Stormwater and Urban Runoff. Hydrology – study of the properties, distribution, and circulation of the earth’s water
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IDF curves show frequency of storms of at least the given intensity over the given duration.
Model i vs D equations
e.g., Guo (J. Hydrologic Eng.11, 506 ) computed that the I-D relationship for 5-yr storms in Chicago over the past century could be described approximately by the following relationship, with a equal to 44.9 for the first half of the century and 61.0 for the second half (tD in min, i in inches/hr):
Model i vs D equations
WA State uses:
Next slide: Table of a and n values for cities throughout WA from WA State Hydraulics Manual, p.2-15.
Tr and N are treated as dimensionless, but must be chosen such that they have the same units (usually, both in years), and Tr >1. For example, for both in years:
1/Tr= likelihood of failure in a given year;1-(1/Tr)= likelihood of not failing in a given year;[1-(1/Tr)]N = likelihood of not failing at all in N consecutive years;1 - [1-(1/Tr)]N = likelihood of failing at least once in N consecutive years;
Example. A culvert on a highway is designed to just barely accommodate a “25-year storm.” What is the chance that it will never flood in its 30-year design life?
Example. What design return period would have to be used to reduce the hydrologic risk to 10%?
Hyetographs describe the varying rainfall intensity during a storm
Slope of this plot at any t is I(t) on previous slide; y(t) on this graph is integral from 0 to t of I(t) values on previous slide
Note: On an IDF plot, this storm would be represented by a single point at I = (1.2 in)/(2.0 h) = 0.6 in/h, D = 2 h, and would fall on a curve that indicates how frequently storms of that intensity and duration occur.
Lower plot normalizes values on x and y axes of upper plot, showing fraction of the precipitation that has occurred as a function of the fraction of the storm duration that has passed.
Note: Rainfall pattern assumed to be independent of magnitude of storm
t0 = time when runoff begins (often taken to be beginning of storm, but sometimes after a lag period)
f0, ff = infiltration rates at t0 and at steady-state (at large t), respectively
k = first-order rate constant, units of time-1
P = total precipitation for whole storm
R = runoff (cumulative, for whole storm)
Ia = initial abstraction; sum of all abstractions prior to the beginning of runoff
F = retention; sum of all abstractions (primarily infiltration) since runoff began
Example. A 71-ac urban watershed includes 60 ac of open area with 80% grass cover and 11 ac of industrial development that is 72% impervious. The soil is in SCS Group B. Estimate Pe and total runoff volume (ac-ft) for a 24-hr rainfall with Ptot= 1.5 in, for AMC-III conditions.
1. Find area-weighted, average CN for AMC-II (baseline) conditions.
2. Adjust CN for soil moisture conditions
3. Compute SD
4. Confirm that initial abstraction is less than precipitation, so that runoff occurs
5. Calculate Pe and total runoff
Most storms: R is <60% of P
Curve that would be obtained by shrinking areas to differential size
Any lag time between pptn and runoff would be hereTime of Concentration: Example Runoff Hydrograph
Time Since Beginning of Runoff
Q = runoff flow rate at the design point (volume/time)
C = runoff coefficient (dimensionless)
i= precipitation intensity (length/time)
A = area contributing to runoff at the design point (initially zero, growing to total watershed area, Atot, at tc) (length2)
Additional coefficient of 1.1-1.25 sometimes included for 25- to 100-yr storms, to account for reduced infiltration during intense storms
Note: Although equation looks like a rainfall-runoff relationship, it is used only to estimate maximum runoff rate, as described next.
From Central Oregon Storm Manual differential size
Example. Estimate the peak runoff generated by a 10-yr storm occurring in a small residential development with the characteristics shown below. The development is in OR Hydrologic Zone 10 and has rolling terrain. Use the Henderson and Wooding eqn from Table 2-8 to estimate the time of concentration.
Basin Area = 1.24 ac
Length of overland flow = 164 ft
Average land slope in basin = 0.02
Development density = 10 houses/ac
Henderson & Wooding eqn, with tc in min, L in ft, i in in/hr:
IDF Curve for Oregon Zone 10 differential size
From table, for urban residential areas (>6 houses/ac), n = 0.08;
L and S are given, but i must be determined.
Guess tc= 5 min; For D = 5 min, i for 10-yr storm is 2.20 in/hr
Guess tc= 10 min; For D = 10 min, i for 10-yr storm is 1.75 in/hr
Guess tc= 12 min; For D = 12 min, i for 10-yr storm is 1.60 in/hr
From Table of runoff coefficients, C for dense residential area with rolling terrain is 0.75 (for Q in cfs, i in in/hr and A in ac).
Using tc= D = 12 min, i = 1.60 in/hr:
Shallow Concentrated Flow
t = flow time (hr)
n = Manning’s coef. for effective roughness for overland flow
L = flow length (m or ft)
P2 = 2-yr, 24-hr rainfall (cm or in)
S = slope
C = 0.029 (metric), 0.007 (US)
Sheet Flow and Channel Flow
Both modeled using t = L/V, with V computed from Manning Eqn.
For sheet flow, values of Rh and n assumed for two surface types:
Paved: Rh = 0.2 ft, n = 0.025
Unpaved: Rh = 0.4 ft, n = 0.050
with w = 16.1 ft/s (4.91 m/s) for paved and 20.3 ft/s (6.19 m/s) for unpaved
qu is “unit peak flow rate” in cfs per mi2 of watershed area per inch of precipitation (csm/in)