Horton Index: Conceptual Framework for Exploring Multi-Scale Links Between Catchment Water Balance and Vegetation Dynamics

Abstract

This paper is motivated to understand the multi-temporal scale characteristics of Horton Index (HI), an indicator of catchment-scale plant water use defined as the ratio of catchment vaporization (total evapotranspiration) to catchment wetting (precipitation minus surface runoff). Based on the generalized proportionality hypothesis, we first develop an analytical framework of HI applicable at multi-temporal scales as a single function of ecological aridity index (EAI), defined as the ratio of potential evapotranspiration to catchment wetting. We successfully validate this framework at the long-term, annual, and monthly scales at 343 natural catchments over the conterminous United States under varying climate and vegetation regimes. We show that vegetation plays an important role in regulating not only the partitioning of catchment wetting into vertical vaporization and horizontal baseflow, but also further partitioning of vaporization into initial and continuing components. Aided by this framework, we reveal emergent space-time similarity patterns between HI’s spatial (inter-catchment, regional) and temporal (within-catchment, inter and intra-annual) variability. On the one hand, HI increases with EAI, both spatially and temporally, following similar trends predicted by the analytical framework. On the other hand, the slopes of HI ∼ EAI relationships, denoted as d (HI)/d (EAI), decreased with EAI both spatially and temporally and, again, following similar trends suggested by the analytical framework. These findings suggest the promising potential of Horton Index as a conceptual yet quantitative framework for improving understanding and modeling of multi-scale ecological and hydrological processes and their interactions.