**3. Results**

We studied the effect of the meteorology, emissions rate and size of the burning area. For illustrative purposes, we report results for the case of sugarcane burning. However, these results are valid for any crop.

#### *3.1. The E*ff*ect of Meteorological Conditions on Pollutant Concentration*

As a first step, we studied the effects of meteorology on the dispersion of pollutants. Arbitrarily, we kept the PM2.5 emission rate constant at 1 g/s over a burning area of 1 ha. As expected, meteorology significantly affects PM2.5 concentration at ground level. Figure 2 presents the daily maximum concentration obtained at any receptor over an extension of 10 km × 10 km, after considering the datasets of 1-h meteorological data listed in Table 2. This figure indicates that the meteorological data No. 2 (Minnesota) induced the highest level of pollutant concentration. This meteorology has an average temperature of 4.5 ◦C and wind speed of 2.7 m/s with no preferential wind direction. Besides low average wind speed, we could not identify a special characteristic of this meteorology that makes it the worst-case scenario. From now on, we only consider this meteorology as it constitutes the scenario that produces the highest concentrations.

**Figure 2.** Maximum average daily PM2.5 concentrations produced at any receptor over an extension of 10 km × 10 km by the burning of sugarcane biomass on a squared 1 ha area, after considering the datasets of 1-h meteorological data listed in Table 2. The arrow identifies meteorology No. 2 (Minnesota), which produced the highest PM2.5 concentrations.

#### *3.2. The E*ff*ect of Emission Rate on Pollutant Concentration*

AERMOD has a linear response to changes in emissions. Aiming to confirm this expected behavior, a base emission of 1 g/s was used. This emission was multiplied by 0.1 and 10. We set these values as the new emissions rates and observed PM2.5 concentrations nearby the emission source as predicted by AERMOD. Figure 3 compares PM2.5 concentration obtained at every receptor in the base case scenario against the corresponding concentrations obtained with different emission rates. This comparison was performed in terms of normalized concentration, i.e., concentration divided by the emission rate. Figure 3 shows that all data points fall within the 45-degree line, regardless of the emission rate, confirming that, according to AERMOD, PM2.5 concentration, at ground level, nearby the emission source is proportional to the emission rate.

**Figure 3.** Comparison of the normalized PM2.5 concentration at ground level obtained by AERMOD when the emission rate is 0.1 and 10 g/s against the normalized concentration when the emission rate is 1 g/s. Normalized concentration is obtained when the resulting concentration is divided by the emission rate in the source. Results were obtained for a burning area of 1 ha and the Minnesota meteorology dataset.

#### *3.3. Determination of the Influence Area*

As explained above, due to the short-term nature of the agricultural burning events, and because those events could happen at any time of the year, the determination of the influence area requires:


Figure 4 shows the maximum daily PM2.5 concentration obtained at each receptor located over a 10 km × 10 km region that surrounds a squared burning area of 1 ha with an hypothetical emission rate of *E* = 18.6 g/s. It shows that, due to the random wind direction, the influence area does not exhibit any regular shape. Therefore, for the case of agricultural burning, we redefined the influence area as the circle whose radio includes all areas where pollutant concentrations exceed the air quality standards defined by local environmental authorities.

Afterwards, we ran a set of cases changing the size of the area source from 1 m<sup>2</sup> to 20 ha and observed their resulting influence areas. As farmers partially control the burning rate by controlling the length and number of lines of starting fire fronts, we considered two alternatives:


(**a**)

(**b**)

**Figure 4.** PM2.5 ground concentration over a 10 km × 10 km region as result of the sugarcane burning on a square area of 1 ha at a burning rate of 18.6 g/s: (**a**) 3D representation of PM2.5 concentration; and (**b**) 2D representation of PM2.5 concentration. The lines in (**b**) represent circumferences centered in the emission source that limit the obtained influence area when the threshold value is 50 μg/m<sup>3</sup> (yellow), 100 μg/m<sup>3</sup> (blue) and 300 μg/m<sup>3</sup> (red).

In real practice, farmers burn with a combination of both alternatives and therefore we considered this third alternative in our simulations. In all cases, we reported the size of the resulting influence area as the radii of the resulting influence area minus the edge-size of the burning area.

We determined the size of the influence area generated by an area source of 1 ha, varying the emission rate. The obtained results are plotted in Figure 5a. It shows that the size of the influence area increases with the emission rate, following a logarithm profile. This profile crosses the area size axis at an emission rate of about 2 g/s. This means that farmers can burn at a rate smaller than this critical rate generating a negligible influence area. For the case of sugarcane, this value means a maximum burning rate of 1.5 ha/day.

When the emission rate remains constant, the size of the influence area remains constant regardless of the size of the burning area (Figure 5b). The burning of 1 m<sup>2</sup> at a given emission rate produces the same size of influence area as the burning of 1 ha at the same emission rate. The difference is that, under these circumstances, it takes 10<sup>4</sup> times longer to complete the burning task of 1 ha than of 1 m2. This result implies that the size of the influence area is determined by the burnings near the edge of the area source. Aiming to observe the variation of these results with the orientation of the area source, we varied it from 0–170 degrees. The results are presented in Figure 5c. For the case of an area source of 1 ha, with an emission rate of 18.6 g/s, under all orientations that we ran, the influence area

was ~2000 m considering PM2.5 as the limiting pollutant. The influence area for PM10 and TSP (Total Suspended Particles) were ~1500 and 500 m, respectively.

**Figure 5.** Size of the influence area generated by agricultural burning as function of: (**a**) emission rate considering different burning area sizes; (**b**) burning area keeping emission rate constant at 18.6 g/s; and (**c**) burning area orientation respect to north, keeping constant the emission rate at 18.6 g/s and the burning area at 1 ha.

Finally, we considered burning areas with shapes different from a square. The area of any irregular polygon can be constructed as the combination of multiple squares of different sizes. Using the principle of superposition, the influence area produced by the area source of irregular shape is the union of the influence areas generated by each independent squared area. Therefore, the influence area generated by the burning of crops cultivated on areas of any shape is the area band that surrounds the burning area. These results are independent of the type of crop or biomass being burned.

#### *3.4. Recommendations for Policy Makers*

In the light of this work, we sugges<sup>t</sup> that policy makers interested in controlling the activity of agricultural burning and/or any open atmosphere biomass burning should be aware of:


(i) the amount of biomass burned per crop; (ii) the emission factors for the relevant pollutants per crop; (iii) the understanding and modeling of the pollutant dispersion phenomena; and (iv) secondary e ffects such as changes in atmospheric dynamics and alterations in the cloud formation processes.


Based on the results obtained in this work, we propose that the environmental authorities:

