Hydrological Basis of the Budyko Curve: Data‐Guided Exploration of the Mediating Role of Soil Moisture

Abstract

We present a data-guided framework to explore the hydrological basis of the Budyko curve, focusing on the role of soil moisture in mediating the partitioning of precipitation into runoff and evaporation and the role of climate in this partitioning. The conceptual framework for the derivation of the Budyko curve builds on empirically based power law relationships for long-term average scaled runoff (Q/P) and scaled evaporation (E/E p), both as functions of long-term average (equilibrium) soil moisture. A second component of the framework is an empirical power law relationship between equilibrium soil moisture and the aridity index, E p /P. Combinations of these empirical power law relationships with the long-term water balance equation give rise to a form of the Budyko curve, which is a close approximation to Budyko's original relationship and is mathematically similar to the Turc-Pike equation, thus supporting the role of equilibrium soil moisture in giving rise to the Budyko curve. In the remainder of the paper, for special cases of the parameter values of the power law relationships, we independently derive both the soil moisture dependence on E p /P as well as the Budyko curve itself that not only reproduces a new Budyko-type curve, but can also explain the spread of the empirical data points away from the mean curve. The paper also raises fresh questions about how the empirical power law relationships that govern the soil-mediated precipitation partitioning may have emerged and the role of vegetation in that mediation. "…hydrologists be aware that the logic of hydrological processes cannot be deduced from algebra" Vit Klemeŝ (1986) ©2020. American Geophysical Union. All Rights Reserved.

Climate Controls on River Chemistry

“…Here we relate mean solute concentrations to climate conditions at each site using a widely used relationship, Budyko equation. Various forms of Budyko equations relate the long‐term ratio of evaporative index to aridity index (Chen & Sivapalan, 2020; Gentine et al., 2012; Reaver et al., 2020). Here we used the original form (Budyko, 1974): $$$\frac{ET}{P}=\frac{1}{{\left[{\left(\frac{P}{PET}\right)}^{\beta }+1\right]}^{1/\beta }}$$$ where P is precipitation, ET is evapotranspiration, the summation of evaporation (from open water, bare soil, and vegetated surfaces), transpiration (from within plant leaves), and sublimation from ice and snow surfaces.…”

“…Here we relate mean solute concentrations to climate conditions at each site using a widely used relationship, Budyko equation. Various forms of Budyko equations relate the long-term ratio of evaporative index to aridity index (Chen & Sivapalan, 2020;Gentine et al, 2012;Reaver et al, 2020). Here we used the original form (Budyko, 1974):…”

Data‐Guided Exploration of the Energy Partitioning at Land Surface in the Contiguous US

“…Nevertheless, these datasets, namely NARR, GLEAM, MOPEX, and Zhang's remote‐sensing data set are all well‐established datasets that have been validated against field measurements. Furthermore, these datasets have been successfully applied in previous studies (Chen & Sivapalan, 2020; Chen et al., 2013; Yin et al., 2019). It is a potential research direction to test our hypothesis with other datasets in the United States and other regions across the world.…”

Hydrological Basis of Different Budyko Equations: The Spatial Variability of Available Water for Evaporation

“…The long‐term available water for evaporation at a point within a catchment is defined as a statistical average over multiple wetting‐drying cycles on a large range of timescales following the definition of the long‐term soil moisture in Chen and Sivapalan (2020), and is denoted as $$\theta $$. The value of $$\theta $$ varies within a catchment due to the spatial heterogeneity of precipitation, soil properties, topography, and vegetation (Fan et al., 2017; Gao et al., 2019; Jothityangkoon et al., 2001; Milly, 1994; Troch et al., 2002; Western et al., 1999).…”

“…Though Budyko equations have been increasingly used for interpreting long‐term water balance, few studies have been conducted to explore the hydrological basis of Budyko equations (Berghuijs et al., 2020). Recently, Chen and Sivapalan (2020) reported the role of long‐term average soil moisture in giving rise to the Budyko curve based on data‐guided empirical relationships, and the soil moisture was assumed as a representation of water storage. In addition to soil moisture, vegetation interception, surface water storage, and shallow groundwater storage could be a significant portion of catchment scale water storage.…”