2 Design StormDesign storm – precipitation pattern defined for use in the design of hydrologic systemServes as an input to the hydrologic systemCan by defined by:Hyetograph (time distribution of rainfall)Isohyetal map (spatial distribution of rainfall)
3 Extreme value (EV) distributions Extreme values – maximum or minimum values of sets of dataAnnual maximum discharge, annual minimum dischargeWhen the number of selected extreme values is large, the distribution converges to one of the three forms of EV distributions called Type I, II and III
4 EV type I distributionIf M1, M2…, Mn be a set of daily rainfall or streamflow, and let X = max(Mi) be the maximum for the year. If Mi are independent and identically distributed, then for large n, X has an extreme value type I or Gumbel distribution.Distribution of annual maximum streamflow follows an EV1 distribution
5 EV type III distribution If Wi are the minimum streamflows in different days of the year, let X = min(Wi) be the smallest. X can be described by the EV type III or Weibull distribution.Distribution of low flows (eg. 7-day min flow) follows EV3 distribution.
6 Design point precipitation Historic data of precipitation is availablePrecipitation data are converted to different durations (Table 3.4.1)Annual maximum precipitation for a given duration is selected for each yearFrequency analysis is performed to derive design precipitation depths for different return periodsThe depths are converted to intensities by dividing by precipitation durations
7 IDF curves by frequency analysis Get annual maximum series of precipitation depth for a given durationUse EV1/Gumbel distribution to find precipitation depth for different return periodsRepeat 1 and 2 process for different durationsPlot depth versus duration for different frequencies
9 Example 14.2.1 From the IDF curve for Chicago, Determine i and P for a 20-min duration storm with 5-yr return period in ChicagoFrom the IDF curve for Chicago,i = 3.5 in/hr for Td = 20 min and T = 5yrP = i x Td = 3.5 x 20/60 = 1.17 in
10 TP 40Hershfield (1961) developed isohyetal maps of design rainfall and published in TP 40.TP 40 – U. S. Weather Bureau technical paper no. 40. Also called precipitation frequency atlas maps or precipitation atlas of the United States.30mins to 24hr maps for T = 1 to 100Web resources for TP 40 and rainfall frequency maps
16 IDF curves for AustinSource: City of Austin, Watershed Management Division
17 Design Precipitation Hyetographs Most often hydrologists are interested in precipitation hyetographs and not just the peak estimates.Techniques for developing design precipitation hyetographsSCS methodTriangular hyetograph methodUsing IDF relationships (Alternating block method)
18 SCS MethodSCS (1973) adopted method similar to DDF to develop dimensionless rainfall temporal patterns called type curves for four different regions in the US.SCS type curves are in the form of percentage mass (cumulative) curves based on 24-hr rainfall of the desired frequency.If a single precipitation depth of desired frequency is known, the SCS type curve is rescaled (multiplied by the known number) to get the time distribution.For durations less than 24 hr, the steepest part of the type curve for required duraction is used
19 SCS type curves for Texas (II&III) SCS 24-Hour Rainfall DistributionsT (hrs)Fraction of 24-hr rainfallType IIType III0.00.00011.50.2830.2981.00.0110.01011.80.3570.3392.00.0220.02012.00.6630.5003.00.0340.03112.50.7350.7024.00.0480.04313.00.7720.7515.00.0630.05713.50.7990.7856.00.0800.07214.00.8200.8117.00.0980.08915.00.8548.00.1200.11516.00.8800.8868.50.1330.13017.00.9030.9109.00.1470.14818.00.9220.9289.50.1630.16719.00.9380.9439.80.1720.17820.00.9520.95710.00.1810.18921.00.9640.96910.50.2040.21622.00.9760.98111.00.2350.25023.00.9880.99124.01.000
20 SCS Method Steps Given Td and frequency/T, find the design hyetograph Compute P/i (from DDF/IDF curves or equations)Pick a SCS type curve based on the locationIf Td = 24 hour, multiply (rescale) the type curve with P to get the design mass curveIf Td is less than 24 hr, pick the steepest part of the type curve for rescalingGet the incremental precipitation from the rescaled mass curve to develop the design hyetograph
21 Example – SCS MethodFind - rainfall hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a one-hour time incrementa = 81, b = 7.7, c = (from Tx-DOT hydraulic manual)FindCumulative fraction - interpolate SCS tableCumulative rainfall = product of cumulative fraction * total 24-hour rainfall (10.01 in)Incremental rainfall = difference between current and preceding cumulative rainfallTxDOT hydraulic manual is available at:
22 SCS – Example (Cont.)If a hyetograph for less than 24 needs to be prepared, pick time intervals that include the steepest part of the type curve (to capture peak rainfall). For 3-hr pick 11 to 13, 6-hr pick 9 to 14 and so on.
23 Triangular Hyetograph Method TimeRainfall intensity, ihtatbTdTd: hyetograph base length = precipitation durationta: time before the peakr: storm advancement coefficient = ta/Tdtb: recession time = Td – ta = (1-r)TdGiven Td and frequency/T, find the design hyetographCompute P/i (from DDF/IDF curves or equations)Use above equations to get ta, tb, Td and h (r is available for various locations)
24 Triangular hyetograph - example Find - rainfall hyetograph for a 25-year, 6-hour duration in Harris County. Use storm advancement coefficient of 0.5.a = 81, b = 7.7, c = (from Tx-DOT hydraulic manual)3 hr3 hrRainfall intensity, in/hr2.246 hrTime
25 Alternating block method Given Td and T/frequency, develop a hyetograph in Dt incrementsUsing T, find i for Dt, 2Dt, 3Dt,…nDt using the IDF curve for the specified locationUsing i compute P for Dt, 2Dt, 3Dt,…nDt. This gives cumulative P.Compute incremental precipitation from cumulative P.Pick the highest incremental precipitation (maximum block) and place it in the middle of the hyetograph. Pick the second highest block and place it to the right of the maximum block, pick the third highest block and place it to the left of the maximum block, pick the fourth highest block and place it to the right of the maximum block (after second block), and so on until the last block.
26 Example: Alternating Block Method Find: Design precipitation hyetograph for a 2-hour storm (in 10 minute increments) in Denver with a 10-year return period 10-minute
27 Design aerial precipitation Point precipitation estimates are extended to develop an average precipitation depth over an areaDepth-area-duration analysisPrepare isohyetal maps from point precipitation for different durationsDetermine area contained within each isohyetPlot average precipitation depth vs. area for each duration
32 Depth (intensity)-duration-frequency DDF/IDF – graph of depth (intensity) versus duration for different frequenciesTP 40 or HYDRO 35 gives spatial distribution of rainfall depths for a given duration and frequencyDDF/IDF curve gives depths for different durations and frequencies at a particular locationTP 40 or HYDRO 35 can be used to develop DDF/IDF curvesDepth (P) = intensity (i) x duration (Td)
33 Probable Maximum Precipitation Greatest depth of precipitation for a given duration that is physically possible and reasonably characteristic over a particular geographic region at a certain time of yearNot completely reliable; probability of occurrence is unknownVariety of methods to estimate PMPApplication of storm modelsMaximization of actual stormsGeneralized PMP charts
34 Probable Maximum Storm Temporal distribution of rainfallGiven as maximum accumulated depths for a specified durationInformation on spatial and temporal distribution of PMP is required to develop probable maximum storm hyetograph
35 Probable Maximum Flood PMF – greatest flood to be expected assuming complete coincidence of all factors that would produce the heaviest rainfall (PMP) and maximum runoffFlood of unknown frequencyMost structures are not designed for PMF, but for greatest floods that may be reasonably expected for local conditions (meteorology, topography, and hydrology)The design flood is commonly called standard project flood derived from standard project storm