Enhancing accurate prediction of soil permeability coefficients using data-driven approaches for soil and water conservation

Soil permeability coefficient (k) is crucial for water conservation, drainage projects, and watershed management. In the present study, for modeling k, two powerful white box data-driven techniques, including Multivariate Adaptive Regression Splines (MARS) and Gene Expression Programming (GEP), and soil physical parameters including water content ( \(\omega\) $\omega$ ), void ratio ( \(e\) $e$ ), liquid limit ( \(LL\) $\mathit{LL}$ ), plastic limit ( \(PL\) $\mathit{PL}$ ), clay content ( \(CC\) $\mathit{CC}$ ) and specific density ( \(\gamma\) $\gamma$ ), were used. MARS provides simple linear functions, and in contrast, GEP presents complex equations for the estimation of k. Therefore, it seems the application of MARS is more straight-forward compared to GEP for the prediction of k. Statistical indices such as coefficient of determination (R²), correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) were used for the evaluation of the generated equations. The MARS model demonstrated high accuracy with R² = 0.9265, R = 0.9625, MAE = 0.0025, and RMSE = 0.0041 for all datasets. In addition, a comparison of MARS with existing data-driven approaches using the ranking mean (RM) method and the objective function (OBJ) parameter indicated that MARS achieved the lowest value of OBJ (0.0033) and the highest value of RM (1.3) compared to existing data-driven approaches. This confirmed the superior performance of MARS in predicting k compared to other data-driven models. Furthermore, graphical evaluations conducted to assess the performance of the GEP and MARS models confirmed better performance of MARS than GEP. The sensitivity and SHAP analysis revealed that the most effective parameters for predicting k were consistent with previous studies.