an illustration of the functioning of different symmetric conformity measures discussed in this article in relation to data sets containing: (a) different correlations and systematic additive distortions; (b) different correlations and systematic multiplicative distortions; and (c) variable additive and multiplicative biases with correlation. For column (c), the values consist of the differences between the metrics calculated on a dataset containing a particular addictive and/or proportional systematic bias, minus the values calculated for the same data sets, but without distortion. As popular as it is, Pearson correlation is only appropriate for measuring the correlation between ui and vi if the two variables follow a linear relationship. If the bivariate result (ui, vi) follows a nonlinear relationship, p⌢ is not an informative measure and difficult to interpret. Willmott6 proposed another index for evaluating the performance of the model based on measured observations, which can be generalized as follows: the RMSE has the same units as the measured and calculated data. Smaller values indicate a better match between the measured and calculated values. We discussed the concepts of coherence and correlation and described different measures that assess the relationships between variables of interest. We focused on measurements and methods to achieve continuous results. For non-continuous results, different methods should be used.
For example, for categorical results, another version of Kendalls Tau, known as Kendalls Tau b, can be used to assess correlation and Kappa to assess compliance.  Among the efficiency-based indices (EF) proposed to evaluate model performance, the nash and Sutcliffe coefficients (Nash and Sutcliffe 1970) and the effectiveness of the Loague and Green (1991) models are widely used. Many researchers (Addiscott and Whitmore in 1987, Martorana and Bellocchi in 1999, Rivington et al. 2005, Moriasi et al. 2007) have found that a model may be considered appropriate on the basis of statistics, but that it may be deficient according to another statistic. Alexandrov et al. (2011) stressed the need for a standardized assessment instrument. If we can accept the use of an index based on MAE and not on MAE, we argue that the right metric should be a slightly modified version of the Mielke index. This argument comes from the idea that, for an index constructed on the basis of the structure of equation (3), the objective should be to define the denominator μ as the maximum value that the meter can take δ. It is important to find the smallest value that maximizes the meter (i.e.
its supremum) in order to guarantee an index with the maximum possible sensitivity. For indices based on the MSE, it is possible to show (see More Information) that the counter can be rewritten as follows: unlike the Pearson correlation, it also applies to nonlinear relationships and thus meets the aforementioned limitation, related to the Pearson correlation. The Nash-Sutcliffe yield (ENS) varies between -∞ and 1.0, and ENS = 1 is the optimal value. ENS≤0.0 indicates unsatisfactory performance and 0<ENS<1 is considered an acceptable area. To summarize the result of this analysis, it is possible to see that all metrics have at least one gap: in one way or another, the small values of the index counterintuitively represent a greater concordance. . . .