Determining the Most Appropriate Solar Inputs for use in Upper Atmosphere Density Models

1. Determining the Most Appropriate Solar Inputs for use in Upper Atmosphere Density Models Sean Bruinsma CNES, 18 avenue Edouard Belin, 31401 Toulouse, France Thierry Dudok de Wit CNRS/LPC2E, 3A avenue de la Recherche Scientifique, 45071 Orléans, France

2. Data Objective: Determine the “best” solar inputs for thermosphere modeling Method: Analyze mean neutral densities and solar and geomagnetic indices using 16 years of data (12/1993 – 07/2010) Daily mean densities through Precise Orbit Computation (‘perturbation method’): 5617 Satellite: Stella Launched: 26 September 1993 Mean altitude: 800 - 835 km Eccentricity: 0.02 Inclination: 98.6° Diameter: 24 cm Mass: 48 kg

3. Data • The solar and geomagnetic proxies used: • • SSN: sunspot number (SIDC Brussels) • • f10.7: 10.7 cm radio flux (* Penticton) • • MgII: MgII index (* LASP Boulder) • • s10.7: s10.7 index from Tobiska (SEM and GOES/X) • • MPSI: magnetic plage strength index (Mount Wilson Observatory) • • Lya: intensity of the Lyman-alpha line at 121.57 nm (LASP Boulder) • • SEM0: central order flux from SOHO/SEM. This is equivalent to the EUV flux integrated from 0.1-50 nm(*) • • SEM1: first order flux from SOHO/SEM. This is equivalent to the EUV flux integrated from 26-34 nm(*) • • XUV: daily minimum value of the GOES X-ray flux in the 0.1-0.8 nm band (*) • Ap, Kp(*): daily planetary geomagnetic index • (*): available in near real time

4. NH: 5 sectors 5 4 3 2 1 kp: planetary average Geomagnetic activity depends on time and longitude: new index al Data Geomagnetic activity: An idea for a new index that will be studied

5. Signal decomposition Decompose all quantities into slowly-varying (DC) and fluctuating (AC) components: X(t) = XDC(t) + XAC(t) Hypothesis: - DC component is in phase with solar proxies and proportional to solar radiative output - AC component may have a memory effect (convolution) The components are separated as follows: - The DC component is computed as the baseline of a 27-day sliding window - The AC component is the signal minus the baseline { XAC(t) = X(t) - XDC(t) }

6. Signal decomposition: DC The DC components are computed for all quantities. Two examples are given below. Density baseline F10.7 baseline NB: the baseline is not affected by geomagnetic storms, whereas the mean is (‘moving average’)

7. COSPAR We have 15 months more of density data

8. Signal decomposition: DC Spearman’s rank correlation coefficient is computed for density and all proxies. Highest correlations r (but hysteresis) with the solar cycle are obtained for: SEM, sf10.7, f10.7, MgII The reconstruction error is normalized with respect to the variability of the proxy. An error of 100% means that the error in the linear model equals the variability of the signal.

9. Signal decomposition: DC The densities are now modeled using a second-order polynomial in P(roxy) for three candidates: XDC(t) = aP2(t) + bP(t) + c Spearman’s rank correlation coefficient is computed again for densities ne and modeled densities S (SEM1), M (MgII) and F (f10.7): Hysteresis and reconstruction error are smallest for M, but also weakest correlation; Longest (and complete) time series for f10.7, followed by MgII, followed by SEM; Predictions most accurate for MgII, followed by f10.7, followed by SEM; Best index?

10. Changes due to 15 months of data ?!

11. Signal decomposition: DC The baseline of the densities (red) and the modeled densities F, M and S A proxy is never better all the time Flat signal: instrument sensitivity

12. Signal decomposition: AC Best proxies for the AC component {XAC(t) = X(t) - XDC(t)} are determined using a wavelet transform for decomposition into different characteristic time-scales, after which the correlation coefficients are computed for all pairs. These values are then plotted In 2D distance maps (right) (the distance between pairs gives their correlation) Densities: red (lne=log ne / sne=ne0.5) Modeled densities: blue (S, M, F) Proxies: black S, M, F Ap/Kp, S, M, F S, M and F S, M, F

13. Signal decomposition: AC

14. Modeling the AC component The linear time-invariant model with which the AC component is modeled is a convolutivemodel: Auto-Regressive with eXogeneous inputs (ARX). The model expresses density y as a function of the geomagnetic and solar activity proxies, u and v, respectively, using the current date t, the day before (t-1), and 2 days before (t-2): y[t] + a1y[t-1] + a2y[t-2] = b0u[t] + b1u[t-1] + b2u[t-2] + c0v[t] + c1v[t-1] + c2v[t-2] (NB: the optimum order of the model is 2 for all variables) The MgII index is used to represent the solar forcing, and we use Ap for the magnetospheric energy input (this is certainly not the best choice, and the creation of a more representative proxy is under way). NB: a comparable ARX model using f10.7 and SEM will be constructed soon

15. Modeling the AC component The observed (red) and modeled densities (blue and green) for medium (left plot) and low (right plot) solar activity. The ARX model has a 20% smaller RMS error than the static model. (NB: ARX results presented here based on the ‘COSPAR’ data set’)

16. Modeling the AC component The RMS error of the (DC+ARX) model is 26% less* than that of the DTM model. * This error concerns the fully reconstructed density (AC + DC)

17. Summary and conclusion • * Density is decomposed into a slowly-varying (DC) and fluctuating (AC) component • * The DC component: • is modeled as the baseline of a 27-day sliding window • the baseline is uncontaminated by geomagnetic activity variations • - the highest correlations and the least hysteresis with the solar cycle are obtained for S (SEM,) F (f10.7), and M (MgII) • * The AC component • is modeled using a convolutivemodel (ARX) • the ARX model is 20% more accurate than a static model • the highest correlations are obtained for SEM, MgII and f10.7 • geomagnetic storms have typical durations of 1-3 day • a more representative proxy than Ap will be used in the future (ATMOP) • * The DTM model error is 26% larger than obtained in this study (DC + AC)