Determination of the most pertinent EUV proxy for use in thermosphere modeling

Two major issues in the specification of the thermospheric density are the definition of proper solar inputs and the empirical modeling of thermosphere response to solar and to geomagnetic forcings. This specification is crucial for the tracking of low Earth orbiting satellites. Here we address both issues by using 14 years of daily density measurements made by the Stella satellite at 813 km altitude and by carrying out a multiscale statistical analysis of various solar inputs. First, we find that the spectrally integrated solar emission between 26-34 nm offers the best overall performance in the density reconstruction. Second, we introduce linear parametric transfer function models to describe the dynamic response of the density to the solar and geomagnetic forcings. These transfer function models lead to a major error reduction and in addition open new perspectives in the physical interpretation of the thermospheric dynamics.

💡 Research Summary

This paper tackles two intertwined challenges in thermospheric density modeling: (1) identifying the most appropriate solar EUV proxy for driving the density and (2) incorporating the intrinsic memory of the thermosphere into the model. Using 14 years (1997 – 2010) of daily mean density measurements from the Stella satellite at ~813 km, the authors perform a multiscale statistical assessment of six candidate solar inputs: the traditional F10.7 radio flux, the Mg II core‑to‑wing index, the integrated 26‑34 nm EUV flux measured by the SOHO/SEM instrument, the s10.7 index derived from SEM, the Lyman‑α line intensity, and a soft X‑ray (0.1‑0.8 nm) proxy (XUV).

The density time series is decomposed into a slowly varying (DC) component and a rapidly varying (AC) component. For the DC part, a baseline extraction method (minimum over a 21‑day sliding window followed by Gaussian smoothing) is used instead of the conventional 81‑day moving average, thereby avoiding contamination by geomagnetic storm spikes. Correlation with each solar proxy is quantified using Spearman’s rank coefficient (r) and a normalized RMS error (relative to the density standard deviation). Linear fits are first applied, then a weakly nonlinear cubic polynomial (ρ̂ = α + βx + γx³) is fitted to capture modest curvature. The SEM‑derived 26‑34 nm flux (denoted S) consistently yields the lowest RMS (≈ 0.18) and the highest r (≈ 0.98), outperforming F10.7 and Mg II across all time scales, including the low‑density periods at the 1995‑96 and 2009‑10 solar minima.

To address the second challenge—thermospheric inertia—the authors introduce a linear time‑invariant Output‑Error (OE) model, a class of discrete transfer‑function models. The model predicts the density ρ̂