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 (Ksat) with decreasing rates, while it increases linearly with snow day fraction (fSWE). The effects of Ksat and fSWE on N are particularly pronounced for larger values (Ksat > 25 mm/h and fSWE > 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.