Improving runoff forecasts by using observed runoff to update the subsurface moisture state in the DDD model

Observed runoff is, in principle, an ideal observation to be used for updating the moisture states in a hydrological model because runoff is 1) integrated catchment scale information (unlike precipitation and snow water equivalent, 2) usually well measured 3) frequently measured and 4) a direct measurement of what the model is supposed to predict. However, the model structure needs to be such that the discrepancies between observed and simulated runoff can easily and unambiguously be translated into altered moisture states. In this study, we have altered the subsurface moisture state in the Distance Distribution Dynamics (DDD). If the model underestimates runoff, more water is added as an extra precipitation event and if the model overestimates runoff, we subtract water by having an extra evapotranspiration event. The magnitude of the precipitation/evapotranspiration event is the sum of small increments (+- 0.5 % of the subsurface storage) which are added or reduced from the models’ subsurface storage until observed and simulated runoff are equal. In the DDD model, precipitation and evapotranspiration are distributed in time according to unit hydrographs (UH) estimated using the calibrated subsurface celerities and the distance distribution describing the distances from points in the hillslopes to the river network. The UHs can be seen as sets of weights distributing the input in time. In such a way the added and subtracted water influences the simulated runoff for a period of time determined by the temporal scale of the UHs which vary from catchment to catchment. The immediate correction on runoff is only due to a fraction of the added/subtracted water which is determined by the UHs. We have tested the updating procedure for 25 Norwegian catchments of different sizes and located all over Norway and in different climatic zones. The model is run on 3h temporal resolution and we tested the efficiency of updating for two levels of runoff; i) if observed runoff is higher 2x mean annual discharge (MAD) and the discrepancy between simulated and observed is more than 20% and ii) if observed runoff is higher than the mean annual flood (MAF) and the discrepancy between simulated and observed is more than 20%. On average for the 25 catchments, updating had a positive effect on the root mean square error for lead times less than 33 hours for events higher than MAF and for lead times less than 42 hours for events higher than 2xMAD.  For lead times less than 18 hours, 69 % of the updates improved the runoff forecasts for events higher than MAF and 70 % for events higher than 2xMAD.