Name: ___________________________
Lab 9: Analysis of hydrological data
MATERIALS NEEDED: Graph paper, calculator.
QUESTION 1: RATING CURVE
PART A: GRAPHING
1. Construct a rating curve using the data for Fall Creek (table 1) using double log paper.
As is common in the US, these discharge measurements are in cubic feet per second (cfs).
By convention discharge is plotted on the x-axis, depth on the y-axis.
2. Draw a best-fit line through the points.
TABLE 1
Summary of Discharge Measurement Data for Fall Creek
U.S. Department of Interior
|
Observation Number |
Date |
Time |
Gauge Ht (ft) |
Discharge (ft3 s-1) |
|
1128 |
07/12/88 |
1420 |
1.89 |
60.1 |
|
1131 |
10/13/88 |
1355 |
1.77 |
48.6 |
|
1134 |
01/10/89 |
1430 |
2.28 |
104 |
|
1137 |
04/04/89 |
0805 |
7.49 |
2270 |
|
1140 |
07/06/89 |
1300 |
2.32 |
99.1 |
|
1143 |
10/04/89 |
0945 |
2.60 |
138 |
|
1146 |
01/03/90 |
1315 |
3.61 |
371 |
|
1149 |
03/27/90 |
1110 |
3.02 |
247 |
|
1152 |
07/03/90 |
1440 |
2.43 |
127 |
|
1155 |
10/03/90 |
1105 |
2.19 |
95.3 |
PART B: ANALYZING THE DATA
1. Use the rating curve (i.e., your best fit line, which is the relationship between depth and discharge) to estimate the discharge at the gauge heights listed in the table below.
|
Gauge Height (ft) |
Discharge (cfs) |
|
2.00 |
|
|
6.50 |
|
|
8.00 |
2. Note that the last gauge height given is higher than any of the stages used in constructing the rating curve. What potential problems do you see with this estimate?
QUESTION 2: HYDROGRAPHS
PART A: GRAPHING
1. Construct a hydrograph for the flood event May 14-22, 1990 at the Millersville gauge using the data in table 3 (next page).
To construct a hydrograph, you must plot discharge and time. Only time and gauge height are provided on the data sheet. Therefore, in order to find the discharge for a particular gauge height, you must use the rating curve you constructed in Question 1 to convert the stage heights to discharge.
2. Precipitation data for this period are provided (table 2 below). Plot these data on the same graph. You can do this by creating a new y-axis on the right hand side of your graph. Think back to lab 1 to decide what type of graph you need to draw for precipitation.
TABLE 2
Precipitation Data Indianapolis May 1990 (inches)
U.S. Department of Interior
|
Date |
14th |
15th |
16th |
17th |
18th |
19th |
20th |
21st |
22nd |
|
12:00 |
0 |
0.39 |
0.72 |
0.08 |
0 |
0 |
0 |
0 |
0 |
|
24:00 |
0 |
0.63 |
0.57 |
0 |
0 |
0 |
0 |
0 |
0 |
TABLE 3
Gauge Heights for Fall Creek at Millersville, Indiana (May 1990)
U.S. Department of Interior
|
Date |
Time |
Gauge Ht (ft) |
Discharge (ft3 s-1) |
|
14th |
12:00 |
6.96 |
|
|
24:00 |
6.57 |
||
|
15th |
12:00 |
5.90 |
|
|
24:00 |
6.35 |
||
|
16th |
12:00 |
8.75 |
|
|
24:00 |
9.63 |
||
|
17th |
12:00 |
9.68 |
|
|
24:00 |
9.19 |
||
|
18th |
12:00 |
8.24 |
|
|
24:00 |
6.80 |
||
|
19th |
12:00 |
5.81 |
|
|
24:00 |
5.20 |
||
|
20th |
12:00 |
4.86 |
|
|
24:00 |
4.61 |
||
|
21st |
12:00 |
4.39 |
|
|
24:00 |
4.24 |
||
|
22nd |
12:00 |
4.03 |
|
|
24:00 |
3.84 |
3. Using your graph determine the lag time for this flood. Mark this on your graph
QUESTION 3: FLOOD FREQUENCY CURVE
PART A: CALCULATING AND GRAPHING PROBABILITIES
1. Construct a Flood Frequency Curve for Fall Creek (data in Table 4, next page) by following these steps:
i) Rank the peak annual discharges for 1950-1964 from highest (1) to lowest (15).
ii) Using the following formula, find P (in decimal and percentage form) for each year. Write your results in the last columns of Table 4.
Where: P = probability of occurrence a flood greater than or equal to the size listed in any single year
m = the rank of each discharge in the sample
n = the sample size (total number of years in this case)
2. Using the probability paper on which the San Gabriel River curve has already been plotted, graph probability (P) (in decimal form) against discharge, and draw a best fit line through your points.
TABLE 4
Fall Creek at Millersville, Indiana: Largest Floods for Each Year (1950 to 1964)
U.S. Department of Interior
|
Water Year |
Date |
Peak Discharge (cfs) |
Rank (m) |
P (Decimal) |
|
1950 |
01/05 |
7400.0 |
||
|
1951 |
02/22 |
5150.0 |
||
|
1952 |
01/28 |
3020.0 |
||
|
1953 |
07/07 |
5130.0 |
||
|
1954 |
04/05 |
2550.0 |
||
|
1955 |
03/02 |
1300.0 |
||
|
1956 |
05/28 |
12900.0 |
||
|
1957 |
06/30 |
4590.0 |
||
|
1958 |
06/11 |
7450.0 |
||
|
1959 |
01/22 |
5770.0 |
||
|
1960 |
02/10 |
2470.0 |
||
|
1961 |
04/25 |
6050.0 |
||
|
1962 |
01/27 |
3500.0 |
||
|
1963 |
03/03 |
9020.0 |
||
|
1964 |
04/21 |
10100.0 |
Probability (P) is related to recurrence interval (RI) by the following formula:
RI = 1/P
Where: P is expressed in decimal not percentage form
EXAMPLE:
If the probability of a certain discharge is .05 (or 5%)
RI = 1/0.05 = 20 years.
3. Using the flood frequency curve for Fall Creek, find probabilities for the following discharges and convert them to recurrence intervals (RI). Be sure to convert P values to decimal form (divide by 100) for these calculations.
|
Discharge (cfs) |
P (Decimal) |
P (Percentage) |
RI (years) |
|
2500 |
|||
|
8000 |
|||
|
10 000 |
|||
|
15 000 |
If you have the RI, you can convert to P and read discharge from your graph.
EXAMPLE:
If you want to find the discharge for the 50-year flood, convert to P:
P = 1/RI = 1/50 = .02 =2%
Then read the graph to find the discharge.
4. Find the discharge for the 20-year flood. Be sure to use the decimal form of P so that you can read your graph.
a) On Fall Creek at Millersville
b) On the San Gabriel River
5. What is the probability of having a flood event of 5000 cfs at:
a) The Fall Creek station
b) The San Gabriel station
PART B: ANALYZING THE DATA
Answer the following questions by comparing the San Gabriel and Fall Creek Flood Frequency curves:
1. Describe how the frequency curves for Fall Creek and the San Gabriel River differ (slope, spreading of data, range of data, etc.).
2. Explain why they differ.
HINT: consider the physical environment, especially climate, of California versus Indiana
3. Suppose you want to estimate the stream discharge for some extreme event, such as the 100-year flood in order to zone for location of housing and commercial development downstream. Which flood-frequency curve do you think will give you the most reliable estimate? Explain why.
4. How could the estimates from these curves be improved?