# Air Pollution Forecasts: An Overview

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, NO

_{2}, CO

_{2}, NO, CO, NO

_{x}, PM

_{2.5}, and PM

_{10}. Internationally, a large number of scholars have conducted research on air pollution and air quality forecasts, concentrating on the forecasting of contaminants.

_{2}, CO

_{2}, NO

_{2}, CO, and sulfate.

_{2}, CH

_{4}, N

_{2}O, and chlorofluorocarbons (CFCs, exemplified byFreon-12), cause a greenhouse effect [7,8]. The burning of fossil fuels and other human activities increase the concentration of greenhouse gases, leading to global warming. This also leads to a rise in sea level, more extreme weather, and melting glaciers and ice caps. More alterations to the environment are inevitable as temperatures continue to climb [7].

_{2}O can produce the greenhouse effect and can also react with stratospheric ozone, resulting in the depletion of the ozone layer and creation of holes in the ozone layer [10,12].

## 2. The Current Status of Pollution Research

#### 2.1. The Current Status of Pollution Emission Inventory Research

#### 2.2. The Health Effect of Pollution

_{2}, SO

_{2}, and PM

_{10}on childhood eczema in Shanghai, China. They selected 3358 preschool children for their 6-year research program. This study indicated that gestational and lifetime exposures to NO

_{2}were risk factors for atopic eczema in childhood; moreover, exposure to SO

_{2}, and PM

_{10}may enhance the effect of NO

_{2}exposure on childhood eczema [33].

_{2.5}for a long time [34]. The study showed that there is a positive correlation between PM

_{2.5}and heart disease mortality. In addition, as the PM

_{2.5}concentration increased, the mortality rate of patients with heart disease increased.

#### 2.3. Air Pollution Assessment

#### 2.4. Study of Air Pollution Control Efficienc

_{2}in each province of China was calculated by Shi et al. using the data envelopment analysis (DEA) method [39]. Wang et al. used a super efficiency DEA model to analyze the atmospheric pollution governance efficiency in various provinces of China from 2004 to 2009 [40]. Xie et al. studied Beijing and built an odd-and-even license plate model by a probabilistic modeling method and the analysis of means to quantify the pollution caused by vehicle exhaust emissions and the actual effect of the license plate limitation rule [41]. Fan et al. indicated that the rate of industrial waste gas governance is low, and there are significant differences in the governance efficiency of different pollutants [42]. Moreover, the Fan et al. research on China’s industrial air pollution control showed that, in different sectors, the air pollution treatment efficiency and its contributions from efficiency change and technology change differ significantly, and the contribution of technology advancement to the efficiency of industrial air pollution treatment are weak [43].

**Remark**

**1.**

#### 2.5. Air Pollution Early Warning and Forecast

_{2}in Turkey [50]. Wang et al. proposed a novel hybrid model, called Complementary Ensemble Empirical Mode Decomposition, Biogeography-Based Optimization based on Differential Evolution, and Linear Least Squares Support Vector Machine (CEEMD-BBODE-LSSVM), for air pollution point and interval forecasting [51]. Xu et al. proposed a robust early warning system that includes an evaluation module, forecasting module, and characteristics estimation module. This system defines the air quality levels and is also used to determine the main pollutants [52].

## 3. Abbreviation Explanation and Error Assessment Index

#### 3.1. Abbreviations

#### 3.2. Error Assessment Method and Index

_{i}represents the forecasting value, and A

_{i}represents the actual value.

## 4. Potential Forecasting Methods

_{2}in a heavily industrialized area in Durban (South Africa). Their proposed model identified periods of elevated SO

_{2}successfully [53]. However, potential prediction without considering the location of pollution sources and emissions of pollutants and the accuracy of prediction is low. Therefore, more statistical models, artificial intelligence, and hybrid models are used currently.

## 5. Statistical Forecast Methods

#### 5.1. Regression Methods

_{i}[56]. When we use the model to forecast y for a particular set of values of x

_{i}, we want to measure how large the error of the forecast might be. All these elements, including dependent and independent variables and error, are part of a regression analysis, and the resulting forecast equation is often called a regression model [57]. Regression analysis is a basic technique in air pollution forecasting.

_{i}are the independent variables, b and b

_{i}are the regression coefficients, and e is the error. It has a normal distribution with a mean of 0.

_{i}represents the pollutant concentrations and meteorological variables at time t, b

_{i}are the regression coefficients, and e is an estimated error term obtained from independent random sampling. The values of b

_{i}can be obtained by using a least squares error technique [58].

_{10}and meteorological variables and then used multilayer regression to forecast the concentration of PM

_{10}. The results show that meteorological variables are important in air pollution forecasting [60].

**Remark**

**2.**

#### 5.2. ARIMA Methods

**Step 1.**Tentative identification

**Step 2.**Parameter estimation

**Step 3.**Diagnostic checking

_{t}= (1 − B)d(1 − B

^{5})

^{D}x

_{i}, is a stationary autoregressive moving average process [61]. The SARIMA model can be written as:

^{α}W

_{t}= W

_{t−}

_{α}; ϕ

_{p}(B) = 1 − ϕ

_{1}B − … − ϕ

_{p}B

_{p}is called a regular (non-seasonal) autoregressive operator of order p; ϕ

_{p}(B

^{s}) = 1 − ϕ

_{1}B

^{s}− … − ϕ

_{p}B

^{ps}is a seasonal autoregressive operator of order p; θ

_{q}(B) = 1 − θ

_{1}B − … − θ

_{q}B

^{q}is a regular moving average operator of order q; Θ

_{Q}(B

^{S}) = 1 − Θ

_{1}B

^{S}− … − Θ

_{Q}B

^{QS}is a seasonal moving average operator of order Q; ε

_{t}is identically and independently distributed as normal random variables with mean zero, variance α

^{2}and cov(ε

_{t}, ε

_{t}

_{−k}) = 0, ∀k ≠ 0 [61].

**Remark**

**3.**

#### 5.3. Projection Pursuit Model (PP)

_{m}is the estimated value of time series {x} at t time; x

_{i}represents K time series forecast factors, its selection is ultimately determined by the data structure; a

_{m}represents the projection direction for the mth content, it satisfies $\Vert {a}_{m}\Vert =1$; G

_{m}is the optimal piecewise linear function of Z

_{m}, called ridge function. It is a numerical function; β

_{m}is the weight coefficients of the contribution of the mth ridge function to X

_{t}.

**Step 1**. Local optimization process

_{m}and β

_{m}, and the ridge functions G

_{m}are determined by the stepwise alternating optimization method.

**Step 2**. Global optimization process

_{u},M

_{u−}

_{1},L,1, determined the number for M, and found the best solution of the minimum M.

_{2}concentration based on historic data [62].

_{2}concentration data according to Equation (9):

**Remark**

**4.**

#### 5.4. Principal Component Analysis Model

**Remark**

**5.**

#### 5.5. Support Vector Regression

_{2}. First, they analyzed and forecasted the influencing factors. Next, as a key step, they preprocessed the daily average concentration of SO

_{2}, covering the period during 2001–2002 in Xi’an by using PCA to reduce the dimensionality of the input factors. Finally, the support vector regression model based on the radial basis function (RBF) kernel was established [67].

**Remark**

**6.**

#### 5.6. Artificial Neural Network

_{j}can be described by the Equation (14) [68]:

_{j}) is an activation function, usually expressed as ${z}_{j}={\sum}_{i=l}^{l}{w}_{ij}{x}_{i}+{b}_{j}$; $\phi \left(x\right)=\frac{1}{1+{e}^{-x}}$; w

_{ij}is the weight of input x

_{i}at neuron j; b

_{j}represent bias of neuron j.

_{j}is a model parameter, often called connection weights; q is the number of hidden nodes.

_{2}and PM

_{10}in four stations in Taiyuan to compare with a hybrid model. The ANN forecast accuracy is shown in Table 8 [68].

**Remark**

**7.**

#### 5.7. Back Propagation Neural Network

**Step 1:**Collect the modeling data that contain historical air pollutants concentrations C and meteorological data M.

**Step 2:**Perform the stationary wavelet transform (SWT) to decompose the time series of C.

**Step 3:**Normalize the meteorological parameters and one level of wavelet coefficients into [0, 1] according to Equation (17):

**Step 4:**Calculate the tth wavelet coefficients of the zth scale using BPNN

_{z}, z = 1, 2, …, l, l + 1 with the tth meteorological data and (t − 1)th wavelet coefficients:

**Step 5:**Perform the inverse SWT to generate the estimated daily pollutants concentrations.

**Step 6:**Output the forecasting result.

**Remark**

**8.**

#### 5.8. Wavelet Neural Network

_{f}(a,b) are the wavelet coefficients, which can reflect the characteristics of the frequency domain parameter a and the time domain parameter b. When parameter a is smaller, the resolution of the frequency domain is lower, but the resolution is higher in the time domain. In contrast, when a is larger, the resolution of the frequency domain is higher, and the resolution is lower in the time domain. Therefore, the wavelet transform can realize the time frequency localization of the fixed size and variable shape of the window.

**Step 1:**The low frequency coefficients of the highest layer are reconstructed after wavelet decomposition, clearly determining the annual change of atmospheric pollutant concentration. By using wavelet decomposition, the lowest two layers with high frequency signals are reconstructed, so abrupt change points of the time series of atmospheric pollutant concentration can be clearly judged.

**Step 2:**The time series of atmospheric pollutant concentration are decomposed into different frequency channels by wavelet decomposition, and then the corresponding time series model is considered. Finally, the predicted values of different frequency channels are combined to obtain the predictive value of the original time series.

**Step 3:**The input samples of the NN prediction model are studied, and the input variables of the NN prediction model are analyzed by using the principle of atmospheric pollution meteorology. Then, the PCA is used to reduce the dimension of the input variables.

**Step 4:**The annual variation trend of atmospheric pollutant concentration time series are segmented by wavelet decomposition and reconstruction. On this basis, the NN prediction model is designed for each segment.

**Step 5:**The decomposed wavelet coefficients are reconstructed to the original scale, and the NN that contains the meteorological elements is applied to analyze the wavelet coefficients of low and medium frequency. For the high frequency wavelet coefficients, the wavelet coefficients of the first few days are used as the input values of the NN model. Finally, the forecast of each wavelet coefficient sequence value is synthetized, and the forecasted value of the original sequence is obtained.

**Remark**

**9.**

#### 5.9. Support Vector Machine (SVM)

- Build an effective forecast factor.
- Select kernel function and parameter values.
- Train the sample to provide the SVM forecast model with optimized parameters, get the support vector, and then determine the structure of the SVM.
- Train the support vector predictor to forecast the test samples.

_{2}as an example and established a forecast model for atmospheric pollutant concentration. The author chose different kernel functions to analyze and compare each function’s mean relative error (MRE) and RMSE. Ultimately, studies showed that different kernel functions have different prediction results. They established the model that combined wavelet decomposition with SVM to forecast urban atmospheric pollutant concentration [67]. Wang et al. improved the forecast accuracy of SVM by using the Taylor expansion forecasting model to revise the residual series [68]. The forecast accuracies are shown in Table 12.

**Remark**

**10.**

#### 5.10. Fuzzy Time Series (FTS) Analysis

**Step 1:**Define and partition the universe of discourse U = (D

_{min}− D

_{1}, D

_{max}+ D

_{2}) into several equal intervals denoted as u

_{1},u

_{2},L,u

_{m}.

**Step 2:**Based on the SARIMA model, determine the FLRs.

**Step 3:**In order to select the best input for FLR, different combination inputs are attempted from single input to two inputs, three inputs and four inputs.

**Step 4:**The optimum length of intervals was calculated by following the average-based length.

**Step 5:**The forecasted outputs are calculated.

#### 5.11. Fuzzy Recognition

_{2}. Fuzzy recognition can be used to forecast the information [75]. The forecast model contains the index weight matrix, which provides a new way of improving the forecast accuracy.

**Remark**

**11.**

#### 5.12. Adaptive Neural Network Fuzzy Inference System

**Layer 1:**In this layer, every node i is an adaptive node and the node function is the membership function to determine the degree of satisfaction. All the parameters in this layer are called antecedent parameters.

_{i}is a linguistic label to node i, and ${o}_{i}^{1}$ is the membership grade of A

_{i}.

**Layer 2:**Every node in this layer is a circle node labeled ${o}_{i}^{2}$ and the output is the multiplies of all incoming signals [79]:

**Layer 3:**The output of every node i is called normalized firing strength. Each node calculates the rate of the ith rule’s firing strength to the sum of all the rules’ firing strengths and normalization [78]:

**Layer 4:**This layer is the conclusion layer, every node i is a square node or adaptive node with a node function. And parameters in this layer will be referred to as consequent parameters [79].

_{i},q

_{i},r

_{i}) is the parameter set of this node.

**Layer 5:**In this layer, the single node is a fixed node that computes the summation of all incoming signals [77].

**Remark**

**12.**

## 6. Three Dimensional Models

#### 6.1. Emissions Methods

- (1)
- Air quality forecasting based on statistical methods. They use statistical methods to analyze existing data, explore changes in the atmospheric environment, and predict concentrations of air pollutants by establishing statistical forecast models between air pollution concentrations and meteorological parameters.
- (2)
- Numerical forecasting based on atmospheric dynamics theory. These methods are based on the understanding of the physical and chemical processes of the atmosphere and use computers to forecast the dynamic distribution of air pollutants concentrations by establishing a numerical model for the transport and diffusion.

#### 6.1.1. The Atmospheric Dispersion Modelling System

#### 6.1.2. The California Puff Model

_{2}from refinery in Oman, and to forecast the concentration of SO

_{2}. The initial phase in their study was to input meteorological data and geographical information to WRF in order to obtain meteorological fields for CALWRF (an interface program). Then, the second phase was to input meteorological fields generated from CALWRF and geophysical data to California Meteorological Model (CALMET). The final step was to extraction meteorological parameters from CALMET output file, and put those meteorological parameters into CALPUFF dispersion model to get predicted concentrations [85]. The process of WRF-CALMET-CALPUFF model is shown in Figure 5.

#### 6.1.3. CMAQ Model

- Meteorology-chemistry interface processor (MCIP)
- Photolysis rate processor (JPROC)
- Initial conditions processor (ICON)
- Boundary conditions processor (BCON)
- CMAQ chemical-transport model (CCTM)

- (1)
- The core of the CMAQ is the chemical transport module CCTM, and it can simulate the transport process, chemical process, and sedimentation process of pollutants.
- (2)
- The initial module ICON and the boundary module BCON provide the initial field and boundary field of pollutants for CCTM.
- (3)
- The photochemical decomposition rate module JPROC calculates the photochemical decomposition rate.
- (4)
- The meteorological chemical interface module is the interface between the meteorological model and CCTM, and it can transform meteorological data into a CCTM identifiable data format.

^{n}is the forecast object which represents the concentration of a particular pollution on the forecasting day (the nth day); the (n − 1)th day is the initial day; ${\widehat{G}}_{m}$ and ${\widehat{A}}_{m}^{M+N+L}$ are coefficient matrices; m is time stage and ${\widehat{S}}_{M+N+L}$ has three forecast factors represented as follows [65]:

- (1)
- ${X}_{L}=\left(\begin{array}{c}{x}_{1}^{n-1}\\ {x}_{2}^{n-1}\\ \dots \\ {x}_{L}^{n-1}\end{array}\right)$represents the monitoring values of L types pollutant concentrations on the initial forecasting day.
- (2)
- ${Y}_{M}=\left(\begin{array}{c}{y}_{1}^{n-1}\\ {y}_{2}^{n-1}\\ \dots \\ {y}_{M}^{n-1}\end{array}\right)$represents the monitoring values of M types atmospheric elements on the initial forecasting day.
- (3)
- ${Z}_{N}=\left(\begin{array}{c}{z}_{1}^{n}\\ {z}_{2}^{n}\\ \dots \\ {z}_{N}^{n}\end{array}\right)$represents the forecast values of N types of pollutant concentrations on the forecasting day.

_{2.5}, PM

_{10}, SO

_{2}, NO

_{2}, and O

_{3}in Tianjin [65].

- (1)
- PC is the forecast value of the pollutant concentration.
- (2)
- “[]” represents the monitoring values on the initial forecasting day (1 represents the average concentration of the whole area, and 2 represents the average concentration of a single observation site) and the monitoring values of the meteorological element.
- (3)
- “{}” represents the CMAQ products for the forecast data.
- (4)
- a
_{1}L a_{n}, b_{1}L b_{m}, c_{1}L c_{l}are coefficients and can be calculated by mathematical methods.

**Remark**

**13.**

- (1)
- When the simulation scale is up to tens of kilometers or because of an uneven surface of the underlying surface, the flow field is more complex, and it is difficult to meet the requirements of the accuracy of the Gaussian smoke flow model.
- (2)
- Deposition and chemical transformation of the Gaussian model can only be treated roughly, when these processes are very important for the study and the Gaussian model is not applicable.

- (1)
- It is assumed that the gradient transport is required to satisfy certain scale conditions so that the diffusion equation is correct when the smoke flow scale is larger than the dominant eddy.
- (2)
- In the convection condition, the relationship between gradient and transport is not established, so the K model cannot be applied.
- (3)
- The requirements for the basic information and input parameters of K model are very high.

#### 6.1.4. Atmospheric Pollution Forecasts in China

- (1)
- Mesoscale meteorological model.
- (2)
- Planetary boundary layer turbulence statistics parameterization (PBLM).
- (3)
- Pollution source model (SM).
- (4)
- Dry and wet deposition model (DSDM).
- (5)
- Concentration calculation model (HRCM).

_{j}P

_{L}, c

_{j}is the volume mixing ratio of chemical substances, P

_{L}= P

_{S}− P

_{t}.

_{z}/P

_{S}− P

_{t}, P is air pressure, P

_{t}is the top pressure of model (P

_{t}= 100 hPa); P

_{S}is the pressure of surface.

_{c}and L

_{c}are the production and consumption rate caused by the chemical reaction.

_{t}is the rate of change in the concentration of material caused by cloud.

_{y}is the rate of change of concentration caused by dry deposition.

_{s}is a source of pollution.

_{xr},d

_{yr},d

_{zr}small volume center at t time, and t

_{0j}is the time when a particle j is away from the source.

_{d}is the dry deposition velocity; ν

_{w}is the wet deposition velocity; $\sum {q}_{i}\delta \left({r}_{i}\right)$ is in the volume τ; and the strength of several sources are located in r = (x

_{i},y

_{i},z

_{i}) as the sum of the q

_{i}sources.

#### 6.2. Meteorological Models

#### 6.2.1. CALMAT Model

#### 6.2.2. WRF and MM5 Model

#### 6.3. Chemical Models

_{3}is over-prediction and the concentration of PM

_{2.5}is under-prediction, the authors proposed the improvement scheme in the paper from meteorological perspective. Werner et al. applied the on-line WRF-Chem model to forecast the concentration of PM

_{10}over Poland. Based on forecast results, the author indicated that WRF-Chem performed better in O

_{3}forecast, confirming the significance of the non-linear processes taken into account in an online coupled Eulerian model, but WRF-Chem was difficult to capture the peak, it needs higher resolution sector based emission data and temporal emission profile. [94]. Table 15 lists the main recent studies on the three dimensional models in different urban areas.

**Remark**

**14.**

## 7. Hybrid Systems

#### 7.1. PCA-ANN

_{2}concentrations at the Taj Mahal in Agra, India [25]. At first, they used PCA to find the correlations between meteorological forecasting variables and air pollutants. Then, the significant variables were taken as the input parameters to propose the reliable physical ANN–multi layer perceptron model for forecasting air pollution in Agra. The forecast results are given in Table 16.

#### 7.2. Multilayer Perceptron Neural Network and Clustering Algorithm

_{i}

^{(i)}and the cluster c

_{j}. This is an indicator of the distance of the n data points from their cluster centers [60].

_{j}]òM

_{FCM}is a fuzzy partition of the data set Z, and V = [ν

_{1},ν

_{2},L

_{,}ν

_{c}] is the vector of prototypes of the clusters, which are calculated according to ${D}_{ikA}={z}_{k}-{\nu}_{i}^{2}.$ This is a square inner product distance norm. The optimal partition U* of Z for the FCM algorithm is reached through the couple (U*,V*) that minimizes locally the objective function J

_{FCM}according to the alternating optimization.

_{10}concentration; WS represents wind speed; WDI is the Wind Direction Index (WDI); T is temperature; HR is the relative humidity.

#### 7.3. Hybrid Artificial Neural Network and Hybrid Support Vector Machine

#### 7.4. CS-EEMD-BPANN Model

**Step 1.**Selection of appropriate predictors based on gray correlation analysis. Some air pollutants (CO, NO

_{2}, O

_{3}, and SO

_{2}) and meteorological factors (WS/D, T, H, and P) might affect the PM concentration, and using the gray correlation analysis to obtain the influence law of PM is a primary concern.

**Step 2.**Use the EEMD technique to filter out the white noise or useless information for selecting influencing factors and PM concentration.

**Step 3.**The data sets with the noise removed are input into the BPANN model to obtain the forecasted values. In this study, the forecast model is a novel BPANN-based multi-step-ahead forecasting model, and the CS algorithm is used to optimize the connection weights and thresholds of the BPANN architecture to make it more stable.

#### 7.5. ICEEMD-SVM-WOA

**Step 1.**ICEEMD is used to decompose the original time series into several intrinsic mode functions (IMFs) for eliminating the negative influence of noise and to exploring the inner characteristics of the data Compared with CEEMD model, the ICEEMD model is mainly improved from two aspects: (a) CEEMD modes contain some residual noise; (b) the signal information appears “later” than in EEMD with some “spurious” modes in the early stages of the decomposition [98].

**Step 2.**The SVM optimized by WOA is employed to build a predictor for each IMF. SVM is used to predict each IMF, among them, WOA is used to obtain the proper weight coefficient of each predictor. The leave-one-out strategy is performed to integrate all forecasted IMFs and then obtain the final forecast result.

**Remark**

**15.**

**Step 1.**Decompose the original series. Some signal processing tools are used in this step, such as wavelet transform, short-time Fourier transform, and EEMD. The main purpose of signal processing is to weaken the redundant content in the signal, remove the mixed noise and interference, and transform the signal into a form for easy processing and analysis for subsequent research.

**Step 2.**Optimize the forecast model. There are many methods available in this step, such as genetic optimization algorithms, Ant colony optimization algorithms, and whale optimization algorithms.

**Step 3.**Construct the forecast model. This is an important step in the study, and several methods can be chosen, such as statistical methods (regression, principal component analysis, etc.) and AI methods (ANN, wavelet NN, etc.).

## 8. Other Methods of Air Pollution Forecasting

#### 8.1. Geographic Methods

_{2}, PM

_{10}and CO concentration in Istanbul, these methods are described in Table 22.

**Remark**

**16.**

#### 8.2. Grey System (GM)

- (1)
- Sequence forecast: A grey forecast model that can reflect the characteristic of the forecast object is constructed based on the observation of the time series.
- (2)
- Catastrophe and abnormal value forecast: Using a grey model to forecast the time that the abnormal value appears and the time that the abnormal value appears in the specific time zone.
- (3)
- Topology forecast: Using the original data curve and finding all the time points in which the fixed value occurs on the curve. The fixed value is used as the frame structure and the number of time points. The model is established to forecast the time point of the fixed value.
- (4)
- System forecast: Establishing a set of interrelated grey forecasting models for the system behavior characteristic and forecasting the change of the coordination among numerous variables in the system.

**Remark**

**17.**

#### 8.3. Natural Source Pollution Forecasting

_{2.5}and CO in wildfires. In their proposed framework, Operational Multiscale Environment modeled with Grid Adaptivity, Real-time remote sending data were used to automatically detect fire pixels, and the output was generated in GIS format. This system will help to assign persons involved in wildfires management, improved work efficiency and reduce fire damage [105].

**Remark**

**18.**

## 9. Conclusions

- Statistical models have a wide application and require less time to build models, but they require a large amount of historical data and have a high dependence on the data time series approach.
- AI methods, such as the NN approach, have good performance and can solve nonlinear data, but the models are unstable and have a high dependence on data. Moreover, most optimization algorithms are easy to be understood and combined with other methods; however, they easily fall into local optima.
- As the most popular method, a hybrid system has good robustness with low risk and strong adaptability and can take advantage of other models. However, the process of building models is relatively complex.
- Traditional AI performance is better than that of statistical methods, but worse than that of the hybrid model.
- Processed original series did better than the unprocessed original series in terms of air pollution forecasting.
- It is proven that forecast performance is better when considering the meteorological variables and the geographic factors.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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List of Assessment Methods | ||
---|---|---|

Types | Main Equations | Meaning of Variables |

Market value method | ${S}_{1}={\displaystyle \sum _{i=1}^{n}}{P}_{i}\times \Delta R$ | S_{1} is the economic loss of environment quality;P is the market price of good i; ΔR is the yield reduction of good i that caused by pollution and ecological damage. |

Opportunity cost method | ${S}_{2}={V}_{2}\times {W}_{2}$ | S_{2} is the opportunity cost of the loss;V _{2} is the Unit opportunity cost of the certain resource;W _{2} is the amount of resources being polluted or damaged. |

Engineering cost method | ${S}_{3}={V}_{3}\times Q$ | S_{3} is the cost of prevention and controlling pollution or destruction;V _{3} is the unit costs of protecting, restoring or replacing the original environmental functions;Q is the unit costs of protecting, restoring or replacing the original environmental functions; |

Abbreviation | Explanation | Abbreviation | Explanation |
---|---|---|---|

ADMS | Atmospheric Dispersion Modelling System | GM | Gray model |

AI | Artificial intelligence | GCA | Gray correlation analysis |

ANN | Artificial neural network | GRNN | General regression neural networks |

ANF | Adaptive neuro-fuzzy | HF | Hybrid forecast |

ARIMA | Autoregressive integrated moving average | HS | Hybrid system |

ANFIS | Adaptive neural network fuzzy inference system | ICEEMD | Improved complementary ensemble empirical mode decomposition |

BPNN | Back-propagation neutral networks | KF | Kalman filter |

CAMx | Comprehensive Air Quality Model with Extensions | MLP | Multi-layer Perceptron |

CALPUFF | California Puff model | MLR | Multiple-linear regress |

CALMET | California Meteorological Model | MM5 | Mesoscale Model 5 |

CS | Cuckoo search | PCR | Principal component regress |

CMAQ | Community Multi-scale Air Quality | PCA | Principal component analysis |

CEEMD | Complete ensemble empirical mode decomposition | PP | Projection pursuit model |

CERC | Cambridge Environment Research Corporation | RM | Rolling mechanism |

DEA | Data Envelopment Analysis | SVM | Support vector machine |

EMD | Empirical mode decomposition | SVR | Support vector regression |

EEMD | Ensemble empirical model decomposition | SWT | Stationary wavelet transform |

FCM | Fuzzy c–Means algorithm | SSA | Singular spectrum analysis |

FTS | Fuzzy time series | WOA | Whale optimization algorithm |

FFNN | Feed-forward neural networks | WRF | Weather Research and Forecasting Model |

FFMLP | Feed forward multi-layer perception | WRF-Chem | Weather Research and Forecasting Model coupled with Chemistry |

GA | Genetic algorithm |

Metric | Definition | Equation |
---|---|---|

MAE | The mean absolute error of N forecasting results | $MAE=\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left|{F}_{i}-{A}_{i}\right|$ |

MSE | The mean squared error of N forecasting results | $MSE=\frac{1}{n}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\left({F}_{i}-{A}_{i}\right)}^{2}$ |

RMSE | The square root of average of the error squares | $RMSE=\sqrt{\frac{1}{N}\times {\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left({F}_{i}-{A}_{i}\right)}^{2}}$ |

NMSE | The normalized average of the squares of the errors | $NMSE=\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\frac{{\left({F}_{i}-{A}_{i}\right)}^{2}}{{F}_{i}{A}_{i}}$ |

MAPE | The average of N absolute percentage error | $MAPE=\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}\left|\frac{{A}_{i}-{F}_{i}}{{A}_{i}}\right|\times 100\%$ |

IA | The index of agreement of forecasting results | $IA=1-{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left({F}_{i}-{A}_{i}\right)}^{2}/{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left(\left|{F}_{i}-\u0100\right|+\left|{A}_{i}+\u0100\right|\right)}^{2}$ |

R | The correlation coefficient | $R=\frac{\left({A}_{i}-\u0100\right)\left({F}_{i}-\overline{F}\right)}{{\sigma}_{F}{\sigma}_{A}}$ |

AE | The absolute error of forecasting results | $AE=\left|{F}_{i}-{A}_{i}\right|$ |

FB | The fractional bias of N forecasting results | $FB=2\left(\u0100-\overline{F}\right)/\left(\u0100+\overline{F}\right)$ |

IOA | The index of agreement | $IOA=1-\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({F}_{i}-{A}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{N}{\left(\left|{F}_{i}-\overline{F}\right|+\left|{A}_{i}+\u0100\right|\right)}^{2}}$ |

Types | Nonlinear Function | Do Transformation | Linear Function |
---|---|---|---|

Hyperbolic function | $Y=a+b\frac{1}{x}$ | $x\text{'}=\frac{1}{x}$ | $Y\text{'}=a+bx\text{'}$ |

Power function | $Y=a{x}^{b}$ | ${Y}^{\prime}=\mathrm{ln}Yx=\mathrm{ln}xA=\mathrm{ln}a$ | $Y\text{'}=A+bx\text{'}$ |

Exponential function | $Y=a{e}^{bx}$ or $Y=a{e}^{\frac{b}{x}}$ | ${Y}^{\prime}=\mathrm{ln}Y,A=\mathrm{ln}a$ or ${Y}^{\prime}=\mathrm{ln}Y,x=\frac{1}{x},A=\mathrm{ln}a$ | $Y\text{'}=A+bx\text{'}$ or $Y\text{'}=A+bx\text{'}$ |

Logarithmic function | $Y=a+b\mathrm{ln}x$ | $x\text{'}=\mathrm{ln}x$ | $Y\text{'}=a+bx\text{'}$ |

S curve type | $Y=\frac{1}{a+b{e}^{-x}}$ | ${Y}^{\prime}=\frac{1}{Y},x={e}^{-x}$ | $Y\text{'}=a+bx\text{'}$ |

Parabolic type | $Y=a+bx+c{x}^{2}$ | ${x}_{1}=x,{x}_{2}={x}^{2}$ | ${Y}^{\prime}=a+b{x}_{1}+c{x}_{2}$ |

SARIMA | MAPE | MAE | MSE | RMSE |
---|---|---|---|---|

Pasir Gudang | ||||

(0,1,1)(0,1,1)^{12} | 11.08 | 5.39 | 37.76 | 6.14 |

(0,1,1)(1,1,0)^{12} | 11.08 | 5.77 | 44.50 | 6.67 |

Johor Bahru | ||||

(1,1,0)(1,1,0)^{12} | 15.28 | 7.06 | 76.05 | 8.72 |

(1,1,0)(0,1,1)^{12} | 9.99 | 4.12 | 21.90 | 4.68 |

(0,1,1)(1,1,0)^{12} | 19.13 | 8.87 | 120.69 | 10.99 |

(0,1,1)(0,1,1)^{12} | 9.77 | 4.22 | 23.82 | 4.88 |

Muar | ||||

(1,1,0)(0,1,1)^{12} | 12.20 | 5.42 | 49.13 | 7.10 |

(0,1,1)(2,1,0)^{12} | 11.32 | 5.10 | 38.62 | 6.21 |

(0,1,1)(0,1,1)^{12} | 10.44 | 4.84 | 33.49 | 5.79 |

Grade | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Range of ${C}_{i}^{1}$ values | (0 ≤ ${C}_{i}^{1}$ ≤ 0.2) | (0.2 ≤ ${C}_{i}^{1}$ ≤ 0.4) | (0.4 ≤ ${C}_{i}^{1}$ ≤ 0.6) | (0.6 ≤ ${C}_{i}^{1}$ ≤ 0.8) | (0.8 ≤ ${C}_{i}^{1}$ ≤ 1) |

Actual Type | Forecast Type | Absolute Error | Relative Error |
---|---|---|---|

2 | 2.399 | 0.399 | 19.9% |

3 | 5.632 | 2.632 | 87.7% |

4 | 4.298 | 0.298 | 7.5% |

5 | 5.439 | 0.439 | 8.8% |

Pollutants | Station 1 | Station 2 | Station 3 | Station 4 | ||||
---|---|---|---|---|---|---|---|---|

MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | |

SO_{2} | 0.0674 | 0.0910 | 0.0524 | 0.0929 | 0.0386 | 0.0636 | 0.0512 | 0.0870 |

PM_{10} | 0.0428 | 0.0631 | 0.0476 | 0.0615 | 0.0485 | 0.0740 | 0.0494 | 0.0872 |

Study Areas | Methods | MAE | MSE | RMSE |
---|---|---|---|---|

Pasir Gudang | SARMIA | 5.39 | 37.76 | 6.14 |

FTS | 5.88 | 53.43 | 7.31 | |

ANN | 3.87 | 32.09 | 5.66 | |

Johor Bahru | SARMIA | 4.12 | 21.90 | 4.68 |

FTS | 5.21 | 33.82 | 5.82 | |

ANN | 2.70 | 12.79 | 3.58 | |

Muar | SARMIA | 4.84 | 33.49 | 5.79 |

FTS | 3.49 | 18.44 | 4.29 | |

ANN | 3.29 | 18.05 | 4.25 |

Model | Air Pollutants | Performance Criteria | |
---|---|---|---|

MAPE | RMSE | ||

W-BPNN | PM_{10} | 15.277 | 15.391 |

SO_{2} | 15.886 | 8.269 | |

NO_{2} | 16.544 | 2.621 | |

BPNN | PM_{10} | 31.266 | 23.624 |

SO_{2} | 22.119 | 12.716 | |

NO_{2} | 35.030 | 5.406 |

Wavelet | Main Equations | Description |
---|---|---|

Haar wavelet | ${\psi}_{H}\{\begin{array}{c}1,0\le x\le \frac{1}{2}\\ -1,\frac{1}{2}\le x\le 1\\ 0,Others\end{array}$ | Haar function is the earliest use of wavelet analysis in the wavelet, and is also the simplest wavelet. The function itself is a step function |

Mexican Hat wavelet | $\psi \left(\mathrm{x}\right)=\frac{2}{\sqrt{3}}{\pi}^{-\frac{1}{4}}\left(1-{x}^{2}\right){e}^{-\frac{{x}^{2}}{2}}$ | Mexican Hat wavelet is the two-order derivative of Gauss function (plus minus) |

Morlet wavelet | $\psi \left(\mathrm{x}\right)=c{e}^{-\frac{{x}^{2}}{2}}\mathrm{cos}\left(5x\right)$ | Morlet wavelet does not have orthogonality and no compact support set, so it can only satisfy the condition of continuous wavelet, but cannot be discrete wavelet transform and orthogonal wavelet transform |

Daubechies wavelet | ${\left|{m}_{0}\left(\omega \right)\right|}^{2}={\left({\mathrm{cos}}^{2}\frac{\omega}{2}\right)}^{N}P\left({\mathrm{sin}}^{2}\frac{\omega}{2}\right)$ ${m}_{0}\left(\omega \right)=\frac{1}{\sqrt{2}}{\displaystyle {\displaystyle \sum _{k=0}^{2N-1}}}{h}_{k}{e}^{-jk\omega}$ | Assuming, $P\left(\mathrm{y}\right)={{\displaystyle \sum}}_{k=0}^{N-1}{c}_{k}^{N-1+k}{y}^{k}$ among them, is the binomial coefficient; Daubechies wavelet function is the standard orthogonal wavelet, which makes it possible to analyze the discrete wavelet transform. |

Pollutants | Station 1 | Station 2 | Station 3 | Station 4 | ||||
---|---|---|---|---|---|---|---|---|

MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | |

SO_{2} | 0.0477 | 0.0840 | 0.0491 | 0.0866 | 0.0266 | 0.0498 | 0.0358 | 0.0602 |

PM_{10} | 0.0393 | 0.0606 | 0.0341 | 0.0518 | 0.0468 | 0.0739 | 0.0420 | 0.0756 |

Study Areas | MAE | MSE | RMSE |
---|---|---|---|

Pasir Gudang | 5.88 | 53.43 | 7.31 |

Johor Bahru | 5.21 | 33.82 | 5.82 |

Muar | 3.49 | 18.44 | 4.29 |

Project | MM5 Model | WRF Model |
---|---|---|

Vertical coordinate | Terrain following height coordinates | Terrain following quality coordinates |

Conservation | Not necessarily conservative | Conservation of mass, momentum and scalar quantity |

Time integral | Leapfrog integration scheme | Three order Runge-Kutta integral scheme |

Horizontal convection | Second order accuracy center format | Five order upwind difference scheme |

Damping filter | Four order smoothing | No requirement |

Typical time step | 3 times the distance of the grid | 6 times the distance of the grid |

Method | Pollutant | Country | Inputs | Ref. |
---|---|---|---|---|

WRF-Chem | PM_{10} | Poland | Meteorological data, emission data | [94] |

Models-3/CMAQ | O_{3} | United States | Meteorological information, emission rates from sources | [27] |

CMAQ-MOS | PM_{10}, NO_{2} | China | Wind field (U, V), temperature field (Ts), relative humidity (RH) | [65] |

CMAQ-ANNs | PM_{10}, SO_{2} | China | Wind field (U, V), temperature field (Ts), relative humidity (RH), concentrations of PM_{2.5}, PM_{10}, SO_{2}, NO_{2}, O_{3} | [65] |

WRF-ADMS | Perfluoromethylcyclohexane | Tunis | Initial and boundary conditions, topography, land use and soil data, exit diameter, release point height, flow rate, temperature, hourly averaged meteorological data | [83] |

Coupled WRF-SFIRE with WRF-Chem | Fire somke | United States | Fuel categories, FINN emission factors, | [95] |

CALPUFF-WRF | SO_{2} | Sultan | land use categories, terrain elevations, surface and upper air meteorological observations or meteorological fields | [85] |

WRF-Chem | O_{3} | United States | No detailed description | [92] |

WRF/Chem-MADRID | O_{3}, PM_{2.5} | United States | No detailed description | [93] |

CALPUFF | Total suspended particulate (TSP) | Israel | Temperature, relative humidity, barometric pressure, 10 min average wind speed and direction, cloud cover, topographic data | [84] |

AERMOD | Total suspended particulate (TSP) | Israel | Meteorological data (Temperature, relative humidity, barometric pressure, 10 min average wind speed and direction) from two site, cloud cover, topographic data | [84] |

Statistical Measures | Ideal Value | Training Value | Validation Value |
---|---|---|---|

R | 1 | 0.89 | 0.91 |

IOA | 1 | 0.99 | 0.98 |

NMSE | 0 | 0.016 | 0.017 |

FB | 0 | 0.001 | −0.021 |

Stations | Clustering Algorithms | Time Window | Number of Cluster | MAE | MSE |
---|---|---|---|---|---|

CRUZ ROJA (CR) | K–means | 1 | 8 | 0.0207 | 0.00085 |

FCM | 1 | 7 | 0.0208 | 0.00083 | |

Nativitas (NA) | K–means | 1 | 2 | 0.0230 | 0.00087 |

FCM | 2 | 5 | 0.2031 | 0.00095 | |

DIF (DF) | K–means | 3 | 8 | 0.0280 | 0.00134 |

FCM | 1 | 3 | 0.0257 | 0.00113 |

Stations | Metric | FFMLP | GA-MLP | MLP_{nomet} | MLR |
---|---|---|---|---|---|

Station 1 | MAE | 14.03 | 15.36 | 18.91 | 17.46 |

RMSE | 20.28 | 22.39 | 27.87 | 26.68 | |

R | 0.78 | 0.73 | 0.53 | 0.59 | |

IA | 0.87 | 0.83 | 0.65 | 0.72 | |

Station 2 | MAE | 14.18 | 14.48 | 16.99 | 17.37 |

RMSE | 19.36 | 19.26 | 22.47 | 23.90 | |

R | 0.70 | 0.65 | 0.48 | 0.53 | |

IA | 0.80 | 0.79 | 0.63 | 0.65 | |

Station 3 | MAE | 19.08 | 20.55 | 27.49 | 24.53 |

RMSE | 26.06 | 28.70 | 38.11 | 35.14 | |

R | 0.80 | 0.73 | 0.43 | 0.55 | |

IA | 0.88 | 0.83 | 0.56 | 0.64 | |

Station 4 | MAE | 7.68 | 7.54 | 10.25 | 11.94 |

RMSE | 12.35 | 12.16 | 16.62 | 17.06 | |

R | 0.82 | 0.83 | 0.54 | 0.55 | |

IA | 0.89 | 0.90 | 0.65 | 0.65 |

Stations | CS-BPANN | EEMD-BPANN | CS-EEMD-BPANN | |||
---|---|---|---|---|---|---|

AE | MAPE | AE | MAPE | AE | MAPE | |

Station 1 | 1.71 | 11.27% | - | - | 1.583 | 9.37% |

Station 2 | 15.45 | 18.53% | 13.82 | 17.56% | 13.86 | 15.78% |

Station 3 | 28.56 | 41.04% | 28.16 | 40.59% | 27.64 | 36.98% |

Study Areas | PM_{2.5} | PM_{10} | SO_{2} | NO_{2} | CO | O_{3} | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MAE | MAPE | MAE | MAPE | MAE | MAPE | MAE | MAPE | MAE | MAPE | MAE | MAPE | |

Taiyuan | 3.197 | 9.204 | 5.517 | 6.689 | 1.497 | 7.831 | 1.765 | 5.614 | 0.024 | 2.820 | 3.392 | 4.225 |

Harbin | 1.781 | 2.260 | 3.203 | 7.457 | 0.533 | 9.351 | 2.420 | 7.236 | 0.023 | 2.921 | 3.430 | 7.900 |

Chongqing | 2.900 | 8.795 | 5.263 | 10.311 | 1.160 | 13.219 | 2.882 | 8.265 | 0.049 | 5.005 | 4.350 | 11.514 |

List of Recent Research on the Application of HS in the Field of Air Pollution | |
---|---|

Author | Main Contribution |

Chen et al. [17] | Combining numerical forecast (WRF) with statistical analysis (temporal synoptic index) to forecast high-PM_{10} concentration in Beijing. This hybrid forecast system forecasts high-PM pollution events is more accurately than current forecast methods. It combines the strengths of various methods while avoiding the disadvantages found when statistical forecast methods are used alone. |

Zhou et al. [99] | Established a hybrid EEMD-GRNN model to forecast the concentration of pollutants in Xi’an, which was shown to be superior to other conventional models. |

Qin et al. [97] | Proposed the CS-EEMD-BPANN model for forecasting PM concentrations in Beijing, Shanghai, Guangzhou and Lanzhou. The forecasting result is improved and this method is more stable than BPNN and EEMD-BPANN. |

Qin et al. [100] | Using an a priori algorithm mined the spatial and temporal associations of intercity PM, also mined cross spatial and temporal associations of PM_{10} and PM_{2.5} in the Jing-Jin-Ji region (China). |

Wang et al. [68] | They used HANN, HSVM and Taylor expansion forecasting model in Taiyuan. The innovation involved in this approach is that it sufficiently and validly utilizes the useful residual information on an incomplete input variable condition. |

Feng et al. [101] | 1. Using trajectory based geographic parameter as an extra input to ANN model; 2. Applying forecast strategy at different scales and then sum them up; 3. The backward trajectories from Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model were used to track the transport corridors of air masses. |

Xu et al. [52] | Proposed ICEEMD-SVM-WOA model and FE model. This model not only forecast the concentrate on air pollutants, but also evaluates the effectiveness of the new forecast system by fuzzy evaluation method. |

Wongsathan et al. [102] | Proposed a fundamental hybrid forecast model. This model can improve the performance of the forecast models, the exogenous variable may be considered as well as the modified of the hybrid algorithm |

Model | Description |
---|---|

Single-site neighborhood model | The main idea of this model is to use the air pollution index of one or more neighboring regions as the input variables of the forecast area. |

Two-site neighborhood model | This model considers two neighboring districts. The rationale for this model is that using more predictor variables should achieve higher accuracy. |

Distance-based model | In this model, the weighted average value of air pollutants is calculated according to the distance between the adjacent regions and the forecasted distance. The model is based on the idea that the effects of air pollutant levels of the neighboring district are inversely proportional to the distance between the two districts. |

Method Types | Authors | Models | Main Conclusions |
---|---|---|---|

Statistical methods | Silibello et al. [108] | Kalman filter (KF) and Hybrid forecast (HF) | Use two adjustment techniques, the HF and the KF, to improve the accuracy of forecasting supplied by an air quality forecast system |

Huebnerova et al. [109] | Generalized linear models with log–link and gamma distribution | It’s shown that the predicted meteorological variables are used to predict well though comparative analysis of the two models | |

Artificial intelligence methods | Catalano et al. [110] | ANN and ARIMAX | Forecasted the extreme concentrations by integrating the two models into an ensemble |

Feng et al. [111] | SVM-GABPNN | Proposed a hybrid model which SVM was used to classify data, GA used to optimize the BPNN model. | |

Bai et al. [24] | W-BPNN | Using wavelet transform to realize feature extraction and characterization of air pollutants | |

Siwek et al. [112] | Wavelet transformation, the multilayer perceptron, radial basis function, Elman network, SVM and linear ARX model | Decomposed the data into the wavelet coefficients and used different NN to individual prediction, then combined the few predictors in the ensemble. This approach does not require very exhaustive information about air pollutants, and it has the ability of allowing the nonlinear relationships between very different predictor variables. | |

Hybrid methods | Feng et al. [101] | Hybrid ANN | Used trajectory based geographic parameter as an extra input to ANN model; using wavelet transformation decomposed original series into a few sub-series with lower variability |

Fu et al. [113] | RM-GM-FFNN | Enhanced FFNN model with RM and GM to assess the possible correlation between different input variables for improving forecast accuracy | |

Song et al. [4] | ANF, Distribution functions, | Proposed interval prediction method and ANF to address the uncertainty of PMs according to the pollutant emission distribution. | |

Three dimensional models | Luo et al. [27] | Models-3/CMAQ | Provided a method of analyzing the change of pollutants’ concentration in the condition of lacking practical pollution data. |

Grell et al. [92] | Fully coupled online chemistry with the WRF model | The accuracy of forecasting of meteorological modules and chemical modules under different conditions of separation and coupling is explored. The result indicate that the ability to predict a slight increase | |

Other methods | Kurt et al. [26] | Neural networks based on geographic forecasting models | The models which considered the geographic factor performed better than the models which unconsidered. |

Pan et al. [103] | GM Grey relational analysis | Selected 30 indexes of 5 categories, and find mainly impact factors by using grey relational analysis, then used GM (1, 1) model to forecast the concentration of pollutants |

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## Share and Cite

**MDPI and ACS Style**

Bai, L.; Wang, J.; Ma, X.; Lu, H.
Air Pollution Forecasts: An Overview. *Int. J. Environ. Res. Public Health* **2018**, *15*, 780.
https://doi.org/10.3390/ijerph15040780

**AMA Style**

Bai L, Wang J, Ma X, Lu H.
Air Pollution Forecasts: An Overview. *International Journal of Environmental Research and Public Health*. 2018; 15(4):780.
https://doi.org/10.3390/ijerph15040780

**Chicago/Turabian Style**

Bai, Lu, Jianzhou Wang, Xuejiao Ma, and Haiyan Lu.
2018. "Air Pollution Forecasts: An Overview" *International Journal of Environmental Research and Public Health* 15, no. 4: 780.
https://doi.org/10.3390/ijerph15040780