Past and Future Trends in Atmospheric Transparency Derived from a Revised Formulation of the Ångström–Prescott Equation

Most studies have focused on extending the applicability of the Ångström–Prescott equation and improving its accuracy in estimating solar irradiation. Only a limited number of studies have addressed atmospheric climatology using the Ångström–Prescott equation. In contrast, this study reformulates the Ångström–Prescott equation to explore its potential for extracting long-term atmospheric transparency information from radiometric measurements. It introduces a new annual formulation of the Ångström–Prescott equation derived from its common monthly version. While the formal structure is preserved, the equation shifts from its usual role, as a solar irradiation estimator, to a new role, as a predictor of long-term atmospheric transparency. The revised equation naturally defines an annual effective sunshine duration, which assigns greater weight to relative sunshine during summer months than during winter months. To enable prediction, the revised Ångström–Prescott equation is combined with Gaussian process regression. The equation provides the historical annual time series, while Gaussian process regression predicts future values and quantifies their associated uncertainty. To demonstrate the predictive capability of the method, it is applied to the analysis and prediction of four annual parameters characterizing atmospheric transparency: mean clear-sky atmospheric transparency, mean cloud transmittance, mean atmospheric transparency, and effective relative sunshine duration. The analysis is conducted using radiometric data collected at 14 stations distributed across Europe. Predictions for the upcoming decade (2024–2033) indicate that, at most stations, mean atmospheric transparency is expected to remain stable or change within approximate margins of −5% to +10%.