Lower-thermosphere response to solar activity: an empirical-mode-decomposition analysis of GOCE 2009-2012 data

Forecasting the thermosphere (the atmosphere's uppermost layer, from about 90 to 800 km altitude) is crucial to space-related applications, from space mission design to re-entry operations, space surveillance and more. Thermospheric dynamics is directly linked to the solar dynamics through the solar UV (ultraviolet) input, which is highly variable, and through the solar wind and plasma fluxes impacting Earth's magnetosphere. The solar input is non-periodic and non-stationary, with long-term modulations from the solar rotation and the solar cycle and impulsive components, due to magnetic storms. Proxies of the solar input exist and may be used to forecast the thermosphere, such as the F10.7 radio flux and the Mg II EUV (extreme-ultraviolet) flux. They relate to physical processes of the solar atmosphere. Other indices, such as the Ap geomagnetic index, connect with Earth's geomagnetic environment. We analyse the proxies' time series comparing them with in situ density data from the ESA (European Space Agency) GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) gravity mission, operational from March 2009 to November 2013, therefore covering the full rising phase of solar cycle 24, exposing the entire dynamic range of the solar input. We use empirical mode decomposition (EMD), an analysis technique appropriate to non-periodic, multi-scale signals. Data are taken at an altitude of 260 km, exceptionally low for a low-Earth-orbit (LEO) satellite, where density variations are the single most important perturbation to satellite dynamics. We show that the synthesized signal from optimally selected combinations of proxy basis functions, notably Mg II for the solar flux and Ap for the plasma component, shows a very good agreement with thermospheric data obtained by GOCE, during periods of low and medium solar activity. In periods of maximum solar activity, density enhancements are also well represented. The Mg II index proves to be, in general, a better proxy than the F10.7 index for modelling the solar flux because of its specific response to the UV spectrum, whose variations have the largest impact over thermospheric density.