Specific Objectives. Be able to: Apply graphical frequency analysis for data that fit the Log- Pearson Type 3 Distribution

Transcription

1 CVEEN 4410: Engineering Hydrology (continued) : Topic and Goal: Use frequency analysis of historical data to forecast hydrologic events Specific Be able to: Apply graphical frequency analysis for data that fit the Log- Pearson : Approach for Type III

2 : Assume you ve acquired a dataset, analyzed it using histograms, and you decide that it probably fits a type III distribution. The next step, then, is to the fit for a LP3 distribution. If the fit is indeed good, then proceed with forecasting estimates. : Approach for Type III

3 : Recipe for LP3 frequency curve analysis: 1. Create a series that consists of the logarithms Yi of the annual maximum flood series 2. Compute the sample mean, standard deviation, Sy, and standardized skew, Cs, of the logarithms of Step 1 3. For selected values of the exceedance (P) obtain values of the standardized variate K from Table 3-4 (round the skew to the nearest tenth) 4. Determine the values of the LP3 curve for the exceedance probabilities selected in Step 3 using the equation in Y is the logarithmic value of the LP3 curve 5. Take the antilogarithm of the Yi values and use them to plot the LP3 frequency curve (if necessary) : Approach for Type III

4 Problem Statement: : Check it these data in spreadsheet file wildcat_creek_runoff_data.xls posted on website. First order of business: calculate the skew of the log data. : Approach for Type III 4

5 Problem Statement: : First order of business: calculate the skew of the log data. : Approach for Type III 5

6 Problem Statement: : First order of business: calculate the skew of the log data. : Approach for Type III 6

7 : Next step: for selected values of the exceedance (P) obtain values of the standardized variate K from Table 3-4 (round the skew to the nearest tenth). : Approach for Type III

8 Exceedance Probability : K : Approach for Type III

9 : Exceedance Probability For all LP3 graphical problems, plot the LP3 frequency curve using abscissa (x-axis) values of 99% exceedance, 50%, 20%, 10%, 4%, 2%, 1% and 0.5%. Recall that exceedance corresponds to the top x-axis of regular paper. Now, how about the ordinate (y-axis) values for your frequency curve? K : Approach for Type III

10 : Exceedance Probability Now, how about the ordinate (y-axis) values for your frequency curve? Well, you have a series of frequency factors, K. Recall that Y = Y + KS y where Y is your random variable (or in this case, the log of your RV). K : Approach for Type III Thus, you may calculate values of Y for your ordinate axis, corresponding to each of the exceedance probabilities (99, 50, 20, 10, 4, 2, 1, 0.5).

11 Exceedance Probability : Thus, you may calculate values of Y for your ordinate axis, corresponding to each of the exceedance probabilities (99, 50, 20, 10, 4, 2, 1, 0.5). Y = Y + KS y But first, let s scale that y- axis, using: K : Approach for Type III

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13 Exceedance Probability : Thus, you may calculate values of Y for your ordinate axis, corresponding to each of the exceedance probabilities (99, 50, 20, 10, 4, 2, 1, 0.5). Y = Y + KS y Now, to calculate Y, recall: The first value, for 99% exceedance P, then, is: Y = (-2.544)(0.144) = or, to plot, use X (or P) = 99%, Y = K : Approach for Type III

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15 Exceedance Probability : Using: Y = Y + KS y with: The second value, for 50% exceedance P, then, is: Y = (0.05)(0.144) = or, to plot, use X (or P) = 50%, Y = K : Approach for Type III

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17 Exceedance Probability : Using: Y = Y + KS y with: The third value, for 20% exceedance P, then, is: Y = (0.853)(0.144) = or, to plot, use X (or P) = 20%, Y = and so on... K : Approach for Type III

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20 : Now, we need to plot the data, to check fit against the frequency curve! : Approach for Type III

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23 Exceedance : Non-Exceedance : Approach for Type III

24 Exceedance : Non-Exceedance : Approach for Type III

25 Exceedance : Non-Exceedance : Approach for Type III

26 : Next time (after midterm exam): we ll start with routing methods, including channel routing and reservoir routing. You re encouraged to read sections 4.1 and 4.2 in your text before next week. : Approach for Type III