Producing calibrated ensemble precipitation forecasts using Neighbourhood Ensemble Copula Coupling
Authors: Trotta Belinda 
Published: March 2024

We introduce Neighbourhood Ensemble Copula Coupling, a technique for post-processing ensemble precipitation forecasts to produce physically realistic, well-calibrated scenarios.Modern precipitation forecasting typically uses ensemble forecasts produced by numerical weather prediction (NWP) models. These ensembles aim to represent the range of probable weather outcomes, and enable us to derive probabilistic predictions (for example, we may predict a 20% chance of at least 10 mm rainfall at a particular location). Because NWP models employ a simplified representation of the atmospheric dynamics, and model processes at a coarse scale, the probabilities derived from the ensemble must be calibrated to accurately describe the probability distribution at the specific forecast locations.Moreover, for many applications, such as flood prediction, as well as a probabilistic prediction of rainfall at each location, it is also useful to know the correlations between different locations. A river is most likely to flood when there is high rainfall at several nearby locations, so the probability of a flood depends on the joint probability distribution of rainfall at these locations. This is not easy to calculate, since the individual distributions are not independent. For example, if there is a rain band and we are unsure how fast it will move, we may know that at a particular forecast time it will rain either in location A or location B, but not both simultaneously. Thus for hydrology applications, scenario-based forecasts are often more useful than probability forecasts, but we still require the ensemble of scenarios to be well-calibrated; that is, the distribution of scenarios at a location should approximate the true expected probability distribution.One popular approach to this problem is Ensemble Copula Coupling (ECC). Given an NWP ensemble forecast, and a probabilistic forecast derived from it, ECC is a method to derive a calibrated ensemble forecast by arranging quantiles of the probabilistic forecast in the order specified by the original ensemble. This process improves the statistical accuracy of the ensemble; in other words, the distribution of the calibrated ensemble members at each grid point more closely approximates the true expected distribution. However, the trade-off is that the individual members are not as physically realistic as the original ensemble, with noisy variation among neighbouring grid points. Also, depending on the calibration method, extremes in the original ensemble are sometimes muted: in particular, reliability calibration, a simple and widely used non-parametric probability calibration method, suffers from this problem. Neighbourhood Ensemble Copula Coupling (N-ECC) is a simple modification of ECC designed to address these drawbacks. Testing N-ECC with the calibrated probability forecasts produced by reliability calibration shows that, compared to standard ECC, our method produces forecasts which are less noisy and more visually plausible, and which also have improved statistical properties. Specifically, the forecast is sharper, so that extremes are better predicted, and the continuous rank probability score (CRPS) is also slightly improved.