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The most frequently used boundary-layer turbulence parameterization in numerical weather prediction (NWP) models are turbulence kinetic energy (TKE) based-based schemes. However, these parameterizations suffer from a potential weakness, namely the strong dependence on an ad-hoc quantity, the so-called turbulence length scale. The physical interpretation of the turbulence length scale is difficult and hence it cannot be directly related to measurements or large eddy simulation (LES) data. Consequently, formulations for the turbulence length scale in basically all TKE schemes are based on simplified assumptions and are model-dependent. A good reference for the independent evaluation of the turbulence length scale expression for NWP modeling is missing. Here we propose a new turbulence length scale diagnostic which can be used in the gray zone of turbulence without modifying the underlying TKE turbulence scheme. The new diagnostic is based on the TKE budget: The core idea is to encapsulate the sum of the molecular dissipation and the cross-scale TKE transfer into an effective dissipation, and associate it with the new turbulence length scale. This effective dissipation can then be calculated as a residuum in the TKE budget equation (for horizontal sub-domains of different sizes) using LES data. Estimation of the scale dependence of the diagnosed turbulence length scale using this novel method is presented for several idealized cases.
The impact of precipitation in shallow cumulus convection on the moisture variance and third-order moments of moisture is investigated with the help of large-eddy simulations. Three idealized simulations based on the Rain in Cumulus over the Ocean field experiment are analyzed: one nonprecipitating, on a smaller domain, and two precipitating cases, on a larger domain with different initial profiles of moisture. Results show that precipitation and the associated cloud organization lead to increased generation of higher-order moments (HOM) of moisture compared to the nonprecipitating case. To understand the physical mechanism and the role of individual processes in this increase, budgets of HOM of moisture are studied. Microphysics directly decreases the generation of HOM of moisture, but this effect is not dominant. The gradient production term is identified as the main source term in the HOM budgets. The influence of the gradient production term on moisture variance is further examined separately in cloud active and nonactive regions. The main contribution to the gradient production term comes from the smaller cloud active region because of the stronger moisture flux. Further analyses of the horizontal and vertical cross sections of moisture fluctuations show that the precipitation-induced downdrafts and updrafts are the main mechanism for the generation of moisture variance. The variance increase is linked to shallow dry downdraft regions with horizontal divergence in the subcloud layer, moist updrafts with horizontal convergence in the bulk cloud layer, and finally wider areas of horizontal divergence in the cloud inversion layer.
The ICON single-column mode
(2021)
The single-column mode (SCM) of the ICON (ICOsahedral Nonhydrostatic) modeling framework is presented. The primary purpose of the ICON SCM is to use it as a tool for research, model evaluation and development. Thanks to the simplified geometry of the ICON SCM, various aspects of the ICON model, in particular the model physics, can be studied in a well-controlled environment. Additionally, the ICON SCM has a reduced computational cost and a low data storage demand. The ICON SCM can be utilized for idealized cases—several well-established cases are already included—or for semi-realistic cases based on analyses or model forecasts. As the case setup is defined by a single NetCDF file, new cases can be prepared easily by the modification of this file. We demonstrate the usage of the ICON SCM for different idealized cases such as shallow convection, stratocumulus clouds, and radiative transfer. Additionally, the ICON SCM is tested for a semi-realistic case together with an equivalent three-dimensional setup and the large eddy simulation mode of ICON. Such consistent comparisons across the hierarchy of ICON configurations are very helpful for model development. The ICON SCM will be implemented into the operational ICON model and will serve as an additional tool for advancing the development of the ICON model.
Toward parametrization of precipitating shallow cumulus cloud organization via moisture variance
(2021)
The influence of the initial vertical moisture profile on precipitating shallow cumulus cloud organization in terms of the column-averaged moisture variance is investigated using large-eddy simulations. Five idealized simulations based on the Rain in Cumulus over the Ocean field experiment with different initial moisture profiles are investigated. All cases simulate precipitating shallow cumulus convection in a marine sub-tropical region under large-scale subsidence. The results show that the moisture variance is mainly generated through the interaction of the moisture flux and the moisture gradient in the gradient production term at the top of the boundary layer. The development is characterized by three regimes: initial, transition, and quasi-steady regime. During the initial regime, the moisture gradient is built up by moisture accumulation until precipitating convection starts. Within the transition regime, precipitation enables mesoscale cloud organization with enhanced convective activity and moisture fluxes. The moisture variance increases from the moist to the dry initial moisture profiles. In a following quasi-steady regime, the moisture variance is approximately preserved. Thereby, the initial moisture gradient between the average sub-cloud layer and the free atmosphere is found to be an important factor for the generation of the quasi-steady column-averaged moisture variance. The result suggests that a resolved-scale variable like the moisture gradient can be used to estimate the quasi-steady state conditions resulting from cloud organization. This finding may serve as a starting point for the parametrization of the subgrid scale cloud organization caused by precipitating shallow convection.
An update of the two-energy turbulence scheme is presented, the 2TE + APDF scheme. The original version of the two-energy scheme is able to successfully model shallow convection without the need of an additional parameterization for non-local fluxes. However, the performance of the two-energy scheme is worse in stratocumulus cases, where it tends to overestimate the erosion of the stable layers. We have identified the causes: the non-local stability parameter does not consider local stratification, the scheme lacks an internal parameter that could distinguish between a shallow convection regime and a stratocumulus regime, and it uses an inflexible turbulence length scale formulation. To alleviate this problem, we propose several modifications: an update of the stability parameter, a modified computation of the turbulence length scale, and the introduction of the entropy potential temperature to distinguish between a shallow convection and a stratocumulus regime. In addition, the two-energy scheme is coupled to a simplified assumed probability density function method in order to achieve a more universal representation of the cloudy regimes. The updated turbulence scheme is evaluated for several idealized cases and one selected real case in the ICOsahedral Nonhydrostatic (ICON) modeling framework. The results show that the updated scheme corrects the overmixing problem in the stratocumulus cases. The performance of the updated scheme is comparable to the operational setup, and can be thus used instead of the operational turbulence and shallow convection scheme in ICON. Additionally, the updated scheme improves the coupling with dynamics, which is beneficial for the modeling of coherent flow structures in the atmospheric boundary layer.
