Probabilistic solar irradiance transposition models

Transposition models convert the solar irradiance received on a horizontal surface to in-plane irradiance. All transposition models to date, unfortunately, only produce deterministic (as oppose to probabilistic) estimates. In modern energy meteorology, having the entire predictive distribution is more desirable than relying only on deterministic estimates. To that end, this paper outlines two strategies for creating probabilistic transposition models (PTMs), that can quantify the various types of uncertainty involved in the modeling process. The first strategy seeks the analytic expressions of measurement, model, and parameter uncertainty, and the final predictive variance is the sum of these three types of uncertainty. On the other hand, the second strategy directly models the overall uncertainty as a whole, and uses ensemble model output statistics to estimate the predictive distribution through optimizing a loss function. Both strategies generate estimates of tilted irradiance with Gaussian predictive distributions. As compared to their deterministic counterparts, PTMs clearly offer more insights on uncertainty quantification, during solar energy system design, simulation, performance evaluation, and power output forecasting.