the last term is proportional to the covariance between X and Y. One way to create an index explicitly containing this term of covariance in the denominator and limit it to always being positive: to summarize the result of this analysis, we can see that all metrics have at least one gap: at some point, the smaller index values are counter-intuitive. 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. The index has the desirable additional property that if there is no additive or multiplier distortion, it takes the value of the correlation coefficient. In the event of distortion, the index takes a value of less than r according to a multiplication coefficient α which can only take a value between 0 and 1. On the basis of the equation (10), it can be demonstrated effectively (see Additional Information) that: Symmetrical, i.e.

it should have the same numerical value when values are switched from and in the equation. This is necessary because it is assumed that there is no comparison for the evaluation of the agreement. 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. Watterson8 proposed to create an index to assess the performance of the climate model by applying a transformation of Arcsine to the Mielke index: Willmott et al. (2011) proposed a new index, dr, and they compared the dr to “mean absolute error (MAE) ” recordings, which vary logically with MAE.

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