Comment on hess-2022-134

Abstract

The widely used Budyko framework defines the water- and energy-limits of catchments. Generally, catchments plot close to these physical limits and Budyko (1974) developed a curve that predicted the positions of catchments in this framework. The original formulation of the curve had no parameters, but later a more general, parameterized form was adopted. Originally, Budyko defined the independent variable as an aridity index with the potential evaporation divided by the precipitation (Ep / P) and used this to predict the ratio of actual evaporation over precipitation (Ea / P). However, the framework can be formulated in different ways and others defined the framework with the potential evaporation as the common denominator for the dependent and independent variables, i.e. P / Ep and Ea / Ep. It is possible to mathematically convert between these formulations, but if the parameterized Budyko curves are fit to data, the different formulations could lead to differences in the resulting parameter values. Here, we tested this for 357 catchments across the contiguous United States. This was done by fitting a parameterized form of the curve for the two different formulations. In this way, we found that differences in n-values due to the used projection could be +/- 0.2. If robust fitting algorithms were used, instead of a linear least squares algorithm, the differences in n-values reduced, but were nonetheless still present. The distances to the curve, often used as a metric in Budyko-type analyses, systematically dependended on the projection, with larger differences for the side of the framework with Ep / P > 1 for a projection with a dryness index and P / Ep > 1 for a projection with a wetness index (i.e. the non-contracted sides od the framework). When using the two projections for predicting Ea, we found that uncertainties due to the used projections could exceed 1.5 %. An important reason for the differences in n-values, curves and resulting estimates of Ea could be found in datapoints that clearly appear as outliers in one projection, but less so in the other projection. We argue here that the non-contracted side of the framework in the two projections should always be assessed, especially for datapoints that appear as outliers. At least, one should consider the additional uncertainty of the projection and assess the robustness of the results in both projections.