Reviews and syntheses: Flying the satellite into your model: on the role of observation operators in constraining models of the Earth system and the carbon cycle

The vehicles that fly the satellite into a model of the Earth system are observation operators. They provide the link between the quantities simulated by the model and the quantities observed from space, either directly (spectral radiance) or indirectly estimated through a retrieval scheme (biogeophysical variables). By doing so, observation operators enable modellers to properly compare, evaluate, and constrain their models with the model analogue of the satellite observations. This paper provides the formalism and a few examples of how observation operators can be used in combination with data assimilation techniques to better ingest satellite products in a manner consistent with the dynamics of the Earth system expressed by models. It describes commonalities and potential synergies between assimilation and classical retrievals. This paper explains how the combination of observation operators and their derivatives (linearizations) form powerful research tools. It introduces a technique called automatic differentiation that greatly simplifies both the development and the maintenance of code for the evaluation of derivatives. Throughout this paper, a special focus lies on applications to the carbon cycle.