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Further development of a model for a broad range of spatial and temporal scales Zavisa Janjic

Further development of a model for a broad range of spatial and temporal scales Zavisa Janjic. NMM-B Dynamical Core. Nonhydrostatic Multiscale Model on B grid (N M M-B) Further evolution of WRF NMM (Nonhydrostatic Mesoscale Model)

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Further development of a model for a broad range of spatial and temporal scales Zavisa Janjic

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  1. Further development of a model for a broad range of spatial and temporal scalesZavisa Janjic

  2. NMM-B Dynamical Core • Nonhydrostatic MultiscaleModel on B grid (NMM-B) • Further evolution of WRF NMM (Nonhydrostatic Mesoscale Model) • Intended forwide range of spatial and temporal scales, from meso to global, and from weather to climate • Evolutionary approach,built on NWP and regional climate study experience by relaxing hydrostatic approximation(instead of extending cloud models to large scales; Janjic et al., 2001, MWR; Janjic, 2003, MAP) • Applicability of the model extended to nonhydrostatic motions • Favorable features of the hydrostatic formulation preserved • The nonhydrostatic option as an add–on nonhydrostatic module • Reduced cost at lower resolutions • Easy comparison of hydrostatic and nonhydrostatic solutions • Pressure based vertical coordinate • Nondivergent flow on coordinate surfaces (often forgotten) • No problems with weak static stability on meso scales

  3. NMM-B Dynamical Core • Conservation of important properties of continuous system(Arakawa, 1966, 1972, …; Janjic, 1977, …; Sadourny, 1968, … ; … aka “mimetic” approach in Comp. Math) • Nonlinear energy cascade controlled through energy and enstrophy conservation • “Finite volume” • A number of first order and quadratic quantities conserved • A number of properties of differential operators preserved • Omega-alpha term, consistent transformations between KE and PE • Errors associated with representation of orography minimized

  4. NMM-B Dynamical Core • Coordinate system and grid • Global lat-lon, regular grid • Regional rotated lat-lon, more uniform grid size • Arakawa B grid (in contrast to the WRF-NMM E grid) h h h vv h h h vv h h h • Pressure-sigma hybrid(Sangster 1960; Arakawa and Lamb 1977; Simmons and Burridge 1981) • Flat coordinate surfaces at high altitudes where sigma problems worst (e.g. Simmons and Burridge, 1981) • Higher vertical resolution over elevated terrain • No discontinuities and internal boundary conditions • Lorenz vertical grid

  5. NMM-B Dynamical Core • Polar filter configuration • “Decelerator” • Tendenciesof T, u, v, Eulerian tracers, divergence, dw/dt, deformation • Physics not filtered • Polar filter formulation • Waves in the zonal direction faster than waves with the same wavelength in the latitudinal direction slowed down • Filter response function quasi 1-2-1 (on filtered part of spectrum) • Time stepping explicit, except for vertical advection and vertically propagating sound waves • NCEP’s WRF NMM “standard” physical package (more options will be available)

  6. Recent upgrades • Recent upgrades • New hybrid vertical coordinate • New Eulerian tracer advection scheme • Gravity wave drag (Kim & Arakawa 1995; Lott & Miller 1997; Alpert, 2004) • RRTM radiation (Mlawer et al. 1997, implemented by Carlos Perez, BSC)

  7. Vertical coordinate PD TOP • Hybrid vertical coordinate (Sangster 1960; Arakawa and Lamb 1977; “SAL”) Inhomogeneity of vertical resolution over high topography at pressure-sigma transition point as sigma layers shrink over high topography. May be a problem with some NCEP models. Pressure range Sigma range

  8. Vertical coordinate • Simmons and Burridge (1981) style pressure-sigma mix (“SB”) for consistency with global data assimilation • A modification of Eckerman (2008) algorithm for generating the coordinate (preferred) with: • Increased resolution at bottom, tropopause and top • Transition point between pressure and sigma-pressure mix around 300 mb (globally) • Transition to pressure point below tropopause • The NCEP GFS vertical coordinate (Iredell) • Sigma pressure transition point at 60 mb

  9. ps=1000 mb ps=750 mb Cumulative distribution of topography height in global NMM-B in 100 m bins ps=500 mb Example: Thicknesses of the NMM B 64 layers, ptop=0, transition at 300 mb

  10. Vertical coordinate … • 5 day hemispheric sample forecasts with different vertical coordinates • 0.3333 deg meridionally (37 km), 64 levels resolution, comparable to operational GFS resolution • ECMWF forecasts, latest available ECMWF forecasts as verification for sanity check

  11. +120 +120 +120 NMMB NMMB SB NMMB SAL GFS +120 +72 SB -- NMMB, Simmons & Burridge-NRL, NMM, 300 mb SAL -- NMMB, Sangster-Arakawa-Lamb, NMM, 300 mb GFS -- NMMB, SB-Iredell, 70 mb, 1 mb ptop ECMWF ECMWF

  12. +120 +120 +120 NMMB NMMB SB NMMB SAL GFS +120 +72 SB -- NMMB, Simmons & Burridge-NRL, NMM, 300 mb SAL -- NMMB, Sangster-Arakawa-Lamb, NMM, 300 mb GFS -- NMMB, SB-Iredell, 70 mb, 1 mb ptop ECMWF ECMWF

  13. Eulerian tracer advection scheme • Transport of “passive” scalars • Conservative (for cyclic boundary conditions, closed domain or rigid wall boundary conditions in combination with continuity Eq.) • Positive definite • Monotone • Affordable • Lagrangian ? • Strict conservation • Open boundary conditions • Eulerian ? • Positive definitness • Monotonicity

  14. Eulerian tracer advection scheme • Eulerian alternative • Conservation through flux cancelations, not forced a posteriori • Quadratic conservative advection scheme coupled with continuity Eq • Crank-Nicholson for vertical advection • Modified Adams-Bashforth for horizontal advection • Advection of square roots of tracers (c.f. Schneider, MWR 1984) provides positive definitness • Quadratic conservation provides tracer mass conservation • Monotonization with a posteriori forcedconservation to correct oversteepening

  15. Eulerian tracer advection scheme • Implemented and tested in • PC version of NMM-B • Global and regional NMM-B • Performance • Satisfactory mass conservation considering other uncertainties • Satisfactory shape and extremes preservation • Cost • Faster than the Lagrangian scheme per time step, BUT • Overall slower than the Lagrangian scheme due to shorter advection step • Stable with longer time steps (2 times), appears safe for standard model tracers

  16. Courtesy Youhua Tang Boundary reached New Eulerian Old Lagrangian

  17. Eulerian tracer advection scheme • PC NMM-B runs • Global domain • 1.4 x 1.0 deg, 32 levels • Polar filtering of advection tendencies • Initial cuboid throughout the atmosphere • Winter case (strong wind)

  18. 2.5 days 5 days 7.5 days 15 days

  19. No monotonization 1-2% initial drop Monotonization 15 days

  20. Courtesy: Barcelona Supercomputing Center (BSC) Designated center within WMO Sand and Dust Storm Warning Advisory and Assessment System (SDS-WAS)

  21. Gravity Wave Drag ACC exceeds 0.60 at day 7 and 8 • Example of large impact of GWD (Kim & Arakawa 1995; Lott & Miller 1997; Alpert, 2004) • Cycle 2009021812 (randomly chosen) • Anomaly Correlation Coefficient, 500 mb, Northern Hemisphere Day 1 2 3 4 5 6 7 8 No GWD 0.995 0.985 0.960 0.924 0.836 0.674 0.517 0.469 GWD 0.996 0.987 0.962 0.929 0.866 0.772 0.689 0.608

  22. NEW RRTM radiation code within NMM-B, Courtesy Carlos Perez Randomly chosen cycle 20090318_12UTC Global AC GLOBAL

  23. Conclusions and plans • Unified model for a wide range of spatial and temporal scales being developed as an extension of the WRF NMM • Evolutionary approach, model built on NWP and regional climate simulation experience, grid point, explicit • Upgraded vertical hybrid coordinate definition • Eulerian positive definite and monotone tracer advection • Positive impact of GWD and upgraded radiation parameterizations • Promising performance, competitive in mini parallels • Experimentation to improve radiation-cloud interaction (Perez, BSC, Vasic) • Work on improved global initial conditions (from GFS spectral coefficients) (Sela, Vasic, Janjic) • Regional version planned to replace the WRF NMM as the regional forecasting model for North America (NAM) in 2010 within NEMS

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