Hydrology 4410 Class 29. In Class Notes & Exercises Mar 27, 2013
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1 Hydrology 4410 Class 29 In Class Notes & Exercises Mar 27, 2013
2 Log Normal Distribution We will not work an example in class. The procedure is exactly the same as in the normal distribution, but first you take the log of the data values
3
4 Log Pearson Type 3 When normal and log-normal distributions do not fit your data, LP3 should be tried. Need to plot both the data points and the probability curve. If they approximately match up, then the LP3 is a correct fit
5 LP3 steps Acquire data set (annual maximum flow values) Take the log of each value Compute the mean, st dev and skew of the log values Refer to the Frequency Factors (K) table provided on the website (from Bedient et al, table 3-4) Find the skew coefficient (first column) that matches your calculated data skew. Make note of this row, as this will be the row used to make your LP3 curve Make a table of (3 columns): Exceedance probabilities (1/T), which are the row labeled on the table as Percent Chance ( ) = 1-F (values are 99, 50, 20, 10, 4, 2, 1, 0.5). Take the corresponding K value (row of number across from your skew coefficient) Plug these K values (8 values) into the following equation: y = values to be plotted across from the exceedance probabilities μ = mean of logarithmic values of data points K = frequency factor value taken from table σ = st dev of logarithmic value of data points Plot the exceedance probabilities vs. the calculated y values on provided probability paper. Remember to plot using the top axis (exceedance probabilities). Remember to scale the vertical axis based on the min and max of the logarithmic values of the data points. Draw a curved line through these points. This is the LP3 frequency curve Plot the log of your data points vs. the Weibull plotting position. If the curve seems to be matching the plotted points, this is a suitable distribution for predicting future events.
6 In Class Exercise See the spreadsheet on the website. Perform the LP3 steps. Answer the following questions What is the 50 year annual runoff Probability that total annual runoff in any one year will be less than 5 inches Probability that total annual runoff will exceed 15 inches
7 See the pre-class video for the step by step work out of plotting the frequency curve and data points
8 What is the 50 year annual runoff
9 What is the 50 year annual runoff 50 year runoff = 2% exceedance probability
10 What is the 50 year annual runoff
11 What is the 50 year annual runoff 50 year runoff = 2% exceedance probability From plot, y = 1.37.
12 What is the 50 year annual runoff 50 year runoff = 2% exceedance probability From plot, y = Q = antilog (1.37)
13 What is the 50 year annual runoff 50 year runoff = 2% exceedance probability From plot, y = Q = antilog (1.37) Q = 10^1.37 Q = 23.5 cfs
14 Probability that total annual runoff in any one year will be less than 5 inches
15 Probability that total annual runoff in any one year will be less than 5 inches Non-exceedance probability
16 Probability that total annual runoff in any one year will be less than 5 inches Non-exceedance probability Since the plot is in log, need take log (5) = 0.70
17 What is the 50 year annual runoff
18 Probability that total annual runoff in any one year will be less than 5 inches Non-exceedance probability Since the plot is in log, need take log (5) = 0.70 From plot, non-exceedance ~= 0.037% chance that total annual runoff will not exceed 5 inches in a year. Make sense??
19 Probability that total annual runoff will exceed 15 inches Exceedance probability Since the plot is in log, need take log (15) = 1.18
20 What is the 50 year annual runoff
21 Probability that total annual runoff will exceed 15 inches Exceedance probability Since the plot is in log, need take log (15) = 1.18 From plot, exceedance ~= 32% chance of having total annual runoff exceed 15 inches
Specific Objectives. Be able to: Apply graphical frequency analysis for data that fit the Log- Pearson Type 3 Distribution
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