Module 11: Average Rainfall Theodore G. Cleveland, Ph.D., P.E, M. ASCE, F. EWRI August 2015 Module 11 1

 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 11 2

 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 11 3

 WRI 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 11 4

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Region of Unit Hydrograph applicability Module 11 6

 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. Module 11 7

 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Constant to reduce the magnitude of the time series ▪Remember to rename these new series, if they are historical, they no longer represent real measurements! Module 11 8

 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. Module 11 9

 Estimate intensity for 5-yr return period for a 30-minute duration i ~ 2.75 inches/hour Module 11 10

 TP-40 - Maps of storm depths for different storm durations and probabilities Module 11 11

 HY-35 Maps of storm depths for different storm durations and probabilities TP40, HY35 both have interpolation guidance to construct values between mapped values. Module 11 12

 TxDOT spreadsheet that tabulates information in the maps. Beware it is units dependent! Module 11 13

 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 Module 11 14

 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 T c has meaning of averaging time, although usually treated as a time of concentration. Module 11 15

 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 D moves this “knee” LEFT/RIGHT Module 11 16

 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 D moves this “knee” LEFT/RIGHT Module 11 17

 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 Module 11 18

 Look up depths by recurrence interval, STORM duration, and location. Module 11 19

 DDF for Austin, TX Module 11 20

 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 Module 11 21

 Ultimately are interested in entire hyetographs and not just the depths or average intensities.  Techniques for developing design precipitation hyetographs 1.SCS method 2.Triangular hyetograph method 3.Using IDF relationships 4.Empirical Hyetographs (Texas specific) This slide adapted from: Module 11 22

SCS (1973) analyzed DDF to develop dimensionless rainfall temporal patterns called type curves for four different regions in the US. 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. 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: Module 11 23

SCS (1973) analyzed DDF to develop dimensionless rainfall temporal patterns called type curves for four different regions in the US. 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. 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. 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 For durations less than 24 hr, the steepest part of the type curve for required duration is used This slide adapted from: Module 11 24

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. 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: Module 11 25

SCS 24-Hour Rainfall Distributions T (hrs)Fraction of 24-hr rainfall T (hrs)Fraction of 24-hr rainfall Type IIType IIIType IIType III Not much difference in the two curves in dimensionless space! This slide adapted from: Module 11 26

 Given T d and frequency/T, find the design hyetograph 1. Compute P/i (from DDF/IDF curves or equations) 2. Pick a SCS type curve based on the location 3. If T d = 24 hour, multiply (rescale) the type curve with P to get the design mass curve 1.If T d is less than 24 hr proceed, use steepest part of the curve for the design storm. 4. Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph This slide adapted from: Module 11 27

 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 = (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: Module 11 28

29 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: Module 11 29

30  Given T d and frequency/T, find the design hyetograph 1. Compute P/i (from DDF/IDF curves or equations) 2. Use above equations to get t a, t b, T d and h (r is available for various locations) Time Rainfall intensity, i h tata tbtb TdTd T d : hyetograph base length = precipitation duration t a : time before the peak r: storm advancement coefficient = t a /T d t b : recession time = T d – t a = (1-r)T d This slide adapted from: Module 11 30

31  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) Time Rainfall intensity, in/hr hr 6 hr This slide adapted from: Module 11 31

32  Given T d and T/frequency, develop a hyetograph in  t increments 1. Using T, find i for  t, 2  t, 3  t,…n  t using the IDF curve for the specified location 2. Using i compute P for  t, 2  t, 3  t,…n  t. This gives cumulative P. 3. Compute incremental precipitation from cumulative P. 4. 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: Module 11 32

33 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: Module 11 33

 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 (50 th percentile) curve Rescale Time Rescale Depth Average Intensity Module 11 34

 Tabular values in the report.  This column scales TIME  This column scales DEPTH Module 11 35

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 Use interpolation to generate uniformly spaced cumulative depths.  Example 3 interpolated external to HMS, but by now we know we can use the fill feature in the time-series manager Module 11 37

 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. Module 11 38

 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 Module 11 39

 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) Module 11 40

 Standard Project Storm  Depreciated Corps of Engineers method.  Not often used, included in HEC-HMS for backward compatibility to earlier (circa 1970s) projects. Module 11 41

 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 Module 11 42

 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. Module 11 43