CRYSTAL MIST: A Field and Modeling Study of Cloud Dispersion in the Middle Troposphere

Wynn L. Eberhard¹, Steve R. Diehl², Dan J. Rusk³, and John A. Hasdal⁴

¹NOAA Environmental Technology Laboratory, Boulder, Colorado

² Kaman Sciences Corp., Colorado Springs, Colorado

³ Aeromet Corp., Tulsa, Oklahoma

⁴ Teledyne Brown Engineering, Huntsville, Alabama

Published in: Preprint Volume, 10^th Joint Conference on the Applications of Air Pollution Meteorology with the Air and Waste Management Association, 11-16 January 1998, Phoenix AZ, by the American Meteorological Society, 307-311.

1. INTRODUCTION

This study investigates the dispersion of puffs in the middle troposphere above the mixed layer. The main purpose was to provide observations for improving and evaluating computer models that predict the fate of toxic materials released as drops in a defensive military scenario. The drops can settle and might eventually contaminate persons on the ground. The project focused on the stable and turbulent layers in the free atmosphere to understand how shear and occasional turbulence increase the horizontal footprint of the cloud of tracer reaching the mixed layer and surface.

The observations provide insights into turbulence and dispersion processes in the stable atmosphere, where measurements are few compared to the data available in neutral and unstable conditions near the surface. A model was developed that satisfactorily replicated the tracer cloud's evolution in size and shape as the tracer fell through quiescent and turbulent layers.

2. CRYSTAL MIST EXPERIMENT

The experimental strategy was to release a small cloud of tracers some distance above a predicted shear layer where the Richardson number Ri was expected to be favorable for the development of turbulence. A suite of remote and in situ sensors tracked the cloud motion and its evolution in size and shape. The microphysical characteristics of the tracer particles are known, permitting accurate calculation of their terminal fall velocities and calibration of the signals from some of the instruments observing the cloud. A relatively dense set of meteorological soundings were collected before, during, and after the observation period. Data from selected cases were processed in a manner convenient for linking the tracer's behavior with the observed meteorology in a modeling study.

A total of eleven tests, each with one release on a separate day, were accomplished. Three of the events occurred in December 1993 at White Sands Missile Range, and the remainder in July 1994 at the Nevada Test Site (NTS). Release altitudes ranged from 4.4 to 10 km. This paper focuses on results from the 13 July case with release at 7.30 km MSL.

The tracer consisted of beads of optical crown glass possessing a high degree of sphericity. Smaller beads were used in some cases to highlight the dispersion processes, and larger beads were used in others to simulate drops large enough to have inertial effects and that might reach the surface with significant concentration. The medium-sized beads used on 13 July had a median diameter of 69.5 µm and an observed terminal fall velocity of 0.38 m s^-1 at about 6.5 km MSL. Measurements with a scanning electron microscope confirmed the narrow size distribution (90% of the particles between 63 and 74 µm diameter) claimed by the manufacturer, which minimized the spread in terminal fall velocities.

The tracer was dispensed by Aeromet's High Altitude Reconnaissance Platform (HARP), a Learjet 36A modified to carry a suite of atmospheric sampling instrumentation. The tracer was quickly ejected from a special wing-mounted pod by the force of gravity and ram air. The "initial" cloud shape, after about 10 seconds had elapsed and most of the turbulence associated with the release had decayed, was typically 200-300 m in length along the flight track and roughly 1/4 this size in the transverse dimensions. The cloud had a lumpy appearance, so the spatial distribution of beads was not smooth. On 13 July 110 kg (~2.3×10¹¹ beads) were released at 1801:38 UTC.

Meteorological profiles were obtained by several means and from a variety of sites, as illustrated in Fig. 1 for 13 July. The pibal data (theodolite tracking of pilot balloons by NTS) proved to be of marginal value due to uncertainty in balloon altitude. A nose-mounted gust probe aboard HARP obtained turbulence data, but these were limited in scope because the flight track was controlled by attempts to measure tracer distributions rather than profiling turbulence near the cloud. The ground-based lidar used natural aerosol particles and its Doppler capability to measure winds before and after the cloud observations, but these profiles failed to reach as high as cloud release altitude. NTS also provided rawinsonde measurements from launches at two sites (Fig. 1) before tracer release and during and after cloud observations. Wind profiles were generated from the recorded rawinsonde data using Fourier transform filtering. The analysis in this report incorporates meteorology only from the rawinsonde data.

The tracer release point and camera locations (Fig. 1) were selected based on a one-day forecast and updates from wind soundings early in the day. This provided a tracer path favorable for observation by ground-based and aircraft instruments.

The cameras provided views of the tracer cloud from different perspectives for about the first half hour after release. Two sites had a pair of cameras (one visible and one infrared) operated at each of two sites (I in Fig. 1) by the Aerospace Corp. Two other sites (V in Fig. 1) had three visible cameras, each with a different field of view, operated by the Atmospheric Research Laboratory. Although attempts to retrieve the three-dimensional shape and size of the cloud met with limited success, triangulation provided a good description of the cloud track in vertical and horizontal.

The ground-based lidar (Post and Cupp 1990) operated by the National Oceanic and Atmospheric Administration (NOAA) provided the data most valuable for model evaluation (e.g., Fig. 2). The system uses coherent detection for high sensitivity and acquired useful data for typically 1 h after release. It is fully eyesafe by virtue of its 10.6 µm wavelength and expanded beam. Interference from background light is negligible (the lidar can even scan across the sun's disk). Its range resolution of 90 m was adequate for resolving the shape and size of the cloud except during the first several minutes after release. The pulse rate was 20 Hz, but pulses were averaged in real time to produce beams at 6.7 Hz rate. (Averaging was necessary to meet limitations on the data recording rate and to reduce random fluctuations in backscatter that are characteristic of diffraction-limited systems like this one.) The lidar repeatedly scanned up and down. During the first few min after release, these vertical sweeps were repeated at the same azimuth for the time (15-60 s) needed for the cloud to advect through the scan plane. Later, the azimuth was changed between each sweep to provide a cycle of typically nine sweeps stepping through the cloud. Automatic, interactive scan control allowed efficient cycles through the cloud and nearby clear air typically every 45 seconds.

Three-dimensional distributions of bead concentration were derived at desired time intervals by synthesizing lidar data from short periods, each roughly centered on a "snapshot" time. Lidar calibration factors were applied first, then the observed settling velocity and the advection by the wind were taken into account. The rawinsonde profiles were not accurate enough for this operation due to errors and separation in time and space. Therefore, a wind profile generated from the lidar track of the backscatter centroid of the cloud was used for advection adjustment early after release, blending into the rawinsonde profile as the cloud became large. Finally, the data were interpolated to a Cartesian grid with spatial filtering corresponding to the sample spacing in the data. Each bead distribution reported here is a synthesis of NOAA lidar measurements lasting about 3 minutes each.

HARP carried cloud microphysics instruments and an upward-viewing lidar. These could obtain more detailed information on the spatial structure of the cloud than the ground-based cameras and lidar, but precisely locating these measurements within the overall cloud proved difficult. For example, on 13 July the bead concentration measured by aircraft penetration 250 s after release was consistent with a flight track through only the fringe of the cloud. After the penetration attempts, HARP flew under the cloud to obtain lidar data from which 2-D profiles of bead concentrations were calculated. This was accomplished successfully 16 times on 13 July. The airborne lidar data clearly reveal (Fig. 3) the lumpy nature of the cloud and its non-Gaussian shape throughout the observing period.

3. CLOUD DISPERSION MODEL

Cloud transport and growth were simulated in a probability density function model called MESO. Diehl et al. (1982) outlined the basics of this model, in which tracer particles individually undergo random displacements to simulate gradient transfer processes, superimposed on mean motion by advection and particle terminal velocity. In the limit of large numbers of particles the technique is actually a numerical solution to the 3-D advection-diffusion equation. Vertical diffusion was of particular interest in Crystal Mist.

An important feature of the model is that it permits diffusivities to be any function of space and time. In the vertical direction, for example, the diffusivity is approximated as a series of adjoining linear segments of the form K(z) = K_o + K₁z (Diehl et al. 1982), allowing the modeling of rapid changes in thin layers of the atmosphere such as can occur with Clear-Air-Turbulence (CAT). The technique permits high-fidelity solutions in high shear regions of the atmosphere. For this study the vertical diffusivity and wind field were specified with a 40 m resolution. The time step t is adjusted so the tracer displacement d is small compared to the change in concentration over the displacement distance, i.e.Dt < d²/(2K). Although the tracer technique does not require a grid, at points in time at which a concentration is desired, a grid is placed in the region of the cloud to estimate the concentration field.

In altitude regions in which the Richardson number Ri is not low, the model estimates the vertical diffusion using an expression derived by Weinstock (1978). By ignoring contributions to turbulent mixing outside the inertial subrange, the eddy diffusivity can be approximated by

where s_w² is the vertical velocity variance and k_o is the wavenumber dividing the inertial and non-inertial subranges given by k_o² = 0.8N²/s_w² where N is the Brunt-Vaisala frequency. Although N can be readily estimated from the potential temperature slope, it is often impractical to measure s_w². However, other investigators using profiling radars have observed that s_w² correlates well with the wind speed in the mid-troposphere (Ecklund et al. 1986). Perhaps due to gravity wave excitation, s_w² also varies with topography and the height of the boundary layer. For this modeling effort, we found it reasonable to set s_w² = 0.008 V_m, where V_m (m s^-1) is the wind speed in the mid-troposphere.

When Ri drops below some critical value Ri_cr ~ 0.25, a highly turbulent CAT layer may develop. Using K-theory assumptions, Pluene (1990) derived an expression for the diffusivity inside a CAT layer of the form

where k is the von Karman constant, DV is the velocity difference across the layer, and DH is the CAT layer thickness given by

where is the potential temperature and g is the gravitational acceleration. Since CAT is probabilistic in nature, Pluene has included a function alpha(Ri) which is equal to one at low values of Ri near Ri_cr and decreases to near zero as Ri approaches or exceeds one.

In practice, Pluene's expressions are difficult to use since they result in diffusivities which are dependent on the altitude sampling interval, which in turn can lead to unrealistically high diffusivities. Keeping Pluene's basic arguments intact, we have postulated the existence of sublayers which limit the maximum mixing length and, thus, the maximum diffusivity in each layer. The result can be shown to be

where n is the number of sublayers across DH. If n is set proportional to DV, the diffusivity becomes independent of the measurement interval. The CAT measurements of Kennedy and Shapiro (1980) were used to test this hypothesis and determine a value for n. A plot (Fig. 4) of the measured diffusivities inside CAT layers against values predicted using (4) with n = aDV, where a = 0.22 s m^-1 shows good agreement over a wide range of diffusivities.

4. 13 JULY RESULTS AND MODEL COMPARISON

Wind profiles on 13 July were obtained from six rawinsondes launched at the times and places indicated in Figs. 5 and 1. These were averaged into two groups of three to form "early" and "late" composite profiles (Fig. 5). The average profile of potential temperature and corresponding predicted diffusivity can be seen in Fig. 6. The intense layer of CAT between 5.5 and 6.1 km MSL was caused by the slow change in the potential temperature over this layer and the relatively high wind shear, dV/dz ~ 0.01 s^-1. (The wind speed profile, which increased from 4 to 9 m s^-1 between 5.5 and 7.5 km MSL, is not shown because of lack of space and because directional wind shear dominated at most heights.) In the diffusivity plot, curves are shown for three times after cloud release using time interpolation between the early and late composite wind profiles.

A lognormal fit was made to the measured bead size distribution to provide a smooth function for simulating the spread in bead settling velocities. The geometric standard deviation was only 1.05.

A comparison between the measured and modeled vertical bead distributions is shown in Fig. 2 for six selected times after release. In general, the shapes and peak values of the modeled distribution agree well with the NOAA lidar data. By 47 min after release the base of the cloud had drifted downward into the predicted CAT layer shown in Fig. 6. By 54 min the cloud was almost totally immersed in the CAT layer, and both the predicted and measured vertical profiles no longer have symmetrical shapes.

Figure 7 contains a plan view of the cloud measured by the NOAA lidar at 48 minutes after release alongside that predicted by the model. Although the measured cloud produced contours 120 m above and below the highest and lowest contours of the simulated cloud, the areas are small indicating that only a small fraction of the actual beads had diffused to these levels. In comparison to the actual cloud, the simulated cloud has approximately the correct length, width and orientation. Fig. 3 shows the vertical cross-section of the cloud measured by the HARP lidar at the same time, illustrating the detail in structure that is somewhat smoothed in the results from the NOAA lidar and especially the model. The modeled cross-section (not shown) has elliptical contours, but they possess a width, height, and tilt from horizontal similar to that observed by the airborne lidar. Although the model cannot be expected to predict the fine details of the actual cloud, it did predict its overall shape and size.

The effect of shear over the vertical extent of the cloud caused it to grow much faster horizontally than vertically. This created a distortion in the general shape of the cloud according to the accumulated affects of the shear. On 13 July after 48 min this had caused the top of the cloud to track counter-clockwise and slightly faster relative to the bottom of the cloud. This elongated cloud was tilted from the horizontal along both the long and narrow dimensions (in plan view) of the cloud.

5. CONCLUSIONS

The Crystal Mist experiment provided an excellent data set for investigating puff transport and diffusion in the free atmosphere above the mixed layer. The glass bead tracer was stable and well-characterized, and the particles were large enough to gradually settle through stable layers into more turbulent layers. Frequent, nearby rawinsondes proved to be the best source of meteorological profiles. Lidars and cameras measured the motion and growth of the tracer cloud.

A model was developed that predicts the profile of diffusivity. Dispersion of the tracer was simulated by a probability distribution function model developed to accommodate the highly variable diffusivity and horizontal shear encountered by the cloud.

Although only some of the Crystal Mist events have been fully reduced and analyzed, a number of tentative conclusions can be drawn, at least for the variable and light wind conditions present during the tests. The agreement with the NOAA lidar and other data shows that the overall shape and size can be modeled up to an hour after cloud release, although predicting the detailed shape of an actual cloud was not possible due to its initial lumpiness and the effects of the larger scales of turbulence. The model appears to correctly predict CAT layers and to handle their dispersive effects with reasonable fidelity. When not in CAT, the estimated vertical diffusivities were small (about 1 - 4 m² s^-1). The effects of horizontal diffusion assuming homogeneous turbulence for the scales simulated in the model) were relatively small, and most of the horizontal growth was explained by the interplay of vertical diffusion and vertical shear. This interplay created clouds whose overall shapes were often elongated and tilted, but sometimes became even more complicated.

Acknowledgments. We thank Julius Lilly and Nancy Byrd of the US Army Space and Strategic Defense Command for sponsorship and guidance, Jeryl L. Wood for NTS coordination, Wayne Einfeld of Sandia National Laboratory for bead size measurements, and others too numerous to name for measurements and analysis.

6. REFERENCES

Diehl, S.R., D.T. Smith and M. Sydor, 1982: Random-walk simulation of gradient-transfer processes applied to dispersion of stack emission from coal-fired power plants. J. Appl. Meteor., 21, 69-83.

Ecklund, W.L., K.S. Gage, G.D. Nastrom and B.B. Balsley, 1986: A preliminary climatology of the spectrum of vertical velocity observed by clear-air Doppler radar. J. Climate Appl. Meteor., 25, 885-892.

Kennedy, P.J., and M.A. Shapiro, 1980: Further encounters with clear air turbulence in research aircraft. J. Atmos. Sci., 37, 986-993.

Pluene, R., 1990: Vertical diffusion in the stable atmosphere. Atmos. Environ., 24A, 2547-2555.

Post, M.J., and R.E. Cupp, 1990: Optimizing a pulsed Doppler lidar. Appl. Opt., 29, 4145-4158.

Weinstock, J., 1978: Vertical turbulent diffusion in a stably stratified fluid. J. Atmos. Sci., 35, 1022-1027.

Fig. 1. Plan view of the experiment on 13 July. P designates where the aircraft penetrated the cloud for bead measurements by microphysical probes, and the dots show where the airborne lidar detected the cloud during underflights. The ground-based NOAA lidar operated from L. R designates locations for rawinsonde launches (Yucca Flat is near the NOAA lidar and Desert Rock about 56 km south). Pibal launches were from the locations marked . V and I show locations of ground-based cameras (see text).

Fig. 2. Vertical bead distribution measured by the NOAA lidar and predicted by the model at various times after release. Profiles at different times are offset along the horizontal axis to be legible.

Fig. 3. Vertical cross-section of tracer cloud measured by the airborne lidar along the transect shown in Fig. 7. Contours have relative values of 0.5, 1, 5, 10, and 20.

Fig. 4. Comparison between diffusivities calculated from turbulence measurements by aircraft inside CAT layers (Kennedy and Shapiro 1980) versus predictions by Eq. 4 using only profile data for the same cases.

Fig. 5. Wind direction profiles on 13 July generated by averaging the three early and three late rawinsonde profiles (times in UTC).

Fig. 6. Potential temperature profiles (left) and their average used to predict the vertical diffusivity profiles (right) at 0, 30, and 60 min after bead release.

Fig. 7. Plan view of the cloud detected by the NOAA lidar (left) at 48 minutes after release and the corresponding model simulation (right). The contours are at different heights showing the area in which bead concentration was 200 m^-3 or greater, which was about 5% of the peak value in this 3-min synthesis of lidar data.