Fluctuations in A Quasi-Stationary Shallow Cumulus Cloud Ensemble

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

A stochastic scale-aware parameterization of shallow cumulus convection across the convective gray zone

The parameterization of shallow cumuli across a range of model grid resolutions of kilometrescales faces at least three major difficulties: (1) closure assumptions of conventional parameterization schemes are no longer valid, (2) stochastic fluctuations become substantial and increase with grid resolution, and (3) convective circulations that emerge on the model grids are under-resolved and grid-scale dependent. Here we develop a stochastic parameterization of shallow cumulus clouds to address the first two points, and we study how this stochastic parameterization interacts with the under-resolved convective circulations in a convective case over the ocean. We couple a stochastic model based on a canonical ensemble of shallow cumuli to the Eddy-Diffusivity Mass-Flux parameterization in the icosahedral nonhydrostatic (ICON) model. The moist-convective area fraction is perturbed by subsampling the distribution of subgrid convective states. These stochastic perturbations represent scale-dependent fluctuations around the quasiequilibrium state of a shallow cumulus ensemble. The stochastic parameterization reproduces the average and higher order statistics of the shallow cumulus case adequately and converges to the reference statistics with increasing model resolution. The interaction of parameterizations with model dynamics, which is usually not considered when parameterizations are developed, causes a significant influence on convection in the gray zone. The stochastic parameterization interacts strongly with the model dynamics, which changes the regime and energetics of the convective flows compared to the deterministic simulations. As a result of this interaction, the emergence of convective circulations in combination with the stochastic parameterization can even be beneficial on the high-resolution model grids

Stochastic Parameterization Toward a New View of Weather and Climate Models

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Comparing ground-based observations and a large-eddy simulation of shallow cumuli by isolating the main controlling factors of the mass flux distribution

Abstract The distribution of the cloud-base mass flux is long thought to be independent of the large-scale forcing. However, recent idealized modelling studies reveal its dependence on some of the large-scale conditions. Such a dependence makes it possible to isolate the observed large-scale conditions similar to those in the large-eddy simulations (LES) in order to compare the observed and modelled mass flux distributions. In this study, we derive for the first time the distribution of the cloud-base mass flux among individual shallow cumuli from the ground-based observations at the Barbados Cloud Observatory (BCO) and compare it with the Rain In Cumulus over the Ocean (RICO) LES case-study. The procedure of cloud sampling in LES mimics the point-wise measurement procedure at BCO to provide a mass-flux metric that is directly comparable with observations. We find a difference between the mass flux distribution observed during the year 2017 at BCO and the distribution modelled by LES that is comparable to the seasonal changes in the observed distribution. This difference between the observed and modelled distributions is diminished and an extremely good match is found by sub-sampling the measurements under the similar horizontal wind distribution and area-averaged surface Bowen ratio to those modelled in LES. This provides confidence in our observational method and also shows that LES produces realistic clouds that can be observed in nature under the same large-scale conditions as imposed in LES. We also confirm that in our case-study the stronger horizontal winds and higher Bowen ratios shift the distributions to higher mass flux values, which is coincident with clouds of larger horizontal areas and not with stronger updrafts. This article is protected by copyright. All rights reserved

Physically constrained stochastic shallow convection in realistic kilometer-scale simulations

A new configuration of a parameterization for shallow convection in the Icosahedral Nonhydrostatic Model (ICON) is described and tested on a single realistic test case. As a test case, a shallow convective day over Germany is simulated using four different configurations of ICON. These configurations differ by the choice of the shallow convection parameterization, which can be deterministic, stochastic, or completely switched off. As the fourth configuration, the ICON large eddy simulation setup is used as a reference against which the three other ICON model configurations are tested and compared at resolutions from 1 to 10 km. It is demonstrated that a deterministic mass flux closure combined with the stochastic sampling of the cloud base mass fluxes corrects the spatial and temporal distribution of cloudiness. The mean vertical structure of the cloud layer and vertical profiles of the thermodynamic variables in the boundary layer are also improved. The stochastic parameterization adapts to the model resolution by its formulation, while a limited scale‐aware behavior is present in the outcome of the simulations. This limitation stems from the resolution dependence of the resolved dynamics, which produces incorrect distributions of cloudiness, and scale‐dependence opposite of what is expected based on the reference large eddy simulation results. The deterministic version of the convection scheme cannot correct the behavior of the resolved dynamics, while the stochastic version corrects the resolved dynamics to some extent and improves the overall behavior across resolutions

Fluctuations in A Quasi-Stationary Shallow Cumulus Cloud Ensemble

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

Fluctuations in a quasi-stationary shallow cumulus cloud ensemble

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

The dependence of shallow cumulus macrophysical properties on large-scale meteorology as observed in ASTER imagery

This study identifies meteorological variables that control the macrophysical properties of shallow cumulus cloud fields over the tropical ocean. We use 1,158 high-resolution Advanced Spaceborn Thermal Emission and Reflection Radiometer (ASTER) images to derive properties of shallow cumuli, such as their size distribution, cloud top heights, fractal dimensions, and spatial organization, as well as cloud amount. The large-scale meteorology is characterized by the lower-tropospheric stability, subsidence rate, sea surface temperature, total column water vapor, wind speed, wind shear, and Bowen ratio. The surface wind speed emerges as the most powerful control factor. With increasing wind speed the cloud amount and cloud top heights show a robust increase accompanied by a marked shift in the cloud size distribution toward larger clouds with smoother shapes. These results lend observational support to the deepening response of a wind-driven marine boundary layer as simulated by large-eddy models. The other control factors cause smaller changes in the cloud field properties. We find a robust increase in cloud amount with increasing stability and decreasing sea surface temperature, respectively, which confirms a well-known behavior of marine stratocumulus also for shallow cumulus clouds. Due to the high resolution of cloud images, we are able to study the lower end of the cloud size distribution and find a robust double power law behavior with a scale break at 590 m. We find a variation in the shape of the cloud size distribution with Bowen ratio, qualitatively consistent with modeling results and suggesting the Bowen ratio as a new potential control factor on shallow cumulus clouds. © 2019. The Authors