and
m = exp(m' + -) (3-43)
2
In these equations, both m and o are known (m is the average hydraulic
conductivity and o is manifestation of the apparent aquifer dispersivity).
Previously it was stated that the total transmissivity of the aquifer was defined as
the average hydraulic conductivity [L/T] times the thickness of the aquifer [L]:
total = Kave L (3-44)
From equation (3-44) an appropriate mean value for the average hydraulic
conductivity may be determined assuming the thickness of the aquifer and total
transmissivity are known. If in addition a suitable value for variance of lognormal
distribution can be estimated from the apparent aquifer dispersivity, then, equations (3-
42) and (3-43) may be used to derive values of the mean (m') and the standard deviation
(a') for normal deviate of log transform hydraulic conductivity.
The probability density function (PDF) curve representing this normal distribution
is a function of m' and o'.
1 I x-m'
f (x)-p exp (3-45)
This curve is symmetrical about the mean value (m'). Figure 3-11 shows a sample
curve of normal distribution with mean and standard deviation values of 2.