Recent extensions of the COSMO TKE scheme related

Recent extensions of the COSMO TKE scheme related to the interaction with non turbulent scales § Separation between turbulence and non turbulent sub grid scale circulations § Additional scale interaction terms in the separated TKE budget § Parameterization and effect of 3 important scale interaction terms with separated: - Horizontal shear modes (e. g. at frontal regions) - Wake modes from SSO blocking (over mountains) § Buoyancy forced thermal circulations (e. g. due to shallow convection or sub grid scale katabatic flows) Considering of non turbulent sub grid scale circulations in the statistical condensation scheme (including non Gaussian effects) Matthias Raschendorfer DWD COSMO Matthias Raschendorfer Offenbach 2009

Partial solution for turbulence by spectral separation: Turbulence is that class of sub grid scale structures being in agreement with turbulence closure assumptions! § Turbulence closure is only valid for scales not larger than - the smallest peak wave length Lp of inertial sub range spectra from samples in any direction, where - the largest (horizontal) dimension Dg of the control volume § Spectral separation by - considering budgets with respect to the scale budgets along the whole control volume - separation averaging these (double averaging) generalized turbulent budgets including additional scale interaction terms COSMO Matthias Raschendorfer Offenbach 2009

Additional circulation terms in the turbulent 2 -nd order budgets: average of the non linear turbulent shear terms turbulent shear term COSMO circulation shear term Matthias Raschendorfer turbulent shear term Offenbach 2009

Physical meaning of the circulation term: § Budgets for the circulation structures: Circulation term is the scale interaction term shifting Co-Variance (e. g. SKE) form the circulation part of the spectrum (CKE) to the turbulent part (TKE) by virtue of shear generated by the circulation flow patterns. production terms depend on: dependent on: CKE TKE the turbulent specific length scales and the turbulent specific velocity scale (= velocity scales ) (= ) and other COSMO circulationturbulencescale statistical scale moments and other We need to consider additional length scales besides the turbulent length scale! Matthias Raschendorfer Offenbach 2009

Separated semi parameterized TKE equation (neglecting molecular transport): expressed by turbulent flux gradient solution time tendency transport of TKE buoyancy production shear production by the mean flow to be parameterized by a non turbulent approach shear production by sub grid scale circulations eddydissipation rate (EDR) labil: neutral: stabil: COSMO Matthias Raschendorfer Offenbach 2009

TKE-production by separated horizontal shear modes: § Separated horizontal shear production term: separate d horizont al shear effective mixing length of diffusion by horizontal shear eddies velocity scale of the separated horizontal shear mode grid scale scaling parameter § horizontal grid plane isotropic turbulence horizontal shear eddy Equilibrium of production and scale transfer towards turbulence: scaling parameter additional TKE source term ………. effective scaling parameter COSMO Matthias Raschendorfer Offenbach 2009

= (dissipation)1/ out_usa_shs_rlme_a_shsr_0. 2 3 Pot. Temperature [K] out_usa_shs_rlme_a_shsr_1. 0 S N frontal zone 06. 02. 2008 00 UTC + 06 h COSMO Matthias Raschendorfer -92 E Offenbach 2009

TKE-production by separated wake modes due to SSO: § SSO-term in filtered momentum budget: blocking term § currently Lott und Miller (1997) SSO-term in SKE-equation: separated sub grid orography COSMO Matthias Raschendorfer Offenbach 2009

= (dissipation)1/ 3 out_usa_rlme_sso out_usa_rlme_tkesso moderate light MIN = 0. 00104324 MAX = 10. 3641 AVE = 0. 126079 SIG = 0. 604423 out_usa_rlme_tkesso – out_usa_rlme_sso S MIN = 0. 00109619 MAX = 10. 3689 AVE = 0. 127089 SIG = 0. 804444 N mountain ridge SSO-effect in TKE budget MIN = -0. 10315 MAX = 0. 391851 AVE = 0. 00100152 SIG = 0. 00946089 COSMO 06. 02. 2008 00 UTC + 06 h Matthias Raschendorfer -77 E Offenbach 2009

A first parameterization of thermal circulations term: § Circulation scale 2 -nd order budgets with proper approximations valid for thermals: circulation scale temperature variance ~ circulation scale buoyant heat flux circulation term vertical separate square for velocity virtual d Bruntscale of temperat. of thermals Väisäläcirculatioascending air frequency n § scaling factor circulation height: e. g. BL-height bottom level virtual pattern length temperat. of scale descending air horizontal updraft scale Simplified max flux approach for the circulations: COSMO horizontal updraft fraction Matthias Raschendorfer current formulatio n using an additiona l assumpti on about the gradie nt turbulent velocity scale Offenbach 2009

Effect of thermal circulation term for stabile stratification: horizontal scale of a • Even for vanishing mean wind and negative turbulent buoyancy there remains agrid positive box definite source term TKE will not Solution even for strong stability vanish COSMO Matthias Raschendorfer Offenbach 2009

measured midnight profile of potential temperature simulated midnight profile of potential temperature COSMO Matthias Raschendorfer Offenbach 2009

Convective modulation of turbulence in a statistical condensation scheme: total oversaturation from normal distribution of turbulence turbulent Gaussian saturation adjustment using average oversaturation upward flow cloud grid scale oversaturation horizontal direction turbulent Gaussian saturation adjustment using average oversaturation downward flow from bimodal distribution of convective circulation to be estimated form relevant 2 nd order scheme describing convective circulations COSMO derivable directly from proper mass flux scheme describing convective circulations Matthias Raschendorfer Offenbach 2009

Conclusions: • Non turbulent sub grid scale modes interact with turbulence through additional shear production in the TKE equation. • 3 D-shear terms have got a significant effect only, when formulated as a scale interaction term producing TKE by shear of a separated horizontal shear mode with its own length scale. • Wake production of TKE by blocking can be formulated as a scale interaction term as well and can be described by scalar multiplication of the horizontal wind vector with its SS 0 -tendencies yielding some effect above mountainous terrain. • Buoyancy forced (convective) circulations can be described either by a mass flux approach or 2 -nd order closure. The according TKE production term is related to the circulation buoyancy heat flux. Interaction of those circulations with the statistical saturation adjustment (cloud scheme) can be formulated by “convective modulation”. Prospect: • We intent to implement the revised formulation of the circulation term together with the “convective modulation” of the statistical cloud scheme and to derive a similar scale interaction term from the current convection scheme as well. • Further we plan to consider the circulation scale fluxes in the 1 -st order budgets leading to additional non local mixing tendencies of the prognostic variables. COSMO user seminar Matthias Raschendorfer Offenbach: 09 -11. 03. 2009

Thank You for attention! COSMO Matthias Raschendorfer Offenbach 2009

About the results of UTCS Tasks (ii)a, c and (iii)a As far as attended by Matthias Raschendorfer DWD COSMO Matthias Raschendorfer Offenbach 2009

Basic scheme of advanced SCdiagnostics: Identical except horizontla operations and w-equation Realistic 3 Drun (analysis) or Forced correction run with SC version Forced test run with SC version mesdat containing geo. -wind, vert. -wind und tendencies for horizontal advektion mesdat only with model variables outdat with correction integrals outdat with similar results compared to compared test run using the 3 D-model COSMO 3 D-run Matthias Raschendorfer Component testing: outdat or mesdat may contain 3 D-corrections and arbitrary measurements (like surface temperature or surface heat fluxes) the model can be forced by. Offenbach 2009

Potential temperature profile too much turbulent mixing atmosphere soil interpolated measurements free forced freemodel forced model withrun prognostic 3 D run 3 Dcorrections starting forced with 3 D with variables and wit measured corrections measured measurements 3 D analysis from 3 D-run surface heat and surface temperature fluxes Stable stratification over snow at Lindenberg COSMO Matthias Raschendorfer Offenbach 2009

Explicit moisture correction: Turbulent fluxes of the non conservative model variables: thermodyna mic non conservative model variables flux-gradient form Conversion matrix: thermodynami c conservative model variables explicit flux correction should vanish due to grid scale saturation adjustment! cloud fraction steepness of saturation humidity Exner factor COSMO Matthias Raschendorfer Offenbach 2009

Time series of model domain averages less low level clouds But there are differences … COSMO Matthias Raschendorfer … due do numerical effects with the Exner-factor treatment of the T -equation Offenbach 2009

SC simulations with 80 layers and “implicit TKE diffusion”: Dew point profiles 50 layers Dew point profiles 80 layers explicit TKE-diffusion with restriction proper for 50 layer configuration considerable difference numerically unstable! implicit TKE-diffusion being unconditional stable almost no difference COSMO Matthias Raschendorfer Offenbach 2009