Environmental Engineering Reference
In-Depth Information
question: which one is the value representing the maximum of the data set? For a 95%
confidence interval, this is a numerical figure, which is larger or equal, compared to 95%
of the members of the data set, and would be exceeded by 5% of the data set values only.
The same applies to minimum values. In order to determine such extremes, equation 12.1
could be applied:
(12.1)
where: X
extr
= extreme value; µ = mean data set value; K = frequency factor; □= standard
deviation of the data set.
The frequency factor is given in statistical tables and varies for different levels of the
confidence interval and different types of distributions of the data sets. The determination
of extreme values, some times known as percentiles, could be represented in a graphical
form, showing the relation between actual concentrations and the confidence interval,
also known as cumulative probability. For a normal distribution, the relation is linear
within a logarithmic representation, and is represented schematically on Figure 12.2. The
line shows the extreme values with respect to concentrations, for each specific level of
confidence. For a 95% cumulative probability, the corresponding point on the line would
show a concentration, which is specific for this data set only. It will be equal or higher
than 95% of the data set observations, and will be exceeded by 5% of the observed values
only. The statistical analysis of a data set would give a specific maximum value for each
monitored parameter at each specific monitoring site.
The implications of the data sets statistical analysis with respect to diffuse pollution
monitoring and control are related to the pollution assessment and applications of
standards and regulatory instruments. Extreme (maximum) values of the observed data
sets should be compared to specified criteria, opposed to the usual practice of comparing
the average values, reflecting much lower cumulative probability. The practical meaning
of this is that in cases of the comparison of average values with limiting criteria, a
considerable number of observations, included in the data set, will exceed the
recommended criteria, and would indicate a violation of the regulatory instrument.
Other implication is related to the frequency of occurrence of the observed extremes,
reflecting the return period or the recurrence interval of the observation. This concept was
explained in Chapter 1, related to hydrological data and is applicable to water quality data
as well.
For each specific data set, the return period is directly related to the frequency of the
observations within a given period of time, and could be determined by equation 12.2.
