*B1(B2)*

Given that the red AVHRR band (B1) is noisy due to the higher errors in the atmospheric correction, we attempt to correct the red band using the parameters from the NIR band. The relationships between them are estimated using MODIS data, which has a robust atmospheric correction and is now a well-established product [28]. We derive the NIR parameters using normal VJB inversion, so one value of V and R for each of the five NDVI populations in each pixel. Then, we apply Equation (10) and continue with the regular VJB method procedure (dependence with NDVI). These relationships are derived in the results section, but are:

$$V\_{B1} = 0.82 \ast V\_{B2} + 0.11$$

$$R\_{B1} = 0.91 \ast R\_{B2} + 0.04.\tag{11}$$

*Stable*

In this inversion, we hypothesize that the instability of AVHRR BRDF parameters is due to performing a matrix inversion using two parameters. This provides occasionally very unstable correction parameters when using noisy data. For this reason, we calculate the VB1 parameter using the NDVI, and the VB2 parameter from the VB1. We finally solve R for each band from the second equation of Equation (6). Again, this is done for each of the 5 NDVI populations within every pixel, after which a linear regression with the NDVI is performed.

$$V\_{B1} = 1.42 \ast N DVI + 0.63$$

$$V\_{B2} = 0.83 \ast V\_{B1} + 0.30.\tag{12}$$
