Evaluation of area-source methane-emission quantification by Uncrewed Aerial Systems using Gauss’s law

Abstract. Quantifying methane emissions from lakes and wetlands remains a persistent challenge. Existing measurement approaches commonly sample only at distinct points (chambers) or integrate over poorly defined and meteorology-dependent footprints (eddy covariance, flux-gradient methods). A different framework for methane-flux estimation from lakes and wetlands entails an aerial cylindrical mass-balance technique in which an aircraft with methane and wind sensors circumscribes a methane source. This creates a control volume, allowing for the enclosed flux to be determined with Gauss's divergence theorem. The suitability of this methodology has not been evaluated for uncrewed aerial systems (UAS). We conducted an observing system simulation experiment (OSSE) that coupled a Gaussian-plume forward model with a simulated Gaussian cylindrical-flux estimation over an idealized methane-emitting lake. Across three experiments, we tested the effects of (i) receptor (points of collocated methane and wind measurements) grid resolution, (ii) methane contamination from a nearby upwind lake, and (iii) the effects of sampling under evolving atmospheric stability, on retrieval accuracy and precision. We introduce nondimensional variables to represent the estimation error from these three effects for a broader set of system configurations. Vertical-receptor resolution was the dominant control on retrieval accuracy, while azimuthal resolution primarily affected precision relative to the vertical resolution. When a nearby lake (~0.1–10 km) with an upwind-methane source was introduced to the simulation, this induced a systematic negative bias compared to the true methane flux. Under prescribed atmospheric-stability transitions, retrieval accuracy degraded monotonically with increased mission duration, with the shortest flights (30 min) preserving the highest flux retrieval accuracy across all stability transitions tested. This is because shorter flights more closely capture a snapshot of the environment before changes in the atmosphere can occur, which can skew methane-flux estimates. However, repeating short flights and averaging the resulting source-flux retrievals improved precision over single flights even across longer (12 h) atmospheric stability transitions. Within our nondimensional framework, signal-to-noise increased retrieval accuracy, but by an amount that was determined by the geometry of the measured lake and observations. The OSSE framework presented here provides a quantitative basis for planning UAS methane-flux-measurement campaigns using cylindrical mass-balance over lakes, wetlands, and possibly other heterogeneous natural methane sources.