By making the substitutions
y(n) = Ln(n), a = Ln(N), b = - H;’s> x(n) = H’(n) .
Equation 3-4 may be written as
y(n) = a + bx(n).
(3-5)
The constants a and b can be found graphically or by fitting a leastsquare régression line to the observations. The parameters N and
may be computed from a and b. The value of N found in this way, is
the value that provides the best fit between the observed distribution of
identified waves and the Rayleigh distribution function. It is generally
a little larger than the number of waves actually identified in the record.
This seems reasonable because some very small waves are generally neglected
in interpreting the record. When the observed wave heights are scaled by
Hyrns, that is, made dimensionless by dividing each observed height by
then data from ail observations may be combined into a single plot.
Points from scaled 15-minute samples are superimposed on Figure 3-3 to
show the scatter to be expected from analyzing individual observations in
this manner.
Data from 72 scaled 15-minute samples representing 11,678 observed
waves hâve been combined in this manner to produce Figure 3-4. The theoretical height appears to be about 5 percent greater than the observed
height for a probability of 0.01 and 15 percent at a probability of 0.0001.
It is possible that the différence between the actual and theoretical
heights of highest waves is due to breaking of the very highest waves
before they reach the Coastal wave gages.
Equation 3-1 can be established rigorously for restrictive conditions,
and empirically for a much wider range of conditions. If Equation 3-1 is
accepted as an exact law, the probability density function can be obtained
in the form
f[(R - AH) < H < (R + AH)] = I ——\ H e ^Hrms
(3-6)
\Hrm,
The height of the wave with any given probability n/N of being exceeded
may be determined approximately from curve a in Figure 3-5 or from the
équation,
b
(3-7)
3-6
y(n) = Ln(n), a = Ln(N), b = - H;’s> x(n) = H’(n) .
Equation 3-4 may be written as
y(n) = a + bx(n).
(3-5)
The constants a and b can be found graphically or by fitting a leastsquare régression line to the observations. The parameters N and
may be computed from a and b. The value of N found in this way, is
the value that provides the best fit between the observed distribution of
identified waves and the Rayleigh distribution function. It is generally
a little larger than the number of waves actually identified in the record.
This seems reasonable because some very small waves are generally neglected
in interpreting the record. When the observed wave heights are scaled by
Hyrns, that is, made dimensionless by dividing each observed height by
then data from ail observations may be combined into a single plot.
Points from scaled 15-minute samples are superimposed on Figure 3-3 to
show the scatter to be expected from analyzing individual observations in
this manner.
Data from 72 scaled 15-minute samples representing 11,678 observed
waves hâve been combined in this manner to produce Figure 3-4. The theoretical height appears to be about 5 percent greater than the observed
height for a probability of 0.01 and 15 percent at a probability of 0.0001.
It is possible that the différence between the actual and theoretical
heights of highest waves is due to breaking of the very highest waves
before they reach the Coastal wave gages.
Equation 3-1 can be established rigorously for restrictive conditions,
and empirically for a much wider range of conditions. If Equation 3-1 is
accepted as an exact law, the probability density function can be obtained
in the form
f[(R - AH) < H < (R + AH)] = I ——\ H e ^Hrms
(3-6)
\Hrm,
The height of the wave with any given probability n/N of being exceeded
may be determined approximately from curve a in Figure 3-5 or from the
équation,
b
(3-7)
3-6