1 / 10

Frequency Analysis

Frequency Analysis. Reading: Applied Hydrology Sections 12-2 to 12-6. Frequency analysis for extreme events . 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.

fay
Download Presentation

Frequency Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. Frequency analysis for extreme events 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 If you know T, you can find yT, and once yT is know, xT can be computed by

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

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

  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

  6. EV-I (Gumbel) Distribution

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

  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

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

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

More Related