Presentation on theme: "Governing Equations IV"— Presentation transcript:
1 Governing Equations IV by Nils Wedi (room 007; ext. 2657)Thanks to Anton Beljaars
2 IntroductionNonhydrostatic model NH - IFSPhysics - Dynamics coupling
3 Introduction – A history Resolution increases of the deterministic 10-day medium-range Integrated Forecast System (IFS) over ~25 years at ECMWF:1987: T 106 (~125km)1991: T 213 (~63km)1998: TL319 (~63km)2000: TL511 (~39km)2006: TL799 (~25km)2010: TL1279 (~16km)2015?: TL2047 (~10km)2020-???: (~1-10km) Non-hydrostatic, cloud-permitting, substan- tially different cloud-microphysics and turbulence parametrization, substantially different dynamics-physics interaction ?
4 Ultra-high resolution global IFS simulations TL0799 (~ 25km) >> ,490 points per field/levelTL1279 (~ 16km) >> 2,140,702 points per field/levelTL2047 (~ 10km) >> 5,447,118 points per field/levelTL3999 (~ 5km) >> 20,696,844 points per field/level (world record for spectral model ?!)
5 Max global altitude = 6503mOrography – T1279Alps
6 Max global altitude = 7185mOrography - T3999Alps
7 Computational Cost at TL3999 hydrostatic vs. non-hydrostatic IFS H TL3999NH TL3999
8 Nonhydrostatic IFS (NH-IFS) Bubnova et al. (1995); Benard et al. (2004), Benard et al. (2005), Benard et al. (2009), Wedi and Smolarkiewicz (2009),Wedi et al. (2009)Arpégé/ALADIN/Arome/HIRLAM/ECMWF nonhydrostatic dynamical core, which was developed by Météo-France and their ALADIN partners and later incorporated into the ECMWF model and adopted by HIRLAM.
9 hybrid vertical coordinate Simmons and Burridge (1981)Denotes hydrostatic pressure in the context of a shallow, vertically unbounded planetary atmosphere.Prognostic surface pressure tendency:withcoordinate transformation coefficient
10 Two new prognostic variables in the nonhydrostatic formulation pressure departure’‘vertical divergence’Define also:With residual residualThree-dimensional divergence writes
14 Numerical solution (Benard et al 2004,2005) Advection via a two-time-level semi-Lagrangian numerical technique as before.Semi-implicit procedure with two reference states with respect to gravity and acoustic waves, respectively.The resulting Helmholtz equation is more complicated but can still be solved (subject to some constraints on the vertical discretization) with a direct spectral method as before.(Benard et al 2004,2005)
15 Hierarchy of test cases Acoustic wavesGravity wavesPlanetary wavesConvective motionIdealized dry atmospheric variability and mean statesIdealized moist atmospheric variability and mean statesSeasonal climate, intraseasonal variabilityMedium-range forecast performance at hydrostatic scalesHigh-resolution forecasts at nonhydrostatic scales
20 Physics – Dynamics coupling ‘Physics’, parametrization: “the mathematical procedure describing the statistical effect of subgrid-scale processes on the mean flow expressed in terms of large scale parameters”, processes are typically: vertical diffusion, orography, cloud processes, convection, radiation‘Dynamics’: “computation of all the other terms of the Navier- Stokes equations (eg. in IFS: semi-Lagrangian advection)”The ‘Physics’ in IFS is currently formulated inherently hydrostatic, because the parametrizations are formulated as independent vertical columns on given pressure levels and pressure is NOT changed directly as a result of sub-gridscale interactions !The boundaries between ‘Physics’ and ‘Dynamics’ are “a moving target” …