AN EVOLUTIONARY APPROACH TO NONHYDROSTATIC MODELING

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AN EVOLUTIONARY APPROACH TO NONHYDROSTATIC
MODELING  Zavisa Janjic, Tom Black, Mattew
Pyle,Hui-ya Chuang, Eric Rogers and Geoff
DiMegoNational Centers for Environmental
Prediction, Camp Springs, Maryland 
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• ? Two Weather Research and Forecasting (WRF)
  Model dynamical cores
• ? NCEP Nonhydrostatic Mesoscale Model (NMM)
• Janjic, Gerrity and Nickovic, 2001, Monthly
  Weather Review Janjic, 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  

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• ? 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 addon
  nonhydrostatic module
• - Easy comparison of hydrostatic and
  nonhydrostatic solutions
• - Reduced computational effort at lower
  resolutions.
• ? Pressure based vertical coordinate.

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• ? 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
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• ? 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).

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• ? 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.
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.
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? 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-Nichol
son/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)
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? The formulation successfully reproduces
classical 2D nonhydrostatic solutions.
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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.
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? WRF NMM model Nonhydrostatic
dynamicsUpgraded 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-Operation
ally run elsewhere.
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? 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.
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? 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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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!
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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
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Mountain waves in the Eta (left) and the NMM
(right)
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Isabel NMM 8 km, 60 lev. GFS data Sea
level Pressure
http//www.nhc.noaa.gov/2003isabel.shtml
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NMM 8 km, 60 lev. GFS data 3 hour Accumulation N
CAR geometrical progression color code
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? NCEP standard verification package,
verification against observations.
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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.
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• ? 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.

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? 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.
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? NCEP standard verification package,
verification against observations.
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? NCEP standard verification package,
verification against observations.
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