Variational inverse modeling within the Community Inversion Framework v1.1 to assimilate [delta].sup.13C and CH.sub.4: a case study with model LMDz-SACS

Atmospheric CH.sub.4 mole fractions resumed their increase in 2007 after a plateau during the 1999-2006 period, indicating relative changes in the sources and sinks. Estimating sources by exploiting observations within an inverse modeling framework (top-down approaches) is a powerful approach. It is, nevertheless, challenging to efficiently differentiate co-located emission categories and sinks by using CH.sub.4 observations alone. As a result, top-down approaches are limited when it comes to fully understanding CH.sub.4 burden changes and attributing these changes to specific source variations. [delta].sup.13 C(CH.sub.4).sub.source isotopic signatures of CH.sub.4 sources differ between emission categories (biogenic, thermogenic, and pyrogenic) and can therefore be used to address this limitation. Here, a new 3-D variational inverse modeling framework designed to assimilate [delta].sup.13 C(CH.sub.4) observations together with CH.sub.4 observations is presented. This system is capable of optimizing both the emissions and the associated source signatures of multiple emission categories at the pixel scale. To our knowledge, this represents the first attempt to carry out variational inversion assimilating [delta].sup.13 C(CH.sub.4) with a 3-D chemistry transport model (CTM) and to independently optimize isotopic source signatures of multiple emission categories. We present the technical implementation of joint CH.sub.4 and [delta].sup.13 C(CH.sub.4) constraints in a variational system and analyze how sensitive the system is to the setup controlling the optimization using the LMDz-SACS 3-D CTM. We find that assimilating [delta].sup.13 C(CH.sub.4) observations and allowing the system to adjust isotopic source signatures provide relatively large differences in global flux estimates for wetlands (-5.7 Tg CH.sub.4 yr.sup.-1 ), agriculture and waste (-6.4 Tg CH.sub.4 yr.sup.-1 ), fossil fuels (+8.6 Tg CH.sub.4 yr.sup.-1) and biofuels-biomass burning (+3.2 Tg CH.sub.4 yr.sup.-1) categories compared to the results inferred without assimilating [delta].sup.13 C(CH.sub.4) observations. More importantly, when assimilating both CH.sub.4 and [delta].sup.13 C(CH.sub.4) observations, but assuming that the source signatures are perfectly known, these differences increase by a factor of 3-4, strengthening the importance of having as accurate signature estimates as possible. Initial conditions, uncertainties in [delta].sup.13 C(CH.sub.4) observations, or the number of optimize