Abstract
Abstract. We present and discuss the use of Bayesian modeling and computational methods for atmospheric chemistry inverse analyses that incorporate evaluation of spatial structure in model-data residuals. Motivated by problems of refining bottom-up estimates of source/sink fluxes of trace gas and aerosols based on satellite retrievals of atmospheric chemical concentrations, we address the need for formal modeling of spatial residual error structure in global scale inversion models. We do this using analytically and computationally tractable conditional autoregressive (CAR) spatial models as components of a global inversion framework. We develop Markov chain Monte Carlo methods to explore and fit these spatial structures in an overall statistical framework that simultaneously estimates source fluxes. Additional aspects of the study extend the statistical framework to utilize priors on source fluxes in a physically realistic manner, and to formally address and deal with missing data in satellite retrievals. We demonstrate the analysis in the context of inferring carbon monoxide (CO) sources constrained by satellite retrievals of column CO from the Measurement of Pollution in the Troposphere (MOPITT) instrument on the TERRA satellite, paying special attention to evaluating performance of the inverse approach using various statistical diagnostic metrics. This is developed using synthetic data generated to resemble MOPITT data to define a proof-of-concept and model assessment, and then in analysis of real MOPITT data. These studies demonstrate the ability of these simple spatial models to substantially improve over standard non-spatial models in terms of statistical fit, ability to recover sources in synthetic examples, and predictive match with real data.
Highlights
1.1 Model and inference settingBayesian statistical techniques are increasingly being used in atmospheric chemistry inverse modeling studies to refine bottom-up trace gas and aerosol source/sink flux estimates
An approach based on Gaussian conditional autoregressive (CAR) spatial models is able, as we show, to define realistic and appropriate spatial structures for geographically dense satellite retrieval data on a lattice, while leading to a computationally tractable methodology for atmospheric tracer inverse modeling
The broader field of atmospheric chemistry inverse modeling has become heavily invested in statistical methods, there has been limited development of what are standard statistical approaches utilizing Bayesian simulation methods, including Markov chain Monte Carlo (MCMC)
Summary
Bayesian statistical techniques are increasingly being used in atmospheric chemistry inverse modeling studies to refine bottom-up trace gas and aerosol source/sink flux estimates. Global-scale atmospheric chemistry inverse modeling studies involving real or synthetic satellite retrievals have generally focused on analyzing monthly or weekly mean measurements that are spatially aggregated to the CTM grid resolution (typically 200–500 km in the horizontal). Previous applications in atmospheric chemistry have generally assumed a diagonal structure for S due to the lack of effective and computationally efficient approaches to identifying and integrating relevant spatial structures This eliminates the computational burden associated with the calculation of the matrix inverse of S in Eq (2). The equations clearly show, that if spatial dependencies in the model errors exist and can be captured by a relevant non-diagonal and structured covariance matrix S , this will impact on the posterior estimates xp of fluxes as well as the associated measures of uncertainties in Sp. The impact can be substantial as demonstrated by some earlier studies (e.g., Chevallier, 2007) and our examples below
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