Hydrological Spaces of Long‐Term Catchment Water Balance

Abstract

Land and water management often relies upon relationships describing the catchment-scale water balance using only a few parameters. The classic Budyko and Turc frameworks are examples of these relationships applicable to large catchments, where the effect of climatic variables on the water balance overshadows that of catchment characteristics, including the catchment ability to store water to supply evapotranspiration. To account for the latter in the list of variables driving evapotranspiration, here we introduce a new framework that includes Budyko and Turc as particular cases. The four variables in this framework are combined to form dimensionless groups, the choice of which leads to the definition of hydrological spaces highlighting different features of the long-term hydrological partitioning. In addition to the Budyko and Turc spaces, suitable for water-and energy-limited catchments, respectively, a new space ensues; this is especially apt to describe catchments where evapotranspiration is mainly controlled by catchment characteristics. An existing stochastic model for the soil water balance is used to specify the relationship between the variables in these different hydrological spaces. This framework, successfully tested here against about 400 catchments in the continental United States, provides a concise yet realistic description of long-term catchment-scale water balance and overcomes some limitations of current models for the estimation of long-term evapotranspiration and runoff in ungauged catchments.

Hydrology without dimensions

“…Since each of the fluxes (L/T=Φ) can be used as a repeating variable, three hydrologic spaces are obtained. Assuming further that φ is a flux related to the storage capacity and the frequency of rainfall, φ = λw 0 , the three spaces (Daly et al, 2019) are found to coincide with specific cases in ( 19): case 1 if R is chosen as repeating variable, case 2 if ET max is chosen, and case 4 when φ is chosen.…”

“…While they did not use dimensional analysis, Turc and Budyko started their work by making what is perhaps the simplest hypothesis of a physical law for the rainfall partitioning (see Dooge, 1992;Daly et al, 2019, and references therein),…”

“…is Budyko's dryness (or aridity) index. If instead one chooses ET max , then the Turc's hypothesis follows (Daly et al, 2019)…”

“…The analysis by Daly et al (2019) shows that by accounting for the ability of a catchment to store water to supply evapotranspiration, the flux φ (referred to as maximum storage rate) serves as a modulator for the relationships of ET with R and ET max for very dry and very wet catchments. In this way, accounting for it, it allows us to expand the Budyko and Turc frameworks, suggesting that they are not equivalent, as often assumed in parametric models, unless φ → ∞.…”

Reinterpreting the Budyko Framework

“…) can be manipulated into a single-parameterBudyko equation (e.g., Harman et al (2011);Daly et al (2019b)). There are likely many more, all equally valid, versions with even starker differences in the shapes of the curves (leading to even larger discrepancies between formulations if the current interpretations of explicit Budyko curves and parametric Budyko equations are maintained).…”