Statistics for Environmental Engineers

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The use of scatterplots is illustrated with data from a study of how phosphorus removal by a wastewater treatment plant was related to influent levels of phosphorus, flow, and other characteristics of wastewater. The matrix scatterplots (sometimes called draftsman’splots), shown in Figure 3.2, were made as a guide to constructing the first tentative models. There are no scales shown on these plots because we are

looking for patterns; the numerical levels are unimportant at this stage of work. The computer automatically scales each two-variable scatterplot to best fill the available area of the graph. Each paired combination of the variables is plotted to reveal possible correlations. For example, it is discovered that effluent total phosphorus (TP-out) is correlated rather strongly with effluent suspended solids (SS-out) and effluent BOD (BOD-out), moderately correlated with flow, BOD-in, and not correlated with SS-in and TP-in. Effluent soluble phosphorus (SP-out) is correlated only with SP-in and TP-out. These observations provide a starting point for model building.

The values plotted in Figure 3.2 are logarithms of the original variables. Making this transformation was advantageous in showing extreme values, and it simplified interpretation by giving linear relations between variables. It is often helpful to use transformations in analyzing environmental data. The logarithmic and other transformations are discussed in Chapter 7.

In Search of Trends

Figure 3.3 is a time series plot of 558 pH observations on a small stream in the Smokey Mountains. The data cover the period from mid-1971 to mid-1981, as shown across the top of the plot. Time is measured in weeks on the bottom abcissa.

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