Preprints
https://doi.org/10.5194/egusphere-2022-1117
https://doi.org/10.5194/egusphere-2022-1117
 
10 Nov 2022
10 Nov 2022
Status: this preprint is open for discussion.

The Wasserstein distance as a hydrological objective function

Jared C. Magyar1,a and Malcolm S. Sambridge1 Jared C. Magyar and Malcolm S. Sambridge
  • 1Research School of Earth Sciences, Australian National University, Canberra, Australia
  • anow at: Physics, School of Natural Sciences, University of Tasmania, Hobart, Australia

Abstract. When working with hydrological data, the ability to quantify the similarity of different datasets is useful. The choice of how to make this quantification has direct influence on the results, with different measures of similarity emphasising particular sources of error (for example, errors in amplitude as opposed to displacements in time and/or space). The Wasserstein distance considers the similarity of mass distributions through a transport lens. In a hydrological context, it measures the ‘effort’ required to rearrange one distribution of water into the other. While being more broadly applicable, particular interest is payed to hydrographs in this work. The Wasserstein distance is adapted for working with hydrographs in two different ways, and tested in a calibration and ‘averaging’ of hydrographs context. This alternate definition of fit is shown successful in accounting for timing errors due to imprecise rainfall measurements. The averaging of an ensemble of hydrographs is shown suitable when differences among the members is in peak shape and timing, but not in total peak volume, where the traditional mean works well.

Jared C. Magyar and Malcolm S. Sambridge

Status: open (until 05 Jan 2023)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2022-1117', Uwe Ehret, 28 Nov 2022 reply

Jared C. Magyar and Malcolm S. Sambridge

Model code and software

The Wasserstein distance as a hydrological objective function Jared Magyar https://doi.org/10.5281/zenodo.7217989

Jared C. Magyar and Malcolm S. Sambridge

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Short summary
Measuring the similarity of distributions of water is a useful tool for model calibration and assessment. We provide a new way of measuring this similarity for streamflow time series. It is derived from the concept of the amount of 'work' required to rearrange one mass distribution into the other. We also use similar mathematical techniques for defining a type of 'average' between water distributions.