Index Of Agreement Interpretation
In this case, the denominator μ is added together by adding up the differences of all X and Y points compared to the average of X. The original version was based on gridded deviations, but was later modified 15 using absolute deviations, arguing that MAD (or MAE in this case, because it refers to errors between forecasts and observations instead of deviation) is a more natural measure of average errors and less ambiguous than RMSD (or RMSE)12. Another refinement of the index16 was intended to remove the predictions from the denominator, but as others have argued14, this amounts to resizing the expression of the coefficient of effectiveness, while the interesting reference point is lost. Again, these indices do not meet the requirement for symmetry. 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 illustrate how the proposed index can be used in real case studies and how it is compared to other metrics, some examples are provided using real data. Geophysical data are generally structured according to the 2 or 3 known spatial dimensions and the temporal dimension, which leads to chronological series of geographic data.