Horizontal Domain, Grid Techniques, and Boundary Conditions:
A brief description of the horizontal characteristics of various NWP models.
INTRODUCTION MESOSCALE MODEL CHARACTERISTICS REGIONAL MODEL CHARACTERISTICS GLOBAL MODEL CHARACTERISTICS RESEARCH MODEL CHARACTERISTICS SUMMARY

REFERENCES

INTRODUCTION DOMAIN: Meteorological computer models are used to aid in predicting various parameters that are of concern in weather forecasting. Before a model can accomplish this, it must be given a specified region in which to compute the desired elements. This specific region is called the domain. Today's models generally operate on either a national or a global domain.  In a global model, also called a spectral model, the domain consists of the atmosphere that encompasses the entire planet. The domain of a national or regional model is a subset of the larger global model and is mainly used to forecast the state of the atmosphere over a specific region of the planet.

GRID TECHNIQUE:  Numerical models function by using a grid scheme.  A grid is an array of points used in representing meteorological data.  The value a grid point holds is the average of all of the values found within that grid square.  A higher number of grid points implies a shorter distance between points, and thus a better resolution (5).  Resolution is usually expressed in kilometers and represents the smallest scale where features can be resolved by the model.   High resolution is critical when longer performance of a model is of extreme significance.  If a model is used to forecast for an extended length of time, chances are there will be problems with initialization which in turn affects the continued use of the model.  Therefore, a higher resolution would reduce this problem.

This grid scheme was developed to produce a reasonable forecast that contains known errors that are easily corrected.  Therefore, the goal of the grid technique is not to produce the most accurate forecast possible, but to eliminate any discrepancies within the run (2).

BOUNDARY CONDITIONS:   On the edge of a model's domain, there exists a problem:  How does the model interpret data that is entering and leaving the domain?  This is where boundary conditions come into play.  They inform the model of the atmospheric conditions of the air entering the model's domain on the upstream side.  This allows the model to accurately evolve the air after it has moved into the domain.  Just as a forecaster can not accurately make a forecast without analyzing the current conditions, a forecast model can not accurately forecast the atmospheric phenomena without ingesting the data on the boundaries.

The following section maps out the various domains, grid techniques, and boundary conditions utilized by the models.
 

MESOSCALE MODELS

MM5

I will use the MM5 model as the sole mesoscale model of disscussion, being that it is the widest used, operational mesoscale model.  There are severel variations of the MM5, here I will disscuss the Air Force WeatherAssociation's (AFWA) implementation of the MM5.  There are three horizontal resolutions used by AFWA; 5, 15, and 45 km(14).  Mission need and data availablitiy dictate which scale is used, i.e., domain in a city may have 5 km resolution, but when using MM5 on a regional domain, 15 or 45 km resolution is used.  Boundary conditions are determined by the flow of meteorological variables i.e., which way the wind is blowing.  Inflow boundary conditions are determined from other, larger scale models, such as the AVN.  Also used are the actual MM5 grid points at the boundary.  These two variables are plugged into a weighing equation to determine the boundary conditions.  Outflow boundary conditions are determined in the same manner.
 

REGIONAL MODELS

NGM - Nested Grid Model

There are three factors pertaining to the NGM model.  The first is the domain.  This model covers all of North America and has an 80 km horizontal resolution.  The grid point spacing grows larger as the latitude increases, with a spacing of 84 km at 45 N and a spacing of 91 km at 60 N (6).  The NGM uses a grid technique, in which one grid (grid B) is "nested" within the outer grid (grid A).  (Fig. 1)  Grid B has a resolution of 80 km, and surrounds all of North America and Grid A has a resolution of 160 km (7). Grid A covers a larger, hemispheric area (3).

ETA Model

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The ETA model covers the United States and most of Mexico and Canada and has a 22 km horizontal resolution (4).  It uses an Arakawa A staggered grid.  This grid is  staggered, meaning the grid points alternate between mass and wind (momentum) points in the same way red and black squares alternate on a checker board.  (Fig. 2)  This coordinate system is created by rotating the earth's entire geographic latitude-longitude grid so as to place the intersection of the equator and the prime meridian over the center of the forecast area.  In doing so, the convergence of the meridians is minimized over this area. (2)  This technique minimizes errors that arise from topographic forcing and geostrophic adjustment (11).

Since the ETA model only covers a small portion of the earth, a problem arises when new air moves into the edge of the domain.  To fix this problem, boundary conditions are established.  Data on the single outer row of points is interpolated from the MRF, and in flow points are extrapolated from the interior domain.  The values on the second row are interpolated from values on the outer row and values from the interior.  True integration of the domain gives the values for the third row.  The boundary conditions are updated every three hours to reduce errors from lateral boundaries (4).

RUC - Rapid Update Cycle

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The RUC model forecasts for the mainland US, some areas of Canada and Mexico, and the surrounding oceanic areas.  It extends further than other models into the ocean and in all directions, especially to the southeast, north, and west (1).  The horizontal grid resolution for the RUC is 40 km, and it works on a grid format called Arakawa C that is much like the one used in ETA (12).

The boundary conditions for RUC are specified from NGM.  The forecasts are initialized at 00Z and 12Z and use NGM data that is twelve hours old.  The lateral boundary conditions are linearly interpolated from NGM data by "nudging" them toward NGM values.  The conditions at the surface are allowed to vary horizontally and are specified as a function of climatology using 13 land use types (1).
 

GLOBAL MODELS

Today's global models do not use the grid technique to analyze forecasts.  Instead, these models use the "spectral technique" which numerically solves wave equations using Fourier analysis techniques. A spectral model represents atmospheric variables, such as pressure and temperature, as a combination of various waves of different wavelengths and amplitudes.  The horizontal resolution of a spectral model is thus stated in terms of the number of waves the model can combine to represent an atmospheric variable.  The larger the number of waves the model can combine, the greater the model's horizontal...  Nearly every global model is a spectral model, as are an increasing number of regional models. (5)

AVN/MRF - Medium Range Forecast

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The AVN/MRF  domain covers the atmosphere surrounding the entire earth.   The AVN/MRF uses a spectral techinique with a T170 (triangular truncation) resolution.  This is an improvement from the T128 resolution used until December 1999.  T170 gives a horizontal resolution of approximately 2.1 degrees, or 80 km.

The AVN/MRF has two types of boundary conditions, physical and dynamic.  Dynamic boundary conditions are used for primitive equations.  Physical boundary conditions are used in finding physical parameterizations such as lower boundary fluxes of heat, moisture, and momentum (12).

ECMWF - European Center Medium Range Weather Forecast

Discussion of ECMWF is limited to three parameters:  1) horizontal resolution of 60 km (13)  2) global coverage  3) utilization of a 216-wave triangular truncation resolution (6).

RESEARCH MODEL

WRF

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The Weather Research and Forecast (WRF) project is developing a next-generation mesoscale forecast model and assimilation system that will advance both the understanding and the prediction of mesoscale precipitation systems and will promote closer ties between the research and operational forecasting communities. The model will incorporate advanced numerics and data assimilation techniques, a multiple relocatable nesting capability, and improved physics, particularly for treatment of convection and mesoscale precipitation. It is intended for a wide range of applications, from idealized research to operational forecasting, with priority emphasis on horizontal grids of 1?10 kilometers. A prototype has been released and is being supported as a community model. Based on its merits, it will be a candidate to replace existing forecast models such as the Mesoscale Model (MM5) at the Pennsylvania State University/National Center for Atmospheric Research, the ETA modal at the National Centers for Environmental Prediction, and the RUC system at the Forecast Systems Laboratory. The first release of the model, WRF 1.0, was November 30, 2000.


WRF TEAM

Summary Each model is in itself unique.  The horizontal resolution you need determines whether you will use a model of regional or global scale.

Mesoscale models, for examing weather on local or convective scales:

        MM5 - up to 5km grid spacing, can discern convection.

Regional models, for concentrating on a region of the United States, such as the Great Plains:

        NGM  - Accounts for all of North America
        ETA   - Covers the United States and most of Mexico and Canada
        RUC  - Includes oceanic surfaces around North America

Global models, for a large area such as the Northern Hemisphere:

        AVN/MRF                  - Covers entire globe, implementing 80 km resolution
        ECMWF            - Covers entire globe, implementing 60 km truncated resolution

Using a global model broadens horizontal boundaries and enables the forecaster to keep an eye on features to assemble an extended forecast.

Factors to aid in determining which model to use:

References 1.  Benjamin, Stanley G. and Kevin J. Brundage, NOAA/ERL Forecast Systems Laboratory and
Lauren L. Monrone,     National Meteorological Center, Development Division NWS/NOAA, June
1994: "Implementation of the Rapid Update Cycle." <http://maps.fsl.noaa.gov/tpbruc.cgi#.

2.  Black, Thomas L.  (June 1994).  "NMC Notes: The New NMC Mesoscale ETA Model:
Description  and Forecast Examples."  Weather and Forecasting.  (265-278).

3.  Hoke, James E., Norman A. Phillips, Geoffrey J. Dimego, James J. Tuccillo, and Joseph G. Sela.
(September 1989): "The Regional Analysis and Forecast System of the National Meteorological
Center." Weather and Forecasting:Volume 4.  (323-334).

4.  Mittelstadt, Jon, WRH-SSD, January 1998: "Western Regional Technical Attachment No.
98-03, January 27, 1998: "The Eta-32 Model."   <http://www.wrh.noaa.gov/wrhq/98TAs/9803/index.html.

5.  Numerical Weather Prediction (NWP) Models.
<http://infosphere.safb.af.mil/users/aws/public_www/public/aws/hqaws/xon/xona/numerical/nwp-info.htm
(.mil only)

6.  Palmer, Chad, USA Today, 1997: "Some Operational Forecast Models."

7.  Rogers, Eric,  Geoffrey DiMego, and David Parrish, February 2000: "Changes to the NCEP Regional Analysis and Forecast System (RAFS): Initial conditions for the Nested Grid Model." <http://sgi62.wwb.noaa.gov:8080/NGMTPB/

8.  Scialdone, John, CEOS-IDN, January 1998: "Aviation Global Analyses and Forecasts from the Spectral Forecsat Model."  <http://www.neonet.nl/ceos-idn/datasets/NMC_AVN.html.

9.    Scialdone, John, CEOS-IDN, January 1998: "Nested Grid Model (NGM) Data, Analyses, and
Forecasts for North America Using the Regional Analysis and Forecast System (RAFS)."
<http://www.neonet.nl/ceos-idn/datasets/NMC_695_NWS0001.html.

10.    Scialdone, John, CEOS-IDN, January 1998: "Medium Range Global Analyses and Forecasts
from the Spectral Forecsat Model."  <http://www.neonet.nl/ceos-idn/datasets/NMC_MRF.html.

11.  Staudenmaier, Mike, NWSO, February 1996: "Western Regional Technical Attachment No.
96-06, February 27, 1996: "A Description of the Meso-ETA Model."

12.  University Corporation for Atmospheric Research, February 2000: "Characteristics of Operational NWP Models." <http://deved.meted.ucar.edu/nwp/pcu2/launpcu2.htm

 13.  Woods, Austin, December 1997: "ECMWF-Forecasting by Computer."
<http://www.ecmwf.int/research/fc_by_computer.html.

 14.  Air Force Weather Association, February 2000:  "AFWA MM5 Use"
<ftp://ws-ftp1.afwa.af.mil/pub/aboutmm5/intro/latbndry.htm

 15.  Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research, : "Development of a next-generation Regional Weather Research and Forecast Model" http://www.mmm.ucar.edu/mm5/mpp/ecmwf01.htm

Erin Evans
Coutrney Radley
Ryan Lawless
Tal Ziv