# Presentation: 090114

## 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 

## ☞ 	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  

- ● 	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

## ☞ 	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.

- ●	 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.

## ☞ 	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)].

- ● 	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)].

## ●	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.

## ●	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)

## ☞ 	The formulation successfully reproduces classical 2D nonhydrostatic solutions.

##                                    Full                                               Analytical (Boussinesque)

-                                    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.

## ☞ 	 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.

## ☞	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.

## ●	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!

## Slide 12

## Slide 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!

## 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 *w**2* at 700 hPa, hours 3-4 average.

- -5/3

## Slide 16

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

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

- _[http://www.](http://www.nhc.noaa.gov/2003isabel.shtml)__[nhc](http://www.nhc.noaa.gov/2003isabel.shtml)__[.](http://www.nhc.noaa.gov/2003isabel.shtml)__[noaa](http://www.nhc.noaa.gov/2003isabel.shtml)__[.](http://www.nhc.noaa.gov/2003isabel.shtml)__[gov](http://www.nhc.noaa.gov/2003isabel.shtml)__[/2003isabel.](http://www.nhc.noaa.gov/2003isabel.shtml)__[shtml](http://www.nhc.noaa.gov/2003isabel.shtml)_

- “Isabel”
- NMM
- 8 km, 60 lev.
- GFS data
- Sea level
- Pressure

## NMM 

- NMM
- 8 km, 60 lev.
- GFS data
- 3 hour
- Accumulation
- NCAR geometrical progression color code

## ●	NCEP standard verification package, verification against observations.

- ●	NCEP standard verification package, verification against observations.

## West

- OTHER PHYS1
- OTHER PHYS2
- WRF NMM PHYS1
- WRF NMM PHYS2

- February 2003
- Vector wind
- All verification times
- Large scale errors clustering by horizontal discretization!

- ●	NCEP standard verification package, verification against observations.

## ☞  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.

## Slide 23

## Slide 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.

## ●	NCEP standard verification package, verification against observations.

- ●	NCEP standard verification package, verification against observations.

## ●	NCEP standard verification package, verification against observations.

- ●	NCEP standard verification package, verification against observations.

## Slide 28

## Slide 29