**2. Methodology**

The dispersion of the atmospheric pollutants generated by the burning of several agricultural crops was simulated using AERMOD over a region with general characteristics (flat terrain) and under multiple meteorological conditions. We observed the size of the influence area generated on each case for di fferent sizes and geometries of the burning areas. Aiming to facilitate the analysis, we identified the crop and the pollutant that produced the largest mass emission per unit of cultivated area. Next, we describe the regions studied, the meteorology considered, the estimation of the emission rates and the methodology used to determine the influence area.

## *2.1. Study Region*

The most frequent cases of agricultural burning occur in areas located on relatively flat terrains enclosed by rectangular polygons, in the surroundings of urban centers [21]. As shown below, the determination of the influence area of agricultural burning occurring in areas delimited by non-regular polygons can be analyzed as a combination of multiple squared areas. Therefore, as a base case, we used a burning area of 1 ha. To evaluate the sensitivity of the model to the size of the burning area, we varied it from 1 m<sup>2</sup> to 20 ha and considered di fferent area orientations. The determination of the influence area generated by agricultural burning in mountainous terrain requires special simulations

for each region considered. Furthermore, traditional dispersion models present problems to estimate accurately the concentration of pollutants under those conditions. Therefore, they are out of the scope of the present work.

A grid of discrete receptors was defined within the computational domain with a resolution of 100 m over an area of 10 km × 10 km, as shown in Figure 1. Although the results do not depend on the location of the area under consideration, for illustrative purposes, we used the Valle del Cauca region, located in southwest Colombia, which is one of the most important areas of sugarcane cultivation. Colombia is the seventh producer of sugarcane worldwide, and where approximately 16,425 ha are burned per year, and where on average 1.5–2 ha are burned per burning event [19].

(**a**) (**b**)

**Figure 1.** (**a**) Top; and (**b**) perspective view of the sugarcane area selected in this work to illustrate the estimation of the influence area generated by agricultural burning. The red square represents a burning area of 1 ha.

#### *2.2. Air Dispersion Model*

In this work, we used AERMOD to study the dispersion of the pollutants produced inside the burning area. As stated above, this model is recommended by the USEPA when their results are planned to be used for regulatory purposes. It is a steady-state model that assumes that pollutants concentration downwind the area source follows a Gaussian distribution in the vertical and horizontal direction of the plume, according to Equation (1).

$$C = \frac{Q}{\mu} \cdot \frac{f}{\sigma\_y \sqrt{2\pi}} \cdot \frac{g}{\sigma\_z \sqrt{2\pi}} \tag{1}$$

where *C* is the pollutant concentration (g/m3); *Q* is the pollutant emission rate (g/s); *u* is the horizontal wind speed along the plume centerline (m/s); *H* is the height of emission plume centerline above ground level (m); σ*z* and <sup>σ</sup>*y* are the vertical and horizontal standard deviation of the emission distribution (m), respectively; and *f* and *g* are the vertical and horizontal dispersion parameters, respectively.

Gaussian models, and specifically AERMOD, do not allow, on the first instance, to model sources that change their position over time. As an approximation, we assumed that the entire emission source area burns simultaneously, but at a rate such that the emission rate of pollutants (g/s) remains constant. In Section 3, we will show that this assumption is acceptable for this study because the size of the influence area is independent of the size of the burning area being considered.
