A new method to identify time to peak in Unit Hydrographs

Catchment response time is an important parameter in hydrological models, particularly in peak flow prediction in catchment scale. Unit hydrographs are hydrological tools that represent the direct runoff response of a catchment to a unit of effective rainfall distributed evenly over a specified duration. They are used to predict the runoff from rainfall events, aiding in flood forecasting, water resource management, and design of drainage systems.The Unit Hydrograph time to peak (Tp), as proposed in the Flood Estimation Handbook in the UK, is a time parameter that represents the response time of runoff to rainfall. In the Flood Estimation Handbook, the ReFH model employs the unit hydrograph model to transform the rainfall to the direct runoff. Notably, the time parameter Tp, representing the time from the start to the peak in the unit hydrograph model, cannot be directly observed from rainfall and runoff time series.In previous studies, the observed values of Tp were obtained through calibration. In practical applications, two common issues are often encountered when determining Tp through calibration:Ambiguity in Tp Determination: Due to the sensitivity of the calibration process to input data and parameter assumptions, the Tp value obtained may not be unique, leading to potential inconsistencies. Overfitting to Observed Data: The calibration process may result in a Tp value that fits the observed data well but lacks generalizability, especially when applied to events or catchments with a higher baseflow index or lower direct runoff. This study introduces a new methodology to directly calculate Tp from rainfall and runoff time series. The principle of this method is based on the definition of Tp, thereby addressing the issues associated with calculating Tp through calibration as mentioned above. In this new method, the observed rainfall and runoff intensities are treated as realizations of random variables. The variance of the timing of rainfall and the variance of the timing of runoff are recognized as measures representing the time scales of rainfall and runoff events. Using these variances, the variance of the timing of the Unit Hydrograph can be derived. Since Tp is the only parameter in the ReFH model that influences the variance of time of the UH, it becomes possible to directly calculate Tp from the computed variance of time of the UH. This eliminates the need for calibration and provides a straightforward way to estimate Tp based on the intrinsic relationship between rainfall, runoff, and the unit hydrograph.In this research, we study the 50 large events in 431 catchments in UK from the CAMELS-GB.The results indicate that Tp calculated using the new method is comparable to Tp obtained through calibration in catchments with a low baseflow index. However, in catchments with large baseflow index, the new method provides more reliable results. Replacing calibration with the new method to calculate Tp allows the ReFH model to be applied to a broader range of catchments.