An Analytical Baseflow Coefficient Curve for Depicting the Spatial Variability of Mean Annual Catchment Baseflow

Catchment baseflow is jointly controlled by climate and landscape properties. Previous studies have recognized that spatial variability of mean annual baseflow coefficient (BFC = Qb/P, ratio of baseflow to precipitation) is primarily controlled by aridity index and storage capacity. However, an analytical solution of BFC in terms of the dominant controlling factors has not yet been established. The objective of this study was to develop an analytical BFC curve to depict spatial variability of BFC based on the "limit" concept of the Budyko framework. The BFC curve relates the baseflow coefficient to aridity index and storage capacity without resolving complex interactions between evapotranspiration and baseflow generation. The proposed BFC curve showed that, in the arid catchments, baseflow coefficient was primarily limited by available water (precipitation, P) and, in the humid catchments, was jointly controlled by both the available energy (potential evapotranspiration, E-p) and catchment retention capability (ratio of catchment storage capacity to P, i.e., S-p/P). Observed hydrological data from 950 catchments in Australia, the conterminous United States and the United Kingdom with diverse hydro-climatic conditions (BFC = 0.001-0.650) were collected to demonstrate the capability of the developed curve. Results showed that the BFC curve captured the spatial variability of observed BFC in the 950 study catchments (R-2 = 0.75, RMSE = 0.058). Mean annual baseflow estimated by the BFC curve agreed well with observed baseflow (R-2 = 0.86, RMSE = 0.19 mm). The developed analytical curve provides an analytical solution for understanding how aridity index and storage capacity control mean annual catchment baseflow, and will improve predictability of baseflow at ungauged basins.