Grantee Research Project Results

Final Report: Lagrangian Modeling of Pollutant Dispersal in the Atmospheric Boundary Layer

EPA Grant Number: R823419
Title: Lagrangian Modeling of Pollutant Dispersal in the Atmospheric Boundary Layer
Investigators: Weil, Jeffrey C.
Institution: University of Colorado at Boulder
EPA Project Officer: Hahn, Intaek
Project Period: October 1, 1995 through September 30, 1997 (Extended to September 30, 1998)
Project Amount: $164,473
RFA: Exploratory Research - Chemistry and Physics of Air (1995) RFA Text |  Recipients Lists
Research Category: Air , Safer Chemicals

Objective:

The overall aim of this research program was to improve our understanding and predictive capability of buoyant plume dispersion due to elevated sources in the convective boundary layer (CBL). The focus was on the prediction of the mean and root-mean-square (rms) fluctuating concentrations due to such plumes. There were two key objectives. The first was to further develop a hybrid Lagrangian dispersion model to address highly buoyant plumes that "loft" or temporarily remain near the top of the CBL and disperse downwards slowly. The hybrid model is a statistical approach based on the meandering of a small plume by the large eddies in the CBL. The second was to modify an analytical probability density function (PDF) model to account for highly buoyant plume dispersion. The key advantage of this model is its capture of the essential physics of dispersion while remaining relatively simple; the simplicity makes the model useful in air quality applications.

Summary/Accomplishments (Outputs/Outcomes):

The model developments, results, and their significance are presented below for each of the two approaches. The degree of plume buoyancy is characterized by the dimensionless buoyancy flux where is the source buoyancy flux, U is the mean wind speed, is the convective velocity scale, and is the CBL depth. In the CBL, the rms turbulence velocities and the eddy length scale are proportional to and respectively. The source buoyancy can be divided into three ranges: low buoyancy for where the plume behavior is similar to that for a nonbuoyant release; moderate buoyancy for and high buoyancy for which corresponds to plume lofting.

In the hybrid Lagrangian model, the mean and rms concentration fields are found by averaging an assumed Gaussian plume concentration field over the PDF of the randomly-varying plume centroid. The two main features are: (1) a Lagrangian particle model to represent the plume centroid meander due to the large CBL eddies, and (2) an entrainment model to describe the rise and growth of a buoyant plume relative to those eddies. The centroid is assumed to behave as a wandering "fluid particle" with random vertical and lateral velocities obtained from a stochastic model. The model equations require an assumed form for the velocity PDFs and the CBL velocity statistics, which are obtained from parameterizations of turbulence measurements.

For buoyant releases, the plume rise velocity is superposed initially on the local random velocity in the environment. Plume material that rises into the elevated inversion can later reenter the CBL due to entrainment by the large CBL eddies. In modeling this behavior, we superpose the incremental velocity changes due to the ambient turbulence and plume buoyancy. The buoyancy increment is proportional to the mean potential temperature difference, between the plume and the environment. The is determined by the source buoyancy and entrainment, and it decreases with travel time or distance.

For low-to-moderate fluxes , the is found from a standard entrainment model for a round bent-over plume as used in an earlier formulation. However, for high buoyancy the plume growth and are obtained from a new model that accounts for the reduced mixing imposed by the highly stable plume-ambient interface. The entrainment velocity is proportional to and inversely proportional to a Richardson number based on and , i.e. , the interfacial stability is incorporated through the Richardson number. The model is consistent with the enhanced lateral spread of lofting plumes as found by Briggs (1985).

The model was evaluated by comparing predicted plume quantities with laboratory convection tank data obtained under another research program; the data covered the range . The main features of the predicted spatial statistics-the mean plume height and the lateral and vertical dispersion parameters-were in reasonable agreement with the data. The mean height and displayed a monotonic increase with distance and plume buoyancy in both the model and experiment, whereas the decreased with near the source. The latter was attributed to: (1) the greater plume rise with increasing , which led to a reduced vertical meander, and (2) the " squashing" of the vertical depth as the rapidly-rising plume was abruptly halted by the elevated inversion.

For the concentration fields, the results showed that the ground-level concentration (GLC) along the plume centerline varied systematically with distance and , and was in general agreement with the experiments (Weil, 1998). An increase in buoyancy led to a significant reduction in the concentrations near the source by comparison to the nonbuoyant case, . In addition, the surface values of the concentration fluctuation intensity, increase, but the trend was not followed for , possibly due to reduced plume meandering.

The hybrid Lagrangian model is an initial effort to predict buoyant plume dispersion and the associated and over a wide range of source buoyancy . . In addition to the results discussed here, it also was found that the modeled values together with a gamma cumulative distribution function could be used to estimate the peak concentration values, e.g., the 99th percentile values. The study also showed that some improvements can and should be made to the model to correct two deficiencies: (1) the modeled concentration contours were nearly normal to the CBL top whereas the data showed that the contours were nearly horizontal there, and (2) laboratory measurements showed that the lofting plume was entrained incrementally into the CBL instead of the plume continuing to grow by entrainment. These deficiencies can be addressed by modeling the plume as a collection of buoyant particles rather than as a meandering plume, and by including removal or "extrainment" of material from the lofting plume. These aspects are currently being addressed under another research program.

In the PDF approach, one assumes that plume sections are emitted into a traveling train of convective elements-updrafts and downdrafts-that move with the mean wind speed in the CBL. The vertical and lateral velocities in each element are assumed to be random variables and characterized by their PDFs. The mean concentration is found from the PDF of tracer particle position, which in turn is derived from the vertical velocity PDF.

In the CBL, the is positively skewed and results in a non-Gaussian vertical concentration distribution. For buoyant plumes, the model was extended earlier by superposing the displacements due to plume rise and the random to obtain the concentration field (Weil et al., 1986). This approach worked well for weak- to-moderate buoyancy , but for high , a separate treatment was required to account for the lofting behavior. However, the above separation did not maintain continuity of the predicted concentration field with

Under this program, we introduced a new and simplified treatment of plume interaction with the elevated inversion. This included an "indirect" source to address the lofting behavior and the dispersion of "nonpenetrating" plumes and a "penetrated" source to account for plume material that initially penetrated the elevated inversion but subsequently fumigated into the CBL. The treatment resulted in a continuous variation of with , thus overcoming a limitation of the earlier PDF models. A novel treatment of plume rise for the indirect source was found using an energy argument governing the descent of buoyant plume elements from the CBL top. In addition, we included the effects of surface shear as well as convection in parameterizing the PDF so that the model is applicable in the limit of a neutral boundary layer. The new model is described in detail in Weil et al. (1997).

The crosswind-integrated concentration (CWIC) distribution was found from the PDF of the particle height, and the concentration was obtained assuming a Gaussian crosswind distribution.

Comparisons between the modeled crosswind-integrated concentration fields and convection tank data showed fair-to-good agreement in the lower half of the CBL. Near the source, the predicted contours exhibited an upward tilt due to the plume rise. However, the predicted contour behavior near the CBL top differed from the measurements due to the assumed quasi-reflection there. Overall, the predicted profiles at the surface were in agreement with the data over a wide range of the buoyancy flux and showed a progressive reduction in the with increasing

The model also was evaluated with GLCs measured near several Maryland power plants and the Kincaid (Illinois) power plant. Correlation plots for each data set exhibited considerable scatter, but the correlation coefficient between the predicted and observed logarithm of the concentration was for both sets, thus demonstrating an overall consistency of model performance. In addition, the statistics of the predicted-to- observed GLC ,were good with a geometric mean near 1 and a geometric standard deviation of ~ 2. These results were similar to those obtained earlier by Weil et al. (1986). Thus, in addition to maintaining a continuous variation of with , ,were good with a geometric mean near 1 and a geometric standard deviation of ~ 2. These results were similar to those obtained earlier by Weil et al. (1986). Thus, in addition to maintaining a continuous variation of

In addition to the high modification, we extended the PDF model to estimate the field using the meandering plume concept of a small plume driven about by the large CBL eddies. The small plume grows through relative dispersion from both buoyancy-induced and ambient turbulence. Initial results showed that the surface variation with downstream distance was qualitatively similar to that obtained in convection tank experiments for low-to-moderate buoyancy. However, further model development and testing of the approach is required to address highly buoyant plumes; this is being carried out partially under another program.

Journal Articles on this Report : 1 Displayed | Download in RIS Format

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Other project views:	All 3 publications	1 publications in selected types	All 1 journal articles

Publications

Type	Citation	Project	Document Sources
Journal Article	Weil JC, Corio LA, Brower RP. A PDF dispersion model for buoyant plumes in the convective boundary layer. Journal of Applied Meteorology 1997;36(8):982-1003.	R823419 (Final)	Full-text: AMS-Full Text HTML Exit Abstract: AMS-Abstract Exit Other: AMS-Full Text PDF Exit

Supplemental Keywords:

air, ambient air, atmosphere, atmospheric dispersion, buoyant plumes, chemicals, engineering, exposure, Lagrangian stochastic modeling, mean and fluctuating concentrations, modeling, physics, risk assessment, toxics., RFA, Scientific Discipline, Air, Geographic Area, particulate matter, air toxics, Environmental Chemistry, State, Atmospheric Sciences, tropospheric ozone, Engineering, Chemistry, & Physics, EPA Region, ambient air quality, Lagrangian approach, ambient aerosol, particulates, air pollutants, stratospheric ozone, atmospheric particles, air quality models, power plants, modeling, ambient emissions, Langraian modeling, buoyant plume dispersal, entrainment model, air pollution models, atmospheric aerosols, Region 8, convective boundry layers, pollution dispersion models

Progress and Final Reports:

Original Abstract

1996

1997