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 ef...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Stockholm University Press
2016-09-01
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| Series: | Tellus: Series B, Chemical and Physical Meteorology |
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| Online Access: | http://www.tellusb.net/index.php/tellusb/article/view/31682/48824 |
| _version_ | 1818006949806997504 |
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| author | Alban Farchi Marc Bocquet Yelva Roustan Anne Mathieu Arnaud Quérel |
| author_facet | Alban Farchi Marc Bocquet Yelva Roustan Anne Mathieu Arnaud Quérel |
| author_sort | Alban Farchi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T05:08:24Z |
| format | Article |
| id | doaj.art-61a6cc28a2bc4f068fb9b35d24df0f54 |
| institution | Directory Open Access Journal |
| issn | 1600-0889 |
| language | English |
| last_indexed | 2024-04-14T05:08:24Z |
| publishDate | 2016-09-01 |
| publisher | Stockholm University Press |
| record_format | Article |
| series | Tellus: Series B, Chemical and Physical Meteorology |
| spelling | doaj.art-61a6cc28a2bc4f068fb9b35d24df0f542022-12-22T02:10:37ZengStockholm University PressTellus: Series B, Chemical and Physical Meteorology1600-08892016-09-0168011910.3402/tellusb.v68.3168231682Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accidentAlban Farchi0Marc Bocquet1Yelva Roustan2Anne Mathieu3Arnaud Quérel4 CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, 77455 Marne la Vallée, France CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, 77455 Marne la Vallée, France CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, 77455 Marne la Vallée, France Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-CRI, SESUC, BMCA, FR-92262 Fontenay-aux-Roses, France Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-CRI, SESUC, BMCA, FR-92262 Fontenay-aux-Roses, FranceThe 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.http://www.tellusb.net/index.php/tellusb/article/view/31682/48824Wasserstein distancenon-local metricstatistical indicatorsverificationFukushima-Daiichi accidentradionuclides |
| spellingShingle | Alban Farchi Marc Bocquet Yelva Roustan Anne Mathieu Arnaud Quérel Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident Tellus: Series B, Chemical and Physical Meteorology Wasserstein distance non-local metric statistical indicators verification Fukushima-Daiichi accident radionuclides |
| title | Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident |
| title_full | Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident |
| title_fullStr | Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident |
| title_full_unstemmed | Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident |
| title_short | Using the Wasserstein distance to compare fields of pollutants: application to the radionuclide atmospheric dispersion of the Fukushima-Daiichi accident |
| title_sort | using the wasserstein distance to compare fields of pollutants application to the radionuclide atmospheric dispersion of the fukushima daiichi accident |
| topic | Wasserstein distance non-local metric statistical indicators verification Fukushima-Daiichi accident radionuclides |
| url | http://www.tellusb.net/index.php/tellusb/article/view/31682/48824 |
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