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 “arealreduction 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historical, they no longer represent real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.
I 
b
(TC  d )
e
• 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
1.
2.
3.
4.
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 24hours (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
SCS 24-Hour Rainfall Distributions
T (hrs)
T (hrs)
Fraction of 24-hr
rainfall
Type II
Type III
Fraction of 24-hr rainfall
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
0.922
0.928
0.938
0.943
9.0
9.5
Not 0.147
much difference
in the two 18.0
0.148
curves
space!19.0
0.163in dimensionless
0.167
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
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
24.0
1.000
1.000
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
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)
i
a
t  b 
c

81
 24 * 60  7 . 7 
0 . 724
 0 . 417 in / hr
P  i * T d  0 . 417 in / hr * 24 hr  10 . 01 in
• Find
– Cumulative fraction - interpolate SCS table
– Cumulative rainfall = product of cumulative fraction * total 24hour 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.)
(hours)
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
Cumulative
Fraction
Cumulative
Precipitation
Incremental
Precipitation
Pt/P24
Pt (in)
(in)
0.000
0.010
0.020
0.032
0.043
0.058
0.072
0.089
0.115
0.148
0.189
0.250
0.500
0.751
0.811
0.849
0.886
0.904
0.922
0.939
0.957
0.968
0.979
0.989
1.000
0.00
0.10
0.20
0.32
0.43
0.58
0.72
0.89
1.15
1.48
1.89
2.50
5.01
7.52
8.12
8.49
8.87
9.05
9.22
9.40
9.58
9.69
9.79
9.90
10.01
0.00
0.10
0.10
0.12
0.12
0.15
0.15
0.17
0.26
0.33
0.41
0.61
2.50
2.51
0.60
0.38
0.38
0.18
0.18
0.18
0.18
0.11
0.11
0.11
0.11
3 .0 0
2 .5 0
P re c ip ita tio n (in )
Time
2 .0 0
1 .5 0
1 .0 0
0 .5 0
0 .0 0
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
T im e (h o u rs )
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
30
Triangular Hyetograph Method
Rainfall intensity, i
ta
Td: hyetograph base length = precipitation duration
tb
ta: time before the peak
r 
ta
Td
h
r: storm advancement coefficient = ta/Td
tb: recession time = Td – ta = (1-r)Td
P 
1
2
h
Td
Time
Td h
2P
Td
• Given Td and frequency/T, find the design
hyetograph
1. 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)
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
31
Triangular hyetograph example
i
a
t  b 
c

81
6 * 60  7 . 7 
0 . 724
 1 . 12 in / hr
P  i * 6  1 . 12 in / hr * 6 hr  6 . 72 in
h
2P
Td

2  6 . 72
6

13 . 44
 2 . 24 in / hr
6
Rainfall intensity, in/hr
• 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
2.24
t a  rT d  0 . 5  6  3 h r
tb  Td  t a  6  3  3 h r
6 hr
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
32
Time
Alternating block method
•
Given Td and T/frequency, develop a hyetograph in Dt
increments
1. Using T, find i for Dt, 2Dt, 3Dt,…nDt using the IDF curve for the
specified location
2. Using i compute P for Dt, 2Dt, 3Dt,…nDt. 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: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
33
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 10minute
Duration
(min)
10
20
30
40
50
60
70
80
90
100
110
120
T d 
e
Intensity
(in/hr)
4.158
3.002
2.357
1.943
1.655
1.443
1.279
1.149
1.044
0.956
0.883
0.820
 f

i  design
96 . 6
T d 
Cumulative
Depth
(in)
0.693
1.001
1.178
1.296
1.379
1.443
1.492
1.533
1.566
1.594
1.618
1.639
0 . 97
 13 . 90
Incremental
Depth
(in)
0.693
0.308
0.178
0.117
0.084
0.063
0.050
0.040
0.033
0.028
0.024
0.021
rainfall
T d  Duration
intensity
of storm
c , e , f  coefficien ts
0 .8
Time
(min)
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
100-110
110-120
Precip
(in)
0.024
0.033
0.050
0.084
0.178
0.693
0.308
0.117
0.063
0.040
0.028
0.021
0 .7
0 .6
P re c ip ita tio n (in )
i
c
0 .5
0 .4
0 .3
0 .2
0 .1
0 .0
0 -1 0
1 0 -2 0 2 0 -3 0 3 0 -4 0 4 0 -5 0 5 0 -6 0 6 0 -7 0 7 0 -8 0 8 0 -9 0
T im e (m in )
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
34
90100
100110
110120
• Dimensionless
Hyetograph is
parameterized to
generate an input
hyetograph that is 3
hours long and
produces the 5-year
depth.
Rescale Depth
Empirical Hyetograph
Average Intensity
– For this example, will
use the median (50th
percentile) curve
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