Acta Geophysica DOI: 10.2478/s11600-009-0051-4

________________________________________________ © 2009 Institute of Geophysics, Polish Academy of Sciences

Plasmaspheric Electron Density Reconstruction Based on the Topside Sounder Model Profiler

Ivan KUTIEV1, Pencho MARINOV2, Anna BELEHAKI3, Norbert JAKOWSKI4, Bodo REINISCH5, Chris MAYER4,

and Ioanna TSAGOURI3

1Geophysical Institute, Bulgarian Academy of Sciences, Sofia, Bulgaria e-mail: ikutiev@geophys.bas.bg (corresponding author)

2Institute for Parallel Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria e-mail: pencho@parallel.bas.bg

3National Observatory of Athens , Institute for Space Applications and Remote Sensing, Athens, Greece, e-mails: belehaki@space.noa.gr, tsagouri@space.noa.gr 4German Aerospace Center, Institute of Communication and Navigation,

Wessling, Germany, e-mails: Norbert.Jakowski@dlr.de, Christoph.Mayer@dlr.de 5University of Massachusetts Lowell, Center for Atmospheric Research,

Massachusetts, USA, e-mail: Bodo_Reinisch@uml.edu

A b s t r a c t

We apply a model-assisted technique to construct the topside elec-tron density profile based on Digisonde measurements. This technique uses the Topside Sounder Model (TSM), which provides the plasma scale height, O+-H+ transition height, and their ratio Rt = HT/hT, derived from topside sounder data of Alouette and ISIS satellites. The Topside Sounder Model Profiler (TSMP) incorporates TSM and uses the model quantities as anchor points for the construction of topside density pro-files. TSMP provides its model ratios with transition height and plasmas-pheric scale height. The analysis carried out indicates that Digisonde derived F-region topside scale height Hm is systematically lower than one derived from topside sounder profiles. To construct topside profiles by using Hm, a correction factor of around 3 is needed to multiply the

I. KUTIEV et al.

neutral scale height in the α-Chapman formula. It was found that the plasmaspheric scale height strongly depends on latitude and its ratio with the F-region scale height expresses large day-to-day variability.

Key words: plasmaspheric electron density, topside sounder model.

1. INTRODUCTION The purpose of the paper is to present the general approach of the model-assisted Digisonde topside profiling developed by Kutiev et al. (2009) and two options of its realization: by using TSMP (Topside Sounder Model Pro-filer) or by using the Vary−Chap scale height (VCSH) function (Reinisch et al. 2007). Both methods represent the topside Ne profile by α-Chapman functions, and the difference between them is the way of introducing the scale height. TSMP uses the classical α-Chapman shape to represent the O+ distribution above the F2 peak hmF2 with a constant scale height provided by Digisonde measurements, while the Vary−Chap function uses a conti-nuously varying scale height. It is important to note that we define the scale height as dh/d(lnNe) which represents the change of height range where the plasma density Ne decreases by a factor e (2.73159…). It is more correct to refer to it as a vertical scale height in contrast to the theoretical plasma scale height along magnetic field lines, or the neutral density Chapman scale height. For simplicity, we omit here the term “vertical”, but it should be borne in mind that the scale heights differ not only by their physical mean-ing, but also by magnitude and spatial and temporal variations (Liu et al. 2007a, b). To construct the Ne profile in the plasmasphere, TSMP calculates a transition height by using the model ratio Rt between scale height and tran-sition height. Thus, TSMP obtains the transition height multiplying the Digi-sonde-derived scale height with the model ratio Rt. The H+ distribution is presented by a simple exponent having a scale height equal to 16 times the Didisonde scale height. The H+ distribution has an anchor point at the transi-tion height, where its density has a maximum and equals that of O+.

O

O O

1exp 1 exp F2( )2

m mm

h h h hN N h

H H+

+ +

⎧ ⎫⎡ ⎤⎛ ⎞− −⎪ ⎪= − − − =⎢ ⎥⎨ ⎬⎜ ⎟⎢ ⎥⎝ ⎠⎪ ⎪⎣ ⎦⎩ ⎭

H

H

| |F2( )exp ,TT

h hN hH+

+

⎛ ⎞−= −⎜ ⎟

⎝ ⎠

where (H ) (O )Ne Ne+ +<< for Th h< , H

| |F2( ) F2( ) exp ,TT

h hNe h hH +

⎛ ⎞−= + −⎜ ⎟

⎝ ⎠

O HF2( )Th N N+ += = at the transition height hT.

PLASMASPHERIC ELECTRON DENSITY BASED ON TOPSIDE SOUNDER MODEL

Here HH + stands for the vertical scale height of the plasmasphere (H+ domi-

nated plasma), and OH + for the topside Chapman scale height of the topside

F region (O+ dominated plasma). Further in the paper, HH + will be denoted

as HP and OH + with HT.

The VCSH method uses the α-Chapman formula for the entire topside Ne profile by varying the scale height. The Vary−Chap function (Rishbeth and Garriott 1969) is given by

( )1 2( ) 1exp 1 exp( ) ,

2H hN Nm y yHm

−⎛ ⎞ ⎡ ⎤= − − −⎜ ⎟ ⎢ ⎥⎣ ⎦⎝ ⎠

where d .( )

m

h

h

hyH h

= ∫

Reinisch and Huang (2001) solved this equation for

[ ]2( )( ) ( ) 1 ln ( ) ,N hH h Hm X h X h

Nm

−⎛ ⎞= −⎜ ⎟⎝ ⎠

where

2

( )1( ) 1 d ,m

h

h

N hX h hHm Nm

⎛ ⎞= − ⎜ ⎟⎝ ⎠∫

2( ) d .

s

m

h

h

N hHm hNm

⎛ ⎞= ⎜ ⎟⎝ ⎠∫

Hm is the Digisonde derived scale height at hmF2, and Nm is the electron density at this height.

2. ADJUSTING THE DIGISONDE TOPSIDE SCALE HEIGHT In the α-Chapman formulation, Hm denotes the neutral scale height at hmF2. In the topside, this formula provides a density distribution with plasma scale height asymptotically approaching a value of 2Hm. Theoretically, this plas-ma scale height corresponds to the plasma temperature Tp = Ti + Te ≈ 2Tn, where Ti, Te, and Tn are the ion, electron, and neutral temperatures, respec-tively. Taking this consideration into account, the Digisonde-derived plasma scale height can be set to 2Hm.

Kutiev et al. (2009) have shown that the TSM O+ scale height (Hs) is systematically larger than 2Hm. Figure 1 shows histograms of 2Hm for Athens (left) and Juliusruh (right), obtained for October 2000 to September 2001 and corresponding TSM values HT. The 2Hm histograms (denoted as Digisonde) are shown by transparent red bars, and the black curves show the fitted normal distribution. The HT histogram (denoted as TSM) is given by blue

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Fig. 1. Histograms of 2Hm for Athens (left) and Juliusruh (right), obtained for Octo-ber 2000 to September 2001 and corresponding TSM values HT. Colour version of this figure is available in electronic edition only.

filled bars. To each value of 2Hm corresponds a model value HT calculated for the same conditions. The average ratio is 1.3 for Athens and 1.2 for Juliusruh. Therefore, the TSM values exceed the Digisonde values by approximately 25%.

Reinisch et al. (2007) have fitted the Vary−Chap scale height formula to ISIS 2 topside sounder profiles to obtain its height and local time variations. They also obtained a correction factor of similar magnitude when they com-pared the topside derived Chapman scale height with the bottomside scale height. Figure 2 shows the local time variations of the correction factor for stations Ebro, Millstone Hill, Qaanaaq, and Jicamarca. The correction factor indicates an increased plasma temperature over the doubled neutral tempera-ture assumed in the α-Chapman formula.

3. PLASMASPHERE Ne PROFILES Kutiev et al. (2009) had assumed that the H+ scale height is simply 16 times the O+ scale height determined by the mass ratio of the two ions. To check this assumption, we selected Ne profiles measured by the ISIS 1 satellite, which had a perigee of 3500 km. Figure 3 shows a sample Ne profile, ob-tained on 5 February 1969. Red dots represent data points, the green line is a smoothed approximation of the Ne profile, pink and dashed blue lines represents O+ and H+ distributions. The gray line marks the transition height hT. It was assumed that the H+ scale height HP at least 500 km above the transition height hT can be represented as the maximum of dh/d(lnNe), in or-der to avoid influence of O+ distribution. In average, the plasmaspheric part of the measured Ne profiles extends 2500 km above the transition height.

PLASMASPHERIC ELECTRON DENSITY BASED ON TOPSIDE SOUNDER MODEL

Fig. 2. Local daily variations of the ratio between the topside derived Chapman scale height and the bottomside scale height for Ebro, Millstone Hill, Qaanaaq, and Jica-marca stations.

Fig. 3. A sample Ne profile, obtained on 7 April 1969. Red dots represent ISIS 1 da-ta points, the green line is a smoothed approximation of the Ne profile, pink and dashed blue lines represent O+ and H+ distributions. The gray line marks the transi-tion height hT. Colour version of this figure is available in electronic edition only.

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Fig. 4. A histogram of HP values accumulated from 14,628 measured profiles.

Fig. 5. A histogram of the bulk distribution of the ratio HP/HT, the key parameter of plasmaspheric Ne profiling. Note that the most probable value of the ratio surpri-singly is not 16, but between 8 and 10.

The procedure of calculating the scale height HP requires at least three meas-ured points for taking a regression line, but in average, the regression in-volves the 5 uppermost data points.

PLASMASPHERIC ELECTRON DENSITY BASED ON TOPSIDE SOUNDER MODEL Figure 4 shows a histogram of HP values accumulated from 14,628 meas-

ured profiles. The most probable H+ scale height value is around 1200 km. For TSMP, a more important parameter is the ratio of the H+ vertical scale height (which expresses the plasmaspheric scale height HP) and the O+ Chapman scale height (which is expressed as A function of the F layer Chapman scale height HT). Figure 5 shows a histogram of the bulk distribution of the ratio HP/HT, the key parameter of plasmaspheric Ne profiling. The most probable value of the ratio surprisingly is not 16, but between 8 and 10. This fact, however, can be expected due to the lower plasma density in the outer plas-masphere and magnetosphere. Figure 6 shows how HP and HT correlate. Their correlation coefficient is 0.86 and the standard deviation around the regression line is 665 km or 40%. Figure 7 shows the average ratio for day-time (red line) and nighttime (blue line) conditions as a function of geomag-netic latitude. Vertical bars show doubled standard deviation for each 10-degree bin on latitude. The ratio HP/HT has a maximum around the equator (±30°) and exhibits a marked decrease towards the poles. The nighttime average ra-tio is slightly higher than the daytime one, but local time dependence is not visible due to the large scatter of data. The daytime and nighttime variations of average curves with geomagnetic latitude are shown again in Figure 8, compared with 1/L (solid dashed) and 1/L5 (dashed gray) variations. The scales of the latter curves are adjusted to fit average scale height ratios. While L = cos−2(glat) represents the length of the plasma flux tubes, L5 is proportional to the total volume of the respective flux tubes. Obviously, the decrease of plasma density in the equatorial plane is reversely proportional to L, not to the total volume of plasma tubes. Fortunately, the latitude varia-tion of HP/HT can easily be introduced in TSMP by representing HP as a function of geomagnetic latitude. We suggest a simple relation HP = [9cos2(glat) + 4]HT to account for latitude changes of HP.

4. TSMP AND VCSH REPRESENTATION OF THE TOPSIDE Ne PROFILE

The plasma scale height in the topside F region and plasmasphere increases continuously with altitude. TSMP represents the scale height variations by three parameters: O+ scale height HT, transition height hT, and H+ scale height HP. HP is expressed by HT, multiplied by a correction factor account-ing for latitude changes. HT is replaced by the scale height Hd derived from Digisonde ionograms and corrected by a factor depending on local time and slightly on latitude. The Topside Sounder Model (TSM), on which TSMP is based, provides the model ratio of HT and hT, denoted as Rt. From Hd and Rt corresponding to the same conditions, the respective transition height is also calculated. The plasmasphere scale height is obtained as [9cos2(glat) + 4]Hd.

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Fig. 6. The correlation between HP and HT. Their correlation coefficient is 0.86 and the standard deviation around the regression line is 665 km or 40%. Colour version of this figure is available in electronic edition only.

Fig. 7. The average ratio for daytime (red line) and nighttime (blue line) conditions as a function of geomagnetic latitude. Vertical bars show doubled standard deviation for each 10-degree bin on latitude. Colour version of this figure is available in elec-tronic edition only.

Therefore, the Digisonde scale height Hd and the TSM ratio Rt are sufficient to construct the whole topside Ne profile.

Vary−Chap scale height (Reinisch et al. 2007) can directly construct the Ne profile by using the α-Chapman formula. Figure 9 shows a sample Ne profile measured by ISIS 2 satellite (left) and extracted Vary−Chap scale height (right). The corrected scale height Hd in this sample is 149 km and stays constant between 300 and 500 km, in agreement with TSM concept for the constant O+ scale height.

PLASMASPHERIC ELECTRON DENSITY BASED ON TOPSIDE SOUNDER MODEL

Fig. 8. The daytime and nighttime variations of average curves with geomagnetic la-titude, compared with 1/L (solid dashed) and 1/L5 (dashed gray) variations. Colour version of this figure is available in electronic edition only.

Fig. 9. A sample Ne profile measured by ISIS 2 satellite (left) and extracted Vary−Chap scale height (right). Colour version of this figure is available in electronic edition only.

5. TSMP-ASSISTED DIGISONDE TOPSIDE PROFILING To illustrate the new topside profiling technique, Fig. 10 shows two exam-ples of profile reconstruction for Juliusruh: at 01:00 LT on 5 December 2000 (left) and at 17:30 LT on 6 October 2000 (right). TSMP-assisted Digisonde profiles are shown in purple, while the red and blue lines represent the O+ and H+ distributions. For comparison, vertical electron density profiles (green) have been extracted from 3D electron density reconstructions based on GPS navigation measurements onboard CHAMP (Heise et al. 2002). The

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(a)

(b)

Fig. 10. Two examples of profile reconstruction for Juliusruh: at 01:00 LT on 5 De-cember 2000 (a) and at 17:30 LT on 6 October 2000 (b). TSMP-assisted Digisonde profiles are shown in purple, while the red and blue lines represent the O+ and H+ distributions. For comparison, vertical electron density profiles (green) have been extracted from 3D electron density reconstructions based on GPS navigation mea-surements onboard CHAMP (Heise et al. 2002). Reproduced with kind permission of American Geophysical Union. Colour version of this figure is available in elec-tronic edition only.

PLASMASPHERIC ELECTRON DENSITY BASED ON TOPSIDE SOUNDER MODEL

3D reconstruction is performed by assimilating the measured TEC between CHAMP and the GPS satellites into the Parameterized Ionospheric Model (PIM), (Daniell et al. 1995). The less pronounced transition height region may be due to the rest influence of the PIM background model and/or the fact that the TEC measurements are primarily upward directed making them less sensitive to vertical structures. This needs further investigation.

6. CONCLUSIONS The present development of the model-assisted Digisonde topside profiling technique leads to the following conclusions:

Digisonde derived F2 layer topside scale height Hm is systematically lower than the one derived from topside sounder profiles. To con-struct topside profiles by using Hm, a correction factor of around 3 is needed to multiply the neutral scale height in the α-Chapman formu-la. This correction factor depends strongly on local time and slightly differs from station to station.

The plasmasphere scale height strongly depends on latitude. Its ratio with the F layer scale height exhibits a large day-to-day variability. In the inner plasmasphere (±30° geomagnetic latitude) the ratio is around 12, and the local time variations are masked by the large scatter. To-wards the poles, the ratio decreases to about 5. The latitude dependence of the ratio can be well approximated by a cos−2(glat) dependence.

To assist constructing topside Ne prodile by using Digisonde-derived scale heights, the TSMP provides its model ratios with transition height and plasmaspheric scale height. With the two model ratios, Digisonde-derived corrected scale height and the plasma density and height of the F layer peak, the topside Ne profile is fully determined.

7. FUTURE WORK The plasmaspheric electron density profile technique presented in this paper has the potential to be applied to the world-wide Digisonde network pro-vided that the correction factor of Hm will be computed at each station loca-tion. Additionally, a more precise plasmaspheric profiling technique can be developed in the future combining the advantages of TSMP and VSCH tech-niques.

Consequently, the method can be adopted by the European Research Net-work of Ionospheric and Plasmaspheric Observation Systems (EURIPOS). This requires a systematic validation including verification with CHAMP-derived TEC and Ne reconstruction, obtained above 400 km, ground-based GPS derived TEC parameters and plasmagrams from the RPI experiment onboard IMAGE. Investigations over a long time series of historical data as

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well as case studies will demonstrate the potential of the proposed method to reliably reproduce the plasmaspheric conditions during quiet and storm intervals. A more systematic validation of the model-assisted Digisonde topside profiling technique is attempted by Belehaki et al. (2009).

Acknowledgements . The work for preparing this paper was sup-ported by NATO Collaborative Linkage Grant CBP.EAP.CLG982569.

R e f e r e n c e s

Belehaki, A., I. Kutiev, B. Reinisch, N. Jakowski, P. Marinov, I. Galkin, C. Mayer, I. Tsagouri, and T. Herekakis (2010), Verification of the TSMP-assisted Digisonde topside profiling technique, Acta Geophys. 58, DOI: 10.2478/ s11600-010-0052-3 (this issue).

Daniell, R.E. Jr., L.D. Brown, D.N. Anderson, M.W. Fox, P.H. Doherty, D.T. Decker, J.J. Sojka, and R.W. Schunk (1995), Parameterized ionospheric model: A global ionospheric parameterization based on first principles models, Radio Sci. 30, 5, 1499-1510.

Heise, S., N. Jakowski, A. Wehrenpfennig, Ch. Reigber, and H. Lühr (2002), Sound-ing of the topside ionosphere/plasmasphere based on GPS measurements from CHAMP: Initial results, Geophys. Res. Lett. 29, 14, 1699, DOI: 10.1029/ 2002GL014738.

Kutiev, I., P. Marinov, A. Belehaki, B. Reinisch, and N. Jakowski (2009), Recon-struction of topside density profile by using the topside sounder model pro-filer and digisonde data, Adv. Space Res. 43, 11, 1683-1687, DOI: 10.1016/ j.asr.2008.08.017.

Liu, L., H. Le, W. Wan, M.P. Sulzer, J. Lei, and M.-L. Zhang (2007a), An analysis of the scale heights in the lower topside ionosphere based on the Arecibo incoherent scatter radar measurements, J. Geophys. Res. 112, A06307, DOI: 10.1029/2007JA012250.

Liu, L., W. Wan, M.-L. Zhang, B. Ning, S.-R. Zhang, and J.M. Holt (2007b), Varia-tions of topside ionospheric scale heights over Millstone Hill during the 30-day incoherent scatter radar experiment, Ann. Geophys. 25, 9, 2019-2027.

Reinisch, B.W., and X. Huang (2001), Deducing topside profiles and total electron content from bottomside ionograms, Adv. Space Res. 27, 1, 23-30 DOI: 10.1016/S0273-1177(00)00136-8.

Reinisch, B.W., P. Nsumei, X. Huang, and D.K. Bilitza (2007), Modeling the F2 topside and plasmasphere for IRI using IMAGE/RPI and ISIS data, Adv. Space Res. 39, 5, 731-738, DOI: 10.1016/j.asr.2006.05.032.

Rishbeth, H., and O.K. Garriott (1969), Introduction to Ionospheric Physics, Aca-demic Press, New York.

Received 7 July 2009 Accepted 13 August 2009