The atmospheric concentration of methane (CH4) - the most significant non-CO2 anthropogenic long-lived greenhouse gas - stabilized between 1999 and 2006 and then began to rise again. Explanations for this behavior differ but studies agree that more measurements and better modeling are needed to reliably explain the model-data discrepancies and predict future change. This dissertation focuses on measurements of CH4 and inverse modeling of atmospheric CH4 fluxes using field measurements at a variety of spatial scales. We first present a new fast-response instrument to measure the isotopic composition of CH4 in ambient air. The instrument was used to characterize mass fluxes and isofluxes (a isotopically-weighted mass flux) from a well-studied research fen in New Hampshire. Eddy-covariance and automatic chamber techniques produced consistent estimates of both the CH4 fluxes and their isotopic composition at sub-hourly resolution. We then characterize fluxes of CH4 from aircraft engines using measurements made with the same instrument during the Alternative Aviation Fuel Experiment (AAFEX), a study that aimed to determine the atmospheric impacts of alternative fuel use in the growing aviation industry. Emissions of CO2, CH4, and N2O from different synthetic fuels were statistically indistinguishable from those of the widely used JP-8 jet fuel. We then present airborne observations of the long-lived greenhouse gas suite – CO2, CH4, N2O, and CO – during two aircraft campaigns, HIPPO and CalNex, made using a similar instrument built specifically for the NCAR HIAPER GV aircraft. These measurements are compared to data from other onboard sensors and show excellent agreement. We discuss the details of the end-to-end calibration procedures and the data quality-assurance and quality-control (QA/QC). Lastly, we quantify a top-down estimate of California’s CH4 emission inventory using the CalNex CH4 observations. Observed CH4 enhancements above background concentrations are simulated using a lagrangian transport model driven by validated meteorology. A priori source-specific emission inventories are optimized in a Bayesian inversion framework to show that California’s CH4 budget is 1.6 ± 0.34 times larger than the current estimate of California’s Air Resources Board (CARB), the body charged with enforcing the California Global Solutions Act and tracking emission changes over time. Findings highlight large underestimates of emissions from cattle and natural gas infrastructure.Earth and Planetary Science