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.