This paper aims to solve the problem of accurately estimating flow duration curves (FDC) in catchments lacking diachronic flow data. Based on 645 sets of observed data in the middle and lower reaches of the Yangtze River (YZR), which include 22 basin characteristic variables, eight machine learning (ML) models (SVM, RF, BPNN, ELM, XGB, RBF, PSO-BP, GWO-BP) were integrated to predict the FDC (quantiles of flow rate corresponding to 15 exceedance probabilities were studied), after which the model most suitable for predicting was determined. Finally, the SHapley Additive exPlanation (SHAP) method was used to determine and quantify the impact of various input variables on different quantiles and the degree of that influence. Results indicate that: (1) The GWO-BP model is the best ML model for predicting FDC among the eight, having good prediction performances throughout the entire duration with determination coefficients (R2) on the testing set of 0.86 to 0.94 and Nash-Sutcliff criterion (NSE) of 0.78 to 0.94. (2) The ML model (BPNN) optimized using swarm intelligence can effectively predict FDC. (3) The predictive impact of variables on different quantiles varies, with and BFI_mean contributes significantly to predicting FDC. The former has a negative effect on the prediction result and has better contribution to predicting higher flow rate (i.e., having higher accuracy in predicting the upper tail of FDC), whereas the latter is the opposite. SHAP’s explanations are consistent with the physical model, revealing local interactions between predictive factors. The results demonstrate that the method proposed in this paper can greatly improve the prediction accuracy and is innovative and valuable in model interpretation and factor selection.

This paper aims to solve the problem of accurately estimating flow duration curves (FDC) in catchments lacking diachronic flow data. Based on 645 sets of observed data in the middle and lower reaches of the Yangtze River (YZR), which include 22 basin characteristic variables, eight machine learning (ML) models (SVM, RF, BPNN, ELM, XGB, RBF, PSO-BP, GWO-BP) were integrated to predict the FDC (quantiles of flow rate corresponding to 15 exceedance probabilities were studied), after which the model most suitable for predicting was determined. Finally, the SHapley Additive exPlanation (SHAP) method was used to quantify the impact of various input variables on different quantiles and the degree of that influence. Results indicate that: (1) The GWO-BP model is the best ML model for predicting FDC among the eight, having good prediction performances throughout the entire duration with determination coefficients ( R 2) on the testing set of 0.86 to 0.94 and Nash-Sutcliff criterion ( NSE) of 0.78 to 0.94. (2) The ML model (BPNN) optimized using swarm intelligence can effectively predict FDC. (3) The predictive impact of variables on different quantiles varies, with and BFI_mean contributes significantly to predicting FDC. The former has a negative effect on the prediction result and has better contribution to predicting higher flow rate (i.e., having higher accuracy in predicting the upper tail of FDC), whereas the latter is the opposite. The results demonstrate that the method proposed in this paper can greatly improve the prediction accuracy.

The flow duration curve (FDC) is the cumulative distribution function, which represents the relationship between the frequency and magnitude of streamflow，and the precipitation duration curves (PDC) follows the same principle. Nowadays, the correlation between the shape of PDC and FDC curves, their respective physical control factors, and their fitting conditions in unmeasured catchments across China have not been fully understood. In this paper, daily precipitation from 698 weather stations across China and streamflow from more than 200 hydrological stations in the middle and lower Yangtze River basin were chosen to analyze the relationship, similarity, regional pattern and response mechanism of fitting parameters between PDC and FDCs. Framework was proposed for modeling FDC, decomposing the Streamflow time series into fast flow and slow flow time series and attributing the shapes of PDC and FDCs to catchment meteorological and geographical characteristics and physical processes. Results indicate that the parameters of PDC and certain FDCs (TFDC, FFDC, SFDC) share similar spatial patterns but the value of parameters and shape of curves varies for the different duration and interactions of the processes. The climate and catchment characteristics such as extreme properties of precipitation, base flow index ( BFI), Pmax*αp and concentration ratio index based on monthly precipitation ( CIM) will influence the shape of normalized PDC and FDCs, which provides a way to predict unmeasured catchments for PDC and FDCs, diagnose catchment rainfall-runoff responses, including similarity and differences between catchments, and can be applied to more future research about processes based on physical controls.