ECMWF Governing Equations 4 Slide 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: T L 319 (~63km) 2000: T L 511 (~39km) 2006: T L 799 (~25km) 2010: T L 1279 (~16km) 2015?: T L 2047 (~10km) 2020-???: (~1-10km) Non-hydrostatic, cloud-permitting, substan- tially different cloud-microphysics and turbulence parametrization, substantially different dynamics-physics interaction ?
ECMWF Governing Equations 4 Slide 4 Ultra-high resolution global IFS simulations T L 0799 (~ 25km) >> 843,490 points per field/level T L 1279 (~ 16km) >> 2,140,702 points per field/level T L 2047 (~ 10km) >> 5,447,118 points per field/level T L 3999 (~ 5km) >> 20,696,844 points per field/level (world record for spectral model ?!)
ECMWF Governing Equations 4 Slide 5 Orography – T1279 Max global altitude = 6503m Alps
ECMWF Governing Equations 4 Slide 6 Orography - T3999 Alps Max global altitude = 7185m
ECMWF Governing Equations 4 Slide 7 H T L 3999 NH T L 3999 Computational Cost at T L 3999 hydrostatic vs. non-hydrostatic IFS
ECMWF Governing Equations 4 Slide 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.
ECMWF Governing Equations 4 Slide 9 Vertical coordinate with coordinate transformation coefficient hybrid vertical coordinate Simmons and Burridge (1981) Prognostic surface pressure tendency: Denotes hydrostatic pressure in the context of a shallow, vertically unbounded planetary atmosphere.
ECMWF Governing Equations 4 Slide 10 Two new prognostic variables in the nonhydrostatic formulation Nonhydrostatic pressure departure vertical divergence Three-dimensional divergence writes With residual residual Define also:
ECMWF Governing Equations 4 Slide 14 Numerical solution 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)
ECMWF Governing Equations 4 Slide 15 Hierarchy of test cases Acoustic waves Gravity waves Planetary waves Convective motion Idealized dry atmospheric variability and mean states Idealized moist atmospheric variability and mean states Seasonal climate, intraseasonal variability Medium-range forecast performance at hydrostatic scales High-resolution forecasts at nonhydrostatic scales
ECMWF Governing Equations 4 Slide 19 Scores T L 1279 L91 ~ 16 km NH H
ECMWF Governing Equations 4 Slide 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 …