Sub-Daily Runoff Simulations with Parameters Inferred at the Daily Time Scale

Abstract:

Concentration times in small and medium-sized watersheds (~100–1000 km²) are commonly less than 24 hours. Flood-forecasting models then require data at sub-daily time scales, but time-series of input and runoff data with sufficient lengths are often only available at the daily time scale, especially in developing countries. This has led to a search for time-scale relationships to infer parameter values at the time scales where they are needed from the time scales where they are available. In this study, time-scale dependencies in the HBV-light conceptual hydrological model were assessed within the generalized likelihood uncertainty estimation (GLUE) approach. It was hypothesised that the existence of such dependencies is a result of the numerical method or time-stepping scheme used in the models rather than a real time-scale-data dependence. Parameter values inferred showed a clear dependence on time scale when the explicit Euler method was used for modelling at the same time steps as the time scale of the input data (1 to 24 h). However, the dependence almost fully disappeared when the explicit Euler method was used for modelling in 1−hour time steps internally irrespectively of the time scale of the input data. In other words, it was found that when an adequate time-stepping scheme was implemented, parameter sets inferred at one time scale (e.g., daily) could be used directly for runoff simulations at other time scales (e.g., 3 h or 6 h) without any time scaling and this approach only resulted in a small (if any) model performance decrease, in terms of Nash-Sutcliffe and volume-error efficiencies. The overall results of this study indicated that as soon as sub-daily driving data can be secured, flood forecasting in watersheds with sub-daily concentration times is possible with model parameter values inferred from long time series of daily data, as long as an appropriate numerical method is used.