CVEN 675 Stochastic
Hydrology
Professor Anthony Cahill
What is Stochastic Hydrology (and
why would want to take it)?
• We often have measurements of system
behavior, but not enough knowledge of
physics
• Model our lack of knowledge as a random
(stochastic) element
• Allows us to make predictions of system
behavior (within some confidence limits)
Examples – Streamflow time series
• USGS has gauging stations throughout
US
• We’d like to predict streamflow – estimate
flooding, recession, water availability, etc.
90000
80000
70000
60000
cfs
50000
40000
30000
20000
10000
0
11/5/2001
12/25/2001
2/13/2002
4/4/2002
5/24/2002
date
7/13/2002
9/1/2002
10/21/2002
Streamflow time series, cont.
• Difference between streamflow time series
and rolling dice – dependence of
sequential observations
• Can we model the time series (for
understanding)?
Streamflow time series, cont.
• Can we predict the streamflow in future
based on past behavior (forecasting)?
18000.
16000.
14000.
12000.
10000.
8000.
6000.
4000.
2000.
0.
0
50
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Example – Rainfall time series
• Different than river time series –
intermittant in time, but still dependence
Rainfall time series cont.
• Use a different method than streamflow
time series for modeling and prediction
Frequency analysis – flood
frequency, storm frequency and
extreme values
• Change the time period of interest so that
events are independent – usually annual
maximum event
600
500
400
I2
mm/hr
I5
I10
300
I25
I50
I100
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100
0
0
10
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m in
50
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Frequency analysis, cont.
• Used extensively for planning, runoff
estimation, etc.
• We are working with rare extreme events
• Need to treat tails carefully
Spatial statistical methods
• Spatial data sets ubiquitous in hydrology
– Rain gauge data
– Hydraulic conductivity
– Soil moisture
Spatial statistics cont.
• Optimal interpolation of point data –
“kriging”
• This is both modeling and prediction
• Very useful in GIS – built into ArcGIS (I
think)
If time permits…
• Fractals in hydrology
• Stochastic groundwater models
Housekeeping
• Books
– Brockwell and Davis, Introduction to Time
Series and Forecasting, 2nd ed.
– Isaaks and Srivastava, Applied Geostatistics
• Software
– In Brockwell and Davis
– I will provide some
– You will write some
Class Web Page
• http://ceprofs.tamu.edu/cahill/teaching675.html
• I’ll put stuff up there
• Including syllabus
Grading
• Homework – 30%
• Two tests – 20% each
– First test in in-class
– Second test is a takehome due the day of the
final (i.e. no in class final), which is Monday,
December 15, 8AM.
• Project – 30%
Project
• Explore some question of interest to you in
stochastic hydrology
• Required: a paper – can be analysis or
review
• Start thinking – due dates
– Topic – October 1
– 1st draft – November 19
– Final version – December 15
• You can talk to me about project anytime
Classroom
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This course is TTVN to Corpus Christi
We will meet in WERC 049
Get used to disembodied interruptions
I will not be using Power Point usually
I will be using software