HW 7 Q DONE
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Date
Dec 6, 2023
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Environmental Hydrology
Homework: #9 Flood frequency analysis
Points: 120
Part I: LP3 distribution and flood frequency analysis (120 points)
1.
Download peak flow data from the USGS by navigating to
https://nwis.waterdata.usgs.gov/usa/nwis/peak
2.
Type in the three site numbers 02311500, 02322500, 02322800 into the box. Ensure
they are separated by a comma.
3.
Scroll down and select “Tab separated data.” Leave the dates blank for all data to ensure
all years are downloaded.
4.
Import your saved data into Excel by navigating to tab
Data>From Text/CSV
. You may
need to separate them out into columns upon importing. Create 3 separate tabs for each
site. Label the tabs with the site number. You will notice that the data are concatenated,
meaning they are all within the same document with data from each site right after the
other.
5.
You can get rid of the header information like we did for the USGS data download, but I
would take a look at what the quality codes are and maybe put them in another tab, as
some of this information will come up in the questions.
6.
After separating these data out, order the data from largest to smallest and in another
column, add the
ranking
number to the data (i.e., 1, 2, 3, ….n) (
5 points
).
7.
Assign probability (single column) using the Gringorten plotting position in the equation
below:
Gringorten plotting position =
i
−
0.44
n
+
0.12
Where i is the
rank
you assigned in part 6. The
Gringorten
plotting position is the
preferred plotting position (probability rank) for data that is thought to fit a LP3
distribution. There are other plotting positions. For the FDC homework you used a
Weibull
plotting position.
Google
plotting positions and name
2 more
highly used plotting
positions. You can also use the Handbook of Applied Hydrology for help
?
(
15 points
).
8.
Create another column that contains the log-transformed (base 10) AMF discharges –
Excel function
=log10(DATA)
(
5 points
).
9.
Calculate the sample mean (Excel function =AVERAGE), sample standard deviation
(=STDEV.S), and skew (=SKEW) for
each
AMF data series. Make sure they are clearly
labeled in the Excel sheet! (
10 points
).
10. Use these data and the method of moments (see slides) to estimate the
parameters of
the LP3 distribution
(
α
,
β,
and
τ
). Make sure they are clearly labeled in the
Excel sheet! (
20 points
).
Done
11. Now here is the tricky part. In Excel, there is no
quantile function
for the LP3
distribution. We have to use the properties of the distribution to estimate the quantiles
(recall quantile function from class). We will be using the built in Gamma functions.
Use the following excel condition for each criteria by examining the
β
value that you
estimated for each site.
If β
>
0
Use τ
+
GAMMAINV
(
1
−
p,α , β
)
If β
<
0
Use τ
−
GAMMAINV
(
p,α ,
|
(
β
)
|
)
12. Find the 2-year, 50-year, 100-year and 500-year return period flood using the LP3
distribution (
40 points
).
done
13. Using the Gringorten plotting position as the input, p, to the gamma function described
above, create a column that generates discharges for each plotting position to compare
with the observed data (
10 points
).
done
14. Plot the observed and LP3 “modeled” data against one another as a function of the
probability. Make any notes on differences (tails, middle) and write that down (
15
points
).
In FT WHITE we see the observed discharge taking a dip towards the end of the
data series, trending away from modeled discharge.
Slight dip for both modeled and observed discharge in Withlacoochee.
15. Take the mean squared error (MSE) of the observed and modeled data. To be fair, MSE
is NOT the best metric for this. But it is also not entirely wrong. It is, however, a useful
error metric to become familiar with. Write down the MSE for each site below (
15
points
).
MSE
Withlacoochee
0.00349
Ft White
0.0113
Hildreth
0.00208
16. What station had the highest MSE? Why do you think that is? (
5 points
)
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The highest MSE that we see here is from Ft White with its 0.0113 as compared to the other
value above. A higher MSE reading means a higher margin of error which pushes the actual
usefulness and accuracy of results just a little bit further from the truth. This could be
accounted for by a few things but more often then not this is usually due to mathematical
error or even faulty observations. To fix this, a value may have been needed to be omitted or
there could be a slight deviation in a made calculation that could be leading to this
comparatively larger MSE reading.