DES 606 : Watershed Modeling with HEC-HMS

DES 606 : Watershed Modeling with

HEC-HMS

Module 9Theodore 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)


• 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


• 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historical, they no longer represent real measurements!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


• HY-35 Maps of storm depths for different storm durations and probabilities

TP40, HY35 both have interpolation guidance to construct values between mapped values.


• TxDOT spreadsheet that tabulates information in the maps. Beware it is units dependent!

http://onlinemanuals.txdot.gov/txdotmanuals/hyd/ebdlkup.xls



• 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



• 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.

€

I =b

(TC + d)e


• 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/DOWNE changes slope of the curve

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/DOWNE changes slope of the curve

D moves this “knee” LEFT/RIGHT


• 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

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

Rainfall Depth

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

1. SCS method

2. Triangular hyetograph method

3. Using IDF relationships

4. 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 SCS (1973) analyzed DDF to develop dimensionless rainfall temporal patterns called type curves for four different regions temporal patterns called type curves for four different regions in the US.in the US.•SCS type curves are in the form of percentage mass SCS type curves are in the form of percentage mass (cumulative) curves based on 24-hr rainfall of the desired (cumulative) curves based on 24-hr rainfall of the desired frequency.frequency.


SCS Method•SCS (1973) analyzed DDF to develop dimensionless rainfall SCS (1973) analyzed DDF to develop dimensionless rainfall temporal patterns called type curves for four different regions temporal patterns called type curves for four different regions in the US.in the US.•SCS type curves are in the form of percentage mass SCS type curves are in the form of percentage mass (cumulative) curves based on 24-hr rainfall of the desired (cumulative) curves based on 24-hr rainfall of the desired frequency.frequency.•If a single precipitation depth of desired frequency is known, If a single precipitation depth of desired frequency is known, the SCS type curve is rescaled (multiplied by the known the SCS type curve is rescaled (multiplied by the known number) to get the time distribution. number) to get the time distribution. •For durations less than 24 hr, the steepest part of the type For durations less than 24 hr, the steepest part of the type curve for required duration is usedcurve for required duration is used


SCS Method• If a single precipitation depth of desired If a single precipitation depth of desired frequency is known, the SCS type curve is frequency is known, the SCS type curve is rescaled (multiplied by the known number) to rescaled (multiplied by the known number) to get the time distribution. get the time distribution.


SCS Method•For durations less than 24 hr, the steepest part of the For durations less than 24 hr, the steepest part of the type curve for required duration is used (i.e. 6-hour as type curve for required duration is used (i.e. 6-hour as shown)shown)

•HEC-HMS has SCS built-in, but does not rescale time – storm must be 24-HEC-HMS has SCS built-in, but does not rescale time – storm must be 24-hours (or analyst rescales external to the program)hours (or analyst rescales external to the program)


0.0

1.0

SCS type curves for Texas (II&III)SCS 24-Hour Rainfall Distributions SCS 24-Hour Rainfall Distributions

T (hrs) Fraction of 24-hr rainfall T (hrs) Fraction of 24-hr rainfall

Type II Type III Type II Type III

0.0 0.000 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 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 1.000

Not much difference in the two curves in dimensionless space!


SCS Method Steps

• Given Td 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 Td = 24 hour, multiply (rescale) the type curve with P to get the design mass curve

1. If Td is less than 24 hr, pick the steepest part of the type curve for rescaling

4. Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph


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

hrin

bt

ai c /417.0

7.760*24

81724.0

inhrhrinTiP d 01.1024*/417.0*


30

SCS – Example (Cont.)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)

Pre

cip

itat

ion

(in

)

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.


31

Triangular Hyetograph Method

• Given Td and frequency/T, find the design hyetograph1.Compute P/i (from DDF/IDF curves or equations)

2.Use above equations to get ta, tb, Td and h (r is available for various locations)

Time

Rain

fall

inte

nsity

, i

h

ta tb

d

a

T

tr

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

d

d

T

Ph

hTP

22

1


32

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)

hrin

bt

ai c /12.1

7.760*6

81724.0

inhrhriniP 72.66*/12.16*

hrtTt

hrrTt

adb

da

336

365.0

Time

Rain

fall

inte

nsity

, in/

hr

2.24

3 hr 3 hr

6 hr

hrinT

Ph

d

/24.26

44.13

6

72.622


33

Alternating block method• Given Td and T/frequency, develop a hyetograph in t

increments1. Using T, find i for t, 2t, 3t,…nt using the IDF curve for the

specified location2. Using i compute P for t, 2t, 3t,…nt. 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.


34

Example: Alternating Block Method

90.13

6.9697.0

d

ed TfT

ci

tscoefficien,,

stormofDuration

intensityrainfalldesign

fec

T

i

d

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

100-110

110-120

Time (min)

Pre

cip

itat

ion

(in

)

Find: Design precipitation hyetograph for a 2-hour storm (in 10 minute increments) in Denver with a 10-year return period 10-minute


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 Time

Res

cale

Dep

thAverage Intensity

• 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

Documents

DES 606 : Watershed Modeling with HEC-HMS