| At present,the horizontal resolutions of mainstream numerical weather prediction(NWP)models have reached the kilometer scale.At this time,the deep cumulus and deep convections can be partially resolved.Therefore,the NWP models with this resolution range are also called ”Convection-Permitting Models”(CPMs).CPMs usually turn off the subgrid cumulus parameterization scheme to achieve better simulation results,which is equivalent to assuming that all turbulent fluxes related to the cumulus have been resolved by the model.But in fact,in the kilometer-scale simulations,the subgrid-scale(SGS)turbulent mixing is as important as that of resolved fluxes within clouds.At this resolution,neither planetary boundary layer schemes which are designed for mesoscale simulations nor the large-eddy closures designed for turbulence-resolving simulations can accurately parameterize the in-cloud SGS turbulent fluxes.Therefore,the resolution range of kilometer-scale is also called the gray zone of deep convection simulations.Through filtering and a priori analysis of the large-eddy simulation(LES)of idealized supercell and squall line cases with a horizontal grid spacing of 50 m,the resolved and SGS turbulent fluxes of heat,water vapor,and other scalars at grid spacings of 250 m,500 m,1 km,2 km,and 4 km are obtained.Through diagnosis,it is found that the magnitude of the vertical SGS fluxes and their contribution to the deep convection is equivalent to that of the resolve fluxes at the resolution of 4 km.And the contribution of the SGS fluxes does not become negligible until 500 m spacing,which confirms that kilometer-scale resolutions are within the gray zone of deep convection simulations.Secondly,in the kilometer-scale resolution range,the SGS fluxes decrease with the refinement of the model resolution,showing a significant scale dependence.By comparing and diagnosing the horizontal and vertical SGS fluxes in deep convective systems,it is found that their magnitudes are in the same order,which indicates that a proper SGS closure scheme for deep convective clouds needs to consider both horizontal and vertical three-dimensional SGS fluxes.Further diagnosis shows that in the vertical direction,the SGS heat fluxes in the updraft region are mainly positive and counter the gradient of resolved potential temperature field.In the horizontal direction,it is not completely the down-gradient lateral entrainment and exchange between the cloud body and the environment.Counter-gradient SGS transport exists in the region where the ascending flow is tilted by the vertical wind shear.In the supercell cases,this horizontal counter-gradient transport only exists in some limited regions,while in the squall line cases,the horizontal counter-gradient SGS fluxes generally exist in the climbing updraft flow at the front of the squall line,transporting the heat and moisture from the front of the squall line to the convective core and to the backside.Based on the results of the a priori analysis,the numerical models must adopt a scale-adaptive three-dimensional turbulence parameterization scheme to simulate the deep convection accurately at kilometer-scale resolutions.And the scheme must be able to reproduce the significant counter-gradient fluxes in the deep convections.In this paper,based on the LES-type closure scheme,we modified and improved the scheme by applying scale-adaptive functions to the scheme parameters.And in this way,a turbulence parameterization scheme suitable for gray-zone resolutions was constructed.Considering the fact that the eddy-viscosity-type closures commonly used in LES are not suitable for deep convections due to its inability to reproduce countergradient fluxes,a nonlinear turbulence closure scheme based on scale similarity is introduced to simulate the SGS fluxes in deep convective clouds.In this scheme,the SGS fluxes are produced by the horizontal gradient of the resolved variables,so this closure is called Hgrad scheme.The diagnosis analysis based on filtering the LES field shows that the Hgrad scheme could produce similar SGS fluxes with that of the filtered LES,and their fields have high spatial correlation coefficients.Moreover,the Hgrad scheme can accurately simulate the counter-gradient fluxes within the cloud due to its scale-similarity framework.In contrast,the traditional 1.5-order turbulent kinetic energy(TKE)scheme based on the eddy-viscosity assumption could not represent the counter-gradient transport,and the correlation coefficients between the modeled and filtered SGS fluxes from the LES are small or even negative.Based on the LES of a supercell,the variation of model parameters in the Hgrad scheme with the resolution is obtained.On this basis,a scale adaptive function is constructed to extend the applicability of the Hgrad scheme to the gray zone for the kilometer-scale simulations of deep convections.Next,the Hgrad scheme is implemented into the Advanced Regional Prediction System(ARPS)to simulate the idealized supercell and squall line at kilometer-scale resolutions.Using the filtered LES as the benchmark,it is found that the Hgrad scheme could reproduce the proper SGS fluxes,especially the counter-gradient fluxes.In contrast,the TKE scheme could not produce the SGS counter-gradient fluxes.And in the simulations with grid spacings coarser than 500 m,the magnitude of the simulated SGS fluxes is also underestimated due to the underestimation of the SGS turbulent kinetic energy.Compared with the TKE scheme,the Hgrad scheme produces stronger horizontal turbulent fluxes,which has different effects on supercell and squall line simulations.In supercell cases,the stronger horizontal mixing between the convective cloud and the environment dilutes the updraft flow,and so that inhibits the updraft.In squall line cases,the stronger transport of heat and moisture from the front side enhances the upward motion.Finally,the Hgrad model is implemented into the most widely used international mesoscale NWP model Weather Research and Forecasting(WRF)model,and the kilometerscale resolution simulations of a tornadic supercell case in Yancheng,Jiangsu Province on June 23,2016,is accomplished.The preliminary results show that compared with the results of the traditional CPM setting,the supercell simulated by the Hgrad scheme,who considers the SGS fluxes in the convective clouds,are significantly different in structure,strength,and organization,as well as the precipitation produced by the weather system.It is found that the Hgrad scheme based on idealized experiment still has much room for improvement in real case simulations.More experiments are needed to optimize the scheme parameters and to explore the interaction between SGS turbulence schemes and other physical parameterization schemes(such as cloud microphysics).Further study is needed to obtain the optimal combination of key physical process parameterization schemes at kilometer-scale resolutions. |
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