NADIR workshop - October 27-28, 2010page 1 / 17 Determining the Most Appropriate Solar Inputs for use in Upper Atmosphere Density Models Sean Bruinsma CNES, 18 avenue Edouard Belin, Toulouse, France Thierry Dudok de Wit CNRS/LPC2E, 3A avenue de la Recherche Scientifique, Orléans, France

NADIR workshop - October 27-28, 2010page 2 / 17 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: km Eccentricity: 0.02 Inclination: 98.6° Diameter: 24 cm Mass: 48 kg Data

NADIR workshop - October 27-28, 2010page 3 / 17 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 nm (LASP Boulder) SEM0: central order flux from SOHO/SEM. This is equivalent to the EUV flux integrated from nm(*) SEM1: first order flux from SOHO/SEM. This is equivalent to the EUV flux integrated from nm(*) XUV: daily minimum value of the GOES X-ray flux in the nm band (*) Ap, Kp(*): daily planetary geomagnetic index (*): available in near real time Data

NADIR workshop - October 27-28, 2010page 4 / 17 Data kp: planetary average Geomagnetic activity depends on time and longitude: new index a NH: 5 sectors Geomagnetic activity: An idea for a new index that will be studied

NADIR workshop - October 27-28, 2010page 5 / 17 Decompose all quantities into slowly-varying (DC) and fluctuating (AC) components: X(t) = X DC (t) + X AC (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 { X AC (t) = X(t) - X DC (t) } Signal decomposition

NADIR workshop - October 27-28, 2010page 6 / 17 The DC components are computed for all quantities. Two examples are given below. Density baseline F 10.7 baseline Signal decomposition: DC NB: the baseline is not affected by geomagnetic storms, whereas the mean is (‘moving average’)

NADIR workshop - October 27-28, 2010page 7 / 17 We have 15 months more of density data COSPAR

NADIR workshop - October 27-28, 2010page 8 / 17 Spearman’s rank correlation coefficient is computed for density and all proxies. Highest correlations  (but hysteresis) with the solar cycle are obtained for: SEM, sf10.7, f10.7, MgII Signal decomposition: DC 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.

NADIR workshop - October 27-28, 2010page 9 / 17 The densities are now modeled using a second-order polynomial in P(roxy) for three candidates: X DC (t) = aP 2 (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): Signal decomposition: DC 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?

NADIR workshop - October 27-28, 2010page 10 / 17 Changes due to 15 months of data ?!

NADIR workshop - October 27-28, 2010page 11 / 17 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

NADIR workshop - October 27-28, 2010page 12 / 17 Best proxies for the AC component {X AC (t) = X(t) - X DC (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=ne 0.5 ) Modeled densities: blue (S, M, F) Proxies: black Signal decomposition: AC Ap/Kp, S, M, F S, M, F S, M and F S, M, F

NADIR workshop - October 27-28, 2010page 13 / 17 Signal decomposition: AC

NADIR workshop - October 27-28, 2010page 14 / 17 Modeling the AC component The linear time-invariant model with which the AC component is modeled is a convolutive model: 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] + a 1 y[t-1] + a 2 y[t-2] = b 0 u[t] + b 1 u[t-1] + b 2 u[t-2] + c 0 v[t] + c 1 v[t-1] + c 2 v[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 A p 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

NADIR workshop - October 27-28, 2010page 15 / 17 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’)

NADIR workshop - October 27-28, 2010page 16 / 17 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)

NADIR workshop - October 27-28, 2010page 17 / 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 convolutive model (ARX) - the ARX model is 20% more accurate than a static model - the highest correlations are obtained for SEM, MgII and f 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)