Log-probability graph

If air quality data at a receptor for any one averaging time are lognormally distributed, these data will plot as a straight line on log probability graph paper (Fig. 4-9) which bears a note Sg = 2.35. Sg is the standard geometric deviation about the geometric mean (the geometric mean is the Nth root of the product of the n values of the individual measurements). 

By this method the number of particles per traverse was calculated. The average number of particles in each size interval was progressively cumulated and the cumulated percentage of particles in each size interval was then calculated for making plots, size versus normalized cumulative percent on log probability graph paper. 

Since the particle size is plotted on a logarithmic scale, the presentation of data on a log-probability graph is particularly useful when the range of sizes is large. The geometric standard deviation can be read from the graph, as with the arithmetic distribution, and is given by ... 

The cumulative distribution above can be plotted on log-probability graph paper. The cumulative distribution curve is shown in Figure 62. Since a straight line is obtained on log-normal coordinates, the particle size distribution is log-normal. 

To simplify plotting of the data as shown in Figure 5, special log-probability graph paper is used. As an example, the data shown in Table 8 have been plotted on this type of graph paper in Figure 7, while erg has been calculated from ... 

Plotting the surface and volume distributions of a log-normal aerosol distribution on a log-probability graph would also result in straight lines parallel to each other (same standard deviation). For the distribution shown in Figure 8.8 with Dpg = 1.0 pm and ag = 2.0, the resulting surface area and volume median diameters are approximately 2.6 pm and 4.2 pm, respectively. 

Sometimes it is necessary to plot on a log-probability graph but the probability scale is not available as such in a spreadsheet. The probability scale can be calculated using the right-hand side of equation (4.19). The probability scale, therefore, will be proportional to erf (2Cx-l). where C is a percentage figure for which the scale is required. 

FIGURE 4.14 Cumulative count and cumulative mass distributions on log-probability graph. 

Deteimine the mass median diameter and geometric standard deviation of this distribution using log-probability graph paper. Use the appropriate conversion equation to determine the count median diameter. 

Measurements of specific surface indicate that 16% of the total specific surface is contributed by particles less than 0.3 pm and 84% by particles less than 1.5 pm. Assuming that the particle size distribution is lognormal, calculate (without the aid of log-probability graph paper) the specific surface median diameter, the CMD, and the GSD. The specific surface is the surface area per gram of particles. 

Figure 14.2b presents the urban aerosol size distribution as cumulative number and volume distributions on a log-probability graph. (See Section 4.5.) The distributions show significant departures from a lognormal distribution, and the contributions of the individual modes are hidden. Figures 14.2c and 14.2d respectively show particle number and volume per unit log interval on an arithmetic scale ver-... 

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