Further development of a model for a broad range of spatial and temporal scales Zavisa Janjic

Zavisa Janjic, Omaha 2009 1

Further development of a model for a broad range of spatial and temporal scales

Zavisa Janjic


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


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



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



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)



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)


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


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


0

500

1000

1500

2000

2500

3000

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

0

500

1000

1500

2000

2500

3000

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

0

500

1000

1500

2000

2500

3000

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

0.7

0.75

0.8

0.85

0.9

0.95

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


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


+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


+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


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



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



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


Courtesy Youhua Tang

New Eulerian

Old Lagrangian

Boundary reached



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



NP

GM

ID

250. mb tracer

17. 1.2008. 12 UTC + 00060


NP

GM

ID

250. mb tracer

17. 1.2008. 12 UTC + 00120

2.5 days 5 days


NP

GM

ID

250. mb tracer

17. 1.2008. 12 UTC + 00180


NP

GM

ID

250. mb tracer

17. 1.2008. 12 UTC + 00360

7.5 days 15 days


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


Courtesy: Barcelona Supercomputing Center (BSC)Designated center within WMO Sand and Dust Storm Warning Advisory and Assessment System (SDS-WAS)


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


GLOBAL

Randomly chosen cycle 20090318_12UTCGlobal

AC

NEW RRTM radiation code within NMM-B, Courtesy Carlos Perez


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

Documents

Further development of a model for a broad range of spatial and temporal scales Zavisa Janjic