Technical note: Do different projections matter for the Budyko framework?

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. Often, the independent variable is defined as an aridity index, which is used to predict the ratio of actual evaporation over precipitation (Ea/P). However, the framework can be formulated 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. In this way, we found that differences in n values due to the projection used could be ± 0.2. If robust fitting algorithms were used, 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 depended on the projection, with larger differences for the non-contracted sides of the framework (i.e., Ep/P>1 or P/Ep>1). When using the two projections for predicting Ea, we found that uncertainties due to the projections used could exceed 1.5 %. An important reason for the differences in n values, curves and resulting estimates of Ea could be found in data points 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 data points 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.