Statistics for Environmental Engineers

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The simplest smoothing method is to plot the data on a logarithmic scale (or plot the logarithm of у instead of у itself). Smoothing by plotting the moving averages (MA) or exponentially weighted moving averages (EWMA) requires only arithmetic.

A moving average (MA) gives equal weight to a sequence of past values; the weight depends on how many past values are to be remembered. The EWMA gives more weight to recent events and progressively forgets the past. How quickly the past is forgotten is determined by one parameter. The EWMA will follow the current observations more closely than the MA. Often this is desirable but this responsiveness is purchased by a loss in smoothing.

The choice of a smoothing method might be influenced by the application. Because the EWMA forgets the past, it may give a more realistic representation of the actual threat of the pollutant to the environment.

For example, the BOD discharged into a freely flowing stream is important the day it is discharged. A 2- or 3-day average might also be important because a few days of dissolved oxygen depression could be disastrous while one day might be tolerable to aquatic organisms. A 30-day average of BOD could be a less informative statistic about the threat to fish than a short-term average, but it may be needed to assess the long-term trend in treatment plant performance.

For suspended solids that settle on a stream bed and form sludge banks, a long-term average might be related to depth of the sludge bed and therefore be an informative statistic. If the solids do not settle, the daily values may be more descriptive of potential damage. For a pollutant that could be ingested by an organism and later excreted or metabolized, the exponentially weighted moving average might be a good statistic.

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