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
1
܏ 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
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
2
܏ 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
3
܏ 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
4
● 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 ψ on Arakawa
" 2# " 2# 2
! ( 2 + 2 ) dA staggered grid C.
"y
A "x
" 2# 2
" 2# 2
" 2# " 2#
! ( 2 ) dA ! ( 2 ) dA ! 2 2 dA
A "x
A "y
A "x "y
"# 2 "# 2
Energy as defined in terms of ψ on Arakawa
[(
! "y ) + ( "x ) ]dA staggered grid C and semi staggered grids B/E.
A
"# 2
"# 2
(
)
dA
(
! "y
! "x ) dA
A
A
" 2#
" 2#
Momentum as defined in terms of ψ on Arakawa
+
dA
2
2
staggered grid C and semi staggered grids B/E.
"
x
"
y
A
" 2#
" 2#
! 2 dA ! 2 dA
A "x
A "y
!
●
A number of quadratic and first order quantities conserved in case of general flow.
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
5
●
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.
1977,
-
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,
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
6
܏ The formulation successfully reproduces classical 2D nonhydrostatic solutions.
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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.
Zavisa Janjic
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.
50 Years of NWP, June 14-17, 2004
7
0
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002
.
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.5
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2 2- 0
.5 2.
.5
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.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
8
܏ 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
9
܏ 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
10
㻔㻓㻛
-3
㻔㻓㻘
-5/3
㻔㻓㻗
●
No spectral gap.
● Transition at few
hundred kilometers from –3
slope to –5/3 slope.
㻔㻓㻖
㻔㻓㻕
㻔㻓㻖
Zavisa Janjic
● Nastrom-Gage (1985,
JAS) 1D spectrum in upper
troposphere and lower
stratosphere from
commercial aircraft
measurements.
㻔㻓㻕
㻔㻓㻔
● 0.01-0.3 m s-1 in the
–5/3 range, high up, not to be
confused with severe
mesoscale phenomena!
50 Years of NWP, June 14-17, 2004
11
8
7
6
5
4
3
-5/3
“Isabel”
NMM,
8 km, 60 lev.
-6.0
-5.5
-3
630 km
-5.0
63 km
-4.5
isabelnmm3648
Zavisa Janjic
-4.0
k^-3
2
1
0
-3.5
-3.0
k^-5/3
50 Years of NWP, June 14-17, 2004
12
8
7
6
5
4
3
-5/3
Atlantic,
NMM-B,
15 km, 32 lev.
2
-3
630 km
-6.0
-5.5
-5.0
-4.5
oceanphy3648
Zavisa Janjic
1
63 km
-4.0
k^-3
-3.5
0
-3.0
k^-5/3
50 Years of NWP, June 14-17, 2004
13
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!
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
14
4.5
4.0
Decaying 3D turbulence,
Fort Sill storm, 05/20/77.
3.5
3.0
NMM-B,
Ferrier microphysics,
1km, 32 levels,
112km by 112km by
16.4km, double periodic.
2.5
2.0
1.5
Spectrum of w2 at 700
hPa, hours 3-4 average.
1.0
-5/3
0.5
0.0
-4.5
-4.0
-3.5
k^-5/3
Zavisa Janjic
-3.0
-2.5
-2.0
ferrier700180240
50 Years of NWP, June 14-17, 2004
15
Eta
NMM
Verification
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
16
Mountain waves in the Eta (left) and the NMM (right)
Eta
Zavisa Janjic
NMM
50 Years of NWP, June 14-17, 2004
17
“Isabel”
NMM
8 km, 60
lev.
951.72 mb
Obs. 953 mb
GFS data
Sea level
Pressure
http://www.nhc.noaa.gov/2003isabel.shtml
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
18
NMM
8 km, 60 lev.
GFS data
3 hour
Accumulation
NCAR
geometrical
progression
color code
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
19
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.
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
20
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.
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
21
܏ 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.
NCAR,
CAPS
NMM
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
22
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.
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
23
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
Zavisa Janjic
Courtesy:
Jack Kain,
Steve Weiss
50 Years of NWP, June 14-17, 2004
24
܏ 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
25
Sep 04,2003
RMS H500
RMS RH700
We st
6
18
30
42
We st
6
18
30
42
Ce ntra l
Ea st
Ala ska
12
6
12
24
18
24
36
30
36
48
42
48
Ce ntra l
Ea st
Ala ska
12
6
12
24
18
24
36
30
36
48
42
48
9 wins
6 wins
1 win
NMM
Eta
Othe r
7 wins
5 wins
4 wins
RMS T850
We st
Ce ntra l
Ea st
Ala ska
6
12
6
12
11 wins
5 wins
0 wins
●
18
24
18
24
NMM
Eta
Othe r
RMS V250
30
36
30
36
42
48
42
48
We st
Ce ntra l
Ea st
Ala ska
NMM
Eta
Othe r
6
12
6
12
9 wins
7 wins
0 win
56.25%
35.94%
7.81%
18
24
18
24
30
36
30
36
42
48
42
48
NMM
Eta
Othe r
NMM
Eta
Othe r
NCEP standard verification package, verification against observations.
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
26
Jan 24,2004, 1 month snapshot
RMS H500
West
Central
East
Alaska
6
12
6
12
18
24
18
24
12 wins
2 wins
2 wins
RMS RH700
30
36
30
36
42
48
42
48
West
Central
East
Alaska
NMM
Eta
Other
6
12
6
12
1 win
15 wins
0 wins
RMS T850
West
Central
East
Alaska
6
12
6
12
5 wins
9 wins
2 wins
18
24
18
24
30
36
30
36
42
48
42
48
NMM
Eta
Other
RMS V250
30
36
30
36
42
48
42
48
West
Central
East
Alaska
NMM
Eta
Other
6
12
6
12
10 wins
1 win
5 wins
43.75%
42.19%
14.06%
●
18
24
18
24
18
24
18
24
30
36
30
36
42
48
42
48
NMM
Eta
Other
NMM
Eta
Other
NCEP standard verification package, verification against observations.
Zavisa Janjic
50 Years of NWP, June 14-17, 2004
27
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
Zavisa Janjic
Courtesy:
Jack Kain,
Steve Weiss
50 Years of NWP, June 14-17, 2004
28
NCEP NMM,
4.5 km, 35 lev.,
Ferrier
NCAR EMC,
4 km, 35 lev.,
Lin
Radar,
2 km
NSSL/SPC
2004 Spring
Program
04/04/28, 00Z
+24 hours
Zavisa Janjic
Courtesy:
Jack Kain,
Steve Weiss
50 Years of NWP, June 14-17, 2004
29