## 3 Field Data Acquisition and Processing
### Evaluation Criteria  
Evaluation criteria are a crucial step in assessing the performance and predictive accuracy of regression models. Many researchers have recommended considering multiple evaluation metrics to gain a comprehensive understanding of the models' performance and to make informed decisions in regression analysis. The criteria for model evaluation were based on utilizing the key performance metrics used in most of the recent studies on the development of machine learning regression models. For this purpose, the coefficient of determination (R\({}^{2}\)), root-mean-squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), index of agreement (IA), and Kling-Gupta Efficiency (KGE) were calculated for training and testing datasets using the formulae given in Equations (29)-(34), where, 'r' is the Pearson's correlation coefficient, '\(\alpha\)' is the measure of variability, 'B' is the bias, 'y\({}_{i}\)' is the actual value, '\(\hat{y}_{i}\)' is the predicted value, and '\(\overline{y}\)' is the mean of 'N' observations. \[R^{2}=1-\frac{\sum(y_{i}-\hat{y}_{i})^{2}}{\sum(y_{i}-\overline{y})^{2}} \tag{29}\]  
\[RMSE=\sqrt{\frac{\sum(y_{i}-\hat{y}_{i})^{2}}{N}} \tag{30}\]  
\[MAE=\frac{|y_{i}-\hat{y}_{i}|}{N} \tag{31}\]  
\[MAPE=\frac{1}{N}\sum_{i=1}^{N}\left|\frac{(y_{i}-\hat{y}_{i})}{y_{i}}\right| \tag{32}\]  
Figure 12: Distribution of the variables in the dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Variable** & **Unit** & **N** & **Mean** & **SE Mean** & **St. Dev** & **Min.** & **Q1** & **Median** & **Q3** & **Max.** & **IQR** \\ \hline B & m & 231 & 5.61 & 0.17 & 2.59 & 2.66 & 3.66 & 4.70 & 6.56 & 11.95 & 2.90 \\ \(l_{l}\)/\(l_{\text{th}}\) & - & 231 & 0.44 & 0.00 & 0.07 & 0.28 & 0.38 & 0.45 & 0.49 & 0.58 & 0.11 \\ \(l_{\text{l}}\)/B & - & 231 & 0.96 & 0.01 & 0.22 & 0.62 & 0.77 & 0.98 & 1.08 & 1.66 & 0.31 \\ B/d & - & 231 & 30.64 & 0.49 & 7.41 & 16.22 & 25.58 & 30.16 & 35.98 & 45.87 & 10.40 \\ \(W\) & kcal/m\({}^{3}\) & 231 & 672.30 & 23.40 & 355.90 & 281.20 & 398.90 & 523.80 & 929.00 & 1778.80 & 530.00 \\ \(\rho_{r}\) & g/cm\({}^{3}\) & 231 & 2.87 & 0.06 & 0.85 & 1.96 & 2.43 & 2.65 & 2.69 & 4.39 & 0.26 \\ \(v_{\gamma}\) & m/s & 231 & 24.04 & 0.50 & 7.63 & 10.41 & 19.02 & 21.72 & 30.65 & 37.89 & 11.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the sample dataset used in this study. \[IA=1-\frac{\sum_{i=1}^{N}(y_{i}-\hat{y_{i}})^{2}}{\sum_{i=1}^{N}( \left|y_{i}-\overline{y}\right|+\left|\hat{y_{i}}-\overline{y}\right|)^{2}} \tag{33}\] \[KGE=1-\sqrt{\left(1-r\right)^{2}+\left(\alpha-1\right)^{2}+\left( \beta-1\right)^{2}} \tag{34}\]  
The R\({}^{2}\) score of a model quantifies the fraction of the variability in the dependent variable that is accounted for by the independent variables within the model. Its value ranges from 0 to 1, where values closer to 1 indicate a better fit. On the other hand, RMSE calculated the average magnitude of the residuals (difference between the observed and the estimated values) by taking the square root of the mean of squared residuals. It provides a measure of the average prediction error, with lower values indicating better prediction accuracy. The advantage of RMSE is that it has the same unit of measurement as that of the dependent variable. In contrast to RMSE, MAE calculates the mean absolute disparity between predicted and actual values, representing a quantitative measure where smaller values signify superior outcomes. MAPE expresses the average percentage deviation between the actual and predicted values, and a lower MAPE value indicates a more accurate model. IA was introduced by [PERSON] [93] and is a standardized gauge of model prediction error whose value ranges from \(-\infty\) to 1. It is calculated as the ratio of mean-square error to potential error; an IA value of 1 signifies perfect correspondence while values closer to zero and negative values denotes poorer agreement.