Priority Project "UTCS"
Towards Unified Turbulence-Shallow Convection Scheme

Last updated: 16 March 2012

Project leader: Dmitrii Mironov (DWD)

Introduction

Representation of shallow convection and boundary-layer turbulence in numerical models of atmospheric circulation is one of the key unresolved issues that slows down progress in numerical weather prediction (NWP). Even in high-resolution limited-area NWP models, whose horizontal grid size is of order 1 km, these phenomena remain at sub-grid scales and should be adequately parameterised. The goal of the present project is to make a step forward along this line.

The project is aimed at (i) parameterising boundary-layer turbulence and shallow non-precipitating convection in a unified framework, and (ii) achieving a better coupling between turbulence, convection and radiation.

Boundary-layer turbulence and shallow convection will be treated in a unified second-order closure framework. Apart from the transport equation for the sub-grid scale turbulence kinetic energy (TKE), the new scheme will carry at least one transport equation for the sub-grid scale variance of scalar quantities (potential temperature, total water). The second-order equations will be closed through the use of a number of advanced formulations, where the key point is the non-local parameterisation of the third-order turbulence moments. The proposed effort is expected to result in an improved representation of a number of processes and phenomena, including non-local transport of heat, moisture and momentum due to boundary-layer turbulence and shallow convection, triggering of deep cumulus convection, and stratiform cloud cover. This in turn is expected to lead to an improved forecast of several key quantities, such as the rate and timing of precipitation and the 2m temperature.

Project tasks

Task (i):
- Comprehensive testing of the new TKE-Scalar Variance scheme (including transport equations for the TKE and for the scalar variances, a sub-grid scale statistical cloud scheme for non-precipitating clouds, and non-local formulation for the turbulence length/time scale) through numerical experiments within the full-fledged three-dimensional COSMO model, including the data assimilation cycle;
- Analysis of results from numerical experiments, verification of numerical results against observational data;
- Coupling of the new scheme with the tiled surface scheme (the development of the tiled surface scheme is underway, c/o Ekaterina Machulskaya and Jurgen Helmert), tuning of the coupled schemes;
- Preparation of documentation.

Task (ii):
Task (ii).a:
- Detailed investigation of the problems with diurnal cycle of the near surface quantities using data from measurements and COSMO-SCM; implementation and verification of a revised surface-layer transfer formulation.
Task (ii).b:
- Generalization of non-local formulation of the turbulence length scale to account for moist processes (effect on phase changes on the scale of turbulence);
- Comprehensive testing of a generalized formulation through single-column and 3D experiments;
- Verification of results in different weather situations;
- Preparation of documentation.
Task (ii).c:
- Development of a unified turbulence-scheme code suitable for COSMO, COSMO-SCM and ICON;
- Development of a positive-definite semi-implicit solver for the TKE equation;
- Development, testing and implementation of a subroutine to solve a generic vertical diffusion equation (using an implicit numerical scheme);
- Testing and verification of an alternative expression of moist correction within turbulence scheme;
- Verification of scale interaction terms (already implemented into COSMO) against data, e.g. ACARS EDR data, using the Turbulence Model Output Statistics (TMOS) package;
- reformulation of the current "circulation term" to become a thermal sub-grid scale orography source term for the TKE.

Task (iii):
- Evaluation of the performance of the SGS cloud schemes, the statistical cloud scheme with the water-ice mixed phase in particular, against satellite data and data from measurements in the surface air layer (e.g. T2m and Td2m);
- Critical assessment of the suitability of the statistical cloud scheme for use in radiation calculations, recommendations towards the use of various SGS cloud schemes within COSMO model.

Work beyond 2012

The priority project UTCS will be completed in September 2012. A detailed scope of work beyond 2012 is difficult to foresee at the moment as it strongly depends on results of the efforts scheduled for 2011-2012. For example, comprehensive testing of the new TKE-Scalar Variance scheme within full-fledged three-dimensional COSMO model depends on the availability of computational resources and may require more time than expected. Hence the operational implementation of the new scheme may occur after the project is formally completed. Furthermore, fine tuning of the new scheme may appear to be needed as the (statistically significant) operational results become available. As to further improvement of turbulence and convection parameterisations for the COSMO model, this is an never-ending task. Future work along this line should be organised within the framework of the COSMO Working Group 3a, e.g. as priority tasks. New priority projects may also be proposed based on the ideas put forward by the COSMO scientists. Those ideas include (i) implementation of a transport equation for the TKE dissipation rate (Veniamin Perov), and (ii) implementation of a canopy/skin layer, implementation of sub-grid scale orography/roughness layer terms into the second-order budget equations using an extended boundary-layer approximation, and a scale separated mass-flux-based treatment of convection that provides volume fractions of convective sub-domains and better accounts for the interaction of convection and turbulence (Matthias Raschendorfer).

References

Abdella, K., and N. McFarlane 1997   A new second-order turbulence closure scheme for the planetary boundary layer. J. Atmos. Sci., 54, 1850-1867.
Abdella, K., and N. McFarlane 1999   Reply. J. Atmos. Sci., 56, 3482-3483.
Abdella, K., and A. C. Petersen 2000   Third-order moment closure through the mass-flux approach. Boundary-Layer Meteorol., 95, 303-318.
Gryanik, V. M., and J. Hartmann 2002   A turbulence closure for the convective boundary layer based on a two-scale mass-flux approach. J. Atmos. Sci., 59, 2729-2744.
Kain, J. S. 2004   The Kain-Fritsch convection parameterization: an update. J. Appl. Meteorol., 43, 170-181.
Kain, J. S., and J. M. Fritsch 1990   A one-dimensional entraining/detraining plume model and its application in convective parameterization. J. Atmos. Sci., 47, 2784-2802.
Kohler, M. 2005   Improved prediction of boundary layer clouds. ECMWF Newsletter, No. 104, 18-22.
Lappen, C.-L., and D. A. Randall 2001   Toward a unified parameterization of the boundary layer and moist convection. Part I: A new type of mass-flux model. J. Atmos. Sci., 58, 2021-2036.
Mironov, D. V. 2001   Pressure-potential-temperature covariance in convection with rotation. Quart. J. Roy. Meteorol. Soc., 127, 89-110.
Mironov, D. V. 2008   Turbulence in the lower troposphere: second-order closure and mass-flux modelling frameworks. Interdisciplinary Aspects of Turbulence, Lect. Notes Phys., 756, W. Hillebrandt and F. Kupka, Eds., Springer-Verlag, Berlin, Heidelberg, 161-221.
Mironov, D. V., V. M. Gryanik, V. N. Lykossov, and S. S. Zilitinkevich 1999   Comments on "A New Second-Order Turbulence Closure Scheme for the Planetary Boundary Layer" by K. Abdella and N. McFarlane. J. Atmos. Sci., 56, 3478-3481.
Mironov, D. V., V. M. Gryanik, C.-H. Moeng, D. J. Olbers, and T. H.Warncke 2000   Vertical turbulence structure and second-moment budgets in convection with rotation: a large-eddy simulation study. Quart. J. Roy. Meteor. Soc., 126, 477-515.
Mironov, D., and C. Jones 2005   Summary of the working group discussion on the representation of convection in high resolution numerical models. Proc. of the HIRLAM/NetFAM Workshop on Convection and Clouds, 24-26 January, 2005, Tartu, Estonia, 113-116. (http://hirlam.fmi.fi/CCWS/Tarturepo_v3.pdf)
Nakanishi, M., and H. Nino 2004   An improved Mellor-Yamada level-3 model with condensations physics: its design and verification. Boundary-Layer Meteorol., 12, 1-31.
Sommeria, G., and J. W. Deardorff 1977   Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci., 34, 344-355.
Pleim, J. E., and J. S. Chang 1992   A nonlocal closure model for vertical mixing in the convective boundary layer. Atmos. Environment., Part A - General Topics, 26, 965-981.
Raschendorfer, M. 1999   Special topic: The new turbulence parameterization of LM. Quarterly Report of the Operational NWP-Models of the Deutscher Wetterdienst, No. 19, 3-12.
Raschendorfer, M. 2001   The new turbulence parameterization of LM. COSMO Newsletter, No. 1, 89-97.
Raschendorfer, M. 2008   Basic conception of a scale separated second order turbulence scheme based on volume averaging including sub grid scale structures of the rigid surface. Unpublished manusript. (A short version of the manuscript is submitted to Acta Geophysica.)
Tiedtke, M. 1988   The Parameterization of Moist Processes. Part 2: Parameterization of Cumulus Convection. Meteorological Training Course, Lecture Series, European Centre for Medium Range Weather Forecasts, Reading, UK, 78 pp.
Tiedtke, M. 1989   A comprehensive mass flux scheme for cumulus parameterization in large-scale models. Mon. Weather Rev., 117, 1779-1800.
Tompkins, A. M. 2002   A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J. Atmos. Sci., 59, 1917-1942.
Tompkins, A. M. 2005   The parameterization of cloud cover. Technical Memorandum, European Centre for Medium-Range Weather Forecasts, Reading, U.K., 23 pp.
Wyngaard, J. C 2004   Toward numerical modeling in the "Terra Incognita". J. Atmos. Sci., 61, 1816-1826.
Zeman, O. 1981   Progress in the modelling of planetary boundary layers. Ann. Rev. Fluid Mech., 13, 253-272.
Zilitinkevich, S. S., V. M. Gryanik, V. N. Lykossov, and D. V. Mironov 1999   Third-order transport and non-local turbulence closures for convective boundary layers. J. Atmos. Sci., 56, 3463-3477.