A stochastic parametrization for deep convection, based on cellular automata, has been evaluated in the high-resolution (2.5 km) ensemble prediction system Hirlam Aladin Regional Mesoscale Operational NWP Ensemble Prediction System (HarmonEPS). We studied whether such a stochastic physical parametrization, whilst implemented in a deterministic forecast model, can have an impact on the performance of the uncertainty estimates given by an ensemble prediction system. Various feedback mechanisms in the parametrization were studied with respect to ensemble spread and skill, in both subgrid and resolved precipitation fields. It was found that the stochastic parametrization improves the model skill in general, by reducing a positive bias in precipitation. This reduction in bias, however, led to a reduction in ensemble spread of precipitation. Overall, scores that measure the accuracy and reliability of probabilistic predictions indicate that the net impact (improved skill, degraded spread) of the ensemble prediction system is improved for 6 h accumulated precipitation with the stochastic parametrization and is rather neutral for other quantities examined.

A cellular automaton (CA) is introduced to the deep convection parametrization of the high-resolution limited-area model Aire Limitee Adaptation/Application de la Recherche a l'Operationnel (ALARO). The self-organizational characteristics of the CA allow for lateral communication between adjacent numerical weather prediction (NWP) model grid boxes and add additional memory to the deep convection scheme. The CA acts in two horizontal dimensions, with finer grid spacing than the NWP model. It is randomly seeded in regions where convective available potential energy (CAPE) exceeds a threshold value. Both deterministic and probabilistic rules, coupled to the large-scale wind, are explored to evolve the CA in time. Case studies indicate that the scheme has the potential to organize cells along convective squall lines and enhance advective effects. An ensemble of forecasts using the present CA scheme demonstrated an ensemble spread in the resolved wind field in regions where deep convection is large. Such a spread represents the uncertainty due to subgrid variability of deep convection and could be an interesting addition to an ensemble prediction system.

Horizontal diffusion in numerical weather prediction models is, in general, applied to reduce numerical noise at the smallest atmospheric scales. In convection-permitting models, with horizontal grid spacing on the order of 1-3 km, horizontal diffusion can improve the model skill of physical parameters such as convective precipitation. For instance, studies using the convection-permitting Applications of Research to Operations at Mesoscale model (AROME) have shown an improvement in forecasts of large precipitation amounts when horizontal diffusion is applied to falling hydrometeors. The nonphysical nature of such a procedure is undesirable, however. Within the current AROME, horizontal diffusion is imposed using linear spectral horizontal diffusion on dynamical model fields. This spectral diffusion is complemented by nonlinear, flow-dependent, horizontal diffusion applied on turbulent kinetic energy, cloud water, cloud ice, rain, snow, and graupel. In this study, nonlinear flow-dependent diffusion is applied to the dynamical model fields rather than diffusing the already predicted falling hydrometeors. In particular, the characteristics of deep convection are investigated. Results indicate that, for the same amount of diffusive damping, the maximum convective updrafts remain strong for both the current and proposed methods of horizontal diffusion. Diffusing the falling hydrometeors is necessary to see a reduction in rain intensity, but a more physically justified solution can be obtained by increasing the amount of damping on the smallest atmospheric scales using the nonlinear, flow-dependent, diffusion scheme. In doing so, a reduction in vertical velocity was found, resulting in a reduction in maximum rain intensity.

Because of the limited resolution of numerical weather prediction (NWP) models, subgrid-scale physical processes are parameterized and represented by gridbox means. However, some physical processes are better represented by a mean and its variance; a typical example is deep convection, with scales varying from individual updrafts to organized mesoscale systems. This study investigates, in an idealized setting, whether a cellular automaton (CA) can be used to enhance subgrid-scale organization by forming clusters representative of the convective scales and thus yield a stochastic representation of subgrid-scale variability. The authors study the transfer of energy from the convective to the larger atmospheric scales through nonlinear wave interactions. This is done using a shallow water (SW) model initialized with equatorial wave modes. By letting a CA act on a finer resolution than that of the SW model, it can be expected to mimic the effect of, for instance, gravity wave propagation on convective organization. Employing the CA scheme permits the reproduction of the observed behavior of slowing down equatorial Kelvin modes in convectively active regions, while random perturbations fail to feed back on the large-scale flow. The analysis of kinetic energy spectra demonstrates that the CA subgrid scheme introduces energy backscatter from the smallest model scales to medium scales. However, the amount of energy backscattered depends almost solely on the memory time scale introduced to the subgrid scheme, whereas any variation in spatial scales generated does not influence the energy spectra markedly.

One desirable property within an ensemble forecast system is to have a one-to-one ratio between the root-mean-square error (rmse) of the ensemble mean and the standard deviation of the ensemble (spread). The ensemble spread and forecast error within the ECMWF ensemble prediction system has been extrapolated beyond 10 forecast days using a simple model for error growth. The behavior of the ensemble spread and the rmse at the time of the deterministic predictability are compared with derived relations of rmse at the infinite forecast length and the characteristic variability of the atmosphere in the limit of deterministic predictability. Utilizing this methodology suggests that the forecast model and the atmosphere do not have the same variability, which raises the question of how to obtain a perfect ensemble.