Modeling Uncertainty of Numerical Weather Predictions Using Learning Methods

Abstract

Weather forecasting is one of the most vital tasks in many applications ranging from severe weather hazard systems to energy production. Numerical weather prediction (NWP) systems are commonly used state-of-the-art atmospheric models that provide point forecasts as deterministic predictions arranged on a three-dimensional grid. However, there is always some level of error and uncertainty in the forecasts due to inaccuracies of initial conditions, the chaotic nature of weather, etc. Such uncertainty information is crucial in decision making and optimization processes involved in many applications. A common representation of forecast uncertainty is a Prediction Interval (PI) that determines a minima, maxima and confidence level for each forecast, e.g. [2°C, 15°C]-95%. In this study, we investigate various methods that can model the uncertainty of NWP forecasts and provide PIs for the forecasts accordingly. In particular, we are interested in analyzing the historical performance of the NWP system as a valuable source for uncertainty modeling. Three different classes of methods are developed and applied for this problem. First, various clustering algorithms (including fuzzy c-means) are employed in concert with fitting appropriate probability distributions to obtain statistical models that can dynamically provide PIs depending on the forecast context. Second, a range of quantile regression methods (including kernel quantile regression) are studied that can directly model the PI boundaries as a function of influential features. In the third class, we focus on various time series modeling approaches including heteroscedasticity modeling methods that can provide forecasts of conditional mean and conditional variance of the target for any forecast horizon. iv All presented PI computation methods are empirically evaluated using a developed comprehensive verification framework in a set of experiments involving real-world data sets of NWP forecasts and observations. A key component is proposed in the evaluation process that would lead to a considerably more reliable judgment. Results show that PIs obtained by the ARIMA-GARCH model (for up to 6-hour-ahead forecasts) and Spline Quantile Regression (for longer leads) provide interval forecasts with satisfactory reliability and significantly better skill. This can lead to improvements in forecast value for many systems that rely on the NWP forecasts.