Plume standard deviations

This solution describes a plume with a Gaussian distribution of poUutant concentrations, such as that in Figure 5, where (y (x) and (y (x) are the standard deviations of the mean concentration in thejy and directions. The standard deviations are the directional diffusion parameters, and are assumed to be related simply to the turbulent diffusivities, and K. In practice, Ct (A) and (y (x) are functions of x, U, and atmospheric stability (2,31—33). 

It is known that the vertical distribution of diffusing particles from an elevated point source is a function of the standard deviation of the vertical wind direction at the release point. The standard deviations of the vertical and horizontal wind directions are related to the standard deviations of particle concentrations in the vertical and horizontal directions within the plume itself. This is equivalent to saying that fluctuations in stack top conditions control the distribution of pollutant in the plume. Furthermore, it is known that the plume pollutant distributions follow a familiar Gaussian diffusion equation. 

Emissions of gases or particles less than 20 microns (larger particles settle more quickly due to gravitational effects) disperse with an origin and plume centerline at the effective stack height. Pollutant concentrations are greatest within one standard deviation of the plume centerline. Thus, the determination of the value of these standard deviations is an important factor in calculating ambient concentrations. 

The assumptions made in tlie development of Eq. 12.6.1 are (1) tlie plume spretid lias a Gaussian distribution in both tlie horizontal and vertical planes witli standard deviations of plume concentration distribution in the horizontal and vertical of Oy and respectively (2) tlie emission rate of pollutants Q is uniform (3) total reflection of tlie plume takes place at tlie eartli s surface and (4) tlie plume moves downwind with mean wind speed u. Altliough any consistent set of units may be used, tlie cgs system is preferred. 

U = mean wind speed affecting plume (m), z = standard deviation of plume concentration in the vertical at distance X (m), y = standard deviation of plume concentration in the horizontal at distance X (m),... 

Problems arise to get informations about the diffusion coeffients Ky and Kz. If equation (3.4) is interpreted as Gaussian distribution, a lot of available dispersion data can be taken into consideration because they are expressed in terms of standard deviations of the concentration distribution. Though there is no theoretical justification the Gaussian plume formula is converted to the K-theory expression by the transformation /11/... 

Summarizing, we have evaluated the general expression (4.3) in the special case in which the standard deviations of the puff distribution are the same in the three coordinate directions and in which the standard deviation is much smaller than the distance from the source at any x, the so-called slender-plume approximation. 

Equation (4.22) is the expression for the mean concentration from a continuous point source of strength q at the origin in an infinite fluid when the standard deviations of plume spread are different in the different coordinate directions and when the slender-plume approximation is invoked. 

Figure 5.9 Standard deviation of the concentration fluctuations along the plume center-line. Also shown is a power law curve.

Figure 5.13 shows the correlation function for sensors that are separated by a fixed distance equal to L. The inner sensor moves throughout the field and its position is denoted by y, as shown in the sketch. The sensor location is normalized by the standard deviation of the time-averaged profiles (see Fig. 5.7). With this scaling, the profiles at the four downstream locations are coincident, which suggests that the integral length scale is the correct scaling length for the sensor separation and that the sensor location is properly scaled by the width of the time-averaged plume.

The release location influences the vertical distribution of the time-averaged concentration and fluctuations. For a bed-level release, vertical profiles of the time-averaged concentration are self-similar and agreed well with gradient diffusion theory [26], In contrast, the vertical profiles for an elevated release have a peak value above the bed and are not self-similar because the distance from the source to the bed introduces a finite length scale [3, 25, 37], Additionally, it is clear that the size and relative velocity of the chemical release affects both the mean and fluctuating concentration [4], The orientation of the release also appears to influence the plume structure. The shape of the profiles of the standard deviation of the concentration fluctuations is different in the study of Crimaldi et al. [29] compared with those of Fackrell and Robins [25] and Bara et al. [26], Crimaldi et al. [29] attributed the difference to the release orientation, which was vertically upward from a flush-mounted orifice at the bed in their study. 

In this expression, 3 represents the increase factor of vertical diffusion due to the plume. Gaussian plume or dispersion models are based on standard deviations of the plume dimensions (crx, cry, oz). These represent a measure of the diffusive capacity of the atmosphere. They are dependent on the turbulence conditions of the atmosphere, the vertical temperature gradient (which helps to establish atmospheric turbulence in the vertical direction) and the transporting distance. 

Figure 12 Variability of trace element concentrations in MORE, expressed as 100 standard deviation/mean concentration. The data for Global MORE are from the PETDB compilation of (Su, 2002). All segments refers to 250 ridge segments from all oceans. Normal segments refers to 62 ridge segments that are considered not to represent any sort of anomalous ridges, because those might be affected by such factors as vicinity to mantle plumes or subduction of sediments (e.g., back-arc basins and the Southern Chile Ridge). The Atlantic MORE, 40-55° S, from which samples with less than 5% MgO have been removed (source le Roux et al., 2002).

FIGURE 4-25a Standard deviations of mass distribution in a Gaussian plume, cry and az, given as a function of both distance downwind from a point source and Pasquill stability categories. Dispersion coefficient as used in this figure means the standard deviation of the plume width or height [L] rather than a Fickian coefficient [L2/T], (From Atmospheric Chemistry and Physics of Air Pollution, by J. H. Seinfeld. Copyright 1986, John Wiley Sons, Inc. Reprinted by permission of John Wiley Sons, Inc.)... 

On a sunny midwinter day, outside London, the wind is from the northwest at 4 m/sec. A plume of smoke is streaming from the stack of a coal-fired power plant. Effective height of the stack is 200 m. Over level terrain, how far downwind does the plume travel before it reaches the ground [use two standard deviations (erf) as your criterion for reaching the ground ]. 

This equation represents a Gaussian distribution, where C (Bq.m 3) represents the radionuclide concentration, Q (Bq.s1) the source strength, and H (m) the corrected source released height. Dispersion parameters, ay (m) and az (m), are the standard deviations of the plume concentration in the horizontal and vertical directions respectively. The atmospheric transport is done at wind-speed (height-independent), u (m.s1), to a sampling position located at surface elevation, z (m), and transverse horizontal distance, y (m), from the plume centre. 

Standard deviations that fix the calculated spread of the Gaussian plume. The more unstable models predict more rapid dispersion. While they may not be suitable for worst-case scenarios, these models are important in real-time modeling. They provide less drastic but more realistic projections. A moderately unstable atmosphere ( D stability ) is assigned a horizontal dispersion coefficient twice as great as a stable atmosphere. Greater instability, or A stability, increases the horizontal dispersion coefficient by another factor of 3. The vertical dispersion coefficients increase even more as the atmosphere becomes less stable. The applied factors are not constant but vary with conditions. The end result is that downwind centerline concentrations may be reduced by factors greater than 100 in progressing from F to A stability. 

The data set should preferably cover a reasonably wide spatial range in a structured way. To allow comparison with arc-wise maximum concentrations, the sensor arrangement should include at least four crosswind or arc-wise sensors with less than one standard deviation of plume width between them, although more than six sensors per arc are recommended. Preferably there is at least one position at each arc where vertical concentration distributions are available. For field data, frequency responses of sensors between 0.1 and 1 Hz are fine for general use (some averaging will often be performed afterwards), unless concentration fluctuations are part of the validation. The relevant time scale for sensor response is the time of flight ulx at a downwind distance, x. 

---