## Appendix A  
The physical interpretation and the mathematical formulas for the various statistical indicators used in this work (i.e., MBE, RMSE, \(\rho\), R\({}^{2}\), \(\sigma\), SEE) are given here. In all expressions below, \(E\) represents estimates and \(O\) indicates observations; \(N\) is the number of observations in a data set.  
The mean bias error (MBE) captures the average bias of the estimates. A positive bias indicates that the predictions from the regression line are overestimated in respect to the observations and vice versa. The formula for MBE is the following:  
\[\text{MBE}=\frac{\sum_{i=1}^{N}\left(E_{i}-O_{i}\right)}{N} \tag{1}\]The root mean square error (RMSE) is frequently used as a measure for the differences between values predicted by a model (in this case the regressions lines) and the observations. These differences are called residuals. The residuals are a measure of how far from the regression line the estimated data points are. The RMSE is, therefore, a measure of how spread out these residuals are. In other words, the RMSE indicates how concentrated the estimated data points around the best-fitted line are. Its formulation is the following:  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{N}\left(E_{i}-O_{i}\right)^{2}}{N}} \tag{10}\]  
The Pearson's correlation coefficient (\(\rho\)) expresses the linear correlation (co-variance) between observations and estimates. Its formula is the following:  
\[\rho=\frac{\sum_{i=1}^{N}\left(O_{i}-\overline{O}\right)\cdot\left(E_{i}- \overline{E}\right)}{\sqrt{\sum_{i=1}^{N}\left(O_{i}-\overline{O}\right)^{2} \cdot\sqrt{\sum_{i=1}^{N}\left(E_{i}-\overline{E}\right)^{2}}}} \tag{11}\]  
where the bars over \(E\) and \(O\) mean the averages of the estimated and observed values in the data sets. With \(\rho=0\), there is no correlation between the estimates and observations data. When \(\rho=1\), the correlation is perfect (the two data sets co-vary), and with \(\rho=-1\), there is an anti-correlation (the two data sets anti-vary).  
The coefficient for determination or coefficient of determination (R\({}^{2}\)) measures how well a model (in this case, the regression lines) predicts an outcome, i.e., an observation. R\({}^{2}\in[0,1]\); for R\({}^{2}=0\), the model's performance is the worst (the observations lie far from the best-fit line), while the model is quite successful for R\({}^{2}=1\) (the observations are very close to or coincide with the best-fit line). In another explanation, R\({}^{2}\) is a measure of the goodness-of-fit of the estimated to the observed values. Its formulation is the following:  
\[\text{R}^{2}=\rho^{2} \tag{12}\]  
The standard deviation (\(\sigma\)) is a statistic that measures the dispersion of a data set (in this case, the observations or the estimations, \(x\)) around their mean value (\(\overline{x}\)). It is given by:  
\[\sigma=\sqrt{\frac{\sum_{i=1}^{N}\left(x-\overline{x}\right)^{2}}{N-1}} \tag{13}\]  
The standard error of estimate (SEE) is a measure of variation in the observations around the computed best-fit line. In other words, it is used to check the accuracy of the estimates made with the regression line. Therefore, the smaller SEE is, the closer the observations to the regression line are. If SEE = 0, the observations fall on the regression line and the model is perfect. Its expression is the following:  
\[\text{SEE}=\sqrt{\frac{\sum_{i=1}^{N}\left(E_{i}+O_{i}\right)^{2}}{N-2}} \tag{14}\]