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Frequency Analysis Reading: Applied Hydrology Sections 12-2 to 12-6

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2 Frequency analysis for extreme events If you know T, you can find y T, and once y T is know, x T can be computed by Q. Find a flow (or any other event) that has a return period of T years EV1 pdf and cdf Define a reduced variable y

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3 Example 12.2.1 Given annual maxima for 10-minute storms Find 5- & 50-year return period 10-minute storms

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4 Frequency Factors Once a distribution has been selected and its parameters estimated, then how do we use it? Chow proposed using: where x fX(x)fX(x)

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5 Normal Distribution Normal distribution So the frequency factor for the Normal Distribution is the standard normal variate Example: 50 year return period Look in Table 11.2.1 or use –NORMSINV (.) in EXCEL or see page 390 in the text book

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6 EV-I (Gumbel) Distribution

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7 Example 12.3.2 Given annual maximum rainfall, calculate 5-yr storm using frequency factor

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8 Probability plots Probability plot is a graphical tool to assess whether or not the data fits a particular distribution. The data are fitted against a theoretical distribution in such as way that the points should form approximately a straight line (distribution function is linearized) Departures from a straight line indicate departure from the theoretical distribution

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9 Normal probability plot Steps 1.Rank the data from largest (m = 1) to smallest (m = n) 2.Assign plotting position to the data 1.Plotting position – an estimate of exccedance probability 2.Use p = (m-3/8)/(n + 0.15) 3.Find the standard normal variable z corresponding to the plotting position (use -NORMSINV (.) in Excel) 4.Plot the data against z If the data falls on a straight line, the data comes from a normal distributionI

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10 Normal Probability Plot Annual maximum flows for Colorado River near Austin, TX The pink line you see on the plot is x T for T = 2, 5, 10, 25, 50, 100, 500 derived using the frequency factor technique for normal distribution.

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