Introduction
Among the unfortunate consequences of increasing population and economic growth in many areas of the world are serious urban and regional air-quality problems. These problems can result from both local emissions and from the transport of pollutants from outside the local area. As a result, understanding regional atmospheric transport is crucial to determining the relationship between source locations and local air quality.
In a previous study of a regional-scale pollution event, Rogers and Bowman (2001) investigated the unusual transport of biomass-burning smoke from Mexico and Central America to the United States during the spring and early summer of 1998 (see also Peppler et al. 2000). Rogers and Bowman (2001) found that, at that time of year, transport from southern Mexico and northern Central America alternates between northward flow toward the United States and westward flow into the Pacific basin. Comparison of particle (air parcel) trajectories with satellite observations of smoke from the fires showed that global atmospheric analyses [e.g., the 2.5° × 2.5° National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis described below] are capable of resolving regional-scale atmospheric transport properties in this situation. During the spring of 1998, drought and widespread agricultural burning led to unusually large smoke production. During May 1998, episodes of northward flow were more common than during other recent years, and at times large amounts of smoke were transported into the central and eastern United States. The heavy amounts of smoke observed in the southeastern United States at that time can be attributed both to unusual smoke production and to abnormally strong northward transport.
This paper describes a quantitative method to characterize the climatological regional-scale transport by relating kinematic particle trajectories to the solutions of the mass conservation equation for a passive trace substance. The climatological description can be used, among other things, to determine the likelihood that a region would be influenced by transport from particular source areas.
The goal of this work is not to characterize the dispersion of a puff or plume from a pollution source, but to provide a quantitative description of the climatological transport by the atmospheric wind field at a given scale. The wind field could be taken from observations, from models, or from assimilated datasets that merge the two. In this study, three-dimensional winds are taken from the NCEP–NCAR reanalysis project data (Kalnay et al. 1996). No attempt is made to include unresolved features of the flow, such as mesoscale circulations, or the effects of subgrid-scale processes, such as boundary layer turbulence. The method presented is quite general, however, and could be applied to velocity fields that include stochastic or deterministic representations of turbulent transport. That is, the approach used here, which is based on the Green's function of the mass conservation equation, could be combined with dispersion models if the dispersion parameters are sufficiently well known. Alternatively, given a database of high- resolution meteorological simulations for a region, the Green's function method can provide a climatological description of transport for that region at all resolved scales.
Data
In this study, trajectories are computed using three- dimensional winds from the NCEP–NCAR reanalysis project data (Kalnay et al. 1996). These data are used because of their temporal and spatial coverage, quality control, and availability. The reanalysis process uses a uniform global data assimilation system. Input data for the reanalysis include global rawinsonde data, Comprehensive Ocean–Atmosphere Data Set (COADS) surface marine data, aircraft data, surface and synoptic data, satellite sounder data, and Special Sensor Microwave Imager (SSM/I) surface wind speeds. The quality and quantity of these data sources vary with time. For this study, data are taken from the 22-yr period 1979–2000. Mean climatological geopotential heights are taken from the long-term climatological means, which are based on the 29-yr period 1968–96.
The reanalysis includes data for temperature, geopotential height, and zonal and meridional winds at 17 pressure levels from 1000 to 10 hPa, and vertical velocity in pressure coordinates at the 12 lowest pressure levels. Data are available on a 2.5° × 2.5° global latitude–longitude grid. The relatively coarse resolution of the model grid for regional-scale analysis is offset by the quality and length of the data record and the uniformity of the assimilation methods. The methods described below can be applied to higher-resolution retrospective datasets as they become available in the future, or to forecast products. Additionally, the NCEP– NCAR reanalysis data are available only in pressure coordinates, which presents some problems where there is elevated terrain. Unfortunately, it is not possible to reconstruct the motion in the original terrain-following coordinates of the NCEP–NCAR model. Given the original model output, however, the trajectories could be computed using terrain-following coordinates. Because the area considered here is mostly low elevation, the errors are not large.
Methods
Green's function method
Both forward and backward trajectories can be computed so that it is possible to evaluate both where air goes to and where it comes from. Recall that the trajectories are computed using the resolved wind field v(x′, t), which in this case omits the direct effects of turbulent mixing in the atmospheric boundary layer. If the characteristics of the boundary layer turbulence are known from observations or model parameterizations, the turbulent component of the velocity could be included in v, using, for example, a stochastic parameterization.
Application to the Texas region
In this study, trajectories for a rectangular region containing the state of Texas are computed using a standard fourth-order Runge–Kutta scheme with a 45-min time step (Bowman and Carrie 2002). Winds are interpolated to the particle locations linearly in both space and time. It is not possible to evaluate 〈G(x, x0, t)〉 for all possible x0. Instead, we evaluate 〈G〉 for a moderately dense, discrete three-dimensional grid of initial conditions. Particles are initialized on a regular latitude–longitude grid with horizontal spacing of ∼30 km × ∼30 km and 18 unevenly spaced pressure levels from 998 to 200 hPa, giving 17 640 particles total. The initial horizontal locations of particles are shown in Fig. 1. Trajectories are initialized each day at these 3D grid locations at 1800 UTC and run forward and backward for 7 days for every day in July from 1979 to 2000. The result is a set of 682 (22 months × 31 days month−1) forward trajectories and 682 backward trajectories for each particle initial location. These will be referred to as grid trajectories. Only trajectories from particles initialized in the lower atmosphere are used here. The modest computation time required to run the complete set of trajectories indicates the relatively low computational cost of the method (roughly 40 h on a single 2.8-GHz Pentium Xeon processor).
The ensemble mean Green's function 〈G(x, x0, t)〉 is estimated by computing the discrete probability distribution function of the particles as a function of x for each x0 on the grid at desired times. The destination grid x does not have to match the initial location grid x0. Note that the ensemble mean Green's function describes the climatological transport properties of the flow, not the dispersion of a single release or “puff.”
Results
Climatological Eulerian flow field
Figure 2 shows the climatological geopotential height at 850 hPa over Texas during July. Lower heights over west Texas indicate the semipermanent area of low pressure in the desert southwest known as the North American thermal low (NATL). West Texas experiences the eastern portion of the counterclockwise circulation around this low. Higher heights in east Texas are connected to the semipermanent area of high pressure in the Caribbean and eastern Atlantic known as the Bermuda high. Central and east Texas are influenced by the western edge of the clockwise circulation around this area of high pressure. Texas lies within the transition zone between these two pressure areas and typically experiences widespread southerly flow during the summer months. The geopotential height climatological description allows us to anticipate that the general character of the particle trajectories in the lower atmosphere will be northward.
Simply using the mean height or wind field, however, does not provide any information about variability of the resolved winds (and the trajectories) from day to day or year to year. That information is contained in the Green's function.
Probability distribution of Houston air particles
For illustration purposes, subsets of 〈G〉 are made of the grid trajectories for four Texas urban areas: Austin, Dallas/Fort Worth, Houston, and San Antonio. The subsets are composed of all the grid trajectories initialized at points surrounding each urban area (Fig. 1). The geographically larger areas of Dallas/Fort Worth and Houston are composed of four grid points, while Austin is composed of two, and San Antonio of one. The distributions are for illustration purposes only and do not represent the actual distribution of sources in these metropolitan areas. Air particle locations in the urban trajectories are plotted every 6 h, and contours are drawn showing the climatological density of particles as they move from their initial locations. These correspond to slices through the multidimensional Green's function. Only particles initialized at the lowest seven altitudes, below approximately 850 hPa, are plotted. Particles above 850 hPa typically lie above the boundary layer and are not influenced by surface sources on short time scales. In this way, a probability distribution of low- level particle transport is created for particles released from the four urban areas at 1800 UTC in July.
As an example, the climatological transport from the Houston area is shown in Fig. 3 at 6, 12, and 24 h after the particle release. The contours of particle density are equivalent to plotting 〈s(x, t)〉 for an initial condition s0, consisting of a constant value within a rectanglar region centered on Houston and zero everywhere else. For plotting purposes, 〈s(x, t)〉 is normalized by the maximum value of 〈s(x, t)〉.
The distributions show that the clockwise circulation around the Bermuda high dominates the transport of particles during July. Particles move north and then northeast. Figure 3a shows that 6 h after release the probability distribution of the particles is essentially circular. The particles move north and are most likely to be approximately 110 km north-northeast of downtown Houston (mean speed of 5.4 m s−1). Figure 3b shows that 12 h after release the distribution remains nearly circular. The particles have continued moving north and are now centered about 240 km north of downtown Houston over rural east Texas (mean speed of 5.5 m s−1). Tyler, a town of 83 650 with occasional summer ozone exceedances attributed to air transported from Houston (Texas Commission on Environmental Quality 2000), lies within the 0.6 isopleth at 12 h. Figure 3c shows that 24 h after initialization the probability distribution is still roughly circular. Particles have moved far enough north to enter the northern edge of the clockwise circulation and have begun to move northeastward (mean speed of 7.1 m s−1). The distribution is centered over Texarkana, roughly 600 km from downtown Houston. The increase in mean speed with increasing time is due to some of the particles moving to higher altitudes where mean wind speeds are larger.
Vertical distribution of Houston air particles
The vertical distribution of particles 6, 12, and 24 h after their release in Houston is shown in Fig. 4. In this case the vertical velocity contains only the large-scale hydrostatic velocity component computed from the continuity equation. The convective transport is not included in the available NCEP–NCAR reanalysis data. The obvious layering evident in Fig. 4a is a result of the initialization of particles at seven discrete levels below 850 hPa. Figure 4b shows that the rate of northward particle motion increases with altitude. A small fraction of the particles move southward. Similarly, continued northward motion, which is much greater above 900 hPa, is evident in Fig. 4c. The increase in the northward movement of the particles with altitude is evidence of increasing wind speed aloft.
Applications of Green's functions
As discussed previously, if the value of x0 is fixed, 〈G(x, x0, t)〉 describes how air initially at x0 disperses throughout the atmosphere as a function of t in a climatological sense. Here, 〈G〉 can be used to estimate the climatological probability of transport for an arbitrary initial distribution, including, for example, both widespread (e.g., biogenic) sources and urban-scale sources, by summing appropriately weighted sources at various initial locations. Figures 5a–5c show 〈s(x, t)〉 at 6, 12, and 24 h for an initial condition that is a combination of localized sources around all four metropolitian areas listed above. For illustration purposes, the initial condition for each urban area has a value of 1, while the remaining initial conditions at all other latitudes and longitudes are assigned a value of 0. The value of s is then calculated using (3). The resulting plots show the climatological probability density of the combined transport from the four urban centers as a function of t. Once again, 〈s(x, t)〉 is normalized by the maximum value of 〈s(x, t)〉. Actual values of s〈(x, t)〉 decrease with time. By superimposing appropriately weighted solutions for multiple initial times, it is also possible to simulate the climatological mean result from a time- varying or steady source (a plume). Simple loss processes (finite lifetime effects) can also be included (not shown).
Figures 6a–6c show backward-in-time calculations of s(x, t) at 6, 12, and 18 h prior to a final condition at Dallas/Fort Worth. The resulting plots show the climatological probability density of sources of air transported toward Dallas/Fort Worth as a function of t. That is, Fig. 6 is a plot of the climatological probability density of particle locations 6, 12, and 18 h prior to arriving at Dallas/Fort Worth. It can be observed that Austin and San Antonio lie within the plotted climatological probability density in Fig. 6c, while Houston lies on its eastern edge. Climatologically (and within the resolution of the NCEP–NCAR reanalysis data) air in Dallas/Fort Worth is not likely to have passed through either San Antonio or Houston in the previous 18 h. This is in part a reflection of the small amount of variability in the lower-tropospheric flow over Texas in the summer season.
Plots of fD(t) illustrate how the ensemble-mean concentration of a trace substance at a destination changes with respect to t for a particular source. Figure 7 shows sample results for two sources, Houston and San Antonio, and two destinations, Tyler and Dallas/Fort Worth. The destinations are the latitudes and longitudes of Tyler and Dallas/Fort Worth. Figure 7 shows fD(t) for three cases: Houston to Tyler, Houston to Dallas/ Fort Worth, and San Antonio to Dallas/Fort Worth. In each case the probability rises from zero, reaches a maximum, and then decreases more slowly. The peak in the curve occurs later when the transport distance is larger. The maximum value of fD at 18 h in the Houston-to- Dallas/Fort Worth case is only 0.0045, as compared with a maximum for fD of 0.0125 in the Houston-to-Tyler case, showing that Tyler is more than 2.5 times as likely to be influenced by air from Houston as is Dallas/Fort Worth. In comparison, transport from San Antonio to Dallas/Fort Worth begins to increase 6 h after initialization, peaks with a value of 0.0025 at 24 h, and then begins a gradual decrease. Dallas/Fort Worth is consistently influenced more by air from Houston than by air from San Antonio over the 48-h period shown. In this manner 〈G(x, x0, t)〉 can be applied to compare the relative likelihood that transport from different sources will affect a chosen destination.
Conclusions
During the summer season the atmospheric circulation over Texas is dominated by the clockwise circulation around the Bermuda high. Trajectories calculated using kinematic Lagrangian methods show that air throughout most of Texas moves northward before gradually curving northeastward as a consequence of the clockwise circulation. Accordingly, particles released in Houston move first north and then northeast, following trajectories through east and northeast Texas over the 24-h period following release. The substantial variability of the trajectories from day to day can be seen in the increasing dispersion of the trajectories with time from release (e.g., Fig. 3). (This climatological dispersion is conceptually different from the dispersion of a “puff” in a single realization of the flow). The climatological variability of the transport is represented by the spreading of the ensemble mean Green's function (Fig. 5) and is substantial, even though small-scale turbulent processes are not resolved in the wind data used. The calculated Green's functions can be applied to questions of regional air quality, such as when and to what extent pollution from a given source impacts another area. If the boundary layer characteristics are known, perhaps from observations or a model, then the effects of boundary layer turbulence could be included in the trajectory calculations and the resulting Green's functions.
Acknowledgments
This research was funded in part by a grant from the Texas Air Research Center, Lamar University, Beaumont, Texas.
REFERENCES
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Peppler, R. A. Coauthors, 2000. ARM Southern Great Plains site observations of the smoke pall associated with the 1998 Central American fires. Bull. Amer. Meteor. Soc 81:2563–2591.
Rogers, C. M. and K. P. Bowman. 2001. Transport of smoke from the Central American fires of 1998. J. Geophys. Res 106:28357–28368.
Texas Commission on Environmental Quality, 2000. Appendix N: Demonstration of transport from the HGA ozone nonattainment area to DFW. Revisions to the State Implementation Plan for the Control of Air Pollution, Attainment Demonstration for the Dallas/Fort Worth Ozone Nonattainment Area, Texas Natural Resource Conservation Commission, Rule Log No. 98046-SIP-AI, 18 pp.
Grid of initial points for trajectory calculations
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
Climatological geopotential height (m) (1968–96) at 850 hPa for Jul
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
Probability distributions for the Houston urban subset for (a) 6, (b) 12, and (c) 24 h after initialization at 1800 UTC. The black rectangle in southeast Texas represents the initial points of the Houston urban subset; dots represent the individual air particles initialized at altitudes below 850 hPa; and the contours represent the value of 〈s(x, t)〉 for an initial condition that is nonzero near Houston and zero everywhere else. At each time the concentration 〈s(x, t)〉 is normalized by the maximum value of 〈s(x, t)〉. Isopleths are drawn at intervals of 0.1
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
Latitude–height distributions for the Houston urban subset for (a) 6, (b) 12, and (c) 24 h after initialization at 1800 UTC
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
Distribution of 〈s(x, t)〉 for a combination of initial conditions at Houston, San Antonio, Dallas/Fort Worth, and Austin for (top) 6, (middle) 12, and (bottom) 24 h after initialization at 1800 UTC
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
Distribution of 〈s(x, t)〉 for a final destination of Dallas/Fort Worth for (top) 6, (middle) 12, and (bottom) 18 h before initialization at 1800 UTC
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
Time variation of 〈s(x, t)〉 for several different values of x0 and x at Houston to Tyler (solid line), Houston to Dallas/Fort Worth (asterisks), and San Antonio to Dallas/Fort Worth (triangles)
Citation: Journal of Applied Meteorology 43, 4; 10.1175/1520-0450(2004)043<0623:LMFCAO>2.0.CO;2
