Symbolic regression-based regionalization of baseflow separation parameter using catchment-scale characteristics

Abstract. Accurate separation of baseflow from streamflow is of utmost importance for understanding catchment hydrological processes and supporting effective water resource management. The Smooth Minima Method is a common baseflow separation technique with a segment length parameter (N) representing the catchment average flow event duration. N is usually predicted by a power function with catchment area or default to 5 days. Yet these estimations are insufficient given the multivariate nature of N with other catchment attributes. In this study, we employ symbolic regression (SR) to search for possible formulation of N with a range of catchment attributes based on 855 catchments across the Contiguous United States. We ultimately identify three mathematical expressions of increasing complexity, achieving R² values of 0.49, 0.50, and 0.54, compared to 0.23 and −0.84 for the power function and constant values. The three expressions reveal that  increases exponentially with catchment area (A) and catchment-averaged soil saturated hydraulic conductivity (K_sat) with decreasing rates, while it increases linearly with snow day fraction (f_SWE). The effects of K_sat and f_SWE on N are particularly pronounced for larger values (K_sat > 25 mm/h and f_SWE > 0.4) and smaller area (A < 100 km²). The different calculations of N are also evaluated in baseflow separation, revealing higher medians of Kling-Gupta Efficiency of at least 0.84, outperforming the literature-suggested formulas for a maximum increment of 0.22. This study highlights the potential of SR for uncovering physically meaningful formulas in optimal baseflow separation.