COSMO

1. General aspects related to physical parameterizations: Sibiu 2013 COSMO Matthias Raschendorfer

2. The primitive equations: advection flux density molecular flux density scalar variables source term • local parameterizations: • molecular flux densities • phase changes sources (cloud microphysics) • radiation flux convergence linearor non-linear functions in all model variables functions in all model variables (including spatial derivatives) dependent on a list ofgeneral validparameters simplified for efficiency reasons using effective parameters Numerical scheme solves filtered equations: : filtered (mean) variable with fluctuation : density weighted mean with fluctuation Non-linearity causes generation of statistical moments: spatial differentiation Non-commutability of filterand (e.g.) multiplication or roughness layer terms: contribution by SGS slopes of model layers or non-atmospheric intersections SGS covariance: Sibiu 2013 COSMO Matthias Raschendorfer

3. The filtered model equations: GS flux density molecular flux density GS source term roughness layer modification of transport SGS flux density SGS source term including roughness layer effects (form drag) form drag SGS contribution by cloud microphysics functions in various covariance terms of scalar variables SGS contribution by cloud microphysics and radiation Sibiu 2013 COSMO Matthias Raschendorfer

4. Parameterizations in terms of grid scale (GS) variables : • Further information (assumptions) about these additional covariance terms has to be introduced: • GS parameterizationsdue to • SGS variability functions in all GS model variables dependent on a list ofadditional parameters • Closure assumptions are additional constraints that can’t be general valid • distinguish different flow structures more or less according to the length scales of their motions • each with specific parameterization assumptions Turbulence: isotropic, normal distributed, only one characteristic length scale at each grid point, forced by shear and buoyancy Circulation: non isotropic, arbitrarily skewed and coherent structures of several length scales, supplied by various pressure forces Convection large vertical scales of coherence, full microphysics, forced by buoyancy feed back Kata- and anabatic density circulations: direct thermal circulation forced by lateral cooling or heating by sloped surfaces of the earth; dominated by SGS surface structures like SSO produced by strong horizontal shear e.g. at frontal zones; dominated by horizontal grid scale Horizontal shear eddies: produced by blocking at SGS surface structures (form drag forces) Wake eddies: belong to wave length of instable gravity waves of arbitrary scales Breaking gravity wave eddies: Sibiu 2013 COSMO Matthias Raschendorfer

5. Closure strategies: • Describing the covariance terms within different frameworks all based on first principals • Introduction of closure assumptions by application of a related truncation procedure • Finding a flow structure separation according to the validity of closure assumptions • Setting up a consistently separated set of parameterization schemes being to some extend general valid • Two different frameworks available: • Higher order closure (HOC):Using budget equations for needed statistical moments that always contain new ones, even such of higher orders and truncating the considered order • Second order closure: fits very well to turbulence source term correlation GS flux density SGS flux density shear production dissipation sink prognostic model variables influenced by pressure force, microphysics and radiation Sibiu 2013 COSMO Matthias Raschendorfer

6. Conditional domain closure (CDC):Using budget equations for conditional averages of model variables (e.g. according to classes of vertical velocity) and building the needed covariance terms by the related truncated statistics • Mass flux closure: fits very well to convection conditional average (representing e.g. the convective updraft or downdraft • budget for a conditional averaged property: inflow via the inner boundary surface volume fraction of the related subdomain downdraft • continuity equation: Inner boundary surface of the subdomain updraft Sibiu 2013 COSMO Matthias Raschendorfer

7. Challenges related to physical parameterizations: Sibiu 2013 COSMO Matthias Raschendorfer

8. Principal Problems: • Radiation parameterization considers cloud properties, but • Precipitating hydrometeors (snow) are not included • SGS variability of cloud properties not properly considered • Moist turbulence using statistical saturation adjustment, but • Turbulent contributions to phase change terms not yet considered in GS budgets • Non equilibrium processes (icing and precipitation) not included Radiation transport Cloud-microphysics Parameterizations of source terms Local parameterizations: integrated in Parameterizations of SGS processes GS parameterizations: • Convection scheme treats micro-physics including precipitation, but • It is not separated against GS • Radiation is not included interaction STIC Circulations Separation Turbulence Missing interaction to be included: • TKE scheme contains interaction terms, but • Some interaction terms are crude estimates and related circulations don’t even have a contribution to transport (mixing) of 1-st order variables as well as TKE • Convection scheme (can we do it without it?): • Does not yet contain any dependency from turbulence • Convective mixing of TKE not yet considered • Is not separated against resolved convection (grey-zone, double counting) • Is not able to give estimates of volume fractions of convective subdomains • Overlap of turbulent and convective contributions to microphysical source terms can’t be treated (no consistent description of cloud processes) Sibiu 2013 COSMO Matthias Raschendorfer

9. Some specific challenges: • Some simplifying approximations are no longer valid due to increased or variable horizontal resolution: longer term 3D-extensions: tilted columns; horizontal diffusion; transport of 2-nd order moments (TKE) • Neglect of horizontal gradients compared to vertical ones, allowing single column solutions • Neglect of up- and downdraft fraction and mean vertical wind speed in convection parameterization (completely unresolved convection) Grey-zone; scale adaptive convection vertically resolved roughness layer: additional form drag; smaller roughness length, modification of turbulent length scale • Roughness layer due to land use is only a small part of the lowest model layer, allowing to treat it in the SAT scheme only • Expensive calculations can be called less frequently (smooth evolution in time) or can even be avoided (single column solutions) Adaptive parameterizations • Application of parameterizations in COSMO and ICON: common physics library: generation of clear interfaces; multi parameterization ensemble; modularization; cleaning up of NAMELISTs; adaptations for surface tiles • using advantage of different approaches short term • More consistent and complete parameterizations: • Avoiding numerical artefacts and instabilities • Avoiding contradictory, artificial or unnecessary approximations • Removing problems with diurnal cycle, stable boundary layer, low level stratus • Consolidation /merging of independent development ongoing improvement; finishing PP UTCS; PT ConSAT and followers automatic parameter estimation; statistical hyper-parameterization or post-processing • Improvement by non-physical extensions: interdisciplinary ; longer term • using direct impact of error estimates • Including non-deterministic aspects stochastic physics Sibiu 2013 COSMO Matthias Raschendorfer

10. Challenges related to parameterization extensions: Sibiu 2013 COSMO Matthias Raschendorfer

11. Non physical parameterization complements: • Trying to improve physical parameterizations using model error estimates: classical verification model diagnostics data assimilation ensemble prediction; probabilistic forecast; error estimate Stochastic physics ? • introduction of additional statistical moments by simulation of stochastic processes Sibiu 2013 COSMO Matthias Raschendorfer

12. Principal of the parameterization complements: Trying to improve physical parameterizations by systematic parameter tuning: • by minimizing the model error of a verification quantity might even decreasecurrentstochastic complement • Stochastic variation of tendencies • stochastic properties of SGS surface tiles or convective cells Stochastic variationsofmodel input: should decreaseexpectation ofstochastic complement Stochastic variationsof parameterizations: Model integration Model output Model input prognostic variables Hyper- parameterization boundary values implicit diagnostics initial values assimilation diagnosticmodel calculation global constants Explicite diagnostics regression coefficients global parameter local (external) parameter • Providing a list of parameter sub sets containing as few as possible parameters, related to specific conditionsand a verification quantity that can be compared with measurements and that is sensitive only to those parameters in the sub set in case of the applicability of that condition. parameter tuning Additional parameters for explicit diagnostics Observations conditional sampling increasing decreasing stochastic complement averaging averaging Superobservation Supercalculation compare Sibiu 2013 COSMO Matthias Raschendorfer