Stochastic parameterization of shallow cumulus convection estimated from high-resolution data

In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES

Stochastic Parameterization of Convective Area Fractions with a Multicloud Model Inferred from Observational Data

Observational data of rainfall from a rain radar in Darwin, Australia, are combined with data defining the large-scale dynamic and thermodynamic state of the atmosphere around Darwin to develop a multicloud model based on a stochastic method using conditional Markov chains. The authors assign the radar data to clear sky, moderate congestus, strong congestus, deep convective, or stratiform clouds and estimate transition probabilities used by Markov chains that switch between the cloud types and yield cloud-type area fractions. Cross-correlation analysis shows that the mean vertical velocity is an important indicator of deep convection. Further, it is shown that, if conditioned on the mean vertical velocity, the Markov chains produce fractions comparable to the observations. The stochastic nature of the approach turns out to be essential for the correct production of area fractions. The stochastic multicloud model can easily be coupled to existing moist convectio