Introduction

Numerous studies have used TROPOMI satellite observations to analyse ${\mathrm{CH}}_4$ emissions. One such study is Sadavarte, et al., 2021 , which concludes that emissions from the Hail Creek open cut coal mine in central Queensland are exceptionally high.

The basic data for the Hail Creek mine reported in Table 1 of Sadavarte, et al., 2021 are reproduced below in Table 1.

In the Supporting Information (Table S4), the authors report an Implied Emission Factor (IEF) of 34.12 g ${\mathrm{CH}}_4$ per kg of raw coal production, at least an order of magnitude higher than the second highest estimate reported by Kholod, et al., 2020 . For convenience, the data relevant to Hail Creek from the original Table S4 are reproduced below in Table 2.

The IEF was calculated by dividing the total estimated methane emissions for 2018-2019 (460 ($\mathrm{Gg}$)) by the combined raw coal production over the same period (7.7 + 5.8 ($\frac{\mathrm{Mt}}{\mathrm{year}}$) ), yielding a two year average IEF of 34.07 ($\frac{g}{\mathrm{kg}}$). The original paper reported IEF of 31.12 ($\frac{g}{\mathrm{kg}}$), the minor difference possibly due to use of the full precision data.

The default IPCC emission factors ( IPCC 2006 Guidelines Volume 2 Chapter 4 , p. 4.18) are expressed as volumetric emissions per unit mass ($\frac{m^3}{t}$), with a recommended conversion factor of 0.67 to ($\frac{g}{\mathrm{kg}}$).

Between May 2022 and September 2023, aircraft measurements were conducted on four days Borchardt, et al., 2025 , yielding annualised emission estimates approximately half of those reported by Sadavarte, et al., 2021 .

The findings of Sadavarte, et al., 2021 and Borchardt, et al., 2025 have been widely cited in the media, including coverage by the Australian Financial Review (30, Nov, 2021) , Bloomberg (25, Mar, 2025) , and a range of advocacy, research, and policy organisations such as Australian Centre for Corporate Responsibility , Australian Conservation Foundation , Climate Council , Methane Zero , Move Beyond Coal , Queensland Conservation Council , Renew Economy , UNEP , UNSW .

Anticipating the availability of observations from the TROPOMI spectrometer and the MERLIN lidar mission, Jacob, et al., 2016 proposed several approaches for estimating emission rates based on probabilistic inversion frameworks. These include the analytical method, adjoint method, and Markov Chain Monte Carlo (MCMC) method. All approaches assume an initial estimate of the emission field, use a CTM to simulate atmospheric concentrations, and determine the optimal emission rates through error weighted statistical fitting between simulated and observed concentrations. An implementation of the adjoint approach, referred to as the Ensemble Kalman Filter Inverse Method, was applied to estimate emissions from the Hail Creek mine by Palmer, et al., 2021 . More recently, a similar inversion framework has been used by the Superpower Institute to estimate emissions for January-June 2023 as part of the Open Methane (beta) project.

Varon, et al., 2018 discuss several approaches to the plume inversion problem based on instantaneous plume observations, in which each satellite image is analysed independently to estimate emissions. These methods include the Gaussian plume inversion method, the source pixel method, the Cross Sectional Flux method (CSF) , and the Integrated Mass Enhancement method (IME) . All of these approaches require identification of the satellite pixels constituting the plume, as well as an estimate of the background concentration field. The CSF method was applied by Sadavarte, et al., 2021 .

The TROPOMI${\mathrm{CH}}_4$ retrieval algorithm has been extended through the introduction of the Weighting Function Modified Differential Optical Absorption Spectroscopy (WFMD) approach by Schneising, et al., 2023 . Version 1.8 of this retrieval additionally incorporates a de-striping procedure to mitigate instrumental artefacts. More recently, Schneising, et al., 2024 developed an adjacent method that enables the simultaneous analysis of CO and CO₂, which has since been applied to quantify emissions from steel plants in Germany.

The TROPOMI WFMD data, was subsequently used by Borchardt, et al., 2025 as a benchmark for comparison with aircraft based measurements over Hail Creek.

In addition, preliminary (beta) emission estimates for January-June 2023 have been produced by the Superpower Institute as part of the Open Methane (beta) project.

The remainder of this Introduction provides an overview of the key concepts required for the subsequent discussion. It begins with a description of the observational datasets, starting with Automatic Weather Station (AWS) measurements from Moranbah Airport. This is followed by an overview of ERA5 reanalysis data obtained from the Copernicus Data Store, which are required inputs for the CSF algorithm, and a brief introduction to the TROPOMI dataset. The concept of the Stable Nocturnal Boundary Layer (SNBL) is then introduced, followed by a short overview of the HYSPLIT model. Finally, the basic equations underlying the CSF, TM and IME methods are derived to clarify the assumptions under which each approach is valid.