1. Basic Hydrology & Hydraulics: DES 601
Module 8
Rainfall Distributions

2. Rainfall distributions
Rainfall distributions represent temporal patterns of a storm.
A rainfall distribution is also called a hyetograph.
Rainfall distributions are used when we need to estimate an entire hydrograph.
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3. Rainfall distributions
Each “block” represents the amount of rainfall for the time interval
The diagram is called “incremental” rainfall
The running sum of the blocks is the cumulative distribution
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4. Rainfall distributions
Distributions are created from historical storms and analyzed to generate statistical models of rainfall – these models are called design storms.
Design storm distributions are typically dimensionless hyetographs
NRCS Type Storms
Empirical Texas Hyetographs
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5. SCS Rainfall Type Curves
SCS(1973) analyzed DDF curves 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.
Intended for use with the SCS Curve Number runoff generation model!
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6. SCS Rainfall Type Curves
Location selects the Type Curve
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7. SCS Rainfall Type Curves
The 24-hour precipitation depth of desired frequency is specified (DDF Atlas), the SCS type curve is rescaled (multiplied by the known number) to get the time distribution.
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8. Rainfall distributions
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9. SCS Rainfall Type Curves
Using the Type Curves
Use DDF Atlas, TP-40, etc. to set total depth, P for the 24 hour storm.
Pick appropriate SCS type curve (location).
Multiply (rescale) the type curve with P to get the design mass curve.
Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph.
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10. Example: Generate SCS Design Storm
Generate a design hyetograph for a 25-year, 24-hour duration SCS Type-III storm in Harris County using a one-hour time increments
Look up 24-hour,25-year depth for Harris County in the DDF Atlas.
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
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11. Example: Generate SCS Design Storm
Look up 24-hour,25-year depth for Harris County in the DDF Atlas.
P ~ 10 inches
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12. Example: Generate SCS Design Storm
SCS Tabulation
DDF Atlas
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13. Exercise: Generate SCS Design Storm
Generate a 24-hour,2-year SCS Design storm for Bexar County.
Use DDF Curve already created for Bexar County.
Select the appropriate Type Curve (Type II or III).
Multiply the depth for 24-hour by the cumulative values in the SCS Tabulation.
Difference the values to obtain incremental hourly depths.
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14. Texas Empirical Hyetographs
Alternative to SCS Type Curves is the Texas Empirical Hyetographs
Based on Texas data.
Reflects “front loading” observed in many real storms.
Rescales time and depth.
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15. Texas Empirical Hyetographs
Rescale Depth
Average Intensity
Rescale Time
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16. Texas Empirical Hyetographs
Use the 50th percentile curve (median storm).
Multiply the time axis by the storm duration.
Multiply the depth axis by the storm depth.
Result is a design storm for given duration and AEP.
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17. Example: Texas Empirical Hyetographs
Construct a design storm for the 3-hour, 2-year rainfall in Harris County using the Texas Empirical Hyetograph
Obtain the depth from the DDF Atlas
Rescale the depth and time using the Texas Empirical Hyetograph
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18. Example: Texas Empirical Hyetographs
2.6 inches
1.3 inches
0 hours
3 hours
1 hours
2 hours
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19. Example: Texas Empirical Hyetographs
Probably easier to use the tabulation
SIR
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20. Rainfall Distributions
These distributions are used in the unit hydrograph methodology to specify a sequence of inputs, each of which generates a response
These responses are then superimposed in time to generate a runoff hydrograph
The “time-step” (block width) needs to be consistent with the UH duration to produce results without “aliasing”
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21. Loss models
A loss model represents all of the processes that abstract or remove water from the gross rainfall volume.
What remains after losses is what runs off- “EXCESS rainfall”.
Losses are a function of TIME
Loss models are often confused with infiltration models. They are not the same thing.
Infiltration is a component of losses, but alone does not account for all observed losses.
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22. Infiltration models commonly incorporated into loss models
Horton’s equation- empirical exponential decay-type model. Usually parameterized by infiltrometer data
Green-Ampt- theoretically based decay model. Usually parameterized from physical characteristics of soil, as represented in tables.
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23. Loss Models Basin loss models in the HDM include:
Initial and Constant rate loss
NRCS Curve Number
Green-Ampt
Table 4-29 in HDM provides use guidance
Loss
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24. Basin response models
Basin response models include unit hydrograph models documented in the HDM including:
Snyder
NRCS DUH
Combined with routing the collective “model” is called a rainfall-runoff model
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25. Timing
Strictly speaking, each unit hydrograph has a particular duration associated with it.
That duration must coincide with the time step size used in discrete aggregation.
Each watershed has a characteristic response time
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26. Timing
The time step size for aggregation must the same as the duration, and the time-to-peak for the watershed must be an integer multiple of that value.
The time-to-peak of the watershed is related to physical characteristics of the watershed- contributing area, slope, etc.
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27. Estimating Timing
The HDM presents several methods to estimate the characteristic time among these are:
Kerby-Kirpich
Snyder’s Unit Hydrograph
Time of Concentration
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28. Time of concentration
Time of concentration, tc = ∑L/V, where L is flow segment length and V is flow segment velocity. tc = toverland + tchannel flow
Estimate tchannel flow with Manning’s eqn.
Assume discharge
Compute velocity
Measure distance
Compute travel time
Estimate toverland from TxDOT HDM
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29. TxDOT HDM overland flow velocity
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30. Time of concentration Kerby Equation for Overland Flow
Can be used in smaller watersheds where overland flow is a substantial component of overall travel time.
Overland flow length can be up to 1200’
Tc = K(LxN)0.467S-0.235
where:
K = (English units conversion coefficient)
L = overland flow distance, in ft.
N = Retardance Coefficient
S = slope of overland flow path, ft/ft
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31. Kerby Retardance Coefficient
Time of concentration
Kerby Retardance Coefficient
Generalized Terrain Condition
Dimensionless Retardance Coefficient (N)
Pavement
.02
Smooth, bare, packed soil
.10
Poor grass, cultivated row crops, or moderately rough packed surfaces
.20
Pasture, average grass
.40
Deciduous forest
.60
Dense grass, coniferous forest, or deciduous forest with deep litter
.80
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32. Time of concentration Kirpich Equation for Channelized Flow
Tc = KL0.770S-0.385
where:
K = (English units conversion coefficient)
L = overland flow distance, in ft.
S = channel slope, ft/ft
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33. Time of concentration
Alternate “ballpark” method – applicable for preliminary design or as a reasonableness check of other methods:
Tc = A0.5
where Tc = Time of Concentration, in hours
A = Contributing watershed area in square miles.
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34. Module 8

35. Summary
The time step size for aggregation must the same as the duration, and the time-to-peak for the watershed must be an integer multiple of that value.
The time-to-peak of the watershed is related to physical characteristics of the watershed- contributing area, slope, etc.
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