## Appendix D Model Performance Metrics  
In addition to the AIC and \(\rho\) indices, model assessment here is mainly based on the SEE, MPE and mean percent standard error (MPSE) indices that rely in on statistics of squared and absolute deviations of observed to predicted values. According to [PERSON] [137] the use of SEE, MPE and MPSE statistics as model performance metrics were first recommended by [PERSON] [138] and have subsequently been used by [PERSON] [130]. We provide ahead related formulae and explanation. Akaike information criterion (AIC):  
\[\text{AIC}=-2l\big{(}\hat{\theta}\big{)}+2p \tag{115}\]  
[PERSON]'s concordance correlation coefficient:  
\[\rho_{C}=\frac{2\rho\sigma_{Y}\sigma_{X}}{\left(\mu_{X}-\mu_{Y}\right)^{2}+ \sigma_{Y}^{2}+\sigma_{Y}^{2}} \tag{116}\]  
with \(\rho\) standing for Pearson's correlation coefficient. The \(\rho_{C}\) index estimates through,  
\[\hat{\rho}_{C}=\frac{2S_{YX}}{\left(\overline{Y}-\overline{X}\right)^{2}+S_{ Y}^{2}+S_{X}^{2}} \tag{117}\]where,  
\[\overline{Y}=\frac{1}{n}\sum y_{i},\ \overline{X}=\frac{1}{n}\sum x_{i}\]  
\[S_{Y}^{2}=\frac{1}{n}\sum(y_{i}-\overline{y})^{2},\ \ S_{X}^{2}=\frac{1}{n}\sum(x_{i}- \overline{x})^{2}\]  
\[S_{XY}=\frac{1}{n}\sum(x_{i}-\overline{x})(y_{i}-\overline{y})\]  
Determination coefficient (\(R^{2}\)):  
\[R^{2}=\frac{\sum\left(\hat{Y}_{i}-\overline{Y}\right)^{2}}{\sum\left(Y_{i}- \overline{Y}\right)^{2}} \tag{100}\]  
Standard error of estimation (SEE):  
\[SEE=\sqrt{\sum\left(y_{i}-\hat{y}_{i}\right)^{2}/\left(n-p\right)} \tag{101}\]  
Mean prediction error (MPE):  
\[MPE=t_{\alpha}(SEE/\overline{y})/\sqrt{n}\times 100 \tag{102}\]  
Mean percent standard error (MPSE):  
\[MPSE=\frac{1}{n}\sum\left|(y_{i}-\hat{y}_{i})/\hat{y}_{i}\right|\times 100 \tag{103}\]  
The AIC index allows comparing performance of different candidate models that fit a set of data. The model with the lowest AIC value is considered the best among competitors. The AIC index establishes a compromise between the goodness of fit of a model and its complexity, which is expressed through linked log-likelihood and number of parameters as a way to penalize inclusion of unnecessary ones. As it is based on information entropy, an AIC index is often interpreted, as an estimate of the information lost when a model is used to represent the process that generates the data. Lin's concordance correlation coefficient (\(\rho_{C}\)) measures how well one variable (Y) reproduces another (X), that is, it represents a measure of the similarity (or agreement) between the two variables. This index can be estimated, with sample sizes of at least ten pairs (x, y). The R square index (\(R^{2}\)) also called determination coefficient interprets through the ratio (SS due to regression/Total SS corrected for the mean) and is mainly intended as a measure of closeness between response values and adjusted linear regression models. This index also measures the proportion of the total variation of the response, around the average, explained by the model. The coefficient of determination takes values between zero and one. When \(R^{2}\) attains its maximum value, one, the response variable is fully explained by the predictive variables of the fitted linear regression model. According to [PERSON] [137] using the coefficient of determination as a fit index aimed to compare performance of biomass models was first suggested by [PERSON] [138]. Nevertheless, for non-linear models a high \(R^{2}\) value does not necessarily associates with high reproducibility strength. The standard error of estimation SEE is of widespread use in statistical texts and also widely reported in statistical software. This index bears a global assessment of goodness of fit of a model to observed data, as it measures the accuracy of (\(\hat{y}_{i}\)) predictions produced by a fitted regression model. This index takes non-negative values.