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☞ Two Weather Research and Forecasting (WRF) Model dynamical cores:

AN EVOLUTIONARY APPROACH TO NONHYDROSTATIC MODELING Zavisa Janjic, Tom Black, Mattew Pyle, Hui-ya Chuang, Eric Rogers and Geoff DiMego National Centers for Environmental Prediction, Camp Springs, Maryland. ☞ Two Weather Research and Forecasting (WRF) Model dynamical cores:

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☞ Two Weather Research and Forecasting (WRF) Model dynamical cores:

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  1. AN EVOLUTIONARY APPROACH TO NONHYDROSTATIC MODELINGZavisa Janjic, Tom Black, Mattew Pyle,Hui-ya Chuang, Eric Rogers and Geoff DiMegoNational Centers for Environmental Prediction, Camp Springs, Maryland

  2. ☞ Two Weather Research and Forecasting (WRF) Model dynamical cores: ● NCEP Nonhydrostatic Mesoscale Model (NMM) Janjic, Gerrity and Nickovic, 2001, Monthly Weather ReviewJanjic, 2003, Meteorology and Atmospheric Physics Black, Tucillo, Parallelization, Optimization, WRF standards ● NCAR Explicit Mass Core (EMC) Klemp, Skamarock, Dudhia, 2000, Online Wicker and Skamarock, 2002, Monthly Weather Review Klemp, Skamarock, Fuhrer, 2003, Monthly Weather Review Michalakes, 2002  

  3. ☞ The NCEP NMM ● Instead of extending cloud models to larger spatial and temporal scales, NMM built on experiences of NWP(Janjic et al., 2001; Janjic, 2003), i.e., - Relaxing the hydrostatic approximation, while - Using modeling principles (Janjic, 1977, 1979, 1984) proven in NWP and regional climate applications. ● No linearizations or additional approximations required, fully compressible system (Janjic, Gerrity, Nickovic, 2001, MWR; Janjic, 2003, MAP). ● The nonhydrostatic effects as an add–on nonhydrostatic module: - Easy comparison of hydrostatic and nonhydrostatic solutions; - Reduced computational effort at lower resolutions. ● Pressure based vertical coordinate.

  4. ☞ Basic discretization principles set up in Janjic, 1977, Beitrage (also used in Eta): ● Conservation of major integral properties (Arakawa, “mimetic” approach, hot topic in Math); - Controlled nonlinear energy cascade through Energy and Enstrophy conservation. ● Cancellation between contributions of the omega-alpha term and the PGF to KE, consistent transformations between KE and potential energy; ● Minimization of pressure gradient force error. ☞ Implementation of the basic principles evolved significantly over time. ● For historical reason, Arakawa E grid still in the initial NCEP formulation, more advanced B grid formulation (NMM-B) also exists (Janjic, 2003, MAP)].

  5. ● For rotational flowand cyclic boundary conditions, horizontal momentum advection on semistaggered grids B/E conserves (Janjic 1984, MWR) appropriate finite difference analogs of: Enstrophy as defined in terms of on Arakawa staggered grid C. Energy as defined in terms of on Arakawa staggered grid C and semi staggered grids B/E. Momentum as defined in terms of on Arakawa staggered grid C and semi staggered grids B/E. ● A number of quadratic and first order quantities conserved in case of general flow.

  6. ● Vertical discretization, vertical coordinate, PGF error. - Pressure-sigma hybrid (Arakawa and Lamb, 1977): Flat coordinate surfaces at high altitudes where sigma problems worst; Higher vertical resolution over elevated terrain; No discontinuities and internal boundary conditions. ● Time stepping. - No redundant computations, high computational efficiency! - Adams-Bashforth for horizontal advection of u, v, T and Coriolis, - Crank-Nicholson/Matsuno for vertical advection of u, v, T (60 levels). - Forward-Backward (Ames, 1968; Gadd, 1974; Janjic and Wiin-Nielsen, 1977, JAS; Janjic 1979, Beitrage) for gravity waves. - Implicit for vertically propagating sound waves (Janjic et al., 2001, MWR). - Split forward, long time steps for physics (Janjic, 1990, MWR)

  7. The cold bubble test. Potential temperatures after 300 s, 600 s and 900 s in the right hand part of the integration domain extending from the center to 19200 m, and from the surface to 4600 m. The contour interval is 10 K. Potential temperature after 360 s, 540 s, 720 s and 900 s. The area shown extends 16 km along the x axis, and from 0 m to 13200 m along the z axis. The contour interval is 10K. ☞ The formulation successfully reproduces classical 2D nonhydrostatic solutions.

  8. Full Analytical (Boussinesque) Deviation of horizontal wind from basic state (uniform 10 m s-1) after 9000 s. The area shown extends 18400 m on each side of the center of the mountain, and from 0 m to 8000 m in the vertical. The contour interval is 0.5 m s-1 and the dashed contours indicate negative values.

  9. ☞ WRF NMM model = Nonhydrostatic dynamics+Upgraded physical package of the NCEP Eta model (Janjic 1990, 1994, MWR; Chen, Janjic and Mitchell, 1997, BLM; Janjic 2000, JAS; Janjic 2001, NCEP Office Note 437), NCAR physics as well. ● Computationally robust, reliable in operations; ● THREE TIMES faster than most established NH models, can be sped up; ● Little noise, no Rayleigh damping and associated extra computational boundary condition at the top with real data with resolutions down to 100 m. ● NWP, convective cloud runs, PBL LES, with resolutions from 50 km to 100 m; ● Operational at NCEP (small domains, initialized and driven by the Eta): - No filtering of mountains. - HiRes Windows, Fire Weather, On Call. ● Quasi-Operationally run elsewhere.

  10. ☞ Atmospheric spectrum. ● The WRF-NMM and the NMM-B well qualified for investigating numerical spectra: - Conservation of rotational energy and enstrophy, more accurate nonlinear energy cascade, - Conservation of total energy provides stable integrations without excessive dissipation (either explicit or built-in finite-difference schemes) that could affect properties of model generated spectra, - Hybrid pressure-sigma vertical coordinate system relatively free of errors associated with representation of mountains in the upper troposphere and in the stratosphere where the sigma coordinate errors are largest, - Explicit formulation of dissipative processes allows precise “dosage” of dissipation.

  11. 108 -3 105 -5/3 104 103 102 103 102 101 ● Nastrom-Gage (1985, JAS) 1D spectrum inupper troposphere and lowerstratospherefrom commercial aircraft measurements. ● No spectral gap. ● Transition at few hundred kilometers from –3 slope to –5/3 slope. ● 0.01-0.3 m s-1 in the –5/3 range, high up, not to be confused with severe mesoscale phenomena!

  12. -5/3 “Isabel” NMM, 8 km, 60 lev. 630 km 63 km -3

  13. -5/3 Atlantic, NMM-B, 15 km, 32 lev. 630 km 63 km -3

  14. No Physics With Physics The Atlantic case, NMM-B, 15 km, 32 Levels No time (and space) for downscale nonlinear energy cascade, physical or spurious energy source needed on small scales!

  15. Decaying 3D turbulence, Fort Sill storm, 05/20/77. NMM-B, Ferrier microphysics, 1km, 32 levels, 112km by 112km by 16.4km, double periodic. Spectrum of w2 at 700 hPa, hours 3-4 average. -5/3

  16. Eta NMM Verification

  17. Eta NMM Mountain waves in the Eta (left) and the NMM (right)

  18. 951.72 mb Obs. 953 mb “Isabel” NMM 8 km, 60 lev. GFS data Sea level Pressure http://www.nhc.noaa.gov/2003isabel.shtml

  19. NMM 8 km, 60 lev. GFS data 3 hour Accumulation NCAR geometrical progression color code

  20. OTHER PHYS1 OTHER PHYS2 WRF NMM PHYS1 WRF NMM PHYS2 Alaska October 2002 Vector wind All verification times Large scale errors clustering by dynamical cores, implications for ensembles! ● NCEP standard verification package, verification against observations.

  21. OTHER PHYS1 OTHER PHYS2 WRF NMM PHYS1 WRF NMM PHYS2 West February 2003 Vector wind All verification times Large scale errors clustering by horizontal discretization! ● NCEP standard verification package, verification against observations.

  22. NCAR, CAPS NMM ☞ Mesoscale Convective Systems, NSSL-SPC Spring Program 2004 ● NMM WRF, 4.5 km, 35 levels, about Central domain, Ferrier microphysics, no parameterized convection, Eta initial and boundary conditions, 00Z, up to 30 hours, available in the morning. ● NMM starting from Eta data needs up to 6 hours to spin up convective systems.

  23. 24 hour 4.5 km forecast of 1 hour accumulated precipitation valid at 00Z April 21, 2004 (better than 12 hour forecasts by operational models). Verifying 2 km radar reflectivity. Courtesy Jack Kain.

  24. NCEP NMM, 4.5 km, 35 lev., Ferrier NCAR EMC, 4 km, 35 lev., Lin Radar, 2 km NSSL/SPC 2004 Spring Program 04/05/28, 00Z ∼ +24 hours Courtesy: Jack Kain, Steve Weiss

  25. ☞ Conclusions ● Promising results of high resolution NWP on meso scales. ● NWP on near-cloud scales successful more frequently and with stronger signal than if only by chance. ● Convective systems direct circulations spun-up by the model, predictable? ● Reemphasized importance of forcing and (micro)physics on meso scales? ● Full potential of mesoscale NWP not yet developed.

  26. ● NCEP standard verification package, verification against observations.

  27. ● NCEP standard verification package, verification against observations.

  28. NCEP NMM, 4.5 km, 35 lev., Ferrier NCAR EMC, 4 km, 35 lev., Lin Radar, 2 km NSSL/SPC 2004 Spring Program 04/06/01, 00Z ∼ +24 hours Courtesy: Jack Kain, Steve Weiss

  29. NCEP NMM, 4.5 km, 35 lev., Ferrier NCAR EMC, 4 km, 35 lev., Lin Radar, 2 km NSSL/SPC 2004 Spring Program 04/04/28, 00Z ∼ +24 hours Courtesy: Jack Kain, Steve Weiss

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