1. Basic Hydrology: Rainfall-runoff based methods – II

2. Rainfall distributions
Rainfall distributions represent temporal patterns of a storm.
Rainfall distributions are presented as a cumulative curve (accumulated depth versus time), or as an incremental curve (depth for a time interval versus time)
A rainfall distribution is also called a hyetograph

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

4. Rainfall distributions
Distributions can be created from historical storms for analysis
Design storm distributions are typically dimensionless hyetographs
NRCS Type Storms
Empirical Texas Hyetographs

5. Rainfall distributions
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.

6. Rainfall distributions
If a single 24-hour precipitation depth of desired frequency is known, the SCS type curve is rescaled (multiplied by the known number) to get the time distribution.

7. Rainfall distributions
For durations less than 24 hr, the steepest part of the type curve for required duration is used (i.e. 6-hour as shown)
1.0
Fractional Depth
0.0
6 hours

8. Rainfall distributions

9. Rainfall distributions
Given duration (Td) and AEP, construct a design hyetograph
Use DDF Atlas, TP-40, to set total depth for the duration
Pick appropriate SCS type curve (location)
If Td = 24 hour, multiply (rescale) the type curve with P to get the design mass curve
If Td is less than 24 hr, pick the steepest part of the type curve for rescaling
Get the incremental precipitation from the rescaled mass curve to develop the design hyetograph

10. Rainfall distributions
Example
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 EBDLKUP)
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

11. Rainfall distributions
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.

12. Rainfall distributions
Dimensionless Hyetograph is parameterized to generate an input hyetograph
Process is similar
Estimate depth
Rescale plot in magnitude and time
Rescale Depth
Average Intensity
Rescale Time

13. 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”

14. 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.

15. 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.

16. Loss Models Basin loss models in the HDM include:
Initial and Constant rate loss
NRCS Curve Number
Green-Ampt (in HDM it is called a loss model)
Table 4-29 in HDM provides use guidance
Loss

17. Basin response models
Basin response models include unit hydrograph models documented in the HDM including:
Snyder
NRCS DUH
Combined with routing (next Lesson) the collective “model” is called a rainfall-runoff model

18. 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

19. 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.

20. Estimating Timing
The HDM presents several methods to estimate the characteristic time among these are:
Kerby-Kirpich
Snyder’s Unit Hydrograph
Time of Concentration

21. 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 with figs. from TxDOT HDM (see pages that follow)

22. TxDOT HDM overland flow velocity

23. Time of concentration Kerby-Kirpich Method
Combines Kerby overland method with Kirpich channel flow method
Will be incorporated into TxDOT HDM with next update

24. 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

25. 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

26. 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

27. 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.

29. 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.