☞ two weather research and forecasting (wrf) model dynamical cores:

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 1

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

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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 PhysicsBlack, Tucillo, Parallelization, Optimization, WRF standards

● NCAR Explicit Mass Core (EMC)

Klemp, Skamarock, Dudhia, 2000, OnlineWicker and Skamarock, 2002, Monthly Weather ReviewKlemp, Skamarock, Fuhrer, 2003, Monthly Weather ReviewMichalakes, 2002

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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)].

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 5

● For rotational flow and 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.

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Momentum as defined in terms of on Arakawa staggered grid C and semi staggered grids B/E.

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● A number of quadratic and first order quantities conserved in case of general flow.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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)

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 7

☞ The formulation successfully reproduces classical 2D nonhydrostatic solutions.

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.

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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.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 8

-2.5

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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.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 11

● Nastrom-Gage (1985, JAS) 1D spectrum in upper troposphere and lower stratosphere from 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!

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Zavisa Janjic 50 Years of NWP, June 14-17, 2004 12

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“Isabel”NMM,8 km, 60 lev. -3

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Zavisa Janjic 50 Years of NWP, June 14-17, 2004 13

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Zavisa Janjic 50 Years of NWP, June 14-17, 2004 14

No Physics With PhysicsThe 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!

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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.

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Zavisa Janjic 50 Years of NWP, June 14-17, 2004 16

Eta NMM

Verification

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 17

Eta NMM

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

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 18

951.72 mbObs. 953 mb

http://www.nhc.noaa.gov/2003isabel.shtml

“Isabel”

NMM 8 km, 60 lev.

GFS data

Sea levelPressure

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 19

NMM 8 km, 60 lev.GFS data3 hourAccumulation

NCAR geometrical progression color code

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 20

OTHER PHYS1OTHER PHYS2WRF NMM PHYS1WRF NMM PHYS2

AlaskaOctober 2002Vector windAll verification times

Large scale errors clustering by dynamical cores, implications for ensembles!

● NCEP standard verification package, verification against observations.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 21

OTHER PHYS1OTHER PHYS2WRF NMM PHYS1WRF NMM PHYS2

WestFebruary 2003Vector windAll verification times

Large scale errors clustering by horizontal discretization!

● NCEP standard verification package, verification against observations.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 22

☞ 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.

NMM

NCAR,CAPS

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 23

24 hour 4.5 km forecast of 1 hour accumulated precipitation valid at00Z April 21, 2004 (better than 12 hour forecasts by operational models).

Verifying 2 km radar reflectivity. Courtesy Jack Kain.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 24

Radar,2 km

NCAR EMC,4 km, 35 lev.,Lin

NCEP NMM,4.5 km, 35 lev.,Ferrier

NSSL/SPC2004 SpringProgram

04/05/28, 00Z ∼ +24 hours

Courtesy:Jack Kain,Steve Weiss

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 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.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 26

Sep 04,2003RMS H500 RMS RH700

W est 6 18 30 42 W est 6 18 30 42Central 12 24 36 48 Central 12 24 36 48

East 6 18 30 42 East 6 18 30 42Alaska 12 24 36 48 Alaska 12 24 36 48

9 w ins NMM 7 w ins NMM6 w ins Eta 5 w ins Eta1 w in Other 4 w ins Other

RMS T850 RMS V250

W est 6 18 30 42 W est 6 18 30 42Central 12 24 36 48 Central 12 24 36 48

East 6 18 30 42 East 6 18 30 42Alaska 12 24 36 48 Alaska 12 24 36 48

11 w ins NMM 9 w ins NMM5 w ins Eta 7 w ins Eta0 w ins Other 0 w in Other

56.25% NMM35.94% Eta7.81% Other

● NCEP standard verification package, verification against observations.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 27

Jan 24,2004, 1 month snapshotRMS H500 RMS RH700

West 6 18 30 42 West 6 18 30 42Central 12 24 36 48 Central 12 24 36 48

East 6 18 30 42 East 6 18 30 42Alaska 12 24 36 48 Alaska 12 24 36 48

12 wins NMM 1 win NMM2 wins Eta 15 wins Eta2 wins Other 0 wins Other

RMS T850 RMS V250

West 6 18 30 42 West 6 18 30 42Central 12 24 36 48 Central 12 24 36 48

East 6 18 30 42 East 6 18 30 42Alaska 12 24 36 48 Alaska 12 24 36 48

5 wins NMM 10 wins NMM9 wins Eta 1 win Eta2 wins Other 5 wins Other

43.75% NMM42.19% Eta14.06% Other

● NCEP standard verification package, verification against observations.

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 28

Radar,2 km

NCAR EMC,4 km, 35 lev.,Lin

NCEP NMM,4.5 km, 35 lev.,Ferrier

NSSL/SPC2004 SpringProgram

04/06/01, 00Z ∼ +24 hours

Courtesy:Jack Kain,Steve Weiss

Zavisa Janjic 50 Years of NWP, June 14-17, 2004 29

Radar,2 km

NCAR EMC,4 km, 35 lev.,Lin

NCEP NMM,4.5 km, 35 lev.,Ferrier

NSSL/SPC2004 SpringProgram

04/04/28, 00Z ∼ +24 hours

Courtesy:Jack Kain,Steve Weiss