Plume models, multiple source

The General Structure of Multiple-Source Plume Models Multiple-source plume (and particularly Gaussian plume) models (Calder 1977) are commonly used for predicting concentrations of inert pollutants over urban areas. Although there are many special-puipose computational algorithms currently in use, the basic element that is common to most is the single-point-source release. The spatial concentration distribution from such a source is the underlying component and the multiple-source model is then developed by simple superposition of the individual plumes from each of the sources. 

Gaussian plume models are easy to use and require relatively few input data. Multiple sources are treated by superimposing the calculated contributions of individual sources. It is possible to include the first-order chemical decay of pollutant species within the Gaussian plume framework. For chemically, meteorologically, or geographically complex situations, however, the Gaussian plume model fails to provide an acceptable solution. 

The earliest and still widely used dispersion model to compute pollutant concentration profiles is the Gaussian plume model for single or multiple source pollution problems. Box-type model techniques, which can take into account nonlinear interactions among different species arising from chemical reactions, have been used in longer-range dispersion computations. 

In another review, Hoffert discussed the social motivations for modeling air quality for predictive purposes and elucidated the components of a model. Meteorologic factors were summarized in terms of windfields and atmospheric stability as they are traditionally represented mathematically. The species-balance equation was discussed, and several solutions of the equation for constant-diffusion coefficient and concentrated sources were suggested. Gaussian plume and puff results were related to the problems of developing multiple-source urban-dispersion models. Numerical solutions and box models were then considered. The review concluded with a brief outline of the atmospheric chemical effects that influence the concentration of pollutants by transformation. 

Puff models such as that in Reference 5 use Gaussian spread parameters, but by subdividing the effiuent into discrete contributions, they avoid the restrictions of steady-state assumptions that limit the plume models just described. A recently documented application of a puff model for urban diffusion was described by Roberts et al, (19). It is capable of accounting for transient conditions in wind, stability, and mixing height. Continuous emissions are approximated by a series of instantaneous releases to form the puffs. The model, which is able to describe multiple area sources, has been checked out for Chicago by comparison with over 10,000 hourly averages of sulfur dioxide concentration. 

The situation in any single plume appears to be complex the Hawaii case is illustrative. Dixon et al. (1997) estimated H2O concentrations of 525 75 ppm in the source for North Arch basalts, a seafloor field of alkalic basalts north of Oahu. Wallace (1998) estimated 450 190 ppm H2O in the source for Kilauea basalts, and Dixon and Clague (2001) inferred 400 30 ppm H2O in the source for Loihi seamount basalts. Dixon and Clague (2001) argue that these differences are consistent with a mantle plume with multiple components, such as a wet rim and dry core plume model as proposed by Sen et al. (1996). 

Calder, K. L. (1977) Multiple-source plume models of urban air pollution—their general structure, Atmos. Environ. 11, 403-414. 

Two types of dispersion models are used to describe these releases when the puff or plumes are neutrally or positively buoyant. When there is an instantaneous release or a burst of material, we make use of a puff model. In this model the puff disperses in the downwind, cross wind, and vertical directions simultaneously. Computer codes written for puff models usually have the capability of tracking multiple puff releases over a period of time. When the release rate is constant with time, the puff model can be mathematically integrated into a continuous model. In this case, dispersion takes place in the cross wind and vertical directions only. The mathematical expressions are those discussed in Section III. The dispersion coefflcients used, however, may differ from those described in Section IV. Plume rise equations from Section V for positively buoyant plumes may be used in conjunction with these dispersion models. The equations of current models indicate that they are well formulated, but the application of the models suffers from poor meteorological irrformation and from poorly defined source conditions that accompany accidental releases. Thus, performance of these models is not adequate to justify their use as the sole basis for emergency response planning, for example. 

The model developed to account for the mixing under eithertype of stable layer employs the idea of complete reflection from the diffusion lid, as in the case for the plume contacting the ground. Now that the plume is trapped between lid and bottom, multiple reflections are allowed for in the model. Thus the continuous point source model becomes... 

---