Functional model of water balance variability at the catchment scale

Abstract

This paper presents analysis of annual water balance variability, (1) regional (between-catchment) variability and (2) between-year (interannual) variability and the symmetry between the two. This involved analysis of the annual water balance in terms of a two-stage partitioning, first, of annual precipitation into quick flow and soil wetting and, subsequently, of the resulting soil wetting into slow flow and vaporization. The nature of this water balance partitioning is explored by completing the above analysis in 377 Model Parameter Estimation Experiment (MOPEX) catchments located across the continental United States. We fitted analytical functional relationships to the partitioning at each stage, producing expressions for the three components of quick flow, slow flow, and vaporization. They indicate that the heterogeneity of water balance partitioning among the MOPEX catchments is underlain by a universal relationship that is transferable regionally. Key nondimensional similarity parameters are identified that serve to connect this invariant regional relationship to site-specific response characteristics. These nondimensional formulations are extended to derive analytical expressions for several common metrics of annual water balance. The ability of the functional theory to predict regional patterns of mean annual water balance and interannual variability in individual catchments is assessed. Our analyses show a close symmetry between spatial (regional) variability of mean annual water balances and general trends of temporal (interannual) variability. The suggested functional theory can thus be the basis for data-based assessments of hydrologic similarity and used to assist with predictions of the effects of long-term climate variability and change, through providing a theoretical framework for “space for time” substitutions.