Hydrologic consistency as a basis for assessing complexity of monthly water balance models for the continental United States

Methods to select parsimonious and hydrologically consistent model structures are useful for evaluating dominance of hydrologic processes and representativeness of data. While information criteria (appropriately constrained to obey underlying statistical assumptions) can provide a basis for evaluating appropriate model complexity, it is not sufficient to rely upon the principle of maximum likelihood (ML) alone. We suggest that one must also call upon a "principle of hydrologic consistency," meaning that selected ML structures and parameter estimates must be constrained (as well as possible) to reproduce desired hydrological characteristics of the processes under investigation. This argument is demonstrated in the context of evaluating the suitability of candidate model structures for lumped water balance modeling across the continental United States, using data from 307 snow-free catchments. The models are constrained to satisfy several tests of hydrologic consistency, a flow space transformation is used to ensure better consistency with underlying statistical assumptions, and information criteria are used to evaluate model complexity relative to the data. The results clearly demonstrate that the principle of consistency provides a sensible basis for guiding selection of model structures and indicate strong spatial persistence of certain model structures across the continental United States. Further work to untangle reasons for model structure predominance can help to relate conceptual model structures to physical characteristics of the catchments, facilitating the task of prediction in ungaged basins.