The Consequences of Elevation Characterization on Simulations of Drainage

Flows in Mountain Valleys

Hoyt Walker John M. Leone, Jr.

This paper was prepared for submittal to the 7th Conference on Mountain Meteorology

Breckendge, CO July 17-21,1995

April 1995

This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

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THE CONSEQUENCES OF ELEVATION CHARACTERIZATION ON SIMULATIONS OF DRAINAGE FLOWS IN MOUNTAIN VALLEYS

Hoyt Walkefl and John M. Leone, Jr.

Lawrence Livermore National Laboratory Livermore, California

1. INTRODUCTION

Many important phenomena in mountain meteorology are sensitive to, or driven by, land surface characteristics. Thus, accurately representing surface-atmosphere interactions within an atmospheric model requires a realistic characterization of the land surface. Such a characterization must be based on data extracted from a geographical database and transformed so that it is consistent with the needs of the numerical model. In such a process, there are two major classes of error that must be understood and minimized whenever possible. The first class involves the accuracy, precision, and resolution of the geographical data itself. The second class is err01

introduced by the transformations used to assimilate the data into the atmospheric model. The general objectives of this research are twofold. to understand the effects of errors within a geographical database upon the accuracy of the atmospheric model simulation and to design optimal techniques for the transformation of the data.

These goals are related to the study of geographic information science. As discussed by Goodchild (19921, geographic information science examines the unique features of spatial data and the most effective ways to analyze and utilize such data. Consequently, understanding how the characteristics of geographic data affect the& use in complex applications, such as atmospheric modeling, falls within the realm of geographic information science. Among the important characteristics to consider are (1) the data model (e.g., vector or raster), (2) the spatial, temporal and categorical resolution of the data, (3) the data accuracy, and (4) the means by which the data are

In the context of atmospheric modeling, the surface features of interest are the elevation, surface roughness, and sensible and latent heat fluxes [Lee, et.al., 19911. These features, expressed in the form of model boundary conditions, must be developed from geographical databases in a way that balances the need for descriptive detail and

PrOCeSSed.

*Corresponding Author Address : Hoyt Walker, Lawrence Livermore National Laboratoq, L-262,7000 East Avenue, Livermore CA 94550

accuracy with the spatial discretization of a specific model simulation. This is due to both the physics and numerical techniques in a model and to the close coupling of the land surface with boundary layer phenomena under many conditions [Pielke, 19841. Elevation data has a particularly critical role in most mesoscale models because such models typically incorporate some f o m of terrain-following coordinate system. Thus the landform not enly affects. the details of the surface interactions, but it also affects the geometry of the grid above the surface. Therefore, the manner in which the terrain is represented can have numerical effects throughout much of the grid.

This paper will focus specifically on elevation data and how it is processed for use in an atmospheric model. For the reasons mentioned, elevation data is a crucial form of geographic information. Because of its static nature, it forms a convenient starting point for looking at the interaction between geographic data and atmospheric models. The development of nocturnal drainage winds is one example of a terrain driven atmospheric flow. This phenomenon offers a useful test case for examining the effects' of elevation data on mesoscale models [Leone & Lee, 19891. Because such winds are driven by inhomogeneities in the temperature field that are caused by the cooling of the sloping land surface relative to the adjacent air, alterations in the representation of that surface can have a significant effect on a simulation of the associated flow. In earlier work, a number of model simulations using idealized terrain have been performed and analyzed walker & Leone, 19941. Here we extend the investigation by conducting a series of model experiments to determine the response of a hydrostatic mesoscale atmospheric model to lower boundary forcing due to variations in the representation of a real mountain valley system during nocturnal cooling. The simulations are intended to examine the model response to the removal of detail in the terrain representation. Such filtering of high frequency variation is often necessary to ensure the stability of the simulation, but determining the most appropriate degree of smoothing is also important. That is, too much high frequency variation can cause model instability while over-smoothing the elevation data can cause significant changes in the nature of the simulation.

2. APPROACH

In this study, a basic drainage flow is defined along the Brush Creek valley system in western Colorado, the site of the ASCOT field experiments (see Clements et.al., 1989), using a mesoscale atmospheric model relying unsmoothed elevation data to define the lower boundary (for this particular situation, unsmoothed elevation data does not cause problems with the stability of the simulation). The elevation data is then altered in various ways and used as the basis for additional simulations. Some specific details of the control simulation and one comparison run are described in the following sections.

2.1 The SABLE Model

The atmospheric model used in these tests is called SABLE (Simulator of the Atmospheric Boundary Layer Environment), a hydrostatic mesoscale model developed at the Lawrence Livermore National Laboratory. SABLE solves the hydrostatic, anelastic, equations for velocity, potential temperature, and Exner function in three dimensions [zhong, et.al. 19911. The equations are solved by using a unique blend of numerical techniques. The prognostic equations for the horizontal velocity components and the potential temperature are solved using trilinear, isoparametric finite elements in space combined with a semi-implicit time integration scheme. The diagnostic equations for vertical velocity and Exner function are solved by integrating up or down vertical columns, respectively, via centered finite differences.

2.2 Terrain Generation

To support this research, elevation data was extracted from a Defense Mapping Agency (DMA) Digital Terrain Elevation Data (DTED) quadrangle covering the Brush Creek area at 3 arc-second resolution. The raw elevation data was transformed to a Universal Transverse Mercator (UTM) projection and resampled using an unweighted mean to a 200 m grid rotated 45 degrees from north. The grid was rotated to permit the use of a model grid that is aligned with the Brush Creek valley, thereby allowing a more efficient use of gridpoints in the simulations. Elevations beyond the grid boundary were accessed to create a buffer regional around the model grid so that various filter stencils could extend beyond the model grid without resorting to artificial boundary condition assumptions.

2.3 ControlRun

A control run was performed using the 200 m Brush Creek elevation data without any smoothing (see Figure la) covering a 7 by 32 km area, i.e., the grid had 36 by 161 nodes in the horizontal directions. The y coordinate ranges from 0 to 32 km (from top to bottom in the figure) while thex coordinate ranges from 0 to 7 km (from left to right).

The lower boundary of the grid is the elevation surface while the upper boundary is flat at an altitude of 4000 m (the minimum and maximum elevations in the grid are 1650 and 2650 m, respectively). The vertical grid was graded with the lowest cell being 20 m.

0

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Figure 1. Contours of the elevation data use for the (a) control and (b) comparison simulations. The contour interval is 100 m with the lowest contour at 1700 m.

Given the goal of isolating the effects of terrain representation on a model run, accurately reproducing any particular physical situation was not of great importance. Thus, a number of simplifying assumptions were made. For example, the Coriolis parameter was set to zero to avoid complicated veering motions. The cross-side valley wind component, u, was assumed 6 be zero at the appropriate lateral boundaries. At the top boundary, both horizontal

wind components, u and v , were set to zero. The lower boundary cooling was specified as a heat flux of -60 W/ m2. The atmosphere was initialized to be slightly stable with a potential temperature lapse rate of 0.002 K/m. Turbulence was modeled using the local Richardson numberdependent K model of McNider and Pielke (1981). The problems were run for 8 hours. These values were used in all of the runs, the only difference being the representation of terrain.

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Figure 2. Wind vectors three grid levels above the terrain for the control run at (a) 4 hours and (b) 8 hours. Every other point is plotted along the x-axis and every fourth point is plotted along the y-axis.

2.3 Comparison Run

The comparison run was based on a smoothed version of the elevation data used in the control run. An 81-point binomial filter (9 by 9) was passed over the elevation data with only the original data used at each step in computing the weighted average to avoid propagation effects (see Figure lb).

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Figure 3. Contours of the temperatures in a cross-valley plane at y = 27 km for (a) 4 hours and (b) 8 hours.

3. RESULTS

3.1 Control Flow Characteristics

The control run successfully integrated for 8 hours. The cooling land surface caused the generation of downslope winds that, given the shape of the Brush Creek valley, develop a distinct jet that gained strength as it moved down Brush Creek until it approached the intersection with the Roan Creek valley. Here, the jet leveled off and began

to diminish as it neared the end of the grid. Wind vectors at grid'points three levels above the surface are shown in Figure 2% which illustrates the flow at 4 hours into the simulation. Figure 2b provides the same information, but at 8 hours, and shows a similar flow pattern over most of the length of the valley; however there is a noticeable lessening of the flow at the mouth of the valley and into the Roan Creek Valley. This results from the pooling of cold air in the lowest areas of the valley system. The accumulation of cold air at the bottom of the valley system between 4 and 8 hours is illustrated in Figures 3a and 3b with temperature contours in a valley cross-section at a y coordinate of 27 km, i.e. out into the Roan Creek valley.

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3.2 Comparison With Smoothed Elevation Run

The general flow in the comparison run, as illustrated in Figures 4a and 4b, shows the same general characteristics as the control flow, Le., the build up of a distinct jet with strong flow into Roan Creek at 4 hours, but with a lessening of flow at the mouth of Brush Creek apparent at 8 hours. While maintaining the same general pattern, the flow over the smoothed terrain is distinctly stronger. This is highlighted in Figures Sa and Sb, which show the maximum down valley flow as a function of distance down the valley. In these plots, the solid line is the maximum jet speed at 8 hours and the dashed line is the speed at 4 hours. The dotted l i e is the elevation of the valley bottom expressed again as a function of distance down the valley. Most of the features discussed above are apparent in this plot, including the formation of the jet down the valley and the lessening of flow at 8 hours near the mouth of the valley. Of particular interest is the increase in the speed of the flow with the smoothed terrain. For example, the maximum speed along the length of the valley increases from 5.8 to 7.2 m / s at 4 hours between the two runs while the maximum speed at 8 hours increases from 5.6 to 6.8 d s .

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Figure 5 . Maximum down-valley wind speeds for the (a) control run and (b) the comparison run. The dashed line is the maximum jet speed at 4 hours and the solid line is the speed at 8 hours. The dotted line is the elevation of the- valley bottom.

Figure 4. Wind vectors three grid levels above the terrain for the comparison run at (a) 4 hours and (b) 8 hours. Every other point is plotted along the x-axis and every fourth point is plotted along the y-axis.

4. CONCLUSIONS

While this work is at a preliminary stage, the results shown here do indicate an interesting sensitivity to the details of the representation of the elevation surface. As suggested above, the question of the smoothness of the terrain is important for a number of reasons. Generally smoothing is necessary to maintain the stability of the model. The simulations presented here highlight another important aspect of this problem. It appears that important, quantitative differences in an atmospheric flow occur depending on the degree of smoothness in the terrain. The unsmoothed, rougher terrain provides a resistance to the flow that has a distinct effect that could have important implications for the application of such models to dispersion predictions.

In future work, we will attempt to confirm the pattern indicated here by developing more comparison runs that reflect different degrees of smoothness. Also, we will attempt to match the results with field experiment data to determine the most appropriate choice of terrain representation for this iype of problem. Other aspects of model sensitivity to terrain representation will be investigated by adding perturbations of known statistical characteristics to a very smooth representation of the Brush Creek terrain. This aspect of the study should provide information concerning the magnitude of the perturbation that causes the onset of change in the general flow characteristics.

.-

5. REFERENCES

Clements, W.E., Archuleta, J.A., and Gudiksen, P.H. (19891, Experimental Design of the 1984 ASCOT Field Study Journal of Applied Meteorology, 28, pp. 405413.

Goodchild, M.F. (1992), Geographical information science, International Journal of Geographical Infornution Sys~ems, 1, pp. 327-334.

Lee, T.J., Pielke, R.A., Kittel, T.G.F., and Weaver, J.F. (1991) Atmospheric modeling and its spatial representation of land surface characteristics, Proceedings of the First International ConferencelWorkshop on Integrating Geographic Information systems And Envuonmental Modeling, National Center for Geographic Information and

Leone, JM., and Lee, R. (1989) Numerical simulation of drainage flow in Brush Creek, Journal of Applied Meteorology. 28, pp. 530-542.

McNider, R.L., and Pielke, R.A. (1981) Diurnal Boundary Layer Development over Sloping Terrain, Journal of the Atmospheric Sciences, 38, pp. 2198-2212

Pielke, R.A. (1 984) Mesoscale Meteorological Modeling, Academic Press.

Walker, H., and Leone, J.M. (1994) The impact of elevation data representation on nocturnal drainage wind simulations, Proceedings of the Sixth Conference on Mesoscale Processes, American Meteorological Society, pp. 544-547.

Zhong, S., Leone, J.M., and Takle, E.S. (1991) Intexaction of the sea breeze with a river breeze in an area of complex coastal heating, Bowrdary- Layer Meteorology, 56, pp. 101-139.

Analysis.

Work peflormed under the auspices of the US. Dqartment of Energy by Lawrence Livermre National L.aboratory under contract w-7405-fig48