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Eta Model
Characteristics: Background Information
December
1998
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Eta Model
Characteristics: Background Information
December
1998
Introduction
This background material outlines the characteristics of the Eta-32 model, specifically, model horizontal and vertical resolution, the Eta coordinate system, and model terrain representation. References used to develop the material are listed at the end.
History
The National Centers for Environmental Prediction (NCEP) "Early" Eta analysis and forecasting system was operationally implemented in June 1993, replacing the Limited-area Fine Mesh model in providing early forecast guidance over North America (Black et al. 1993, Rogers et al. 1995). The June 1993 system consisted of
In 1995, two major improvements in mesoscale forecast guidance from NCEP were implemented. First, NCEP began twice-daily forecasts of a 29-km, 50 level Eta model (Black 1994) over the contiguous United States and adjacent areas in March 1995. A 33-h forecast from the Eta-29 (Meso Eta) was run from 0300 and 1500 UTC initial conditions after a 3-h spin-up cycle from the first guess of the AVN model. Second, in October 1995, NCEP implemented the Eta-48 system to replace the 80-km Early Eta (Rogers et al. 1996). This included an increase in horizontal resolution to 48-km and the use of the Eta Data Assimilation System (EDAS) to produce an analysis and first guess more consistent with the forecast model than that obtained from the GDAS.
On February 2, 1998, NCEP implemented the Eta-32 model in the "early slot," replacing the Eta-48, and the Eta-32 in the 0300 and 1800 UTC time slots, replacing the Eta-29, which ran at 0300 and 1500 UTC. The Eta-32 uses a new data assimilation system called the 3DVAR (3-Dimensional Variational) Data Assimilation Scheme.
A "bundle of changes" in the spring of 1998 upgraded the convective parameterization and changed the NCEP jobstream so that the Eta-32 produces 48-h forecasts twice a day at 0000 and 1200 UTC, a 33-h forecast at 0300 UTC, and a 30-h forecast at 1800 UTC.
Horizontal Resolution
In an effort to improve the quality and timeliness of NCEP's mesoscale forecast guidance over North America, a series of enhancements to the Early Eta system have been operationally implemented, including an increase in resolution from 48-km/38 levels to 32-km/45 levels with little change in the size of the horizontal domain.
The choice of 32-km/45 levels to replace the 48-km/38 level configuration represented a compromise among several factors
The Eta-32 output is available for NTRANS on the same 80-km grids as the Eta-48. The impact of horizontal resolution and mapping to the 80-km grid is to effectively increase the size of features that can be resolved on the model output. Although the current Early Eta has a 32-km resolution, many details can get smoothed by mapping the output fields to an 80-km grid. Technically, resolvable features should be on the order of approximately 150-km, but due to the mapping of the output to an 80-km grid, the details of smaller features may be lost.
Horizontal Domain
The resulting 32-km horizontal domain covers all of North America, as did the 48-km grid. The various horizontal domains of the Eta are shown in Figure 1. The eastern boundary of the 32-km grid is close to that of the 48-km in order to capture as much of the tropical Atlantic as possible and to keep Puerto Rico inside the domain. Similar reasoning was employed at the northern boundary for Alaska. The biggest difference is seen along the western boundary, where Hawaii, although still inside the 32-km grid domain, is much closer to the boundary than with the 48-km grid.
Figure 1. Horizontal Domains of the Three Eta Models
In order to reduce lateral boundary errors due to the western boundary being closer to Hawaii, the Eta-32 boundary conditions are updated every 3 hours from the latest (6-h old) run of the AVN. This is an improvement over the Eta-48, which used 6-h updates from the AVN run that were 12 hours old.
Vertical Resolution
General characteristics of the model's vertical structure include
As with the horizontal grid, the choice of 45 vertical layers represents a compromise between the 38 levels in the Eta-48 and the 50 levels in the Eta-29. Figure 2 shows the vertical layer distribution in the Eta-32 model. Note the concentration of layers in the boundary layer and near the upper jet level (vicinity of 250 hPa). This allows for better definition of these regions.
Figure 2. Vertical Layers for the 45 Layer Eta-32 Model
In order to allow the Eta-32 to better resolve low-level mesoscale structures in mountainous areas (such as the western U.S. and Alaska), most of the extra model levels were added below 700 hPa.
The lack of vertical resolution over high terrain has been blamed for many problems that Western Region forecasters have seen in the Planetary Boundary Layer (PBL), for example, light winds (Staudenmaier and Mittelstadt 1997). The Eta-32 has 45 vertical levels, more than the Eta-48 (38 levels) but less than the Eta-29 (50 levels). The actual distribution of vertical layers over high terrain is better than the Eta-48 but worse than the Eta-29. Near 700 hPa, the vertical depth of the layer is 32 hPa, 28 hPa, and 22 hPa in the Eta-48, Eta-32, and Eta-29 models respectively. Hence, the Eta-32 is better than the Eta-48, but is not expected to substantially correct the PBL problems over complex, high terrain.
Eta Coordinate
The eta coordinate was defined in order to remove or reduce the errors that are known to occur when computing the pressure gradient force, advection, and horizontal diffusion along steeply sloped terrain. When the surface is sloped, the temperature changes on a sigma surface are partially a result of hydrostatic temperature changes due to change in elevation rather than just the actual horizontal temperature gradient. Since temperature changes in the vertical are much larger than in the horizontal, they have a dominating influence on the pressure gradient calculation that can lead to larger temperature errors. These errors can be quite large in the sigma terrain following coordinate system near steep or complex terrain.
Figure 3 provides a graphical depiction of these effects. T1, T2, and T3 are located at 3 points within a grid box in the model. Since the vertical temperature gradient (change between T1and T2) is large, T3 (located at the same elevation as T2) will be considerably colder than T1 due to the elevation change. The model will assume that the gradient between T1 and T3 is the horizontal temperature gradient when, in fact, it is mostly due to the elevation gain. This miscalculation of the temperature gradient translates to a much stronger horizontal pressure gradient calculation than is representative of the real world. This is why sigma coordinate models often forecast unrealistic pressure gradients near steep terrain.
Figure 3. Terrain-following Sigma Coordinate System
In the eta coordinate, the surface terrain heights exist at a discrete set of values or steps. These steps or values are dependent upon the vertical resolution of the model and the height of the mountains. Because of this, terrain appears step-wise rather than smooth and continuous as in the sigma coordinate. Figure 4 illustrates the depiction of terrain in the eta coordinate. For a given range of surface elevations, the eta coordinate allows the terrain to exist on more than one eta surface while in the sigma coordinate, the terrain can only exist on one sigma surface.
Since eta is normalized by a constant value of sea level pressure (1013 hPa) rather than the station pressure, which varies considerably over mountainous terrain, each eta surface is flat when lying over mountains. This allows for more accurate calculation of the horizontal pressure gradient terms because we are not introducing errors due to elevation changes between adjacent grid points.
Figure 4. Eta Coordinate Depiction of Terrain
Model Terrain Representation
In general, model terrain is much smoother than in reality, even in the eta coordinate. Terrain smoothing can be a large source of error in regions affected by small-scale terrain features. However, terrain smoothing is done partly because airflow over complex terrain will otherwise generate small-scale noise in the model that can mask the large-scale signal. For example, vertical motion changes induced by complex terrain can mask the large-scale vertical motion field.
The Eta model uses step-mountain topography in which, after interpolation to the eta native grid, the step-mountain is raised or lowered to the closest vertical interface. The mountain is represented as discrete steps whose tops coincide exactly with the model layer interfaces. Figure 5 illustrates how terrain is handled in the eta coordinate. Points (1) and (2) are raised and lowered respectively to the .9 eta surface and point (3) is raised to the .8 eta surface.
Figure 5. Eta Step-Mountain Topography
Since the resolution of the model has a profound effect on its depiction of topography, it is expected that the Eta-29 and Eta-32 model orography would show considerably more detail than the Eta-48. Figure 6 shows the Eta-32 model's topography over California as compared to the Eta-48 and Eta-29. Pay particular attention to the better differentiation between the Sierra Nevada and Cascade ranges in northern California in the higher resolution models.
Figure 6. Comparison of the Various Eta Model Terrain Depictions over the West
An exception is between the Eta-29 and Eta-32 models' depictions of the Great Basin in northern Nevada. The Eta-29 terrain shows most of the region at one elevation, while in the Eta-32, this region is depicted on 3 different steps. The difference is due to a modification of the Eta model orography algorithm toward one that is more "valley-favoring" by adding more small-scale detail. Although grid-cell mean terrain height, by definition, will continue to be higher than the elevation of individual stations (which are usually located in valleys), the differences will be less pronounced with the new algorithm in the Eta-32.
Figure 7 depicts the model terrain over the contiguous United States. In general the mountains are spread over a greater horizontal domain than exist in real life. This is a result of terrain averaging over each grid box, which causes the model's representation of the terrain slope to be too shallow. Note that the terrain smoothing spreads mountains over a larger horizontal region.
Figure 7. Eta-32 Model Terrain
A direct consequence of insufficient terrain slope in the model is to define the vertical motion and precipitation fields shifting away from the mountains and the steepest terrain. Figure 8 illustrates how the inadequate definition of the Sierra Nevada mountains has shifted the maximum vertical motions westward away from the steepest topography. The maximum upward forcing is misplaced west of the highest peaks of the Sierra.
Figure 8. Eta-32 700 hPa Heights/Relative Humidity and Omega Output
A more tangible impact of the smoothing of terrain is the subsequent misplacement of precipitation in the vicinity of complex terrain, especially in regions where the terrain is steep. Figure 9 illustrates the resulting precipitation field for the same example shown in Figure 8. The problem is not only linked to inadequate terrain resolution but also simplified microphysics. As a result, the Eta model often predicts precipitation too far west, away from mountain peaks, and does not allow enough precipitation on the immediate downwind side of mountain ranges. Note both of these effects in Figure 9. Maximum precipitation is also shifted westward from the higher peaks.
Figure 9. Eta-32 QPF Output for Same Event as Figure 8
References
Black, T. L., 1994: The new NMC mesoscale Eta model: Description and forecast examples. Wea. Forecasting, 9, 265-278.
Black, T. L., D. G. Deaven, and G. J. DiMego, 1993: The step-mountain Eta-coordinate model: 80-km "early" version and objective verifications. NWS Technical Procedures Bulletin 412, NOAA/NWS, 31 pp. (Available from National Weather Service, Office of Meteorology, 1325 East-West Highway, Silver Spring, MD 20910)
DiMego, G. J., 1988: The National Meteorological Center Regional Analysis System. Mon. Wea. Rev., 116, 977-1000.
Junker, N., 1998: Semi-intelligent use of the Eta model. PowerPoint Presentation presented at the COMAP Symposium on Numerical Weather Prediction at UCAR, Boulder, 1998.
Mittelstadt, J., 1998: The Eta-32 Model. WR-Technical Attachment 98-03.
Rogers, E., D. G. Deaven, and G. J. DiMego, 1995: The regional analysis system for the operational Eta model: Original 80-km configuration and future changes. Wea. Forecasting, 10, 810-825.
Rogers, E., T. L. Black, D. G. Deaven, G. J. DiMego, Q. Zhao, M. Baldwin, N. W. Junker, and Y. Lin, 1996: Changes to the operational "Early" Eta analysis/forecast system at the National Centers for Environmental Prediction. Wea. Forecasting, 11, 391-413.
Staudenmaier, M., and J. Mittelstadt, 1997: Results of the Western Region evaluation of the Eta-10 model. WR-Technical Attachment 97-18.
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