Analytical Expression of Horton Index Using Generalized Proportionality Hypothesis

Abstract:

Horton Index (HI) quantifies partitioning of total infiltrated precipitation into vertical plant vaporization and lateral subsurface drainage at the catchment-scale. Most studies on HI remain empirical since Robert Horton introduced it about a century ago. We present a one-parameter analytical expression of the HI as a function of the terrestrial ecosystem aridity index based on the generalized proportionality hypothesis. We then successfully validate it at 357 near-natural catchments over the conterminous U.S. across gradients of climate, landscape, and vegetation types. Our major findings include: 1) the derived equation captures between-catchments variability of HI with a single parameter, hence vegetation adaptation to long-term climate across ecoregion; 2) it captures catchment vegetation adaptation to between-years and seasonal climate dynamics; 3) the optimal parameters are statistically significantly related to topographic and vegetation characteristics; 4) alike inter-annual, the maximum-seasonal HI exhibit space-time symmetry, indicating the similarity of vegetation adaptation to water availability across biomes.