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The goal of the GHG-CCI project (http://www.esa-ghg-cci.org/) of ESA's Climate Change Initiative (CCI) is to generate global atmospheric satellite-derived carbon dioxide (CO2) and methane (CH4) data sets as needed to improve our understanding of the regional sources and sinks of these important greenhouse gases (GHG). Here we present an overview about the latest data set called Climate Research Data Package No. 3 (CRDP3). We focus on the GHG-CCI project core data products, which are near-surface-sensitive column-averaged dry air mole fractions of CO2 and CH4, denoted XCO2 (in ppm) and XCH4 (in ppb) retrieved from SCIAMACHY/ENVISAT (2002-2012) and TANSO-FTS/GOSAT (2009-today) nadir mode radiance observations in the near-infrared/shortwave-infrared spectral region. The GHG-CCI products are primarily individual sensor Level 2 products. However, we also generate merged Level 2 products ("EMMA products"). Here we also present a first GHG-CCI Level 3 product, namely XCO2 and XCH4 in Obs4MIPs format (monthly, 5°×5°).

We investigate and contrast the differences between the discretize-then-differentiate and differentiate-then-discretize approaches to the numerical solution of parameter estimation problems. The former approach is attractive in practice due to the use of automatic differentiation for the generation of the dual and optimality equations in the first-order KKT system. The latter strategy is more versatile, in that it allows one to formulate efficient mesh-independent algorithms over suitably chosen function spaces. However, it is significantly more difficult to implement, since automatic code generation is no longer an option. The starting point is a classical elliptic inverse problem. An a priori error analysis for the discrete optimality equation shows consistency and stability are not inherited automatically from the primal discretization. Similar to the concept of dual consistency, We introduce the concept of optimality consistency. However, the convergence properties can be restored through suitable consistent modifications of the target functional. Numerical tests confirm the theoretical convergence order for the optimal solution. We then derive a posteriori error estimates for the infinite dimensional optimal solution error, through a suitably chosen error functional. This estimates are constructed using second order derivative information for the target functional. For computational efficiency, the Hessian is replaced by a low order BFGS approximation. The efficiency of the error estimator is confirmed by a numerical experiment with multigrid optimization.

Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients of a state–of–the–art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of flux–limited numerical algorithms. Ph. D.

Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the intergrid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided for the discontinuous Galerkin (DG) method. The adjoint model development is considerably simplified by decoupling the adaptive mesh refinement mechanism from the forward model solver, and by selectively applying automatic differentiation on individual algorithms. In forward models discontinuous Galerkin discretizations can efficiently handle high orders of accuracy, $h/p$-refinement, and parallel computation. The analysis reveals that this approach, paired with Runge Kutta time stepping, is well suited for the adaptive solutions of inverse problems. The usefulness of discrete discontinuous Galerkin adjoints is illustrated on a two-dimensional adaptive data assimilation problem.

Data Assimilation (DA) involves the combination of observational data with the underlying dynamical principles governing the system under observation. In this work we combine the advantages of the two prominent advanced data assimilation systems, the 4D-Var and the ensemble methods. The proposed method consists of identifying the subspace spanned by the major 4D-Var error reduction directions. These directions are then removed from the background covariance through a Galerkin-type projection. This generates an updated error covariance information at both end points of an assimilation window. The error covariance information is updated between assimilation windows to capture the ``error of the day''. Numerical results using our new hybrid approach on a nonlinear model demonstrate how the background covariance matrix leads to an error covariance update that improves the 4D-Var DA results.

DENSERKS is a Fortran sensitivity equation solver package designed for integrating models whose evolution can be described by ordinary differential equations (ODEs). A salient feature of DENSERKS is its support for both forward and adjoint sensitivity analyses, with built-in integrators for both first and second order continuous adjoint models. The software implements explicit Runge-Kutta methods with adaptive timestepping and high-order dense output schemes for the forward and the tangent linear model trajectory interpolation. Implementations of six Runge-Kutta methods are provided, with orders of accuracy ranging from two to eight. This makes DENSERKS suitable for a wide range of practical applications. The use of dense output, a novel approach in adjoint sensitivity analysis solvers, allows for a high-order cost-effective interpolation. This is a necessary feature when solving adjoints of nonlinear systems using highly accurate Runge-Kutta methods (order five and above). To minimize memory requirements and make long-time integrations computationally efficient, DENSERKS implements a two-level checkpointing mechanism. The code is tested on a selection of problems illustrating first and second order sensitivity analysis with respect to initial model conditions. The resulting derivative information is also used in a gradient-based optimization algorithm to minimize cost functionals dependent on a given set of model parameters.

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- conomists 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 observa- tions 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). For the 2003–2012 decade, global methane emissions are estimated by top-down inversions at 558 Tg CH₄ yr⁻¹, range 540–568. About 60 % of global emissions are anthropogenic (range 50–65 %). Since 2010, the bottom-up global emission inventories have been closer to methane emissions in the most carbon-intensive Representative Concentrations Pathway (RCP8.5) and higher than all other RCP scenarios. Bottom-up approaches suggest larger global emissions (736 Tg CH₄ yr⁻¹range 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 top-down budget, it is likely that some of the individual emissions reported by the bottom-up approaches are overestimated, leading to too large global emissions. Latitudinal data from top-down emissions indicate a predominance of tropical emissions (~64 % of the global budget, < 30°N) as compared to mid (~32 %, 30–60°N) and high northern latitudes (~4 %, 60–90°N). Top-down inversions consistently infer lower emissions in China (~58 Tg CH₄ yr⁻¹, range 51–72, - 14 %) and higher emissions in Africa (86 Tg CH₄ 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. The data presented here can be downloaded from the Carbon Dioxide Information Analysis Center (http://doi.org/10.3334/CDIAC/GLOBAL_ METHANE_BUDGET_2016_V1.1) and the Global Carbon Project.

Following the recent Global Carbon Project (GCP) synthesis of the decadal methane (CH₄) budget over 2000–2012 (Saunois et al., 2016), we analyse here the same dataset with a focus on quasi-decadal and inter-annual variability in CH₄ 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 2000–2012, but this increase is not linear over the 13 years. Despite differences between individual studies, the mean emission anomaly of the top-down ensemble shows no significant trend in total methane emissions over the period 2000–2006, during the plateau of atmospheric methane mole fractions, and also over the period 2008–2012, during the renewed atmospheric methane increase. However, the top-down ensemble mean produces an emission shift between 2006 and 2008, leading to 22 [16–32] Tg CH₄ yr⁻¹ higher methane emissions over the period 2008–2012 compared to 2002–2006. This emission increase mostly originated from the tropics, with a smaller contribution from mid-latitudes and no significant change from boreal regions. The regional contributions remain uncertain in top-down studies. Tropical South America and South and East Asia seem to contribute the most to the emission increase in the tropics. However, these two regions have only limited atmospheric measurements and remain therefore poorly constrained. The sectorial partitioning of this emission increase between the periods 2002–2006 and 2008–2012 differs from one atmospheric inversion study to another. However, all topdown studies suggest smaller changes in fossil fuel emissions (from oil, gas, and coal industries) compared to the mean of the bottom-up inventories included in this study. This difference is partly driven by a smaller emission change in China from the top-down studies compared to the estimate in the Emission Database for Global Atmospheric Research (EDGARv4.2) inventory, which should be revised to smaller values in a near future. We apply isotopic signatures to the emission changes estimated for individual studies based on five emission sectors and find that for six individual top-down studies (out of eight) the average isotopic signature of the emission changes is not consistent with the observed change in atmospheric ¹³CH₄. However, the partitioning in emission change derived from the ensemble mean is consistent with this isotopic constraint. At the global scale, the top-down ensemble mean suggests that the dominant contribution to the resumed atmospheric CH₄ growth after 2006 comes from microbial sources (more from agriculture and waste sectors than from natural wetlands), with an uncertain but smaller contribution from fossil CH₄ emissions. In addition, a decrease in biomass burning emissions (in agreement with the biomass burning emission databases) makes the balance of sources consistent with atmospheric ¹³CH₄ observations. In most of the top-down studies included here, OH concentrations are considered constant over the years (seasonal variations but without any inter-annual variability). As a result, the methane loss (in particular through OH oxidation) varies mainly through the change in methane concentrations and not its oxidants. For these reasons, changes in the methane loss could not be properly investigated in this study, although it may play a significant role in the recent atmospheric methane changes as briefly discussed at the end of the paper.

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 (similar to 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). For the 2003-2012 decade, global methane emissions are estimated by top-down inversions at 558 TgCH(4) yr(-1), range 540-568. About 60% of global emissions are anthropogenic (range 50-65 %). Since 2010, the bottom-up global emission inventories have been closer to methane emissions in the most carbon-intensive Representative Concentrations Pathway (RCP8.5) and higher than all other RCP scenarios. Bottom-up approaches suggest larger global emissions (736 TgCH(4) yr(-1), range 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 top-down budget, it is likely that some of the individual emissions reported by the bottom-up approaches are overestimated, leading to too large global emissions. Latitudinal data from top-down emissions indicate a predominance of tropical emissions (similar to 64% of the global budget, amp;lt;30 degrees N) as compared to mid (similar to 32 %, 30-60 degrees N) and high northern latitudes (similar to 4 %, 60-90 degrees N). Top-down inversions consistently infer lower emissions in China (similar to 58 TgCH(4) yr(-1), range 51-72, -14 %) and higher emissions in Africa (86 TgCH(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. The data presented here can be downloaded from the Carbon Dioxide Information Analysis Center (http://doi.org/10.3334/CDIAC/GLOBAL_METHANE_BUDGET_2016_V1.1) and the Global Carbon Project. Funding Agencies|Swiss National Science Foundation; NASA [NNX14AF93G, NNX14AO73G]; National Environmental Science Program - Earth Systems and Climate Change Hub; European Commission [283576, 633080]; ESA Climate Change Initiative Greenhouse Gases Phase 2 project; US Department of Energy, BER [DE-AC02-05CH11231]; FAO member countries; Environment Research and Technology Development Fund of the Ministry of the Environment, Japan [2-1502]; ERC [322998]; NERC [NE/J00748X/1]; Swedish Research Council VR; Research Council of Norway [244074]; NSF [1243232, 1243220]; National Science and Engineering Research Council of Canada (NSERC); Chinas QianRen Program; CSIRO Australia; Australian Bureau of Meteorology; Australian Institute of Marine Science; Australian Antarctic Division; NOAA USA; Meteorological Service of Canada; National Aeronautic and Space Administration (NASA) [NAG5-12669, NNX07AE89G, NNX11AF17G, NNX07AE87G, NNX07AF09G, NNX11AF15G, NNX11AF16G]; Department of Energy and Climate Change (DECC, UK) [GA01081]; Commonwealth Scientific and Industrial Research Organization (CSIRO Australia); Bureau of Meteorology (Australia); Joint DECC/Defra Met Office Hadley Centre Climate Programme [GA01101]