EnviFlux (v1.0): a simplified surface flux inversion tool based on four-dimensional variational data assimilation (4D-Var)

Abstract. This paper introduces EnviFlux, which is a software tool (written in C++) to study the inverse problem of estimating the distribution of fluxes of a trace gas at the Earth's surface. This is done using a four-dimensional variational technique, which combines information from (i) synthetic observations of the trace gas spanning a defined time window, (ii) a transport model linking the initial concentration and surface fluxes to predictions of the observations, and (iii) a-priori information. The novelty of this system – compared to those that attempt to solve for real data – is in its relative simplicity and low cost, allowing new ideas to be assessed and understood quickly and cheaply. This is in line with many other developments in data assimilation that are often first explored using so-called "toy" systems. Part of this paper is to document this system, which is sufficiently complex to allow assimilation of in situ and total column amount (TCA) observation in arbitrary configurations, and has a flexible background error covariance model, but is simple enough to be run relatively quickly. Another part of this paper uses EnviFlux to explore the effect of model error and observation bias on inferred surface fluxes in two example scenarios and with two observation types, namely surface in situ (SIS) and TCA. The first is a highly idealised case with a flux pair (a localised source and a localised sink), where no a-priori information concerning their positions is provided. It is found that model errors in the assimilation can severely affect the inferred flux positions and amounts, but observation biases do not affect the positions, but do affect the amounts. The second scenario is closer to a real-world example of methane flux estimates where an a-priori is refined with observations. The effect of model error is less than for the first scenario, but is still evident, and the observation biases affect the flux amounts. In both cases, the SIS observations allow a more accurate estimate of surface flux characteristics than the TCA observations, even though the experiments are setup to allow a fair comparison of the two. The last part of the paper raises some research questions that EnviFlux could help address, and the appendices describe the particular background error covariance scheme used.