Comparison of uncertainty quantification methods for cloud simulation

Quantification of evolving uncertainties is required for both probabilistic forecasting and data assimilation in weather prediction. In current practice, the ensemble of model simulations is often used as a primary tool to describe the required uncertainties. In this work, we explore an alternative approach, the so-called stochastic Galerkin (SG) method, which integrates uncertainties forward in time using a spectral approximation in stochastic space. In an idealized two-dimensional model that couples nonhydrostatic weakly compressible Navier–Stokes equations to cloud variables, we first investigate the propagation of initial uncertainty. Propagation of initial perturbations is followed through time for all model variables during two types of forecast: the ensemble forecast and the SG forecast. Series of experiments indicate that differences in performance of the two methods depend on the system state and truncations used. For example, in more stable conditions, the SG method outperforms the ensemble of simulations for every truncation and every variable. However, in unstable conditions, the ensemble of simulations would need more than 100 members (depending on the model variable) and the SG method more than a truncation at five to produce comparable but not identical results. As estimates of the uncertainty are crucial for data assimilation, secondly we instigate the use of these two methods with the stochastic ensemble Kalman filter. The use of the SG method avoids evolution of a large ensemble, which is usually the most expensive component of the data assimilation system, and provides results comparable with the ensemble Kalman filter in the cases investigated