Downwind Box Calculation

The determination of the downwind box geometry is carried out through three sequential operations, as described on page 16575 of Sadavarte, et al., 2021 :

We start with a smaller rectangular mask of dimension (length x breadth) 0.4 x 0.2° placed at the source in the downwind direction inferred from boundary layer average ERA5 meteorology to define the area containing the plume (Figure S1). Next, we rotate this mask from -40 to +40° at 5° intervals around the inferred ERA5 wind direction such that the average XCH4 enhancement in the rectangular mask is maximal. After we set the new wind direction, the length of the rectangular mask in the downwind direction (along the x-axis) is varied to define the end of the plume. This end is fixed by incrementing the length of the rectangular mask by 0.1° intervals until the difference between ${\mathrm{XCH}}_4$ enhancement of two consecutive increments is less than 5 ppb. Similarly, the width of the rectangular mask (along the y-axis) was fixed by incrementing the width in the lateral direction of the plume at an interval of 0.05° until the incremental change in ${\mathrm{XCH}}_4$ enhancement is less than 5 ppb.

The determination of the downwind box geometry depends on how enhancement is defined, which is not uniquely prescribed. One possible interpretation defines enhancement as the difference between the observed ${\mathrm{XCH}}_4$ field and the estimated background, with all pixels exhibiting zero or negative differences masked out. Under this definition, enhancement values are strictly non-negative.

An alternative interpretation defines enhancement simply as the difference between the observed ${\mathrm{XCH}}_4$ field and the background concentration, without masking negative values. Under this definition, enhancement values may be negative and are retained in subsequent calculations. In the context of atmospheric dispersion, negative values typically represent net removal through absorption. Such processes are outside the scope of this analysis and are assumed to be negligible over the timescale relevant to plume evolution.

To illustrate this issue, consider Figure 7 below. The left panel shows the behaviour of the algorithm when no masking is applied to the enhancement field. Brown pixels represent the true plume, characterised by a uniform enhancement of 10 ($\mathrm{ppb}$), while the blue pixels indicate additional areas considered by the plume adjustment algorithm during the downwind box expansion process.

In the left panel, no masking is applied. The incremental change in mean enhancement resulting from the proposed box expansion is 4 ($\mathrm{ppb}$), which does not exceed the continuation threshold 5 ($\mathrm{ppb}$). Consequently, the algorithm rejects this expansion and terminates the adjustment step.

In the right panel, the pixel with a negative enhancement -3 ($\mathrm{ppb}$) is masked out. As a result, the mean enhancement increase associated with the proposed box expansion is 7 ($\mathrm{ppb}$), which exceeds the continuation threshold. Consequently, the algorithm accepts this expansion and proceeds to the next iteration.

Below, we discuss the outcomes of each of the three downwind box adjustment operations separately.

Adjustment of downwind box direction

A rectangular box with dimensions 0.4° × 0.2° was applied to the image, and the mean ${\mathrm{XCH}}_4$ enhancement was computed for box rotations spanning -40° to +40°. The maximum average enhancement of 5.83 ($\mathrm{ppb}$) was obtained at a rotation of +5°, corresponding to an azimuth of 264.362°. The results of this rotation analysis are summarised in Table 10.

Adjustment of downwind box length

The purpose of this step is to extend the downwind box length until the incremental increase in mean enhancement becomes negligible. Specifically, the box is lengthened iteratively until the increase in average enhancement falls below a predefined threshold of 5 ($\mathrm{ppb}$). This procedure aims to maximise the number of plume pixels captured by the box model while avoiding unnecessary inclusion of background pixels. The method implicitly assumes that further extension of the box does not intersect emissions from other independent plumes. The procedure terminates at the distance of 110 km. See Table 11.

Adjustment of downwind box width

The width adjustment is performed in the same manner as the length adjustment, incrementally expanding the box width until the increase in average enhancement falls below the prescribed threshold. In this case, the procedure terminates at a box half-width of 27.5 ($\mathrm{km}$). The results of the width adjustment step are summarised in Table 12.

Main constructs

The key elements constructed by the algorithm are illustrated in Figure 8 below.