This study proposes a framework for developing a probabilistic lag time (PLT) equation by taking into account uncertainty factors, including the rainfall factor (i.e., the maximum rainfall intensity), the hydraulic factor (i.e., the roughness coefficient in the river), and the geometrical factors (the catchment area, the length, and the basin slope). The proposed PLT equation is established based on the lag time equation by means of the uncertainty and risk analysis, i.e., the advanced first-order and second-moment approach. Hourly rainfall data in the Bazhang River watershed are used in the model development and application. The results indicate that compared with observed lag times extracted from historical events, the observed ones are mostly located within the 95% confidence interval of the simulated lag times. In addition, the resulting underestimated risk from the PLT equation can reasonably represent the degree of the difference between the estimated lag time and observed lag time. Consequently, the proposed PLT equation not only estimates the lag time at specific locations along the river, but also provides a corresponding reliability.

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