A Second-Order Stationarity-Based Confidence Assessment Method for Temperature Forecast

Remote sensing observations have the potential to improve the accuracy of temperature forecasts. However, the task of quantifying the confidence in these predictions remains challenging. Existing methods for confidence estimation, such as Bootstrap and Bayesian models, often suffer from computational inefficiencies and may impose modifications on the underlying predictor structures. To address these limitations, this letter introduces a novel and efficient confidence assessment framework for temperature forecasting, termed the second-order stationarity-based confidence assessment (SOS-CA). The proposed method is premised on the assumption that the second-order differences in temperature data adhere to a Gaussian distribution. Leveraging this assumption, SOS-CA employs statistical techniques to evaluate the Gaussianity of these second-order differences. Predictions that exhibit greater second-order stationarity are deemed to possess higher confidence. Moreover, we present a rigorous theoretical proof establishing the asymptotic equivalence of the mathematical transformations underpinning the SOS-CA methodology. To enhance its applicability, SOS-CA is extended to multiple variants to accommodate diverse forecasting scenarios. Extensive experiments using real-world remote sensing data substantiate the effectiveness of the proposed approach, demonstrating that SOS-CA achieves performance on par with or superior to existing methods while significantly reducing computational overhead.