Wetlands comprise the single largest global source of atmospheric methane, but current flux estimates disagree in both magnitude and distribution at the continental scale. This study uses atmospheric methane observations over North America from 2007 to 2008 and a geostatistical inverse model to improve understanding of Canadian methane fluxes and associated biogeochemical models. The results bridge an existing gap between traditional top-down, inversion studies, which typically emphasize total emission budgets, and biogeochemical models, which usually emphasize environmental processes. The conclusions of this study are threefold. First, the most complete process-based methane models do not always describe available atmospheric methane observations better than simple models. In this study, a relatively simple model of wetland distribution, soil moisture, and soil temperature outperformed more complex model formulations. Second, we find that wetland methane fluxes have a broader spatial distribution across western Canada and into the northern U.S. than represented in existing flux models. Finally, we calculate total methane budgets for Canada and for the Hudson Bay Lowlands, a large wetland region (50-60• N, 75-96• W). Over these lowlands, we find total methane fluxes of 1.8 ± 0.24 Tg C yr −1 , a number in the midrange of previous estimates. Our total Canadian methane budget of 16.0 ± 1.2 Tg C yr −1 is larger than existing inventories, primarily due to high anthropogenic emissions in Alberta. However, methane observations are sparse in western Canada, and additional measurements over Alberta will constrain anthropogenic sources in that province with greater confidence.

Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include nonnegativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each. This paper investigates the applicability of several approaches to bounded inverse problems. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two Markov chain Monte Carlo (MCMC) methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing option for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach.

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Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include non-negativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each.

This paper investigates the applicability of several approaches to bounded inverse problems and is also the first application of Markov chain Monte Carlo (MCMC) to estimation of atmospheric trace gas fluxes. The approaches discussed here are broadly applicable. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two MCMC methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing alternative for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach

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