HYMACS: A HYbrid and non-local MAss-flux Convection Scheme for non-hydrostatic NWP modelsVolker Kuell

1, Almut Gassmann

2, Andreas Bott

1

1Meteorological Institute, University of Bonn, Germany;

2Max Planck Institute for Meteorology, Hamburg, Germany; email: vkuell@uni-bonn.de

1) IntroductionConvection can redistribute significant amounts of moisture, heat and mass on small temporal and spatialscales. Furthermore convection can cause severe precipitation events and is thus of major interest fornumerical weather prediction (NWP). As a subgrid scale phenomenon convection usually has to be para-meterised in NWP models.

3) Convection scheme

2) Hosting modelAs the hosting model for our convection parameterisation scheme we use the COSMO-LM model, whichis part of the operational weather forecast model chain of the German Meteorological Service (DWD)(Steppeler et al., 2003). We use the model version 3.19 with a grid size of about 7 km, 40 s timestepand 10 min convective update interval. However, the algorithms of HYMACS are suitable for any othernon-hydrostatic model. It delivers convective tendencies of temperature, total density and specificmoisture components which can easily be converted to other prognostic variables.

poster.objposposter.obj

Classical mass flux convection schemes assume grid box sizes much larger than the scale of convectivecirculation. Thus, the convective mass transport is confined in the local grid column and no net masstransport occurs on the grid scale. In contemporary NWP models with high horizontal resolutions, whereconvection becomes partially resolved, this approach leads to a conceptual problem. To overcome this,we propose a hybrid mass flux convection scheme (HYMACS) in which only the small scale convectiveupdraught and downdraught are parameterised, whereas the environmental subsidence is determinedby the grid scale equations. Therefore, HYMACS produces a net convective mass flux exerting pressuregradient forces to the grid scale model.

Flux divergences of heat and moisture components are treated analogously.

References:Bechtold, P., E. Bazile, F. Guichard, P. Mascard, and E. Richard, 2001: A mass flux convection scheme for regional and global models. Q. J. R. Meteorol. Soc., 127, 869-886.Fritsch, J. M., and C. F. Chappell, 1980: Numerical prediction of convectively driven mesoscale pressure systems. Part I: Convective parameterizations. J. Atmos. Sci., 37, 1722-1733Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: The Kain-Fritsch scheme. Meteorol. Monographs, 24, 165-170Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large scale models. Mon. Weather Rev., 117, 1779-1800Weisman, M. L., and J. B. Klemp, 1982: The dependence of numerically simulated convective storms on vertical wind shear and buoyancy. Mon. Weather Rev., 110, 504-520Weisman, M. L., and R. Rotunno, 2004: "A theory for strong long-lived squall lines" revisited. J. Atmos. Sci., 61, 361-382.Steppeler, J., G. Doms, U. Schättler, H.W. Bitzer, A. Gassmann, U. Damrath, and G. Gregoric, 2003: Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteorol. Atmos. Phys., 82, 75-96.

4) Idealised cases

5) Real cases

7) Conclusions

Acknowledgements:

6) Outlook: gust fronts

For intercomparison purposes the COSMO-LM 3.19 has been run with the HYMACS and Tiedtke scheme (Tiedtke, 1989), which is also used inthe operational version, and the Kain-Fritsch scheme (Kain and Fritsch, 1993). We present case studies for a) 5.7.2006 and b) 28.6.2006. After theinitialisation with DWD analyses (at 6:00 GMT for each case) a free model run follows with hourly input of lateral boundary data only (also fromDWD analyses). In each case the total model domain covers the area from south-western France (~0°E, 44°N) to the mid Baltic Sea (~18°E, 56°N)with 200x200 grid points and 35 model layers. The maps only show the part of the model domain situated over Germany.

Figure 4: Case a): Radar reflectivity data from DWD radar network and convective precipitation rates from COSMO-LM simulations with threedifferent convection schemes. (Here, over Germany there is practically no grid scale precipitation.) The maps show the situation at 14:00 GMT,when a convergence line passes over Germany.

Gust fronts generated by the outflow of downdraught cold pools are important for theinitialisation of secondary convective cells and interaction and self-organistation of con-vective cells. In classical approaches the convective temperature tendencies are addedto the environmental temperature at each timestep, i.e. the cold downdraught air isalways mixed with the environment and thus cannot form a realistic grid scale cold pool.In our scheme the cold pool and gust front will be treated as subgrid scale phenomenaand will be parameterised utilising the properties of the downdraught.

c2 uc1u

Tenvv - T

downv = ?

wind shear ? T

envv - T

downv = ?

wind shear ?

Tdownv

Mdown

Figure 5: As Figure 4, but for case b). The maps show the situation at 12:00 GMT with a warm and moist airmass over southern Germany anda colder and drier airmass over northern Germany. (Here, over Germany the grid scale precipitation is mainly below 0.5 mm/h.)

Figure 7: The cold pool is para-meterised by means of the massflux and virtual temperature ofthe downdraught. The directionof the gust front propagation canbe determined from the minimumvirtual temperature differencebetween the cold pool and theneighbouring grid boxes and theoptimal wind shear criterion ∆u~cby Weisman and Rotunno (2004).Cold pool strength and gust frontpropagation direction can be con-verted to a "trigger bonus" for theneighbouring grid boxes.

Subgrid mass transport: We follow a suggestion by Kain and Fritsch (1993) "... to solve for thecompensating environmental motions on the resolvable scale by including convective masssource and sink terms in a resolvable scale continuity equation." Besides the grid scale massflux we introduce a subgrid scale convective mass flux Jm, conv parameterised by the up- and

downdraught mass fluxes Mu and Md (ρ and v are the grid scale total density and velocity).

Cloud model: The cloud model describes the thermodynamics in the cloud, the relative fluxes ofmass, heat, moisture components, and precipitation. In the updraught, a mixed liquid/ice phaseis included. A number of details have been adopted from the scheme by Bechtold et al. (2001).Entrainment and detrainment rates are parameterised following Tiedtke (1989).

Trigger function: The trigger function determines where and when convection is started. It hasbeen adopted from the scheme of Fritsch and Chappell (1980) which derives a virtual tempera-ture increment from the grid scale vertical velocity.

Closure assumption: This determines the total amount of mass to be transported in the convectivecell. We have chosen a horizontal mass flux convergence closure which converts the grid scalehorizontal mass flux convergence into a subgrid scale updraught. Together with the trigger fromFritsch and Chappell (1980) this effectively suppresses the undesirable grid scale convection.

Figure 2: Grid scale wind direction (arrows) and horizontal wind velocity in m/s(color code) for the dry (a) and moist (b) experiment after 30 min of convection.The entrainment and detrainment regions are marked by black rectangles. Inthe dry experiment only mass (no heat) is transported, i.e. the temperature ofthe detrained air is set equal to the environmental temperature. In the moistexperiment full thermodynamics is considered in the updraught.

Figure 3: Temporal development of the grid scalevertical wind (in m/s) in the convectively active gridcolumn of the dry idealised experiment (cf. Figure 2a).After the start (0 h) and end of convection (1 h) gravitywaves are radiated which accomplish the hydrostaticadjustment.

In idealised experiments with a) a dry stable atmosphere and with b) a moist conditionally unstable atmosphere (temperature and moistureprofiles from Weisman and Klemp, 1982) a single convective grid column in the centre of the model domain is triggered. The massflux cor-responds to a turnover time of 1h for a 60 hPa thick source layer.

low grid resolution medium grid resolution high grid resolution ∆x > 20...50 km ∆x = 1...50 km ∆x << 1 km convection=subgrid scale convection partially resolvable convection=grid scaleuse classical convection scheme use hybrid convection scheme explicit modelling of convection

Figure 1: grid resolution and treatment of convection in a numerical model

Real cases continued...

Figure 6: Temporal development of the precipitation rates in the real case simulationsa) (left) and b) (right). Shown are total (solid lines) and convective precipitation rates(dotted lines) from the simulations with the HYMACS (red), Tiedtke (green) and Kain-Fritsch scheme (blue) averaged over the whole model domain.

HYMACSTiedtkeKain-Fritsch

Prtot

Prconv

HYMACSTiedtkeKain-Fritsch

Prtot

Prconv

The authors thank the German Meteorological Service (DWD) for providing theCOSMO-LM as a hosting model for the new hybrid convection scheme and for pro-viding radar reflectivity data from the DWD radar network. This work is funded bythe Deutsche Forschungsgemeinschaft (DFG) within the scope of the Schwerpunkt-programm 1167 "Quantitative Niederschlagsvorhersage" under grant Bo998/7-2.

The new hybrid parameterisation scheme HYMACS overcomes the conceptionalproblem into which classical schemes in highly resolved hosting models run,when convection becomes partially resolvable. In contrast to the classicalschemes, which only pass convective temperature/moisture tendencies to thehosting model (thermodynamic feedback), HYMACS also produces convectivedensity (or pressure) tendencies due to its subgrid scale vertical mass transport(dynamic feedback). These feedbacks together generate the dynamics (e.g. gridscale winds and gravity waves) necessary for the hydrostatic adjustment afterconvective excitation of the atmosphere as demonstrated by means of idealisedcases. In real case simulations HYMACS produces precipitation amounts similarto the classical schemes. The maximum of the diurnal variation is shifted to (morerealistic) later local times compared to the Tiedtke scheme. Spatial precipitationpatterns appear more organised and clustered which is due to the stronger inter-action between the convective cells. In contrast to the Tiedtke and Kain-Fritschscheme, HYMACS well reproduces both frontal and non-frontal convection asshown in two case studies. The self-organisation of convective cells is planned tobe further enhanced by means of a gust front parameterisation.

tJm, conv( v)

∆x2

Mu Md

z

ρ∂∂

∂+

∆

ρ +

∆

= 0 with Jm, conv

∆

=1

∂ z

∂∂

+

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