  Measurement-based methane inventories, which involve surveying oil and gas
facilities and compiling data to estimate methane emissions, are becoming the
gold standard for quantifying emissions. However, there is a current lack of
statistical guidance for the design and analysis of such surveys. The only
existing method is a Monte Carlo procedure which is difficult to interpret,
computationally intensive, and lacks available open-source code for its
implementation. We provide an alternative method by framing methane surveys in
the context of multi-stage sampling designs. We contribute estimators of the
total emissions along with variance estimators which do not require simulation,
as well as stratum-level total estimators. We show that the variance
contribution from each stage of sampling can be estimated to inform the design
of future surveys. We also introduce a more efficient modification of the
estimator. Finally, we propose combining the multi-stage approach with a simple
Monte Carlo procedure to model measurement error. The resulting methods are
interpretable and require minimal computational resources. We apply the methods
to aerial survey data of oil and gas facilities in British Columbia, Canada, to
estimate the methane emissions in the province. An R package is provided to
facilitate the use of the methods.
