Comparison of geostatistical and response surface methodology for estimating soil saturated hydraulic conductivity

Soil saturated hydraulic conductivity (Ks) is a critical parameter for modeling water and solute transport in soils. Conventional laboratory measurements of Ks are labor-intensive, costly, and susceptible to measurement errors, underscoring the need for more reliable estimation techniques. This study systematically compares the performance of Ordinary Kriging (OK), Ordinary Co-Kriging (OCK), and Response Surface Methodology (RSM) for Ks estimation, thereby integrating geostatistical and statistical optimization frameworks. Soil samples were collected from 135 locations within the surface layer (0-30 cm), and Ks along with key soil physicochemical properties were determined. In the geostatistical domain, OK based on a spherical semivariogram (R² = 0.81; nugget/sill = 10.19%) yielded moderate predictive ability (R² = 0.70, RMSE = 3.62 mm day^-1, MAE = 10.02 mm day^-1), whereas OCK employing an exponential cross-semivariogram (R² = 0.91; nugget/sill = 0.45%) substantially improved accuracy (R² = 0.85, RMSE = 3.21 mm day^-1, MAE = 9.43 mm day^-1). By contrast, RSM achieved the highest predictive performance, with a quadratic model producing R² = 0.94 and Adeq Precision = 49.2. Optimization within the experimental range indicated a maximum Ks of 137.18 mm day^-1 at 8.9% clay and 86% sand. Collectively, these findings demonstrate that while OK and OCK provide valuable insights into the spatial dependence of Ks, RSM offers superior predictive accuracy and practical applicability for optimizing soil hydraulic functions in water resources and agricultural management.