An Atmospheric Simulation System for Aviation

Requirements over Northern Latitudes

Dr. Ananthakrishna Sarma

Center for Atmospheric Physics, SAIC, 1710 SAIC Dr., McLean, VA 22102

Phone: 703-676-7017; e-mail sarmaa@saic.com

Abstract

Most aviation accidents and disasters can be linked in one way or another to weather

conditions – fog and precipitation, icing, high winds, and turbulence. Complex terrain features

contribute to the formation of these inclement weather scenarios. The current operational

numerical weather prediction (NWP) models lack the ability to resolve and effectively represent

the complex terrain features especially that of the data-sparse Northern latitudes. The Operational

Multiscale Environment model with Grid Adaptivity (OMEGA) presents a new paradigm in NWP,

well-suited for application to meteorological modeling over such environments. In this paper the

details of OMEGA and its applicability to aviation forecasting over Northern latitudes are

presented.

A. Introduction

Weather impacts all aspects of aviation. Most aviation accidents and disasters can be linked in one way or

another to weather conditions – fog and precipitation, icing, high winds, and turbulence. Even though most airports

and surrounding regions are instrumented with meteorological instruments, there are significant regions of the world

which are data sparse. Alaska and its surrounding region are notorious for rapidly changing and often harsh

weather. The conditions are made worse by the very rugged terrain in that part of the world as well. The complex

terrain, long and tortuous coastlines, and the lack of many surface and upper air observations strains the abilities of

conventional weather prediction models to accurately predict the weather conditions over remote airports in this

region. In this paper, the Operational Multiscale Environment model with Grid Adaptivity (OMEGA), a new

paradigm in weather forecasting will be discussed. OMEGA is built upon a triangular, unstructured adaptive grid

which facilitates the resolution of complex terrain features. Also, the grid of OMEGA is free of polar singularities,

which makes it a unique model that can simulate weather on a global to local scale using high-resolution only where

it is needed to resolve developing fine-scale weather features in the area of interest.

B. OMEGA

The major advantages of OMEGA over the current state-of-the-art include the ability to resolve the surface

terrain down to scales of 1 km and along with that the local perturbations on the larger scale wind field. This local

wind field perturbation is of extreme importance in determining terminal operations at an airport. However, in order

to calculate this local perturbation, it is important to include all of the physical parameters and processes, which

affect the local flow. These include not only the topography, but also the land use, the land/water composition, the

vegetation, the soil moisture, the snow cover (if appropriate), and the surface moisture and energy budgets. The

inclusion of this additional physics, some of which is only appropriate because of the increased spatial resolution,

represents an additional advance in the state-of-the-art. A detailed description of OMEGA can be found in

Bacon et al.1. Gopalakrishnan et al.

2 presents the application of OMEGA, including dynamic adaptation, to

hurricane track forecasting and a comparison against observations for 20 forecasts covering 8 storms.

C. Computational Grid

A unique feature of OMEGA is its unstructured grid. The flexibility of unstructured grids facilitates the

gridding of arbitrary surfaces and volumes in three dimensions. In particular, unstructured grid cells in the

horizontal dimension can increase local resolution to better capture the underlying topography and the important

physical features of atmospheric circulation flows and cloud dynamics. The underlying mathematics and numerical

implementation of unstructured adaptive grid techniques have been evolving rapidly, and in many fields of

The 26th Congress of International Council of the Aeronautical Sciences (ICAS) <br>including 14 - 19 September 2008, Anchorage, Alaska

AIAA 2008-8915

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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application there is recognition that these methods are

more efficient and accurate than the traditional

structured grid approach3,4

. OMEGA represents the first

attempt to use this CFD technique for atmospheric

simulation.

OMEGA is based on a triangular prism

computational mesh that is unstructured in the horizontal

dimension and structured in the vertical (Figure 1). The

rationale for this mesh is the physical reality that the

atmosphere is highly variable horizontally, but generally

stratified vertically. While completely unstructured

three-dimensional meshes have been used for other

purposes5,6

the benefit of having a structured vertical

dimension in an atmospheric grid is a significant

reduction in the computational requirements of the

model. Specifically, the structured vertical grid enables

the use of a tri-diagonal solver to perform implicit

solution of both vertical advection and vertical diffusion.

Since in many grids the vertical grid spacing is one or

more orders of magnitude smaller than the horizontal

grid spacing, the ability to perform vertical operations

implicitly relaxes the limitation on the timestep

significantly.

D. Grid Refinement / Adaptation

Two types of grid adaptation options are available in OMEGA – 1) Static, and 2) Dynamic. Static

adaptation creates a numerical grid resolving static features such as land-water boundaries, terrain gradients, and/or

any other feature that the user includes in the adaptation scheme with a resolution that smoothly varies from the

maximum to the minimum specified.

The level of refinement can be varied

over the computational domain by

changing the limits of resolution for

various regions in it. Dynamic

adaptation adds the periodic re-

adaptation of the grid to regions that

require high resolution during the

course of a simulation (e.g., frontal

zones, hurricane circulation, pollutant

plumes). This feature is also referred

to as “solution adaptation” as the grid

adapts to the evolving solution.

The computational grid does

not change during the course of a

simulation when using only static

adaptation; the grid adapts to static

features at the beginning of the

simulation. The grid adapts by default

to terrain gradient and land-water

boundaries. The user may select other

features to be added to the adaptivity

criteria; for example the user can

decide to add resolution to an area of

interest. Figure 2 shows an example

of an OMEGA grid.

Figure 1: The OMEGA coordinate system and

vertical alignment of OMEGA grid.

ABQ

Ladron Pk

Polvadera MtnStrawberry Pk

Figure 2: An example of the OMEGA computational grid showing

the terrain detail. In this example, the area of interest was in the

lower right hand portion of the picture, in the vicinity of Strawberry

Peak, New Mexico.

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Dynamic adaptation consists of three major steps taken at pre-set time intervals: (1) specific variables or

their gradients are evaluated to see if they meet the adaptivity criteria; (2) the mesh is refined or coarsened

depending on the pre-specified criteria; and (3) the physical variables are interpolated to the new cell centers. Figure

3 shows an example of dynamic grid adaptation in which the grid adapts to an evolving hurricane. In this case the

adaptation criteria were set to pressure perturbation, which is the difference between the local pressure and a

reference initial pressure.

The unstructured triangular grid facilitates

accurate representation of mountains as well as

coastal features. Conventional weather forecast

model use a stair-stepped representation and hence

need to use extremely high resolutions in order to

resolve coastal features that are not aligned in an N-

S or E-W direction. An example of flow influenced

by such complex terrain is shown in Figure 4, which

shows the ambient winds being blocked by the

island of Taiwan.

OMEGA has a comprehensive set of

physical parameterizations, which deal with the

simulation of a variety of atmospheric processes

ranging from solar and terrestrial radiation, cloud

microphysics, parameterizations to account for

subgrid-scale convection, turbulence generation by

mountainous terrain as well as wind shear and

convection, and atmosphere-surface interactions.

Table 1 shows a list of the physical

parameterizations included in OMEGA.

In this paper, the advantages of using

OMEGA to support aviation operations in Northern

latitudes are discussed. Issues such as complex

terrain induced flow patterns, and the resulting turbulence are included. A series of simulations are performed using

varying resolutions to emphasize the impact of resolving local terrain on forecast accuracy. The advantages of

adaptive grid refinement are explored in these scenarios.

Figure 3: In this simulation of Hurricane Floyd (1999) the grid adapts to regions of low pressure and high

wind speed. A resolution range of 10 to 50 km was used in this example. As the storm evolves (the 3 panels in

this figure are 24 hours apart from each other), the grid resolution increases where it is needed most,

resulting in an accurate track prediction. The background color indicates wind speed with red indicating

high winds. The yellow dotted line indicates the observed track of the storm.

Figure 4: Unstructured triangular grid of OMEGA

facilitates the generation of atmospheric circulations

forced by complex terrain. This figure shows the near

surface winds indicated by the streamlines.

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E. Simulations and Results

A primary advantage of OMEGA in the simulation of atmospheric processes over Northern latitudes is its

ability to treat the entire globe including the poles without any grid singularity. Traditional models using rectilinear

grids have to resort to treating the globe in pieces, each using a modified coordinate system and then trying to stitch

together the solution.

Table 1. An Overview of OMEGA

Governing equations 3D fully non-hydrostatic, prognostic

Grid structure Unstructured triangular prisms, terrain following

Grid adaptivity Adaptation to surface properties and evolving weather

Coordinate system Rotating Cartesian coordinates

Numerics Finite volume with Smolarkiewicz corrective scheme

PBL Viscous sublayer, surface, and transition layers

Turbulence closure 1.5 order, 2.5 level turbulent kinetic energy closure

Cumulus param. Kain-Fritsch and Modified Kuo schemes

Microphysics Extensive bulk-water parameterization

Radiation Shortwave absorption by water vapor and longwave emissivities of water vapor and

carbon dioxide

Lower boundary Based on Monin-Obukhov similarity theory

Upper boundary Rigid, free-slip surface

Lateral boundaries Radiative and large scale nudging boundary condition

Initialization Based on 4D data assimilation

Dispersion Eulerian and Lagrangian aerosol and gas dispersion

Figure 5 shows an example of an OMEGA global grid with grid resolution ranging from 30 – 200 km. The

grid consisted of 110,000 cells in each of its 35 layers. In this example the adaptation was to terrain and land-water

boundaries. A 48-hour simulation was performed with initial conditions derived from the Global Forecast System

(GFS) of the National Centers for Environmental Prediction (NCEP). As this is a global case no boundary

conditions were required. The results were quantitatively compared against the surface and rawinsonde observations

collected from the World Meteorological Organization (WMO) stations. There were approximately 5000 surface

observations and 500 rawinsonde soundings for each of 12-, 24-, 36-, and 48-hour forecast times (even though there

are more stations reporting, some stations had to be eliminated from the list due to data errors and delayed data

arrival). For this quantitative analysis three statistical errors were calculated. These are the Mean Error (ME), Mean

Absolute Error (MAE) and the Root Mean Squared Error (RMSE), which are defined as follows.

( )

( )∑

∑

∑

=

=

=

−=

−=

−=

N

i

ii

N

i

ii

N

i

ii

OMN

OMN

OMN

1

2

1

1

1 (RMSE)Error SquaredMean Root

1 (MAE)Error AbsoluteMean

1 (ME)Error Mean

where Oi represents the set of observations, Mi the corresponding model forecast, and N is the total number of

observation-forecast pairs. The Mean Error represents the average bias, the MAE the true error, and the RMSE the

scatter in the forecast. A positive bias would mean an over-prediction, while a negative bias will mean an under-

prediction. These errors for temperature and wind speed forecasts are given in Figure 6. The results show very low

bias in the forecast quantities. Also, the error in temperature is less than 2°C for the 48 hour period. The wind

speed error is less than 6 kts.

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Another advantage of the OMEGA grid is its ability to represent the terrain at the required resolution. The

inclusion of such terrain details facilitates the formation of terrain forced flows in the boundary layer. Figure 7

shows a regional grid over the Alaskan region with high resolution over Anchorage. The background resolution

ranged from 40 – 60 km. The grid was refined over Anchorage and its surroundings to a resolution down to 6 km

(the smallest edge produced by the grid generator had an edge length of 4.5 km.) The grid had a total of nearly

20,000 cells in each of its 36 layers. The vertical resolution of the grid is a maximum near the ground surface. In

this case the cell thickness of the first layer was set not to exceed 30 m. The layers increased in thickness above this

at a stretch factor of 1.15. This setting generated a grid that reached up to 20 km MSL. Note that the complex

coastline of Alaska is resolved reasonably well. The Cook Inlet, Kodiak Island, Kenai Peninsula and Mt. McKinley

are clearly visible.

Figure 5: An OMEGA global grid in which the cell edge resolution ranged from 30 km – 200 km. The

figure shows the eastern (top left), western (top right), northern (bottom left) and southern (bottom right)

hemispheres. Note that the grid topology remains the same in all hemispheres and there are no singular

points requiring special treatment.

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OMEGA was initialized using the GFS output from NCEP. The GFS files also provided the boundary

conditions for the simulation. This simulation was done in a static adaptation mode. Figure 8 shows the overall

near-surface flow pattern as indicated by the streamlines 12 hours after the model initialization.

An accurate terrain representation is necessary to forecast weather in such complex terrain situations.

Complex terrain can force flow to converge or diverge in a horizontal sense. It can also cause air to move up or

down, accelerating, or decelerating the flow in the process. Such changes to the flow can create turbulence due to

induced shear. OMEGA uses a 1.5 order, 2.5 level turbulent kinetic energy closure suggested by Mellor and

Yamada7, which explicitly keeps track of turbulent kinetic energy (TKE) creation and transport. The dissipation of

TKE is parameterized as a function of the magnitude of the TKE at any given time.

Figure 9 shows the variation of TKE across the simulation domain as well as in the vertical during the

daytime hours. The TKE is indicated by a derived field, the eddy diffusivity for momentum. Note that the flow

constrained in the valley north of Anchorage towards Fairbanks shows stronger turbulence generated due to wind

shear.

F. Summary

OMEGA is a modeling system that is well suited for forecasting meteorological conditions over the

northern latitudes, especially over regions containing complex terrain (mountains and coastal areas). The OMEGA

system contains all the datasets required for generation of the computational grid including global terrain elevation

and land cover datasets and climatological data such as deep soil temperature, and soil moisture. The model has

been validated over various atmospheric conditions ranging from small and short scale phenomena such as local

dispersion of airborne contaminants to large and long scale systems such as snow storms and hurricanes. The

system is automated to do operations for any region of the world with minimal user interaction.

Figure 6: Temperature (top panel) and wind speed (bottom panel) error statistics for a global OMEGA

simulation using the grid shown in Figure 5. The errors at 12-, 24-, 36- and 48-hour forecast times are

shown in these figures.

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Mt. McKinley

Kodiak Island

Kenai Peninsula

Figure 7: OMEGA grid showing terrain elevation over Alaska. Top left panel shows the overall

computational domain. Top right panel shows the high-resolution grid over Anchorage, Cook Inlet and the

surroundings. The bottom panel shows a three-dimensional representation of this high-resolution region.

Mt. McKinley can be prominently seen at the top middle of this panel.

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Figure 8: Top panel shows the near surface wind pattern over Alaska indicated by streamlines 6 hours

after model initialization. Notice the convergence between Kodiak Island and the Kenai Peninsula. The

bottom panel zooms in on the region indicated by the yellow rectangle in the top panel. The flow pattern is

seen in greater detail including an eddy at the mouth of Cook Inlet.

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G. References

1Bacon, D. P., N. N. Ahmad, Z. Boybeyi, T. J. Dunn, M. S. Hall, P. C-S. Lee, R. A. Sarma, M. D. Turner, K. W.

Waight, S. H. Young, J. W. Zack, 2000: A Dynamically Adapting Weather and Dispersion Model: The

Operational Multi-scale Environment model with Grid Adaptivity (OMEGA). Mon. Wea. Rev., 128, 2044–

2076. 2Gopalakrishnan, S. G., D. P. Bacon, N. N. Ahmad, Z. Boybeyi, T. J. Dunn, M. S. Hall, Y. Jin, P. C. S. Lee, D. E.

Mays, R. V. Madala, R. A. Sarma, M. D. Turner, and T. R. Wait, 2002: An Operational Multiscale

Hurricane Forecasting System. Mon. Wea. Rev., 130, 1830-1847. 3Baum, J. D., and R. Löhner, 1989: Numerical simulation of shock-elevated box interaction using an adaptive finite

element shock capturing scheme. Proc. of the 27th Aerospace Science Meeting, AAIA-89-0653. 4Schnack, D. D., I. Lottati, Z. Mikic, and P. Satyanarayana, 1993: MHD simulation on an unstructured, adaptive

mesh (abstract). EOS, Trans. of Am. Geophys. Union, 74, SH11A-16 (fall meeting). 5Baum, J. D., H. Luo, and R. Löhner, 1993: Numerical simulation of a blast inside a Boeing 747. AIAA 24th Fluid

Dynamics Conference, AIAA 93-3091, 8 pp. 6Luo, H., J. D. Baum, R. Löhner, and J. Cabello, 1994: Implicit schemes and boundary conditions for compressible

flows on unstructured meshes. 32nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA

94-0816, 12 pp. 7Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems.

Rev. Geophys. Space Phys., 20, 851-875.

A

B

Figure 9: Turbulence indicated by the eddy diffusivity field for momentum in these panels. The top panel

is a horizontal layer at approximately 500 m AGL, while the lower panel is a cross section along the thick

yellow line AB drawn in the top panel. The cross section shows Mt. McKinley on the left and terrain of the

Kenai Peninsula on the right. A height scale in km is shown to the left of this panel.