performed by Francáois
et al. (2000). Model input variables were soil and leaf optical properties, incident solar radiation from simulations of
the atmospheric radiative transfer model 6S (Vermote et al.,
1997) that took account for numerous atmospheric situations,
and measurements of Leaf Area Index (LAI). Simulations of
actual albedo and Skye estimates are described in details by

é

ể

ỉ é


ẳ

ẵ

 é ểậ í

ã ẳ ẳắắ

(1)

3 Methodology
3.1 Position of the problem
From the definition given in Sect. 1, the instantaneous albedo
ì ì à is expressed as following ( ì and ì are respectively the solar zenith and azimuth angles):


ấ

ẳẳẳềẹ

ì



ẳẳềẹ

ì à




ấ

ẳẳẳềẹ
ẳẳềẹ

ì

ì à ấ
(2)

ấ

where is the wavelength. The spectral albedo or hemispherical reflectance
ì ì à represents the fraction of
the spectral incoming solar radiation ấ
reflected in the
whole hemisphere. It is expressed through the bidirectional
reflectance ì ì à ( and are respectively the
view zenith and azimuth angles):


ấấ

ắ

ẳ

ì

ì à


ắ


ẳ

ì

ì



à

ểì

ìề





(3)

PolDER provided measurements of bidirectional reflectances ì ì à in the four considered channels. From
these directional samplings, we estimated hemispherical re ì ì à by inverting BRDF kernel-driven modflectances
els, and then the instantaneous albedo using a simple spectral
extrapolation procedure. Both aspects are presented below.
3.2 Retrieving hemispherical reflectance using BRDF kerneldriven models
The philosophy of a BRDF kernel-driven model is to express the bidirectional reflectance ì ì à thanks

to a linear combination of ề kernels ặ (a kernel is a predefined function of view and solar angles):


ì



ì à

ề
ẵ

ô ặ

ì



ì à

(4)

where ô are the weighting coefficients. The number and
the formulation of the kernels ặ differ from one model to
another. Among the large number of kernel-driven models
that were developed these last years, we have chosen to test
three of them: Walthall (Walthall et al., 1985), Roujean (Roujean et al., 1992) and MRPV (Engelsen et al., 1996). Several studies showed that MRPV was the most accurate model
both for the accuracy of the fitting and the extrapolation capabilities, while Walthall and Roujean were often presented as
robust models (Baret et al., 1997; Wanner et al., 1997; Weiss



Journal: Physics and Chemistry of the Earth
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First author: Jacob

3

Coefficient

Blue

Green

Red

Near Infra-Red

Set

(445 nm)

(560 nm)

(665 nm)

(865 nm)

0

0


0.57

0.46

0

0.68

0.08

0.35

0.06

0.69

0.001

0.35

Set nÓ 1

Set nÓ 2
Set nÓ 3

Model
MRPV
Roujean


Table 1. Sets of coefficients for the computation of the albedo as a linear
combination of wave-band hemispherical reflectances.

Walthall

Error

Blue

Green

Red

NIR
0.0280

RMSE

0.0138

0.0118

0.0129

RRMSE

24.6%

11.0%


11.8%

08.3%

RMSE

0.0112

0.0123

0.0138

0.0290

RRMSE

20.1%

11.6%

12.7%

08.6%

RMSE

0.0116

0.0136


0.0150

0.0303

RRMSE

20.8%

12.8%

13.6%

09.0%

Table 2. Absolute and relative RMSE between observed and retrieved
BRDF through the three kernel-driven models for the 10 April 1997.

et al., 2000). We should notice that Roujean and Walthall are
linear models, while MRPV is a semi-linear one.
The weighting coefficients « might be obtained by inverting the model from the multi-angular data set. This was
performed for each pixel and each PolDER channel using
the procedure described by Weiss et al. (2000). The retrieved
BRDF through these coefficients were then integrated to obin the PolDER chantain the hemispherical reflectances
½
).
nels (
3.3 Spectral extrapolation from PolDER channels
The spectral extrapolation was based on the assumption
that for a given wavelength ¾ ¿¼¼   ¿¼¼¼ nm, the hemispherical reflectance
´ × ³× µ is a linear combination of

´ × ³× µ estimated in the
the hemispherical reflectance
four channels PolDER. Then, it was possible to express the
albedo as:
´

×

³× µ

½

¬

´

×

³× µ

(5)

Several studies have been devoted to the determination of
the coefficients ¬ , but there is not at the present time any
proposition for the PolDER sensor. In this context, we have
chosen to test three sets of coefficients proposed by Weiss
et al. (1999) when considering blue, green, red and near infrared channels (corresponding to 445, 560, 665 and 865
nm). These coefficients were obtained from a linear regression calculated over numerous soil coverage situations by the
radiative transfer model DISORD (Myneni et al., 1992), between 400 and 2500 nm. These simulations were representative of several kinds of canopies at three different latitudes
and for three days corresponding to different seasons. Coefficient sets are given in Table 1. The relative accuracy of these

linear regressions was estimated as the Root Mean Square Error (RMSE) between simulated and retrieved albedo: it was
about 7%.

4 Results and validation
4.1 Performances of BRDF kernel-driven models
We evaluated the BRDF retrieval performances of the kerneldriven models by calculating for each pixel the absolute RMSE
and the relative RMSE (RRMSE) between observed ( Ó × )

and retrieved ( Ö Ø ) bidirectional reflectances:

ÊÅË
ÊÊÅË

Ú
Ù
ÈÑ
Ù
Ù
Ø
½

ÊÅË
Ó×

´

Ó ×´ µ

 


Ñ

Ö Ø ´ µµ¾

(6)
(7)

Ó×
where
is the mean value of the Ñ observed bidirectional reflectances. Results showed that the greatest errors occurred for pixels located on both the Alpilles mountain chain and field edges. In the first case, this might be
explained by the inadequacy of BRDF models when they are
applied to mountainous areas. In the second case, it might
be explained by the combination of registration inaccuracy
and spatial variability. Table 2 presents the RMSE and the
RRMSE over the whole site for a representative day. The errors in the blue channel were more important whatever was
the model, and maybe induced by the perturbations occurring in this channel such as the inaccuracy of the sensor calibration or the residual noise due to atmospheric diffusion
by aerosols. The BRDF retrieval performances of the three
models were very similar and slightly better for MRPV at
550, 670 and 865 nm. However, this model presented a
great sensitivity to the perturbations mentioned previously.
This high sensitivity could be explained by the semi-linear
model formulation. When considering BRDF retrieval performances without pixels located on both the mountain chain
and field edges, the models gave slightly better results, with
a lower RRMSE about 3 to 5%. On the other hand, these
performances were quite better when considering only pixels located on the field measurements, with a RRMSE divided by 2. We explained this by the homogeneity around
field measurements locations, inducing small perturbations
due to the combination of image registration inaccuracy and
spatial variability.
The comparison of the hemispherical reflectance estimates
over the whole site showed differences between MRPV and

the two others models. These differences were more important in the blue channel, for which MRPV provided numerous unrealistic values such as hemispherical reflectances
close to one. Moreover, we observed that differences between models decreased with respect to the wave-band. There-


Journal: Physics and Chemistry of the Earth
MS No.: ???
First author: Jacob

4
Channel 865nm
0.35

0.6
0.55
0.3

ρh from Walthall’s model

0.5
0.45
0.25

0.4

0.35
0.2

0.3

0.25


0.15

0.2
0.2

0.25

0.3

0.35
0.4
0.45
ρ from Roujean model

0.5

0.55

0.6

h

Fig. 1. Comparison of hemispherical reflectance estimates from Walthall’s
and Roujean’s models for the channel 865 nm when considering pixels located on field measurements. The solid line represents the linear regression
between the estimates from the two models.

fore, the hemispherical reflectance retrieval through kerneldriven BRDF models should be more stable with an increase
of the wavelength. This observation was in agreement with
the conclusions of Baret et al. (1997). When considering

only pixels located on field measurements, Roujean overestimated the hemispherical reflectance as compared to the
others models (see an example with Fig. 1), while the underestimation was observed for MRPV at 443 and 670 nm, and
for Walthall at 550 and 865 nm.
4.2 Validation of albedo estimates
Albedo calculations have been performed considering the
three BRDF kernel-driven models and the three sets of coefficients. Therefore, nine albedo maps were computed for each
day of the experiment (see for example Fig. 2). These maps
depicted albedo values between 0.1 and 0.4. This important
variability was explained by the simultaneous presence on
the site of vegetative surfaces and bare soils. As expected,
the lowest values corresponded to well vegetated fields or
wet bare soils, while the highest ones corresponded to dry
bare soils or very sparse vegetation.
Since the field data and PolDER pixels had different footprints (Sect. 2), we assessed the impact of the spatial variability on the airborne albedo estimates by computing the relative
standard deviation (standard deviation / mean value) inside
both 3¢3 and 5¢5 PolDER pixel windows. The results, between 1 and 2%, underlined the negligible effect of the spatial variability around field measurement locations as much
as the window size was smaller than the field one. Therefore,
we decided to perform the validation by extracting PolDER
estimates through 3¢3 pixels windows.
An example of comparison between field and airborne estimates of the albedo is given in Fig.3 for one kernel-driven

Fig. 2. Albedo map for the 29 July 1997 using the MRPV model and the
coefficient set nÓ 3. The Alpilles mountain chain has been removed.

model and one set of coefficients. These comparisons showed
that were no differences between Kipp and Skye estimates after the corrections of the latter (Sect.2). For each of the nine
possibilities, we computed the absolute RMSE as in eq.6 and
relative RMSE (RRMSE) as in eq.7, as well as the absolute
bias (Bias) and relative bias (RBias) calculated as:


ÈÅ

×
Ê

´

½

×

È ÓÐ

Ê´ µ

 

Ò

 × ØÙ ´

µµ

(8)

Å
Ò

×
 × ØÙ


(9)

where È ÓÐ Ê is the albedo estimated from PolDER data,
Ò  × ØÙ
Ò  × ØÙ
is the albedo measured in-situ, and
is the mean value of the Å field data. The results are given
in Table 3. Airborne retrievals were systematically higher
than field estimates. Considering each model, an important
overestimation occurred with the first coefficient set that corBRDF Model

RMSE

RRMSE

Bias

RBias

MRPV & set 1

0.0530

27.2%

0.0480

24.7%


MRPV & set 2

0.0345

17.7%

0.0285

14.7%

MRPV & set 3

0.0320

16.4%

0.0251

12.8%

Roujean & set 1

0.0532

27.7%

0.0504

26.2%


Roujean & set 2

0.0378

19.7%

0.0333

17.3%

Roujean & set 3

0.0348

18.1%

0.0301

15.6%

Walthall & set 1

0.0428

22.2%

0.0387

20.1%


Walthall & set 2

0.0280

14.6%

0.0217

11.3%

Walthall & set 3

0.0255

13.2%

0.0183

9.5%

& Coefficient set

Table 3. Absolute and relative RMSE and Bias between airborne and field
estimates of the albedo. The solid line represents the linear regression between the in-situ and airborne estimates.


Journal: Physics and Chemistry of the Earth
MS No.: ???
First author: Jacob


5

0.3

BRDF Model

0.28

& Coefficient set

0.26

a

b

RMSEÍ

RRMSEÍ

MRPV & set 1

0.911

0.065

0.0223

9.2%


MRPV & set 2

0.810

0.065

0.0185

8.3%

MRPV & set 3

0.818

0.061

0.0190

8.7%

0.22

Roujean & set 1

0.919

0.066

0.0169


7.0%

0.2

Roujean & set 2

0.804

0.071

0.0167

7.4%

Roujean & set 3

0.816

0.065

0.0164

7.4%

Walthall & set 1

0.986

0.041


0.0182

7.9%

0.16

Walthall & set 2

0.866

0.048

0.0172

8.0%

0.14

Walthall & set 3

0.879

0.042

0.0174

8.2%

Airborne estimates


0.24

0.18

0.12
0.1
0.1

Field estimates from Kipp sensors
Field estimates from Skye sensors
0.15

0.2
In−situ estimates

0.25

0.3

Fig. 3. Comparison between field and airborne albedo for the whole ReSeDA experiment, considering the MRPV model and the coefficient set n¼ 3.

responded to the contributions of the red and NIR channels,
while this overestimation decreased with a decrease in the
red and NIR channels contributions. The comparison from a
model to another with the same set of coefficient showed that
the highest estimates were obtained with Roujean, while the
lowest ones corresponded to Walthall. These observations
were explained as following:
– Roujean provided the highest hemispherical reflectances
whatever was the channel, and therefore the highest albedo

values;
– since the absolute value of the bias between Walthall
and MRPV hemispherical reflectances was lower in the
red (0.0004) than in the NIR (-0.0125), Walthall yielded
the lowest albedo values with the set of coefficient n Ó 1 ;
– Walthall provided the lowest albedo values with the sets
of coefficients n Ó 2 and nÓ 3 because it yielded the lowest
hemispherical reflectances in the green and NIR channels.
These results showed that the albedo retrieval strongly depends on the hemispherical estimates, and then requires accurate ones. Besides, the RMSE and bias were generally
close from a model to another, while the high RMSE values were partially induced by the bias. At the present time,
we think that this general overestimation could result from
either the hemispherical reflectance estimates or the assumptions used when calibrating the linear combination (Sect.3).
Indeed, the simulations performed by Weiss et al. (1999) to
estimate the coefficients corresponded to the spectral interval [400 - 2500] nm, while the whole solar spectrum ranges
between 300 and 3000 nm. Therefore, the incident solar radiation were lower than the actual one, by 6-8% referring to the
works of Avaste et al. (1962). At a lower extent, the accuracy
of these sets of coefficients was affected by the spectral difference between the radiative transfer model simulations and

Table 4. Coefficient of the linear regression between field and airborne estimates of the albedo (a: slope, b: offset), and RMSE between PolDER
estimate and the linear regression (RMSEÍ ).

the PolDER wave-bands, as well as by the residual noises
due to instrumental and atmospheric effects.
In order to assess the accuracy that it would be possible
to achieve, we calculated the coefficients of the linear regression between predicted (or airborne) and observed (or insitu) estimates, as well as the absolute and relative unsystematic RMSE (RMSEÍ and RRMSEÍ ) (see the Table 4). The
RMSEÍ computes the scattering around the linear regression
as the RMSE between the predicted values corrected from
this regression and the actual ones (Kustas et al., 1996). The
coefficients of the linear regression suggested that considering only hemispherical reflectances in red and NIR induced
mainly an offset, while using more wave-bands seemed to

provide an overestimation of low albedo values and an underestimation of high ones. Finally, the RMSE Í computations
showed that it would be possible to achieve an absolute accuracy between 0.0164 and 0.0223 for albedo values ranging
from 0.1 to 0.25 after the removal of slopes and offsets. This
would correspond to a relative accuracy ranging between 7
and 9%. We should notice that in this case, the result corresponding to the lower discrepancy would be obtained with
the Roujean model when considering the hemispherical reflectances in the red and the NIR channels.

5 Conclusions
The objective of this study was to map albedo on the ReSeDA experiment site, using the airborne multi-spectral and
multi-directional Vis-Near Infra-Red PolDER remote sensing data. Moreover, these high spatial resolution and multitemporal data allowed to perform a validation with less problems related to mixed pixels and over cycles of several crops.
The multi-directional information was extracted through
BRDF kernel-driven models. We tested three models (MRPV,
Roujean and Walthall) that gave similar results for both the
BRDF retrieval and the hemispherical reflectance estimation.
However, results showed that the data set acquired in the blue
channel have to be considered with care; and that the MRPV


Journal: Physics and Chemistry of the Earth
MS No.: ???
First author: Jacob
model was the most sensitive to inaccuracy of both radiometric processing and image registration.
The multi-spectral information was used by computing the
albedo as a linear combination of the hemispherical reflectances in PolDER channels. We tested three sets of coefficients previously proposed as generic ones by Weiss et al.
(1999).
The validation thanks to field measurements underlined an
overestimation whatever were the BRDF model and the set
of coefficients. This could be explained by either the hemispherical reflectance estimates or the assumptions used for
the calibration of the linear combination. The first point
could results from the PolDER measurements or the kerneldriven model retrievals. The second point could result from

the underestimation of the incident solar radiation. This could
be improved by considering the whole solar spectrum when
calibrating the linear regression. We observed that the removal of this overestimation should yield an absolute accuracy between 0.0164 and 0.0223 for albedo values ranging
from 0.1 to 0.25 (which corresponds to a relative accuracy
between 7 and 9%). Another possibility could be to take into
account surface properties through the NDVI when calibrating the linear combination, as proposed by Song and Gao
(1999).
In the future, these maps could be used as a reference for
validation at larger scale considering sensors such as NOAA
/ AVHRR for instance, and as inputs for surface energy balance calculation models (Jacob et al., 2000). However, one
should note that for pixels far from the site center, the PolDER directional sampling quality was very poor and therefore that these results must be considered with care.
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