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CEE 5324 –Advanced Hydrology – Lecture 14 Flood Frequency: Concepts and Tools Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Today’s Agenda Please turn off all cell phones! Questions? Suggested Reading: Chow Chapter 12 Flood Frequency Frequency Analysis Calculating/Graphing Population Curve Normal and Log-normal distributions Tools: Matlab & Excel Obtaining and Manipulating Flood Data The need for “LPIII” Probability Tables: “z” Probability Tables: Other ways… In Excel, to get z=f(probability) use: Cell Formula: =NORMINV(0.95, 0, 1) Probability Mean Std. Dev. Above cell formula returns: z=1.644…. In Excel, to get probability=f(z) use: Cell Formula: Cum. Dist. =NORMDIST(1.644954, 0, 1, TRUE) z Mean Std. Dev. Above cell formula returns: p=0.95… Flood Frequency Tools: Matlab programs gen_probplot.m probplot.m Excel spreadsheet: log_probability_plot.xls PeakFQ (coming next time) Flood Frequency Tools: Matlab gen_probplot.m Place text datafile (assumed “moglandia.txt”) and gen_probplot.m file in same directory (assumed “c:\cee5324”) Change to correct directory: >> cd c:\cee5324 Load vector (column) of data into matlab: >> load ‘moglandia.txt’ Store loaded data in “a” variable: >> a = moglandia; Set “lognorm” variable (1=log-normal, 0=otherwise) >> lognorm = 0 (or lognorm = 1) Flood Frequency Tools: Matlab probplot.m Place “moglandia.txt” probplot.m file in same directory (assumed “c:\cee5324”) Change to correct directory: >> cd c:\cee5324 Program automatically loads “moglandia.txt”, edit program if other text filename Program automatically assumes log-normal probability distribution and labels y-axis as being discharge. Flood Frequency Tools: Excel log_probability_plot.xls Paste downloaded data from USGS website in columns A (flood date) and B (peak flow). Place sorted (largest to smallest) flows in column D Adjust formula in column F so it uses correct “n” value for plotting position formula Adjust formulas in G3, G4, G5 for correct number of years of observed data Adjust vertical axis on “Chart” tab for appropriate range of flood data. Obtaining Flow Data: Daily Flows: http://waterdata.usgs.gov/nwis/dv Annual Maxima: http://nwis.waterdata.usgs.gov/usa/nwis/peak Use only this USGS site for flood frequency analysis Obtaining, Plotting, and Analyzing actual data From USGS Peak flow site Use query builder to select gage location “Output formats”: Choose “Tab-separated” or “peakfq” format Download resulting data, import into Matlab or Excel for further manipulation and analysis Plotting actual data i p n 1 Plotting position equation (Weibull): 6 Annual Peak Discharge, (ft 3/s) 10 5 10 4 10 99 95 90 80 70 60 50 40 30 20 10 5 Annual Exceedence Probability, (%) 1 Plotting Population Curve: Log-normal For New River at Radford we get: Mean of log(Q)’s: X 4.61 Standard Deviation of log(Q)’s: S 0.241 Population Curve: log( Q) X S z 4.61 (0.241) z If p=0.5, z =0.0 log( Q) 4.61 (0.241) (0.0) 4.61 Q 40,700 ft 3 /s Plotting population curve: Log-normal 6 Annual Peak Discharge, (ft3/s) 10 5 10 4 10 99 95 90 80 70 60 50 40 30 20 10 5 Annual Exceedence Probability, (%) 1 Comparison of Frequency Distributions Log-normal distribution Log-Pearson Type III distribution Calculating sample statistics To plot population curve, first need these moments: Mean: 1 n X Xj n j 1 Standard Deviation: 1 2 X j X s n 1 j 1 n Skew (needed if doing LPIII): n X j X n G 3 j 1 (n 1)( n 2) s 3 0.5 Plotting Population Curve-LPIII For New River at Radford we get: Mean of log(Q)’s: X 4.61 Standard Deviation of log(Q)’s: S 0.241 Skew: G 0.707 Population Curve: log( Q) X SK 4.61 (0.241) K If p=0.5, K=-0.11578 log( Q) 4.61 (0.241) (0.11578) 4.58 Q 38,200 ft 3 /s Plotting population curve-LPIII 6 Annual Peak Discharge, (ft3/s) 10 5 10 4 10 99 95 90 80 70 60 50 40 30 20 10 5 Annual Exceedence Probability, (%) 1 Plotting population curve - Comparison 6 Annual Peak Discharge, (ft3/s) 10 5 10 4 10 99 95 90 80 70 60 50 40 30 20 10 5 Annual Exceedence Probability, (%) 1 PEAKFQ PEAKFQ is a USGS program that automates the Bulletin 17B flood frequency analysis procedure in a relatively painless windows-driven interface. http://water.usgs.gov/software/PeakFQ/code/5.2/DOS/PKFQWin_5.2.exe Reasons to use PEAKFQ Reasons to use PEAKFQ Automates flood frequency analysis (FFA) consistent with Bulletin 17B methods No more tedious hand calculations! Manages more elaborate analyses that: Automatically excludes data inappropriate for FFA Automatically manages historic flood information Performs FFA for various skew options PEAKFQ: Skew Options Station Skew: the skew value derived using the method of moments for the gage data as we have previously learned. Generalized Skew: the skew value derived from map at right: Weighted: mixture of Station and Generalized Skew. PEAKFQ: Weighted Skew Example: New River at Radford, VA G = 0.707 (derived from observed flood record at station) G = 0.433 (derived from map on previous slide) MSEG = 0.303 (derived from map on previous slide) MSEG = 0.177 (see next slide) RESULT: GW = 0.606 PEAKFQ: MSE of Station Skew Coef. Example: New River at Radford, VA A=(-0.33) + 0.08 * 0.707 = -0.2734 B=0.94 – 0.26 * 0.707 = 0.7562 N=43 (see PEAKFQ output or simply count years in used record between 1896 and 1938). MSEG = 10^([-0.2734] – 0.7562[log10(43/10)]) = 0.177 Reasons to use PEAKFQ Reasons to use PEAKFQ Automates flood frequency analysis (FFA) consistent with Bulletin 17B methods No more tedious hand calculations! Manages more elaborate analyses that: Automatically excludes data inappropriate for FFA Automatically manages historic flood information Performs FFA for various skew options