des 606 : watershed modeling with hec-hms module 11 theodore g. cleveland, ph.d., p.e 29 july 2011
TRANSCRIPT
DES 606 : Watershed Modeling with
HEC-HMS
Module 11Theodore G. Cleveland, Ph.D., P.E
29 July 2011
Module 11: 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 11: 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 11: 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 11: ARF in Texas
Module 11: 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historical, they no longer represent real measurements!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.
http://onlinemanuals.txdot.gov/txdotmanuals/hyd/ebdlkup.xls
Author added this row, not in on-line version
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.
€
I =b
(TC + d)e
Design Storms for Texas
• 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
Design Storms for Texas
• 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
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
• 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.
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.•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
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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.
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 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)
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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!
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
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)
• 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*
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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.
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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.
This slide adapted from: www.ce.utexas.edu/prof/maidment/GradHydro2010/.../DesignStorms.ppt
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
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 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.
• Example 3 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.