Technical Note: Methods for interval constrained atmospheric inversion of methane

Abstract. Three interval constrained methods, including the interval constrained Kalman smoother, the interval constrained maximum likelihood ensemble smoother and the interval constrained ensemble Kalman smoother are developed to conduct inversions of atmospheric trace gas methane (CH₄). The negative values of fluxes in an unconstrained inversion are avoided in the constrained inversion. In a multi-year inversion experiment using pseudo observations derived from a forward transport simulation with known fluxes, the interval constrained fixed-lag Kalman smoother presents the best results, followed by the interval constrained fixed-lag ensemble Kalman smoother and the interval constrained maximum likelihood ensemble Kalman smoother. Consistent uncertainties are obtained for the posterior fluxes with these three methods. This study provides alternatives of the variable transform method to deal with interval constraints in atmospheric inversions.