SzR is a measure of dynamic correspondence. Smaller values suggest better consistency. RMSE, ME, STD are linked by the following formula From the time series selected in Figure 6, we can better estimate the differences in the numerical value of the different metrics compared to the data analyzed (time profiles and dispersal diagrams). By focusing on the profiles of Figure 6c,d collected on very dry areas, the best performance of n compared to AC is clear. Both profiles have limited temporal variability and reduced correlation. AC has a negative (and a-bounds) value of €1,668 for profile c and a positive and higher value (0.227) for the d profile, which has a lower correlation and clear distortion. Rather, it shows a value below both correlations, and decreases for the d profile relative to c. It is interesting to note that the d profile tells us that the application of a linear transformation would greatly improve the agreement. Legates, D.
R. – McCabe, G. J. A refined index of the model`s performance: a counter-response. International Journal of Climatology 33, 1053-1056. Quantifying the proximity of two data sets is a common and necessary undertaking in the field of scientific research. The pearson-moment r correlation coefficient is a widespread measure of the degree of linear dependence between two sets of data, but gives no indication of the similarity of the values of these series in size. Although a number of indices have been proposed to compare a dataset to a reference, little data is available to compare two datasets with equivalent (or unknown) reliability. After a brief review and numerical testing of the metrics designed to accomplish this task, this document shows how an index proposed by Mielke can, with a minor modification, satisfy a number of desired characteristics, namely a dimensional, limited, symmetrical, easy to calculate and directly interpretable in relation to r.
We therefore show that this index can be considered a natural extension to r, which regulates the downward r value according to the distortion between the data sets analyzed. The document also proposes an effective way to unravel the systematic and non-systematic contribution to this agreement on the basis of own decompositions. The use and value of the index are also illustrated on synthetic and real data sets. Another common approach is to take into account that a statistical model can be adapted to the data. In this case, a measure of match can be inferred from the determination coefficient, which indicates how well the data corresponds to the chosen model. For linear models, the determination coefficient corresponds to the r square and varies from 0 to 1. Another interesting feature is that this number represents the share of variance explained by the model. One of the drawbacks of R and R2 is that they only measure the strength of the relationship between the data, but they do not give any indication as to the size of the data sets. 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. The equation (10) provides effective evidence (see additional information): To illustrate how the proposed index can be used in real case studies and how it is compared to other metrics, some examples of actual data are provided. 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. It is often interesting to evaluate separately the evolution over time of spatial concordance and the patterns of temporal correspondence with the dedicated protocols23.