WATERSHEDS - Water Quality Engineering in Natural Systems - page 213

where p r , p a , and p t pollutant inputs (g/m·d) can be esti-
mated using the relations

direct function of the rainfall rate. Equation (6.16) inte-
grates to

p r LIT =

(6.13)

m t m ( ) = ( )exp( 0 − k it )

(6.17)

U

= 1 p a

2 (

ATMFL SW )( ) (6.14)

where m (0) is the initial mass stored on the street (M).
The constant k U has been found almost independent of
particle size within the range studied, 10 µ m to 1 mm,
and is commonly taken as 0.19 mm −1 by urban runoff
models that utilize this concept. Equation (6.17) is
sometimes modified by assuming that not all the solids
are available for transport, is which case

= 1

p t

2 (

TE TD RCC )( )( ) (6.15)

where LIT is the litter and street refuse deposition
rate (g/m·d), ATMFL is the dry atmospheric deposi-
tion rate (g/m 2 ·d), SW is the street width (m), TD is the
traffic emission rate (g/axle·m), TE is the traffic density
[axles/d]), and RCC is the road condition factor
(dimensionless).
A model of sediment accumulation during the winter
is very different from that described by Equation (6.9),
since the effect of wind and traffic on sediment accumu-
lation on streets is much different in the winter com-
pared with the summer, and snow removal practices and
application of deicing chemicals further complicate the
process. Snow piles are effective traps of street pollut-
ants, including large amounts of salt. Since solids and
pollutants are incorporated into snow and are not
removed from the snowpack by wind and traffic, the
accumulation rate is almost linear and hence much
higher than in nonwinter periods. For this reason, the
quantity of accumulated pollutants near the curb at the
end of the snow period is very high. The possibility of
reducing the quantity of street pollutants during winter
is very limited, since the use of sweeping equipment is
not possible when snow piles and frozen ice are located
on the sides of the streets. A strategy of transporting
heavily polluted snow to appropriately designed snow
deposit areas has been proposed; however, techniques
for identifying snow that is “heavily polluted” tend to
be highly uncertain.

m t ( ) = am ( )exp( 0 − k it ) (6.18)

U

where a is the availability factor (dimensionless), which
accounts for the nonhomogeneous makeup of particles
and the variability in travel distance of dust and dirt
particles. The availability factor can be estimated using
the empirical relation

.

(6.19)

a = 0 057 0 04 1 1 . + . i

where i is in mm/h, and the maximum value for a is 1.0.
The advantage of incorporating the availability factor is
partially offset by introducing an additional washoff
parameter that must be estimated.
The buildup and washoff models given by Equations
(6.7) and (6.16) are primarily used to predict the buildup
of solids on impervious surfaces and removal by surface
runoff. These models have also been used to predict the
buildup and washoff of other contaminants not nor-
mally associated with solids accumulation, such as total
petroleum hydrocarbons-diesel (TPh-D), dissolved
organic nitrogen, and zinc. Of course, the model param-
eters depend on the contaminant being simulated.
The buildup and wash-off models given by Equations
(6.7) and (6.16) can be combined with analytical rainfall
runoff models to relate pollutant loads directly to rain-
fall characteristics (e.g., Chen and Adams, 2006a,b).
Buildup and washoff models have also been used to
simulate the transport of contaminants not normally
associated with vehicular traffic, for example, to simu-
late the fate and transport of roadside-applied herbi-
cides, which can have significant adverse impacts on
primary productivity in receiving waters (Massoudieh
et al., 2005).

Wash-Off Models. The simplest and most widely used
model of wash-off is based on the following first-order
removal concept:

dm
dt

= − k im (6.16)

U

where m is the mass of solids remaining on the surface
(M); t is the time (T); k U is a constant called the urban
wash-off coefficient, , which depends on street surface
characteristics (L −1 ); and i is the rainfall intensity (LT −1 ).
Equation (6.16) assumes that the rainfall event pollut-
ant washoff load is proportional to the accumulated
pollutant mass on the catchment surface before the
runoff event, and the pollutant washoff load is a

EXAMPLE 6.3

A 100-m segment of an 8-m-wide urban roadway drains
into a nearby lake where water-quality standards are