**Instructor:** Dr. David
G Tarboton , Engr 230, 797-3172, email: dtarb@usu.edu.

3 credits, Spring semester.

**Texts:** Loucks, D. P., E. van Beek, J. R. Stedinger, J. P. M. Dijkman and M. T. Villars, (2005), Water Resources Systems Planning and Management: An Introduction to Methods, Models and Applications, UNESCO, Paris, 676 p, http://hdl.handle.net/1813/2804 (This entire book is online. We will cover only chapters 2 and 7)

Bras, R. L. and I. Rodriguez-Iturbe, (1985), Random Functions and Hydrology, Addison-Wesley, Reading, MA, 559 p. (Also Paperback from Dover Books on Advanced Mathematics, ~$15 Amazon.com).

You will be also be referred to chapters and research papers from a variety of sources.

**Prerequisites:** The following prerequisite skills are required.

- Probability and Statistics. An understanding of probability and statistics, comprising random variables, probability distribution and density functions, moments, and common probability distribution forms.
- Mathematics. An understanding of calculus and algebra as the language of science and engineering used to express a quantitative understanding of physical phenomena.
- Computational skills. An ability to use computers to process, analyze and plot data, using appropriate software (e.g. spreadsheets or programming language). WWW browser use.

- Introduction. What is Stochastic Hydrology? Synthetic streamflow generation, Reservoir reliability.
- Random variables, probability distributions and moments.
- Multiple random variables and joint distributions. Conditional and joint probability.
- Nonparametric probability distribution estimation.
- Models to represent the relationship between variables. Linear regression, kernel regression, local regression, splines, neural networks.
- Time series models of hydrologic processes. Univariate and multivariate.
- Multivariate time series, Disaggregation, Principal Components, Singular Spectrum Analysis.
- Long term persistence: Hurst phenomenon, fractals.
- Nonparametric methods applied to hydrologic time series, streamflow, precipitation.
- Frequency Domain Analysis. Power Spectrum, Multi-taper spectra, Spectra for unevenenly spaced data.
- Spatial Processes and Random Fields. Applications to Rainfall. Generation of random fields by sampling from the spectrum and the turning bands method. Kriging.
- Optimal estimation of dynamic systems, Kalman Filter, Ensemble Kalman Filter.

Homework 40%

Midterm 25%

Final Exam 35%

2. Incomplete grades will not be given except under extenuating circumstances as allowed for by University policy. Incomplete grades will not be given for poor performance.

3. Make up exams will only be given in cases of severe personal hardship or illness.

4. Examinations will be a combination of a closed book portion testing knowledge of definitions and basic principles from memory and an open book portion where reference to the text will be necessary for solution of the problems. The use of programmable calculators is permitted.