This work extends previous calculations of carbon dioxide sources and sinks to take account of the varying quality of atmospheric models. It uses an extended version of Bayesian statistics which includes the model as one of the unknowns. I performed the work as an example of including the model in the description of the uncertainty.

This paper describes the methods for combining models and data to understand how nutrients and pollutants move through natural systems. The methods are analogous to the process of weather forecasting in which previous information is combined with new observations and a model to improve our knowledge of the internal state of the physical system. The methods appear highly diverse but the paper shows that they are all examples of a single underlying formalism.

Observations can reduce uncertainties in past, current, and predicted natural and anthropogenic CO₂ fluxes. They provide independent information for verification of actions as requested by the Paris Agreement. Quantitative network design (QND) is an objective approach to optimise in situ networks and space missions to achieve an optimal use of the observational capabilities. We describe recent progress and advocate an integrated QND system that simultaneously evaluates multiple data streams.

This paper briefly reviews data assimilation techniques in carbon cycle data assimilation and the requirements of data assimilation systems on observations. We provide a non-exhaustive overview of current observations and their uncertainties for use in terrestrial carbon cycle data assimilation, focussing on relevant space-based observations.

The use of inverse modeling for quantifying emissions of greenhouse gases is increasing. Estimates are very difficult to evaluate objectively, however, due to limited atmospheric observations and the lack of direct emissions measurements at compatible scales. Diagnostic tools have been proposed to partially circumvent these limitations. This paper presents the first systematic review of the scope and applicability of these tools for atmospheric inversions of long-lived greenhouse gases.

We present the Joint Research Centre Two-stream Inversion Package (JRC-TIP) for retrieval of variables characterising the state of the vegetation–soil system. The system provides a set of land surface variables that satisfy all requirements for assimilation into the land component of climate and numerical weather prediction models.

This paper provides the formalism and examples of how observation operators can be used, in combination with data assimilation or retrieval techniques, to better ingest satellite products in a manner consistent with the dynamics of the Earth system expressed by models.

Plankton models have become an integral part in marine ecosystem and biogeochemical research. These models differ in complexity and in their number of parameters. How values are assigned to parameters is essential. An overview of major methodologies of parameter estimation is provided. Aspects of parameter identification in the literature are diverse. Individual findings could be better synthesized if notation and expertise of the different scientific communities would be reasonably merged.

We reviewed recent efforts to estimate state- and national-scale carbon dioxide and methane emissions from individual anthropogenic source sectors in the United States. State and federal greenhouse gas regulations almost always target reductions from specific source sectors, and reliable emission estimates are important to support and evaluate these policies. We also describe a number of forward-looking opportunities that would improve sector-specific estimates.

The aim of this paper is to present an overview of inverse modeling methods, developed over the years, for estimating the global sources and sinks of the greenhouse gas methane from atmospheric measurements. It provides insight into how techniques and estimates have evolved over time, what the remaining shortcomings are, new developments, and promising future directions.

Model projections of the response of the terrestrial biosphere to anthropogenic emissions are uncertain, in part due to unknown fixed parameters in a model. Data assimilation can address this by using observations to optimise these parameter values. Using multiple types of data is beneficial for constraining different model processes, but it can also pose challenges in a DA context. This paper demonstrates and discusses the issues involved using toy models and examples from existing literature.

The marine cycle of calcium carbonate (CaCO₃) influences the distribution of CO₂ between atmosphere and ocean, and thereby climate. We constrain export of biogenic CaCO₃ (globally: 0.72–1.05 Gt C yr⁻¹) and dissolution within the water column (~ 80 %) in a novel Monte Carlo set-up with the Bern3D model based on alkalinity data. Whether CaCO₃ dissolves in the upper ocean remains unresolved. We recommend using constant (saturation-independent) dissolution rates in Earth system models.