Zbigniew Piotrowski1), Bogdan Rosa, Damian Wójcik,

Michał Ziemiański

Institute of Meteorology and Water Management – National Research Institute

1)Zbigniew.Piotrowski@imgw.pl

Towards soundproof dynamical core for COSMO model – high resolution weather prediction for the Alps

COSMO-EULAG development at the Polish hydrological and meteorological service (IMGW-PIB)

Activities started in 2009 within the „Conservative Dynamical Core”priority project of COSMO consortium(http://www.cosmo-model.org/content/tasks/pastProjects/cdc/default.htm)

Goal of the project was ``to get a dynamical core with some explicit conservation properties, the most important one being mass conservation. This should be achieved with no reduction of accuracy or efficiency. A further goal (probably connected with the former) is to improve the capability of the model to work in steep terrain.''

Within the project, IMGW with the help of MeteoSwiss and DWD took the task „... to demonstrate that the EULAG itself, and the basic ideas defining the EULAG construction, can be used as a robust and credible base for construction of future operational weather models, and especially the COSMO model.”

COSMO-EULAG operationalization (CELO) – the new priority project of COSMO for 2012-2016

After a successful accomplishment of a series of idealized and semi-realistic Alpine flow tests performed with EULAG model, see topical issue of Acta Geophysica „Modeling Atmospheric Circulations with Sound-Proof Equations”, COSMO consortium approved new priority project CELO with aim „To deliver fully operational weather prediction package” with anelastic dynamical core, without data assimilation in the scope of this project.

Current efforts concentrate on: - full integration of EULAG dynamical core (DC) with COSMO framework - consolidation and optimization of the DC forumulation, in particular proper link to parameterizations and the soil model - testcases focusing on examination of a series of meteorological scenarios with 2.2 km, 1.1 km, 0.55 km and 0.27 km horizontal resolution

Two fundamental algorithms: MPDATA advection + GCRK pressure solverTwo optional modes for integrating fluid PDEs:• Eulerian - control-volume and Lagrangian - trajectory wise integral

Optional fluid equations (nonhydrostatic):• Anelastic• Compressible/incompressible Boussinesq• Incompressible Euler/Navier-Stokes’• Fully compressible, explicit or (prototype) semi-implicit• Anelastic MHD (unique ability to reproduce MHD solar cycles !)• Anelastic for fully unstructured grid formulation

Available strategies for simulating turbulent dynamics:• Direct numerical simulation (DNS)• Large-eddy simulation, explicit and implicit (LES, ILES)Portfolio of applications from microturbulence to orographic flows (e.g Rotunno et al, 1999), evolution of sand dunes (Ortiz et al. 2009) to stellar.

EULAG model for multiscale flows

Numerical design

⇒ system implicit with respect to all dependent variables.

On grids co-located with respect to all prognostic variables, it can be inverted algebraically to produce an elliptic equation for pressure

solenoidal velocity contravariant velocity

subject to the integrability conditionBoundary conditions on

Boundary value problem is solved using nonsymmetric Krylov subspace solver - a preconditioned generalized conjugate residual GCR(k) algorithm

(Smolarkiewicz and Margolin, 1994; Smolarkiewicz et al., 2004)

Imposed on

All principal forcings are assumed to be unknown at n+1

Smolarkiewicz et al., J. Comput. Phys. 227 (2007), 'Building resolving large-eddy simulations and comparison with wind tunnel experiments'

Current state of COSMO-EULAG dynamical core

We run prototype COSMO with anelastic dynamical core on MeteoSwiss 2.2 km/1.1 km operational domain with limited set of parameterizations of COSMO (currently no tuning of parametrizations to EULAG)

We compare against Runge-Kutta dynamical core with same range of parameterizations and with the results of operational MeteoSwiss forecast

We achieve good results given the stage of the project

COSMO – EULAG is stable and robust, the results are rich in detail due to small effective diffusion (stability of the model does not depend on any numerical filtering or explicit diffusion)

ESTS

Case study: role of shallow convection

parameterization

Computational domain :• (WE x NS) = (520 x 350) / (1014 x 678) / (806 x 806) (2.2km ) / (1.1km ) / (0.55km) • standard operational COSMO-2 model of Meteo-Swiss vertical distribution of levels (61),

Gal-Chen coordinate system with top at 23588.50m, • Lateral absorber width = 45km / 23km / 11.0km• Top sponge base height = 15km

Model setup

1.1km2.2km

0.55km

10th SRNWP Workshop, Offenbach/Main, 14 May 2013

Dynamics :• Saturation adjustment is on• Numerical diffusion turned off „on” for Runge-Kutta• Semi-Lagrangian advection of moist quantities

Microphysics :• Standard COSMO microphysics parameterization including ice, rain, snow and graupel

precipitation

Radiation :• Calculated every 15 minutes (2.2km) or 6 minutes (1.1km and 0.55km) of simulation Other parameterizations :• Vertical turbulence model with surface layer fluxes• Standard COSMO surface model

Orography:• Operational Meteo-Swiss for 2.2 km, recalculated from SRTM for 1.1 and 0.55 km• standard Cosmo orography filtering was applied

Initial and boundary data for all simulations are interpolated from COSMO – 7 forecast of MeteoSwiss.

Model setup

10th SRNWP Workshop, Offenbach/Main, 14 May 2013

Synoptic map for 27.07.2012 Synoptic map for 28.07.2012

Test case

• Surface weak and shallow low-pressure system• Some (rather weak) upper-air forcing

10:00 UTC 14:00 UTC

16:00 UTC 18:00 UTC

Test case : MSG High Resolution Visible (HRV) channel

ESTS

Spatial structure of convectionComparision of Runge-Kutta and

EULAG dynamical cores with and without shallow convection

parameterization

Cloud radiance (high res.) 14:00 UTC

CE 2.2km SCP on CE 2.2km SCP off

MSG infrared band

RK eq. 2.2km SCP on RK eq. 2.2km SCP off

Cloud radiance (high res.) 14:00 UTC

MSG infrared band

CE 1.1km SCP on CE 1.1km SCP off

CE 0.5km SCP off

CE 0.5km SCP on

Summary : convective cloud pattern

●Qualitatively, while the SCP have minor impact on RK 2.2 km spatial pattern of convective clouds, it significantly influences the pattern of the CE convective clouds, for all resolutions tested (from 2.2 to 0.55 km)

●In CE, the forecasts without SCP result in less extensive spread of convective clusters which is also more in agreement with observations, for the analyzed case

●In CE with SCP, the spatial pattern of convective clouds is similar across tested resolutions, during the day

●In CE without SCP, the spatial pattern of convective clouds is similar across resolutions for early stages of the convection, for later stages the pattern differs between resolutions

Conclusions and remarks

EULAG dynamical core was tested within COSMO framework for stable and convective NWP scenarios over the Alps for 2.2 km, 1.1 km and 0.55 km resolutions, with good results,

Current coupling is simplistic (first order contributions from physics and diffusion of COSMO parameterizations and diffusion operator)

Full integration with COSMO framework in progress, systematic quantitative assessment of results is expected

'PantaRhei' project at ECMWF investigates the possibilitiesof coupling or merging EULAG numerics with IFS for futurenon-hydrostatic weather prediction

Selected challenges of merging COSMO and EULAG

Standarizing treatment of boundary conditions

Merging EULAG A-grid approach with default COSMO C-grid

Making good use of the lowest model level at the surface (0 m) in the EULAG core

Changing focus from multi to single (or limited) application – code structure, performance, etc.

Accurately coupling to COSMO physics packages

Allowing for the accurate formulation of generalized vertical coordinate

• Multidimensional positive definite advection transport algorithm (MPDATA).

Starts with iteration of upwind scheme, then applies nonlinear corrective iterations of upwind with negative diffusion

1. MOTIVATION Computation of the inverse metric coefficients

Equations are derived based on the assumption that 16 differential identities:

are satisfied. For the transformation at hand:

we are left with 10 nontrivial identities:

computational space(ordered like Cartesian grid)

x,y,z – physical coordinates, here in lat-lon-z for EULAG DC

1. MOTIVATION Metric term formulations – impact on cloud area fraction

Standard formulation of EULAG DC with hard-coded Gal-Chen coordinate transform.

New metric terms definitionindependent of Gal-Chen coordinate transform,

Default COSMO metric term formulation