DES 606 : Watershed Modeling with HEC-HMS Module 9 Theodore G. Cleveland, Ph.D., P.E 29 July 2011

Module 9: Design Storms Precipitation pattern defined for use in the design of hydrologic system Serves as an input to the hydrologic system Can by defined by: Hyetograph (time distribution of rainfall) Isohyetal map (spatial distribution of rainfall)

Module 9: Design Storms Spatial distribution could also be by use of Theissen weights or something similar. Reasonable concern that point values could be too large, hence occasional use of Areal Reduction Factors

Module 9: Design Storms WRI 99-4267 ARF for Texas Design Storms A design storm for a point is the depth of precipitation that has a specified duration and frequency (recurrence interval). The effective depth often is computed by multiplying the design-storm depth by a “depth-area correction factor” or an “areal-reduction factor.”

Module 9: ARF in Texas

Module 9: ARF in Texas Region of Unit Hydrograph applicability

ARF and Weighted Gages As a practical matter, ARF results suggest that for the range of UH applicability, point values could be reduced by as much as 40% The ARF and Theissen weights would combine for multiple-gages systems Theissen weights are area fractions, thus recover actual areas and use for ARF specification. Apply the ARF to the rainfall time series.

ARF and Weighted Gages The “methods” of preparing such data have been addressed already. Use Theissen weights (or other scheme) as appropriate. Use the HEC-HMS Fill/Multiply By a Constant to reduce the magnitude of the time series Remember to rename these new series, if they are historical, they no longer represent real measurements!

Design Storm Estimates Could use observed data and prepare your own Depth-Duration-Frequency relationship Outside scope of this training course. Use existing Depth-Duration-Frequency (DDF) or Intensity-Duration-Frequency (IDF) tools for a study area These produce point estimates! If area on the large side, consider ARF.

Concept of IDF for Design Estimate intensity for 5-yr return period for a 30-minute duration i ~ 2.75 inches/hour

Design Storms for Texas TP-40 - Maps of storm depths for different storm durations and probabilities

Design Storms for Texas HY-35 Maps of storm depths for different storm durations and probabilities TP40, HY35 both have interpolation guidance to construct values between mapped values.

Design Storms for Texas TxDOT spreadsheet that tabulates information in the maps. Beware it is units dependent! http://onlinemanuals.txdot.gov/txdotmanuals/hyd/ebdlkup.xls

Design Storms for Texas Link is good (verified 5 AUG 11) Reports intensity instead of depth. Multiply by time to recover depth. Author added this row, not in on-line version http://onlinemanuals.txdot.gov/txdotmanuals/hyd/ebdlkup.xls

Design Storms for Texas What the spreadsheet and the maps represent is a hyperbolic model that relates time and intensity. The values e,b, and d parameterize the model. The value Tc has meaning of averaging time, although usually treated as a time of concentration.

Design Storms for Texas D moves this “knee” LEFT/RIGHT The values e,b, and d parameterize the model. The shaded polygon is a hull that encloses TP-40 and HY-35 for Harris Co., TX (barely visible open circles) The “design equation” curve is the EBDLKUP.xls curve for Harris Co., TX B moves this curve UP/DOWN E changes slope of the curve

Design Storms for Texas D moves this “knee” LEFT/RIGHT Aside: The “blue” cloud is a simulation using the empirical hyetographs and PP1725 for Harris Co. The solid red dots are maximum observed intensity regardless of location (some dots are from Texas) The empirical curves represent an alternative model. B moves this curve UP/DOWN E changes slope of the curve

Design Storms for Texas DDF Atlas is an alternative to TP40, HY35 and the EBDLKUP.xls Uses data more recent that these other tools Provides guidance for interpolation and extrapolation Works in depth – the native unit in HMS

Rainfall Depth Look up depths by recurrence interval, STORM duration, and location.

Local Information DDF for Austin, TX

Local Information IDF for Houston, TX Most Metropolitan areas in Texas (USA) have similar DDF/IDF charts and tables published. Serve as a basis for Design Storms

Design Precipitation Hyetographs Ultimately are interested in entire hyetographs and not just the depths or average intensities. Techniques for developing design precipitation hyetographs SCS method Triangular hyetograph method Using IDF relationships Empirical Hyetographs (Texas specific) This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

SCS Method SCS (1973) analyzed 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. This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

SCS Method SCS (1973) analyzed 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 duration is used This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

SCS Method 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. This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

SCS Method For durations less than 24 hr, the steepest part of the type curve for required duration is used (i.e. 6-hour as shown) HEC-HMS has SCS built-in, but does not rescale time – storm must be 24-hours (or analyst rescales external to the program) 1.0 0.0 This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

SCS type curves for Texas (II&III) SCS 24-Hour Rainfall Distributions T (hrs) Fraction of 24-hr rainfall Type II Type III 0.0 0.000 11.5 0.283 0.298 1.0 0.011 0.010 11.8 0.357 0.339 2.0 0.022 0.020 12.0 0.663 0.500 3.0 0.034 0.031 12.5 0.735 0.702 4.0 0.048 0.043 13.0 0.772 0.751 5.0 0.063 0.057 13.5 0.799 0.785 6.0 0.080 0.072 14.0 0.820 0.811 7.0 0.098 0.089 15.0 0.854 8.0 0.120 0.115 16.0 0.880 0.886 8.5 0.133 0.130 17.0 0.903 0.910 9.0 0.147 0.148 18.0 0.922 0.928 9.5 0.163 0.167 19.0 0.938 0.943 9.8 0.172 0.178 20.0 0.952 0.957 10.0 0.181 0.189 21.0 0.964 0.969 10.5 0.204 0.216 22.0 0.976 0.981 11.0 0.235 0.250 23.0 0.988 0.991 24.0 1.000 Not much difference in the two curves in dimensionless space! This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

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 location If Td = 24 hour, multiply (rescale) the type curve with P to get the design mass curve If Td is less than 24 hr, pick the steepest part of the type curve for rescaling Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

Example 9 – SCS Method Find - rainfall hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a one-hour time increment a = 81, b = 7.7, c = 0.724 (from Tx-DOT hydraulic manual) Find Cumulative fraction - interpolate SCS table Cumulative rainfall = product of cumulative fraction * total 24-hour rainfall (10.01 in) Incremental rainfall = difference between current and preceding cumulative rainfall This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

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. This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

Triangular Hyetograph Method Time Rainfall intensity, i h ta tb Td Td: hyetograph base length = precipitation duration ta: time before the peak r: storm advancement coefficient = ta/Td tb: recession time = Td – ta = (1-r)Td Given Td and frequency/T, find the design hyetograph Compute P/i (from DDF/IDF curves or equations) Use above equations to get ta, tb, Td and h (r is available for various locations) This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

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 = 0.724 (from Tx-DOT hydraulic manual) 3 hr 3 hr Rainfall intensity, in/hr 2.24 6 hr Time This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

Alternating block method Given Td and T/frequency, develop a hyetograph in Dt increments Using T, find i for Dt, 2Dt, 3Dt,…nDt using the IDF curve for the specified location Using 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. This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

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 This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt

Empirical Hyetograph Dimensionless Hyetograph is parameterized to generate an input hyetograph that is 3 hours long and produces the 5-year depth. For this example, will use the median (50th percentile) curve Rescale Depth Average Intensity Rescale Time

Tabular values in the report. This column scales TIME This column scales DEPTH

Dimensional Hyetograph

Dimensional Hydrograph Use interpolation to generate uniformly spaced cumulative depths. Can use Excel and high-order polynomial. HEC-HMS has built-in linear interpolation tools. Example 2 interpolated external to HMS, but by now we know we can use the fill feature in the time-series manager

Hyetographs The methods presented, except for the SCS 24-hour all require processing external to HMS. The empirical hyetograph, combined with DDF atlas is Texas specific. In absence of local guidance would suggest this as the preferred Texas method. Beware in West Texas – not a lot of data supporting the empirical hyetograph, most data is on I-35 corridor, Gulf Coast, and East Texas. The DDF uses New Mexico data, so is believed to be appropriate for estimating storm depths.

Other Design Storms The previous discussion develops storms that are put into HEC-HMS through the Time-Series Manager as a Rain gage. Other “built-in” options are Frequency storm Standard Project Storm

Other Design Storms Frequency Design Storm Enter a frequency (probability) Enter intensity “duration” (lengths of pulses) Enter storm “duration” Enter accumulated depths at different portions of the storm (dimensional hyetograph) Enter storm area (HMS uses this value for its own ARF computations)

Other Design Storms Standard Project Storm Depreciated Corps of Engineers method. Not often used, included in HEC-HMS for backward compatibility to earlier (circa 1970s) projects.

Summary Design storms are precipitation depths for a location for a given storm duration and a given probability. DDF Atlas EBDLKUP.xls, TP40, HY35 Design hyetographs are the time-redistribution of these depths. SCS Triangular Empirical

Summary Intensities are average intensities that produce to observed depth. DDF, IDF curves convey same information. Depth is the natural (and measured) variable. Area Reduction Factors may be appropriate for larger watersheds represented by point gages. Theissen weights are for spatial distribution of gages ARFs are computed externally and applied to the time series before areal weighting.

Summary HEC-HMS models multiple gages in the Meterological Model Manager Example 8 illustrated how to set-up multiple gages Weights were supplied