## 3 Methods
### Data
The study area considered in this work is contained between \(-9.5\) and \(-45.5\) degrees latitude, and \(129.5\) and \(167.5\) degrees longitude, covering the eastern portion of Australia, including parts of SA, NT and of the Pacific Ocean; it is depicted by a checkerboard pattern in Figure 5. This area will be referred to here as the study area. All the ozone/aerosol data are from the 2019-2020 Australian bushfire period covering the dates from 1 September 2019 to 29 February 2020 and will be called the study time period. There is a total of 182 days between these two dates. On the 68 th day (7 November 2019), the first sign of bushfire aerosol emissions appears and the last relatively small emission of bushfire aerosols occurs on the 159 th day (6 February 2020). Total sum ozone (TSO) and total sum aerosol (TSA) values are also computed. These total sum values are equal to the sum of all cell values contained within the rectangular region. We have defined three regions, located on or off the east coast of Australia, and they will be referred to as Region 1, Region 2 and Region 3. The longitude (lon) and latitude (lat) coordinates of their respective left/right and top/bottom edges, and a description of their location on the map of these rectangular regions are as follows:  
* Region 1--lon 160.5-165.5 and lat \(-29.5\)--\(32.5\), Pacific Ocean approximately 500 km east of the midpoint between Sydney and Brisbane. * Region 2--lon 146.5-151.5 and lat \(-36.5\)--\(39.5\), Coast of Victoria. * Region 3--lon 148.5-153.5 and lat \(-31.5\)--\(34.5\), Coast of NSW. The three regions are displayed in Figure 5.  
The choice of these three regions was guided by the following considerations:  
1. The location of the source of the majority of aerosol emissions; which were associated with the bushfires reported in Victoria and New South Wales (NSW). 2. The average wind direction during the time period; in a north-easterly direction towards Region 3. Figure 5: Outline of the map of Australia showing the locations of the three regions. The regions in order from top to bottom: Region 1 (Blue), Region 2 (Red) and Region 3 (Green). The checkerboard shading pattern identifies the study area. 3. These choices could potentially simplify the task of finding the correct day offset (the time delay or day offset between the release of aerosol and the resultant changes in ozone). The location of Region 3 (NSW) was selected because, on a number of days, it had an unusually high level of aerosol, and hence had a higher chance for interactions between aerosol and ozone to occur and improved the ability of the methods to more accurately detect that relationship. We are also interested in the time delay, or day offset, between the release of aerosol and the resultant changes in ozone. Whatever the number of days offset may be, say 3 days, aerosol disperses in the atmosphere and is transported by the wind during these 3 days. From the visual inspection of the aerosol plot (see Figure 6), it is observed that aerosol ends up spreading over a significant area around where Region 3 is located. For better causal modeling we have included additional parameters, the aerosol for each grid cell within the study area, the cumulative number of days since 3 November 2019 (cdate) and the day of the year (day) over the dates of the study time period. From the visual inspection of the Ozone plot (see Figure 7), it is observed that the ozone levels diminish, and these areas of decrease are observed over all the regions over the 20 days post November 3. Also, as a comparison, Figures 8 and 9 display the time series profiles for Total Sum Ozone and Total Sum Aerosol, respectively, over time and all 3 regions. Figure 6: Observed from data of daily gridded aerosol values plot of entire study area over the 20 days from 3 November 2019. Figure 8: Time series plot of Total Sum Ozone for each region. Figure 7: Observed from data of daily gridded ozone values plot of entire study area over the 20 days from 3 November 2019.