# Multi-Site and Multi-Pollutant Air Quality Data Modeling

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## Abstract

**:**

_{2}, CO, PM

_{2.5}, and PM

_{10}, over time. At every monitoring timestamp t, we observe one station × feature matrix ${\mathbf{x}}_{t}$ of the pollutant data, which represents a spatio-temporal process. Traditional methods of prediction of air quality typically use data from one station or can only predict a single pollutant (such as PM

_{2.5}) at a time, which ignores the spatial correlation among different stations. Moreover, the air pollution data are typically highly non-stationary. This study has explicitly overcome the limitations of these two aspects, forming its unique contributions. Specifically, we propose a de-trending graph convolutional LSTM (long short-term memory) to continuously predict the whole station × feature matrix in the next 1 to 48 h, which not only captures the spatial dependency among multiple stations by replacing an inner product with convolution, but also incorporates the de-trending signals (transforms a non-stationary process to a stationary one by differencing the data) into our model. Experiments on the air quality data of the city of Chengdu and multiple major cities in China demonstrate the feasibility of our method and show promising results.

## 1. Introduction

_{2}, CO, PM

_{2.5}, PM

_{10}, etc. Based on this air quality data matrix, an air quality index (AQI) can be calculated to inform the public of the air quality at present [1]. However, the general public is more interested in predicting future air quality rather than real-time reporting. This prediction not only benefits people’s daily activities (such as developing travel plans or avoiding routes with poor air quality), but also improves their health by wearing masks to reduce exposure to air pollution. It also provides policy implications for the government.

_{2.5}. To predict the level of another pollutant, e.g., carbon monoxide CO, a different model needs to be trained. Second, to improve the performance for prediction, some methods [8,12] choose to incorporate extra knowledge, such as the weather forecasting results [12] or the traffic data [8]. In practical applications, it is not convenient to collect additional information and synchronize it with air quality data. When data from multiple stations are available, the geographic correlation between these stations is expected to contribute to air quality prediction [8,12]. However, most existing methods can only process data from one station at a time, leaving spatial correlations between multiple stations ignored [3,4,10] or partially considered [8,12]. Last but not least, air quality data usually represent a high degree of non-stationarity, as shown in Figure 1, where the mean value of the data varies over time, making the modeling problem even more difficult. Ignoring the non-stationarity in the data can lead to unacceptable prediction errors and severely weaken the predictive power of the model. Therefore, learning potential spatio-temporal features from non-smooth processes is particularly important for prediction.

- 1.
- Firstly, we introduce a de-trending operation into the traditional LSTM model to effectively eliminate the long-term trend in non-stationary data. This improvement enables our model to more accurately capture the changing patterns in non-stationary data.
- 2.
- Secondly, we utilize a diffusion graph convolution to extract the spatial correlations present in the air quality data across multiple stations. This innovative method not only improves prediction accuracy, but also has important implications for understanding and predicting air pollutant spread and impacts.
- 3.
- Lastly, we propose two distinct models based on LS-deGCN for multi-site air quality prediction and evaluate them on air quality data from Chengdu and seven other major cities. The experimental results demonstrate that the proposed models significantly outperform other existing methods in terms of prediction accuracy and stability.

## 2. Literature Review and Research Gaps

_{2.5}data in the years 2013–2016 from the city of Beijing based on a flexible non-stationary hierarchical Bayesian model. Mukhopadhyay and Sahu [20] proposed a Bayesian spatio-temporal model to estimate the long-term exposure to air pollution levels in England. Since the air quality records are typically monitored over time, Ghaemi et al. [18] designed a LaSVM-based online algorithm to deal with the streaming of the air quality data. Along another direction, the Granger causality has been proposed to analyze the correlations among the air pollution sequences from different monitoring stations [7,8,12]. Suppose that the sequence of air pollutant records from one station is denoted by ${\mathbf{x}}_{t}$, and the sequence of a factor (such as the geographical correlation) from another station by ${\mathbf{y}}_{t}$, then the mathematical representation of the Granger causality is given by

_{2.5}level in Beijing. Fan et al. [11] also used the LSTM as a framework to predict air quality in Beijing based on air pollution and meteorological information. Compared with [28], the data used in [11] are collected from multiple stations, while the data from different stations are analyzed separately by ignoring the spatial correlation. In big cities, there is usually more than one station deployed to monitor air pollutants and meteorological information. The correlations among readings from different stations are highly informative in forecasting future air quality; thus, the spatial information should be incorporated. Xu et al. [29] proposed a multi-scale three-dimensional tensor decomposition algorithm to deal with the spatio-temporal correlation in climate modeling. In deep learning, a convolutional neural network (CNN) has advantages in extracting spatial features, while the RNN has superior performance in processing sequence data. Therefore, it is expected to achieve more accurate prediction by combining convolution and RNN in the analysis of spatial and temporal data. Huang and Kuo [9] proposed to stack a CNN over LSTM to predict the level of PM

_{2.5}. However, this modification results in a non-time series model, which may result in a loss of power when quantifying sequential air quality data.

_{2}, PM

_{2.5}) and meteorological parameters (e.g., air pressure, air temperature, and air humidity). As shown in Figure 2, the air quality data of the city of Chengdu involves nine monitoring stations and nine features. The entire data, thus, can be treated as a three-dimensional tensor $\mathcal{X}\in {\mathbb{R}}^{M\times N\times T}$, with respect to the three axes station × feature × time. The third dimension T corresponds to the number of timestamps, which indicates the sequential nature of the data $\mathcal{X}$.

_{2.5}, from Station 4 and Station 5, respectively. In the records of CO and PM

_{2.5}, there is a significant change from four stations to five stations, and their patterns are similar. The area where Station 5 is located seems to be more polluted than the area where Station 4 is located, and this information is useful for government policy making in different regions. The similar oscillating patterns in the records of the two stations imply that the rows and columns in the matrix station × feature are correlated and further series correlation over time can also be observed. However, there seems no obvious daily periodicity or “weekends/holidays” effect from the data.

## 3. Proposed Models

#### 3.1. Non-Stationary Diffusion Convolutional LSTM

#### 3.2. Two New Models

#### 3.3. Selection of Tuning Parameters l and ${\Delta}_{t}$

## 4. Experiments and Results

#### 4.1. Baselines

- 1.
- Linear regression: This is one of the most commonly used approaches to modeling the relationship between a dependent variable y and covariates $\mathbf{x}$.
- 2.
- Support vector regression: Equipped with a radial basis kernel, it extends linear regression by controlling how much error in regression is acceptable.
- 3.
- LSTM sequence-to-scalar (seq2scalar): Samples under this model are constructed in the same way as those under the seq2seq model. The difference is that we take the target y as one of the nine pollutants one by one; that is, we need to train nine separate models for the nine pollutants.

_{2}, CO, SO

_{2}, O

_{3}, PM

_{2.5}, and PM

_{10}) and the three meteorological measurements.

#### 4.2. Data Description and Preprocessing

_{2}, and O

_{3}were missing, which mainly occurred between June 2014 to January 2016 due to the sensor dysfunction. As a result, we only used data from seven stations and there are 35,064 instances for each station. Each air quality instance consists of the concentration of six air pollutants: NO

_{2}, CO, SO

_{2}, O

_{3}, PM

_{2.5}, and PM

_{10}, and three meteorological measurements including air pressure, air temperature, and air humidity. Therefore, the observed data are in the form of $\mathcal{X}\in {\mathbb{R}}^{M\times N\times T}$, where $M=7$, $N=9$, and $T=$ 35,064.

_{2.5}emission, then we can use the mean or the median of the PM

_{2.5}level within that frame as the target.

#### 4.3. Training

#### 4.4. Visualization of Predictions

_{3}(the third column) reported at different locations show very different patterns, and in the third frame, stations 2 and 5 reported a much higher value than other stations. The proposed model can make an accurate prediction of O

_{3}for each station. We also observe that the values of air pressure in the third frame are much lower than the other three frames, and the level of suspended particulate matter, PM

_{10}and PM

_{2.5}, in the last frame is serious, with the level of PM

_{10}from stations 1 and 6 being the top two highest. These trends are all correctly predicted by our proposed seq2seq model. From the visualization results, we conclude that (1) the patterns of the nine air quality measurements are different from one another and (2) the proposed model can make an accurate prediction based on all of the nine measurements from seven stations.

_{2.5}, PM

_{10}, SO

_{2}, CO, NO

_{2}, and O

_{3}) from 2 December 2013 to 29 February 2020 for each city. Figure 6 shows that the performance of air quality prediction for seven cities is not as good as that for the seven stations from the same city of Chengdu. One possible reason is that the spatial correlation among seven stations in Chengdu is much stronger than the seven cities that are far away from each other. This is consistent with our general understanding, thus proving the effectiveness of the proposed LS-deGCN in capturing spatial associations.

#### 4.5. Evaluation with Three Metrics

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AQI | Air quality index |

CNN | Convolutional neural network |

GCN | Graph convolution network |

GNN | Graph neural network |

LSTM | Long short–term memory |

LS-deGCN | Long–short de-trending graph convolutional network |

NLP | Natural language processing |

RNN | Recurrent neural network |

RMSE | Root mean squared error |

MAE | Mean absolute error |

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**Figure 1.**A sketch of non-stationary records of the features of temperature, pressure, PM

_{2.5}, and O

_{3}.

**Figure 2.**There are nine stations spatially distributed in Chengdu city, and CO and PM

_{2.5}levels at stations 4 and 5 are recorded on an hourly basis. (

**a**) Nine monitoring stations in the city of Chengdu. (

**b**) Spatial graph $\mathcal{G}=(V,E,A)$. V, E, and A denote the vertex set, edge set, and adjacent matrix of the graph, respectively. (

**c**) The records of levels of CO and PM

_{2.5}from station 4 and station 5 over one week. From panel (

**a**), we observe a long geographic distance between stations 4 and 5 and a strong correlation between the CO and PM

_{2.5}readings at these two stations in panel (

**c**). Spatial correlation: stations 3 and 9 have the same readings, so 9 is removed. We also removed station 8 because 40% of the data was missing. Panel (

**b**) illustrates the spatial dependency graph among the seven stations we studied.

**Figure 3.**Overview of the proposed model framework. (

**a**) Depicts the original spatial graph among the seven stations constructed based on their geographical distance; (

**b**) illustrates the process of diffusion graph convolution, which takes the geographical graph as input and outputs a refined graph; (

**c**) demonstrates the de-trending process; (

**d**) displays prediction using the seq2frame mode; and (

**e**) presents prediction using the seq2seq mode.

**Figure 4.**Mean squared errors for the training and validation datasets under (

**a**) the seq2frame model, and (

**b**) the seq2seq model, with the time lag $l=48$ and the window width ${\Delta}_{t}=48$.

**Figure 5.**Visualization of the four ground-truth station × feature frames randomly selected from the testing dataset (

**right panel**) and the corresponding prediction (

**left panel**) by the seq2seq model with time lag $l=24$ and ${\Delta}_{t}=48$. The color transition from light blue to dark blue corresponds to an increase in value from small to large, with all values normalized to the range [0, 1].

**Figure 6.**Visualization of the four ground-truth station × feature frames randomly selected from the testing dataset (

**right panel**) and the corresponding prediction (

**left panel**) by the seq2seq model for seven major cities in China. The color transition from light blue to dark blue corresponds to an increase in value from small to large, with all values normalized to the range [0, 1].

Datasets | Description |
---|---|

Training | Data from 1 January 2013 to 31 December 2015 |

Validation | Data from 1 January 2016 to 1 June 2016 |

Testing | The remaining data |

**Table 2.**Comparison of the root mean squared error (RMSE) among different methods based on the Chengdu testing dataset, where a smaller RMSE indicates a better result.

Models | $\mathit{l}=1$ | $\mathit{l}=24$ | $\mathit{l}=48$ | |
---|---|---|---|---|

Linear regression | 1.78 | 1.82 | 2.23 | |

Support vector regression | 1.61 | 1.93 | 1..98 | |

${\Delta}_{t}$ = 24 | LSTM seq2scalar | 1.04 | 1.12 | 1.25 |

Non-stationary LS-deGCN seq2frame | 0.58 | 0.78 | 1.1 | |

Non-stationary LS-deGCN seq2seq | 0.56 | 0.77 | 0.87 | |

Linear regression | 1.67 | 1.79 | 2.03 | |

Support vector regression | 1.52 | 1.76 | 1.95 | |

${\Delta}_{t}$ = 48 | LSTM seq2scalar | 0.87 | 0.92 | 0.95 |

Non-stationary LS-deGCN seq2frame | 0.45 | 0.62 | 0.67 | |

Non-stationary LS-deGCN seq2seq | 0.39 | 0.56 | 0.57 |

**Table 3.**Comparison of accuracy among different methods based on the Chengdu testing dataset, where a higher value of accuracy indicates a better result.

Models | $\mathit{l}=1$ | $\mathit{l}=24$ | $\mathit{l}=48$ | |
---|---|---|---|---|

Linear regression | 0.5634 | 0.5367 | 0.5278 | |

Support vector regression | 0.5763 | 0.5598 | 0.5557 | |

${\Delta}_{t}$ = 24 | LSTM seq2scalar | 0.7021 | 0.7167 | 0.7198 |

Non-stationary LS-deGCN seq2frame | 0.7234 | 0.7545 | 0.7517 | |

Non-stationary LS-deGCN seq2seq | 0.7365 | 0.7652 | 0.7482 | |

Linear regression | 0.5612 | 0.5423 | 0.5186 | |

Support vector regression | 0.5834 | 0.5654 | 0.5521 | |

${\Delta}_{t}$ = 48 | LSTM seq2scalar | 0.6825 | 0.7212 | 0.7237 |

Non-stationary LS-deGCN seq2frame | 0.7235 | 0.7866 | 0.7655 | |

Non-stationary LS-deGCN seq2seq | 0.7655 | 0.8123 | 0.7785 |

**Table 4.**Comparison of the mean absolute error (MAE) among different methods based on the Chengdu testing dataset, where a smaller MAE indicates a better result.

Models | $\mathit{l}=1$ | $\mathit{l}=24$ | $\mathit{l}=48$ | |
---|---|---|---|---|

Linear regression | 0.0175 | 0.0211 | 0.0234 | |

Support vector regression | 0.0158 | 0.0147 | 0.0186 | |

${\Delta}_{t}$ = 24 | LSTM seq2scalar | 0.0148 | 0.0167 | 0.0166 |

Non-stationary LS-deGCN seq2frame | 0.0092 | 0.0091 | 0.0101 | |

Non-stationary LS-deGCN seq2seq | 0.0077 | 0.0089 | 0.0093 | |

Linear regression | 0.0178 | 0.0198 | 0.0211 | |

Support vector regression | 0.0153 | 0.0132 | 0.0201 | |

${\Delta}_{t}$ = 48 | LSTM seq2scalar | 0.0136 | 0.0142 | 0.0154 |

Non-stationary LS-deGCN seq2frame | 0.0080 | 0.0079 | 0.0091 | |

Non-stationary LS-deGCN seq2seq | 0.0071 | 0.0078 | 0.0083 |

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## Share and Cite

**MDPI and ACS Style**

Hu, M.; Liu, B.; Yin, G.
Multi-Site and Multi-Pollutant Air Quality Data Modeling. *Sustainability* **2024**, *16*, 165.
https://doi.org/10.3390/su16010165

**AMA Style**

Hu M, Liu B, Yin G.
Multi-Site and Multi-Pollutant Air Quality Data Modeling. *Sustainability*. 2024; 16(1):165.
https://doi.org/10.3390/su16010165

**Chicago/Turabian Style**

Hu, Min, Bin Liu, and Guosheng Yin.
2024. "Multi-Site and Multi-Pollutant Air Quality Data Modeling" *Sustainability* 16, no. 1: 165.
https://doi.org/10.3390/su16010165