Radiometric operations
Contents
fAPAR estimation and atmospheric correction (Gobron et al., 2006)
This procedure, published by Gobron et al. (2006), uses the TOAreflectances in the BLUE, RED and NIR bands (R_{aB}, R_{aR}, R_{aN}) and combines the atmospheric correction and fAPARextraction as follows (the functions Fn and bandspecific parameter sets P_{ni} are explained later):
 BRDFcorrection with the RPVmodel: First the directional R_{ai} in the three bands i are converted into more standardized hemispherical reflectances ρ_{ai} via the equation ρ_{ai} =F_{1}(R_{ai}, θ_{s}, Φ_{s}, θ_{v}, Φ_{v}, P1_{i})which also uses the known angles and the bandspecific parameter sets P_{1i}.
 Atmospheric correction: Next, "rectified" surface reflectances are computed for RED (ρ_{sR}) and NIR (ρ_{sN}) with the following equations: ρ_{sR} = F_{2R}(ρ_{aB}, ρ_{aR}, P_{2R}) and ρ_{sN} = F_{2N}(ρ_{aB}, ρ_{aN}, P_{2N}), where P_{2R/N} are bandspecific parameter sets. The underlying idea is that the radiative state of the atmosphere can be assessed from the reflectance differences between the BLUE and the other bands (the BLUE is indeed very susceptible for atmospheric scattering).
 Finally fAPAR is estimated from the rectified reflectances and parameter set P_{3}, via fAPAR= F_{3}(ρ_{sR}, ρ_{sN}, P_{3}).
To define the specific functions F_{n} and parameter sets P_{ni}, Gobron et al. (2006) coupled three simulation models: 6S links the satelliteregistered radiance L_{a} with the surface reflectance ρ_{s}, the latter is simulated via Gobron's SemiDiscrete canopy reflectance model (SDRM), while the leaf optical properties (one of the SDRMinputs) are predicted by PROSPECT. All three models require additional information, such as the leaf chlorophyl content (PROSPECT), the LAI (SDRM) and the atmospheric aerosol content (6S). A multitude of "scenario's", i.e. combinations of all these external parameters, is defined in advance. All together they should represent the variability observed in the real world (all vegetation types x atmospheres x viewing conditions ...). The coupled model is then run to compute for each scenario a number of outputs, which also include fAPAR (via the adapted SDRM) and the mentioned intermediate reflectances (BRDFcorrected ρ_{aB}/ρ_{aR}/ρ_{aN} and rectified ρ_{sR}/ρ_{sN}). The functions F_{n} and parameter sets P_{ni} are then defined by statistical analysis of the scenario database. De facto, the functions F_{n} are ratio's of polynomials and the parameter sets P_{ni} contain their coefficients.
Compared to SMAC, the combined approach of Gobron et al. (2006) does not need ancillary information on the distribution of ozone, water vapour and aerosols. But the method is only applicable for sensors such as VGT and MODIS which (in addition to the omnipresent RED and NIR) also have a BLUE band. This band lacks for AVHRR, for which another method to derive fAPAR is used (see fAPAR (Weiss et al., 2010)).
Go back to SPOTVEGETATION or TERRAMODIS preprocessing.
Land Surface Temperature (LST)
For the determination of the land surface temperature the split window method of Coll & Caselles (1997) is implemented. The brightness temperatures from channel 4 (TIR4) and channel 5 (TIR5) of AVHRR are combined with the surface emissivity (correcting for grey bodies) and the atmospheric water content is taken into account. The surface emissivity is derived from the vegetation cover fraction, in this case derived from the NDVI with the following method.
Method to calculate the vegetation cover fraction:
The vegetation cover fraction (P_{v}) is calculated using the median of the pixels with the 5% highest NDVI values is NDVI, and the median of the pixels with the 5% lowest NDVI value is NDVI_{g}.
with
Pv  : Vegetation fraction [] 
NDVI  : Normalized Difference Vegetation Index of the pixel [] 
NDVIg  : maximum Normalized Difference Vegetation Index of a bare soil pixel [] 
NDVIv  : minimum Normalized Difference Vegetation Index of a fully vegetated pixel [] 
The emissivity (ε, ) is calculated according to Valor and Caselles (1996) and Rubio et al. (1997).
with:

: pixel emmissivity [] 
_{v}

: the emmissivity of a fully vegetated pixel [] 
_{g}

: the emmissivity of a bare soil pixel [] 
d_{}

: the estimated mean error on the values of _{v} and _{g} [] 
The difference of emissivity (∆ε) as a function of the vegetation cover fraction (P_{v}) is calculated as:
with:

: pixel emmissivity difference between channel 4 and 5 [] 
_{(PV=1)}

: the difference in emmissivity of a fully vegetated pixel [] 
_{(PV=0)}

: the difference in emmissivity of a bare soil pixel respectively [] 
Corrections of the atmospheric influence on the brightness temperature:
with:
, and offset  : corrections for emissivity and water content in the atmosphere [] 
W  : the water content in the atmosphere [g.cm^{2}] 
Finally the land surface temperature (LST) is determined according to the splitwindow principle (Coll and Caselles, 1997).
LST = BT4 + [1.34 + 0.39 ^{.} (BT4  BT5)] ^{.} (BT4  BT5) + 0.56 + offset
with:  
BT4, BT5: the brigtness temperatures of channel 4 and 5 [K] 
Parameters and their default values
parameter  value 

_{v}

0.985 
_{g}

0.960 

0.02 
_{(PV=1)}

0.0023 
_{(PV=0)}

0.009 
Additional details can be found in Coll and Caselles,1997; Rubio et al., 1997 and Valor and Caselles, 1996.