Deep and Probabilistic Solar Irradiance Forecast at the Arctic Circle

TL;DR

This work tackles Arctic-region solar irradiance forecasting with 36-hour ahead predictions, leveraging LSTMs in both deterministic and probabilistic formulations. By integrating 20 Norwegian stations with CAMS-RAD, NORA3, and CAMS McClear, the authors build rich input features and deploy clear-sky injection to stabilize Arctic seasonality. They compare a deterministic LSTM against MLP and smart-persistence baselines, and evaluate probabilistic variants using Quantile Regression and Maximum Likelihood Estimation with Gaussian, Weibull, and Johnson distributions (SU/SB), revealing a trade-off between point accuracy and uncertainty calibration. The study finds that while the deterministic LSTM often yields the best RMSE, probabilistic approaches—especially Johnson SB/SU and QR—offer valuable calibration and competitive predictive performance, suggesting MLE as a viable alternative for probabilistic solar forecasting in high-latitude settings. The results have practical implications for day-ahead market operations in the Arctic, where data sparsity and seasonal variability challenge traditional forecasting methods.

Abstract

Solar irradiance forecasts can be dynamic and unreliable due to changing weather conditions. Near the Arctic circle, this also translates into a distinct set of further challenges. This work is forecasting solar irradiance with Norwegian data using variations of Long-Short-Term Memory units (LSTMs). In order to gain more trustworthiness of results, the probabilistic approaches Quantile Regression (QR) and Maximum Likelihood (MLE) are optimized on top of the LSTMs, providing measures of uncertainty for the results. MLE is further extended by using a Johnson's SU distribution, a Johnson's SB distribution, and a Weibull distribution in addition to a normal Gaussian to model parameters. Contrary to a Gaussian, Weibull, Johnson's SU and Johnson's SB can return skewed distributions, enabling it to fit the non-normal solar irradiance distribution more optimally. The LSTMs are compared against each other, a simple Multi-layer Perceptron (MLP), and a smart-persistence estimator. The proposed LSTMs are found to be more accurate than smart persistence and the MLP for a multi-horizon, day-ahead (36 hours) forecast. The deterministic LSTM showed better root mean squared error (RMSE), but worse mean absolute error (MAE) than a MLE with Johnson's SB distribution. Probabilistic uncertainty estimation is shown to fit relatively well across the distribution of observed irradiance. While QR shows better uncertainty estimation calibration, MLE with Johnson's SB, Johnson's SU, or Gaussian show better performance in the other metrics employed. Optimizing and comparing the models against each other reveals a seemingly inherent trade-off between point-prediction and uncertainty estimation calibration.

Figures (5)

• Figure 1: Averaged error distribution of RMSE across the 36 hour output window.
• Figure 2: Point prediction results plotted for every 36 hours of forecast. Grey vertical lines designate the beginning of each 36 hours window.
• Figure 3: PICP values showing the observed coverage (x) of probability distributions within set intervals (y). Tighter fit to the black line is optimal.
• Figure 4: Reliability diagram showing frequency (x) of true observations falling within quantiles (y) of the predicted probability distributions. Tighter fit to the black line is optimal.
• Figure 5: Probabilistic results plotted for every 36 hours of forecast. An example for summer is on the left side, while winter is shown on the right. Output windows of 36 hours are shown by the grey vertical lines. The error bands show the estimated 90% and 50% confidence intervals. MLE-G stand for MLE assuming a Gaussian distribution, while MLE-JSu/Jsb stands for MLE, with Johnson's SU and SB distribution respectively.