ATBD of Land Surface Albedo from BRDF Model Parameters
Generated from Multi-temporal GCOM-C Surface Reflectance
Junichi Susaki
Kyoto University
March 2022 (v1.00)

1. Overview of Algorithm
The authors examined two algorithms for generating GCOM-C/SGLI surface albedo products, namely,
one based on a BRDF model using several sets of reflectance and one based on multi-regression models
using a single set of reflectances [1, 2]. The experimental results show that the former algorithm generates
an albedo with acceptable RMSEs, whereas the albedos estimated by the multi-regression-based algorithm
have relatively less stable estimates. The latter algorithm requires landcover classification and, more
importantly, may be affected by larger variance when the surface reflectance near a hot-spot geometry isused. Therefore, we conclude that the BRDF-based algorithm can be applied to SGLI operational albedo
products. In this paper, we introduce the method for estimating the albedo based on a BRDF model.

2. Method
2.1 Kernels
A kernel used for estimating the BRDF and terrestrial albedo is a function of the bidirectional reflectancedetermined by the viewing and illumination geometries. In general, we consider two types of scatteringobserved from an object on the terrestrial surface, namely, volumetric scattering and geometric scattering.
We assumed the semi-empirical kernel-driven BRDF model expressed by Eq. (1):𝑅 𝜃 ,𝜃 ,𝜙𝑓𝑓 𝐹 𝜃 ,𝜃 ,𝜙𝑓 𝐹 𝜃 ,𝜃 ,𝜙 .

(1)Here, i, v and  are solar zenith angle, viewing zenith angle and relative azimuth angle, respectively. f0,f1, and f2 are unknown coefficients. Users can select any combination of volumetric- and geometricscattering kernels for F1 and F2, the values of which are determined once the illumination and viewing
geometries are given. Murakami [3] reported that the algorithms for SGLI products use BRDF model
reported by [4]:𝐹 𝜃 ,𝜃 ,𝜙𝜋

𝜙𝑐𝑜𝑠𝜙𝑡𝑎𝑛𝜃𝑡𝑎𝑛𝜃

𝐹 𝜃 ,𝜃 ,𝜙4𝑐𝑜𝑠𝜃
3𝜋

𝑡𝑎𝑛𝜃

𝛼𝑡𝑎𝑛𝜃
2𝜋(2)

𝛼

𝑐𝑜𝑠𝛼

𝑠𝑖𝑛𝛼(3)

131/ ℎ𝛼/ 1.5𝜋/1802𝑡𝑎𝑛𝜃

𝑡𝑎𝑛𝜃

𝑐𝑜𝑠𝜙(4)𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙(5)𝑡𝑎𝑛𝜃

acos 𝑐𝑜𝑠𝜃𝑡𝑎𝑛𝜃

∆ /𝜋𝜋2𝑐𝑜𝑠𝜃1∆𝑠𝑖𝑛𝜙𝑐𝑜𝑠𝜃

2.2 Estimation of Kernel-driven BRDF Model Parameters
The three unknown coefficients in Eq. (1) are determined by minimizing the least-squares error function
expressed as∑𝜀∑𝑅 𝜃 ,𝜃 ,𝜙𝑓𝑓 𝐾 𝜃 ,𝜃 ,𝜙𝑓 𝐾 𝜃 ,𝜃 ,𝜙,(6)

where n is the number of samples and r is the observed reflectance. The above approach may estimate
negative values, and thus in SGLI products, the non-negative values are estimated by adding the constraint.
See the details reported by [3] for understanding the estimation of BRDF model parameters in SGLI
products.

2.3 Narrowband Albedo Estimation
With the estimated BRDF model parameters, we estimate the narrowband albedo, which is an albedo fora relatively narrow wavelength range. In most cases, the wavelength range is equivalent to the bands
designed for satellite sensors. Before estimating the narrowband albedo, we start with the narrowband
black-sky and white-sky albedos. The black-sky albedo is a virtual albedo in the absence of a diffuse
component, while the white-sky albedo is a virtual albedo in the absence of a direct component when thediffuse component is isotropic. The black-sky and white-sky albedos are expressed respectively as

𝑎

𝜃 ,𝜆∑

𝑓 𝜆 ℎ 𝜃 ,(7)

𝜆∑𝑓 𝜆 𝐻 ,

(8)𝑎whereℎ 𝜃/

1𝜋(9)𝐹 𝜃 , 𝜃 , 𝜙 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 𝑑𝜃 𝑑𝜙𝐻2/ℎ 𝜃 sin 𝜃 cos 𝜃𝑑𝜃.

(10)

The actual albedo a() at wavelength  is expressed as a linear combination of the black-sky and white-sky
albedos by using the atmospheric optical depth ():𝑎 𝜆𝑆 𝜃 ,𝜏 𝜆 𝑎

𝜆1𝑆 𝜃 ,𝜏 𝜆𝑎

𝜃 ,𝜆 .

(11)

Here, S denotes the fraction of diffuse skylight.

2.4 Narrowband to Broadband Conversion
The broadband albedo is defined for wider wavelength ranges, such as 0.3–3.0 m or 0.3–5.0 m.
However, no sensor measures the radiance over such a wide wavelength range; therefore, it is impossible
to estimate the broadband albedo directly from observed sensor data. Instead, the broadband albedo isestimated by extrapolation, expressed as a linear regression model of several narrowband albedos. This
conversion is called as narrow-to-broadband (NTB) conversion.
We collected in situ BRF data and albedo data for several types of land cover and used them to determine
the coefficients of NTB conversion. We constrained the coefficients to be non-negative and determinedthem by minimizing Akaike’s information criterion (AIC) [5]. For a given model, AIC assesses its
performance by evaluating both the number of variables used in the model and the sum of the errors. Notethat VN6 was excluded from the calculation because its radiance may be saturated in land cover with highreflectance. The obtained model of NTB conversion [2] is𝛼0.2233𝛼0.4005𝛼

where 𝛼 is the narrowband albedo of band i.

0.1463𝛼,(11)For calibration, we used the reflectances of barren land (11 points), deciduous broadleaf forest (threepoints), and paddy fields (one point), and the RMSE for the 15 points was 0.010. To validate Eq. (6), we
used barren land (nine points), deciduous broadleaf forest (three points), and grassland (two points); theRMSE was 0.023, which is acceptable. Figure 1 shows the scattergram of actual albedo versus that
estimated by NTB conversion.

NTB conversion for SGLI
0.30

Estimated albedo

Calibration
Validation

0.25
0.20
0.15
0.10
0.10

0.15
0.20
0.25
Actual albedo

0.30

Fig. 1. Scattergram of actual albedo versus that estimated by narrow-to-broadband(NTB) conversion for SGLI. “Calibration” denotes the calibration data used todetermine Eq. (6), and “Validation” denotes the validation data.

3. Accuracy Assessment
We then examined the validity of both the BRDF-based and multi-regression-based methods forestimating surface albedo by applying SGLI data. Because the spatial resolution of SW3 (i.e., 250 m) isfiner than that of the other shortwave bands (i.e., 1 km), we again examined the possible combinations ofSGLI bands as independent variables of the regression model under the condition that SW3 is included in
the independent variables. We found VN8, VN11, and SW3 to be the best combination in terms of AIC.
We compared the temporal albedo estimated by the two different approaches. One approach is to use
multi-regression models generated from the data of vegetated areas. The other approach is to use the BRDF
model parameters provided in SGLI atmospheric-corrected land surface reflectance (RSRF) products [3].
The BRDF model parameters are generated as a by-product of RSRF, and the processing uses the kernels
reported by [4]. We used the long-term field data measured in four sites listed in Table 1(a) to 1(d):Yamashiro deciduous broadleaved secondary forests; Takayama evergreen coniferous forests; Takayama

deciduous broadleaf forests; Fujiyoshida natural evergreen needle-leaf forests. The regression models,
LC21 and LC04 were generated as follows:LC21: Regression models for SGLI generated by using the data sets of “Barren or sparsely vegetated(IGBP LC16)” and “Deciduous broadleaf forest (IGBP LC4)” in POLDER-3 BRDF DB. The
applied model was selected by referring to NDVI.

vegetation: NDVI ≥ 0.5 and 443 ≤ 0.2;

non-vegetation: 0 ≤ NDVI < 0.4 and 443 ≤ 0.2;

LC04: Regression models for SGLI generated by using the data sets of “Deciduous broadleaf forest(IGBP LC4)” in POLDER-3 BRDF DBFor comparison, we generated albedos from BRDF model parameters provided by SGLI and MODIS.
Figures 2 to 5 and Tables 2 to 5 show the validation results of the estimated temporal albedos.

Table 1. Names and geolocations of study areas.
(a) Yamashiro (deciduous broadleaf forest) [6]Area

Latitude, longitude

Yamashiro Test Field, Forest Research and34°47'25.0"N,Management Organization, Kyoto Pref., Japan

135°50'27.3"E(b) Takayama (planted evergreen coniferous forest) [7]Area

Latitude, longitude

Takayama evergreen coniferous forest site,36º 08' 23" N,Gifu Pref., Japan

137º 22' 15" E(c) Takayama (deciduous broadleaf forest) [8]Area

Latitude, longitude

Mase, Paddy Flux Site, Tsukuba, Ibaraki,

36°03'14.3"N,Japan

140°01'36.9"E(d) Fuji-yoshida (natural evergreen needle-leaf forest) [9]Area

Latitude, longitude

Fujiyoshida forest meteorology research

35.45454 N,site, Yamanashi, Japan138.76225 E

4. Discussion
Figure 2 to 5 show the curve of the albedo estimated by using BRDF model parameters. Figures 2 and5 indicate that the MODIS/BRDF-driven albedos have the best agreement with the measured albedos inYamashiro with deciduous broadleaved secondary forests and Fujiyoshida with natural evergreen needleleaf forests. Figures 3 and 4 indicate that all albedos are not well estimated in Takayama with evergreen
coniferous forests and Takayama with deciduous broadleaf forests. Another feature is that the albedo data
estimated from BRDF model parameters are moving-average data because the parameters were estimatedusing eight-day surface reflectance. It was found that the estimated albedo is more robust against the errorthat contaminates the reflectance than is that of “Regression”. While the estimated eight-day albedo haslower temporal resolution than that of daily “Regression”, the albedo products may prioritize robustness
over temporal resolution. Considering these features, we recommend using the BRDF-based method rather
than the multi-regression-based method for generating albedo of better quality.

5. Conclusions
In this paper, we examined two algorithms for generating GCOM-C/SGLI surface albedo products,
namely, one based on a BRDF model using several sets of reflectance and one based on multi-regression
models using a single set of reflectances. Regarding the latter algorithm, we simulated the multi-angular
SGLI surface reflectance from the POLDER-3 surface reflectance, and we generated datasets of simulated
albedo and multi-angular reflectance via a kernel-driven BRDF model. We derived multi-regression models
at an arbitrary geometry of solar zenith, sensor zenith, and relative azimuth angles for three land-coverclasses, namely, vegetation, non-vegetation, and snow/ice. The experimental results show that the former
algorithm, especially one used for MODIS products, generates an albedo with acceptable RMSEs, whereas
the albedos estimated by the multi-regression-based algorithm have relatively less stable estimates. Thelatter algorithm requires landcover classification and, more importantly, may be affected by larger variancewhen the surface reflectance near a hot-spot geometry is used. Therefore, we conclude that the BRDFbased algorithm can be applied to SGLI operational albedo products.

Yamashiro (2018)
0.25

Albedo

0.2

0.15

0.1

0.05

50100

Measured

LC21150

LC04

200
DOY
SGLI/BRDF

250

300

MODIS/BRDF

350

SGLI/BRDF_CONST(a)Yamashiro (2019)
0.25

Albedo

0.2

0.15

0.1

0.05

0Measured50

LC21100

150200DOY

LC04

SGLI/BRDF

(b)

250

MODIS/BRDF

300

350

SGLI/BRDF_CONSTYamashiro (2020)
0.25

Albedo

0.2
0.15
0.1
0.05
0050

Measured100

LC21150

LC04200
DOY

SGLI/BRDF

250

300

MODIS/BRDF

350

SGLI/BRDF_CONST(c)
Figure 2. Temporal albedo of Yamashiro, Japan estimated from SGLI data. Each item denotes as follows:LC21: Regression models for SGLI generated by using the data sets of “Barren or sparsely vegetated(IGBP LC16)” and “Deciduous broadleaf forest (IGBP LC4)” in POLDER-3 BRDF DB. The
applied model was selected by referring to NDVI.

vegetation: NDVI ≥ 0.5 and 443 ≤ 0.2;

non-vegetation: 0 ≤ NDVI < 0.4 and 443 ≤ 0.2;

LC04: Regression models for SGLI generated by using the data sets of “Deciduous broadleaf forest(IGBP LC4)” in POLDER-3 BRDF DB

BRDF: BRDF model parameter-based estimation for SGLIMODIS/BRDF: BRDF model parameter-based estimation for MODIS

Table 2. Root-mean-square errors of estimated temporal albedo for Yamashiro, Japan.
Yamashiro
Year

SGLI/

MODIS/

SGLI/

BRDF

BRDF

BRDF const

0.02350.03050.0161 (99)0.02940.01950.01820.03550.0207 (94)0.03600.02610.02560.03220.0256 (102)0.0337lc21

lc04

2018 (55)0.02452019 (62)2020 (54)(sample #)Takayama evergreen coniferous (2018)
0.2

Albedo

0.15

0.1

0.05

050

100

Measured

LC21

150

LC04

200
DOY
SGLI/BRDF

250

300

MODIS/BRDF

350

SGLI/BRDF_CONST(a)Takayama evergreen coniferous (2019)
0.2Albedo

0.15

0.1

0.05

00

Measured50

LC21100

150200DOY

LC04

SGLI/BRDF

(b)

250

MODIS/BRDF

300

350

SGLI/BRDF_CONSTTakayama evergreen coniferous (2020)
0.2

Albedo

0.15

0.1

0.05

00

Measured50

LC21100

150200DOY

LC04

SGLI/BRDF

250

MODIS/BRDF

300

350

SGLI/BRDF_CONST(c)
Figure 3. Temporal albedo of evergreen coniferous forests, Takayama, Japan estimated from SGLI data. See
the caption of Figure 2 for each item.

Table3. Root-mean-square errors of estimated temporal albedo for evergreen coniferous forests,
Takayama, Japan.
Takayama evergreen coniferous
Year

SGLI/

MODIS/

SGLI/

BRDF

BRDF

BRDF const

0.04270.0646

0.0372 (96)0.06110.03620.03590.05340.0432 (107)0.05150.03540.03440.05380.0407 (69)0.0480

lc21

lc04

2018 (42)0.04382019 (70)2020 (37)(sample #)Takayama deciduous broadleaf (2018)
0.3

Albedo

0.25
0.2
0.15
0.1
0.05

050

Measured

LC21

100

150

200
DOY

LC04

SGLI/BRDF

250

MODIS/BRDF

300

350

SGLI/BRDF_CONST(a)Takayama deciduous broadleaf (2019)
0.3
0.25

Albedo

0.2
0.15
0.1
0.05
0050

Measured100

LC21LC04

150200DOY

SGLI/BRDF

(b)

250

MODIS/BRDF

300

350

SGLI/BRDF_CONSTTakayama deciduous broadleaf (2020)
0.25

Albedo

0.2
0.15
0.1
0.05
00

Measured50

LC21100

150200DOY

LC04

SGLI/BRDF

250

MODIS/BRDF

300

350

SGLI/BRDF_CONST(c)
Figure 4. Temporal albedo of deciduous forests, Takayama, Japan estimated from SGLI data. See thecaption of Figure 2 for each item

Table 4. Root-mean-square errors of estimated temporal albedo for deciduous broadleaf forests,
Takayama, Japan.
Takayama deciduous broadleaf
Year

SGLI/

MODIS/

SGLI/

BRDF

BRDF

BRDF const

0.02580.03820.0248 (92)0.03700.04780.04770.03830.0261 (78)0.04220.03890.03890.03020.0371 (59)0.0337lc21

lc04

2018 (35)0.02832019 (61)2020 (32)(sample #)Fuji‐yoshida (2018)
0.2

Albedo

0.15

0.1

0.05

00

Measured50

LC21100

150

200
DOY

LC04

SGLI/BRDF

250

MODIS/BRDF

300

350

SGLI/BRDF_CONST(a)Fuji‐yoshida (2019)
0.2

Albedo

0.15

0.1

0.05

00

Measured50

LC21100

150200DOY

LC04

SGLI/BRDF

(b)

250

MODIS/BRDF

300

350

SGLI/BRDF_CONSTFuji‐yoshida (2020)
0.2

Albedo

0.15

0.1

0.05

00

Measured50

LC21100

150200DOY

LC04

SGLI/BRDF

250

300

MODIS/BRDF

350

SGLI/BRDF_CONST(c)
Figure 5. Temporal albedo of deciduous forests, Fuji-yoshida, Japan estimated from SGLI data. See thecaption of Figure 2 for each item.

Table 5. Root-mean-square errors of estimated temporal albedo for Fuji-yoshida, Japan.
Fuji-yoshida
YearSGLI/MODIS/

SGLI/

BRDF

BRDF

BRDF const

0.01470.01850.0166 (126)0.01890.01560.01580.02040.0073 (116)0.02040.01570.01530.02670.0076 (116)0.0251

lc21

lc04

2018 (47)0.01512019 (67)2020 (65)(sample #)Acknowledgement
We express our thanks to Yuji Kominami and Satoru Takanashi of the Kansai Research Center, Forestryand Forest Products Research Institute (FFPRI) for providing the opportunity to obtain measurements inYamashiro Experimental Forest. We also express our thanks to Shohei Muraya, National Institute ofAdvanced Industrial Science and Technology (AIST), Japan, and Taku M. Saitoh, Gifu University, Japanfor providing the long-term field data.

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