{"title":"基于沃瑟斯坦距离的气候误差度量","authors":"Carlos Veiga Rodrigues , Io Odderskov","doi":"10.1016/j.apenergy.2025.126392","DOIUrl":null,"url":null,"abstract":"<div><div>A novel theoretical framework is introduced for generating error metrics free from time-lag errors, specifically designed for long-term wind resource assessment. The proposed metrics enable an enhanced comparison of climate statistics by focusing on the steady-state wind flow conditions rather than transient events. Generally, error between models and observations is characterized through metrics such as the Root Mean Squared Error (RMSE) and its Standard Deviation (STDE). However, these are influenced by time-lags that can distort the evaluation of wind speed predictions if the aim is the characterization of climate and long-term characteristics. No standardized metrics exist that fully eliminate time-lag influences when estimating climate error. The proposed methodology decomposes RMSE and STDE into statistical moments and relates these to the quantile functions of probability distributions. The moments are equated to Wasserstein distances which are used to extract time-independent error metrics. This procedure is applicable to both analytical distributions, such as the Weibull distribution, and empirical distributions from sample-based statistics. Numerical experiments were conducted to validate the effectiveness of the proposed climate metrics, demonstrating the ability to achieve near-zero RMSE for time series with similar statistical distributions, whereas conventional RMSE exceeded 20 % due to phase error.</div></div>","PeriodicalId":246,"journal":{"name":"Applied Energy","volume":"398 ","pages":"Article 126392"},"PeriodicalIF":11.0000,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Climate error metrics based on Wasserstein distances\",\"authors\":\"Carlos Veiga Rodrigues , Io Odderskov\",\"doi\":\"10.1016/j.apenergy.2025.126392\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A novel theoretical framework is introduced for generating error metrics free from time-lag errors, specifically designed for long-term wind resource assessment. The proposed metrics enable an enhanced comparison of climate statistics by focusing on the steady-state wind flow conditions rather than transient events. Generally, error between models and observations is characterized through metrics such as the Root Mean Squared Error (RMSE) and its Standard Deviation (STDE). However, these are influenced by time-lags that can distort the evaluation of wind speed predictions if the aim is the characterization of climate and long-term characteristics. No standardized metrics exist that fully eliminate time-lag influences when estimating climate error. The proposed methodology decomposes RMSE and STDE into statistical moments and relates these to the quantile functions of probability distributions. The moments are equated to Wasserstein distances which are used to extract time-independent error metrics. This procedure is applicable to both analytical distributions, such as the Weibull distribution, and empirical distributions from sample-based statistics. Numerical experiments were conducted to validate the effectiveness of the proposed climate metrics, demonstrating the ability to achieve near-zero RMSE for time series with similar statistical distributions, whereas conventional RMSE exceeded 20 % due to phase error.</div></div>\",\"PeriodicalId\":246,\"journal\":{\"name\":\"Applied Energy\",\"volume\":\"398 \",\"pages\":\"Article 126392\"},\"PeriodicalIF\":11.0000,\"publicationDate\":\"2025-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Energy\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0306261925011225\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENERGY & FUELS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Energy","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0306261925011225","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENERGY & FUELS","Score":null,"Total":0}
Climate error metrics based on Wasserstein distances
A novel theoretical framework is introduced for generating error metrics free from time-lag errors, specifically designed for long-term wind resource assessment. The proposed metrics enable an enhanced comparison of climate statistics by focusing on the steady-state wind flow conditions rather than transient events. Generally, error between models and observations is characterized through metrics such as the Root Mean Squared Error (RMSE) and its Standard Deviation (STDE). However, these are influenced by time-lags that can distort the evaluation of wind speed predictions if the aim is the characterization of climate and long-term characteristics. No standardized metrics exist that fully eliminate time-lag influences when estimating climate error. The proposed methodology decomposes RMSE and STDE into statistical moments and relates these to the quantile functions of probability distributions. The moments are equated to Wasserstein distances which are used to extract time-independent error metrics. This procedure is applicable to both analytical distributions, such as the Weibull distribution, and empirical distributions from sample-based statistics. Numerical experiments were conducted to validate the effectiveness of the proposed climate metrics, demonstrating the ability to achieve near-zero RMSE for time series with similar statistical distributions, whereas conventional RMSE exceeded 20 % due to phase error.
期刊介绍:
Applied Energy serves as a platform for sharing innovations, research, development, and demonstrations in energy conversion, conservation, and sustainable energy systems. The journal covers topics such as optimal energy resource use, environmental pollutant mitigation, and energy process analysis. It welcomes original papers, review articles, technical notes, and letters to the editor. Authors are encouraged to submit manuscripts that bridge the gap between research, development, and implementation. The journal addresses a wide spectrum of topics, including fossil and renewable energy technologies, energy economics, and environmental impacts. Applied Energy also explores modeling and forecasting, conservation strategies, and the social and economic implications of energy policies, including climate change mitigation. It is complemented by the open-access journal Advances in Applied Energy.