# Measuring Gas Flaring in Russia with Multispectral VIIRS Nightfire
## 2 Method
### Cloud-Free Aggregation of Radiative Heat from Flares  
For the given aggregation time interval (month, year), we extracted time series of VNF detections inside the cluster boundaries of an individual flare to estimate the mean temperature, averaged coordinates, radiative heat \(RH\) (combustion energy, radiant heat)  
Figure 2: Examples of high spatial resolution imagery available in Google Earth for hotspots detected with VIIRS Nightfire produced by oil and gas sector related gas flares (first row) and other anthropogenic and natural sources (second row). and flare shape. If the flare was detected in multiple pixels on the same image, we selected the detection with maximum radiance in M10 spectral band. By averaging the coordinates of the maximum radiance within the flare boundaries, with time we could locate an individual flare with a precision of a few hundred meters relative to the daytime images from Google Earth for frequently detected gas flares [16]. Before aggregation, we interpolated missing radiative heat values when the flare was detected only in one SWIR spectral band, and it was not possible in VNF to estimate its size and temperature by Planck curve fitting. For these detections in the Stefan-Boltzmann law of radiative heat,  
\[RH=\sigma T^{4}S, \tag{1}\]  
we assume that the flare temperature \(T\) has its mean value, and the flare surface area \(S\) is a fraction of the pixel footprint equal to the ratio of the observed radiance in SWIR band M10 and the radiation of black body at the same temperature and wavelength, defined by the Planck law. VIIRS observes the Earth at satellite zenith angles ranging from zero (nadir) to 70 degrees (edge of scan). In examining the observed signals from flares, we found that flares tend to have higher radiance when viewed at high satellite zenith angles due to the buoyancy of the hot gas relative to the surrounding air. Thus, flare footprints appear larger when viewed from the side and smaller when viewed from straight above (the nadir view) [6]. The expression of this in VIIRS data is that the flares have higher radiance when viewed at an oblique angle when compared to the nadir, yet the temperature remains stable across all viewing angles. The three-dimensional shape of flares can be modeled as an ellipsoid, based on the apparent size of flares versus the satellite zenith angle. The footprint viewed by satellite from a zenith angle \(\alpha\) will be:  
\[S(\alpha,H,R)=\pi R\sqrt{(H^{2}+R^{2}-(H^{2}-R^{2})\cos(2\alpha))/2}, \tag{2}\]  
where \(H\) and \(R\) are flare width and height, respectively. For frequently observed flares, it is generally possible to calculate the aspect ratio \(H/R\) using non-linear regression of Equation (2) to the set of flare footprints from different satellite zenith angles. It has been previously observed that typical flare geometry has an aspect ratio in the range of 1-4, with an average of 1.6 [6] (p. 6). To compensate for the variability of the zenith angle, in the time series aggregation we correct the detected flare surface area as if it is viewed from aside (zenith angle 90\({}^{\circ}\)). To avoid the signal attenuation through thick clouds, we aggregate only cloud-free observations and normalize the mean radiative heat (\(RH\)) for the detection frequency:  
\[\text{norm}(RH)=\text{mean}(RH)\ ^{*}N(\text{cloud-free detections})/N(\text{cloud-free observations}), \tag{3}\]  
where cloud-free observations indicates the number of VIIRS scans for the Nightfire-identified hotspot contour of interest which are undisturbed by cloud cover, while cloud-free detections indicates the number of cloud-free observations with a successful gas flare detection within the same contour. The quotient of the two variables thus results in gas flare detection frequency (\"_pct_\" in the Nightfire catalog). Cloud-free detections were identified with the VIIRS cloud mask product [33]. Testing indicated that detections through thin clouds with a cloud optical thickness less than 0.01 can also be used for the cloud-free aggregation [34].