Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident

Abstract

A B S T R A C TThe verification of simulations against data and the comparison of model simulation of pollutant fields rely on the critical choice of statistical indicators. Most of the scores are based on point-wise, that is, local, value comparison. Such indicators are impacted by the so-called double penalty effect. Typically, a misplaced blob of pollutants will doubly penalise such a score because it is predicted where it should not be and is not predicted where it should be. The effect is acute in plume simulations where the concentrations gradient can be sharp. A non-local metric that would match concentration fields by displacement would avoid such double penalty. Here, we experiment on such a metric known as the Wasserstein distance, which tells how penalising moving the pollutants is. We give a mathematical introduction to this distance and discuss how it should be adapted to handle fields of pollutants. We develop and optimise an open Python code to compute this distance. The metric is applied to the dispersion of cesium-137 of the Fukushima-Daiichi nuclear power plant accident. We discuss of its application in model-to-model comparison but also in the verification of model simulation against a map of observed deposited cesium-137 over Japan. As hoped for, the Wasserstein distance is less penalising, and yet retains some of the key discriminating properties of the root mean square error indicator.

Uncertainty quantification of pollutant source retrieval: comparison of Bayesian methods with application to the Chernobyl and Fukushima Daiichi accidental releases of radionuclides

“…We chose K h = 25 000 m 2 s −1 as tuned in Winiarek et al . () with the primary goal to mitigate through diffusion significant model error and the resulting detrimental double‐penalty effect (Farchi et al ., ).…”

“…In contrast, the FDNPP accident set-up has a much finer spatial resolution which may require a significant K h . We chose K h = 25 000 m 2 s −1 as tuned in Winiarek et al (2014) with the primary goal to mitigate through diffusion significant model error and the resulting detrimental double-penalty effect (Farchi et al, 2016).…”

“…The downside of the approach is the too high accuracy implicitly ascribed to quasi-null observations whose reliability is often questionable (e.g. Farchi et al, 2016). Several solutions are possible to mitigate this effect.…”

Optimal transport for variational data assimilation

“…Having elements with integral 1 (or constant integral) may seem restrictive. Removing it is possible by using a modified version of the Wasserstein distance, presented for example in Chizat et al (2015) or Farchi et al (2016). For simplicity we do not consider this possible generalization and all data have the same integral.…”

“…This distance is also widely used in computer vision, for example in classification of images (Rubner et al, 1998(Rubner et al, , 2000, interpolation (Bonneel et al, 2011) or movie reconstruction (Delon and Desolneux, 2010). More recently, Farchi et al (2016) used the Wasserstein distance to compare observation and model simulations in an air pollution context, which is a first step toward data assimilation.…”