*2.2. Methods*

An outline of the methodology is shown in Figure 1 We first use MODIS data to obtain relationships between the BRDF parameters, so we can use them to build different models with AVHRR data. They are then applied to MODIS and AVHRR data, using parameters derived every 3 years, and for the full time series. With these, we derive BRDF correction parameters, which are used to calculate the normalized time series using Equation (9). The normalized NDVI is obtained from the normalized red and NIR reflectances. Finally, given the lack of BRDF field measurements that can be used as a reference to evaluate the best method, we derive the noise of the time series before correction and after the model inversions. This allows us to compare the noise improvement depending on the different BRDF model inversion used, and the number of years employed. The noise is calculated using the statistical difference between the center measurement of three successive triplets and the linear interpolation between the two extremes [18]:

$$Noise(y) = \sqrt{\frac{\sum\_{i=1}^{n-2} \left( y\_{i+1} - \frac{y\_{i+2} - y\_i}{day\_{i+2} - day\_i}(day\_{i+1} - day\_i) - y\_i \right)^2}{N - 2}}.\tag{1}$$

**Figure 1.** Flow diagram of the methodology followed by this study.
