Abstract
Abstract. We propose an approach to stochastic parameterisation of shallow cumulus clouds to represent the convective variability and its dependence on the model resolution. To collect information about the individual cloud lifecycles and the cloud ensemble as a whole, we employ a large eddy simulation (LES) model and a cloud tracking algorithm, followed by conditional sampling of clouds at the cloud-base level. In the case of a shallow cumulus ensemble, the cloud-base mass flux distribution is bimodal, due to the different shallow cloud subtypes, active and passive clouds. Each distribution mode can be approximated using a Weibull distribution, which is a generalisation of exponential distribution by accounting for the change in distribution shape due to the diversity of cloud lifecycles. The exponential distribution of cloud mass flux previously suggested for deep convection parameterisation is a special case of the Weibull distribution, which opens a way towards unification of the statistical convective ensemble formalism of shallow and deep cumulus clouds. Based on the empirical and theoretical findings, a stochastic model has been developed to simulate a shallow convective cloud ensemble. It is formulated as a compound random process, with the number of convective elements drawn from a Poisson distribution, and the cloud mass flux sampled from a mixed Weibull distribution. Convective memory is accounted for through the explicit cloud lifecycles, making the model formulation consistent with the choice of the Weibull cloud mass flux distribution function. The memory of individual shallow clouds is required to capture the correct convective variability. The resulting distribution of the subgrid convective states in the considered shallow cumulus case is scale-adaptive – the smaller the grid size, the broader the distribution.
Highlights
To set a path towards the development of a stochastic shallow-cloud parameterisation for numerical atmospheric models, we study how the unresolved convective processes relate to the resolved grid-scale variables in an ensemble of shallow cumulus clouds
We propose a generalisation of the theory of fluctuations in a convective ensemble by including the system memory and by considering the impact of the diversity in cloud lifecycles on the cloud-base mass flux distribution shape
Subgrid-scale convective processes can be related to the mean large-scale field through a parameterisation that comprises a deterministic component, a stochastic component and the convective memory carried by the finite lifecycles of clouds
Summary
To set a path towards the development of a stochastic shallow-cloud parameterisation for numerical atmospheric models, we study how the unresolved convective processes relate to the resolved grid-scale variables in an ensemble of shallow cumulus clouds. From the previous studies of deep convective cloud fields using CRMs and the coarse-graining methods, it is known that the subgrid- to grid-scale relation is neither fully deterministic nor diagnostic, which suggests that stochastic and memory components should be included in a parameterisation These components are sensitive to the spatial and temporal scales of a numerical model. We propose a generalisation of the theory of fluctuations in a convective ensemble by including the system memory and by considering the impact of the diversity in cloud lifecycles on the cloud-base mass flux distribution shape This provides a stochastic and memory term in the subgrid- to grid-scale relation, and a deterministic component is retained in adequate proportion, depending on the grid scale. Different formulations of the stochastic model are discussed, and tested against LES results, to decide on minimal and consistent representation of all relevant features of subgrid convection and its variability (Sect. 4)
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