University of Texas at Austin

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University of Texas at Austin GIS in Water
Resources Professor Dr. David Maidment
Probabilistic Model for Flooding in Guadalupe
River
By Andres Perez
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Objectives

• Find the monitoring point from ARC GIS
• Obtain hydrologic data from USGS
• Use the probabilistic models
• Obtain values of the parameters in the
  probabilistic models
• Use the Chi-square statistics test
• Obtain maximum flow values for 25, 50, and 100
  years

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Guadalupe River basin
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Distribution Model for Maximum Flow in Rivers
The distribution model for predict the maximum
flows for different period return are 1. 2
Parameters log normal 2. 3 Parameters log normal
3. Extreme type I 4. Pearson III 5. Log Pearson
III 6. Gamma 3 parameters
2 Parameter Log Normal Distribution The
probability density function for the Log Normal
Distribution is
where x hydrologic data y ln(x) natural
log of x my mean of the population y sy
variance of the population of y
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Estimation of the Parameters of Distribution
Model
a. Maximum Likelihood Estimation The maximum
likelihood estimates the distribution parameters
such that product of the likelihoods of the
individual events (L) is maximized. In terms of
an equation this becomes an estimation of a, b
... such that
is maximized. b. Method of Moments Estimation The
method of moments uses the calculation of the rth
moment about the origin of a distribution.
The probability function p(x) is then directly
substituted into the equation and the
distribution parameters are solved for directly.
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HYDROLOGIC DATA From USGS Process of down from
web www.USGS.gov/ Maps, Products
Publications/ National water-Data-NWISweb/ Surface
Water/ Texas/ Peak-flow data/ Station Cuero ID
08175800)
De Witt County, Texas Hydrologic Unit Code 12100204 Latitude  2905'25", Longitude  9719'46" NAD27 Drainage area 4,934  square miles Contributing drainage area 4,934  square miles Gage datum 128.64 feet above sea level NGVD29

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RESULTS
Graphics of Distribution Model Software SMADA
http//cee.ucf.edu/software/
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CHI SQUARE TEST For doing the Chi-square test the
equation is
Where k, is the data are divided interval of
class
Oi, is the observed frequency for interval

• Ei, is the expected frequency for interval
• This test is for choose the better model
  probabilistic that better adjust
• or represent to the data from the river.

Result of Chi square test of Log Normal 2
parameters
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Result of Chi square test of Log Pearson type III
k Interval 1 2 3 4 5 6 7 8 9 10  
Low limit 0 4704.9 9409.7 14141.5 18819.3 23524.1 28228.9 32933.7 37638.5 42343.2  
Upper limit 4704.8 14141.4 14114.4 18819.2 23524 28228.8 32933.6 37638.4 42343.2 4700000  
Oi 3 8 5 8 4 1 0 1 2 10  
Ei 3 8 7 5 3 3 2 1 1 9  
(Oi-Ei)2/Ei 0 0 0.571 1.8 0.333 0.5 2 0 1 0.111 6.315
Conclusion of Chi square test Chi square
calculated is compare with the value Chi square
from table
Where K-1-p is degrees freedom p is quantity of
parameter to estimate a is significance level
Then 9.133 lt 14.07 is good 6.315 lt 14.07 is
good this is better Log Pearson III
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The better probabilistic model after Chi square
test Cuero Station is Log Pearson Type III
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RESULT Summary of Maximum Flow in Guadalupe
River for different of Return of Period (
CFS)
N Name station Return Period ( Years) Return Period ( Years) Return Period ( Years)   Better Model Better Model
    25 50 100 200 Probabilistic  
1 Victoria 137947.90 196129.90 269144.90 359549.00 2 Parameter Log Normal 2 Parameter Log Normal
2 Cuero 181606.80 295073.80 467236.30 725641.00 Log Pearson Log Pearson
3 New Braunfels 69183.98 105698.80 155166.30 220984.50 Log Pearson Log Pearson
4 Sattler 25583.60 35240.01 46579.79 59798.85 3Parameter Log Normal 3Parameter Log Normal
5 Comfort 131107.60 189152.00 260230.60 345443.00 Log Pearson Log Pearson
6 Kerrville 141994.00 187003.00 234840.10 285210.30 Pearson Pearson
7 Hunt 67744.19 85524.45 103929.50 122910.30 Pearson Pearson

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Return of Period of 25 Years
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Return of Period of 50 Years
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Return of Period of 100 Years
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Picture flooding Guadalupe River in Victoria
October 20 1998
Deaths and Damages During the 1998 Flood
http//pubs.usgs.gov/fs/FS-147-99/
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Conclusion

• In 1932, the historic discharge maximum peak was
  in the high basin, and in 1998 it was in the low
  basin
• The value of these two years (1932 and 1998)
  largely distorted the probabilistic models.
• The probabilistic models, which are better
  adjusted to the peak stream flow, are Pearson
  Type III and Log Normal.
• The maximum value of flow shows the spatial
  variability of the storm in the basin.

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Thank You