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Zavisa Janjic, Omaha 2009 1
Further development of a model for a broad range of spatial and temporal scales
Zavisa Janjic
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 motionsFavorable features of the hydrostatic formulation preserved
The nonhydrostatic option as an add–on nonhydrostatic module
Reduced cost at lower resolutionsEasy 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
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 preservedOmega-alpha term, consistent transformations between KE and PEErrors associated with representation of orography minimized
NMM-B Dynamical Core
Zavisa Janjic, Omaha 2009 4
Coordinate system and gridGlobal lat-lon, regular gridRegional rotated lat-lon, more uniform grid sizeArakawa B grid (in contrast to the WRF-NMM E grid)
h h h v vh h h v vh h h
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 terrainNo discontinuities and internal boundary conditions
Lorenz vertical grid
NMM-B Dynamical Core
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 formulationWaves 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
Zavisa Janjic, Omaha 2009 6
Recent upgrades
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)
Zavisa Janjic, Omaha 2009 7
PD
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
TOPPD
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
Zavisa Janjic, Omaha 2009 9
0
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0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
0
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1500
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0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
0
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0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
0.7
0.75
0.8
0.85
0.9
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1
1 6 11 16 21 26 31 36 41 46 51 56
Cumulative distribution of topography height in global NMM-B in 100 m bins
ps=1000 mb ps=750 mb
ps=500 mb
Example: Thicknesses of the NMM B 64 layers, ptop=0, transition at 300 mb
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
Zavisa Janjic, Omaha 2009 11
+72
+120 +120+120
+120
ECMWF ECMWF
SB SAL GFSNMMB NMMBNMMB
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
Zavisa Janjic, Omaha 2009 12
+120 +120+120
+72+120
ECMWF ECMWF
SB SAL GFSNMMB NMMBNMMB
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
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 definiteMonotoneAffordable
Lagrangian ?
Strict conservationOpen boundary conditions
Eulerian ?
Positive definitnessMonotonicity
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 advectionModified 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
Zavisa Janjic, Omaha 2009 15
Eulerian tracer advection scheme
Implemented and tested in
PC version of NMM-BGlobal and regional NMM-B
Performance
Satisfactory mass conservation considering other uncertaintiesSatisfactory shape and extremes preservation
CostFaster than the Lagrangian scheme per time step, BUTOverall slower than the Lagrangian scheme due to shorter advection stepStable with longer time steps (2 times), appears safe for standard model tracers
Zavisa Janjic, Omaha 2009 16
Courtesy Youhua Tang
New Eulerian
Old Lagrangian
Boundary reached
Zavisa Janjic, Omaha 2009 17
Eulerian tracer advection scheme
PC NMM-B runs
Global domain1.4 x 1.0 deg, 32 levelsPolar filtering of advection tendencies Initial cuboid throughout the atmosphereWinter case (strong wind)
minimum= .0000E+00 maximum= .0000E+00 interval= .0000E+00
NP
GM
ID
500. mb tracer
17. 1.2008. 12 UTC + 00000
Zavisa Janjic, Omaha 2009 18
minimum= .0000E+00 maximum= .0000E+00 interval= .0000E+00
NP
GM
ID
250. mb tracer
17. 1.2008. 12 UTC + 00060
minimum= .0000E+00 maximum= .0000E+00 interval= .0000E+00
NP
GM
ID
250. mb tracer
17. 1.2008. 12 UTC + 00120
2.5 days 5 days
minimum= .0000E+00 maximum= .0000E+00 interval= .0000E+00
NP
GM
ID
250. mb tracer
17. 1.2008. 12 UTC + 00180
minimum= .0000E+00 maximum= .0000E+00 interval= .0000E+00
NP
GM
ID
250. mb tracer
17. 1.2008. 12 UTC + 00360
7.5 days 15 days
Zavisa Janjic, Omaha 2009 19
0.00000
1.00000
1 378 755 1132 1509 1886 2263 2640 3017 3394 3771 4148 4525 4902 5279 5656
Series1
0.00000
1.00000
1 378 755 1132 1509 1886 2263 2640 3017 3394 3771 4148 4525 4902 5279 5656
Series1
15 days
No monotonization
Monotonization
1-2% initial drop
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)
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
Zavisa Janjic, Omaha 2009 22
GLOBAL
Randomly chosen cycle 20090318_12UTCGlobal
AC
NEW RRTM radiation code within NMM-B, Courtesy Carlos Perez
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