## 2 Materials and Methods
### Evaluation Metrics  
The study employs six evaluation metrics to assess model performance: the coefficient of determination (R\({}^{2}\)), root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE), mean bias error (MBE), and the ratio of performance to interquartile range (RPIQ).  
R\({}^{2}\), RMSE, MAE, MARE, and MBE are widely used evaluation metrics in the fields of soil spectral data prediction and artificial intelligence [45]. R\({}^{2}\) reflects the correlation between the actual soil SOM content and the model's predicted values. The closer R\({}^{2}\) is to 1, the higher the model's accuracy, as shown in Equation (16). RMSE indicates the deviation between the actual soil SOM content and the model's predicted values. It is negatively correlated with model stability, as shown in Equation (17). MAE measures the accuracy of the predictive model. The smaller the MAE, the higher the model's accuracy, as shown in Equation (18). MBE measures the tendency to overestimate or underestimate parameter values. A positive bias means the error is overestimated, while a negative bias means the error is underestimated. This metric quantifies overall bias and captures the average deviation in predictions, as shown in Equation (19). MARE measures the degree of deviation between the predicted and actual values by calculating the relative error between them and taking the average of their absolute values, as shown in Equation (20).  
The Relative Percent Difference (RPD) reflects both the reliability and accuracy of a model, and it is widely used by many soil researchers [46; 47]. However, there is no consensus on the threshold values based on statistical studies. For example, [PERSON] et al. defined the RPD threshold for evaluating SOM prediction models as follows: RPD < 2 indicates that the model does not meet prediction requirements, while RPD > 3 indicates that the  
Figure 4: BAK-CNN-SVM model flowchart.  
model performs excellently [48]. In contrast, [PERSON] et al. defined the two thresholds as 1.4 and 2 [49]. Additionally, the standard deviation (SD) used in RPD cannot accurately describe the distribution range of a population in a skewed distribution. Spectral data are influenced by various physicochemical properties of the sampling points, and ideal normal distribution conditions are rare, further affecting the evaluation of models using the RPD metric. RPD is shown in Equation (20).  
[PERSON] et al. [50] proposed a new evaluation metric based on quartiles: the Ratio of Performance to Interquartile Distance (RPIQ), which better describes the distribution of a population regardless of its shape. Quartiles play a key role in population distribution: Q1 indicates that 25% of the samples are below this value, while Q3 indicates that 75% of the samples are below this value. The interquartile range (IQ) is calculated as Q3 minus Q1, representing the span of the middle 50% of the population around the median. Compared to RPD, RPIQ is not affected by the SD and addresses the existing limitations of using near-infrared spectroscopy for soil characterization. RPIQ is shown in Equation (21).  
\[R^{2}=1-\sum_{i=1}^{n}\frac{(x_{i}-\widehat{x_{i}})^{2}}{(x_{i}-\overline{x_{ i}})^{2}} \tag{15}\]  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\widehat{x_{i}})^{2}}{n}} \tag{16}\]  
\[MAE=\frac{\sum_{i=1}^{n}|x_{i}-\widehat{x_{i}}|}{n} \tag{17}\]  
\[MARE=\frac{1}{n}\sum_{i=1}^{n}\left|\frac{x_{i}-\widehat{x_{i}}}{x_{i}}\right| \tag{18}\]  
\[MBE=\frac{\sum_{i=1}^{n}(x_{i}-\widehat{x_{i}})}{n} \tag{19}\]  
\[RPD=\frac{SD}{RMSE} \tag{20}\]  
\[RPIQ=\frac{Q3-Q1}{RMSE} \tag{21}\]  
where \(n\) represents the total number of samples. \(x_{i}\), \(\widehat{x_{i}}\), and \(\overline{x_{i}}\) denote the actual value, predicted value, and mean value of the soil SOM content for the \(i\)-th sample, respectively.