Global TEC measurement capabilities of the doris system

Adv. Space Res. Vol. 11. No. lO,pp.(lO)5l—(lO)54, 1991 Printed in Great Britain. All rightsreserved.

0273—1177/91 $0.00 + .50 Copyright © 1991 COSPAR

GLOBAL TEC MEASUREMENT CAPABILITIES OF THE DORIS SYSTEM R. Fleury, F. Foucher and P. Lassudrie-Duchesne Centre National d’Etudes des Télécommunications, CentreLAB, Département Géophysique Externe appliquée a la Radioélectricité, BP 40,22301 Lannion France

AZSTRACT

DORIS is a high precision satellite orbit determination and ranging system based on Doppler shift measurements from dual frequency signals propagated between ground stations and a satellite. An algorithm is presented to derive the space variations of the Total Electron Content (TEC) on a. global scale from the DORIS Doppler data. TEC latitudinal profiles obtained with a DORIS platform on board SPOT-2 are given as illustrative examples. INTRODUCTION The DORIS ranging system consists of a satellite-borne platform and a network of automatic ground stations. Dual frequency signals (400/2000 MHz) are emitted from the ground stations and received at the satellite platform where the carrier Doppler shifts are evaluated. The DORIS system is currently under test with a platform on board the SPOT-2 imaging satellite and a ground network of about 30 stations. In the future, the DORIS system is scheduled to be operated on the TOPEX/POSEIDON ocean altimetric satellite with a denser network of ground stations. In this paper, the problem of deriving the ionospheric Total Electron Content (TEC) from the DORIS Doppler data is adressed. Since the TEC is a key parameter both for ionospheric modelling and for correcting ionospheric effects on space systems, the derivation of TEC data from satellite Doppler measurements has been extensively studied in the past. It is known that Doppler measurements from a single ground station Cannot lead to a unique solution for the TEC unless some assumptions are made on the TEC space variations (e.g. /1/). A two-station algorithm has been proposed /2/ for processing Doppler data from the NNSS polar orbiting satellites. A new algorithm is presented here that combines measurements from a number of stations to yield a set of TEC profiles for each satellite revolution. For SPOT-2, a nearly sun-synchronous satellite,, most of the TEC profiles lie inside a 2-hour local time interval. TEC EVALUATION ALGORITHM Let us denote by af~and ~ the Doppler shifts, relative to the upper and lower frequencies and f~respectively. The differential Doppler Afd, defined by £~s.fd — (~/~.)£~.e, is related to the TEC by the relation (e.g. /3/) dI

5

CD

—

(1)

•.~—

where I~denotes the slant TEC (i.e. the TEC along the line of sight) and CD is a constant. An unknown integration constant appears when Equation (1) is integrated to obtain the TEC. The slant TEC Is can be converted into vertical, TEC I~, ty means of an obliquity factor (e.g. /2/) defined as

I~ V

j

N~secc~dr (2) rsNedr

(10)51

R. Fleury et al.

(10)52

where

Ne is

the electron

density in

the ionosphere,

r

5 the geocentric altitude of the satellite, r0 the earth radius and a is the zenith angle of a current point along the path. The greatest contribution to the integrals comes from a point located slightly above the F-layer peak, at an altitude estimated to be 400 km (i.e. r11, — r~+ 400 km). The position of this point is referred to as the “ionospheric point” of the path. To a good approximation, the seca factor can be replaced by seccç, and taken out of the upper integral in Equation (2), (i.e. K — sec~). The vertical TEC defined by Equation (2) corresponds to the position of the subionospheric point. Several Doppler ground stations G~(1 1 p) are assumed to track a single satellite S. For each station, Equation (1) takes the form (3)

~di

where ~ is the slant TEC along the path Ce-S and ~ is the Doppler shift on this path. Using Equation (2), the slant TEC along the i-th path can be converted to a vertical TEC at the subionospheric point of the path by —

Denoting by yield

0

K~. I,~ the

with

latitude

EK~(8) ~

(0))

K~— seca.,~

of

—

the

f~(8)

(4)

current subionospheric point, Equations (1) and (4)

with

f~(0)— ~

(0)

/

(5)

~-

Equation (5) holds for 8 in the interval ®~corresponding to the observations from the i-tb station. Unless additional conditions are imposed, Equation (5) has an infinite number of solutions. Assuming now that the longitudinal variations of the TEC are negligible over a few hundred kilometers, the TEC I,, becomes a unique function of the latitude ‘V~°~ —

I~~(O) for 8E l~, (i

I

p)

where ®~is the interval of observations corresponding to the i-th station. It is shown in /3/ that a unique solution can found to Equation (5) when 0 belongs to a latitude interval ® made up of overlapping ®~. Improvements have been brought to this algorithm in order to make it suitable for simply contiguous, or even slightly disjoined O~. Since the TEC small scale variations are smoothed out irs the integration process, I~(O) accounts only for the large and medium scaleandvariations of the on TEC.~. Hence, IV(O) is ofassumed to be thatchosen dI~/d8and 2I~/d82 exist are continuous The solution Equation (5) such is then such d that the following condition holds

~Jo~~ where

I~) - f~]d0 +

J

[___~d0

is minimum,

(6)

is an arbitrary weighting factor.

In order to compute an approximate solution of Equation (5), a mesh with step h is defined on ‘9. Denoting by I’~’(0) this approximate solution, I~ (0) is required to be a cubic spline (i.e., a twice-derivable piecewise polynomial of 3-rd order with continuous first and second derivatives). The following inequality then holds is I

~1/2

Id ~ J~[.......(~. 1,h ~

12 -

f~] dO

I

J

~

Is2 c1~J~ + c2 —

where c1 and c2 are constants. This enables appropriate values for

(7)

and h to be chosen.

SIMULATION RESULTS Assuming the Bent ionospheric model /4/ for March 1990 (R12 — 150) and station network ~ . TheTEC main of error are (i) parameters similar to those of the DORIS system, the16vertical was causes computed as a function the TEC The conversion approximation given by Equation (2), (ii) the of theslant-to-vertical latitude (Fig. 1-a). r.m.s. error is 3xl0 assumption of longitude invariance of the TEG in the vicinity of the satellite track. Fig. 1-b shows another example of simulation results relative to the SPOT-2 track of 20-25 March 1990. The r.m.s. error is 8.7x1016 m~2, a typical value for simulation results.

TheDORlSSysteni

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EXPERIMENTAL RESULTS WITH SPOT-2 Results obtained with actual data from SPOT-2 for the above mentionned period of 20-25 March 1990 are shown in Fig. 2. This period follows a magnetically disturbed period beginning during the night of 18 March (K-Wingst a 5-6). A solar flare of class Xl/2B occured on 19 March at 05:08 UT followed by a proton event beginning at 07:05 UT on the same day. A strong SSC was observed on 20 March at 22:43 UT. The geomagnetic field was in storm conditions for about 24 hours following the SSC. Fig. 2 shows the response of the ionosphere to these solar and magnetic perturbations. The daytime TEC on 20 March is typical of the quiet-state ionosphere with a latitudinal profile roughly similar to that given by the Bent model. On the following days, a daytime positive phase is clearly visible around 10:30 LT at equatorial latitudes while the ionosphere at other latitudes remains virtually undisturbed or slightly depressed. The data of 24-25 March show the ionosphere slowly returning to normal with equatorial TEC values still above those predicted by the Bent model. CONCLUSION The DORIS orbit determination system can be used as a source of TEC data for ionospheric modelling and other scientific purposes. An algorithm has been presented for deriving the average latitudinal TEC variations along the satellite track. Both simulation results and the preliminary experimental results obtained with SPOT-2 seem promising for deriving the large scale variations of the TEC. However, field tests using independent TEC measurements still have to be carried out to assess precisely the limitations of the proposed method. ACKIqOWLEDGEMENTS This work was partly supported by CITES (Centre National d’Etudes Spatiales). The contributions of Pr, Ciavaldini (University of Nantes) and Mr. Ph. Escudier (CNES) are gratefully acknowledged. REFERENCES 1.

P. Lassudrie-Duchesne, A new approach to the derivation of the total electron content using Doppler measurements from a single ground station, International Beacon Symposium (1JRSI-COSPAR), Univ. Oulu, Finland, 121-134 (1986).

2.

R. Leitinger, C. Schmidt, A. Tauriainen, An Evaluation Method Combining the Differential Doppler Measurements from Two Stations that Enables the Calculation of the Electron Content of the Ionosphere, J. Geophys., 41, 201-213 (1975).

3.

F. Foucher, R. Fleury, P. Lassudrie-Duchesne, Correction of ionospheric effects for the precise orbit determination of satellites, in : Operational Decision Aids for Exploiting or Mitigating Electromagnetic Propagation Effects, AGARD CP-453, 33.1-33.12 (1989).

4.

S.K. Llewellyn, R.B. Bent, Documentation and description of the Bent ionospheric model, AFCRL-TR-73-0657 (1973).

16

TEC C10 120.

rn2J

,

MARCH 1990 •.....

,

i~o TEC

C1016 ~—2j

MARCH 1990

120

100

100 .

-

LATITUDE C’]

(a)

,

LATITUDE C~]

(b)

Fig. 1. Typical examples of simulation results (thick lines) assuming the Bent ionospheric model (thin lines). Horizontal lines indicate observation intervals of stations.

R. Fleury et al.

(10)54

20/03/90

TEC [1016 rn2]

~

,

120

-

o —90

-60

;~—‘-;—-T -30 0

.......

a

90

22/03/90

1110 TEC £1016 rn~2]

21/03/90

2

120

~

30 60 LATITUDE C’]

TEC [1016

‘

—90

,

—60

~‘7•’~7T —30

1110 TEC [1016rn~2]

120,

—‘

0

30 60 LATITUDE C’]

90

23/03/90

12O_

-.

100

100

!SO

‘-7’-3O”0~3O6O~90 LATITUDE C’]

214/03/90

16 m2] 1110 TECI C10 I

I

I

I

120

O’~’0Th~’60

‘90 LATITUDE C~]

I

1110

I

—--—

~

TEC C1016 ~‘.2]

25/03/90 I

I

I

120 1~/~

0 —90

I

—60

—30

I

0

I

30 60 LATITUDE C’]

90

Fig. 2. Experimental results (thick SPOT-2 for the period 20-25 values (thin lines) are for crossings take place around interval 284-300 ‘ E.

0 _______________________ —go —so —30

,

0

30 60 LATITUDE C’]

lines) obtained with DORIS on March 1990. The Bent model comparison purposes. Equator 10:30 LT in the longitude

i,

90