1. COSMO Sibiu 2013 Matthias Raschendorfer Towards Separated Turbulence Interacting with Circulations (STIC):

2. - slope in case of TKE turbulence microphysicsresolved structures : largest turbulent wave length convective peak neutral stabile labile Spectral characteristics of turbulence and circulations: - circulations generally are related with …………………………………… additional spectral peaks - or they cause different peak wavelengths in vertical direction compared to the horizontal directions: …. larger peak wavelength in vertical direction in case of labile stratification at least a two-scale-problem anisotropic peak wave length catabatic peak unresolved structures BL workshop Matthias Raschendorfer circulations smaller peak wavelength in vertical direction in case of stabile stratification COSMO Sibiu 2013

3. Principle of a general valid GS parameterization by scale separation:  Closure of the 2-nd order budget equationsclosure assumptions = further information  Limited (not general valid ) solution: e. g. for sub grid scale turbulence  General valid sub grid scale closure:  General valid 2-nd order closure assumptions can’t exist!  Assumptions can only be valid for special conditions: or for sub grid scale convection! Separation of sub grid scale flow in different classes Application of specific (rather easy) closure assumptions for each class Combination of particular parameterizations Consideration of interaction between different classes use of different schemes for turbulence, convection or SSO blocking usually missing in current models! Spectral separation by - averaging these budgets along the whole control volume ( double averaging ) - considering budgets with respect to the separation scale turbulent budgets Matthias Raschendorfer DWD Separated Turbulence Interacting with Circulations COSMO Sibiu 2013

4. average of the non linear turbulent shear terms circulation shear term Additional circulation terms in the turbulent 2-nd order budgets: BL workshop Matthias Raschendorfer turbulent shear term COSMO Sibiu 2013

5. Separated semi parameterized TKE equation (including scale interaction sources): buoyancy production eddy- dissipation rate ( EDR ) labil: neutral: stabil: time tendency transport (advection + diffusion) shear production by sub grid scale circulations expressed by turbulent flux gradient solution to be parameterized by a non turbulent approach shear production by the mean flow : with respect to the separation scale L buoyant part of buoyant and wake part of mean (horizontal) shear production of circulations, according Kolmogorov : correction factor in case of sloped model layers Matthias Raschendorfer DWD COSMO Sibiu 2013

6.  Separated horizontal shear production term: effective mixing length of diffusion by horizontal shear eddies velocity scale of the separated horizontal shear mode scaling parameter  Equilibrium of production and scale transfer towards turbulence: scaling parameter horizontal shear eddy isotropic turbulence horizontal grid plane TKE-production by separated horizontal shear modes: grid scale ……….effective scaling parameter separated horizontal shear additional TKE source term Matthias Raschendorfer DWD  Already used for EDR forecast ;to be tuned and verified for operational use COSMO Sibiu 2013

7.  SSO-term in filtered momentum budget: blocking term TKE-production by separated wake modes due to SSO: currently Lott und Miller (1997)  Pressure term in kinetic energy budget: wake source sources of mean kinetic energy MKE buoyancy production sources of sub grid scale kinetic energy SKE pressure transport expansion production from inner energy DWD Matthias Raschendorfer  Contribution taken form SSO scheme:already operational COSMO Sibiu 2013

8. virtual potential temperature of ascending air circulation scale temperature variance ~ circulation scale buoyant heat flux TKE source term TKE-Production by thermal circulations:  Circulation scale 2-nd order budgets with proper approximations valid for thermals : separated thermals virtual potential temperature of descending air vertical velocity scale of circulation buoyant production of sub grid scale kinetic energy can be derived directly form current mass flux convection scheme Matthias Raschendorfer DWD  Two contributions: - one taken form convection scheme:already used for EDR forecast ; to be verified - one being a crude estimate of surface induced density flows:active since years COSMO Sibiu 2013

9. Matthias Raschendorfer DWD pot. temperature [K] Wind speed [m/s] reference including horizontal shear – and SSO- production including horizontal shear –, SSO- and convective production mountain ridge COSMO-US: cross section across frontal line and Appalachian mountains COSMO Sibiu 2013

10.  A single 2-nd order scheme for the whole SGS range requires horizontal grid scales being sufficient small to allow turbulence closure as a general valid asumption.  We can’t do it without a convection scheme, in particular if we think for global simulations (ICON)  A 2-nd order scheme for non precipitating (shallow) convection only, might be an option.  Mass flux approach is better adapted to coherent flows than 2-nd order closure  Convection may be partly resolved (grey zone) and fundamental assumptions applied to classical mass flux schemes are no longer fulfilled.  Mass flux convection scheme needs to be reformulated to be scale adaptive. What’s about the turbulence interaction in the convection scheme? Matthias Raschendorfer DWD COSMO Sibiu 2013

11. Matthias Raschendorfer COSMO Conditional domain closure (CDC) : : domain of dimension : volume fraction of : mass budget (continuity equ.) L s : largest non- convective wave length  Foundation of alternative mass flux equations  Solvable also for volume fraction, if conditions for sub –domain definition are used  Turbulent properties can be used for lateral mixing and triggering  Separation against turbulence and grid scale possible COSMO Sibiu 2013

12. Non-turbulent (convective) modulation of normal distributed patterns in a statistical condensation scheme: cloud turbulent variation normal distr. non turbulent variation bi/tri-modal convective variation grid scale horizontal direc. range of up to L- scale patterns range of up to L s - scale pat- terns multimodal common PDF : separation scale for turbulence : horizontal scale of largest normal distr. patterns (turbulence, wakes, gravity waves, etc) : local over saturation Matthias Raschendorfer DWD COSMO Sibiu 2013

13. Conclusion: Matthias Raschendorfer DWD  Generalization of the closure scheme by scale separation -Classical turbulence closure will only be valid, if all sub-grid structures are in accordance with turbulence closure assumptions -Usually other sub-grid processes are present and in the near surface SBL they are even dominant  The presence of non-turbulent sub-grid scale structures needs to be considered  Physical reason for the problems with a classical scheme -Separation of turbulence by a sub-filter only smoothing “turbulence” provides variance equations for turbulence automatically containing shear production terms by non-turbulent sub-gird processes ( scale transfer terms )  The non-turbulent structures can’t be described by turbulence closure, rather we necessarily need separate schemes for them with specific closure assumptions, in particular specific length scales.  The additional production terms can’t be introduced only by treating all scalar variances by prognostic equations that introduce turbulent transport of them (UTCS-extension) but no additional sources for TKE.  Turbulent fluxes remain in flux gradient form, those by non-turbulent flow structures do not.  Already (partly) implemented TKE-production by scale transfer from kinetic energy of … - wakes generated by surface inhomogeneity (from SSO-blocking scheme) already operational - thermal circulation by surface inhomogeneity (due to differential heating/cooling)only crude approximation - horizontal eddies generated by horizontal shear (e.g. at frontal zones)not yet verified - Convection circulation (buoyant production from convection scheme)not yet verified COSMO Sibiu 2013

14.  Switching on the implemented scale interaction terms after verification against SYNOP data (operational verification)  Reformulation of the surface induced density flow term (circulation term) in the current scheme to become a thermal SSO production dependent on SSO parameters  Expression of direct sub grid scale transport by SSO eddies and horizontal shear eddies  Considering TKE-transport by circulations  Setting up a first estimate of convective modulation of a turbulent saturation adjustment  Integration of prognostic equations for scalar variances (and skewness of oversaturation) as an option  Implementation of a scale separated mass flux convection interacting with turbulence and providing volume fractions of convective sub domains (final step of STIC)  All further implementations in the common CÓSMO/ICON module not before this is ready for use in COSMO! Next steps: Matthias RaschendorferCOSMO Sibiu 2013 DWD

15. Matthias Raschendorfer Moscow: 06-10.09.2010COSMO L s : largest non- convective wave length Simplified diagnostic budgets in advection form do not contain volume fractions and are solved by vertical integration Substitute pure mass flux equation ( continuity equation ) of traditional mass flux scheme by equation for vertical velocity -Direct buoyancy impact using Boussinesq-approximation instead of dynamical de- and entrainment parameterization using grid scale humidity convergence Boundary values from largest non convective mode - No parameterization of boundary mass flux using humidity convergence - No artificial vertical displacement or lateral mixing for boundary values - No distinction between shallow and deep convection ; each level can be a starting point for updrafts or downdrafts -Automatic trigger of convection by turbulence using largest non convective wave mode Solving for volume fractions by using construction constraints for the convective sub domains - Explicit expression of convective flux densities and total source terms (clouds and precipitation) by convective averaging Performing scale interaction and scale separation against turbulence and grid scale convection -Stopping integration when single cell diameter > horizontal grid scale: cut off against grid scale convection -Reducing separation scale when single cell diameter < separation scale: reduction of turbulence due to convection -Identification of the lateral mixing sink of convective kinetic energy (detrainment) to be the convective source of TKE -Stopping integration when vertical velocity < that of turbulence triggered initial cell: cut off of against turbulence : generalized velocity including molecular and slope effects