Spatio-temporal characteristics of particulate matter in Delhi, India due to the combined effects of fireworks and crop burning during pre-COVID festival seasons

Abstract

Air pollution is a common threat to all major cities worldwide for its harmful effects on human health, economy and sustainability. Occasionally, air quality is further degraded by several human activities and events. Particularly, the National Capital Territory (NCT) of Delhi, India, is susceptible to the after-effects of firecrackers bursting during Diwali, the festival of lights. Coincidentally, these effects are further accentuated by the crop residue burning prevalent in the adjoining states. In this study, the combined impacts of Diwali and stubble burning are examined around Delhi area. Spatio-temporal behavior of air pollutants, PM_2.5 and PM₁₀ (Particulate Matter with diameter $\le 2.5\,\upmu$m and $\le 10\,\upmu$m, respectively), is investigated on a weekly scale using geostatistical approach for the pre-COVID years of 2018 and 2019 to unravel short term trends, and the cause-effect relationships are explored. For both the years 2018 and 2019, North-West Delhi recorded, on an average, higher weekly mean concentrations of PM_2.5 by $10.5\%$ and $4.25\%$, and PM₁₀ by $13.11\%$ and $4.94\%$ respectively, compared to other districts. Further statistical analysis reveals that the total number of weekly crop-burning instances is correlated to the weekly mean PM levels. In order to get finer microscopic view, spatio-temporal trends of PM values are thoroughly examined on daily and hourly scale for the Diwali Week in Delhi for both the years by analyzing the effects of firecrackers bursting and stubble burning. Backward trajectory analysis indicates occurrences of pollutants transportation from neighbouring states.

Appendices

Appendices

Appendix A: details about the dataset and models

1.1 Appendix A.1: dataset quality

The PM_2.5 dataset has 9.17% and 7.09% missing values for 2018 and 2019 respectively. On the other hand, the PM₁₀ dataset contains 16.78% and 14.46% missing values for 2018 and 2019 respectively. The detailed QA/QC information for PM data by CPCB can be accessed at https://cpcb.nic.in/quality-assurance-quality-control/.

The fire count data is sourced from the Collection 6 MODIS active fire detection algorithm and fire products. Common challenges in the data may arise from geo-location errors or issues during the reprocessing phase. While the disparity between the Near Real Time and standard versions is typically under 100 ms, there are instances where this error may extend to several kilometers. For detailed insights into quality-related concerns, refer to the relevant information available at https://www.earthdata.nasa.gov/learn/find-data/near-real-time/firms/mcd14dl-nrt.

1.2 Appendix A.2: ordinary block Kriging

Kriging (Isaaks and Srivastava 1989) is a group of geostatistical techniques to interpolate the value of a random field at an unobserved location from observations of its value at nearby locations. Ordinary Kriging is one of the linear variants of kriging which assumes intrinsic stationarity of the random field under consideration. It expresses its estimates as a linear combination of the values at available locations. The solution to an Ordinary Kriging system is expressed in terms of the covariances between the values at known locations and locations at which the values are to be estimated. These covariance values are derived by modeling a variogram. A variogram describes the spatial continuity of a spatial random field Z(x). It is visualized as a plot of semivariance $\gamma (h)$ versus lag distance h. Matheron (1962) defined the theoretical variogram as: $2 \gamma (h)=Var (Z(x+h)-Z(x))$. As mentioned above, the aim is to estimate a suitable variogram function from the underlying observed data which will then be used for kriging. The steps used for the same have been well presented by Cressie (1993). While there are rules of thumb for selecting an appropriate lag size, the choice of the lag size is solely based on the creation of a variogram that can be effectively interpreted. With the available 38 data points, the empirical variogram is plotted. This empirical variogram is then fitted by a theoretical model (satisfying necessary mathematical conditions). The best theoretical fit is determined on the basis of the sum of squares error between the empirical variogram and a particular theoretical model. The fitted model parameters are then utilized to yield the covariance values required to solve the Ordinary Kriging system. This is how Ordinary Kriging utilizes spatial continuity to estimate values at point locations where the values are to be estimated. Ordinary Block Kriging (Isaaks and Srivastava 1989) is the extension of ordinary kriging to estimate block average values. For this, each block is discretized into points covering equal area. The values at these points contribute to the block average estimate. So, the ordinary block kriging predictor $Z^{*}(A)$ of the value for block A is the linear combination of Z(x) evaluated at each sample $x_{i}$, $i = 1,\ldots , n$.

$$\begin{aligned} Z^{*}(A)= \sum _{i=1}w_{i}Z(x_{i}) \end{aligned}$$

(A.2.1)

and the corresponding solution is given by:

$$\begin{aligned} \begin{pmatrix} w_{1}\\ . \\ . \\ . \\ w_{n} \\ \lambda \end{pmatrix}= \begin{pmatrix} \widetilde{C}_{11} &{}. &{}. &{}. &{} \widetilde{C}_{1n} &{} 1 \\ . &{}. &{}. &{}. &{}. &{}. \\ . &{}. &{}. &{}. &{}. &{}. \\ . &{}. &{}. &{}. &{}. &{}. \\ \widetilde{C}_{n1} &{}. &{}. &{}. &{} \widetilde{C}_{nn} &{} 1 \\ 1 &{}. &{}. &{}. &{} 1 &{} 0 \end{pmatrix} \begin{pmatrix} \overline{\widetilde{C}}_{1A}\\ .\\ .\\ .\\ \overline{\widetilde{C}}_{nA} \\ 1 \end{pmatrix}, \end{aligned}$$

(A.2.2)

where $w_{i}$ represents the weight assigned to the ith sample, $\widetilde{C_{ij}}$ represents the point to point covariance between values at $x_{i}$ and $x_{j}$, $\lambda$ is a constant and $\widetilde{C}_{1A}$ represents the point to block covariance, calculated as per the below equation. Each j below corresponds to each of the discretized points for the block A and $|A|$ denotes the number of discretized points. $\overline{\widetilde{C}}_{iA}=\frac{1}{|A|}\sum _{j|j\in A}\widetilde{C_{ij}}$. In the process of solving the Ordinary Block Kriging system, the original data, in the latitude/longitude coordinate system, have been transformed to EPSG:24378 projected coordinate system followed by the variogram modeling. The variogram models are then used to find the solution of the kriging system. All the variograms are found to be omnidirectional. The spherical variogram model (Isaaks and Srivastava 1989) was chosen for empirical fitting from the observed data due to its simplicity and capacity to well interpret environmental variables. Notably, the week-wise fitted variogram parameters for PM_2.5 and PM₁₀ are provided in Table 2. The analysis has been performed in 2 stages, the first stage involving the interpolation of the pollutant concentrations at the block level and the second stage involving the collation of the block average pollutant concentration values at the district level. The district level mean pollution has then been analyzed to find spatial insights.

1.3 Appendix A.3: HYSPLIT model

HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory model), is an atmospheric transport and dispersion modeling framework, developed by National Oceanic and Atmospheric Administration (NOAA), USA. The model is used to simulate the movement and dispersion of the atmospheric pollutants considering the underlying meteorological conditions. Primarily, this model provides the trajectory of the pollutants by tracking the evolution of the air particle movements over time. In addition, this modeling framework helps the users understand the locations of the pollutants that are likely to settle. There are two types of approaches for modeling atmospheric dispersion: Eulerian model, which solves advection–diffusion equation on a fixed grid, whereas, a Lagrangian models’ computational grid can define the source emissions at any resolution where the advection and diffusion calculations are performed independently (Draxler and Hess 1998). This model follows a hybrid approach between Eulerian and Lagrangian methods.

The following parameters, such as, the atmospheric stability, corresponding atmospheric mixing and pollutant dispersion rate are required to be obtained in order to generate the trajectories. The horizontal and vertical puff dispersion equations are formulated in terms of the turbulent velocity components (Draxler and Hess 1998). These velocity components are dependent on several parameters, such as pollutant vertical mixing coefficient (K_z), sub-grid scale horizontal mixing coefficient (K_h) (computed from velocity deformation), stability parameters like friction velocity, obukhov length etc (Draxler and Hess 1998). These parameters are obtained from meteorological variables. The model uses the following meteorological databases for extracting meteorological data: (a) GFS 0.25°, (b) GDAS 0.5°, (c) GDAS 1°, (d) Global Reanalysis 2.5° to simulate the puff trajectories using advection–diffusion equations under the Lagrangian model settings.

The surface field parameters such as surface pressure (PRSS), 10 m wind speed components (U10M, V10M), Planetary Boundary Layer Height (PBLH), pressure level of tropopause and upper-level fields with different pressure levels, temperature, vertical wind speed and several other parameters are used by the HYSPLIT model for generating the pollutant trajectories (Stein et al. 2015). The model was validated using real-dispersion data from Tracer experiments like ANATEX GGW, CAPTEX experiments (Draxler and Stunder 1988; Chai et al. 2018). HYSPLIT is considered as an effective tool for identifying the pollutant sources for a single or multiple atmospheric pollutant puffs/particles in different studies since its development (Ashrafi et al. 2014).

1.4 Appendix A.4: regression models

We developed multiple linear regression (MLR) models using the independent variables as the external fire factor namely the daily fire count in the neighboring states (OutFire) and daily median wind speed observations in Delhi (WS) spanning 9 weeks of pre, during and post-Diwali for the concerned duration of this study. The MLR models have been developed for two different scenarios, where the response variables are designated as daily averaged concentrations of PM_2.5 and PM₁₀ respectively.

For PM_2.5 as response variable, the MLR model is given as

$$\begin{aligned} \mathrm {PM_{2.5}}= - 142.55 \hspace{2pt}\textrm{WS} + 0.0599\hspace{2pt} \textrm{OutFire} + 273.62 \end{aligned}$$

(A.4.3)

For PM₁₀ as response variable, the MLR model is given as

$$\begin{aligned} \mathrm {PM_{10}}= - 221.10\hspace{2pt} \textrm{WS} + 0.0596 \hspace{2pt}\textrm{OutFire} + 477.30 \end{aligned}$$

(A.4.4)

The p values corresponding to the coefficients of the two regression models (Eqs. A.4.3, A.4.4) were observed to be less than 0.05 for each of the cases. As a result, the MLR models provide strong evidence of statistically significant impact of Stubble burning and Wind Speed on PM concentrations.