Illustration of the performance of the λf and λ correspondence indices discussed in this article on datasets with different correlations and systematic additive or multiplicative distortions. The transformation of the Arcsinus function is justified by Watterson to allow linear convergence to unity, while preserving the original characteristics of the Mielke8 index. Quantifying the proximity of two sets of data is a frequent and necessary undertaking in scientific research. The pearson-moment correlation coefficient r is a widely used measure of the degree of linear dependence between two data series, but gives no indication of the size of the values in these series. Although a number of indices have been proposed to compare a data set with a reference, little data is available to compare two data sets of equivalent (or unknown) reliability. After a brief examination and numerical testing of the metrics designed to accomplish this task, this paper shows how an index proposed by Mielke can fulfill a number of desired properties, namely in a dimensional, limited, symmetrical, easy-to-calculate and directly interpretable way with respect to r. We therefore show that this index can be considered as a natural expansion of r that regulates the value of r as a function of the distortion between the data series analyzed. The document also proposes an effective way to disentangle the systematic and non-systematic contribution to this agreement on the basis of self-cutting. The use and value of the index are also illustrated using synthetic and actual data sets. Non-compliance between time series from two Earth observation satellites, according to different compliance measures described in the text, calculated and recorded with the statistical software R (version 3.2.1, www.R-project.org/). Willmott6,20 suggested that its convergence indices could provide additional information by separating the effects due to the systematic components of the spreads. This idea can be generalized to any index formulated with equation (3) by breaking down the gaps into their systematic and non-systematic components, and then defining as and defining new systematic and non-systematic indices.
The non-system index, can be interpreted as the value that the default index would accept if all distortions are ignored, which therefore relates to the noise around a line that passes through the data. The systematic index, , is more difficult to enter. A better way to understand the information it contains is to present it as the proportion of deviations that consist of systematic noise. The selected time series, which are available in Figure 6, allow for a better assessment of the differences in the numerical value of the different metrics with respect to the data analyzed (time profiles and scatter plots). Focusing on the profiles of Figure 6c, d, collected in very dry areas, the best performance of λ is highlighted compared to AC. Both profiles show limited temporal variability and reduced correlation. AC shows a negative (and out-of-bounds) value of − 1.668 for profile c and a positive and higher value (0.227) for profile d, with lower correlation and clear distortion. λ rather displays a value lower than the two correlations and the decrease in the profile d with respect to c. Interestingly, profile d informs us that applying a linear transformation would significantly improve the chord.. . .