Multiple-criteria calibration of a distributed watershed model using spatial regularization and response signatures

This paper explores the use of a semi-automated multiple-criteria calibration approach for estimating the parameters of the spatially distributed HL-DHM model to the Blue River basin, Oklahoma. The study was performed in the context of Phase 2 of the DMIP project organized by the Hydrology Lab of the NWS. To deal with the problem of ill conditioning, we employ a regularization approach that constrains the search space using information contained in a priori estimates of the spatially distributed parameter fields developed from soils and other geo-spatial datasets. Unlike the commonly used spatial-multiplier method, our more general approach allows the parameters to depart non-uniformly (to some degree) from the a priori spatial pattern. The approach reduces the number of unknowns to be estimated using historical input-output data from 860 to 35. Two commonly used summary statistics of the model residuals, MSE and MSEL, are used to optimize fitting of the model to both the peaks and the recession periods of the time series data. A signature measure approach is used to select parameter sets that are close to Pareto-optimal in terms of MSE and MSEL, but which provide more consistent representation of the hydrologic behavior of the watershed as summarized by measures derived from the flow duration curve. While the results support the methods used in this analysis and show considerable improvement over the a priori parameter estimates, we find that the basin has some peculiar behaviors (including time non-stationarity) that the HL-DHM model as implemented is not set up to reproduce.