Volume-Based Imperviousness for Storm Water Designs
James C. Y. Guo1
Abstract: The concept of low impact development 共LID兲 is to apply decentralized on-site runoff source control to preserve the watershed
hydrologic and ecological functions. An integrated layout using bioretention and vegetated landscape can decrease the developed runoff
volume and peak flow. One of the key factors in urban hydrology is the imperviousness in the watershed. The conventional approach is
to weight the imperviousness by the subareas in the watershed. Obviously, the area-weighted method has become inadequate when coping
with LID because LID takes the flow path into consideration. When an impervious area directly drains onto a pervious area, the
area-weighted method fails to count for the additional soil infiltration loss. In this study, the conventional area-weighted method is
modified with a paved area reduction factor that converts the area-weighted imperviousness to its effective imperviousness. A family of
curves was also developed for engineering applications. When a cascading process is introduced to the runoff flow path, the paved area
reduction factor can be determined using the impervious to pervious area ratio and the infiltration to rainfall intensity ratio.
DOI: 10.1061/共ASCE兲0733-9437共2008兲134:2共193兲
CE Database subject headings: Stormwater management; Runoff; Water quality; Hydrology; Urban areas; Rehabilitation; Retention
basins.
Introduction
Urbanization affects storm water runoff by increasing the volume
and rate of storm runoff, the concentration of pollutants in storm
water, and the amount of pollutants transferred into receiving waters 共USEPA 1983兲. The impact of urbanization increases as the
watershed imperviousness increases. The influx of commercial,
residential, and industrial sources distribute pollutants into an
urban area. Pollutants wash off paved surface and are quickly
conveyed through overland flows and waterways 共Driscoll et al.
1989兲. Over the years, many storm water best management practices 共BMPs兲 have been developed to reduce the runoff volume
and pollutant concentrations. In general, the implementation of
storm water BMP takes the following four steps to dispose of
on-site storm water 共UDFCD 2001兲: 共1兲 to reduce runoff peaks
and volumes by minimizing directly connected impervious areas
共MDCIA兲; 共2兲 to provide water quality capture volume for an
on-site retention process; 共3兲 to stabilize downstream banks and
stream beds along the waterways; and 共4兲 to implement BMPs for
special needs in industrial and commercial developments within
the tributary area. The principle behind MDCIA is twofold: to
reduce impervious areas and to direct runoff from impervious
surfaces over grassy areas to slow down runoff and promote soil
infiltration. Draining a paved area onto another pervious area can
reduce runoff volumes, rates, pollutants, and cost for drainage
infrastructure. Several approaches are used to reduce the imperviousness of a development site, including 共1兲 the reduction of
1
Professor, Dept. of Civil Engineering, Univ. of Colorado at Denver/
HSC, Denver, CO 80217. E-mail: [email protected]
Note. Discussion open until September 1, 2008. Separate discussions
must be submitted for individual papers. To extend the closing date by
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and possible publication on January 4, 2007; approved on June 25, 2007. This
paper is part of the Journal of Irrigation and Drainage Engineering,
Vol. 134, No. 2, April 1, 2008. ©ASCE, ISSN 0733-9437/2008/2-193–
196/$25.00.
paved area; 共2兲 an increase of porous pavement; 共3兲 filtering runoff by grass buffers; and 共4兲 infiltration by porous cascading
planes. For example, the use of modular block porous pavement
or reinforced turf in low-traffic zones, such as parking areas and
infrequently used service drives, such as fire lanes, can significantly reduce the site imperviousness. This practice can reduce
the size of downstream storm sewers and detention basins. Draining an impervious area onto a landscaped area slows down the
runoff flow and increases the soil infiltration. In general, regional
drainage facilities are designed using a lumped method, whereas a
BMP device shall be sized by a flow-path dependent method. A
lumped model applies a lumped parameter to represent the drainage characteristics of the entire tributary area 共Chow 1964; Guo
2001兲. For instance, the area-weighted method is widely employed to determine the watershed runoff coefficient for a small
catchment. However, the conventional area-weighted method
takes no consideration of the flow path. As a result, it fails to
quantify the difference between a driveway that drains onto a
grass buffer and a grassy area that drains onto a driveway. Both
cases are represented by the same imperviousness when evaluated
by the conventional method. Imperviousness is a sensitive factor
in a hydrologic study. For instance, the rational method for peak
flow predictions and the modified Federal Highways Administration method for sizing small on-site retention volumes are highly
sensitive to the catchment imperviousness 共FAA 1970; Guo
1999兲. With the advancement in storm water BMPs and low impact development 共LID兲, the area-weighted method has to be
modified for on-site hydrologic studies. This is an increasing
concern in storm water BMPs and LID. The current practice in
dealing with runoff cascading planes is to rely on computer simulation. For instance, the option of “pervious outlet” is available in
SWMM5 to model the runoff flow from an impervious area onto
the pervious area 共Rossman 2005兲. The option of “impervious
outlet” is derived to model the runoff flow from a pervious area to
downstream impervious area. However, neither direct solution
nor design chart has ever been developed to convert areaweighted imperviousness to effective imperviousness.
JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / MARCH/APRIL 2008 / 193
from upper paved plane 关L2 / T兴; X = length of reach 关L兴; d = flow
depth 关L兴; n = Manning’s roughness coefficient; So = slope for
reach; t = time; and ⌬t = time interval. The values of all variables
at time t serve as the initial condition. At time, t + ⌬t, the only
unknown in Eq. 共1兲 is the flow depth, d, that can be solved simultaneously using Eqs.共1兲–共4兲.
To apply Eqs.共1兲–共4兲, to the upper impervious plane, Eq. 共2兲
has qi = 0 and f = 0 for all times. For the lower pervious plane, the
inflow, qi, is defined by the inflow hydrograph generated from the
upper impervious plane. Having calculated the overland flow hydrograph at the outlet of the lower pervious plane, the total runoff
volume produced by this cascading-plane system is calculated by
共Guo 2004兲
t=Tb
Fig. 1. Illustration of cascading-plane and central-channel models
This paper applies the kinematic wave theory to model the
overland flow through the cascading planes that represent a
MDCIA layout, such as an infiltrating bed or grassy buffer that
receives runoff from a driveway or roof. For a given MDCIA
layout, the area-weighted imperviousness can be directly calculated by the area components in the watershed. But, the effective
imperviousness that counts for the additional infiltration loss
needs to be determined by a new approach. It is suggested that the
effective imperviousness be weighted using the runoff volumes
separately generated from the impervious and pervious areas. In
this study, a range of impervious to pervious area ratios and infiltration to rainfall intensity ratios are selected to develop a family of curves. Using these curves, the area-weighted method is
modified to directly calculate the effective imperviousness for a
specified MDCIA layout.
VT =
q共t兲⌬t
兺
t=0
共5兲
in which VT = total unit-width runoff volume 关L2兴 and Tb = base
time of runoff hydrograph.
Watershed Imperviousness
The area-weighted method implies that an urban watershed can be
modeled by separate impervious and pervious planes, and both
planes produce runoff flows separately and independently. As
illustrated in Fig. 1共b兲, the watershed is represented by left-paved
and right-pervious planes. Both planes are under the same
rainfall, but they produce overland flows separately. At the outfall point, the resultant hydrograph is the sum of these two overland flows. This concept has been incorporated into SWMM5
共Rossman 2005兲 to predict urban runoff. Following the conventional method, the area-weighted imperviousness is directly calculated by the area components as
should be 1
Cascading-Plane Model
A cascading landscape is to spread the runoff flow generated from
the upper impervious plane onto the pervious plane for additional
infiltration loss. In this study, the cascading-plane model illustrated in Fig. 1共a兲 was derived to simulate the overland flow
in series. The upstream plane is set to be 100% paved and the
downstream plane is set to be 100% pervious. Both planes
are under the same rainfall event. Applying kinematic wave to
the unit-width overland flow, the flow on a plane is described
as 共Woolhiser and Liggett 1967; Wooding 1965; Morgali and
Linseley 1965; Guo 1998兲
关Ie共t兲 + Ie共t + t兲兴
关q共t兲 + q共t + ⌬t兲兴 V共t + ⌬t兲 − V共t兲
共1兲
X−
=
2
2
⌬t
Ie = I − f +
qi
X
V = Xd
1.49 5/3
d 冑So
q=
n
共2兲
Ka =
Ai ⫻ 100% + A P ⫻ 0%
Ar
=
共Ai + A P兲
共1 + Ar兲
共6兲
where Ka = area-weighted imperviousness 共%兲; Ai = impervious
area; A p = pervious area; and Ar = impervious to pervious area
ratio. For a cascading system, the effective imperviousness is not
readily known. For mathematical convenience, the cascading
planes in Fig. 1共a兲 are converted into the central-channel model
with the same length of flow path. The unit width of the centralchannel model is further divided into the left-paved and rightpervious planes as
Wi + W p = 1
共7兲
where Wi = left-paved width, and W p = right-pervious width. Mathematically, the value of Wi is equivalent to the watershed effective
imperviousness as
Wi = k
共8兲
Wp = 1 − k
共9兲
共3兲
共4兲
where Ie = excess rainfall intensity 关L / T兴; I = rainfall intensity
关L / T兴; q = unit-width flow rate 关L2 / T兴; V = unit-width storage volume in reach 关L2兴; f = infiltration rate 关L / T兴; qi = unit-width inflow
where k = effective imperviousness 共%兲. In this study, Eqs. 共1兲–共5兲
are separately applied to the left-paved and right-pervious planes
to generate overland flows. Because the overland flow volume is
linear to the plane width, the total runoff volume produced by the
left-paved and right-pervious planes is summed as
194 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / MARCH/APRIL 2008
Table 1. Effective Imperviousness for Various Conditions
Fig. 2. Unit-width hydrographs generated by 400-ft planes under 1 h
uniform rainfall depth of 64.2 mm and f / I = 0.5
V T = W iV i + W pV p
共10兲
in which Vi = left-paved runoff volume and V P = right-pervious
runoff volume. Substituting Eqs. 共8兲 and 共9兲 into Eq. 共10兲 yields
k=
VT − V P
Vi − V P
共11兲
The effective imperviousness, k, can be solved using Eqs. 共5兲 and
共11兲 for a given MDCIA layout.
Modified Area-Weighted Method
This study begins with the tests of the accuracy of the numerical
model developed for the cascading-plane system. For instance,
the numerical model was examined to produce the overland flow
hydrograph under a uniform rainfall distribution at 2.53 in./h
共62.4 mm/h兲 that is equivalent to the 1 h 100-year event in the
City of Denver. The ratio, f / I, was set to be 0.50. The cascading
system has an upper 200 ft 共62 m兲 paved plane that drains onto
the lower 200 ft pervious plane on a slope of 1.0%. As recommended 共UDFCD 2001兲, Manning’s roughness of 0.016 is applied
to the upper paved plane and 0.15 is applied to the lower pervious
plane. Applying the same parameters to the central-channel
model, the overland flow was separately produced by the leftpaved and right-pervious planes. These three hydrographs are
plotted in Fig. 2. The numerical results for this case closely agree
with the theoretical kinematic wave solution. For this case, the
cascading-plane system produced a unit-width runoff volume of
Fig. 3. Unit-width hydrographs generated by 400-ft planes under 1 h
nonuniform rainfall depth of 64.2 mm and f / I = 0.5
f / I ratio
Impervious-to-pervious
area ratio
Ar
0.25
0.50
0.75
1.00
Area weighted
impervious
共%兲
0.25
0.50
1.00
1.50
2.00
3.00
0.20
0.33
0.49
0.59
0.65
0.73
0.18
0.30
0.45
0.55
0.61
0.69
0.17
0.28
0.43
0.52
0.59
0.67
0.15
0.26
0.39
0.47
0.53
0.61
0.20
0.33
0.50
0.60
0.67
0.75
56.1 ft2 共5.2 m2兲, whereas the left-paved plane generated
84.1 ft2 共7.8 m2兲 and the right-pervious plane generated 31.4 ft2
共2.9 m2兲. Substituting these volumes into Eq. 共11兲, the effective
imperviousness is calculated to be 0.46 for this case. In this study,
a further investigation on the nonuniform rainfall distribution
was also conducted using the 1 h 100 year rainfall distribution recommended for the Denver area in Colorado 共UDFCD
2001兲. Such a rainfall distribution is similar to the 2 h rainfall
centered in the SCS 24 h Type 2 curve. Fig. 3 presents the resultant overland flow hydrographs produced by the nonuniform
rainfall distribution. The effective imperviousness for the nonuniform rainfall in Fig. 3 was found to be 0.45 for f / I = 0.50. As
expected, the effective imperviousness is not sensitive to rainfall distribution because the runoff volume under a runoff hydrograph is mainly determined by the rainfall excess, not its time
distribution.
With the aforementioned, a systematic approach was employed to investigate a range of the design parameters. For
instance, the impervious to pervious area ratios, Ar, ranges from
0.25, 0.5, 1.0, 1.5, 2.0, to 3.0 and infiltration rate to rainfall intensity ratios, f / I. ranges from 0.25, 0.50, 0.75, to 1.0. The effective imperviousness ratios for various combinations are calculated
and summarized in Table 1. As shown in Fig. 4, the normalized
family curves are produced using the parameter of f / I and Ar.
At Ar = 1.0, the conventional area-weighted method results in
an imperviousness of 50%, but the study found that the effective imperviousness varies from 38.2 to 48.8%, depending on
f / I ratio. As expected, the higher the f / I ratio, the lower the
effective imperviousness. This study reveals that the conventional
area-weighted method sets the upper limit for these family curves.
In other words, it is confirmed that all cascading landscapes can
reduce the runoff volume. Using Table 1 as the database, a nondimensional regression equation was derived as
Fig. 4. Effective imperviousness percentages for cascading
landscaping planes
JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / MARCH/APRIL 2008 / 195
Notation
Fig. 5. Paved area reduction factor
k = 0.6197Ar0.7065e关−0.2881共f/I兲+0.1759Ar兴
with r2 = 99.37 共12兲
in which r2 = correlation coefficient. For the purpose of engineering practice, it would be convenient if the area-weighted method
could be modified to predict its effective imperviousness. In this
study, a paved area reduction factor 共PARF兲 is introduced to the
area-weighted method as
k = RKa =
RAr
共1 + Ar兲
共13兲
Where R = PARF. Eq. 共13兲 is the modified area-weighted method
for watershed imperviousness. The values of R were derived from
Fig. 4 and then plotted in Fig. 5. PARF for the cases studied
varies in a narrow range between 0.78 and 0.92. The average of
PARF is approximately 0.84 for the cases studied.
Conclusions
Storm water BMPs and innovative LID need to cope with the full
spectrum of runoff events. For instance, the natural streams need
to pass the major event, the sewer systems must be adequate for
the minor event, and the on-site BMPs have to accommodate
more frequent microevents. Both lumped and distributed design
methods have to be jointly used to design the regional and on-site
storm water quality and quantity control systems. Hydrologic
methods were developed with assumptions and limitations. It is
important to establish some consistency among methods. Otherwise, the entire system will fail to maintain the same risk level
selected for the design 共Guo 2002兲. Watershed imperviousness is
a key parameter in urban hydrology. This study confirms that the
cascading MDCIA layout can reduce the runoff volume and peak
flow because of the porous flow path. To be convenient, a PARF
is introduced to modify the area-weighted method for calculating
the effective imperviousness. In this study, PARF was found to
vary in a narrow range between 0.78 and 0.92. If the on-site soil
infiltration rate or design rainfall intensity is not readily available,
the average value of 0.84 can be used to convert the areaweighted to its effective imperviousness. Of course, when the
detailed on-site hydrologic information is available, the design
curves in Fig. 4 or Eq. 共12兲 provide direct solution for effective
imperviousness.
The following symbols are used in this paper:
Ai ⫽ impervious area;
A p ⫽ pervious area;
Ar ⫽ impervious to pervious area ratio;
d ⫽ flow depth;
f ⫽ soil infiltration rate;
I ⫽ rainfall intensity;
Ie ⫽ rainfall excess intensity;
Ka ⫽ area-weighted imperviousness in percent;
k ⫽ equivalent area imperviousness;
n ⫽ Manning’s roughness coefficient;
q ⫽ unit-width outflow;
qi ⫽ unit-width inflow from upper plane onto lower
plane;
r2 ⫽ correlation coefficient;
So ⫽ slope for reach;
Tb ⫽ base time for runoff hydrograph;
t ⫽ time;
V ⫽ unit-width storage volume in reach;
VT ⫽ unit-width total runoff volume;
Wi ⫽ width of impervious plane;
W P ⫽ width of pervious plane;
X ⫽ length of reach; and
⌬t ⫽ time interval.
References
Chow, V. T. 共1964兲. Handbook of applied hydrology, Chaps. 17 and 21,
McGraw-Hill, New York.
Driscoll, E. D., DiToro, O., Gaboury, D., and Shelley, P. 共1989兲. “Methodology for analysis of detention basins for control of urban runoff
quality.” EPA440/5-87-001, U.S. Environmental Protection Agency,
Washington, D.C.
Federal Aviation Administration 共FAA兲. 共1970兲. “Airport drainage.”
AC No. 150/5320-5B, Dept. of Transportation, Washington, D.C.
Guo, J. C. Y. 共1998兲. “Overland flow on a pervious surface.” IWRA Int. J.
Water, 23共2兲.
Guo, J. C. Y. 共1999兲. “Detention storage volume for small urban catchments.” J. Water Resour. Plann. Manage., 125共6兲, 380–382.
Guo, J. C. Y. 共2001兲. “Rational hydrograph method for small urban watersheds.” J. Hydrol. Eng., 6共4兲, 352–356.
Guo, J. C. Y. 共2002兲. “Overflow risk analysis for storm water quality
control basins.” J. Hydrol. Eng., 7共6兲, 428–434.
Guo, J. C. Y. 共2004兲. “Hydrology-based approach to storm water detention basin design using new routing schemes.” J. Hydrol. Eng., 9共4兲,
333–336.
Morgali, J. R., and Linseley, R. K. 共1965兲. “Computer analysis of overland flow.” J. Hydraul. Eng., 3, 81–100.
Rossman, L. A. 共2005兲. Storm water management model user’s manual,
version 5 (SWMM5), Office of Research and Development, USEPA,
Cincinnati.
Urban Drainage and Flood Control District 共UDFCD兲. 共2001兲. Urban
storm water drainage criteria manual, Vol. 3, UDFCD, Denver.
U.S. Environmental Protection Agency 共USEPA兲. 共1983兲. “Results of
the nationwide urban runoff program.” NTIS Final Rep. No. PB84185545, Washington, D.C.
Wooding, R. A. 共1965兲. “A hydraulic model for a catchment-stream problem.” J. Hydrol., 3, 254–267.
Woolhiser, D. A., and Liggett, J. A. 共1967兲. “Unsteady one-dimensional
flow over a plane—The rising hydrograph.” Water Resour., 3共3兲, 753–
771.
196 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / MARCH/APRIL 2008