determining the most appropriate solar inputs for use in upper atmosphere density models

NADIR workshop - October 27-28, 2010 page 1 / 17

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

Sean BruinsmaCNES, 18 avenue Edouard Belin, 31401 Toulouse, France

Thierry Dudok de WitCNRS/LPC2E, 3A avenue de la Recherche Scientifique, 45071 Orléans,

France


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: StellaLaunched: 26 September 1993Mean altitude: 800 - 835 kmEccentricity: 0.02Inclination: 98.6°Diameter: 24 cmMass: 48 kg

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

Data


Data

5 4 3 2 1

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


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) }

Signal decomposition


The DC components are computed for all quantities. Two examples are given below.

Density baseline

F10.7 baseline

Signal decomposition: DC

NB: the baseline is not affected by geomagnetic storms, whereas the mean is (‘moving average’)


We have 15 months more of density data

COSPAR


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


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.


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?


Changes due to 15 months of data ?!



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


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 plottedIn 2D distance maps (right)

(the distance betweenpairs gives their correlation)

Densities: red(lne=log ne / sne=ne0.5)

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


Signal decomposition: AC


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] + 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



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’)



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)


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 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)

determining the most appropriate solar inputs for use in upper atmosphere density models

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