Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions 1Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA
2Department of Global Ecology, Carnegie Institution for Science, Stanford, CA, USA
Received: 11 July 2013 – Published in Geosci. Model Dev. Discuss.: 06 September 2013 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.
Revised: 11 December 2013 – Accepted: 09 January 2014 – Published: 13 February 2014
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.
Citation: Miller, S. M., Michalak, A. M., and Levi, P. J.: Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions, Geosci. Model Dev., 7, 303-315, doi:10.5194/gmd-7-303-2014, 2014.