Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions

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.