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

The 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.