# Measuring Gas Flaring in Russia with Multispectral VIIRS Nightfire
## 2 Method
### Calibration of the Flared Gas Volume Estimates Based on the Average Radiative Heat of Flares  
Regression methodology was developed to determine the calibration for the VIIIRS Nightfire response in terms of flared gas volume using national-level reporting of upstream flaring for 47 countries provided by Cedigaz [6] (p. 8). Cedigaz includes only flare volumes at oil fields in its reported data [4]. In Russia in particular, there is a substantial volume of flaring at natural gas and gas condensate fields (see Section 3), which is not included in the Cedigaz estimates. Only flares related to oil fields in Russia were used for the calibration. At the time of the calibration study, the Cedigaz data were available for the years 2012-2017.  
Non-linearity was introduced by applying an exponent to the source area in the calculation of a modified \(RH\) from Equation (1)'s estimate, \(RH\)', for each flare. As part of the calibration process, the value of the exponent was tuned to achieve the highest possible R\({}^{2}\) coefficient of determination between reported flare volumes and \(RH\)'. For the calibration, annual \(RH\)' estimates from all of the upstream gas flaring sites within the national boundaries were summed, with normalization for cloud cover and the number of valid night-time observations. To determine the optimal exponent for modulating the source areas for estimating \(RH\)', source areas were modulated using exponents ranging from 0.4 to 1.0 and evaluating the coefficient of determination R\({}^{2}\) between \(RH\)' and the reported data. The highest R\({}^{2}\) occurred for an exponent \(D\) = 0.7 [6] (p. 8).  
\[RH^{\prime}=\sigma T^{4}S^{D}. \tag{4}\]  
The linear regression relating the Cedigaz reported \(BCM_{i}\) and \(RH\)' estimated by VIIRS Nightfire is  
\[BCM_{i}=b_{0}+b_{1}\times RH^{\prime}_{i}+\varepsilon_{i}, \tag{5}\]  
where \(i\) = 1... \(n\), and \(n\) is the number of countries in the Cedigaz report, and the residuals \(\varepsilon_{i}\) are the regression errors [43]. The linear model is significant at the 5% level and it explains 83% of the variability in the response.  
We found that the intercept \(b_{0}\) is not significant for the linear model at the 5% level, and thus simple regression through the origin (RTO) [44] can be used for calibration:  
\[BCM_{i}=b_{1}\times RH^{\prime}_{i}+\varepsilon_{i}. \tag{6}\]  
Using the ordinary least squares, the estimated RTO slope \(b_{1}\) with 95% confidence intervals is  
\[b_{1}=0.0294\pm 0.0017 \tag{7}\]  
The 95% prediction interval for an individual country/year varies in a narrow range from \(\pm\)3 to \(\pm\)3.5 BCM within the full range of the observed national-level sums of \(RH\)' from 0 to 700. Predicted total flared volume for all the countries with the Nightfire-detected flares (not only from the Cedigaz dataset) varied year by year in a range from 137 to 142 BCM with 95% prediction interval \(\pm\)30 BCM. National-level correlation between the sources is presented in Figure 3. Exact regression slope coefficients can be found in Table S1 in the Supplementary Materials section.  
In Figure 3, it is apparent that observations for some countries form their own distinct groups. Cedigaz reported almost non-existent flaring in Saudi Arabia, while significant flaring activity is observed with Nightfire. Algeria appears to be another noticeable outlier, with Cedigaz's estimates falling outside of the 95% confidence intervals, which could possibly be attributed to significant flaring at natural gas upstream and downstream facilities. Gas flaring in Venezuela and Iran tends to be underestimated with Nightfire, presumably due to Nightfire's tendency to underestimate large flares (see Section 4.2), which are typical for these countries.