Table of indexes of agreements and agreements on the data sets examined in this paper, with different correlations and systematic additive or multiplier distortions. The first case of study is satellite measurements of the Standardized Difference Vegetation Index (NDVI) obtained from October 1, 2013 to May 31, 2014 on Northwest Africa. The spatial resolution is 1 km and the temporal resolution is a decade (a decade is a period that results from the division of each calendar month into 3 parts, which can take values of 8, 9, 10 or 11 days). The data are obtained from two different instruments on two different satellite platforms: SPOT-VEGETATION and PROBA-V (these are called VT and PV for simplicity). PV data is available through the copernicus Global Land Service Portal24, while VT archive data is provided courtesy of the GFC MARSOP25 project. Although the geometric and spectral characteristics of satellites and data processing chains have been as close as possible, differences between products are still expected because the instruments are not identical. The aim here is to quantify where the time series do not coincide in the region. Since there is no reason to argue that one should be a better reference than the other, a symmetrical match index should be applied to each pair of time series, resulting in values that can be attributed geographically. To calculate these new derivative indices, we must first characterize the relationship between X and Y, which then allows the calculation and finally that of δ.

The theoretical relationship between X and Y is considered linear: . Willmott6 uses an ordinary regression to the smallest square to appreciate a and b. This may be acceptable if the X-Dataset is considered a reference, but not if one tries to get an agreement without taking a reference, because there is a violation of the symmetry between X and Y, i.e. a regression from X to Y does not correspond to that of Y to X. To solve this problem, Ji-Gallo9 proposes to use a geometric model of average functional relationship (GMFR) 21.22, for which b and a are derived as follows: Mielke7,17 proposed another definition of the μ denominator based on a non-parametric approach with random permutations. In this case, the baseline consists of the sum of the differences between each point and each other point. Such an index can be generalized for different γ values as such: Willmott66,20 has proposed that its indexes of concordance provide additional information by dissociating the effects due to the systematic components of non-systematic deviations. This idea can be generalized to any index formulated by the equation (3) by breaking down the differences into their systematic and non-systematic components, and then defining as and defining new systematic or non-systematic indices.