MATH 411 - SPRING 1997

Sample Modeling Exercise #1 - A Data Arrangement Problem

You are a consultant for the South Florida Water Management District,
which is a large organization charged with the responsibility to manage
and control all water flows in South Florida. One of the District's
responsibilities is to plan for a variety of impacts of alternative
hydrologic scenarios over the next 30 years. They have asked you for
help with the following specific problem.

The District has developed a large computer model, at very high
expense, to predict water flows across the entire southern section of
the State. This model uses as input historical knowldege of rainfall
inputs across this region, with good data over the past 30 years. They
would like to use their model to predict patterns of hydrology over the
next 30 years, but obviously do not have available future rainfall
patterns. Your problem is: How should they use the record of rainfall
data they have (see the attached) in their computer code to predict
water patterns over the next 30 years? Note that the initial plan their
hydrologists have decided upon is to simply take the historical
rainfall, assume that the next thirty years will be exactly like the
past thirty years, and use the entire sequence in the computer runs.

Assignment #1: Think about the above and do the following:

(1) Determine for yourself a variety of different ways they might use
the historical data to drive the computer model, and make a list of
these.

(2) If you believe the approach their hydrologists suggest to plan for
future hydrology is appropriate, state so and why.

(3) If you believe one or more of the alternative methods you state in
(1) is superior to the method the District hydrologists plan to use,
state so, give reasons why their approach is flawed and why your
methods are superior. Don't try to derive any exact math for this, but
feel free to use illustrations if you'd like.

(4) Carefully write a 1-2 page report explaining your suggestion in a
clear enough manner that a manager at the District with little math
background would understand it. Stop.

Due Friday January 24, at which point you should be ready to discuss
your results in class and defend your comments in (2) and (3).