Use of Assimilation Analysis in 4D-Var Source Inversion: Observing System Simulation Experiments (OSSEs) with GOSAT Methane and Hemispheric CMAQ

Abstract

We previously introduced the parametric variance Kalman filter (PvKF) assimilation as a cost-efficient system to estimate the dynamics of methane analysis concentrations. As an extension of our development, this study demonstrates the linking of PvKF to a 4D-Var inversion aiming to improve on methane emissions estimation in comparison with the traditional 4D-Var. Using the proposed assimilation–inversion framework, we revisit fundamental assumptions of the perfect and already optimal model state that is typically made in the 4D-Var inversion algorithm. In addition, the new system objectively accounts for error correlations and the evolution of analysis error variances, which are non-trivial or computationally prohibitive to maintain otherwise. We perform observing system simulation experiments (OSSEs) aiming to isolate and explore various effects of the assimilation analysis on the source inversion. The effect of the initial field of analysis, forecast of analysis error covariance, and model error is examined through modified 4D-Var cost functions, while different types of perturbations of the prior emissions are considered. Our results show that using PvKF optimal analysis instead of the model forecast to initialize the inversion improves posterior emissions estimate (~35% reduction in the normalized mean bias, NMB) across the domain. The propagation of analysis error variance using the PvKF formulation also tends to retain the effect of background correlation structures within the observation space and, thus, results in a more reliable estimate of the posterior emissions in most cases (~50% reduction in the normalized mean error, NME). Our sectoral analysis of four main emission categories indicates how the additional information of assimilation analysis enhances the constraints of each emissions sector. Lastly, we found that adding the PvKF optimal analysis field to the cost function benefits the 4D-Var inversion by reducing its computational time (~65%), while including only the error covariance in the cost function has a negligible impact on the inversion time (10–20% reduction).

Source Attribution of Societal Impacts of PM2.5 Pollution from Regional to Hemispheric Scales

“…A number of studies have demonstrated the effectiveness of adjoint modelling applications such as population-weighted average concertation of pollutants (Koo et al, 2013), premature mortality and health benefits of reducing anthropogenic emissions (Lee et al, 2015;Turner et al, 2015;Pappin and Hakami, 2013a;Pappin et al, 2015 andZhao et al, 2020), nonattainment with the national air quality standards (Hakami et al, 2006;Henze et al, 2009;Pappin and Hakami, 2013b), climate (Lacey et al, 2017;Henze et al, 2012;Karydis et al, 2012;Zhao et al, 2013), crop and vegetation (Lapina et al, 2014, Lyu et al, 2019, economic instruments such as cap and trade program (Mesbah et al, 2012 and and constraining emissions through inverse modelling (Chen et al, 2021;Voshtani et al, 2023).…”