Seasonal variability of degrees of freedom and its effect over time series and spatial patterns of atmospheric gases from satellite: application to carbonyl sulfide (OCS)

Degrees of freedom or d.o.f. of satellite-based retrievals characterize their independence from the constraints assumed in the inversion process. In the context of Optimal Estimation (OE), the condition is expressed in terms of the background state, which, in a Bayesian meaning, is our best prior knowledge about the parameters we want to estimate. In effect, even if the background is static, it could add artifacts to the retrievals, which modify the seasonal cycle or the spatial patterns of 2-D fields.The issue has been addressed with an analytical treatment based on the OE theory. We derive formulas, which allow us to assess the modulation introduced by d.o.f. variability. The methodology will be exemplified with the help of observations from the Infrared Atmospheric Sounder Interferometer (IASI) onboard the European MetOp satellites. Both time series and 2-D fields of observations will be considered. The analysis will focus mainly on carbonyl sulfide (OCS) variability in the atmosphere, a new clue to how much carbon plants take up, hence of primary interest to the carbon cycle and the climate. However, our methodology can be applied to any gas or retrieved parameter. For the OCS, we have found that d.o.f. variability is of no concern in the tropics. Still, it becomes crucial at Mid-latitudes where the seasonal cycle can add spurious variability to temporal and spatial patterns.