20 Apr 2022
20 Apr 2022
Status: this preprint is currently under review for the journal HESS.

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

Remko Christiaan Nijzink and Stanislaus Josef Schymanski Remko Christiaan Nijzink and Stanislaus Josef Schymanski
  • Catchment and Ecohydrology Group (CAT), Environmental Research and Innovation (ERIN), Luxembourg Institute of Science and Technology (LIST), Belvaux, Luxembourg

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.

Remko Christiaan Nijzink and Stanislaus Josef Schymanski

Status: open (until 15 Jun 2022)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-134', Anonymous Referee #1, 11 May 2022 reply
    • AC1: 'Reply on RC1', Remko C. Nijzink, 19 May 2022 reply
  • RC2: 'Comment on hess-2022-134', Anonymous Referee #2, 18 May 2022 reply

Remko Christiaan Nijzink and Stanislaus Josef Schymanski

Data sets

Budyko repository Remko Nijzink

Remko Christiaan Nijzink and Stanislaus Josef Schymanski


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Short summary
Most catchments plot close to the empirical Budyko curve, that allows for estimating the long-term mean annual evaporation and runoff. The Budyko curve can be defined as a function of a wetness index or a dryness index. We found that differences can occur and that there is an uncertainty due to the different formulations.