1. Basic Hydrology & Hydraulics: DES 601
Module 10
Response Models (Unit Hydrograph)

2. 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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3. Response models
Response models convert the excess precipitation signal into a direct runoff hydrograph at the point of interest
Precipitation
Losses
Loss Model
Excess Precipitation
Response (Transform)
Runoff
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4. Response models Precipitation Precipitation Loss Excess Excess Runoff
Tlag
Excess
Runoff TP
Loss TD
Time
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5. Timing
Strictly speaking, each unit hydrograph has a particular duration associated with it, D in the diagram
That duration must coincide with the time step size used in discrete aggregation
Thus a D-hour unit hydrograph is a response to a D-hour “pulse” of excess precipitation.
The flow associated with that response is reported every D-hours until there is no further response (TD in the diagram)
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6. Timing
Each watershed has a characteristic response time, Tlag and TP in the diagram
The characteristic time of the watershed is related to physical characteristics of the watershed- contributing area, slope, etc.
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.
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7. Estimating Timing
The HDM presents several methods to estimate the characteristic time among these are:
Kerby-Kirpich
Overland and Channel Flow
NRCS Method
Sheetflow, Shallow Concentrated, Channel
NRCS Upland Method
Rule-of-Thumb Check
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8. Kerby-Kirpich 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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9. 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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10. 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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11. NRCS Method for Time of concentration
Time of concentration, tc = ∑L/V, where L is flow segment length and V is flow segment velocity. tc = tsheetflow +tshallowconcentrated+ tchannel flow
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12. NRCS Method for Time of concentration
Time of concentration, tc = ∑L/V, where L is flow segment length and V is flow segment velocity. tc = tsheetflow +tshallowconcentrated+ tchannel flow
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13. NRCS Method for Time of concentration
Time of concentration, tc = ∑L/V, where L is flow segment length and V is flow segment velocity. tc = tsheetflow +tshallowconcentrated+ tchannel flow
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14. NRCS Method for Time of concentration
Time of concentration, tc = ∑L/V, where L is flow segment length and V is flow segment velocity. tc = tsheetflow +tshallowconcentrated+ tchannel flow
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15. NRCS Upland Method
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16. Rule-of-Thumb Check
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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17. Module 8

18. 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.
Module 10