ARTICLE IN PRESS

WAT E R R E S E A R C H 41 (2007) 3025 – 3031

Available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/watres

Mathematical interpretation of pollutant wash-off from

urban road surfaces using simulated rainfall

Prasanna Egodawattaa,, Evan Thomasb, Ashantha Goonetillekea

a
School of Urban Development, Queensland University of Technology, G.P.O. Box 2434, Brisbane Qld., 4000, Australia
b
Gold Coast City Council, PO Box 5042, Gold Coast MC, Qld., 9729, Australia

art i cle info ab st rac t

Article history: In the context of stormwater quality modelling, an in-depth understanding of underlying
Received 13 July 2006 physical processes and the availability of reliable and accurate mathematical equations,
Received in revised form which can replicate pollutant processes are essential. Stormwater pollutants undergo three
22 March 2007 primary processes, namely, build-up, wash-off and transport, before accumulating into
Accepted 27 March 2007 receiving waters. These processes are expressed mathematically by equations in storm-
Available online 22 May 2007 water quality models. Among the three processes, wash-off is the least investigated. This
Keywords: paper presents the outcomes of an in-depth investigation of pollutant wash-off processes
Pollutant wash-off on typical urban road surfaces.
Urban water quality The study results showed that a storm event has the capacity to wash-off only a fraction
Rainfall simulation of pollutants available and this fraction varies primarily with rainfall intensity, kinetic
energy of rainfall and characteristics of the pollutants. These outcomes suggest that the
exponential equation commonly used for mathematically defining pollutant wash-off
would need to be modified in order to incorporate the wash-off capacity of rainfall.
Consequently, the introduction of an additional term referred to as the ‘capacity factor’ CF
is recommended. CF primarily varies with rainfall intensity. However, for simplicity three
rainfall intensity ranges were identified where the variation of CF can be defined. For
rainfall intensities less than 40 mm/h, CF varies linearly from 0 to 0.5. For rainfall intensities
from 40 to around 90 mm/h, CF is a constant around 0.5. Beyond 90 mm/h, CF varies between
0.5 and 1.
& 2007 Elsevier Ltd. All rights reserved.

1. Introduction of mathematical procedures which are used to describe the

water quality response of a catchment to a particular storm
Stormwater runoff pollution is one of the most significant event or a period of time (Akan and Houghtalen, 2003;
environmental issues in urban areas. Pollutant loads originat- Zoppou, 2001). A model can be used to estimate concentration
ing from urban catchments is significantly higher when of pollutants originating from a catchment and these
compared to rural catchments, leading to adverse impacts estimations are used for decision making.
on receiving water quality (House et al., 1993; Novotny et al., A stormwater quality model incorporates mathematical
1985; Sartor et al., 1974). formulations to replicate three pollutant processes; pollutant
In this context, stormwater quality modelling plays an build-up, pollutant wash-off and pollutant transport. Differ-
important role in the development of appropriate manage- ent mathematical formulations are available to replicate each
ment strategies. A stormwater quality model is a combination pollutant process with varying levels of accuracy and degree

Corresponding author. Tel.: +61 731384396; fax: +61 731381170.

E-mail address: p.egodawatta@qut.edu.au (P. Egodawatta).
0043-1354/$ - see front matter & 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.watres.2007.03.037
 ARTICLE IN PRESS
3026 WAT E R R E S E A R C H 41 (2007) 3025– 3031

Nomenclature k wash-off coefficient

t time
CF capacity factor W weight of the material mobilised after time t
Fw fraction wash-off W0 initial weight of the material on the surface
I rainfall intensity

of complexity. Most models use suspended solids as their The surroundings of all three sites was grassed and
primary indicator pollutant. The general assumption is well maintained with no construction or demolition activities
that the most of the other stormwater pollutants such as in the vicinity. Therefore, it can be assumed that the
nutrients, heavy metals and hydrocarbons are adsorbed to pollutants on the road surfaces would primarily originate
suspended solids (Akan and Houghtalen, 2003; Herngren from traffic, from atmospheric sources or emissions. A street
et al., 2005; Sartor et al., 1974). sweeper operates every 6 weeks within the region. The
Accuracy and reliability of a model is dependent on the sweeper is more involved in cleaning the gutter area rather
precision of the mathematical formulation of pollutant than the road surface where the research was focused on.
processes. Therefore, the in-depth understanding of the Therefore, it can be assumed that the influence of street
pollutant processes is the key to better modelling approaches. sweeping on the amount of initially available pollutants is
In nature, these processes are complex and are influenced by minimal.
a range of parameters such as rainfall, runoff, climatic, land
use and surface characteristics (Sartor et al., 1974; Vaze and 2.2. Rainfall simulation
Chiew, 2002). The complex nature and variability together
with a range of parameters create inherent difficulties in the A specially designed rainfall simulator as shown in Fig. 1 was
development of accurate and reliable mathematical replica- used to generate the artificial rainfall events. The rainfall
tion of pollutant processes. simulator consists of three Veejet 80100 nozzles connected to
This paper presents the outcomes of a pollutant wash-off a nozzle boom and stands at 2.5 m above the ground level.
study using simulated rainfall on typical urban road surfaces The nozzle boom swings in either direction with controlled
in Gold Coast, Queensland State, Australia. The use of speed and delay. Water is supplied to the nozzle boom by
simulated rainfall provides greater flexibility and control of pumping from an externally located tank. De-mineralised
the fundamental rainfall parameters such as intensity and water spiked to replicate typical rainfall quality in the region
duration and thereby helps to eliminate some of the variables, was used for the simulation. The simulator was designed to
which inherently increases the complexity of stormwater re-produce natural rainfall events as closely as possible.
quality research. It can also overcome the constraints of Important characteristics of natural rainfall as noted in
variability and random nature associated with natural rainfall literature are rainfall intensity, drop size distribution and
events. Consequently, the use of simulated rainfall enables kinetic energy (Best, 1950; Hudson, 1963; Rosewell, 1986). The
the generation of a large volume of data in a relatively short speed and delay of the nozzle boom was calibrated in order to
period of time (Herngren, 2005). make sure it simulates the selected rainfall intensities. It was
verified that the drop size distribution and kinetic energy of
each event is closely replicated. Details on the design and
2. Materials and methods operation of rainfall simulator can be found in Herngren
(2005).
2.1. Study area
2.3. Experimental design and sample collection
Three urban road surfaces were selected from the Gold Coast
region, Queensland State, Australia. Gold Coast has a 2.3.1. Simulation intensities and durations
sub-tropical climate with wet summers and dry winters. Water quality research is primarily focused on long-term
All three sites were located in typical urban residential pollutant yield from catchments. Pollutant yield could be
areas. Characteristics of the three sites are given in Table 1. influenced by each and every significant storm event within

Table 1 – Characteristics of road sites

Site Living standard/Urban-form Slope of the Texture depth of

road (%) the surface (mm)

Lauder Ct. Medium-socio-economic single detached 10 0.66

housing
Gumbeel Ct. Medium-socio-economic duplex housing 7.2 0.92
Piccadilly Pl. High-socio-economic single detached housing 10.8 0.83
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Fig. 1 – Sketch of rainfall simulator. (Herngren, 2005).

Table 2 – Simulation durations and intensities

Intensity (mm/h) Durations (min) 2.3.2. Field investigations

Study sites on the selected roads were identified so that they
1 2 3 4 are straight sections about 50 m long with uniform slope.
Seven plot surfaces equidistant from the road edge and
20 10 20 30 40
40 10 15 25 35
centre line and of area 3 m2 (2  1.5 m) were demarcated at
65 10 15 20 30 each site. The relative fraction of different pollutants was
86 10 15 20 25 assumed to be uniform throughout the length and width of
115 5 10 15 20 the road as the traffic volume is relatively low and the
133 5 10 15 20 pollutant re-distribution would be limited. The total amount
of pollutant build-up on the road surfaces was determined by
collecting samples using a vacuum cleaner from the most
downstream plot at each study site. The amounts collected
were 32.6, 9.3 and 10.6 g from Gumbeel Ct., Lauder Ct. and
a given period of time rather than a small number of Piccadilly Pl. sites, respectively. The respective samples
uncommon events with high average recurrence interval belonged to 77, 27 and 36 antecedent dry days of build-up.
(ARI). In this context, investigation of pollutant wash-off for a The particle size distributions of the collected samples are
wide range of storm events is important. A study was shown in Fig. 2.
conducted to identify the range and variation of rainfall The validity of using a vacuum cleaner for collecting
intensities within the region. This was done by statistically pollutant samples has been confirmed in previous research
analysing maximum 5 min rainfall intensities obtained (Herngren, 2005; Vaze et al., 2000). A calibration study found
from every significant storm event during a 5-year period that the efficiency of the vacuum system for collecting and
(1999–2003). In order to encompass the applicable range of retaining particulates was within satisfactory range. The
intensities, the six rainfall intensities as shown in Table 2 minimum efficiency recorded was 92% for 1–10 mm particle
were simulated. The rainfall durations were selected based on size range. The overall efficiency was 97%. The rainfall
results published by Herngren (2005). He observed that there intensities were simulated over each study plot starting from
was no significant wash-off of pollutants beyond a threshold the second most downstream plot and moving upstream for
value of rainfall duration. the next rainfall intensity. The runoff samples were collected
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3028 WAT E R R E S E A R C H 41 (2007) 3025– 3031

100
Gumbeel Ct.

Fraction Wash-off (FW )

20 mm/hr 40 mm/hr 65 mm/hr 86 mm/hr 115 mm/hr 133 mm/hr
Lauder Ct.
80 1
Piccadilly Pl.
0.8
Percentage

60 0.6
0.4
40
0.2
20 0
0 10 20 30 40
0 Rainfall Duration (min)
1 10 100 1000
Particle size (µm)

Fraction Wash-off (FW )

40 mm/hr 65mm/hr 86mm/hr 115mm/hr 133mm/hr
Fig. 2 – Particle size distribution of build-up samples. 1
0.8
0.6
using a catch tray and the vacuum system and stored in 0.4
drums as described by Herngren (2005). 0.2
0
2.4. Laboratory analysis 0 10 20 30 40
Rainfall Duration (min)
As suspended solids were adopted as the indicator pollutant,
the primary emphasis was to determine parameters such as 20mm/hr 40mm/hr 65mm/hr 86mm/hr 115mm/hr 133 mm/hr
Fraction Wash-off (FW )

1
total suspended solids (TSS) and particle size distribution.
Testing for TSS was undertaken according to Test Method No. 0.8
2540D (APHA, 1999). Particle size distribution was determined 0.6
using a Malvern Mastersizer S particle size analyser. The 0.4
analyser used was a reverse Fourier lens of 300 mm diameter
0.2
and was able to analyse particles in the range of 0.05–900 mm.
0
In this range, the manufacturer has specified a reading 0 10 20 30 40
accuracy of 72% of the volume median diameter (Malvern
Rainfall Duration (min)
Instrument Ltd., 1997).
Fig. 3 – Variation of fraction wash-off with rainfall intensity
and duration: (a) Gumbeel Ct. site, (b) Lauder Ct. site and
3. Results and discussion (c) Piccadilly Pl. sites.

Suitable analytical parameters were selected after an initial

trial analysis using all possible parameters. It was noted that
wash-off is influenced by rainfall intensity, rainfall duration surfaces. Secondly, though the initial pollutant availability in
and runoff volume. These three parameters highly correlate the three different sites was significantly different, wash-off
with each other and therefore the degree of influence they patterns are similar. The initial pollutant availability at
exert individually cannot be clearly discerned (Chiew and Gumbeel Ct. site was 32.6 g and it was 9.3 and 10.6 g at Lauder
McMahon, 1999; Chui, 1997; Mackay, 1999). Initial analysis Ct. and Piccadilly Pl. sites, respectively. This suggests that the
revealed that very little information can be gained by relating influence of initial pollutant availability on pollutant wash-off
wash-off to runoff volume. Therefore, rainfall intensity and processes is not significant.
duration was selected as the primary variables for the
analysis. Fig. 3 shows the variation of ‘fraction wash-off’ of 3.1. Mathematical replication of pollutant wash-off
pollutants for the three study sites. Fraction wash-off (Fw) is
defined as the weight ratio of cumulative washed-off pollu- Pollutant wash-off from an impervious surface is commonly
tants to the initially available pollutants (build-up). Definition replicated as an exponential equation in the form of (Sartor
of Fw enables to eliminate the influence of initially available et al., 1974).
pollutants on the wash-off process and thus the results from
W ¼ W0 ð1  ekIt Þ (1)
different sites can be compared.
From the information in Fig. 3, two main conclusions can be Different derivations of this equation have been used in
derived. Firstly, the highest Fw is in the range of 0.8 and 0.9 various stormwater quality models, such as, US EPA’s Storm-
and belongs to the 133 mm/h intensity rainfall simulated for water Management Model (SWMM) and US Army Corps’s
around 20 min duration. Reference to storm events in the STORM model (Huber and Dickinson, 1988; USACE, 1977).
study region, this is in the range of a 10 years ARI event. This In this study, the original exponential equation (Eq. (1))
would mean that the most common storm events are not proposed by Sartor et al. (1974) was tested in order to replicate
capable of removing all of the build-up pollutants on road observed wash-off patterns. The equation was re-written in
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WAT E R R E S E A R C H 4 1 (200 7) 302 5 – 303 1 3029

order to incorporate Fw: cleaner runoff. This suggests that a rainfall event has the
capacity to mobilise only a fraction of solids on the road
W
Fw ¼ ¼ ð1  ekIt Þ. (2) surface and once it reaches that capacity, relatively clean
W0
runoff results even though a significant fraction of pollutants
However, the equation did not replicate the observed wash- is still available. The equation proposed by Sartor et al. (1974)
off pattern satisfactorily. It is evident from Fig. 4 that the is based on the assumption that every storm event has the
fraction wash-off approaches a finite value o1 which varies capacity to remove all the available pollutants from that
with the rainfall intensity. This phenomenon was visually surface if it were to continue for an adequate duration. The
observed during the rainfall simulation where the latter part findings from the current study confirmed the need to modify
of most of the less intense rainfall events produces relatively the wash-off equation.
The exponential pollutant wash-off equation (Eq. (2)) was
modified by introducing the ‘capacity factor’ (CF) and can be
written as
W
Fraction Wash-off (FW )

1 Fw ¼ ¼ CF ð1  ekIt Þ. (3)
W0
0.8
CF will have a value ranging from 0 to 1 depending on the
0.6 rainfall intensity. However, other factors such as road surface
0.4 condition, characteristics of the available pollutants and slope
0.2 of the road may also have an influence on CF and are
0 discussed below.
0 10 20 30 40 50
Rainfall Duration (min) 3.2. Estimation of wash-off parameters

To use the modified wash-off equation (Eq. (3)), the parameters

Fraction Wash-off (FW )

1 k and CF must be estimated. The wash-off coefficient k is an

empirical parameter with units (mm1) and no direct physical
0.8
meaning. Water quality models such as SWMM use a constant
0.6 value for k. However, there is evidence to claim that k is site
0.4 specific (Millar, 1999). The value of k may vary with the
0.2 pollutant type, rainfall intensity, catchment area and catch-
0 ment slope (Alley, 1981; Alley and Smith, 1981; Millar, 1999).
0 10 20 30 40 50 However, the use of a constant value for k will reduce the
Rainfall Duration (min) complexity of the wash-off equation. It has been noted by
Huber and Dickinson (1988) that a constant value is used for
the SWMM model and it performs relatively well in the
estimation process. In the study, the best possible values for CF
Fraction Wash-off (FW )

1
and k were determined using the theory of least squares. Fig. 4
0.8
illustrates the replication equation developed and Table 3
0.6 shows the CF and k values determined for the different sites.
0.4 The validity of Eq. (3) was evaluated by analysing the mean
0.2 and coefficient of variation (CV). Mean was calculated by
averaging the ratio between predicted value to observed value
0
0 10 20 30 40 50 for each data point. CV was calculated by dividing the
standard deviation from the expected return, which is one.
Rainfall Duration (min)
The mean and CV for each site is given in Table 4.
Fig. 4 – Performance of the replication equation for pollutant According to Table 4, all three values for the mean are close
wash-off for: (a) Gumbeel Ct. site, (b) Lauder Ct. site and (c) to one and therefore, it can be argued that the overall
Piccadilly Pl. sites.

Table 3 – Estimated values for CF and k

Site Wash-off coefficient k Capacity factor CF

20 mm/h 40 mm/h 65 mm/h 86 mm/h 115 mm/h 133 mm/h

4
Gumbeel Ct. 5.6  10 0.20 0.48 0.50 0.50 0.73 1.00
Lauder Ct. 8.0  104 — 0.48 0.54 0.54 0.80 0.89
Piccadilly Pl. 8.0  104 0.30 0.45 0.49 0.49 0.66 0.94
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3030 WAT E R R E S E A R C H 41 (2007) 3025– 3031

Table 4 – Validity of the pollutant wash-off equation For rainfall intensities ranging from 40 to around 90 mm/h, CF
has a relatively constant value of 0.5. This indicates that the
Parameter Gumbeel Ct. Lauder Ct. Piccadilly Pl. rainfall intensities in this range have the capability to mobilise
only around 50% of the pollutants available. The D50 for the
Mean 1.12 0.98 0.98 initially available pollutants is in the range of 100–150 mm and
CV (%) 27 7 12 the D50 of the wash-off samples for the 40, 65 and 86 mm/h
rainfall intensities is in the range of 50–100 mm. This suggests
that most of the smaller particle sizes are subjected to wash-off
during these events and the rainfall intensities are not capable
1 of creating adequate turbulence to mobilise larger particles.
Gumbeel Ct. However, the upper limit of the constant CF (90 mm/h) could
0.8 Lauder Ct. change with the texture depth of the road and particle size
Capacity Factor ( C F )

distribution of the pollutants available. Rainfall events with

Picccadilly Pl.
intensity more than 90 mm/h have a greater capability to
0.6
mobilise solid pollutants. It is hypothesised that this is due to
the relatively high degree of turbulence in the overland flow.
0.4
The pollutant export study done in the same urban catchment
by Egodawatta et al. (2006) confirmed the higher mobilisation
0.2 capacity of high intensity rainfall events which results in
relatively higher pollutant concentrations and larger average
0 size of the wash-off particles.
0 20 40 60 80 100 120 140
Rainfall Intensity (mm/hr)

Fig. 5 – Variation of CF with rainfall intensity. 4. Conclusions

The outcomes from this research suggest that a rainfall event

has a specific capacity to mobilise pollutants and invariably
performance of the prediction equation is quite good.
remove only a fraction of the available pollutants. This
However, the CV values indicate that there are significant
confirms the need to modify the commonly adopted pollutant
errors in estimating each data point. The performance of the
wash-off equation for better replication of pollutant removal.
wash-off equation for Gumbeel Ct. data is poor whereas the
It is recommended that the typical exponential equation is
performance of the equation for Lauder Ct. and Piccadilly Pl.
modified by introducing an empirical term, referred to as the
are satisfactory. The variation between observed data and
capacity factor, CF. CF represents the rainfall event’s capacity
predicted data would be due to reasons such as the build-up
to mobilise pollutants from paved surfaces. Kinetic energy of
data being non-representative for the site and errors in the
the rainfall events and the turbulence created in overland
calculation of the equation parameters. Gumbeel Ct. site had
flow are the decisive factors influencing CF. High intensity
significantly high amount of pollutants. As such there can be
rainfall events can mobilise relatively coarser particles due to
a greater possibility of selecting a non-representative sample.
the creation of high turbulence in overland flow.
Considering the above, the most appropriate values for the
CF primarily varies with rainfall intensity. However, for
CF and k would be the values obtained for Lauder Ct. and
simplicity three rainfall intensity ranges were identified where
Piccadilly Pl. road sites. The constant k value of 8.0  104 is
variation of CF can be defined. For the rainfall intensities less
proposed for use in the prediction equation and CF values
that 40 mm/h, CF varies linearly from 0 to 0.5. For rainfall
could be averaged. However, care should be taken when using
intensities from 40 to around 90 mm/h, CF is a constant around
these values particularly when the initial pollutant avail-
0.5. Beyond 90 mm/h CF varies between 0.5 and 1.
ability is comparatively high.

R E F E R E N C E S
3.3. Understanding the wash-off process

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