Sampling variability under extreme skewness: sample size guidance for future methane measurement campaigns

William Stewart Daniels , Dorit M Hammerling 

Methane emissions from the oil and gas sector follow highly right-skewed distributions, making it hard to accurately quantify average emissions with a limited number of measurements. In this study, we probe the statistical implications of sampling (i.e., measuring) from these highly right-skewed distributions, using six US oil and gas basins as an example. For each basin, we provide a minimum sample size that bounds error in the average emission rate estimate introduced by sampling variability. We find that the largest emissions drive sample behavior, and by extension, sample size requirements; samples will underestimate (overestimate) average emissions if super-emitters are observed below (above) their true frequency. Importantly, we show that very large sample sizes can be necessary to mitigate this sampling effect. Furthermore, we find that a one-size-fits-all sampling strategy across basins is suboptimal; differences in super-emitter characteristics between basins necessitate a more tailored sampling approach. To increase the practical applicability of this study, we provide a web tool that both reproduces our findings and performs the same analysis on any user-uploaded distribution of emission rates; the flexibility of this tool enables highly targeted sample size guidance. This work has broad utility across fields where samples are taken from right-skewed distributions.