Using a Multimedia Aquivalence Model to Evaluate the Environmental Fate of Fe, Mn and Trace Metals in an Industrial City, China

: The rapid expansion of urban impervious surface areas complicates urban-scale heavy metal circulation among various environmental compartments (air, soil, sediment, water, and road dust). Herein, a level III steady-state aquivalence model evaluated the fate of heavy metals in Nanjing, China. Iron was the most abundant heavy metal in all environmental compartments, while cadmium was the rarest. Most simulated concentrations agreed with measured values within three logarithmic residuals. In the simulated heavy metal cycle, industrial emission contributed almost the entire input, whereas sediment burial was the dominant output pathway. The transfer ﬂuxes between bottom sediment and water were the highest. Thereinto, the contribution of sediment resuspension for Fe and Mn was signiﬁcantly higher than that to the other metal elements, which could partly explain why Fe and Mn are the major blackening ingredients in malodorous black rivers. Road dust was also an important migration destination for heavy metals, accounting for 3–45%, although soil and sediment were the main repositories of heavy metals in the urban environment. The impact of road dust on surface water should not be neglected, with its contribution reaching 4–31%. The wash-o ﬀ rate constant W for road dust–water process was proved to be consistent with that for ﬁlm–water and was independent of the type of heavy metals. Sensitivity analysis highlighted the notable background value e ﬀ ect on Fe and Mn.


Introduction
Urban streams, rivers, and lakes are the final link of the urban water cycle. They receive a variety of point source and diffuse pollutants from other urban environmental media [1], including atmospheric deposition [2][3][4], soil erosion [5,6], and tailwater discharge [7][8][9]. Consequently, the receiving water readily deteriorates and even turns black and malodorous. As the city grows, the hardened impermeable area of urban roads is constantly expanding. In Shenzhen, it has been found that, when the impermeable area of the urban watershed exceeds 36.9%, irreversible river water quality degradation will occur [10]. In Korea, it is suggested that the proportion of the impervious surface area should be controlled within 10% in watersheds to mitigate water quality degradation [11]. Although the threshold of the impervious surface impact on stream health varies at different locations, the impact of urbanization on water quality in watersheds has been increasing in recent years [12]. Road dust accumulated on impervious surface areas can absorb various pollutants under the influence of intrinsic and extrinsic factors [13]. The contribution of urban runoff caused by rain wash-off to river water pollutants cannot be ignored [14,15]. Accordingly, road dust has gradually become a major environmental phase potentially threatening the urban water environment. In addition to exogenous

Characteristics of the Study Area
Located in the lower reaches of the Yangtze River in southeast coastal area of China (118 • 22 E-119 • 14 E, 31 • 14 N-32 • 37 N), Nanjing city has a subtropical monsoon climate with four distinct seasons and abundant rainfall. The average annual rainfall is 1106.5 mm, the relative humidity is 76%, and the annual average temperature is 15.4 • C. The terrain is relatively flat. The flow rates of urban rivers are slow. The black and odorous water bodies are easy to form. In addition, Nanjing is a nationally important comprehensive industrial production base with a GDP totaling 95.15 billion dollars in 2011. Nanjing has a high electronic chemical production capacity, a very large vehicle manufacturing scale, and advanced rail transit equipment and power grid industries. In this study, five environmental media, namely air, soil, water, sediment, and road dust, were selected. Road dust collection and heavy metal content determination were conducted by our research group.

Collection of Road Dust and Determination of Heavy Metal Content
As the impervious surface of Nanjing city is relatively concentrated, the locations of the sampling points were set based on the land use type of the city. In total, 23 road dust sampling points were arranged, and each sampling point was cleaned with a brush to collect approximately 300 g samples, which were then transferred to a polyethylene sealed bag with a plastic shovel. The samples were sent to the laboratory as soon as possible after collection. The bulk samples were separated by an electric vibrating machine with a series of nylon screens with mesh openings of 250, 125, 75, and 37 µm overlaid in sequence on the machine. About 150 g dried bulk sample was put on the top screen with mesh openings of 250 µm. When the electric vibrating machine started, the particles were sieved though the series overlaid screens and separated into sub-samples (250-500, 125-250, 75-125, 37-75, and <37 µm). The heavy metal content was tested after the bulk and sub-samples were freeze-dried. According to the detection method of national standard GB15618-1995, 0.5 g samples were digested with hydrofluoric, nitric and perchloric acids and aqua regia. Cadmium (Cd), copper (Cu), nickel (Ni), lead (Pb), and zinc (Zn) were detected by inductively coupled plasma mass spectrometry (ICP-MS). Chromium (Cr), manganese (Mn), and iron (Fe) were detected by inductively coupled plasma optical emission spectrometry (ICP-OES).
For the air, soil, water, and sediment, heavy metal concentration data were collected through literature research. Descriptive statistical results of the reference data, including arithmetic mean (AM), geometric mean (GM), median, minimum value (Min), maximum value (Max), number (N), and standard deviation (SD), are provided in the Supplementary Materials (Table S1). Table 1 is a partial summary of the descriptive statistics results. and road dust, in Nanjing, China. The migration and transformation processes involved in this model are shown in Figure 1, including atmospheric dry and wet deposition, diffusion, sediment resuspension and deposition, road dust wash-off, etc.
Atmosphere (1) Road dust (5) Surface water (2) Sediment ( The basic principle of the multimedia model is the law of mass conservation. The modeling basis consists of establishing a series of mass balance equations for the pollutants in the study area. In this study, metal circulation was assumed to be stable. That is, for the five main environmental compartments in the system, the inflow fluxes are equal to the outflow fluxes. The metal flux exchanges between adjacent compartments were calculated separately using the aquivalence approach (N = D × Q ). Based on the conceptual model, the mass balance equation for each compartment is summarized in Equations (1)- (5).  The basic principle of the multimedia model is the law of mass conservation. The modeling basis consists of establishing a series of mass balance equations for the pollutants in the study area. In this study, metal circulation was assumed to be stable. That is, for the five main environmental compartments in the system, the inflow fluxes are equal to the outflow fluxes. The metal flux exchanges between adjacent compartments were calculated separately using the aquivalence approach (N = D × Q). Based on the conceptual model, the mass balance equation for each compartment is summarized in Equations (1)- (5). Water: Soil: Water 2020, 12, 1580 5 of 16 Road dust: In the equations above, N (mol/h) is the transfer flux, D (m 3 /h) is the transport parameter of the pollutant, and D reflects the speed of mass transfer in a process. The higher the D value is, the higher the transmission rate is. The equilibrium criterion, aquivalence (Q, mol/m 3 ), was proposed to replace fugacity, and Z (dimensionless) is the fugacity capacity. When the Z value is high, the corresponding fugacity increases little after the pollutant is absorbed by the compartment, and the pollutant tends to remain in the compartment; otherwise, it tends to escape. The molar concentration (C, mol/m 3 ) is the product of the aquivalence Q and fugacity capacity Z (C = Z × Q). E A and E W refer to the amounts of heavy metal pollutants discharged into the air and water in Nanjing, respectively (Table S2). The model initialized the compartmental (water, soil, sediment, and road dust) concentrations to the corresponding background values. The initial concentrations in the air compartments were 0.
The Z value for heavy metals in road dust, as particle-sorbed chemicals, is the same as that for aerosols whose major source for heavy metals is the re-suspended road dust [60]. As for those environmental compartments in direct contact with water, the Z values for heavy metals in soil, sediment and SPM was calculated based on the partition coefficients summarized in the supplementary materials (Table S3). In light of the film-water transfer process in the fugacity model, the mass transfer coefficient, k rw (m/h), of the road dust-water process, is described by k rw = T r × W, where T r is the road dust thickness (m) and W is the wash-off rate constant (h −1 ). To estimate a reasonable value applicable to steady state rather than event-specific conditions, we determined W by dividing the total amount of contaminants into five ranges of grain size (250-500, 125-250, 75-125, 37-75, and <37 µm) of road dust washed out by the one unwashed.
where P i is the wash-off percentage of road dust on a grain size fraction i (%), M i is the mass of a particular grain size fraction per unit area (mg/m 2 ), and C i is the measured concentration of the metal in the road dust with a grain size i (mg/kg). The wash-off percentages of road dust on each grain size fraction from impervious surface was determined on the basis of the mean mass load per unit area (around 20 mg/m 2 ) [39]. According to the transport factor F w (%) [40], P i for the five grain size fractions (250-500, 125-250, 75-125, 37-75, and <37 µm) was estimated to be 6%, 11.6%, 18%, 40%, and 68%, respectively. With regard to other parameters associated with air, water, soil, and sediment, they were determined pursuant to empirical parameters listed in the Supplementary Materials. MATLAB R2019a was run to calculate the simulated concentrations in five environmental compartments (see the MATLAB Live Script in the Supplementary Materials).
As shown in Table 2, the calculated results are close to the wash-off rate constant of organic pollutants (0.25) [61]. Therefore, the rate constant is also applicable to heavy metals in road dust and is not affected by the chemical properties of pollutants. However, we do not consider residual in the rainwater pipe network or storm water treatment.

Sensitivity Analysis
Sensitivity analysis was performed to assess how each input parameter affects the model output and to identify the most influential inputs. The sensitivity coefficient (SC) was calculated as the proportion of the change in output compared to that in the tested parameters by considering their ranges as follows: where X 1.01 indicates that the input parameter is increased by 1%, that is, the value of the parameter is 101% of its mean. Y 1.01 represents the output of the model when the test parameter is increased by 1%.

Model Parameterization for Nanjing
Model parameters involving environmental and physicochemical parameters were obtained from the current relevant literature and databases and were used in the model to simulate the fate and transport of heavy metals in Nanjing. Herein, a total surface area of 6.41 × 10 9 m 2 was selected. The air compartments were defined at 1000 m according to previous studies [62]. The density of the total suspended particulates was an empirical value of 1.5 × 10 15 µg/m 3 [63]. The water area covered 7.42 × 10 8 m 2 with an average depth of 2.48 m [64]. A depth of 10 cm was assumed for the sediment underlying the water. The urban soil and impervious surface areas were 3.08 × 10 9 and 2.10 × 10 9 m 2 , respectively ( Figure 2). where X1.01 indicates that the input parameter is increased by 1%, that is, the value of the parameter is 101% of its mean. Y1.01 represents the output of the model when the test parameter is increased by 1%.

Model Parameterization for Nanjing
Model parameters involving environmental and physicochemical parameters were obtained from the current relevant literature and databases and were used in the model to simulate the fate and transport of heavy metals in Nanjing. Herein, a total surface area of 6.41 × 10 9 m 2 was selected. The air compartments were defined at 1000 m according to previous studies [62]. The density of the total suspended particulates was an empirical value of 1.5 × 10 15 µg/m 3 [63]. The water area covered 7.42 × 10 8 m 2 with an average depth of 2.48 m [64]. A depth of 10 cm was assumed for the sediment underlying the water. The urban soil and impervious surface areas were 3.08 × 10 9 and 2.10 × 10 9 m 2 , respectively ( Figure 2).

Model Simulation and Verification
The pre-processed data involving road dust, soil, atmospheric fine particulate matter (PM 2.5), surface water, sediment, and suspended particulate matter (SPM) are summarized in Table 3. The iron concentration is the highest in all environmental compartments listed, while cadmium has the lowest concentration. This is basically in line with the abundance of elements in the crust. Compared with the background values for river water in the Yangtze River system [65], the concentration proportions of Fe and Mn were not more than 0.5 (0.31 and 0.32, respectively), while the value for Cd was as high as 43.68. For the solid media, including road dust, soil, sediment, and suspended particles, the Cd concentration was 2.09-13.65 times the soil background value [66], while the Fe and Mn variations were small (1.16-2.15 and 1.04-1.64, respectively). This suggests that iron and manganese are less affected by human activities, which implies that, compared with Cd, Fe and Mn are greatly influenced by the initial value of the model-the background value. Furthermore, different environmental media are affected by human activities to different degrees. Many countries

Model Simulation and Verification
The pre-processed data involving road dust, soil, atmospheric fine particulate matter (PM 2.5), surface water, sediment, and suspended particulate matter (SPM) are summarized in Table 3. The iron concentration is the highest in all environmental compartments listed, while cadmium has the lowest concentration. This is basically in line with the abundance of elements in the crust. Compared with the background values for river water in the Yangtze River system [65], the concentration proportions of Fe and Mn were not more than 0.5 (0.31 and 0.32, respectively), while the value for Cd was as high as 43.68. For the solid media, including road dust, soil, sediment, and suspended particles, the Cd concentration was 2.09-13.65 times the soil background value [66], while the Fe and Mn variations were small (1.16-2.15 and 1.04-1.64, respectively). This suggests that iron and manganese are less affected by human activities, which implies that, compared with Cd, Fe and Mn are greatly influenced by the initial value of the model-the background value. Furthermore, different environmental media are affected by human activities to different degrees. Many countries and organizations have developed sophisticated systems of standards for controlling the discharge of pollutants to air, water, and soil. However, emission standards for pollutants associated with urban street dust, such as restrictions on the use of heavy metals in tires and brake pads, are lacking. The Fe, Mn, Zn, Cr, Ni, Cu, Pb, and Cd metal element concentrations simulated by the multimedia aquivalence model were compared with observed concentrations as follows (Figure 3). The difference between the simulated and measured logarithmic molar concentrations did not exceed 3. This indicated that the model can simulate the heavy metal concentration in various environmental compartments successfully. Nevertheless, the largest cadmium variation in road dust reached 2.96. This might be related to the uncertainty of the input parameters, most of which were obtained from the literature and not from specific field investigations for the purpose of modeling [25,31]. Consequently, the sensitivity of the input parameters is examined below. For the five environmental compartments, the average logarithmic residual errors of air (1.60), soil (0.70), sediment (1.27), and road dust (0.32) were lower than that of water (2.03). This was consistent with the results of a previous study [68]. It is speculated that the larger deviation observed for the aqueous phase may be attributed to the assumption that the water depth remained consistent, and the water was uniformly mixed. Moreover, most of the simulated concentrations were higher than the measured concentrations, which might be because the maximum allowable emission concentration is used for the simulated pollutant emission concentration, and the emission amount varies from industry to industry.

The Transport and Fate of Fe, Mn, and Trace Metals in the Urban Multimedia Environment
The transfer flux N (mol/h), the product of the aquivalence Q (mol/m 3 ) and the transport or

The Transport and Fate of Fe, Mn, and Trace Metals in the Urban Multimedia Environment
The transfer flux N (mol/h), the product of the aquivalence Q (mol/m 3 ) and the transport or transformation parameter D (m 3 /h), describes the transport and fate of heavy metals in urban environments. For the whole open environmental system, the simulation results reveal that, out of all the pathways, industrial atmospheric pollutant emissions occupied almost all the heavy metal inputs, while sediment burial (77.52%) was the main output for most heavy metals. This was consistent with a study in an oilfield [25]. Water advection outflow and infiltration into groundwater accounted for 13.59% and 8.89% of the output fluxes, respectively. Diffusion into the stratosphere and air advection outflow contributed little to the output flux. For the exchange between adjacent environmental media in the system, the transport fluxes varied greatly among the different metals. The iron flux was the highest, reaching 117,585 mol/h. Nevertheless, the main transport flux was contributed by the interaction between the sediment and overlying water (Figure 4a). The migration of heavy metals from the water phase to the sediment phase was dominant (41%), but there was still a difference among the different metals, with higher proportions for cadmium (46.37%) and chromium (45.15%). Thus, sediment burial is not the best way to treat heavy metal pollutants. It is important to explore alternative strategies to inhibit the release of heavy metals from sediment.

The Transport and Fate of Fe, Mn, and Trace Metals in the Urban Multimedia Environment
The transfer flux N (mol/h), the product of the aquivalence Q (mol/m 3 ) and the transport or transformation parameter D (m 3 /h), describes the transport and fate of heavy metals in urban environments. For the whole open environmental system, the simulation results reveal that, out of all the pathways, industrial atmospheric pollutant emissions occupied almost all the heavy metal inputs, while sediment burial (77.52%) was the main output for most heavy metals. This was consistent with a study in an oilfield [25]. Water advection outflow and infiltration into groundwater accounted for 13.59% and 8.89% of the output fluxes, respectively. Diffusion into the stratosphere and air advection outflow contributed little to the output flux. For the exchange between adjacent environmental media in the system, the transport fluxes varied greatly among the different metals. The iron flux was the highest, reaching 117,585 mol/h. Nevertheless, the main transport flux was contributed by the interaction between the sediment and overlying water (Figure 4a). The migration of heavy metals from the water phase to the sediment phase was dominant (41%), but there was still a difference among the different metals, with higher proportions for cadmium (46.37%) and chromium (45.15%). Thus, sediment burial is not the best way to treat heavy metal pollutants. It is important to explore alternative strategies to inhibit the release of heavy metals from sediment.  The mass distribution rule of each heavy metal was basically in agreement with the concentration distribution ( Table 3). The total mass of iron accumulated in the various environmental compartments was still the largest, reaching 60 billion tons, followed by manganese (3 billion tons). Cadmium had the smallest mass, with only 350,000 tons. However, as shown in Figure 4b, the mass proportion of each environmental phase has a certain regularity. Soil and sediment were the largest sinks of heavy metals in the urban environment, accounting for 27-51% and 13-68%, respectively. It also suggests that sediment and soil can be difficult to clean thoroughly once contaminated with heavy metal pollutants. Road dust was also an important migration destination for heavy metals, accounting for 3-45%. This indicates that impermeable roads are a significant place for metal accumulation, which is ignored in numerous studies [23,68,69]. Hence, targeted restoration measures should be developed and taken for the sustainable development of the city. In contrast, the masses for the water and air phases are negligible.

Sensitivity Analysis
The sensitivity of 25 heavy metal parameters was identified. As shown in Figure 5, compared with the other environmental media, the number of highly sensitive parameters for the heavy metal concentrations in the air phase is much lower. Only the atmospheric background concentration (C A ) and advection output rate (Q 10 ) significantly affect the heavy metal concentration in the gas phase. The water and sediment phases both have almost the same parameter sensitivity except the density and background value. Interestingly, there are several common parameters that have opposite effects on both phases. They include the partition coefficients between sediment and water (K se ) and between suspended particles and water (K p ), sediment deposition rate (G_ SD ), molecular diffusion coefficient in sediment pore water (B 4 ), and volume fraction of solids in water (v 23 ). This may occur due to the dynamic equilibrium of heavy metals between the aqueous phase and sediment. For road dust and soil, the response of the heavy metal concentration to the partition coefficients (K so ) is still positive, but for the parameters related to wash off and erosion (W and G SW ), the response is negative. Iron and manganese are less sensitive to most parameters compared to the other elements. However, this is the opposite for the background value and density. This may occur because the soil background values of Fe and Mn in the model were much higher than the concentration changes caused by transfer and transformation.

Distribution and Migration of Heavy Metals Among Multimedia in Urban Environment
Although soil and sediment are the main repositories of heavy metals in the urban environment, the total amount of heavy metals in urban street dust cannot be ignored, with a mass fraction ranging from 3.2% to 44.9%. However, many studies on multi-media models have done little to study this increasingly important environmental phase [23,36]. Even when studied, most researchers have focused on organic film attached to impervious road surfaces, including polychlorinated biphenyls (PCBs) [70] and polycyclic aromatic hydrocarbons (PAHs) [35], with little research on heavy metals. As for toxic heavy metal-lead, its mass load of street dust is almost half that of sediment, probably due to its extensive sources including automobile exhaust, brake pad wear, tire wear, paint, and mining emissions [71][72][73]. Moreover, lead was accumulated more than cadmium, copper, and zinc. This was consistent with the research results in Xi'an, China [74]. Unfortunately, this study only considered the influence of weather on the composition of road dust, including atmospheric deposition and precipitation scour, and did not calculate statistics on the heavy metal emissions from road dust, which will be carried out in the following studies. Nevertheless, the smallest accumulation of heavy metals in road dust is on the order of magnitude of one million tons. This can be attributed to the fact that the composition of heavy metals in road dust is influenced by both internal and external adsorption [13].
Although iron itself is not toxic, it and manganese (Mn), two of the abundant metals in the Earth's crust, are the major blackening ingredients in malodorous black rivers. Table 3 shows that the

Distribution and Migration of Heavy Metals among Multimedia in Urban Environment
Although soil and sediment are the main repositories of heavy metals in the urban environment, the total amount of heavy metals in urban street dust cannot be ignored, with a mass fraction ranging from 3.2% to 44.9%. However, many studies on multi-media models have done little to study this increasingly important environmental phase [23,36]. Even when studied, most researchers have focused on organic film attached to impervious road surfaces, including polychlorinated biphenyls (PCBs) [70] and polycyclic aromatic hydrocarbons (PAHs) [35], with little research on heavy metals. As for toxic heavy metal-lead, its mass load of street dust is almost half that of sediment, probably due to its extensive sources including automobile exhaust, brake pad wear, tire wear, paint, and mining emissions [71][72][73]. Moreover, lead was accumulated more than cadmium, copper, and zinc. This was consistent with the research results in Xi'an, China [74]. Unfortunately, this study only considered the influence of weather on the composition of road dust, including atmospheric deposition and precipitation scour, and did not calculate statistics on the heavy metal emissions from road dust, which will be carried out in the following studies. Nevertheless, the smallest accumulation of heavy metals in road dust is on the order of magnitude of one million tons. This can be attributed to the fact that the composition of heavy metals in road dust is influenced by both internal and external adsorption [13].
Although iron itself is not toxic, it and manganese (Mn), two of the abundant metals in the Earth's crust, are the major blackening ingredients in malodorous black rivers. Table 3 shows that the abundance of Fe, Mn, and other trace metals in five environmental phases was similar to that in the Earth's crust and soil background. Studies have shown that iron and manganese in river water are mainly derived from major clay minerals in sediment, including nontronite, saponite, and pennantite [21]. This was validated by the large transfer flux of iron and manganese between sediment and water (Figure 4a), which can be regulated by microorganisms [75]. Moreover, the exchange rates between sediment and water will increase with organic pollution of urban river [76]. As a result, it can be inferred that heavy metal, especially Fe and Mn, transfer between sediment and water in black and odorous water bodies will be more frequent. This will be beneficial to our further study of heavy metals in black and odorous water.

Effects of Heavy Metals in Multimedia on Urban Water Quality
The contributions calculated by the ratio of the fluxes from one medium compared to the total input fluxes quantify the sources of those metal pollutants associated with water quality impairment. The results indicate that despite the differences, endogenous sediment had the largest impact on urban water bodies (19.7-89.9% shown in Table 4). This may be affected by hydrodynamic conditions and bioturbation/bioirrigation [77,78]. This is the reason many studies have focused on the immobilization of heavy metals in sediment [79][80][81][82]. Research has shown that hydraulic mulches exhibit the highest release potential for heavy metals (4-70% of the total concentration), while netting/blanketing has the lowest release potential, particularly for Pb (0-8%) [83]. Furthermore, the main migration routes of the different metals from the sediment to the overlying water are also different. Among them, the surprising finding is that the main migration pathway for Fe and Mn is sediment resuspension. In particular, the iron proportion is as high as 17.3%. This also explains why iron and manganese are more likely to adhere to suspended particles and cause water to turn black. For the other metallic elements, such as Ni, Cu, Zn, and Cd, it has been suggested that resuspension events could cause water quality deterioration over time in both anoxic and oxic sediments [84]; notwithstanding, the main release behavior of these metal elements is diffusion. This is likely due to a combination of the fact that iron occurs at much higher concentrations than the other metals and that iron is transformed to its reduced (soluble) form at a much lower redox potential. Consequently, reductive dissolution is less effective at transforming particulate iron [85], followed by manganese and lead. The reason is that their dissolution conditions (low pH and oxidation-reduction potential (ORP)) are difficult to achieve in a natural neutral water environment. Atmospheric deposition did not contribute as much as sediment (1.57-10.78%), but it is still important for urban waters. This conclusion is also applicable to oligotrophic open oceans and alpine lakes [86][87][88]. Compared with wet deposition, the contribution of atmospheric dry deposition is smaller for the eight heavy metals studied, with the proportion ranging from 0.47% to 3.22%. This proportion is similar to that in Lake Tahoe, where dry deposition contributed 0.03-5.7% of heavy metals [88]. This indicates that deposition in Nanjing is dominated by wet deposition instead of dry deposition. Wet deposition of heavy metals is more susceptible to regional climate characteristics, especially precipitation patterns. The eastern coastal areas of China, such as the Pearl River Delta Region [89], are affected by monsoons and experience abundant rainfall, leading to an increase in wet deposition, while dry deposition of heavy metals tends to predominate in arid and semiarid areas inland [90]. In addition, the deposition flux of wet particles is much higher than that of dry particles, which also indicates that, although wet particle deposition has a larger influence on polluting the urban receiving water, it also has a larger positive effect on the removal of atmospheric particles. Regrettably, this model does not consider the difference between the dry and wet deposition fluxes of the different metal elements, which are often affected by more complex factors, such as the water solubility of metallic elements [91]. Therefore, parameters need to be added to further optimize it.
Compared with the contributions (18-50%) in some U.S. cities [85,92,93], the impact of urban nonpoint source pollution, including road dust and soil, is relatively similar. Nevertheless, for the eight heavy metals, which are commonly found in urban storm runoff [94,95], the proportion of heavy metals carried by road runoff exceeds that of point source tailwater discharge mainly from 82 industrial enterprises among the 13 districts and counties of Nanjing. Despite the fact that metal element concentrations in runoff can vary with the time, location, and intensity of rainfall [96], this result was in line with that of the greater Los Angeles region (CA, USA), where the annual cumulative loading of total copper, lead, and zinc from three watersheds (the Los Angeles River, Ballona Creek, and Dominguez Channel) far exceeded the pollutant discharge amount from industrial point sources such as power-generating stations and oil refineries [97]. As mentioned in the literature, unlike industrial point source pollution, which has fixed treatment sites and mature treatment technologies, the control and mitigation measures of urban nonpoint source pollution are generally still in the research stage [98][99][100] and are relatively lacking in practical applications. Therefore, urban road runoff should be given sufficient attention for management.

Conclusions
A multimedia aquivalence model coupled with road dust on impervious surfaces was applied to assess the fate and transport of Fe, Mn, Zn, Cr, Ni, Cu, Pb, and Cd in a developed industrial city of China. The results indicate that the model can simulate the observed concentrations well, with an average logarithmic residual smaller than 3. Iron was the most abundant heavy metal in five environmental compartments. In the simulated heavy metal cycle, the transfer fluxes between bottom sediment and water were the highest. Thereinto, the contribution of sediment resuspension for Fe and Mn was significantly higher than that to the other metal elements, which could partly explain why Fe and Mn are the major blackening ingredients in malodorous black rivers. Road dust was also an important migration destination for heavy metals, accounting for 3-45%, although soil and sediment were the main repositories of heavy metals in the urban environment. The impact of road dust on surface water should not be neglected, with its contribution reaching 4-31%. The wash-off rate constant W for the road dust-water process was proved to be consistent with that for film-water and was independent of the type of heavy metals. This study not only lays a foundation for the follow-up study on the migration and transformation of heavy metals in black and odorous water, but also couples road dust into the multi-media model properly, revealing its potential impact on urban water bodies, which is conducive to the sustainable development of urban water environment.
Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4441/12/6/1580/s1, Table S1: The descriptive statistics of observed concentration of metals in multimedia in Nanjing, Table S2: Discharge of heavy metal pollutants, Table S3: Summary of partition coefficients used in the model; MATLAB Live Script.