Repeat Problem using the lognormal and three-parameter gamma distributions.
Problem
For the data of Problem 1, fit a log Pearson 3 distribution to the peak flows, using the method of moments described in this text. Use the weighted skew coefficient computed in Problem 2.
(a) Compute estimated flows for return periods listed in Table.
(b) Plot the fitted CDF on lognormal probability paper.
(c) Using the Cunnane plotting-position formula (with parameter a = 0.4), plot enough of the measured flows to provide a comparison similar to Figure. Discuss the fit.
Problem 1
This problem asks you to perform a descriptive analysis using real data of interest to you. The problem should be done using spreadsheet or similar software.
(a) Download a series of annual maximum flows for a river of interest to you. USGS data may be obtained starting at the website http://water.usgs.gov/nwis/. Import the data into your spreadsheet or similar software. Convert the lines of text data into columnar data.
(b) Note the characteristics of the basin from its description in the USGS files. What are the basin area and latitude and longitude of the gage? Are there diversions, controls, or storage (e.g., reservoirs) upstream?
(c) Plot the time series of peak flows and log10 (flows) vs. water year. The series of logio (flows) should have a lower coefficient of variation. Does the shape of the time-series plot of flows suggest that the time-series of river peak flows is nonstationary? If so, discuss possible reasons.
(d) Compute and plot relative-frequency histograms for the flows and log (flows). Discuss any difference in skewness evident from the two plots.
(e) Compute the following statistics for the series of flows and for the series of log10 (flows): number, average, unbiased variance, unbiased standard deviation, coefficient of variation, unbiased skewness, maximum, and minimum.
Problem 2
For the data of Problem, compute a weighted skew coefficient according to the Bulletin 17B method.
Problem
This problem asks you to perform a descriptive analysis using real data of interest to you. The problem should be done using spreadsheet or similar software.
(a) Download a series of annual maximum flows for a river of interest to you. USGS data may be obtained starting at the website http://water.usgs.gov/nwis/. Import the data into your spreadsheet or similar software. Convert the lines of text data into columnar data.
(b) Note the characteristics of the basin from its description in the USGS files. What are the basin area and latitude and longitude of the gage? Are there diversions, controls, or storage (e.g., reservoirs) upstream?
(c) Plot the time series of peak flows and log10 (flows) vs. water year. The series of logio (flows) should have a lower coefficient of variation. Does the shape of the time-series plot of flows suggest that the time-series of river peak flows is nonstationary? If so, discuss possible reasons.
(d) Compute and plot relative-frequency histograms for the flows and log (flows). Discuss any difference in skewness evident from the two plots.
(e) Compute the following statistics for the series of flows and for the series of log10 (flows): number, average, unbiased variance, unbiased standard deviation, coefficient of variation, unbiased skewness, maximum, and minimum.
Table
Frequency Factors K for Gamma and Log Pearson Type 3 Distributions
Source: IACWD (1982).
Figure
Comparison of four fitted CDFs for Siletz River flows, 1925–1999.
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