ATBD of BRF calculation from GCOM-C surface reflectance data (G4C)
Hiroshi Murakami,
JAXA/EORC,
Oct. 2018 (v1.000)
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N = 28 days (parameter), but the statistics are weighted to the target average period(e.g., 8 days)

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
1/24deg binning (Level-3)
1-day

8-day

Cloud properties
Aerosol properties by NP
Aerosol properties by POL

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(tsoz^2+tsaz^2-2*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./(1.+alp/(1.5*d2r))) -1./3.
Where, d2r=pi/180, and pi=3.14159265(2) Regression to the Kernel
To avoid negative value, the coefficients, c0, c1, and c2 are calculated by minimize thecost,
cost= S^2 +w1+w2+w12S^2 =Σi{ ( Rs_i -( c0 + c1 * knl(1)_i + c2 * knl(2)_i) )^2}
w1=exp(-10.+c1/uk1*10.)*wk0
w2=exp(-10.+c2/uk2*10.)*wk0
w12=( c1/uk1* c2/uk2)^2*wk0
where Rs_i is the level-2 surface reflectance of day=i. uk1=0.1, uk2=1.0, andwk0=0.04*0.04.
3. Output parameters(1) 8-bit QA_flag
0:Nodata
1:Land2:Insufficient sample number (N<4)

3:Regression error
4:Out of range
5:Spare6:Spare7:Spare(2) **_Ninput
Input data number.
(3) **_Nused
Used data number.
(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. A simple RMS is stored in theocean or areas of insufficient sample number.
(8) **_MIN
Minimum of RSRF variables.
(9) **_MAX
Maximum of RSRF variables.
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.