Understanding the dynamic nature of Time-to-Peak in UK streams

In flood forecasting and design for peak flows, understanding and characterizing the hydrologic response to rainfall events is vitally important. One of the key parameters utilized to characterize the catchment response time is the Time-to-Peak (Tₚ), which represents the net rise time of a storm hydrograph, or the time from when a precipitation event begins to contribute to stream discharge, to the time that peak flow (Qₚ) is reached. Previously, influencing factors on Tₚ have been static in nature with no consideration of the variability in Tₚ due to size of the storm event and the antecedent moisture conditions of the watershed (seasonal effects). Using ~1400 storm event observations and the corresponding catchment characteristics of 153 stream gauges across the United Kingdom (UK), the importance of different factors on estimating Tₚ are evaluated. These data points span three decades, and this breadth of temporal data allowed meaningful annual trends to be observed, and seasonal variations in soil moisture to be identified and applied. A new “wetness coefficient” is applied herein, to reflect the antecedent conditions within a catchment. The Qₚ is selected as a dynamic variable, utilized to represent the magnitude of a given storm, due to the demonstrated correlation with Tₚ. An explicit equation based on gene expression programming is designed, which accounts for the dynamic nature of Tₚ through Qₚ and seasonal moisture effects. The results of the proposed model are compared to the results of the existing equation for Tₚ prediction in the UK, outlined by the Flood Estimation Handbook (FEH). The proposed equation (with Nash-Sutcliffe Coefficient, R² and RMSE values equal to 0.60, 0.66 and 3.64, respectively), has improved characteristics compared with the traditional FEH equation (Nash = 0.42, R² = 0.54, and RMSE = 4.37). A forensic analysis of the contributing factors for Tₚ involves development of an empirical model with improved prediction accuracy, by accounting for the dynamic inputs, improving previous models both statistically, as well as in the hydrologic understanding of the catchment response.