1. CE 3354 ENGINEERING HYDROLOGY Lecture 7: Flood Frequency (Bulletin 17B)

2. OUTLINE  Probability estimation modeling (continued)  Bulletin 17B

3. SAN SABA RIVER EXAMPLE  Examine concepts using annual peak discharge values for the San Saba River  Data are on class server

4. SAN SABA RIVER EXAMPLE  Take the raw data, and sort large to small, and write rank numbers YearQpeak 17/23/1938130000 29/16/1936101000 39/8/198090500 47/15/199065400 59/26/194660000 69/17/197459200 710/6/193057200 810/5/194149200 95/1/195648000 1011/3/200047000 114/26/192244000 1210/13/192943400 134/19/195741000 148/2/197835400 156/17/195831900 169/6/193231300 1710/17/194230800 1811/17/200426900 1910/4/195321100 204/15/197718900 219/9/193518100 2210/9/196117900 234/18/193417600 2410/4/195915000

5. SAN SABA RIVER EXAMPLE  Apply Weibull PP Formula YearQpeak 17/23/19381300000.01136 29/16/19361010000.02273 39/8/1980905000.03409 47/15/1990654000.04545 59/26/1946600000.05682 69/17/1974592000.06818 710/6/1930572000.07955 810/5/1941492000.09091 95/1/1956480000.10227 1011/3/2000470000.11364 114/26/1922440000.125 1210/13/1929434000.13636 134/19/1957410000.14773 148/2/1978354000.15909 156/17/1958319000.17045 169/6/1932313000.18182 1710/17/1942308000.19318 1811/17/2004269000.20455 1910/4/1953211000.21591 204/15/1977189000.22727 219/9/1935181000.23864 2210/9/1961179000.25 234/18/1934176000.26136 2410/4/1959150000.27273

6. SAN SABA RIVER EXAMPLE  Plot points on probability paper

7. SAN SABA RIVER EXAMPLE  Same data, showing both Weibull and Blom PP

8. SAN SABA RIVER EXAMPLE  At this point, a visual line of best fit represents an empirical CDF to infer probability and magnitudes.  The next step is to fit a probability distribution  Normal  Log-Normal

9. BEARGRASS CREEK EXAMPLE  Fit Normal Distribution (conventional MOM)  CMM pp. 363-377

10. BEARGRASS CREEK EXAMPLE  Using the Distribution  Once Fit, the distribution parameters are used to estimate magnitudes for arbitrary probabilities.  Estimate discharge for 20-yr ARI

11. BEARGRASS CREEK EXAMPLE  Using the Distribution  Once Fit, the distribution parameters are used to estimate magnitudes for arbitrary probabilities.  Estimate discharge for 100-yr ARI

12. BEARGRASS CREEK EXAMPLE  Fit LogNormal Distribution (conventional MOM)  CMM pp. 363-377

13. BEARGRASS CREEK EXAMPLE  Using the Distribution  Once Fit, the distribution parameters are used to estimate magnitudes for arbitrary probabilities.  Estimate discharge for 20-yr ARI

14. PROBABILITY ESTIMATION MODELING  Rank observations  Compute plotting positions  Plot Empirical Cumulative Distribution  Select Probability Model (Normal, lognormal, …)  Fit the model to the Empirical Cumulative Distribution  Use the model to infer magnitudes at desired cumulative probabilities

15. BULLETIN 17B METHODS

16.  Important concept- skew  “Bulletin 17C” is out for public comment at this time; dramatic update  Easiest is to use USGS PeakFQ computer program  Implements CMM pp 398-405 (with quite a bit of added features)  Will be replaced by a new 17C version VERY SOON  The input file is a fixed format “CARD IMAGE” file  Cannot contain TABS, must use whitespace  Download from USGS website

17. BULLETIN 17B METHODS  Bulletin 17B included on server  PeakFQ user manual included on server (need to get file formats correct)  Outlier analysis is semi-automated  PeakFQ will report if there are high and low outliers above/below criterion  User must then flag values (use a minus sign to skip a value) and reanalyze

18. TRANSPOSITION OF GAGE RESULTS

19. SUMMARY  Probability estimation modeling fits probability distributions to observations  The fitted distributions are used to extrapolate and estimate magnitudes associated with arbitrary probabilities  Examples with Normal, LogNormal, and Gumbell in Excel were presented  Bulletin 17B using PeakFQ was demonstrates as was outlier identification (using the software)  Newer software in next few years to replace PeakFQ

20. NEXT TIME  More on 17B/17C/log Pearson type III  Regression equations