On the probabilistic skill of dual‐resolution ensemble forecasts

Increasing spatial resolution and increasing ensemble size both tend to improve the skill of ensemble forecasts. Due to computational constraints, a balance needs to be found in operational NWP. Here, we examine a scenario where ensembles are formed by pooling k lower‐resolution and m higher‐resolution members such that the overall computational cost is equal to the constraint. The approach is applied to medium‐range weather forecasts with ECMWF's Integrated Forecasting System using horizontal resolutions of 18, 29 and 45 km and ensemble sizes ranging from 8 to 254 members. The methodology is similar to the multi‐level Monte‐Carlo approach but does not use stochastic perturbations that are shared between members at different levels. Probabilistic skill is quantified for 850 hPa temperature verified against analyses and 2 m temperature verified against station observations. Generally, dual‐resolution ensembles with similar numbers of lower and higher‐resolution members provide the optimal configuration for 2 m temperature prediction. In contrast, single‐resolution ensembles appear to be the most skilful for 850 hPa temperature. The dual‐resolution ensembles are a special kind of multi‐model ensemble. An analytic model describing the skill of such a multi‐model ensemble is developed and its parameters are estimated from the actual verification statistics. The model is capable of describing the general differences in behaviour between 2 m temperature and 850 hPa temperature. A 5‐day dual‐resolution ensemble forecast of 2 m temperature (°C) with horizontal resolutions of 45 and 18 km. Producing one of the higher‐resolution members requires the same computational resources as 16 lower‐resolution members. The aim is to maximize the probabilistic skill of such dual‐resolution ensembles. How many higher‐resolution members should the ensemble have, given fixed computational resources?