# CEE6430

## Probabilistic Methods in Hydrosciences (FALL 2006)

For the skeptics who doubt this course:
With many calculations, one can win; with few one cannot. How much less chance of victory has one who makes none at all! –Sun Tzu ‘Art of War’

For those who thought the course was very important in their lives:
There are three kinds of lies: lies, damn lies, and statistics. –Benjamin Disraeli

And the Verdict
Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise –John Tukey

#### BACKGROUND

Real world problems include variables whose values are uncertain – example: rainfall at TTU campus on September 15, 2008; tomorrow’s average temperature at Cookeville, Tennessee. Furthermore, most systems of interest to the engineer contain components whose response to certain input varies in time (dynamic) -example: the rainfall-runoff transformation of a hydrologic model. The probabilistic property of natural and man-made systems are most apparent (but not limited to) in the field of Hydrosciences (as the examples show). Such systems with dynamic components that contain uncertain parameters, variables, or accept uncertain input are commonly known as stochastic-dynamic systems. Click here for Figure.

#### OBJECTIVES: WHAT THIS COURSE PROVIDES

The course provides basic techniques for the analysis and synthesis of stochastic-dynamic systems with real-world applications. The material in this course can be used to solve three main classes of problems: (1) Estimation; (2) Prediction and (3) Optimal Control of systems that are observed remotely or directly. For example, consider the problem of rainfall estimation from multiple satellites and ground radars, the problem of flood prediction, and the problem of optimal control of a multipurpose reservoir system.

#### COURSE DELIVERABLES: THE NET ‘GAIN’ FOR THE STUDENT

Against a semester-long labor of staying awake during a 3 hour long lecture, the student can (hopefully) expect to understand the probabilistic concepts and appreciate their real-world application with particular focus on hydrological sciences. Additional (but not necessary) outcomes may be an enhancement of the student’s effectiveness in authoring and presenting market-quality research work to stay competitive.

#### PREREQUISITES

Beyond the basic course on elementary Statistics and Probability, students are expected to have working knowledge on computing (any language will suffice) and differential calculus.

#### MODUS OPERANDI: INSTRUCTIONAL FORMAT

Instruction will follow an essentially active learning format with basic concepts taught by providing real-world examples stressing assumptions. Difficult (and often sleep-inducing) theoretical derivations will be separated out in notes and avoided in class. Open-book mode of responding to grading exercises will be the most preferred method of evaluating progress of a student’s understanding (no memorizing needed!). The lion share of the evaluation criteria will be based on assessing the student’s capacity for independent thinking, creativity in identifying a real-world application of probabilistic concepts and clarity in presenting
his ideas on a proposal. Hence, 65% of the grading will be based on a class project that is the student’s most comfortable area of research. Work towards the class project will evolve on a regular one-to-one mentorship (bi-weekly) culminating in a 30 min end-semester presentation and a final report. Efforts will be made to train students in the art of delivering quality presentations to enhance their marketability at scientific meetings and job interviews.

Homework: 25%
Mini Projects (4): 40%
Quizzes and Class interaction: 10%
End-semester Class Project: 25%<

#### HOMEWORK AND CLASS POLICY REQUIREMENTS

Homework and quizzes should be answered in a concise and legible fashion. The Class Project and mini projects should be documented (electronically) in the form of a short paper structured in the following way:

• Formulation of the problem
• Literature review (very brief) – not needed for mini projects
• Description of the methodology proposed to solve the problem. This should include discussion of all the assumptions made.
• Flow chart of the algorithm (if any) used.
• Listing of the computer program. The program should be well documented by using the comments.
• Presentation of the results including their discussion.
• Final discussion including the main findings of the project, the limitations of the methodology used, and the recommendations for future research.

The document should be limited to about 10-15 pages of double-spaced text. It should be prepared neatly.

#### RECOMMENDED BOOKS

Text:

• Probability and Statistics for Engineers and Statistics – Walpole, Myers, Myers and Ye (Prentice Hall).
• Random Functions and Hydrology – Bras and Rodriguez-Iturbe (Dover).
• Probability, Random Variables and Stochastic Processes – Papoulis and Pillai (McGraw-Hill).

Other References (available for loan anytime from my office):

For Refreshing concepts on Probability and Statistics:

• Introduction to the Theory of Statistics – Mood (McGraw Hill).
• Fundamentals of Probability – Saeed Ghahramani (Prentice-Hall)

For Special Topics:

• On Error Propagation: Multivariate Error Analysis – Clifford (Applied Science Publishers).
• On Monte Carlo Techniques: A Primer for the Monte Carlo Method – Sobol (CRC Press).

INSTRUCTIONS ON WRITTEN ASSIGNMENTS

The student will be required to submit various types of written assignments during the semester. The instructor requires that all written portions of the assignments be done in a professional manner (neatness, grammar, sentence structure, and spelling). Substandard work will be returned without a grade. Once the student has returned the corrected assignment, the instructor will determine the effect on the assignment grade. All laboratory and course project reports will be prepared using a word processing program.