This study examines the characteristics of several model parameter perturbation methodologies for ensemble simulations of cloud microphysical processes in convection. A simplified 1D model is used to focus the results on cloud microphysics without the complication of feedbacks to the dynamics and environment. Several parameter perturbation methods are tested, including non‐stochastic and stochastic with various distributions and parameter covariance. We find that an ensemble comprised of different time‐invariant parameters (non‐stochastic) exhibits little bias, but small spread. In addition, its behavior does not respect the time evolution of convection through its various phases. Stochastic parameter (SP) methods in which no inter‐parameter covariance is applied produce greater spread, but significant bias. The bias is particularly large for lognormal parameter perturbation distributions. The ensemble spread is retained and the bias reduced when time‐varying parameter covariance is applied. In this case, the SP scheme is able to adapt to the time and state‐dependent covariance structures and produce ensemble characteristics that are consistent with the specific microphysical processes operating at any given time. The results suggest that SP schemes would benefit from inclusion of parameter covariances, and specifically those that vary with the state of the system. It also suggests that a Normal or LogNormal SP scheme with no covariance may significantly impact the ensemble bias. Finally, the results indicate that high temporal and spatial resolution observations may be needed to characterize the variability in parameter values and covariance.

<p><span lang="EN-US">It has long been known that microphysics parameterizations are among leading sources of model uncertainty in storm and convective scale weather prediction.  The uncertainty results from combination of imperfect knowledge of the microphysics processes, inability to explicitly resolve them at computationally feasible spatial and phase-space resolutions, as well as from inherent limited predictability of micro to turbulent scale processes.   Representing these in the context of improving probabilistic prediction skill using ensembles has been the subject of many studies, but remains an outstanding problem.  The problem is especially acute in storm and convective scale ensemble prediction, where there may be strong coupling of errors between ensemble data assimilation and forecasting.  </span></p> <p><span lang="EN-US">Over the last decade, the inclusion of stochastic representation of model uncertainty associated with physical parameterizations has emerged as a viable approach for representing the intrinsic uncertainties of the microphysical parameterizations.  This study examines sensitivity of storm scale ensemble simulations to representation of microphysics parameterization uncertainties using a cloud resolving model.  We compare several stochastic parameter (SP) perturbation methods, including various parameter distributions and parameter covariance models, applied to physical parameters in a bulk microphysics parameterization.  The study follows a prior study, in which a 1D column version of the 3D cloud resolving model was used to test non-stochastic and several SP perturbation methods for which the parameter perturbation statistical distributions were based on Markov Chain Monte Carlo (MCMC) inversions with synthetic observations. That study indicated that SP schemes produce significantly more ensemble variance of microphysics states than non-stochastic, and that inclusion of parameter covariances, and specifically those that vary with the state of the system, improve their performance. </span></p> <p><span lang="EN-US">The current study investigates impacts of SP scheme configurations on microphysics with dynamical feedbacks in 3D ensemble simulations.  The statistical parameter distributions used for the SP scheme are obtained as in the 1D study using MCMC inversions with synthetic observations. The results are evaluated in terms of changes to the ensemble mean and variance of microphysical and dynamical states and the simulated column integral microphysics-sensitive satellite-based observable quantities. We discuss the results and note the implications for convective scale ensemble data assimilation and forecasting. </span></p>

<p>It has long been known that model physics uncertainty can contribute as much or more to errors in forecasting and data assimilation as errors in initial conditions. Many studies have attempted to include the effects of model physics uncertainty in data assimilation by introducing static perturbations to model parameters. In such studies, parameter values are modified at the beginning of a simulation and remain unchanged throughout the duration of the forecast. Uncertainty is spanned by generating an ensemble of forecasts, each member having a different set of parameter values. Other studies have implemented dynamic perturbations to parameters, introducing methods that modify parameter values online in a stochastic fashion.</p><p> </p><p>We present here the results of a study that investigates the sensitivity of convective cloud structures to static and stochastic cloud microphysical parameter perturbations. Static parameter values are drawn from a database produced by a Markov chain Monte Carlo algorithm, while stochastic perturbations are applied via a stochastically perturbed parameterization (SPP) scheme. Both static parameter perturbations and SPP are applied to multiple microphysical parameters within a Lagrangian column model, used in several prior published studies. The 1D column microphysics model is forced with prescribed time-varying profiles of temperature, humidity and vertical velocity in such a way as to emulate the environment inside of a convective storm. This modeling framework allows for investigation of the effect of changes in model physics parameters on the model output in isolation from any feedback to the cloud-scale dynamics. </p><p> </p><p>The results are evaluated in terms of changes to the ensemble mean and variance of time evolving profiles of hydrometeor mass quantities, the microphysics processes within the model as well as in terms of the simulated column integral microphysics-sensitive satellite-based  observables. The outcomes of our experiments indicate a high degree of sensitivity of the to the way in which the SPP scheme is implemented. In particular, the distributions from which parameters are drawn, as well as the decorrelation time scale, have a large effect on the simulation outcomes. We discuss the results of SPP, compare with our static perturbation experiments, and note the implications for convective scale data assimilation. </p>

Using physical parameterizations of micro-to turbulent scale processes in weather and earth system (ES) numerical models is unavoidable. Explicit representation of a full range of underlying degrees of freedom is both unfeasible and undesirable because of intrinsic unpredictability at these scales (Craig & Cohen, 2006). Accordingly, parameterizations of subgrid scale processes are and will remain among leading sources of model uncertainty. Understanding and accounting for the impacts of this uncertainty continues to be one of the outstanding challenges for environmental modeling and prediction.Over the last two decades, the inclusion of stochastic representation of unresolved variability of sub-grid scale processes in weather and ES models has emerged as a viable approach to representing the intrinsic uncertainties of physical parameterizations in the context of improving probabilistic prediction skill using ensembles (