One-Day Offset between Simulated and Observed Daily Hydrographs: An Exploration of the Issue in Automatic Model Calibration

Abstract:

The literature of hydrologic modelling shows that in daily simulation of the rainfall-runoff relationship, the simulated hydrograph response to some rainfall events happens one day earlier than the observed one. This one-day offset issue results in significant residuals between the simulated and observed hydrographs and adversely impacts the model performance metrics that are based on the aggregation of daily residuals. Based on the analysis of sub-daily rainfall and runoff data sets in this study, the one-day offset issue appears to be inevitable when the same time interval, e.g. the calendar day, is used to measure daily rainfall and runoff data sets. This is an error introduced through data aggregation and needs to be properly addressed before calculating the model performance metrics. Otherwise, the metrics would not represent the modelling quality and could mislead the automatic calibration of the model. In this study, an algorithm is developed to scan the simulated hydrograph against the observed one, automatically detect all one-day offset incidents and shift the simulated hydrograph of those incidents one day forward before calculating the performance metrics. This algorithm is employed in the automatic calibration of the Soil and Water Assessment Tool that is set up for the Rouge River watershed in Southern Ontario, Canada. Results show that with the proposed algorithm, the automatic calibration to maximize the daily Nash-Sutcliffe (NS) identifies a solution that accurately estimates the magnitude of peak flow rates and the shape of rising and falling limbs of the observed hydrographs. But, without the proposed algorithm, the same automatic calibration finds a solution that systematically underestimates the peak flow rates in order to perfectly match the timing of simulated and observed peak flows.