Abstract. The global methane (CH 4 ) budget is becoming an increasingly important component for managing realistic pathways to mitigate climate change. This relevance, due to a shorter atmospheric lifetime and a stronger warming potential than carbon dioxide, is challenged by the still unexplained changes of atmospheric CH 4 over the past decade. Emissions and concentrations of CH 4 are continuing to increase, making CH 4 the second most important human-induced greenhouse gas after carbon dioxide. Two major difficulties in reducing uncertainties come from the large variety of diffusive CH 4 sources that overlap geographically, and from the destruction of CH 4 by the very short-lived hydroxyl radical (OH). To address these difficulties, we have established a consortium of multi-disciplinary scientists under the umbrella of the Global Carbon Project to synthesize and stimulate research on the methane cycle, and producing regular (∼ biennial) updates of the global methane budget. This consortium includes atmospheric physicists and chemists, biogeochemists of surface and marine emissions, and socio-economists who study anthropogenic emissions. Following Kirschke et al. (2013), we propose here the first version of a living review paper that integrates results of top-down studies (exploiting atmospheric observations within an atmospheric inverse-modelling framework) and bottom-up models, inventories and data-driven approaches (including process-based models for estimating land surface emissions and atmospheric chemistry, and inventories for anthropogenic emissions, data-driven extrapolations). . Top-down inversions consistently infer lower emissions in China (∼ 58 Tg CH 4 yr −1 , range 51-72, −14 %) and higher emissions in Africa (86 Tg CH 4 yr −1 , range 73-108, +19 %) than bottom-up values used as prior estimates. Overall, uncertainties for anthropogenic emissions appear smaller than those from natural sources, and the uncertainties on source categories appear larger for top-down inversions than for bottom-up inventories and models.The most important source of uncertainty on the methane budget is attributable to emissions from wetland and other inland waters. We show that the wetland extent could contribute 30-40 % on the estimated range for wetland emissions. Other priorities for improving the methane budget include the following: (i) the development of process-based models for inland-water emissions, (ii) the intensification of methane observations at local scale (flux measurements) to constrain bottom-up land surface models, and at regional scale (surface networks and satellites) to constrain top-down inversions, (iii) improvements in the estimation of atmospheric loss by OH, and (iv) improvements of the transport models integrated in top-down inversions.

Abstract. The global methane (CH4) budget is becoming an increasingly important component for managing realistic pathways to mitigate climate change. This relevance, due to a shorter atmospheric lifetime and a stronger warming potential than carbon dioxide, is challenged by the still unexplained changes of atmospheric CH4 over the past decade. Emissions and concentrations of CH4 are continuing to increase making CH4 the second most important human-induced greenhouse gas after carbon dioxide. Two major difficulties in reducing uncertainties come from the large variety of diffusive CH4 sources that overlap geographically, and from the destruction of CH4 by the very short-lived hydroxyl radical (OH). To address these difficulties, we have established a consortium of multi-disciplinary scientists under the umbrella of the Global Carbon Project to synthesize and stimulate research on the methane cycle, and producing regular (~biennial) updates of the global methane budget. This consortium includes atmospheric physicists and chemists, biogeochemists of surface and marine emissions, and socio-economists who study anthropogenic emissions. Following Kirschke et al. (2013), we propose here the first version of a living review paper that integrates results of top-down studies (T-D, exploiting atmospheric observations within an atmospheric inverse-modelling framework) and bottom-up models, inventories, and data-driven approaches (B-U, including process-based models for estimating land surface emissions and atmospheric chemistry, and inventories for anthropogenic emissions, data-driven extrapolations). For the 2003–2012 decade, global methane emissions are estimated by T-D inversions at 558 Tg CH4 yr−1 (range [540–568]). About 60 % of global emissions are anthropogenic (range [50–65 %]). B-U approaches suggest larger global emissions (736 Tg CH4 yr−1 [596–884]) mostly because of larger natural emissions from individual sources such as inland waters, natural wetlands and geological sources. Considering the atmospheric constraints on the T-D budget, it is likely that some of the individual emissions reported by the B-U approaches are overestimated, leading to too large global emissions. Latitudinal data from T-D emissions indicate a predominance of tropical emissions (~64 % of the global budget,

Abstract. At the beginning of 2009 new space-borne observations of dry-air column-averaged mole fractions of atmospheric methane (XCH 4

Abstract. Following the recent Global Carbon Project (GCP) synthesis of the decadal methane (CH 4 ) budget over 2000, we analyse here the same dataset with a focus on quasi-decadal and inter-annual variability in CH 4 emissions. The GCP dataset integrates results from topdown studies (exploiting atmospheric observations within an atmospheric inverse-modelling framework) and bottom-up models (including process-based models for estimating land surface emissions and atmospheric chemistry), inventories of anthropogenic emissions, and data-driven approaches.The annual global methane emissions from top-down studies, which by construction match the observed methane growth rate within their uncertainties, all show an increase in total methane emissions over the period [2000][2001][2002][2003][2004][2005][2006][2007][2008][2009][2010][2011][2012], but this increase is not linear over the 13 years. Despite differences between individual studies, the mean emission anomaly of

Inverse problems are of utmost importance in many fields of science and engineering. In the variational approach inverse problems are formulated as PDE-constrained optimization problems, where the optimal estimate of the uncertain parameters is the minimizer of a certain cost functional subject to the constraints posed by the model equations. The numerical solution of such optimization problems requires the computation of derivatives of the model output with respect to model parameters. The first order derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through first order adjoint sensitivity analysis. Second order adjoint models give second derivative information in the form of matrix-vector products between the Hessian of the cost functional and user defined vectors. Traditionally, the construction of second order derivatives for large scale models has been considered too costly. Consequently, data assimilation applications employ optimization algorithms that use only first order derivative information, like nonlinear conjugate gradients and quasi-Newton methods.In this paper we discuss the mathematical foundations of second order adjoint sensitivity analysis and show that it provides an efficient approach to obtain Hessian-vector products. We study the benefits of using of second order information in the numerical optimization process for data assimilation applications. The numerical studies are performed in a twin experiment setting with a two-dimensional shallow water model. Different scenarios are considered with different discretization approaches, observation sets, and noise levels. Optimization algorithms that employ second order derivatives are tested against widely used methods that require only first order derivatives. Conclusions are drawn regarding the potential benefits and the limitations of using high-order information in large scale data assimilation problems.