Homework #11  2020, Earth Surface Processes, Humphrey

There are a lot of calculations in this homework, take your time and think a little.

 

We have talked about the variability of river discharge.  There are many ways of looking at how river discharge varies.  A useful type of plot is shown below, which nicely shows that the Laramie river typically has only one flood (snow melt dominated) in early summer.

 

 

For this exercise, we are going to look at something that is of major interest to many, the question of the likelihood of large floods.

First, we will at some better quality data than the Laramie River.

 

Question 1, recurrence intervals (or what the media loves to report, the eponymous ‘100 year floods’)

Grey River, at Dobson New Zealand

1968 to 2004

year

Max flow (m3/s)

 

 

1997

5950.8

 

 

1988

5840.4

 

 

1998

5670.0

 

 

1970

4899.1

 

 

1994

4844.5

 

 

1977

4841.4

 

 

1984

4814.3

 

 

1983

4228.2

 

 

1969

4203.4

 

 

1972

4125.6

 

 

1975

4117.8

 

 

1980

4039.4

 

 

1973

4012.5

 

 

1979

4000.9

 

 

1982

3975.2

 

 

1996

3866.7

 

 

2000

3809.5

 

 

1974

3771.7

 

 

1968

3678.3

 

 

2002

3517.9

 

 

1976

3463.4

 

 

1981

3448.9

 

 

1993

3422.3

 

 

2001

3342.7

 

 

1978

3302.9

 

 

2004

3224.6

 

 

2003

3221.9

 

 

1989

3217.1

 

 

1995

3185.8

 

 

1992

3177.6

 

 

1991

3091.4

 

 

1999

3070.0

 

 

1990

2806.8

 

 

1971

2420.5

 

 

1987

2385.4

 

 

1986

2364.9

 

 

1985

1794.8

 

 

 

Mean 3761.0

 

 

 

 

 

 

 

 

To start our thinking about river floods, we will look at some (good quality) data from the Grey river in New Zealand.

a.       Calculate the recurrence intervals for floods on the Grey River.  Recurrence intervals are what are usually somewhat misleadingly quoted in the popular media as the 100 year flood or whatever the news person wants to emphasize.  There are a variety of methods to calculate recurrence interval, but probably the simplest is as follows: order your data from largest to smallest (this I have done for you).  Now apply the following formula to each datum:

Tr = (N+1)/n,  where N is the total number of observations, n is the ranking in the above list from top to bottom (eq the second from the top is n=2) and Tr is the recurrence interval in years.

b.       Plot the recurrence intervals on a semi log plot.  Use log time on the x-axis and discharge on a linear y-axis.  We will use a log axis, however there is considerable discussion in the literature about the expected shape of a recurrence interval curve, or more precisely, how floods should be distributed in time.  (If you would like to investigate this more, look up Gumbel Distribution on the web.)  We use a semi-log plot since it is straightforward to plot, not because it is correct.

c.       Use your plot to estimate the 100year flood on the Grey river.  Comment on the accuracy of your prediction.

d.       The channel forming discharge for a meandering river is typically about the 2year flood.  What is the 2 year flood on the Grey River.

 

Question 2 Now here is some data from the Laramie river at Laramie: (this is the best there is!)

 

Flow measurements as reported on UPRR quarterly Discharge Monitoring Reports (DMR) for WDEQ Permit WY0032590,

Laramie Tie Plant.

Year

Oct       Nov      Dec      Jan      Feb      March Apr      May      June    July      Aug      Sept

Streamflow (cfs)

1987     8.1        77        49        -           54        65        62        157       46        22        7.8        4.5

1988     28        40        26        7.9        7.0       68        201       508       680       48        8.9        5.5

1989     17        44        34        7.1        2.0        61        nr         16        45        13        11        13

1990     36        75         60        27        30        189       36        30        351       50        20        10

1991     7.9        41        76        11         24        104       20        169       612       19        21        11

1992     -           -           -           -           -           -           -           -           231

1993     49        102       147       196       264       309       39        407       1016     115       11        36

1994     14        38        67        177       209       93        53        288       77         7.6       7.0        4.7

1995     45        55        53        86        65        68        6.8        111       1281     281      14        15

1996     51         62        88        77        68        79        107       552       1136     420       20        21

1997     115       128       115       55        62        82        101       503       1277     149       110       87

1998     34         55        63        70        75        87        100       305       425       139       66         29

1999     20        18        67        56        60        75        68         496      1126     267      20        17

2000     18        40        13        84        72        45        54        297       101       18        6          13

2001     56         20        54        77         90        75        21        177       66        11        18        26

2002     11        16        21        160       207       174       32        68        56

2003     18         49        68        28        22        22        20        230       556       -           -           14

2004     131       122       113       68        83        72

2005     47        49        81        94        98        90        53        306       1115     95        80        16

2006     188       201       200       126       109       107       159       386       105       187       109       115

2007     143       104       68        200       186       281       146       549       378       78        109       34

2008     -           -           -           68        68        68        98        469       1715     316       180       169

 

The above table shows typical problems with flood analysis.  Real data sets have missing and questionable data.  The above table lists measurements taken once a month, obviously it probably misses the actual flood peaks.  There are more subtle problems with stream data: even if you find more continuous data (e.g. USGS typically reports daily discharge), the actual discharge is not measured, but estimated from river depth.  Any bed or bank erosion or deposition will create errors in this depth based estimate, this is especially a problem at high flows when erosion/deposition is common.  The biggest problem with the Laramie river data, is that over time, various water projects have diverted water from the river.  As a result, the flood data is not ‘stationary’, in other words the flood data does not represent a sample from the same river over time.  The river has been changing, so that we can’t trust the old data to predict the future.

This question is just to get you thinking about real world data.

a) Calculate the average discharge for the depth of winter in January and the peak of summer in July. 

b) Now re-read the above paragraph about how the data is collected and comment on which average has less error? (hint: what happens in the river in winter?)

c) (Hard, there are no ‘correct’ answers, but I would like you to say something) if you had to use the data in the table for a specific purpose, such as calculating average yearly discharge for planning purposes:

1- how would you use the data for April 1995?

2- And how would you deal with the data for 2002 thru 2004.

3- Is there anything you can do with the 1992 data?

 

Question 3.

Use Google Earth to find the width of the Laramie river near Optimist Park, specifically near the bridge on W Garfield st..

a) The largest flood in the above record was in 2008, at 1715cfs.  How deep would this flow have been under the Garfield bridge, IF the river stayed in its banks.  Use Manning’s equation.  [hint remember discharge is w*v*d, and you will have to convert from cfs to m^3/s]

b) Using the same technique as in question 1, find the channel forming discharge.

c) If you are brave, estimate the 100 year flood on the Laramie River!