Work Status:

1. Priority Project UTCS • Work Status: • The project implementation is somewhat delayed due to the uncertainty about the future of some project participants • A review about analogies between turbulence and convection parameterization (a basis for the development) is ca. half-way through (the work is foreseen in the framework of the UTCS Task 1, performed by Dmitrii Mironov) • An extended documentation of the existing LM turbulence scheme, including a review of turbulence parameterization and basic ideas for further development in particular toward an UTCS, is to a large extent ready (Task 1, Matthias Raschendorfer) • Various aspects of the treatment of the sub-grid scale cloudiness with the statistical cloud scheme, including its relation to the treatment of the grid-scale water vapour, cloud water and cloud ice, and its consistent use within various physical parameterisation schemes of the LM, are (being) explored (Tasks 1 and 5, Euripides Avgoustoglou and Paola Mercogliano) • With the aim to slow down cumulus convection scheme, a number of modifications in the cumulus convection scheme (Tiedtke 1989), which have been successfully tested in the GME, are being tried out within the LM (Task 4, Axel Seifert, Jan-Peter Schulz, Detlev Majewski, Dmitrii Mironov) • Outlook: • The project is (expected) to proceed as scheduled • However, some changes in the project plan may have to be introduce, both in terms of FTEs and in terms of schedule (hopefully minor changes), due to unavailability of human resources

2. Priority Project UTCS About UTCS Task 4. “... with the UTCS in LM, the mass-flux deep convection scheme should be slowed down.” • Changes in the T89 Cumulus Convection Scheme: • Saturation adjustment in the T89 is performed with due regard for the cloud water-cloud ice mixed phase • (in the original T89, the cloud condensate is either water or ice as dependent on temperature) • Modified evaporation of convective precipitation • (with the 80% environment air humidity threshold compared to 95% before) • Modified generation of convective precipitation • (no detrained cloud condensate is added to the updraught precipitation flux) • Modified turbulent entrainment (E) / detrainment (D) formulation • (now dependent on potential temperature difference between the updraught and the environment) • Modified convective trigger function • (convective test parcel now originates from the lowest well mixed sub cloud layer, before from the lowest model level) • Detrained convective cloud condensate is passed to the microphysics scheme in the form of tendencies • (in the original T89, detrained convective cloud condensate is evaporated instantaneously) Research team members: Axel Seifert, Jan-Peter Schulz, Detlev Majewski, Dmitrii Mironov

3. Precipitation:GME vs. Exp_1009 LME Convective precipitation Curves are the results of averaging over the area “Germany” (47N-55N, 6E-15E) and over 20 00 UTC forecasts over the period from 01.04.2006 to 20.04.2006. Left panel: operational GME vs. Exp_1009 (with changes in the microphysics scheme and in the Tiedtke convection scheme, first of all, the water-ice mixed phase). Dot-dashed lines show convective precipitation, dashed lines - grid-scale precipitation, and solid lines - total precipitation. Right panel: observations.

4. About UTCS Task 1: “Analytical derivation…of the unified Turbulence- shallow convection scheme” A first non local extension of the current turbulence scheme: The circulation term in the TKE equation derived by spectral separation Matthias Raschendorfer DWD Bucharest 2006 COSMO Matthias Raschendorfer

5. Turbulence closure: • Considering 2-nd order budgets: shear production sub grid scale macroscopic transport molecular dissipation neglected outside the laminar layer phase change production molecular flux density pressure transport pressure destruction buoyancy source Bucharest 2006 COSMO Matthias Raschendorfer

6. What is the idea of turbulence closure? • Primary turbulent closure assumptions: Bucharest 2006 COSMO Matthias Raschendorfer

7. Secondary turbulent closure assumptions: • spectral density of contributing modes follows a power law in terms of wave length in each direction: inertial sub range spectrum • whole spectrum in a given direction is determined by a singlepeak wave length • the peak wave length is thesamefor samples in all directions: isotropic length scale • pressure correlation and dissipation can be closed using a single turbulent master length scale for each location Bucharest 2006 COSMO Matthias Raschendorfer

8. What is the remaining difficulty with circulations (beside sub grid icing and precipitation)? • they are related with at least one additional spectral peak • or they cause different peak wavelengths in vertical direction compared to the horizontal directions: • anisotropic peak wave length • larger peak wave length in vertical direction in case of labile stratification at least a two scale problem convective peak in vertical spectrum Resolved Structures - slope in case of TKE labile neutral stabile Circulations Turbulence Microphysics catabatic peak : largest turbulent wave length Bucharest 2006 COSMO Matthias Raschendorfer

9. What is the problem? • In general there are non turbulent, arranged circulation structurespresent as well: • different length scales of sub grid structures • Sub grid cloud – radiation interaction • Sub grid phase changes (cloud processes) -> boundary layer clouds More general closure assumptions valid for both, turbulence and circulations Impossible without knowing moments of as much classes as we have length scales for Separation of turbulence and circulations with adopted closure assumptions for each class and related quite easy particular solutions Bucharest 2006 COSMO Matthias Raschendorfer

10. How to find a particular solution for turbulence? 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 smallestpeak wave length Lp • and the largestdimension Dg of the control volume Spectral separation by considering budgets with respect to the separation scale and averaging these budgets along the whole control volume Bucharest 2006 COSMO Matthias Raschendorfer

11. Turbulent budgets: Mean of the non linear turbulent shear term First part of the circulation shear term • Partly parameterized TKE equation: turbulent buoyancy dissipation shear shear by circulation motions Bucharest 2006 COSMO Matthias Raschendorfer

12. Physical meaning of the circulation term: Budgets for the circulation structures: CKE Circulation term is the scale interaction term shifting SKE or any other variance form the circulation part of the spectrum (CKE) to the turbulent part (TKE) by virtue of shear generated by the circulation flow patterns. TKE Bucharest 2006 COSMO Matthias Raschendorfer

13. Parameterization of the circulation term for thermal driven (direct) circulations: • In the CKE budget: • scale interaction loss = buoyant production • In the budget for circulation scale heat and moisture flux : • scale interaction loss+ pressure destruction= buoyant production • In the budget for circulation scale temperature variance : • scale interaction loss = vertical flux divergence from the surface • flux gradient form of temperature variance flux with a vertical constant circulation scale diffusion coefficient • In all budgets: • a vertical constant circulation time scale • a mass flux approach for circulation patterns Bucharest 2006 COSMO Matthias Raschendorfer

14. Circulation term ~ circulation scale temperature variance ~ circulation scale buoyant heat flux horizontal updraft fraction difference between updraft and downdraft boundary layer height • other circulation scale 2-nd order moments have a similar representation • turbulent and circulation scale flux densities can be added: • in the first order budgets • as input for the statistical condensation scheme Bucharest 2006 COSMO Matthias Raschendorfer

15. Effect of the circulation term for stabile stratification: • Even for vanishing mean wind and negative turbulent buoyancy there remains a positive definite source term TKE will not vanish Solution even for strong stability

16. Simulated midnight profile of potential temperature

17. Conclusions: • The main problems with the inclusion of non turbulent circulations is, besides • sub grid scale freezing and – precipitation: • Occurrence of at least one additional length scale spectral scale separation • There is a first simple solution of describing vertical circulation flux densities • actually used only to describe the scale interaction term in the TKE equation circulation term • Due to this extension the turbulence scheme is able to produce a physical solution even for strong stability • The circulation scale flux densities can be used in the 1-st order budgets and the statistical condensation scheme • The approach can be extended (prognostic equations for circulation scale variances) Bucharest 2006 COSMO Matthias Raschendorfer