An important point about the non-cryptic index is that, although it does not take into account any bias, it does not mean that it corresponds to the correlation. The two also do not correspond α in the case of Difference can be appreciated by looking at a cloud of dots and turning it. This changes their correlation, but thanks to the clean fences, will remain the same. This also leads to positive values for when, which can be interpreted as noise levels in the data. 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: to summarize the result of this analysis, we can find that all metrics have at least one gap: in one way or another, the smaller index values are counter-intuitively more consistent.

For everyone, it is also unclear how they can be related to the correlation coefficient. In addition, Ji-Gallo AC has highly undesirable behaviours in the presence (but also in the absence) of bias. While the Mielke index is mathematically expensive, the index, with its simplified expression, appears to be an appropriate candidate for data comparisons if the correlation is zero or positive. However, the mathematical formulation proposed by the author does not indicate how the correlation coefficient is related. We believe that this last point deserves further investigation, as the index user generally has a clear understanding of what a correlation value means, but does not know the values that the agreement index takes itself. First generalization of the problem by indicating that we are looking for an index that quantifies the agreements between the X and Y records. The records are measured in the same units and with the same support. For most geospatialized grid data, this means that both have the same spatial and temporal resolutions. An optimal match should be as follows: spatial correspondence between time series from two Earth observation satellites, according to different compliance metrics described in the text, calculated and represented with the R statistics software (version 3.2.1, www.R-project.org/). Figure 4 shows a geometric representation of the difference between these non-cryptic squares and the total squares calculated in relation to the 1:1 line. Figure 4 also shows geometrically how these non-cryptic squares in the surface differ from what is proposed by Willmott6 and Ji-Gallo9 using the formulations of the equation (19) and (20).