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.

A new turbulence scheme with two prognostic energies is presented. The scheme is an extension of a turbulence kinetic energy (TKE) scheme following the ideas of Zilitinkevich et al. but valid for the whole stability range and including the influence of moisture. The second turbulence prognostic energy is used only for a modification of the stability parameter. Thus, the scheme is downgradient, and the turbulent fluxes are proportional to the local gradients of the diffused variables. However, the stability parameter and consequently the turbulent exchange coefficients are not strictly local anymore and have a prognostic character. The authors believe that these characteristics enable the scheme to model both turbulence and clouds in the planetary boundary layer. The two-energy scheme was tested in three idealized single-column model (SCM) simulations, two in the convective boundary layer and one in the stable boundary layer. Overall, the scheme performs better than the standard TKE schemes. Compared to the TKE schemes, the two-energy scheme shows a more continuous behavior in time and space and mixes deeper in accordance with the LES results. A drawback of the scheme is that the modeled thermals tend to be too intense and too infrequent. This is due to the particular cutoff formulation of the chosen length-scale parameterization. Long-term three-dimensional global simulations show that the turbulence scheme behaves reasonable well in a full atmospheric model. In agreement with the SCM simulations, the scheme tends to overestimate cloud cover, especially at low levels.

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 vertical heat and moisture exchange in the convective boundary layer over mountainous terrain is investigated using large-eddy simulation. Both turbulent and advective transport mechanisms are evaluated over the simple orography of a quasi-two-dimensional, periodic valley with prescribed surface fluxes. For the analysis, the flow is decomposed into a local turbulent part, a local mean circulation, and a large-scale part. It is found that thermal upslope winds are important for the moisture export from the valley to the mountain tops. Even a relatively shallow orography, possibly unresolved in existing numericalweather prediction models, modifies the domain-averaged moisture and temperature profiles. An analysis of the turbulent kinetic energy and turbulent heat and moisture flux budgets shows that the thermal circulation significantly contributes to the vertical transport. This transport depends on the horizontal heterogeneity of the transported variable. Therefore, the thermal circulation has a stronger impact on the moisture budget and a weaker impact on the temperature budget. If an upper-level wind is present, it interacts with the thermal circulation. This weakens the vertical transport of moisture and thus reduces its export out of the valley. The heat transport is less affected by the upper-level wind because of its weaker dependence on the thermal circulation. These findings were corroborated in a more realistic experiment simulating the full diurnal cycle using radiation forcing and an interactive land-surface model.