key: cord-0952162-prt8u6e1 authors: Gao, Mingyun; Yang, Honglin; Xiao, Qinzi; Goh, Mark title: COVID-19 lockdowns and air quality: Evidence from grey spatiotemporal forecasts date: 2022-01-11 journal: Socioecon Plann Sci DOI: 10.1016/j.seps.2022.101228 sha: 8217494dde8974f09ee9a90344876f571e6d5c2f doc_id: 952162 cord_uid: prt8u6e1 This paper proposes a novel grey spatiotemporal model and quantitatively analyzes the spillover and momentum effects of the COVID-19 lockdown policy on the concentration of PM2.5 (particulate matter of diameter less than 2.5 μm) in Wuhan during the COVID-19 pandemic lockdown from 23 January to 8 April 2020 inclusive, and the post-pandemic period from 9 April 2020 to 17 October 2020 inclusive. The results suggest that the stringent lockdowns lead to a reduction in PM2.5 emissions arising from a momentum effect (9.57–18.67%) and a spillover effect (7.07–27.60%). Strict lockdown policies to restrict movement control and to enforce working from home 22 in order to combat the COVID-19 pandemic has helped major industrial centres in Asia such 23 as Wuhan to return to economic normalcy. Consider the series of lockdown policies from 23 24 January to 8 April 2020 enforced on Wuhan and other cities in Hubei, China to curb the 25 outbreak of COVID-19. This strict lockdown policy imposed on the Wuhan Metropolitan Area 26 (WMA) involved suspending factory production, movement control, and working from home 27 was an unprecedented move, albeit at massive economic and social costs [1] . Nevertheless, it 28 was effective in controlling the outbreak [2], resulting in a spillover effect on reducing CO2 29 # Mingyun Gao and Honglin Yang contributed equally to this manuscript. 3 since the future value is known in the next period. 60 Since the outbreak of COVID-19, several studies have been undertaken to discuss the 61 spillover effect of a lockdown on air quality. For instance, Li and Tartarini [13] quantified the 62 effect of the lockdown measures on outdoor air pollution levels in Singapore. Studying the 63 spatiotemporal impact of COVID-19, Liu et al. noted that the lockdown reduced the overall 64 amount of air pollutants in California [14] , and found that the mitigation policies reduced the 65 overall trend of NO2 emissions in most target countries [15] . Assessing the level of PM2.5 from 66 the 50 most polluted capital cities globally, Rodríguez-Urrego [16] found that cities under 67 quarantine decreased PM2.5 by 12.5% on average, when comparing the air pollutants before 68 and during COVID-19. Perera et al. modeled the potential future health benefits to children 69 and adults, and reported that the air quality in New York continued to improve during the 70 COVID-19 lockdown [17] . Such spillover effects of the lockdown policies are measured 71 through the comparative analysis of the air pollutants during COVID-19 and those before the The traditional air quality prediction methods focus on statistical or econometric models, 85 which are based on economic or geographical phenomenon (such as seasonality, periodicity or 86 spatiotemporal patterns [19] ). Table 1 lists these representative methods. there has been a marked improvement in the air quality in Wuhan [51] . To measure the spillover 151 effect on environmental improvement during a lockdown, this study has therefore chosen 152 WMA as the study area when constructing the PM2.5 forecasting model. where a is the development coefficient of the model, and b is the grey input of the model. 227 Moreover, the whitenization differential equation of the GM(1, 1) model is given by Equation (4) (4) 230 For Equation (4), given the initial condition (1) (5) 233 Then, (0) x , the prediction of (0) x , can be obtained using Equation (6) 234 (6) 235 The GM(1,1) model is the most basic grey model used to characterize the discrete time 236 series with an approximate differential equation. The GM(1,1) model and its extensions 237 consider only the temporal dependence but rarely discuss spatial dependence in the dataset. where f is a spatial dependence function. In the most general case, a weight matrix is used 245 to depict this functional spatial dependence. For the original spatiotemporal data matrix of Equation (9), let its accumulated generated 268 data be denotes the accumulated generated 269 observation in location i at moment k， 2,3, , kn  . Then, (1) X is obtained using Figure 2 , the spatial sequence, (1) () Xk , can be formulized with the FAR model (Equation (8)) from a spatial viewpoint at moment k . By considering both 275 temporal and spatial dependence, this paper constructs the spatiotemporal differential equation 276 (Equation (11)) for the STGM(1,1) model while ignoring the spatial error  as follows. 277 278 Definition 3. The spatiotemporal differential equation (Equation (11)) is labeled as the 279 whitenization differential equation of STGM(1,1), with According to Equation (11), the rate of change of the cumulative consumption (1) . Further, the background value of this grey derivative can be written as Equation (13): 13 In grey modeling, the background sequence (1) . In Equation (15), 301 a and b are the parameter matrices to be estimated. 302 For spatial unit i , its parameters, , can be estimated through Theorem 1, 303 which provides an estimation method for i P . 304 , and the least squares estimation of i P satisfies into Equation (14) yields (1) (1) , (2) (2) For the estimation value of the reference sequences i P , using ( 2,3, , ) kn  on the left-hand side, we obtain the sequence Then, the parameter sequence   The above equations are then converted into matrix form, namely, The proof of Theorem 3 is now complete. The steps of this combined model are as follows: 375 Step 1. Collect the original data space-time series ,, Step 2. Determine the spatial weight matrix W , and test W based on Moran's I test. Step 3. Form the accumulated generated observation matrix Step 4. Find the model prediction value sequence Step 5. Forecast the remainder component using LSTM, and form the forecast of ,, i k d y . Step 6. Verify the results and analyze the errors of this model. As shown in Figure 6 , the major parameter matrix of the spatiotemporal differential 409 Equation (9), W is a spatial weight matrix whose spatial structure is referred from the literature The STGM results are compared against four models, i.e., GM(1,1) without spatial 419 dependence, multi-variable grey model (MGM) [69] , ARIMA, and STARMA [70] . The metrics, 420 MAPE and STD, are used to evaluate these results. Table 3. 460 The left of Figure 7 shows that there is a spatial effect in the PM2.5 concentration of these 486 cities. As shown in Figure 1 the cyan curves are always the lowest, which means that there will be more spillover effects 538 from reducing the PM2.5 concentration if the lockdown period were to be extended. 539 These spillover effects are spatial heterogeneous. On the right of Figure 10 , the difference 540 between the cyan and the other curves in Wuhan is always larger than those in the other cities, 541 suggesting a greater spillover effect in Wuhan. This is due to the social structure or economic 542 differences of these cities. Hence, the policies instituted during a lockdown should be tuned to 543 local conditions notably the environmental and economic concerns. Table 4 . the lockdown policies should be adjusted based on economic and environmental considerations. Lockdown is gradually dying out. 594 On the other hand, the air pollution from traffic also is affected by the momentum effect. 595 Although the daily traffic travel has been close to pre-epidemic levels since April 22th 2020, Declaration of competing interests 628 The authors declare that they do not have any competing financial interest nor personal 629 relationships that could have appeared to influence the work reported in this paper. 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