Download Peak Flow Freq Anal - Oregon State University

FE 532 - Forest Hydrology
Frequency Analysis – Peak Flows
Date Due:
You need to carry out a partial duration frequency analysis of peak flows for the Oak Creek
Watershed above the stream gauging station at the forest boundary. The data includes peak
flows from six water years at Oak Creek and is located in T://Teach/Classes/FE532/PS#6-Freq
Anal Peak Flows/Oak Creek Peak Flows.xls.
First of all, graph the data using a graph with log-probability axis. I have chosen the logprobability distribution (or extreme value Type I distribution) because you can do it in Sigma
Plot. If you don’t want to use Sigma Plot then you can plot the data on the 2- or 3-cycle logprobability paper available to you in the Graph Paper subdirectory of T://Teach/Classes/FE532.
Use the Gringorton plotting position formula:
TR 
n  1  2a
ma
where, TR is the return period of the data point of interest, n is the sample size, m is the rank, and
a = 0.375. [Remember to correct TR by the correction factor for the partial series analysis.]
After the data are plotted, develop three cumulative frequency distributions; these distributions
are the Gumbel distribution, the log-normal distribution, and the log Pearson Type III
distribution. For these distributions use the Chow equation,
QTR  x  s  KTR
where, QTR is the magnitude of the peak flow that will be equaled or exceeded with a recurrence
interval of TR, x the mean of the peak flow series, s is the standard deviation of the peak flow
series, and K TR is the frequency factor for the frequency distribution with a recurrence interval
TR. Calculate peak flow values for the 2-, 5-, 10-, 25-, 50-, and 100-year return period events for
each of the frequency distributions
As you will recall the frequency factors for the Gumbel Distribution can be calculated in closed
form using the equations listed below.
Kp = -0.7797(0.5772 + ln[ln(1/p)])
KTr = -0.7797(0.5772 + ln[ln(TR/TR-1)])
where Kp or K TR is the frequency factor for the probability of exceedance, p, or return period, TR,
of interest, respectively. Be sure to correct the frequency factor for the true return period using
the correction factor.
Realize that for the log-normal and log Pearson Type III distributions you are dealing with the
distributions of the log of the peak flow values. The mean, standard deviation, and the skew
coefficient of the data must be determined. Since you are dealing with distributions of log values
the generic Chow equation above will have to be expressed in log form. These equations are
listed below:
Generic Chow equation in log form:
log QTR  log Q peaks  KTR  slog Qpeaks
Mean:
Standard deviation:
Skew Coefficient:
log QTR 
 log Q
n
 log Q
slog Qpeaks 
Cs 
peaks

peak
 log Q peak
n 1
n log Q peak  log Q peak
n  1n  2slog Q


2

3
3
peak
The frequency factors for both of the distributions can be determined from the accompanying
table (Table 3.4). The frequency factors for the log normal distribution are the ones for a skew
coefficient, Cs, of zero (0). For the log Pearson Type III distribution, the skew coefficient must
be calculated and then the frequency factor is determined using the attached table (Table 3.4) and
the appropriate skew coefficient.
When all the values of the requested peak flows for the three distributions have been calculated,
you should plot them, along with a fitted line, on the same graph. You can either plot the
cumulative frequency distributions over the data, on a separate page, or both. You should be
able to look at and compare the different distributions. [An example of the type of graph for the
cumulative frequency distributions is attached.]