ATBD of BRF calculation from GCOM-C surface reflectance data (G4C)
Hiroshi Murakami,
JAXA/EORC,
Aug. 2021 (v3000: Main revisions of Ver. 3 is underlined)
1. Introduction
GCOM-C BRDF product (processing tag name is G4C) derive coefficients of the kernelsof bi-directional reflectance function (BRF) are derived from N days of GCOM-C
atmospheric corrected surface reflectance (RSRF product) (see Fig. 1).
 Kernel developed by Maignan et al., 2004 is used
 In the case of 8-days mean, N = 28 days (parameter), but the statistics are weighted tothe target average period (see section 2 (2))
 Nadir reflectance is calculated at the solar angles of the observation latitude and thedate

250m TOA radiance (LTOA)
32daysVegetation
NDVI, EVI, Shadow index

Land atmospheric correction

FAPAR, LAI

Land surface reflectance (250m)
Direction & Biomass
250m tile statistics and BRF

Above-ground biomass (1km)
Veg. roughness index (1km)

8-day
month

Cloud properties
Aerosol properties by NP

1/24deg binning (Level-3)
1-day

Aerosol properties by POL

8-day

month

Fig. 1 Operation flow around the GCOM-C Land Atmospheric Correction
The part marked by the red color indicates this process (G4C).

2. Method(1) BRF kernel
Bi-directional reflectance is modeled by the following equation,

Reflectance = c0 + c1  knl(1) + c2  knl(2)Coefficients c0, c1, and c2 is the target variables of the process. BRF kernel knl(1,2) iscalculated using satellite zenith (saz), satellite azimuth (saa), and relative azimuth (rea=solar -satellite azimuth) angles (Maignan et al., 2004).
rsaz =saz  d2r
rsoz=soz  d2r
rrea=rea  d2r
csaz=cos(rsaz)
csoz=cos(rsoz)
crea=cos(rrea)
tsaz=tan(rsaz)tsoz=tan(rsoz)
calp=csoz  csaz+sin(rsoz)  sin(rsaz)  crea
alp=acos(calp)
dlt=sqrt(tsoz2+tsaz2 −2  tsoz  tsaz  crea)knl(1)=((pi−rrea)  crea+sin(rrea))  tsoz  tsaz/(2  pi) − (tsoz+tsaz+dlt)/piknl(2)=(4./3. /pi)/(csoz+csaz)  ((pi/2−alp)  calp +sin(alp))  (1. +1. /(hspt+alp /(1.5  d2r) )) −1./3.
where, d2r=pi/180, and pi=3.14159265
The parameter hspt is originally 1.0, however, it set to 5.0 to be stable regression (afterVer. 2).
(2) Temporal weighting for 8-day statistics
Data from day=d0−20 to day=d0+7 (d0 is the start day of the target 8-day) are inputted
to use enough number of samples for the regression. The data on a day are weighted forthe regression.
wj(d) = 0.0004 / (0.0004 + ( d /30. )2  wk0), when d <0
wj(d) = 1.0, when d >=0,where d = day−d0, and wk0=0.04  0.04 (corresponding to the regression error S=0.04).
The weight of Level-2 data samples recovered from previous days (the number is Nrcv)
are reduced by wrcv as follows.
wj(d) = wj(d)  wrcv,
where wrcv = (10 − Nused ) / Nrcv, or wrcv = 0.5 if wrcv>0.5.
(3) Regression to the Kernel
To avoid negative value, the coefficients, c0, c1, and c2 are calculated by minimize thecost,
cost= S2 +w1+w2+w12
S2 = d{ ( Rs_d −( c0 + c1  knl(1)_d + c2  knl(2)_d) )2  wj(d) }w1= exp(−10.+c1/uk1  10.)  wk0 (c1≧0); w1= exp(−10.−c1/uk1  100.)  wk0 (c1<0)
w2= exp(−10.+c2/uk2  10.)  wk0(c1≧0); w2= exp(−10.+c2/uk2  100.)  wk0 (c2<0)
w12 = ( c1/uk1  c2/uk2)2  wk0
where Rs_d is the level-2 surface reflectance of day=d, knl_d is the BRF kernel of day=d,
uk1=0.1, and uk2=1.0.
3.

Output parameters

Table 1 QA_flag bit
BitExplanation(1) 8-bit QA_flag0

No data

See Table 1

1Land (1) or water (0)2Insufficient sample number (N<4)

3BRDF kernel regression error

4

Out of range

5

Spare

6Spare7Spare(2) **_Ninput
Input data number.
(3) **_Nused
Used data number which does not include therecovered samples(4) **_Date
Date identificator of RSRF/'//trim(inpm).
(5) **_AVE

This is an average of RSRF variables (Polarization data), nadir normalized RSRF
variables (thermal infrared data), or nadir normalized RSRF variables or 2nd-minimum(other variables or the ocean area).
(6) **_c0, _c1, _c2
c0, c1, and c2 coefficients of the BRF kernel.
Note Rs_VN08P and Rs_PI01 are used for the c0-2 of VN08P (“RN08K” in the file name),and Rs_VN11P and Rs_PI02 is used for the c0-2 of VN11P (“RN11K” in the file name).
(7) **_RMS
Root mean square (RMS) of BRDF model regression is stored to refer the possible errorof the reflectance. A simple RMS is stored in the ocean or areas of c1, c2 = 0 due toinsufficient sample number.
(8) **_MIN
Minimum of RSRF variables.
(9) **_MAX
Maximum of RSRF variables.

In the standard processing, the following RSRF variables are processed:
Rs_VN01~11, Rs_VN08P, Rs_VN11P, Rs_PI01~02, Rs_SW01~04, Tb_TI01~02, GEOV,GEOI, GEOP, and SWR
The name tags of the output files are:
RV01~11Q, RN08K, RN11K, RP01~02K', RS01~04K, RT01~02Q, GEOVQ, GEOIQ,GEOPK, and SWR_Q.
4. Reference
F. Maignan, F.-M. Breon, R. Lacaze, Bidirectional reflectance of Earth targets: Evaluation ofanalytical models using a large set of spaceborne measurements with emphasis on the Hot Spot,
Remote Sensing of Environment 90 (2004) 210–220.