Stormwater and Urban Runoff

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Stormwater and Urban Runoff

• Hydrology study of the properties,
  distribution, and circulation of the earths
  water
• Our Interest understanding and predicting
  patterns in the loads (i.e., flow rates) of water
  at specified locations so that we can safely,
  efficiently, and productively manage it (divert
  it, control its release to aquifers or surface
  flows, etc.)
• Focus on rainfall-runoff relationship
  (snowmelt-runoff also important but beyond our
  scope)

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Rainfall Patterns and Fates

• Spatial domain of interest watershed (catchment
  or drainage area drainage basin includes area
  that contributes underground flow)
• Rainfall patterns
• Typically characterized by intensity-duration-freq
  uency (IDF) curves
• Rainfall typically quantified as the depth of
  water that the given amount of rain could
  generate if distributed uniformly over the entire
  watershed
• Intensity average rate of precipitation
  (rainfall quantity/time, mm/h or in/h)
• Duration conventional meaning
• Frequency Frequency of storms with the specified
  duration and at least the specified intensity
  (yr-1) often quantified by its inverse the
  recurrence interval or return period, Tr

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Rainfall Patterns and Fates
IDF curves show frequency of storms of at least
the given intensity over the given duration.
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Rainfall Patterns and Fates
Model i vs D equations
e.g., Guo (J. Hydrologic Eng. 11, 506 2006)
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)
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Rainfall Patterns and Fates
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.
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Hydrologic Risk

• Hydrologic risk, J likelihood of an event with
  recurrence interval Tr occurring at least once
  within a specified design period of N time units

Tr and N are treated as dimensionless, but must
be chosen such that they have the same units
(usually, both in years), and Tr gt1. For example,
for both in years
1/Tr likelihood of failure in a given
year1-(1/Tr) likelihood of not failing in a
given year1-(1/Tr)N likelihood of not
failing at all in N consecutive years1 -
1-(1/Tr)N likelihood of failing at least
once in N consecutive years
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Hydrologic Risk
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?
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Rainfall Hyetographs
Hyetographs describe the varying rainfall
intensity during a storm
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Cumulative Rainfall Hyetographs
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.
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SCS 24-Hr Hyetograph Types
Note Rainfall pattern assumed to be independent
of magnitude of storm
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SCS 24-Hr Hyetograph Regions
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Rainfall Patterns

• Example 2-2 in text demonstrates conversion of
  IDF data and SCS hyetograph types to hyetographs
  for particular return periods
• Determine total precipitation for rainfall event
  of interest from IDF curves
• Determine SCS hyetograph type for location of
  interest
• For each time interval, determine incremental
  expected precipitation

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Rainfall Patterns and Fates

• Possible short-term fates of rainfall
• Interception capture of water before it hits
  the ground (on vegetation, buildings, etc.)
• Depression storage retention in low spots on
  land surface (note capture by buildings
  sometimes put in this category rather than
  Interception)
• Infiltration into soil might subsequently be
  taken up by plants, enter an aquifer, or
  re-appear at the surface as a spring or a feed
  into a stream
• Runoff our primary concern also called
  effective or excess precipitation, Pe
• Interception, depression storage, and
  infiltration collectively referred to as
  abstractions

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Modeling Rainfall Fate

• Interception
• Vegetative interception significant only early in
  storm, since plants rapidly reach their holding
  capacity
• Vegetative interception sometimes modeled as Lint
  cPm, where P is total precipitation, and c and m
  depend on vegetation type (c typically 0.15-0.40,
  m typically 0.6-0.9)
• Might be significant over longer times for
  buildings, depending on drainage system
  typically estimated as 0.05-0.1 inch
• Depression storage
• Usually much smaller than infiltration and, like
  interception, important primarily early in storm
• Typical estimates of 0.2-0.4 inch for permeable
  areas 0.05-0.1 inch for impermeable

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Modeling Rainfall Fate

• Infiltration
• Several models have been proposed consider just
  one here the Horton equation (1940)

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
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Modeling Rainfall Fate

• Runoff
• Several models have been proposed most widely
  used is the SCS (Soil Conservation Service, now
  the Natural Resources Conservation Service)
  curve number model.
• Model starts with a mass balance on
  precipitation

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
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Modeling Total Runoff The SCS Model

• Define SD as the soil moisture deficit when
  runoff begins (tR) i.e, the capacity for
  additional retention that remains when runoff
  begins
• F/SD is the fraction of the soil moisture deficit
  at tR that is ultimately utilized
• P - Ia is the maximum runoff that can occur, if
  no abstractions occur from tR forward
• Model assumption The fraction of SD that is
  ultimately utilized is the same as the fraction
  of the potential maximum runoff that is realized
• Alternative statement of the assumption the
  water distributes itself between infiltration and
  runoff in the same proportion as the ratio of the
  maximum possible infiltration to the maximum
  possible runoff at the time when runoff begins

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Modeling Total Runoff The SCS Model

• Substituting the mass balance equation into the
  equation for the model assumption and carrying
  out some algebra yields

• Ia has been found to be approximately
  proportional to SDIa 0.2 SD is a common
  assumption, in which case R depends only on SD

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Modeling Total Runoff The SCS Model

• SD assumed to be independent of storm parameters,
  but to depend on soil type, land use, and
  antecedent soil moisture condition (AMC)
• Four soil groups (labeled A-D) and multiple land
  use categories defined
• Each soil group/land use category assigned a
  curve number (CN) for intermediate AMC
  (designated AMC-II)

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Modeling Total Runoff The SCS Model

• Curve numbers are adjusted for low (AMC-I) or
  high (AMC-III) moisture content, as follows
• Then, SD is computed from CN as
• Finally, R is computed as indicated previously

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Modeling Total Runoff The SCS Model
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.
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Modeling Total Runoff The SCS Model
2. Adjust CN for soil moisture conditions
3. Compute SD
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Modeling Total Runoff The SCS Model
4. Confirm that initial abstraction is less than
precipitation, so that runoff occurs
5. Calculate Pe and total runoff
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Modeling Total Runoff The SCS Model
Most storms R is lt60 of P
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Design for Runoff Management

• Design for conveyance of runoff away from
  watershed
• Focus on peak runoff at the discharge (design)
  location, not cumulative amount of runoff during
  and after storm
• Design based on protection against a storm of a
  pre-determined recurrence period
• Peak discharge occurs once all parts of the
  watershed contribute flow to the design location
• Design approach
• Define time required before peak discharge is
  reached (i.e., longest time needed for water
  falling anywhere in the watershed to reach design
  location) as the time of concentration, tc
• Choose design value for recurrence period
• Relate peak flow to parameters describing storm
  and watershed characteristics (storm intensity
  and duration, time of concentration, watershed
  area, land cover, expected abstractions, etc.)

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Time of Concentration Example Watershed

• Assume
• 2.5-hr storm
• Runoff from each area starts at tavg and
  continues until tavg2.5 hr
• Define t 0 as time when runoff begins (perhaps
  later than beginning of precipitation

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Time of Concentration Example Runoff Hydrograph
Time Since Beginning of Runoff
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Design For Runoff Conveyance

• Estimating tc
• Many empirical equations (see Table 2-8)
• One common approach is to estimate flow velocity
  from average ground slope and land cover, and use
  travel distance to convert to time of flow from
  point expected to most remote (in time)

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Design For Runoff Conveyance

• Estimating Qmax using the Rational Method
• Assume storm has uniform intensity, i, over
  watershed area and during full storm duration
  (justifiable only for relatively short storms
  over small areas 10s of ac, or less)
• Assume runoff from unit area of watershed is
  directly proportional to rainfall intensity, so
  runoff rate at design point is

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.
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From Central Oregon Storm Manual
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Design For Runoff Conveyance

• Estimating Qmax using the Rational Method
• According to the rational method assumption,
  runoff rate per unit of contributing area is
  proportional to storm intensity, i, which is
  steady
• For storms with a given Tr, i decreases with
  increasing duration
• For storms with steady i, Aactive and Q reach
  their maximum values at t tc, and then remain
  at those values until the end of the storm
• Therefore, since Q CiA
• For a given Tr, to maximize i, use shortest D
• For a given i, to maximize Aactive, use D ? tc
• To design for (approximate) maximum Q (i.e.,
  maximum i A), use shortest D that is ? tc i.e.,
  use D tc
• Note if tc lt 5 min, WA State Hydrology Manual
  specifies that tc 5 min should be used.

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Estimating Qmax Using the Rational Method
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
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IDF Curve for Oregon Zone 10
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Estimating Qmax Using the Rational Method
From table, for urban residential areas (gt6
houses/ac), n 0.08 L and S are given, but i
must be determined.

• TE approach
• Assume a value for i or tc
• If tc was guessed, assume storm duration D tc
• Determine D or i from IDF curve (whichever was
  not assumed)
• Compute tc from Henderson Wooding
• Repeat until D tc

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Estimating Qmax Using the Rational Method
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
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Estimating Qmax Using the Rational Method
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
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Design For Runoff Conveyance

• SCS method estimates tc in three categories
• Shallow concentrated flow (e.g., in gullies)
• Sheet flow over the land surface
• Channel flow, in clearly-defined channels

Shallow Concentrated Flow
t flow time (hr) n Mannings 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)
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Design For Runoff Conveyance
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 Yielding with w 16.1 ft/s (4.91 m/s)
for paved and 20.3 ft/s (6.19 m/s) for unpaved
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Design For Runoff Conveyance

• Estimating Qmax using the SCS (NRCS) Method
• Multi-step empirical equations leading to
  estimate of Qmax
• Choose total precipitation, P (not Tr), for
  design storm
• Determine CN for area and conditions of interest
  use P and CN to estimate Ia / P from Table 2-10

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Design For Runoff Conveyance

• Estimating Qmax using the SCS (NRCS) Method
• Multi-step empirical equations leading to
  estimate of Qmax
• Use estimated Ia / P and SCS Storm Type (IA, I,
  II, or III) to estimate coefficients C0, C1, C2
  from Table 2-9
• Insert coefficients and tc into equations on p.64
  to estimate Qmax

qu is unit peak flow rate in cfs per mi2 of
watershed area per inch of precipitation (csm/in)
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Design For Runoff Conveyance

• Qmax from the SCS (NRCS) Method