Name: _________________________
Geography 302: Climate and Landscapes
Assignment 3: Stream Discharge Curves
Most stream gauging in the United States is done by the United States Geologic Survey (USGS), and basic data for the network can be found at http://waterdata.usgs.gov. In this exercise, we will examine historical flow characteristics for the Ohio River at Cincinnati and the Little Miami River at Milford. A discussion of the terms and units can be found at http://waterdata.usgs.gov/nwis-w/OH/display.cgi?text=help.html.
Part I.
Figures 1a and 1b show the peak annual discharge (in CFS) for both gauging stations. This represents the largest flood of the water year (Oct 1 - Sept 30). Note that the period of record differs. These graphs were generated using the data sets or-pad.dat and lm-pad.dat , which were downloaded from the web site and modified.
Use the graphs or data sets to find the average, maximum, and minimum peak annual discharge for each stream.
Table 1: Peak Flow Data (CFS)
Stream
Average Maximum Minimum Period
of Record
Ohio River _________ _________ _________ _________
Little Miami _________ _________ _________ _________
Do the minimum/maximum flow years coincide in both streams? List several reasons that might explain this pattern.
The dashed line in Figure 1 represents a best fit to the data. There appears to be a trend toward increasing peak flow in the Ohio River, but decreasing in the Little Miami. Even if we isolate the period of overlap (1916-1975), the same pattern is observed. How might you explain this?
Part II.
Histograms have been generated showing the frequency of annual peak discharge events. As you can see from Figure 2, the distribution of data is distinctly non-normal. Explain how the pattern is not normal, and why this might be so.
Part III.
The annual peak flow data represents yearly floods, and this information can be used to develop flood recurrence statistics. The example below is for the Ohio River data for the period 1858-1975 (n = 118 years).
The recurrence interval refers to the average length of time (in years) between two floods events of equal or larger magnitude. Numerically, it is equal to:
RI = (n + 1) / m,
where n = number of observations (118 years) and m = the rank of the flood event.
Thus, the first step is to rank order (sort) the annual peak flow data from the largest magnitude event (m = 1) to the smallest (m = 118). This has been done and is presented as Table 2. The infamous year 1937 ranks as number 1. Thus, based on the length of the data record, the recurrence interval = (118+1) / 1, or 119 years.
This information is plotted on a log-linear curve as Figure 3. The log of the RI is plotted on the x-axis, and peak annual discharge is plotted on the y-axis. The solid line is a linear best-fit that can be used to estimate the recurrence interval for a given peak discharge.
Using the data from Table 1, what is the RI of an average Ohio River flood? _________ years
We can also calculate the probability that, in a given year, a flood of given magnitude will occur.
P = 1 / RI
where P = probability of the flow being equaled or exceeded in any one year. For example, a 25-yr flood has a 4% chance of occurring in any given year; a 10-yr flood has a 10% chance. Of course, exactly which year it will happen is unpredictable.
From Table 2, you can see that the probability of a flood greater or equal to the 1937 event (894,000 CFS; RI = 119 yrs) is .84% in any given year.
What is the P for an average flood on the Ohio River? ____ %
Now, perform similar calculations for the Little Miami data. You will need to use a program like Excel to sort and analyze the data. Create a table similar to Table 2 and a figure similar to Figure 3. Determine the RI and P of an average flood on the Little Miami? How do these values compare with those for the Ohio River?
Part IV.
Figure 4 shows the average daily discharge data for the Little Miami river over the period 1 October 1938 to 30 September 1998; the data file is called lm-daily.dat or called lm-daily.xls. Explain the apparent periodicity in the time series. What do the spikes represent? What do the periods of very low discharge represent?
Hand in your (neat and legible) answers to the questions directly on this exercise. The table and figure created in Part III should be on separate sheets of paper. Due by ________________.