The general formulation for runoff components estimation and attribution at mean annual time scale

Abstract. Estimating runoff components, including surface flow, baseflow and total runoff is essential for understanding precipitation partition and runoff generation and facilitating water resource management. However, a general framework to quantify and attribute runoff components is still lacking. Here, we propose a general formulation through observational data analysis and theoretical derivation based on the two-stage Ponce-Shetty model (named as the MPS model). The MPS model characterizes mean annual runoff components as a function of available water with one parameter. The model is applied over 662 catchments across China and the contiguous United States. Results demonstrate that the model well depicts the spatial variability of runoff components with R² exceeding 0.81, 0.44 and 0.80 for fitting surface flow, baseflow and total runoff, respectively. The model effectively simulates multi-year runoff components with R² exceeding 0.97, and the proportion of runoff components relative to precipitation with R² exceeding 0.94. By using this conceptual model, we elucidate the responses of surface flow and baseflow to available water and environmental factors for the first time. The surface flow is jointly controlled by precipitation and environmental factors, while baseflow is mainly influenced by environmental factors in most catchments. The universal and concise MPS model offers a new perspective on the long-term catchment water balance, facilitating broader application in large-sample investigations without complex parameterizations and providing an efficient tool to explore future runoff variations and responses under changing climate.