1. Convection mini-workshop, Hamburg, July 14, 2004 Parameterization of convection Andreas Chlond Department Climate Processes *Thanks to F. Nober, P. Bechthold, A. Tompkins and the ECMWF

2. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Outline Introduction  Why do we have to parameterize?  What is a parameterization? How to parameterize?  Classical approach  Super-parameterization  Parameterization of intermediate complexity

3. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Why do we have to parameterize? Climate und regional models predict coarse grained, large-scale variables Small scales processes are not resolved by large- scale models, because they are sub-grid scale The effect of the the sub-grid processes on the large-scale has to be presented statistically The procedure of expressing the effect of sub-grid processes is called a parameterization  Turbulence, convection, clouds, radiation etc.

4. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection What is a parameterization? The statistical contribution of sub-grid processes must, therefore, be expressed in terms of the large-scale parameters themselves. The mathematical procedure involved is generally called a parameterization. SUBROUTINE vdiff (kidia,kfdia,klon,klp2,ktdia,klev,klev, & & paclcm,paphm1,papm1,pgeom1,pum1,pvm1,pxm1) ! Description: !-- Computation of the exchange coefficients IMPLICIT NONE ! Scalar arguments with intent(In): INTEGER, INTENT (IN) :: kfdia, kidia, klev, klevm1, klevp1,& & klp2, ktdia, ktrac DO jl = kidia, kfdia zdu2 = MAX(zepdu2,pum1(jl,klev)**2+pvm1(jl,klev)**2) zqmitte = (pqm1(jl,klev)+zqs(jl)*zhsoil(jl))/2. zmult4 = zfux*zmult5 - 1. zcons = zcons12*paphm1(jl,klevp1)/(ptm1(jl,klev)* & & (1.+vtmpc1*pqm1(jl,klev)-pxm1(jl,klev))) END DO From Nature To its Representation

5. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection What is convection doing? Convection is of crucial importance for the global energy and water balance (Convection transports heat, water vapor, momentum … and chemical constituents upwards …. Water vapor then condenses and falls out -> net convective heating/dryingConvection transports heat Convection generates and/or influences a number of phenomena important to forecasting (thunderstorms, heavy precipitation, hurricanes) An important parameter for the strength of convection is CAPE Convection affects the atmosphere through condensation / evaporation and eddy transports

6. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Convection parameterization – How? Conventional approach: Start from first principles and write down exact equations for the process under consideration Close equations (Closure problem)  Introduce additional (empirical) information  Calibrate constants (observations, PRMs)

7. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Task of convection parametrisation(1) total Q1 and Q2 To calculate the collective effects of an ensemble of convective clouds in a model column as a function of grid-scale variables Recall: these effects are represented by Q 1 -Q R, Q 2 and Q 3 Hence: parametrization needs to describe CONVECTIVE CONTRIBUTIONS to Q1/Q2: condensation/evaporation and transport terms and their vertical distribution.

8. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Task of convection parametrisation (2): in practice this means : Determine vertical distribution of heating, moistening and momentum changes Cloud model Determine the overall amount of the energy conversion, convective precipitation=heat release Closure Determine occurrence/localisation of convection Trigger

9. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Types of convection schemes Schemes based on moisture budgets –Kuo, 1965, 1974, J. Atmos. Sci. Adjustment schemes –moist convective adjustement, Manabe, 1965, Mon. Wea. Rev. –penetrative adjustment scheme, Betts and Miller, 1986, Quart. J. Roy. Met. Soc., Betts-Miller-Janic Mass-flux schemes (bulk+spectral) –entraining plume - spectral model, Arakawa and Schubert, 1974, J. Atmos. Sci. –Entraining/detraining plume - bulk model, e.g., Bougeault, 1985, Mon. Wea. Rev., Tiedtke, 1989, Mon. Wea. Rev., Gregory and Rowntree, 1990, Mon. Wea. Rev., Kain and Fritsch, 1990, J. Atmos. Sci., Donner, 1993, J. Atmos. Sci., Bechtold et al 2001, Quart. J. Roy. Met. Soc. –episodic mixing, Emanuel, 1991, J. Atmos. Sci.

10. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection The “Kuo” scheme Closure: Convective activity is linked to large-scale moisture convergence Main problem: here convection is assumed to consume water and not energy

11. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Adjustment schemes e.g. Betts and Miller, 1986, QJRMS : When atmosphere is unstable to parcel lifted from PBL and there is a deep moist layer - adjust state back to reference profile over some time-scale, i.e., T ref is constructed from moist adiabat from cloud base but no universal reference profiles for q exist. However, scheme is robust and produces “smooth” fields.

12. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection The bulk mass-flux approach Aim: Look for a simple expression of the eddy transport term Condensation term Eddy transport term

13. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection The bulk mass-flux approach: Cloud – Environment decomposition Total Area: A Cumulus area: a Fractional coverage with cumulus elements: Define area average:

14. The bulk mass-flux approach Simplifications : Neglect subplume correlations The small area approximation: Define convective mass-flux: Then:

15. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection The bulk mass-flux approach With the above we can rewrite: To predict the influence of convection on the large-scale with this approach we now need to describe the convective mass-flux, the values of the thermodynamic (and momentum) variables inside the convective elements and the condensation/evaporation term. This requires, as usual, a cloud model and a closure to determine the absolute (scaled) value of the mass-flux.

16. A bulk mass flux scheme: What needs to be considered Entrainment/Detrainment Downdraughts Link to cloud parameterization Cloud base mass flux - Closure Type of convection shallow/deep Where does convection occur Generation and fallout of precipitation

17. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Outline Introduction  Why do we have to parameterize?  What is a parameterization? How to parameterize?  Classical approach  Super-parameterization  Parameterization of intermediate complexity

18. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Convection parameterization – How? Run a 2D CSRM as a “super-parameterization” in a GCM This idea was first suggested by W. Grabowski of NCAR Super- Parameterization:

19. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Grabowski’s approach

20. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection What do we get? Explicit deep convection Explicit fractional cloudiness Explicit cloud overlap and possible 3d cloud effects Convectively generated gravity waves But A GCM using a super-parameterization is three orders of magnitude more expensive than a GCM that uses conventional parameterizations. On the other hand super- parameterizations provide a way to utilize more processors for a given GCM resolution

21. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Outline Introduction  Why do we have to parameterize?  What is a parameterization? How to parameterize?  Classical approach  Super-parameterization  Parameterization of intermediate complexity

22. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection An ensemble of potentially different clouds has to be described by ONE AVERAGED cloud. Dynamical and microphysical details are not represented Due to the mass-flux approach the information about cloud cover and vertical velocity is not available. Problems with mass-flux schemes Convection parameterization – How? Parameterization of intermediate complexity: The ensemble approach

23. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection LES vs. SCM: Diurnal variation of cloud cover (ARM case)

24. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Cumulus-Prey-Predator Model (1) Philosophy (adapted from population dynamics): Different possible clouds correspond to different species. These species are in competition for an external food supply. In case of clouds this food is given by CAPE (Convective Available Potential Energy)

25. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection 1 2 K_22 K_12 K_21 F_1 F_2 K_11

26. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Cumulus-Prey- Predator Model (2) Mathematical: Search for the cloud ensemble (consisting of the possible clouds) that is most effective in consuming CAPE. The solution of the Lotka – Volterra – Equation does it! The interaction between the different cloud types and the clouds and the non-convective processes is determined by the energetic of the system. Cloud – Field – Model

27. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection ECHAM GCM Input data: vertical profiles of temperature and humidity Cloud – Field - Model Cloud Model Calculation of interaction coefficients Cloud Spectrum Output data: heating rates transport, precipitation

28. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Comparison: Cloud – Field – Model, LES and ECHAM5 (1)

29. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Comparison: Cloud – Field – Model, LES and ECHAM5 (1)

30. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection We should discuss and must decide … Classical approach  Simple, but to take conventional approach much beyond were we are now, it seems likely that we will have to make the parameterizations very complicated Super-Parameterization  More expensive, but SPs can use thousands of processors with good computational efficiency. Parameterization of intermediate complexity  Good compromise

31. Convection mini-workshop, Hamburg, July 14, 2004 Andreas Chlond: Parameterization of convection Heating Rates ECHAM (zonal mean, DJF) (K/day) ConvectionStratiform Clouds Vertical DiffusionRadiation