Background:
In order to better understand how to read peak discharge data, processes were conducted to shed light on how to graph, calculate, and analyze discharge data. The National Atlas, United States Geological Survey (USGS) website, and Microsoft Excel were used to acquire and analyze all of the data from the Little Blackfoot River in Montana, and the La Crosse River in Wisconsin. Microsoft Excel was used to model peak discharge figures and determine exceedence probability and recurrence interval figures. Then, the recurrence interval figures were graphed on Gumbel and log-Gumbel graph paper by hand to determine which graph fit the data to a straight-line trend more accurately. Finally, a hypothesis was developed, attempting to determine what conditions caused the peak discharge events to be higher in the La Crosse River.
Introduction
This assignment focused on the peak discharge figures of two different streams at a single one of their gaging stations. The first stream was the La Crosse River, which is located in west-central Wisconsin, at Stream Gage Site 05383000. This gaging station was located near West Salem, Wisconsin (Figure 1) and its records span from 1914-1978. The second stream was the Little Blackfoot River, which is located in west-central Montana, at Stream Gage Site 12324590. The gaging station was located near Garrison, Montana (Figure 2) and its records span from 1973-2011. The United States Geological Survey (USGS) was used to acquire stream gage data for both of these rivers. After the data was acquired, the objective of the assignment was to gain a better understanding of how to interpret recurrence interval data and exceedence probability data. Then, a hypothesis was constructed to determine why two watersheds with similar drainage area could have such variance in their peak discharge events. This hypothesis states that the reason the average peak discharge events of the La Crosse River are so much higher is because 1) the La Crosse has a higher Mean Annual Precipitation than the Little Blackfoot and 2) the Little Blackfoot is on the leeward side of a large mountain in Montana.
Methods
Acquire Data From the USGS Website:
In order to being this assignment, the peak discharge data was gathered from the USGS website. This was done by opening the USGS website and navigating to the National Water Information Systems Interface. From here, the Data Category of Surface Water, then Peak-Flow Data were selected. The parameters of Hydrologic Region, Drainage Area, and Number of Observations were selected to assist in narrowing down the target drainage size, location, and ensure the quality of data. For this personalized assignment, 386-410 square miles was input for drainage area, the hydrologic regions of the Pacific Northwest and the Upper Mississippi were input, and a minimum record of thirty years was designated to ensure that there was enough data to fully highlight peak discharge events. The results were selected to be displayed via a map interface on the USGS website. In order to view comparable data, the size of drainage area could have no more than a 10% difference between the two sizes.
Once the data was displayed through the map interface, a stream gage station was selected depending on personal preference. Figure 1 and Figure 2 are clipped images of the map interface displayed on the USGS website. Through a hyperlinked path of the site number, access was gained to data gathered by the stream gage. The description of each stream was saved for further reference and the peak streamflow data was exported as a “tab-separated file”. This process was repeated for two different stream gages and data was gathered for La Crosse River, Near West Salam, Wisconsin (05383000) and Little Blackfoot River, Near Garrison, Montana (12324590).
After this, Microsoft Excel was used for the rest of the assignment, in order to analyze peak discharge data. The tab-separate files were opened in Excel and any excess data was deleted, leaving only the name designation, and the peak streamflow data. A column was added to show water year, which runs from October 1 through September 30. This process was repeated for the other tab-separated file.
Analyzing Flood Data With Microsoft Excel:
After acquiring all of the data off of the USGS website, it was ready to be analyzed using Microsoft Excel. The two tab-separated files were imported to Excel on two different worksheets and any unnecessary data was deleted. The correct water year was assigned to each collected peak discharge event. Water years start on October 1st and end on September 30th. These results can be seen in Appendix I for the La Crosse River data and Appendix II for the Little Blackfoot River data. Following this the data was added to a table. The x-axis for these tables contained the water year for every year on record while the y-axis contained peak discharge values. This was carried out for both sets of data, which can be seen in Chart 1 and Chart 2. These charts were in the form of bar graphs and showed the amount of peak discharge in order of when they occurred with the earliest years first.
Following this, the objective was to determine the exceedence probability and the recurrence interval for the peak discharge events of each separate dataset. Exceedence probability is the likelihood that a discharge event will be surpassed in a given year. This is denoted as EP = m / (n + 1) where (m) is magnitude in comparison to the other ranked events and (n) is the number of years on record. The recurrence interval is the average time, in number of years, in which a discharge event of a given size will occur. This is denoted as RI = (n + 1) / m. To gather the data to figure this out two new worksheets were opened and the peak discharge column was copied over. The peak discharges were sorted using the Sort Descending option in Excel and they were assigned a numerical rank, with 1 being the highest rank. From here, the equations listed above were formulated in Excel and the exceedence probability and recurrence intervals for all peak discharge events were calculated (Appendix III and Appendix IV).
Creating Flood Frequency Curves:
Now that all the recurrence interval data was calculated, the data was ready to be plotted by hand on flood frequency graphs. The two types of graphs were arithmetic and logarithmic and were referred to respectively as Gumbel and log-Gumbel probability paper. This graph paper is used by the USGS and flood analysts to calculate the frequency that a discharge event will occur in a given year. Both rivers were plotted on the Gumbel graph and the La Crosse River was plotted on the log-Gumbel as well. The Gumbel differed from the log-Gumbel in that the y-axis on the Gumbel graph was spaced evenly, while the y-axis on the log-Gumbel was spaced logarithmically.
Results
National Atlas Results:
Through the processes described above, data was acquired that allowed for analysis. The National Atlas allowed for Mean Annual Precipitation Data (MAP), which showed that the MAP of Garrison, MT was in the range of 10.1-15.0 inches per year from 1961-1990 (Figure 3). The MAP for the La Crosse River area was in the range of 30.1-35.0 inches per year from 1961-1990 (Figure 4). The MAP from 1961-1990 was used because this sufficiently encompassed a large amount of time from both of the studies. The Little Blackfoot River gage used was on record from 1973-2011, while the La Crosse River was on record from 1914-1978.
Excel Results:
The data that was brought in and analyzed through Microsoft Excel yielded the exceedence probability and recurrence interval data as seen in Appendices III and IV. Through Excel, the ability to see the peak discharge event in order of when it occurred is also possible. For the La Crosse River, the largest recorded peak discharge event occurred in 1935 (Chart 1). The peak discharge for this event 8,200 cfs, with a recurrence interval of 59.00 years, and an exceedence probability of 1.7%. For the Little Blackfoot River, the largest recorded peak discharge event occurred in 1981 (Chart 2). The peak discharge for this event was 8,650 cfs, with a recurrence interval of 40.00 years, and an exceedence probability of 2.5%.
Probability Paper Results:
Gumbel probability paper is used to plot flood frequency data that is more or less linear in progression. This allows the vertical axis to be an arithmetic progression instead of a logarithmic progression. The Gumbel probability paper results showed that while the La Crosse River had a much higher average discharge, the Little Blackfoot River had the highest peak discharge overall. The ability to fit the plotted data to a linear fit line was very practical for both sets of data. The log-Gumbel probability plot is generally used to plot flood frequency data that is characterized by extremely high variation. The La Crosse River was plotted on the log-Gumbel probability paper and the result was a generally concave down, curved graph. This result was not conducive to plotting a linear fit line.
Discussion
Given all the results and the interpretation of the data, they hypothesis that the La Crosse River exhibits higher average discharge events because of a higher mean annual precipitation and the location of the gage on the Little Blackfoot on the leeward side of a mountain seem to have been upheld. When looking at the mean annual precipitation maps for both areas, it is very obvious that the La Crosse River has a higher mean annual precipitation. There are also no features that would impede a precipitation event from falling on the La Crosse. The Little Blackfoot River, however, has a number of large mountains directly to the west. These mountains have a much greater mean annual precipitation than the area to the east of the mountains. The leeward sides of mountains are much drier than the windward sides, so this could account for the noticeably drier climate found to the eastern side of the mountains.
This leeward theory is supported when looking at the Gumbel probability paper. The La Crosse, on average, has a much higher and steeper fit line than the Little Blackfoot has. This means that the average discharge for the La Crosse is greater than that of the Little Blackfoot. The same would be said for the mean annual precipitation. That being said, the highest peak discharge event for the Little Blackfoot is 450 cfs higher than that of the La Crosse. This can most likely be accounted for by understanding that, because this area is much more arid than that of the La Crosse, when a large precipitation event does occur that effects the Little Blackfoot, the effects will be much greater. This could most likely be attributed to impermeable soil due to hardening with a lack of precipitation. This leads to greater runoff and higher peak discharges. This idea can be supported when examining the discharge events more carefully. There is a very large gap between the highest and second highest peak discharge events from the Little Blackfoot. The highest, as stated before, was 8650 cfs, while the second highest was only 3650 cfs, a difference of 5000 cfs.
Conclusion
Through the use of the National Atlas, United States Geological Society, and Microsoft Excel, the peak discharge events of the La Crosse River and the Little Blackfoot River were analyzed. Both of these rivers had a similar drainage area, though had very different reactions to discharge events. While the La Crosse had, on average, higher peak discharge events, the Little Blackfoot had the highest at 8650 cfs. The low discharge was hypothesized to be due to an almost 20 inch decrease in mean annual precipitation in the Little Blackfoot. The Little Blackfoot was on the leeward side of a mountain range that, according to maps gathered from the National Atlas, exhibit a much higher mean annual precipitation than the areas on its leeward side. This mountain was hypothesized to act as a windbreak that impeded precipitation from reaching the area of Garrison, MT in large amounts.
 |
| Figure 1: This is a map of Wisconsin taken from the USGS website. The gage that is highlighted in yellow is the gage used to record discharge for the La Crosse River, Gage Station # 05383000. |
 |
| Figure 2: This is a map of Montana taken from the USGS website. The gage that is highlighted in yellow is the gage used to record discharge for the Little Blackfoot River, Gage Station # 12324590. |
 |
| Figure 3: Mean Annual Precipitation Map for the Little Blackfoot River and surrounding area. The stream in the center of the picture represents the Little Blackfoot River. The mean annual precipitation here falls in the range of 10.1-15.0 inches per year. |
 |
| Figure 4: Mean Annual Precipitation Map for the La Crosse River and surrounding area. The stream in the center of the picture represents the La Crosse River. The mean annual precipitation here falls in the range of 30.1-35.0 inches per year. |
 |
| Figure 5: Legend for the Mean Annual Precipitation Maps for Figures 3 and 4. |
 |
| Chart 1: Peak Discharge Per Water Year for the La Crosse River, Near West Salem, WI, Gaging Station # 05383000. |
 |
| Chart 2: Peak Discharge Per Water Year of the Little Blackfoot River, Near Garrison, MT, Gaging Station # 12324590. |
 |
| Chart 3: This is a plot of the recurrence intervals of the La Crosse River (the red line) and the Little Blackfoot River (the green line) on Gumbel probability paper. |
 |
| Chart 4: This is a plot of the recurrence interval of the La Crosse River on log-Gumbel probability paper. |
Appendices
Appendix 1:
|
# Sites in this file include:
|
# USGS
05383000 LA CROSSE RIVER NEAR WEST SALEM, WI
|
|||
|
Site #
|
QPk Date
|
Water Year
|
QPk
|
|
|
5383000
|
6/28/14
|
1914
|
1800
|
|
|
5383000
|
2/23/15
|
1915
|
1800
|
|
|
5383000
|
1/29/16
|
1916
|
1850
|
|
|
5383000
|
3/24/17
|
1917
|
2990
|
|
|
5383000
|
3/18/18
|
1918
|
3130
|
|
|
5383000
|
3/16/19
|
1919
|
3900
|
|
|
5383000
|
6/16/20
|
1920
|
2600
|
|
|
5383000
|
6/10/21
|
1921
|
1150
|
|
|
5383000
|
2/24/22
|
1922
|
2920
|
|
|
5383000
|
4/4/23
|
1923
|
2480
|
|
|
5383000
|
8/20/24
|
1924
|
2600
|
|
|
5383000
|
6/15/25
|
1925
|
2120
|
|
|
5383000
|
8/22/26
|
1926
|
1920
|
|
|
5383000
|
7/21/27
|
1927
|
1370
|
|
|
5383000
|
9/15/28
|
1928
|
5160
|
|
|
5383000
|
6/16/29
|
1929
|
1170
|
|
|
5383000
|
2/21/30
|
1930
|
3270
|
|
|
5383000
|
6/23/31
|
1931
|
635
|
|
|
5383000
|
6/8/32
|
1932
|
2380
|
|
|
5383000
|
3/31/33
|
1933
|
4310
|
|
|
5383000
|
4/4/34
|
1934
|
3890
|
|
|
5383000
|
8/6/35
|
1935
|
8200
|
|
|
5383000
|
3/18/36
|
1936
|
3020
|
|
|
5383000
|
3/8/37
|
1937
|
1100
|
|
|
5383000
|
9/11/38
|
1938
|
3490
|
|
|
5383000
|
3/20/39
|
1939
|
1510
|
|
|
5383000
|
6/24/40
|
1940
|
1140
|
|
|
5383000
|
9/16/41
|
1941
|
3020
|
|
|
5383000
|
6/30/42
|
1942
|
4170
|
|
|
5383000
|
5/31/43
|
1943
|
2790
|
|
|
5383000
|
3/13/44
|
1944
|
2150
|
|
|
5383000
|
5/23/45
|
1945
|
4590
|
|
|
5383000
|
1/7/46
|
1946
|
4170
|
|
|
5383000
|
6/30/47
|
1947
|
2900
|
|
|
5383000
|
2/29/48
|
1948
|
2300
|
|
|
5383000
|
3/23/49
|
1949
|
2020
|
|
|
5383000
|
3/7/50
|
1950
|
2900
|
|
|
5383000
|
3/29/51
|
1951
|
1630
|
|
|
5383000
|
7/20/52
|
1952
|
2470
|
|
|
5383000
|
3/19/53
|
1953
|
1320
|
|
|
5383000
|
7/5/54
|
1954
|
1730
|
|
|
5383000
|
6/3/55
|
1955
|
3650
|
|
|
5383000
|
4/3/56
|
1956
|
5720
|
|
|
5383000
|
2/26/57
|
1957
|
984
|
|
|
5383000
|
2/27/58
|
1958
|
1310
|
|
|
5383000
|
4/1/59
|
1959
|
3270
|
|
|
5383000
|
5/8/60
|
1960
|
1780
|
|
|
5383000
|
3/27/61
|
1961
|
4490
|
|
|
5383000
|
3/29/62
|
1962
|
2150
|
|
|
5383000
|
3/25/63
|
1963
|
2060
|
|
|
5383000
|
4/7/64
|
1964
|
1020
|
|
|
5383000
|
3/3/65
|
1965
|
2610
|
|
|
5383000
|
2/8/66
|
1966
|
5940
|
|
|
5383000
|
6/16/67
|
1967
|
3620
|
|
|
5383000
|
6/21/68
|
1968
|
2360
|
|
|
5383000
|
6/27/69
|
1969
|
1750
|
|
|
5383000
|
3/4/70
|
1970
|
1800
|
|
|
5383000
|
7/2/78
|
1978
|
7600
|
|
Appendix II:
|
# Sites in this file include:
|
#
USGS 12324590 Little Blackfoot River near Garrison MT
|
|||
|
Site #
|
QPk Date
|
Water Year
|
QPk
|
|
|
12324590
|
5/21/73
|
1973
|
266
|
|
|
12324590
|
1/15/74
|
1974
|
2700
|
|
|
12324590
|
6/19/75
|
1975
|
3650
|
|
|
12324590
|
5/11/76
|
1976
|
1820
|
|
|
12324590
|
4/9/77
|
1977
|
319
|
|
|
12324590
|
5/19/78
|
1978
|
1200
|
|
|
12324590
|
5/24/79
|
1979
|
1120
|
|
|
12324590
|
5/25/80
|
1980
|
2920
|
|
|
12324590
|
5/22/81
|
1981
|
8650
|
|
|
12324590
|
2/21/82
|
1982
|
1440
|
|
|
12324590
|
5/27/83
|
1983
|
959
|
|
|
12324590
|
5/16/84
|
1984
|
1540
|
|
|
12324590
|
4/2/85
|
1985
|
1250
|
|
|
12324590
|
2/24/86
|
1986
|
1710
|
|
|
12324590
|
3/4/87
|
1987
|
536
|
|
|
12324590
|
5/14/88
|
1988
|
424
|
|
|
12324590
|
4/7/89
|
1989
|
2220
|
|
|
12324590
|
5/30/90
|
1990
|
1090
|
|
|
12324590
|
5/19/91
|
1991
|
906
|
|
|
12324590
|
4/30/92
|
1992
|
175
|
|
|
12324590
|
5/15/93
|
1993
|
816
|
|
|
12324590
|
4/25/94
|
1994
|
730
|
|
|
12324590
|
6/6/95
|
1995
|
1640
|
|
|
12324590
|
2/9/96
|
1996
|
2860
|
|
|
12324590
|
5/25/97
|
1997
|
1630
|
|
|
12324590
|
7/4/98
|
1998
|
1980
|
|
|
12324590
|
6/3/99
|
1999
|
881
|
|
|
12324590
|
5/31/00
|
2000
|
177
|
|
|
12324590
|
5/15/01
|
2001
|
687
|
|
|
12324590
|
4/6/02
|
2002
|
746
|
|
|
12324590
|
3/13/03
|
2003
|
1280
|
|
|
12324590
|
3/8/04
|
2004
|
711
|
|
|
12324590
|
6/4/05
|
2005
|
1500
|
|
|
12324590
|
6/10/06
|
2006
|
649
|
|
|
12324590
|
6/7/07
|
2007
|
901
|
|
|
12324590
|
6/5/08
|
2008
|
1130
|
|
|
12324590
|
4/13/09
|
2009
|
1530
|
|
|
12324590
|
6/17/10
|
2010
|
1450
|
|
|
12324590
|
6/9/11
|
2011
|
2810
|
|
Appendix III:
|
# Sites in this file include:
|
#
USGS 05383000 LA CROSSE RIVER NEAR WEST SALEM, WI
|
||
|
Sorted Peaks
|
Ranks
|
EP
|
RI
|
|
8200
|
1
|
1.7%
|
59.00
|
|
7600
|
2
|
3.4%
|
29.50
|
|
5940
|
3
|
5.1%
|
19.67
|
|
5720
|
4
|
6.8%
|
14.75
|
|
5160
|
5
|
8.5%
|
11.80
|
|
4590
|
6
|
10.2%
|
9.83
|
|
4490
|
7
|
11.9%
|
8.43
|
|
4310
|
8
|
13.6%
|
7.38
|
|
4170
|
9
|
15.3%
|
6.56
|
|
4170
|
10
|
16.9%
|
5.90
|
|
3900
|
11
|
18.6%
|
5.36
|
|
3890
|
12
|
20.3%
|
4.92
|
|
3650
|
13
|
22.0%
|
4.54
|
|
3620
|
14
|
23.7%
|
4.21
|
|
3490
|
15
|
25.4%
|
3.93
|
|
3270
|
16
|
27.1%
|
3.69
|
|
3270
|
17
|
28.8%
|
3.47
|
|
3130
|
18
|
30.5%
|
3.28
|
|
3020
|
19
|
32.2%
|
3.11
|
|
3020
|
20
|
33.9%
|
2.95
|
|
2990
|
21
|
35.6%
|
2.81
|
|
2920
|
22
|
37.3%
|
2.68
|
|
2900
|
23
|
39.0%
|
2.57
|
|
2900
|
24
|
40.7%
|
2.46
|
|
2790
|
25
|
42.4%
|
2.36
|
|
2610
|
26
|
44.1%
|
2.27
|
|
2600
|
27
|
45.8%
|
2.19
|
|
2600
|
28
|
47.5%
|
2.11
|
|
2480
|
29
|
49.2%
|
2.03
|
|
2470
|
30
|
50.8%
|
1.97
|
|
2380
|
31
|
52.5%
|
1.90
|
|
2360
|
32
|
54.2%
|
1.84
|
|
2300
|
33
|
55.9%
|
1.79
|
|
2150
|
34
|
57.6%
|
1.74
|
|
2150
|
35
|
59.3%
|
1.69
|
|
2120
|
36
|
61.0%
|
1.64
|
|
2060
|
37
|
62.7%
|
1.59
|
|
2020
|
38
|
64.4%
|
1.55
|
|
1920
|
39
|
66.1%
|
1.51
|
|
1850
|
40
|
67.8%
|
1.48
|
|
1800
|
41
|
69.5%
|
1.44
|
|
1800
|
42
|
71.2%
|
1.40
|
|
1800
|
43
|
72.9%
|
1.37
|
|
1780
|
44
|
74.6%
|
1.34
|
|
1750
|
45
|
76.3%
|
1.31
|
|
1730
|
46
|
78.0%
|
1.28
|
|
1630
|
47
|
79.7%
|
1.26
|
|
1510
|
48
|
81.4%
|
1.23
|
|
1370
|
49
|
83.1%
|
1.20
|
|
1320
|
50
|
84.7%
|
1.18
|
|
1310
|
51
|
86.4%
|
1.16
|
|
1170
|
52
|
88.1%
|
1.13
|
|
1150
|
53
|
89.8%
|
1.11
|
|
1140
|
54
|
91.5%
|
1.09
|
|
1100
|
55
|
93.2%
|
1.07
|
|
1020
|
56
|
94.9%
|
1.05
|
|
984
|
57
|
96.6%
|
1.04
|
|
635
|
58
|
98.3%
|
1.02
|
Appendix IV:
|
# Sites in this file include:
|
#
USGS 12324590 Little Blackfoot River near Garrison MT
|
||
|
Sorted Peaks
|
Ranks
|
EP
|
RI
|
|
8650
|
1
|
2.5%
|
40.00
|
|
3650
|
2
|
5.0%
|
20.00
|
|
2920
|
3
|
7.5%
|
13.33
|
|
2860
|
4
|
10.0%
|
10.00
|
|
2810
|
5
|
12.5%
|
8.00
|
|
2700
|
6
|
15.0%
|
6.67
|
|
2220
|
7
|
17.5%
|
5.71
|
|
1980
|
8
|
20.0%
|
5.00
|
|
1820
|
9
|
22.5%
|
4.44
|
|
1710
|
10
|
25.0%
|
4.00
|
|
1640
|
11
|
27.5%
|
3.64
|
|
1630
|
12
|
30.0%
|
3.33
|
|
1540
|
13
|
32.5%
|
3.08
|
|
1530
|
14
|
35.0%
|
2.86
|
|
1500
|
15
|
37.5%
|
2.67
|
|
1450
|
16
|
40.0%
|
2.50
|
|
1440
|
17
|
42.5%
|
2.35
|
|
1280
|
18
|
45.0%
|
2.22
|
|
1250
|
19
|
47.5%
|
2.11
|
|
1200
|
20
|
50.0%
|
2.00
|
|
1130
|
21
|
52.5%
|
1.90
|
|
1120
|
22
|
55.0%
|
1.82
|
|
1090
|
23
|
57.5%
|
1.74
|
|
959
|
24
|
60.0%
|
1.67
|
|
906
|
25
|
62.5%
|
1.60
|
|
901
|
26
|
65.0%
|
1.54
|
|
881
|
27
|
67.5%
|
1.48
|
|
816
|
28
|
70.0%
|
1.43
|
|
746
|
29
|
72.5%
|
1.38
|
|
730
|
30
|
75.0%
|
1.33
|
|
711
|
31
|
77.5%
|
1.29
|
|
687
|
32
|
80.0%
|
1.25
|
|
649
|
33
|
82.5%
|
1.21
|
|
536
|
34
|
85.0%
|
1.18
|
|
424
|
35
|
87.5%
|
1.14
|
|
319
|
36
|
90.0%
|
1.11
|
|
266
|
37
|
92.5%
|
1.08
|
|
177
|
38
|
95.0%
|
1.05
|
|
175
|
39
|
97.5%
|
1.03
|
Sources
Faulkner, Douglas J., Dr. "Lab 4: Moisture in the Atmosphere." Lecture. Print.
"Map Maker." National Atlas of the United States. N.p., n.d. Web. 08 Nov. 2013. <http://nationalatlas.gov/mapmaker>.
"USGS Water Data for the Nation." USGS Water Data for the Nation. United States Geological Society, n.d. Web. 08 Nov. 2013. <http://waterdata.usgs.gov/nwis>.
Faulkner, Douglas J., Dr. "Lab 4: Moisture in the Atmosphere." Lecture. Print.
"Map Maker." National Atlas of the United States. N.p., n.d. Web. 08 Nov. 2013. <http://nationalatlas.gov/mapmaker>.
"USGS Water Data for the Nation." USGS Water Data for the Nation. United States Geological Society, n.d. Web. 08 Nov. 2013. <http://waterdata.usgs.gov/nwis>.
