Improved Parameterization for Turbulence-Circulation Interaction Study

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

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

3. Principle ofa general valid GS parameterization by scale separation: • Closure of the2-nd order budget equations closure assumptions = further information • Limited (not general valid ) solution: • General valid 2-nd order closure assumptions can’t exist! e. g. for sub grid scale turbulence • Assumptions can only be valid for special conditions: or for sub grid scaleconvection! • General valid sub grid scale closure: use of different schemes for turbulence, convection or SSO blocking Separationof sub grid scale flow in different classes Application of specific (rather easy) closure assumptions for each class Combination of particular parameterizations usually missing in current models! Consideration of interactionbetween different classes Spectral separation by • considering budgets with respect to the separation scale • averaging these budgets along the whole control volume (double averaging) turbulent budgets Separated Turbulence Interacting with Circulations DWD Matthias Raschendorfer COSMO Sibiu 2013

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

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

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

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

8. TKE-Production by thermal circulations: • Circulation scale 2-nd order budgets with proper approximations valid for thermals: circulation scale temperature variance ~ circulation scale buoyant heat flux TKE source term vertical velocity scale of circulation virtual potential temperature of ascending air separated thermals buoyant production of sub grid scale kinetic energy can be derived directly form current mass flux convection scheme virtual potential temperature of descending air • 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 DWD Matthias Raschendorfer COSMO Sibiu 2013

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

10. What’s about the turbulence interaction in the convection scheme? • 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. DWD Matthias Raschendorfer COSMO Sibiu 2013

11. Conditional domain closure (CDC) : : domain of dimension Ls: largest non-convective wave length : volume fraction of • 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 : mass budget (continuity equ.) COSMO Matthias Raschendorfer COSMO Sibiu 2013

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

13. Conclusion: • Physical reason for the problems with a classical scheme • 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 • Generalization of the closure scheme by scale separation • 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 fluxesremain in flux gradient form, those by non-turbulent flow structuresdo not. • Already (partly) implemented TKE-production by scale transfer from kinetic energy of … • wakesgenerated 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 DWD Matthias Raschendorfer COSMO Sibiu 2013

14. Next steps: • 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! DWD Matthias Raschendorfer COSMO Sibiu 2013

15. Ls: largest non-convective wave length : generalized velocity including molecular and slope effects • 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 ofdynamical 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 • Noartificial 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 • Stopping integration when vertical velocity < that of turbulence triggered initial cell: cut off of against turbulence • 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 COSMO Moscow: 06-10.09.2010 Matthias Raschendorfer