1. Zavisa Janjic, Omaha 2009 1 Further development of a model for a broad range of spatial and temporal scales Zavisa Janjic

2. Zavisa Janjic, Omaha 2009 2 NMM-B Dynamical Core Nonhydrostatic Multiscale Model on B grid (NMM-B) Further evolution of WRF NMM (Nonhydrostatic Mesoscale Model) Intended for wide 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. Zavisa Janjic, Omaha 2009 3 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 NMM-B Dynamical Core

4. Zavisa Janjic, Omaha 2009 4 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 v v 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 NMM-B Dynamical Core

5. Zavisa Janjic, Omaha 2009 5 Polar filter configuration “Decelerator” Tendencies of 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) NMM-B Dynamical Core

6. Zavisa Janjic, Omaha 2009 6 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. Zavisa Janjic, Omaha 2009 7 Vertical coordinate 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 TOP PD

8. Zavisa Janjic, Omaha 2009 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. Zavisa Janjic, Omaha 2009 9 Cumulative distribution of topography height in global NMM-B in 100 m bins p s =1000 mbp s =750 mb p s =500 mb Example: Thicknesses of the NMM B 64 layers, ptop=0, transition at 300 mb

10. Zavisa Janjic, Omaha 2009 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. Zavisa Janjic, Omaha 2009 11 +72 +120 ECMWF SBSALGFSNMMB 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

12. Zavisa Janjic, Omaha 2009 12 +120 +72+120 ECMWF SBSALGFSNMMB 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

13. Zavisa Janjic, Omaha 2009 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. Zavisa Janjic, Omaha 2009 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 forced conservation to correct oversteepening

15. Zavisa Janjic, Omaha 2009 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. Zavisa Janjic, Omaha 2009 16 Courtesy Youhua Tang New Eulerian Old Lagrangian Boundary reached

17. Zavisa Janjic, Omaha 2009 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. Zavisa Janjic, Omaha 2009 18 2.5 days5 days 7.5 days 15 days

19. Zavisa Janjic, Omaha 2009 19 15 days No monotonization Monotonization 1-2% initial drop

20. Zavisa Janjic, Omaha 2009 20 Courtesy: Barcelona Supercomputing Center (BSC) Designated center within WMO Sand and Dust Storm Warning Advisory and Assessment System (SDS-WAS)

21. Zavisa Janjic, Omaha 2009 21 Gravity Wave Drag 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 ACC exceeds 0.60 at day 7 and 8

22. Zavisa Janjic, Omaha 2009 22 GLOBAL Randomly chosen cycle 20090318_12UTC Global AC NEW RRTM radiation code within NMM-B, Courtesy Carlos Perez

23. Zavisa Janjic, Omaha 2009 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