Introduction

Despite recent reductions in point source pollution in China and many other countries, urban runoff pollution contaminated with road-deposited sediments (RDS) remains a considerable environmental problem (Bressy et al. 2012, Gasperi et al. 2014, Zhang et al. 2015a, b). It is generally accepted that RDS from impervious surfaces is an important carrier of pollutants in urban surface runoff (Pitt et al. 2005, Wijesiri et al. 2016a, Zhao et al. 2010). Therefore, the quantification and the prediction of RDS wash-off are critical for the estimation and the reduction of pollutant load in support of the design of urban storm water best management practices (BMPs) (Haddad et al. 2014, Wijesiri et al. 2016b, Yi et al. 2014).

One of the first methods proposed for the estimation of wash-off load is the event mean concentration (EMC) equation method (Sansalone and Buchberger 1997, Shen et al. 2016); however, it is difficult to use for predictions. A number of mathematical models have been developed to predict RDS wash-off, one of the earliest which is the original exponential equation method (Sartor et al. 1974). The exponential equation method is a function of the available mass and rainfall intensity. The amount of RDS wash-off is expressed in proportion to the surface runoff raised to a certain power. The basic form of this method is the core component of the Storm Water Management Model (Rossman 2007) and it has been adapted by many researchers (Soonthornnonda et al. 2008; Wang et al. 2011, Wijesiri et al. 2015b). Even though the exponential equation method has been used widely to predict RDS wash-off in urban areas, it does have some limitations. For example, it requires considerable sampling work for parameterization, which can be difficult because of the randomness of rain events. Furthermore, the parameters of the exponential equation generally vary with many factors, especially topography and rainfall characteristics; thus, uncertainties can occur in the model predictions for pollutant loads in different places appeared when using the same parameter set (Bonhomme and Petrucci 2017, Liu et al. 2012b). Therefore, a simple and effective method that could avoid the process of rainfall sampling and provide accurate predictions of wash-off load was needed.

RDS is an important carrier of pollutants and a source of total suspended solids (TSS) in surface runoff (Wijesiri et al. 2015a). The use of RDS for predictions of wash-off load simplifies the sampling process because RDS sampling is controllable. Some researchers have used the differences of RDS amounts or an RDS index to incorporate the RDS of different grain sizes when estimating wash-off loads (Vaze and Chiew 2002, Zhao et al. 2016). Although these methods have been used in other studies, their prediction capabilities have seldom been verified. Therefore, it is necessary to explore whether simple RDS-related methods could replace continuous sampling work or complex models in providing estimations of wash-off particle loads.

China promoted the “Sponge City” program in 2014, which was intended to overcome the problems of urban storm flooding and urban diffuse pollution (Gao et al. 2015, Mao et al. 2017; MOHURD 2015). However, RDS removal performance needs to be evaluated before and after low-impact development (LID) BMP engineering as part of the assessment of LID-BMP effectiveness (MOHURD 2015). For example, during the operation of LID-BMP constructions, the degradation of the treatment performance of infiltration systems due to clogging has been reported. Therefore, the particle loads during rainfall events should be evaluated to elucidate the long-term particle-trapping performance of infiltration systems.

It is generally acknowledged there is urgent need to provide engineers with a simple and effective tool for the estimation of RDS wash-off load at the LID-BMP design scale. Therefore, this study compared four methods used to estimate small-scale RDS wash-off load. Two were direct sampling or modeling methods: (1) the EMC equation method based on field observations and the exponential equation method based on observations of natural rainfall in a small area. The other two methods calculate wash-off load indirectly based on RDS: the RDS mass difference before and after rainfall event method based on field observations and the RDS index model based on the wash-off percentage of each RDS size fraction using simulated rainfall in a small area. This research had a number of objectives: (1) to compare and analyze the applicability of the four selected methods to the estimation of small-scale RDS wash-off load; (2) to find a simple and effective tool for the estimation of RDS wash-off load for storm water management engineers at the LID design scale; and (3) to validate the applicability of the indirect estimation of particle loads using static RDS.

Materials and methods

Study site description

The study sites were located in Longgang District in Shenzhen, China, which is a mixed of industrial and residential areas. The average annual rainfall of Longgang is 1933 mm and the mean annual temperature is 22.4 °C. The study area has a largely complete pipeline construction and sewage interception network that prevents domestic sewage from polluting the Longgang River; thus, urban runoff contaminated with RDS is one of the most important sources of pollution for the Longgang River during the rainy season.

A considerable amount of small-scale LID-BMP infrastructure will be constructed over the coming years in Shenzhen under the Sponge City program. Thus, RDS wash-off load must be evaluated to support the design of the urban LID-BMP constructions (MOHURD 2015). Following on-site investigations of land use, traffic characteristics, and street management, it was considered that a newly built area (NBA), built-up area (BUA), and conservation area (CA) could be taken as representative of areas modified by LID-BMP constructions. The main characteristics of the study catchments are listed in Table 1. The BUAs typically include the developed industrial and residential areas constructed over a decade ago. They have some open areas, high population density, and high traffic volumes, and the frequency of street cleaning is usually less than twice daily. NBAs represent semi-open sites built less than 10 years ago. They usually include the new residential districts where the traffic volume is low and the frequency of street sweeping is more than twice daily. The time over which an area has built up is the principal standard for determining whether it is categorized as an NBA or a BUA. CAs have high proportions of green space, and they represent typical undeveloped parts of the urban areas of Shenzhen. The locations of the study and of the sampling sites are shown in Fig. 1.

Table 1 Characteristics of the road study sites
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Fig. 1
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Study area and sampling site locations in Longgang District, Shenzhen, China. a represents the map of Shenzhen; b represents the map of Longgang District; c represents the map of study catchments and their surroundings. NBA newly built areas, BUA built-up areas, CA conservation areas

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Field experiment design of RDS sample collection and RDS wash-off

Field observation of RDS wash-off during rainfall events

Runoff samples were collected on 8/12/2016, 8/26/2016, 5/4/2017, 5/13/2017, and 5/15/2017 and categorized according to their average intensities: < 5 mm/h (low), 5–10 mm/h (medium), and > 10 mm/h (high) categories, respectively (Table 2). Samples were collected from the gully pits beside selected asphalt roadsides (Table 1). The drainage areas of RDS wash-off were 60, 200, and 150 m2 in NBA, BUA, and CA, respectively.

Table 2 Rainfall parameters for three rainfall events in the study area
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A stainless steel device was designed specifically based on the size of the gully pits for the sampling and the volume estimation of the surface runoff. Flow quantifying was assessed visually and the accuracy of the flow rates was verified before the device was used for monitoring runoff. A water gauge was installed in the device to observe the water level and to calculate the runoff volume. In addition, the wash-off samples were taken from the device continuously after the surface runoff began until no further runoff was generated. The first four samples were taken at 5-min intervals during the first 15 min after the surface runoff began and subsequent samples were taken at 10-min intervals. The collected samples were later analyzed for TSS (Americ 1971). The EMCs of wash-off particles are shown in Table 3.

Table 3 RDS and runoff characteristics for rainfall events in the study area
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RDS sample collection and grain size fraction

RDS samples were collected from the NBA, BUA, and CA 1 day before and 1 day after the five rain events, i.e., 8/12/2016, 8/26/2016, 5/4/2017, 5/13/2017, and 5/15/2017; the rainfall characteristics are listed in Table 2. RDS samples were collected from a 3 × 4-m area using a domestic vacuum cleaner (Philips FC8264) and then analyzed according to grain sizes. Using polyester sieves, the samples were sorted into particle size fractions of < 44, 44–62, 62–105, 105–149, 149–250, 250–450, 450–1000, and > 1000 μm (Zhao et al. 2010), which are typically referred to as clay, very fine sand, fine sand, medium sand, coarse sand, and very coarse sand, respectively (Sutherland 2003). The finest particles were removed from the vacuum system using a brush. Finally, to remove moisture, all the RDS samples were dried at 100 °C for 24 h. Then, they were weighed using an electronic scale immediately after removal from the oven. The RDS amounts both before and after the rain events, and the proportions of fine particles, are listed in Table 3.

Direct and indirect methods for estimation of wash-off loads

To find a simple and effective method for the quantification of small-scale RDS wash-off to support LID-BMP engineering, this study analyzed and compared the two direct and two indirect methods mentioned in Section 1. Concise results of the comparison of the four quantifying RDS wash-off methods are shown in Table 4. It should be noted that we assumed the TSS load of the runoff was equal to the RDS wash-off load in this study.

Table 4 A concise comparison of four quantifying RDS wash-off methods
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EMC equation method

EMCs were calculated by integrating the product of runoff rate and concentration and dividing it by total runoff volume (Kim et al. 2007). The total mass emission can be calculated as the sum of runoff volume and runoff concentration. This method has been used widely to calculate pollutant loads during storms (Ju et al. 2011; Qin et al. 2013). The equation is as follows:

$$ {M}_{\mathrm{w}}={\sum}_{i=1}^n{C}_i\times {V}_i, $$
(1)

where C i is pollutant concentration and V i is runoff flow rate discharged at time t.

Exponential equation method

In the exponential equations, wash-off is calculated based on the pollutants on the catchment surface of a given land use type under the flow conditions of a rainfall-runoff events (Rossman 2007). The equation forms the core element of the Storm Water Management Model and the Model for Urban Sewers and it has also been adapted for pollutant load estimation (Zheng et al. 2014; Soonthornnonda et al. 2008). The equation is as follows:

$$ W={C}_1{q}^{C_2}B, $$
(2)

where W is the amount of load (per unit area) (g/m2), C 1 is the wash-off coefficient, C 2 is the wash-off exponent, q is the runoff rate per unit area (mm/h), and B is the pollutant buildup in mass units.

RDS mass difference before and after rainfall event

This method uses a “black-box” approach, which ignores the particle transportation process, to compare the difference of RDS masses before and after rainfall event (Vaze and Chiew 2002). The equation is as follows:

$$ {M}_{\mathrm{w}}={M}_{\mathrm{before}}-{M}_{\mathrm{after}}, $$
(3)

where M before is the RDS mass before the rain event and M after is the RDS mass after the rain event.

RDS index model

The RDS index model was developed by Zhao et al. (2014). It estimates the RDS potential contribution to surface runoff based on the product of the source and transport factors of RDS. This method is based on a simulation experiment and it has also been adapted for pollutant load estimation (Zafra et al. 2017). The equation is as follows:

$$ {M}_{\mathrm{w}}={\sum}_{i=1}^n{M}_{\mathrm{i}}\times {F}_{\mathrm{w}\mathrm{i}}, $$
(4)

where M w is the total mass of RDS wash-off amount (g/m2), M i is the initial mass of RDS with a corresponding particle size on the surface (g/m2), F w is the percentage of each RDS size fraction washed off the surface (%), as mentioned in Zhao et al. (2014), and n is the number of particle size fractions.

Results

Results of direct observation and modeling methods

Field observation of surface runoff and estimation of wash-off load by the EMC equation

The variations of TSS concentrations, flow rate, and the estimations of particle wash-off loads by the EMC method during the studied rainfall events are shown in Fig. 2. The observed wash-off loads in the BUA, NBA, and CA ranged from 0. 05 to 69.32 g/m2 during the five events (Fig. 3). The TSS loads for the NBA, BUA, and CA were 0.09, 1.25, and 0.10 g/m2 on 8/12/2016; 0.66, 1.66, and 0.13 g/m2 on 8/26/2016; 5.05, 69.32, and 1.50 g/m2 on 5/4/2017; 1.75, 4.53, and 0.05 g/m2 on 5/13/2017; and 0.85, 7.4, and 0.21 g/m2 on 5/15/2017, respectively. Previous studies have indicated that TSS loads in surface runoff are affected by factors such as traffic volume, RDS amount, antecedent dry days, and rainfall characteristics (Alias et al. 2014; Vaze and Chiew 2002). This study found that particle wash-off loads were highest in the BUA because the BUA had the largest RDS amount. The greatest TSS load was found during the 5/4/2017 event, because the average rainfall intensity of that event was greater in comparison with the other rain events.

Fig. 2
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The particle loads during the wash-off process in five events. NBA newly built area, BUA built-up area, CA conservation area

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Fig. 3
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The estimated wash-off particle loads by EMC methods in five events. NBA newly built area, BUA built-up area, CA conservation area

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Field observation of surface runoff and estimation of wash-off load by the exponential equation

The exponential equations were calibrated and then used to estimate the wash-off loads of the five rain events. The parameters of the exponential equations used for the three sites are shown in Table 5, and the calculated wash-off loads were shown in Fig. 4. The discrepancies in the parameters (Table 5) associated with the different sites suggest that the pollutant parameters were affected by geographical characteristics (Baek et al. 2015). The particle loads in the NBA, BUA, and CA were 0.25, 3.27, and 0.04 g/m2 on 8/12/2016; 0.160, 1.570, and 0.035 g/m2 on 8/26/2016; 3.61, 67.43, and 1.76 g/m2 on 5/4/2017; 0.58, 6.24, and 0.16 g/m2 on 5/13/2017; and 1.45, 5.07, and 0.17 g/m2 on 5/15/2017, respectively (Fig. 4). The estimated wash-off loads were similar to the results obtained using the EMC method with errors ranging from 0 to 89%. The errors were derived only from the calibration processes, which explains why the estimated wash-off loads were similar.

Table 5 Calibrated parameters of exponential equations in study sites
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Fig. 4
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The estimated wash-off particle loads by exponential equations in five events. NBA newly built area, BUA built-up area, CA conservation area

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Results of indirect RDS-related methods

Prediction of wash-off loads in surface runoff by the RDS difference method

Variations in the RDS amount 1 day before and 1 day after the five rainfall events were observed (Fig. 5). The rainfall events on 8/12/2016, 8/26/2016, 5/4/2017, 5/13/2017, and 5/15/2017 reduced the total RDS mass obviously by 6.28, 1.91, 7.93, 6.20, and 5.37 g/m2 in the NBA; 6.04, 17.48, 11.08, 1.33, and 12.89 g/m2 in the BUA; and 3.44, 1.16, 12.74, 7.91, and 2.51 g/m2 in the CA, respectively. The removal amounts showed obvious differences related to different rainfall characteristics. The RDS removal amount varied from 1.16 to 17.48 g/m2, i.e., much higher than the wash-off loads estimated by the EMC method (Fig. 2). A possible reason for this is redeposition and resuspension of solids, resulting in some RDS particles being washed out of the study catchments and deposited in other areas; thus, the effective RDS wash-off loads could be much smaller. Both the RDS removal amount and the wash-off percentage in the 5/4/2017 rain event were higher than the RDS removal amounts in the other rain events because the long durations of the rain events resulted in thorough RDS wash-off and the low possibility of sediment redeposition. In general, RDS reductions based on RDS mass differences were much higher than the wash-off loads estimated by the EMC method.

Fig. 5
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Mass of RDS before and after rain events. Fw is the percentage of road-deposited sediments washed off the surface. NBA newly built area, BUA built-up area, CA conservation area

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Prediction of wash-off loads in surface runoff by the RDS index models

The total wash-off loads of RDS of different grain sizes calculated using the RDS index models ranged from 0.19 to 2.39 g/m2 (Fig. 6). The particle loads for the NBA, BUA, and CA were 0.32, 1.27, and 0.26 g/m2 on 8/12/2016; 0.30, 1.10, and 0.19 g/m2 on 8/26/2016; 4.09, 15.62, and 5.53 g/m2 on 5/4/2017; 6.63, 2.92, and 0.91 g/m2 on 5/13/2016; and 1.06, 2.57, and 0.58 g/m2 on 5/15/2016, respectively. The above results were much lower than obtained using the RDS difference method but similar to those derived using the EMC method, except in the CA. Because the RDS index model considered the RDS wash-off ability based on different grain sizes under different rainfall characteristics, its results were more reasonable and closer to those obtained using the EMC methods. The errors of the estimated wash-off loads in the CA were larger because of the lower RDS amount before rain events. In general, the results derived from the RDS index model were close to those obtained using the EMC method.

Fig. 6
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Wash-off load of particles calculated with RDS index models in three sites. NBA newly built area, BUA built-up area, CA conservation area

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Discussion

Reliability of prediction methods

For all methods, prediction reliability is essential in application to the quantification of runoff particle loads. To verify their reliability, a multimethod multisite approach is useful for elucidating the uncertainties of assessment results that occur commonly when a single method is used at a single site (Wang et al. 2011; Li et al. 2010). In this study, four methods with differing degrees of complexity were selected to quantify runoff particle loads at three sites during five natural rainfall events (Table 6). It was assumed that the results of runoff particle loads calculated by the EMC equation method could be set as standard results. When taking the results calculated by the EMC equation as standard results, the degree of agreement of the methods to the standard results in descending order was exponential equation method > the RDS index model > the RDS mass difference. The results of the RDS-related methods were generally higher than those derived using EMC methods or the modeling method, although the differences varied between events and between sites. The TSS obtained using the EMC method ranged from 0.05 to 69.32 g/m2. The results of the modeling methods (0.04 to 67.43 g/m2) based on continuous observations were similar to those of the EMC methods. The estimated loads of the RDS index models were between 0.19 to 15.62 g/m2, i.e., a less extreme trend than the observation results. This was because the mobility of particles and their associated pollutant concentrations are determined by the rainfall intensity. When choosing the parameter Fw for the load calculation, the average rainfall intensity can ignore the instantaneous variations. Therefore, this method might overestimate particle loads when the observation result is small and underestimate particle loads when the observation result is large. The results of the RDS mass difference method were much higher than derived by the EMC method because the former method ignores RDS redeposition. Generally, when the actual rainfall intensity was close to the standard rainfall intensity level, the results calculated using the multimethod multisite approach implied that the RDS index model method could be a useful tool for the estimation of runoff particle loads.

Table 6 Errors of exponential equation, RDS mass difference, and RDS index model
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Complexity of prediction methods

Simplicity and ease of use are prerequisites for a method to become popular in its application. Certain factors such as input data availability, including the flexibility of field sampling, parameter estimation through calibration, and the complexity of the simulation process determine the degree of complexity of prediction methods (Liu et al. 2012a, Rossman 2007; Sage et al. 2015). By estimating the wash-off loads at various sites under different rainfall characteristics, this study found that the degree of complexity of the studied methods in descending order was the exponential equation method > the EMC equation method > the RDS index model > the RDS mass difference. When taking both reliability and complexity into consideration, it was found that the RDS index model method was more advantageous than the other methods for the estimation of runoff particle loads.

Applicability of prediction methods for wash-off particle loads

As LID-BMP construction is becoming increasingly popular in China, a simple and effective tool is needed for the estimation of amount of RDS wash-off driven by natural rainfall events at the LID-BMP service scale. Typically, LID-BMP construction sites are often scattered and comprise small parcels of land with high spatial heterogeneity, which would involve considerable preliminary parameterization work and uncertainty in the calculated wash-off load results (Bonhomme and Petrucci 2017, Kanso et al. 2005; Wijesiri et al. 2016c). In this study, the RDS wash-off process was observed and the wash-off particle load in runoff was estimated at three sites at the LID-BMP service scale. The results suggest that the RDS index model could be used as a simple and effective tool for LID-BMP engineering.

Conclusions

This study used a multimethod multisite approach to compare and analyze the applicability of four methods for quantifying small-scale wash-off particle load in runoff. The four methods (i.e., the RDS mass difference before and after rainfall event method, the EMC equation method, the exponential equation method, and the RDS index model) were applied to estimate the particle load in runoff during five natural rainfall events in three urban areas in Longgang District (Shenzhen, China). When taking the results calculated by the EMC equation as standard results, the degree of agreement of the methods with the standard results in descending order was exponential equation method > RDS index model > RDS mass difference. When considering all factors (e.g., flexibility of field sampling, number of parameters, and complexity), the degree of complexity of the studied methods in descending order was exponential equation method > EMC equation method > RDS index model > RDS mass difference. Consequently, with consideration of the applicability of the prediction methods to LID-BMP engineering, the results suggested that the RDS index model could be adopted as a simple and effective tool for supporting the design of urban storm water BMPs.