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CEIE 340 Lecture 2 Statistics and Hydrology

CEIE 340 Lecture 2 Statistics and Hydrology - Watershed...

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1 Water Resource Engineering CEIE 340 Sayedul H. Choudhury, Ph.D. Watershed Characteristics Today’s Topics square6 Statistical Terminology square6 Probability square6 Random Variables square6 Probability of Discrete and Continuous Random Variables square6 Moments of a Sample or Distribution Function square6 Mean square6 Variance and standard deviation square6 Skewness square6 Distribution Function square6 Binomial Distribution square6 Normal Distribution square6 Regression Analysis

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2 Why Use Statistics in Hydrology? square6 Randomness in data square6 Weather data square6 Precipitation square6 Streamflow square6 Establish design criteria Applications square6 Hydrologic and hydraulic design square6 Storm square6 Flooding square6 Dam failure square6 Drought
3 Probability square6 The likelihood of an event where, n = the number of observations on the random variable x that result in outcome x 0 N = the total number of observations on x square6 An event is defined as the occurrence of a specified value of the random variable (e.g. probability of rain tomorrow). N n ) x p(x = = 0 Probability Example square6 The height of the coffer dam depends on the level of flooding that can be expected during the period of construction. square6 10 years of annual peak flow (largest flow in each year) data are available square6 Assume, we can allow only a 10% chance that the flood level will exceed the height of the cofferdam during the 1-yr construction period, i.e. p(x=x 0 ) = 0.10 square6 Therefore, set the height of the cofferdam between the largest and the second largest floods

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4 Random Variables square6 Two types of random variables – discrete and continuous random variables square6 Need to distinguish because the computation of probabilities is different for the two types square6 Discrete random variable is one that only takes distinct values (yes/no, integer, etc), e.g. the
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CEIE 340 Lecture 2 Statistics and Hydrology - Watershed...

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