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The flow duration curve (FDC) is a hydrologically meaningful representation of the statistical distribution of daily streamflows. The complexity of processes contributing to the FDC introduces challenges for the direct exploration of physical controls on FDC. In this paper, the controls of climate and catchment characteristics on FDC are explored using a stochastic framework that enables construction of the FDC from three components of streamflow: fast and slow flow (during wet days) and slow flow during dry days. The FDC during wet days (FDC_w) is computed as the statistical sum of the fast flow duration curve (FFDC) and the slow flow duration curve (SFDC_w), considering their dependency. FDC is modeled as the mixture distribution of FDC_wand the slow flow duration curve during dry days (SFDC_d), by considering the fraction of wet days (δ) for perennial streams and bothδand the fraction of days of zero streamflow for ephemeral streams. The Kappa distribution is employed to fit the FFDC, SFDC_w, and SFDC_dfor 300 catchments from Model Parameter Estimation Experiment (MOPEX) across the United States. Results show that the 0–20th percentile of FDC is controlled by FFDC and SFDC_w, the 90–100th percentile of FDC is controlled by SFDC_d, and the 20–90th percentile of FDC is controlled by three components. The relationships between estimated Kappa distribution parameters and climate and catchment characteristics reveal that the aridity index, the coefficient of variation of daily precipitation, timing of precipitation, time interval between storms, snow, topographic slope, and slope of recession slope curve are dominant controlling factors.

The time compression (or time condensation) approximation (TCA) is commonly used in conjunction with an infiltration capacity equation for predicting the postponding infiltration rate, or, more generally, infiltration under time‐varying precipitation. In this paper a power function relationship for TCA between infiltration capacity and its time derivative is proposed for infiltration in the presence of a shallow water table. The results show that the exponent (β) in the power function relationship is not a constant but decreases as infiltration proceeds. The change ofβindicates that the TCA relationship changes during infiltration and further suggests the necessity of using different TCA relationships for predicting infiltration rate during different stages after ponding. We argue that the change ofβis due to the gradual dynamic change of the relative role of gravity and capillarity during infiltration. A Péclet number (Pe) is proposed for measuring the relative effect of gravity and capillarity. In the early times of infiltration when Pe < 1, with the increase ofPe,βdecreases roughly from 3.5 to 2 for clay, silty clay loam, and silty loam, and from 3 to 2 for sandy loam and sand; during the longer times whenPe > 1,βhas a linear relationship withPe. The relationship betweenPeandβprovides an objective approach to select the suitable TCA function during different infiltration stages after ponding.