Abstract: During the past two decades, there have been significant efforts to better quantify emissions of environmentally important trace gases along with their trends. In particular, there has been a clear need for robust estimates of emissions on policy-relevant scales of trace gases that impact air quality and climate. This need has driven the expansion of the observing network to better monitor the changing composition of the atmosphere. This chapter will discuss the use of various data assimilation and inverse modelling approaches to quantify these emissions, with a focus on the use of satellite observations. It will discuss the inverse problem of retrieving the atmospheric trace gas information from the satellite measurements, and the subsequent use of these satellite data for quantifying sources and sinks of the trace gases.

This chapter provides a summary of the flux of carbon through various oceanic volcanic centers such as mid-ocean ridges and intraplate settings, as well as what these fluxes indicate about the carbon content of the mantle. By reviewing methods used to measure the carbon geochemistry of basalts and then to estimate fluxes, the chapter provides insight into how mantle melting and melt extraction processes are estimated. The chapter discusses how the flux of carbon compares with other incompatible trace elements and gases. From there, the chapter discusses whether the budget of carbon in the ocean mantle can be explained by primordial carbon or whether carbon recycling is required to balance the budget.