Simulation of the Impact of Urban Forest Scale on PM 2.5 and PM 10 based on System Dynamics

: In the context of ecological civil construction in China, a ﬀ orestation is highly valued. Planting trees can improve air quality in China’s large cities. However, there is a lack of scientiﬁc analysis quantifying the impact urban forest scale has on the air quality, and what scale is advisable. The problem still exists of subjective decision-making in a ﬀ orestation. Similar studies have rarely analyzed the long-term e ﬀ ect research of urban forests on air improvement. Using as an example, the city of Wuhan, this paper identiﬁes the regularity between particulate matter concentration and adsorption of sample leaves, and establishes a system dynamics model of "economy, energy and atmospheric environment.” By combining this regularity with the model, the long-term impact of forest scale on particulate matter and atmospheric environment was simulated. The results show that if the forest coverage rate reaches at least 30%, the annual average concentrations of inhalable particulate matter (PM 10 ) and ﬁne particulate matter (PM 2.5 ) can both reach the Grade I limit of national Ambient Air Quality Standard by 2050. The current forest cover is 22.9% of the administrative area. Increasing the forest cover by 600 km 2 would increase this percentage to 30% of the total area. In the long run (by the year 2050), however, we showed that this increase would only reduce the annual concentration of PM 2.5 and PM 10 by 1–2%. Therefore, about 90% of the concentration reduction would still rely on the traditional emission reduction measures. More other ecological functions of forests should be considered in a ﬀ orestation plan.


Introduction
Particulate matter (PM), including the inhalable particulate matter (PM 10 ) and fine particulate matter (PM 2.5 ), is harmful to human health [1]. In particular, PM 2.5 has a greater negative impact on human health. PM 2.5 can float in the atmosphere for a long time and spread on a large scale via atmospheric circulation [2]. Moreover, the large specific surface area of PM 2.5 allows it to easily adsorb heavy metals and toxic organic compounds, enter the human respiratory system, penetrate into the alveoli via blood, and subsequently, cause various illnesses, such as cardiovascular disease, respiratory disease, lung cancer or other diseases [3][4][5]. For every 10 µg/m 3 increasing in PM 2.5 , the death rate from cardiovascular disease and lung cancer increases by 6-8% [6]. Afforestation can play an important role in mitigation of PM pollution [7][8][9], aside from reducing emissions at the source [10]. China is now vigorously promoting the construction of an ecological civilization, where afforestation is highly

Leaf Sample Collection
Leaf sample collection is aimed at analyzing the relationship between PM concentration and adsorption on leaves per unit time, which is the key to setting the variables and supporting the subsequent simulation in SD.
Evergreen leaves have a better PM adsorption than fallen leaves [25]. According to a survey of plant diversity in Wuhan city [36], two kinds of evergreen broad-leaved trees (Cinnamomum Camphor and Magnolia Grandiflora), which are the most popular trees and convenient to collect, were selected as the research subjects. Elements such as weather, location, time, duration and tree species were taken into account in sample collection.

Location and Time of Sampling
We chose non-street trees in Huazhong University of Science and Technology (Figure 1). The trees were far away from the influence of road dust, which can better reflect the PM adsorption capability of leaves in the overall pollution background during a period of 20 days from 11-30 May 2019.  The data to be used in the research (in 2016) include:

1.
Socio-economic data: GDP (primary, secondary and tertiary production) and energy consumption (coal, oil products, gas and non-fossil energy consumption); 2.
Atmospheric environment data: PM 10 , PM 2.5 annual concentration; SO 2 , NO x , VOCs, NH 3 , PM 10 and PM 2.5 emissions; and atmospheric chemical compositions of PM 10 and PM 2.5 ; 3.
Urban forest-related data: forest coverage area, coverage rate, PM 10 and PM 2.5 adsorption per unit area of forest.

Leaf Sample Collection
Leaf sample collection is aimed at analyzing the relationship between PM concentration and adsorption on leaves per unit time, which is the key to setting the variables and supporting the subsequent simulation in SD.
Evergreen leaves have a better PM adsorption than fallen leaves [25]. According to a survey of plant diversity in Wuhan city [36], two kinds of evergreen broad-leaved trees (Cinnamomum Camphor and Magnolia Grandiflora), which are the most popular trees and convenient to collect, were selected as the research subjects. Elements such as weather, location, time, duration and tree species were taken into account in sample collection.

Location and Time of Sampling
We chose non-street trees in Huazhong University of Science and Technology ( Figure 1). The trees were far away from the influence of road dust, which can better reflect the PM adsorption capability of leaves in the overall pollution background during a period of 20 days from 11-30 May 2019.

Leaf Quantity Collection
About 20 Cinnamomum Camphor leaves (2-3 branchlets) were collected each time, and every 10 leaves were taken as one sample, a total of two samples. Four leaves of Magnolia Grandiflora were collected, and two leaves were taken as a sample, a total of two samples. The leaves were gently placed into a plastic bag for storage. The amount of leaves can meet the requirements of the experiment.

Measure of Leaf's Floated PM
The PM was observed to be "floated PM" or "deposited PM" on the leaves. A floated PM means that the PM that is attached to the leaf surface and is easy to wash off with water. In contrast, the deposited PM has attached to the leaf surface for a long time and could not be easily washed away. As deposition is a time-related and complex process, it is hard to know how long the deposited particles were attached for, but we tried to analyze the time the floated ones were.
The floated PM was filtered by filter paper during gently washing the dust on the leaves. Then, the filter paper was dried and weighed with electronic analysis balance (precision 0.1 mg). The weight difference between filter paper after drying (W 1 is the weight of filter paper and PM) and filter paper before filtering (W 0 is the filter paper self-weight) is the PM adsorption (W 1 -W 0 ).

A Comparison of PM Concentration and Adsorption by Leaves
PM 10 and PM 2.5 adsorption were estimated at 50% and 95% of the measurement of floated PM respectively [37][38][39]. Thus, analysis between PM concentrations and their adsorptions was conducted correspondingly.

Correlation between PM Concentration and Leaf PM Adsorption
The higher the concentration, the higher the PM adsorption on leaves [13,14]. But concentration is a time-dependent value, and the accumulated duration time of floated PM is vague [15]. Therefore, we assumed that the duration time was 1 day, 2 days or 3 days respectively, and analyzed the correlation between background concentration of different time and the amount of floated PM to identify for how long the floated PM on the leaf accumulates.

Estimation on the Amount of PM Adsorbed by Green Leaves Per Unit Area
The Equation (1) was adopted to estimate the hourly PM adsorption per unit area of tree cover. The reason why the hourly PM retention should be determined is that the concentration is measured once per hour, and the daily or yearly value is the 24-h or 365-day average value, which is a mean instantaneous value. Thus, the retention, no matter if it is a day, a few days or longer, is a time-related and cumulative amount, and the two ('concentration and adsorption') should scale correspondingly with time duration.
where W is PM adsorption by sample leaves (g), M is the amount of PM adsorption per unit area (g m −2 h −1 ), H is the effective height of tree's foliage quantity (m), n is a multiple of sample leaf quantity per cubic meter (m −3 ) and D is the duration of PM retention by sample (h). With PM 10 or PM 2.5 concentration as the independent variable (X) and the corresponding adsorption per unit area of green leaves as the dependent variable (Y), the scattered diagram of 'concentration-adsorption' was drawn (Equation (2)). Then, calculated the regression coefficient to establish the equation and test the regression equation.
The expected result in this part was that the PM 10 and PM 2.5 adsorption would decrease with the decrease of background concentration, and the fitted regression curve would reflect the statistical feature. If an apparent exception appeared, possible problems in sample processing were examined and data with significant differences were excluded.

System Analysis
Many factors, like industrial production, energy consumption and environmental governance, will have impacts on atmospheric environment and PM concentration. The system boundary of the SD model involves urban energy consumption, industrial production, the atmospheric environment and forest scale.

Economic Subsystem
Under the city's development background, economic condition is the driving factor of the model. Industrial structure and emission per unit of polluting GDP determine the initial atmospheric emission status in the model. According to the social and economic development plan, the primary, secondary and tertiary production and their growth rate will be set. Over time, the industrial structure has been continuously optimized with the proportion of the secondary decreasing and the tertiary increasing. The emission per unit GDP, air pollutants and PM concentration will have been continuously reduced.

Energy Subsystem
Energy consumption determines emission level. With the optimization of the energy structure, the proportion of clean energy use will increase to reduce emissions from the source and reduce PM concentration.

Environmental Subsystem
Discharged pollutants are reduced through a series of end-treatment measures, including controlling various pollutant emissions, improving the management system and legal system, strengthening the supervision, etc. Additionally, large areas of tree cover can intercept and absorb PM. The basic systematic causal relationship is illustrated in Figure 2. The expected result in this part was that the PM10 and PM2.5 adsorption would decrease with the decrease of background concentration, and the fitted regression curve would reflect the statistical feature. If an apparent exception appeared, possible problems in sample processing were examined and data with significant differences were excluded.

System Analysis
Many factors, like industrial production, energy consumption and environmental governance, will have impacts on atmospheric environment and PM concentration. The system boundary of the SD model involves urban energy consumption, industrial production, the atmospheric environment and forest scale.
Under the city's development background, economic condition is the driving factor of the model. Industrial structure and emission per unit of polluting GDP determine the initial atmospheric emission status in the model. According to the social and economic development plan, the primary, secondary and tertiary production and their growth rate will be set. Over time, the industrial structure has been continuously optimized with the proportion of the secondary decreasing and the tertiary increasing. The emission per unit GDP, air pollutants and PM concentration will have been continuously reduced.
Energy Subsystem.
Energy consumption determines emission level. With the optimization of the energy structure, the proportion of clean energy use will increase to reduce emissions from the source and reduce PM concentration.
Discharged pollutants are reduced through a series of end-treatment measures, including controlling various pollutant emissions, improving the management system and legal system, strengthening the supervision, etc. Additionally, large areas of tree cover can intercept and absorb PM. The basic systematic causal relationship is illustrated in Figure 2. . Systematic causal diagram. B represents balance, which has a negative feedback loop. "+" is reinforcement and "−" is balance.

Variables and SD Flows
From the perspective of variable function of SD model, it has five categories: state, rate, auxiliary, constant and control variables. Figure 3 is the simplified SD flow diagram of economic, energy and the environmental (including urban forest) systems, which generalizes the basic feedback

Variables and SD Flows
From the perspective of variable function of SD model, it has five categories: state, rate, auxiliary, constant and control variables. Figure 3 is the simplified SD flow diagram of economic, energy and the environmental (including urban forest) systems, which generalizes the basic feedback relationship of all variables in the model. State variables include: three industrial productions, pollutant discharged volumes, PM 10 and PM 2.5 concentrations and energy consumptions. Main control variables include: industrial growth rates, energy growth rates, emission control factors, contribution rates of various precursors of PM 10 and PM 2.5 , etc. Their values were set comprehensively with the relevant plan objectives. A rate variable can change the state variable stock. Auxiliary variables are also very important. They connect other variables in the model and change under the influence of other variables. A constant is a stable objective quantity, or a quantity that does not change in a simulation. In the model operation, all variables and values will feedback dynamically (for variables, see Appendix B, Table A3). Key auxiliary variables, in value, are changed under other variable changes. They are the important nodes that connect subsystems in series. Key nodes and the corresponding equation numbers in the model are illustrated in Figure 3.  i.e., SO2, NOx, VOCs, NH3, primary PM2.5 and primary PM10. "Energy consumption" has four resources; i.e., coal, gas, petroleum and non-fossil energy. "GDP" is composed of the primary, secondary and tertiary production. Additionally, PM concentration includes PM2.5 and PM10 concentrations. They are classified as internal and external sources of PM concentrations.

Differentiation of Internal and External Sources of PM Concentration
The study target of the model was the whole area of Wuhan city. Industrial, energy structure optimization and environmental-end treatment were all urban internal actions. As PM pollution is not only from internal sources, external influence should not be ignored. We tried to solve the problem according to the research by Xue [40], by indicating the ratio of internal and external sources of PM2.5 of all provinces and key city cases in China. Wuhan contributed 60% as internal sources and 40% was from external sources. The ratio of PM10 is 70% from internal and 30% from external sources. Therefore, the average annual concentration of PM can be decomposed in the model. The internal PM concentration can be predicted in the city according to Wuhan development goals, and the external can be predicted according to the national macro goals, such as the national 13th Five-year Environmental Plan. The sum of the two concentrations is the average annual concentration of PM. In addition, the influence by tree quantity and quality on the concentration from external sources will also be reflected in the model. It generalizes the actual complex model which can be seen in Appendix B. In this figure, the "Discharged volume" includes six air pollutants; i.e., SO 2 , NO x , VOCs, NH 3 , primary PM 2.5 and primary PM 10. "Energy consumption" has four resources; i.e., coal, gas, petroleum and non-fossil energy. "GDP" is composed of the primary, secondary and tertiary production. Additionally, PM concentration includes PM 2.5 and PM 10 concentrations. They are classified as internal and external sources of PM concentrations.

Proportionality Factor
The proportionality factor is a specific air pollutant discharged volume per billion CNY of GDP. Its function is to convert the increment of GDP to the increment of a discharged volume quantitatively in a SD model dynamic simulation. The mathematical expression is shown as Equation (3) The energy adjustment factor is a ratio of the energy use after adjusting the energy structure and before adjusting it to the base year. The mathematical expression is shown as Equation (4), where, i stands for a specific air pollutant; ε is the energy consumption elasticity coefficient; and r (GDP) is the growth rate of GDP.
Energy ad justment f actor(i) Conversion Rate The conversion rate refers to the ratio of the contributed component derived from the annual discharged volume of a specific air pollutant to PM 10 or PM 2.5 volume and this discharged volume itself. In the SD model, this variable is a very important auxiliary one that constructs a link between the annual discharged volume and the annual PM 10 or PM 2.5 concentration in the quantitative relationship. The conversion rate is based on statistical data and does not have any actual physical and chemical significance, and it is only in the service for the SD model. The mathematical expression is shown as Equation (5), where, i is a pollutant and PM Volume is the mass of PM 10 or PM 2.5 existing over the city in the average state. Contribution rate indicates a pollutant to PM 10 or PM 2.5 determined by chemical composition.
Adsorption by Trees In SD model, six precursor air pollutants should be considered. According to the regularity in Section 2.2, we set a variable named Decrement per unit area of PM 10 or PM 2.5 , which represents the reduction of unit area in different PM concentrations (Equation (6)). Then, Equation (7) is for the adsorption levels of different pollutants. The a is the same coefficient in Equation (2), and i stands for a pollutant.
Decrement per unit area = a × Concentration Adsorption(i) = Forest cover × Contribution rate(i) ×Decrement per unit area (7)

Differentiation of Internal and External Sources of PM Concentration
The study target of the model was the whole area of Wuhan city. Industrial, energy structure optimization and environmental-end treatment were all urban internal actions. As PM pollution is not only from internal sources, external influence should not be ignored. We tried to solve the problem according to the research by Xue [40], by indicating the ratio of internal and external sources of PM 2.5 of all provinces and key city cases in China. Wuhan contributed 60% as internal sources and 40% was from external sources. The ratio of PM 10 is 70% from internal and 30% from external sources. Therefore, the average annual concentration of PM can be decomposed in the model. The internal PM concentration can be predicted in the city according to Wuhan development goals, and the external can be predicted according to the national macro goals, such as the national 13th Five-year Environmental Plan. The sum of the two concentrations is the average annual concentration of PM. In addition, the influence by tree quantity and quality on the concentration from external sources will also be reflected in the model. The initial values of GDP and PM 10 in the SD model were the data in 2001. The growth rate of industrial GDP, the growth rate of energy consumption and the end treatment factor of emission reduction were all based on the historical growth and reasonable estimation. The tested trend of GDP and PM 10 concentration from 2001 to 2015 was simulated and then checked with the real value. 2.
Sensitivity analysis. This refers to an uncertainty analysis that the degree of change in certain factors impact on one or a set of key indicators from the view of quantitative analysis. The industrial structure adjustment can influence on the simulation of the whole model, which can reflect the sensitivity of the model to a large extent. Therefore, we selected the coefficients of 'polluting GDP' in the economic subsystem, that is, α 2 and α 3 for sensitivity test, and adjusted one parameter at a time in a certain reasonable range. By the way, α 1 corresponds to agriculture, whose scale and influence are too small to analyze.

Scenarios Settings
Three scenarios were set up for the simulation: "non-forests, current forests and increased forests" with coverage rates of 0%, 22.88% and 30% respectively. The pollution emissions; social and economic development; air conditions; and PM adsorption by trees was simulated from 2016 to 2050 under the current sustainable development trend. Through the scenario simulations we tried to predict the time that the air quality of PM can reach the standard and how much effect of different forests on PM reduction will be.

Regularity Between PM Concentration and Adsorption by Leaves
As already stated, leaves were collected during a period of 20 days from May 11 to May 30 in 2019, with the exception of the rainy days on 12, 15, 25, 26 and 30. The PM 10 and PM 2.5 adsorptions by two kinds of trees were estimated at 95% and 50% of the sample weight measured, and the adsorption of the overall sample was estimated at the mean adsorption of the two kinds of leaves.
Based on Equation (1), the PM adsorption per unit area (M-PM) can be calculated by sample weight (W-PM). (1) Cinnamomum camphor. The newly planted trees were young and small. The tree height was 5 m (up to the quality standard of third types of arbor trees) [41]; the effective height of tree canopy was 3 m; and the leaf quantity per cubic meter was 10 times that of the sample. (2) Magnolia grandiflora. Tree height was 5 m; the effective height of the canopy was 3 m; and the leaf quantity per cubic meter was 15 times that of the sample. Therefore, M-PM can be calculated (Appendix A, Tables A1 and A2). For example, the sample adsorption weight of PM 2.5 in Cinnamomum camphor leaves was 0.0023 g. Since it was the cumulative amount of one day, 0.0023 g was divided by 24 h, which corresponds to the unit time of PM 2.5 concentration monitoring. Then, according to the volume of leaves, the sample size was multiplied by 30 to get 0.0029 g/m 2 , which represents the PM 2.5 capacity of Cinnamomum camphor leaves with canopy cover per unit area (1 m 2 ) per unit time (1 h).
From Tables A1 and A2, the correlations between the average PM 10 of the overall sample (M-PM 10 ) and the PM 10  concentrations on the given day, indicating that the higher probability of floated PM on the leaf surface was accumulated on one day (within 24 h), and the longer or shorter the time, the lower the correlation was.
On this basis, the linear correspondences of the 'concentration-adsorption' of PM 10 and PM 2.5 can be obtained according to Equation (2) (Figure 4). (1) The linear correspondence between PM 10 concentration and adsorption on Cinnamomum camphor leaf was Y = 0.00004X, and that between PM 10 concentration and Magnolia grandiflora was Y = 0.0001X. The linear regression between PM 10 concentration and the overall level per unit area was Y = 0.00009X (Figure 4a-c). (2) the regularities between PM 2.5 concentration and Cinnamomum camphor, Magnolia grandiflora and the overall level were Y = 0.00004X, Y = 0.0002X and Y = 0.0001X (Figure 4e-f).

Reality Check
The test results show ( Figure 5) that the maximum error between the real and simulated GDP was −10.1%, the minimum error was 0.5%, the average error rate was −1.4% and the correlation coefficient r = 0.99. The maximum error of PM10 concentration was −20.2%, the minimum error was −0.8%, the average error rate was −2.5% and the correlation coefficient r = 0.75. The forecast accuracy and correlation of GDP and PM10 were good, and the result of model reality check was reasonable.

Sensitivity Analysis
The weight coefficient of polluting GDP (α2 = 0.8 in Basic Group) was adjusted to 0.9 and 0.7

Reality Check
The test results show ( Figure 5) that the maximum error between the real and simulated GDP was −10.1%, the minimum error was 0.5%, the average error rate was −1.4% and the correlation coefficient r = 0.99. The maximum error of PM 10 concentration was −20.2%, the minimum error was −0.8%, the average error rate was −2.5% and the correlation coefficient r = 0.75. The forecast accuracy and correlation of GDP and PM 10 were good, and the result of model reality check was reasonable.

Reality Check
The test results show ( Figure 5) that the maximum error between the real and simulated GDP was −10.1%, the minimum error was 0.5%, the average error rate was −1.4% and the correlation coefficient r = 0.99. The maximum error of PM10 concentration was −20.2%, the minimum error was −0.8%, the average error rate was −2.5% and the correlation coefficient r = 0.75. The forecast accuracy and correlation of GDP and PM10 were good, and the result of model reality check was reasonable.

Sensitivity Analysis
The weight coefficient of polluting GDP (α2 = 0.8 in Basic Group) was adjusted to 0.9 and 0.7 respectively in test Group 1 and Group 2, with the change ranges of 12.5% and −12.5%. In Group 1, the predicted PM2.5 concentration changes were −0.6% in 2030 and −1.5 % at the end of 2050 compared to Basic Group. In Group 2 it changed 0.6% and 2.0 % correspondingly. In the other test, the value of α3 (α3 = 0.1 in Basic Group) was adjusted to 0.15 and 0.2 in test Group 1 and Group 2, increasing the range of 50% and 100%. In Group 1, the predicted PM2.5 concentration changed 2.0% and 7.1% in 2030 and 2050 compared to the Basic Group. In Group 2, it changed 4.1% and 13.2% correspondingly ( Table 1).

Sensitivity Analysis
The weight coefficient of polluting GDP (α 2 = 0.8 in Basic Group) was adjusted to 0.9 and 0.7 respectively in test Group 1 and Group 2, with the change ranges of 12.5% and −12.5%. In Group 1, the predicted PM 2.5 concentration changes were −0.6% in 2030 and −1.5 % at the end of 2050 compared to Basic Group. In Group 2 it changed 0.6% and 2.0 % correspondingly. In the other test, the value of α 3 (α 3 = 0.1 in Basic Group) was adjusted to 0.15 and 0.2 in test Group 1 and Group 2, increasing the range of 50% and 100%. In Group 1, the predicted PM 2.5 concentration changed 2.0% and 7.1% in 2030 and 2050 compared to the Basic Group. In Group 2, it changed 4.1% and 13.2% correspondingly (Table 1). From the sensitivity analysis results (Table 1), the change rate of the predicted PM 2.5 result was far less than the adjustment range of the coefficient for a simulation period of 15 to 35 years. Therefore, the stability of the complex system is good. By 2035, the PM 10 concentration in S2 will be 11.09 µg/m 3 lower than that in S1, and 10.66% better in the air quality. S3 will be 1.51 µg/m 3 lower than that in S2 and be better 1.45%. By 2050, PM 10 concentration in S2 will be 12.54 µg/m 3 lower than that in S1, and be better 12.06%. S3 will be 1.11 µg/m 3 lower than that in S2, and be better 1.07%. Similarly, in 2035, the PM 2.5 concentration in S2 will be lower by 8.00 µg/m 3 than in S1, and the corresponding air quality improves by 11.43%. It will be lower by 1.27 µg/m 3 in S3 than that in S2, and the improvement is 1.81%. By 2050, PM 2.5 concentration in S2 will drop more by 9.67 µg/m 3 than S1 and improved by 13.81%. It will be lower by 1.16 µg/m 3 in S3 than that in S2, and improved by 1.66%.

SD Model Prediction and Analysis
In S2, the PM concentration in the city is decreased, and the yearly PM absorption of forest per unit area is also decreasing. In the years of 2016-2020, the average urban forest can remove the pollution emissions of SO 2 , NO x , VOCs, NH 3 , primary PM 2.5 and primary PM 10 in amounts: 2.83, 2.31, 4.43, 1.45, 1.58 and 2.93 tons, respectively. By 2050, their removal amounts will be 0.24, 1.01, 1.58, 0.77, 0.17 and 0.24 tons. In S3, the average annual reduction of the six pollutants before 2020 is 3. 05, 2.53, 4.85,  1.60, 1.70 and 3.15 tons, respectively, and by 2050, the reduction is 0.31, 1.27, 1.99, 0.97, 0.21 and 0.31 tons, respectively. Therefore, S3 is a better state of urban development. By 2050, both PM 10 and PM 2.5 can reach the Grade I limit, and the forest scale is recommended to reach at least 2570 km 2 .
However, it should be noted that the effect of added forests on the improvement of PM concentration is actually small, only about 1-2%, about 90% of which comes from the source control. The results revealed that the overall effect of trees on air quality is limited. Much of the improvement in air quality depends on emission reductions, not on the trees (Figure 6). However, it should be noted that the effect of added forests on the improvement of PM concentration is actually small, only about 1-2%, about 90% of which comes from the source control. The results revealed that the overall effect of trees on air quality is limited. Much of the improvement in air quality depends on emission reductions, not on the trees (Figure 6).

Uncertainty Analysis
Due to the complexity of the system and the long period of time from 2016 to 2050, there are inevitable estimation errors when setting the parameters of control variables. The basic rule for setting these parameters is based on current planning with a sustainable development trend. There are two kinds of key settings of variables that need to be properly discussed.
Decrement per unit area. This refers to the PM adsorption by trees per unit area. The physical process of adsorption is complex. Different regions, time, climatic conditions, vegetation species, etc., may lead to value of the variable changing observably. What samples to collect and how to measure the PM adsorption on leaf are worth discussing.
Tree species in Wuhan, are 53% deciduous trees, and the scale of sycamore trees is second only to Cinnamomum camphor trees [36]. However, deciduous trees usually shed their leaves in the heavily polluted autumn and winter and lose the good effects of PM retention. We also found that the leaf surface of sycamore trees would adhere to a large number of villi instead of PM, which has been confirmed in the literature [42]. Therefore, we did not consider sycamores in the leaf selection. Among the common evergreen trees, we only selected the two most common trees for experimental analysis. Inevitably, from the time, batches, tree species, collecting location and other aspects, the sample of two species is limited; the results will have errors. At the same time, due to the limited samples, the statistical relationships of 'concentration-adsorption' of PM 10 and PM 2.5 are worth an in-depth study.
The methods for measuring PM include the weighing method, scanning electron microscopy (SEM), particle size analysis, etc. [42]. Studies show that [43][44][45], the weighing method is a widely used method but may lead to a low-accuracy result. The SEM image is very clear, but the sample size selected is small, and it comes with a high cost and slow scanning speed. If the laser particle size analyzer is used, the water-soluble substances on the leaf surface particles will be washed away, causing errors in the results. In addition, SEMs and particle size analyzers interpret the adsorption capacity of leaf from the number of particles and it is difficult to determine how long the PM takes to attach. Using the weighing method can evaluate the trend and meet the needs of the research with low cost.
Parameter settings of control variables. The control variables included: industrial growth rate, energy growth rate, end-treatment factor and contribution rate of a pollutant to PM. These values of control variables were determined at the current stage by referring to the corresponding 13th Five-year Plan, while the parameters after 2020 could only be estimated. As China enters a transition stage, cities will transform from development to protection, the energy structure will be more green and economic growth will inevitably slow down. Therefore, it is expected that the pollution and intensity of end treatment will gradually decrease, and the overall environmental condition of city will be gradually improved. Additionally, Wuhan has made great efforts to reduce SO 2 emission in recent years, and it has already reached the standard. It is more difficult to control NO x , VOCs and NH 3 that have a wide range of sources. Primary PM 10 and PM 2.5 could be contained by measurements of controlling road and construction dust. Therefore, the contribution rates of SO 2 , primary PM 10 and PM 2.5 will drop, and the rates of NOx, VOCs and NH 3 will rise correspondingly (specific parameter settings are available in Appendix C).
Regarding the understanding of the floated PM and deposited PM, some scholars also proposed the very similar concept, called surface PM and the in-wax PM [44,45]. But from only their descriptions in articles, it is difficult to evaluate whether the connotations are same as ours.

Innovation and Policy Implications
This study was essentially a dynamic analysis of the human-earth system reflecting the relationship and influence of urban forest scale on PM. The important innovation was to establish the integrated model based on the SD that put multi-variables together, such as particle concentration, forest impact, emissions, social and economic factors. It simplifies the complex physicochemical processes of atmospheric transmission and diffusion with annual average values as the main modeling data, connects the quantitative conversion relationship between each subsystem and can be used to predict the state of each variable in the model. There are two kinds of key variable nodes in the model reflecting the dynamic connection. The first is the relationship between different PM concentrations and adsorption by forests, and the second is the variable of transformation from pollutant to particle concentration. The original method could be used to study the capacity and carrying capacity of atmospheric environment [30]. Forest scale is also one natural variable attributed expression of environmental carrying capacity. The SD-based method can simulate the impact of forest on air quality in the context of urban development. In terms of the research object and method, the highly related studies have not been seen yet.
At present, the Chinese government vigorously promotes ecological civil construction and green development strategies with the priority of ecological protection along the Yangtze river. The scale of afforestation and forest coverage rate will be further improved. But the scientific, systematic analysis and planning are insufficient to know how many trees should be planted and where to plant them. This study compensates for this defect by simulating the impact of different forest scales on an urban atmospheric environment in the context of comprehensive consideration of social factors. The prediction results can provide a reference for afforestation and support for the future planning.
A previous study we conducted, "GIS-Based Urban Afforestation Spatial Pattern and a Strategy for PM 2.5 Removal," explored the impact of different distributions of newly added forests in Wuhan on PM 2.5 and proposed suggestions [46]. One conclusion was that it is of limited significance to consider the forest distribution in city's whole administrative region with the same scale of afforestation. Therefore, the reference for this study is that the forest extent plays the main role in mitigating PM, regardless of the influence of the spatial heterogeneity of new forests.

Prospect
In view of the deficiencies mentioned above, subsequently, (1) sample collection should be increased in terms of vegetation types, batches and duration to enhance the accuracy and reliability of statistical analysis of samples [12]. (2) In addition, in the long run, once trees are planted, they are generally not replanted. Therefore, tree planting should also consider the multiple functional elements of their ecological services. This is also the research content that is expected to be further carried out in the study of forest distribution. Meerow and Newell have published an article on this subject [47]. We will constantly improve the scientific nature of forest planning.

Conclusions
In the context of ecological civil construction in China, afforestation is highly valued, but its planning is subjective. There is a lack of scientific analysis on what scale of urban forest should be considered to plant and how it may affect on air quality. As a case study of Wuhan, this paper modeled a 'social-economic-environmental' system based on SD to simulate the long-period impact of different urban forest scales on atmospheric environmental quality from 2016 to 2050 under a certain sustainable development trend, and we came to the following findings.

1.
The amount of PM retained on leaves is proportional to the concentration, and floated and deposited PM is found on the leaves. Floated PM can be washed off, and the deposited PM is adsorbed solidly to the leaf. Furthermore, through correlation analysis, there is a high positive correlation between the floated PM 10 , the PM 2.5 and the corresponding average concentration on one day. Therefore, the linear correspondences of 'concentration (X)-adsorption (Y)' are conducted, that is Y = 0.00009X for PM 10 and Y = 0.0001X for PM 2.5 according to the overall samples respectively. This provides support for the SD modeling of PM 10 and PM 2.5 capacity by leaf under the change of concentration.

2.
Using SD is an effective way to model the dynamic human-earth system, when combined with the statistical regularity of PM adsorption by forests, in order to predict the impact of different forest scales on urban air quality. The simulation results showed if there were no trees in the city, the annual average concentration of PM 10 would be 10-12 µg/m 3 higher than the current situation, and the annual average concentration of PM 2.5 would be 8-10 µg/m 3 higher. In the overall improvement of particle concentration, the contribution of trees accounted for was about 10%. At least 30% forest cover will help PM concentrations reach the Grade I limit of air quality standard by 2050.

3.
Urban forests can reduce particle pollution, and more trees are better. However, it should be recognized that 30% of the forest cover will only reduce the particulate matter concentration by 1%-2% in the long run compared with the current cover rate of 22.9% (an increased 600 km 2 of forest). Around 90% of the particulate matter reduction is still based on traditional measures to reduce emissions from the source. Besides, the forest's service of air improvement and environmental purification, plus ecological services, including leisure tourism, soil and water conservation, flood storage and other functions, should be involved in the afforestation plan.

Acknowledgments:
We would like to thank Yuanli Zhou for his help with the language, and the two anonymous reviewers for their crucial advice.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix B
Variables and SD Flows Diagram