Ionospheric Slab Thickness and Total Electron Content Determined in Australia

1. INTRODUCTION

TEC is the total electron content (electrons/m2) of a vertical column of 1 m2 cross-section from the height of a GPS satellite (20 000 km) to ground level.  TEC is measured in TEC Units (TECU) where 1 TECU = 1016 electrons/m2.  The present set of measurements of TEC in South Australia at Salisbury (latitude 34.77°S, longitude 138.63°E) commenced in July 1991 to satisfy a need for extended TEC data in the southern hemisphere.  This was desirable as a reliable basis for providing the correction for the ionospheric time difference in the reception of radio transmissions at 1227.60 MHz compared with 1575.42 MHz from Global Positioning System (GPS) satellites; (1 ns of time difference corresponds to 2.8 TECU and 0.3 metres of signal path from satellite to receiver).Ionospheric corrections of approximately 10 to 50 TECU for (vertical) TEC are inferred from Figure 2 which correspond to approximately 1 to 5 metres in the vertical component of signal path.  Corrections of this magnitude are usual in the position determination of a GPS receiver at ground level.

Errors in TEC measurements include those due to receiver offset bias and satellite offset bias which are time delay errors produced in the hardware of the receiver and satellite respectively between signals at the two GPS frequencies.  These errors were removed as much as practicable from the TEC data.  A Rockwell UH60 GPS receiver was used until April 1994, and subsequently an Ashtech 12 receiver (which required a large offset bias correction).

2. CORRECTED GPS TEC

Figure 1 : A comparison of GPS TEC versus latitude measured at Salisbury with model prediction from IRI and PIM.

Figure 2 : Midday TEC values are plotted against the smoothed values of sunspot number for the specified season in each year. Regression coefficient, R², is indicated for each seasonal plot.

Goodwin and Breed (1999) provided the correction as follows. TEC is equal to slant TEC x cos(i) where slant TEC is measured along the signal path from satellite to receiver, and I is the incidence angle of the ray on the ionosphere assumed to be at a median height of 400 km.  Observations are made at latitude 35°S.  It is assumed that satellites with subionospheric points at latitudes of 45°S and 25°S have the same “slant correction factor”, cos(i₁).  Satellites at latitude 35°S were shown by Goodwin and Breed (1999) to have an average “slant correction factor”, cos(i₂) which was greater than cos(i₁).  (In fact, i₂ corresponds to a set of subionospheric points at latitude 35°S which have a mean difference in longitude from that of the observation point equivalent to a difference of approximately 3° of latitude).  The above considerations provide the ratio of the TEC correction at 45°S and 25°S to that at 35°S.

Furthermore, it is assumed that the slope of the corrected GPS TEC versus latitude plot is the same as the slope for the original measurements at 45°S and 25°S.  The above information is sufficient basis to provide a corrected TEC versus latitude plot shown in Figure 1.

Model values for only ionospheric TEC (September 1994) are shown; these values were computed for a time when (compared with the GPS TEC values) the model values would be approximately 3 TECU higher due to slightly greater solar activity, but would be 2 TECU less than for the corresponding GPS TEC values because of the absence of protonospheric TEC in the models.  The corrected GPS TEC and model values should therefore be similar in magnitude, which is demonstrated in Figure 1.  Two different TEC models used : The International Reference Ionosphere (IRI 1990) (Bilitza, 1990) and the Parameterised Ionospheric Model (PIM, Version 1.4 Feb. 1996) (Daniell et al, 1995).  The IRI allows TEC predictions to a maximum height of 3000 km while PIM allows the calculation of electron density (and hence TEC) to an altitude of 1600 km.

In Figure 1 the plot for the corrected GPS TEC has a greater slope than that predicted from IRI and PIM.  It is possible that appreciable observational errors, such as those around latitude 25°S, could have led to an error in the “corrected slope” of a magnitude that could account for the discrepancy.  The apparently negative corrected GPS TEC values at higher latitudes could also be attributable to appreciable observational errors.

3. PROTONOSPHERIC TEC DETERMINED FROM GPS TEC

Measurements of GPS TEC are immediately useful in determining the retardation of a radio signal from a GPS satellite to a ground receiver, so that a correction may be applied in determining a receiver's location.  However, in using GPS TEC for ionospheric purposes, it is normally desirable to estimate, and deduct, the protonospheric TEC component.

The protonosphere, or plasmasphere, is the region above the O⁺/H⁺ transition height.  The protonosphere is normally considered to occur from 2000 km to 35 000 km, the height of the plasmapause, with only a small TEC contribution to the protonosphere occurring between 20 000 km (the height of GPS satellites) and 35 000 km.  The protonosphere corresponds to approximately 10% of the combined ionosphere-protonosphere in the daytime when the electron density in the ionosphere is high, and 40 - 50% of the night-time TEC when the ionospheric electron density is low.  These percentages are representative of the protonosphere over a solar cycle; the percentages will normally be lower near solar maximum and higher near solar minimum.  The protonosphere has no internal ionisation production.  It is enhanced by an upward diffusion of ionisation from the ionosphere during the day, and depleted by a downward diffusion at night.

The contribution of protonospheric TEC to the total GPS TEC is considered in terms of the diurnal ratio of the daytime maximum TEC to the night-time minimum TEC as follows.  Using the diurnal TEC ratios in Table 1, a comparison is made between the TEC measurements of Essex (1978) determined using the Faraday rotation technique for the ionosphere (up to 2000 km) and the present GPS TEC measurements (up to 20 000 km).  Both sets of measurements are for southern Australia in the declining phase of a solar cycle.

Table 1  Essex (1978); Diurnal TEC ratios* obtained from Faraday rotation measurements of TEC recorded in Melbourne.
 

TEC ratios	1971	1972	1973	1974	Average diurnal TEC ratios  for ionosphere
Summer	4.1	4.3	5.7	6.0	5.0
Equinox	6.4	5.9	6.2	6.3	6.2
Winter	5.2	5.4	4.8	5.2	5.2
Mean	5.2	5.2	5.6	5.8	5.5

Breed and Goodwin (present);Diurnal TEC ratios*obtained from GPS measurements of TEC recorded at Salisbury (near Adelaide).
 

TEC ratios	1991	1992	1993	1994	1995	Average diurnal  GPS TEC ratios	Average diurnal TEC ratios for ionosphere **
Summer	3.4	6.0	1.8	3.6		3.7	6.7
Equinox	5.1	4.8	2.9	2.0		3.7	6.7
Winter	4.4		1.7	2.7	2.6	2.9	5.2
Mean						3.4	6.2

**Diurnal TEC ratio for ionosphere

=(90/50) x Diurnal GPS TEC ratio.

The ionospheric TEC is expected to be 90% of the GPS TEC for the day-time maximum, and approximately 50% for the night-time minimum.  In Table 1 the present average diurnal GPS TEC ratios are therefore multiplied by 90/50 to produce the approximate average TEC ratios for the ionosphere.  The reasonable measure of agreement between 6.2 (with an estimated error of approximately ± 12%) for the present mean diurnal ratios and 5.5 for those of Essex (1978) indicate that ionospheric TEC can be determined by removing the protonospheric TEC from GPS TEC.

Figure 2 shows midday TEC values plotted seasonally against smoothed values of sunspot number from 1991 to 1995.  The regression coefficient, R², is indicated for each seasonal plot.  TEC is related to sunspot number, S, by an equation (Huang,1978) of the form

where A and B are constants dependent on season and time of day.

*The Diurnal TEC ratio is the ratio of daytime maximum TEC to night-time minimum TEC.

Table 2 Approximate values of constants A and B for the equation, TEC = A + B x S are listed for the seasons; S is the sunspot number. (Errors associated with the seasonal Salisbury values are estimated at ± 10%).
 

	Salisbury (34.6°S) (Present work)		Sagamore Hill (38.6°N) Huang (1978)
Seasons	A	B	A	B
Summer	22.5	0.19	7 - 12	0.1 - 0.15
Autumn	15.9	0.31	10 - 15	0.2 - 0.25
Winter	11.0	0.23	5 - 10	0.25 - 0.3
Spring	15.1	0.17	5 - 10	0.25 - 0.3
Median	15.5		8.5

Midday values of A and B shown in Table 2 were derived for the present GPS TEC data, using a linear regression. These are compared with ionospheric TEC data of Huang (1978) obtained at a similar latitude from Faraday rotation observations up to a height of 2000 km.  Since the parameter, A, is a TEC offset, it follows that the inclusion of protonospheric TEC in the present GPS TEC data has the effect of increasing this offset.  It follows that the difference between the values of A for the two data sets is a rough estimate of the protonospheric TEC between 2000 km and 20 000 km heights.  In Table 2 the difference between the present median A-value (for seasonal midday values in 1991 - 1995) and that of Huang (1978) is 15.5 - 8.5 = 7 TECU, which is a rough estimate of the protonospheric TEC at midday.  Another example is the difference between the summer A-values which is 22.5 - 9.5 = 13 TECU for the summer midday protonosphere.

Figure 3 : Hourly average TEC values derived from GPS and Faraday rotation measurements at Salisbury and the calculated protonospheric electron content for December 1992 are shown.

Figure 3 shows the diurnal variation in protonospheric TEC at 2000 km to 20 000 km determined from the difference between GPS TEC and Faraday rotation TEC recorded near Salisbury in December (summer) 1992, in the declining phase of the solar cycle.  The median protonospheric TEC is 7.2 TECU.  Similarly, the summer midday protonosphere has a TEC of 15 TECU, which is in reasonable agreement with the rough estimate of 13 TECU determined from Table 2.

Earlier workers (Almeida et al, 1970; Davies et al, 1976; Kersley et al, 1978) calculated protonospheric TEC from measurements of the retardation of transmissions along fixed paths to ground receivers from the geostationary satellite, ATS-6, located over the equator at an altitude of 35 000 km.  They combined two techniques, as follows.  In the Faraday rotation technique, slant TEC was measured up to 2000 km.  In the differential phase technique, slant TEC was measured up to 35 000 km.  It follows that the difference between these two measurements is the slant TEC of the protonosphere.  They recorded slant protonospheric TEC in Aberystwyth (U.K.), Hamilton (eastern U.S.A.) and Boulder (middle North America).

Figure 4 : Equinoctial electron content of the protonosphere from Salisbury in 1994, compared with measurements from three northern hemisphere sites.

In Figure 4, the diurnal variation of (vertical) protonospheric TEC observed at Salisbury (near Adelaide) is plotted.  A line of best fit is sketched through the plotted points which each have an estimated accuracy of ± 8 TECU.  The “dip” in TEC around 07:00 UT could be attributed to the limitations in the accuracy of the data.

The Salisbury diurnal variation is similar to the variation of the slant protonospheric TEC observed in Aberystwyth but opposite to that observed in Hamilton.  Kersley (1978) suggested that this difference between the Aberystwyth and Hamilton observations arises because the protonosphere at Aberystwyth has a conjugate point at a mid-latitude, whereas Hamilton has a conjugate point in an auroral latitude where the electron content is much lower than at mid-latitudes.  The similarity with Aberystwyth could arise because Adelaide observations also relate to a conjugate point at a middle geographic latitude, namely at latitude 52.8°N, longitude 144.2°E, in the region north of Japan, just off the east coast of Russia.

Protonospheric TEC may also be determined from GPS TEC by deducting model ionospheric TEC (IRI and/or PIM).  Another approach would be to deduct from GPS TEC the Navy Navigation Satellite System (NNSS) TEC measurements.  NNSS TEC refers to a height up to 1000 km, and so a 'correction' of approximately 2 TECU (corresponding to TEC from 1000 km to 2000 km) must be deducted from the protonospheric TEC calculated in this way.

Table 3  Combined midday and midnight median protonospheric TEC are listed, calculated from GPS TEC (measured at Salisbury) minus model ionospheric TEC (which is the mean of IRI and PIM TEC relating to the ionosphere up to 3000 km and 1600 km respectively).
 
 

Combined midday and midnight  protonospheric TEC (TECU)	1991	1992	1993	1994	1995
SUMMER (Nov - Feb)		4 (7 Jun)			9.5  (5 days Feb)
EQUINOX (Mar, Apr, Sep, Oct)	-1     (15 Oct)	5     (21 Mar)	7       (2 Apr)	15 (5 Mar,16 Sep)	10.5 (18 Apr)
WINTER (May - Aug)	5 (22 Apr)		0 (9 Jun)	7 (9 Jun)	6.5 (5 days Jun)

The electron content of the protonosphere does not change much diurnally, but it is significantly depleted during major magnetic storms, and can take several days to recover to pre-storm values.  For this reason in 1991/92, shortly after solar maximum, magnetic storms led to reduced protonospheric TEC compared with 1994/95, approaching solar minimum, as seen in Table 3 in which midday and midnight data are combined.  Although Table 3 was determined for only a limited number of days, it does support the suggestion that in 1991 - 1993 the GPS measurements would contain a smaller component from the protonosphere.  From this observation, coupled with the occurrence of larger values of ionospheric TEC near solar maximum, it is concluded that in 1991 -1993 GPS TEC would be approximately the same as ionospheric TEC.

4. IONOSPHERIC SLAB THICKNESS

Slab thickness may be regarded as the depth of an imaginary ionosphere which has the same TEC as the actual ionosphere and uniform electron density equal to the maximum electron density of the actual ionosphere.

By definition,

where N_mF₂ is the peak F₂ region electron density (electrons/m³), and TEC is the total electron content (electrons/m²) of a vertical column of 1 m² cross-section up to the 'top' of the ionosphere, taken for convenience to be 2000 km.

Slab thickness includes information on both the topside and bottomside ionosphere, and indicates the electron density versus height profile; for instance, the 'sharper' the peak electron density, the smaller is the slab thickness.

The values of N_mF₂ which were used to compute slab thickness were calculated using the following relationship (eg. Goodwin et al (1995a)):

where f_oF₂, the F₂ region ordinary critical frequency in MHz, is measured from ionograms recorded at 5-minute intervals at Salisbury.  Values of slab thickness were determined at Salisbury from July 1991 to February 1995 for 3 to 5 days per month.

This period was during the descending phase of solar cycle 22 which had a broad peak from mid-1989 to late 1991, and reached a minimum in May 1996.  The present paper relates to earlier work (Goodwin et al, 1995a, 1995b; Breed et al, 1995; Breed, 1996).

Slab thickness values determined from GPS TEC include the electron contents of both the ionosphere (up to 2000 km) and most of the protonosphere (from 2000 to 20 000 km). In ionospheric studies, slab thickness would more appropriately be defined as the slab thickness of the F₂ region only, ie:

where TEC(F₂) is the total electron content of the ionospheric F₂ region, that is GPS TEC from which had been deducted the protonospheric TEC, (as well as, desirably, the daytime E and F₁ region TEC).

In the present paper, slab thickness is determined from GPS TEC recorded in 1991 - 1993 near solar maximum when the protonospheric component was minimal.This calculated slab thickness is therefore taken to be approximately equal to ionospheric slab thickness.

Figure 5 shows diurnal plots of slab thickness in different seasons in 1993 for Salisbury.  (In Figures 5-8, seasons are: summer: November-February; winter: May-August; equinox: March, April, September, October; autumn: March, April; spring: September, October).  TEC observations were made on 3-5 days each month.  For Salisbury UT is 9.5 hours behind local time (Central Standard Time, CST); 20.30 UT is around sunrise (SR) and 08.30 UT is around sunset (SS).  A pre-dawn peak in the slab thickness at 18.00 to 21.00 UT (03.30 - 06.30 CST) may be observed in these plots.  The pre-dawn peak was also found in the seasonal plots from 1991 to 1995, except during summer in 1991/92 and 1992/93 when the solar influence was maximal.

The pre-dawn peak is explained in terms of the lowering of the F-layer height just before sunrise into a region of greater neutral air density.  This causes a corresponding increase in the loss rate of ionisation due to recombination especially in the lower F₂ region which includes the electron density peak, N_max (Titheridge, 1973).  As a result, there is a faster decrease in N_max compared with the decrease in TEC, since approximately 70% of the total electron content occurs above the peak in the topside ionosphere, where the loss rate is lower.  Thus, an enhancement occurs in the slab thickness, (TEC/N_max).

Figure 5 indicates that the slab thickness is greater at night than in the day, and at midday (02.30 UT) it is greater in summer than in winter.  These observations agree with those of earlier workers in Australasia (Titheridge, 1973; Essex, 1978; McNamara, 1982) who used Faraday rotation measurements of TEC.

The winter night-time enhancement in slab thickness is due to a lowering (Titheridge, 1973) of the O⁺/H⁺ transition height (between the ionosphere and the protonosphere) at a time when solar influence is minimal.  This transition height can descend to as low as 420 km near midnight in winter.  The scale height (inversely proportional to atmospheric molecular weight) is greater above the O⁺/H⁺ transition height.  It follows then that the further down the penetration of the O⁺/H⁺ transition height into the ionosphere, the greater the average ionospheric scale height, and hence the greater the slab thickness (which is directly proportional to scale height).

Figure 6 : Latitudinal variations in slab thickness measured from Salisbury for summer 1991/1992 and 1992/1993 are shown.

Figure 7 : Latitudinal variations in slab thickness measured from Salisbury for equinox 1991/1992 and 1992/1993 are shown.

Figure 8 : Latitudinal variations in slab thickness measured from Salisbury for the years 1991 - 1992 are shown in winter.

Figure 9a : A comparison of diurnal slab thickness values from GPS measurements and predictions from the IRI and PIM ionospheric models.

Figure 9b : A comparison of diurnal slab thickness values from GPS measurements and predictions from the IRI and PIM ionospheric models.

During 1991 to 1993, near solar maximum, GPS TEC had a comparatively small protonospheric component, and so slab thickness derived from GPS TEC was then a more reliable measure of the ionosphere than at other times in the solar cycle.  Figure 6 shows latitudinal plots of slab thickness for summer (midday and midnight, November to February) in 1991/92 and 1992/93.  Summer slab thickness is seen to be approximately constant (versus latitude) around 500km at midday and around 300 km at midnight, with no substantial latitudinal change.  In Figure 7 similar plots are shown for the equinoctial months (March, April, September and October) in 1991/92 and 1992/1993. Again slab thickness is approximately constant against latitude with values of around 500 km at midday 1991/92, 300 km at midday 1992/93, 300 km at midnight 1991/92 and 400 km at midnight 1992/93. Figure 8 shows similar plots for winter (May to August) 1991 and 1992 for which slab thickness is approximately constant at around 250 km at midday and around 400 km at midnight.  Once more there is no substantial latitudinal change.  These observations, which indicate an absence of latitudinal dependence of slab thickness in any season, are in agreement with the conclusions of Davies and Liu (1991) and Liu and Davies (1990). The present observations also indicate that near solar maximum and in summer, midday slab thickness is greatest, whereas midnight slab thickness is least.

Finally, in Figure 9, there is a good agreement between two days' slab thickness determinations near solar maximum in October, 1991 and March, 1992, compared with slab thickness calculated from the IRI and PIM models.  Slab thickness values of the order of 350 km were both observed and predicted.

5. DISCUSSION AND CONCLUSIONS

The present measurements of GPS TEC, which are centred around Salisbury at 35°S latitude, are the only southern hemisphere TEC data extended in time, from 1991 onwards.  In particular, midday TEC is seen to decrease with declining solar activity.

The determination of the protonospheric TEC component (from approximately 2000 km to 20 000 km) is exemplified in the present paper by deducting Faraday rotation measurements of TEC from GPS TEC.

In 1991 - 1993, near sunspot maximum, when protonospheric TEC is negligibly small, slab thickness derived from GPS TEC is approximately the same as ionospheric slab thickness.  In short, at times near solar maximum, GPS TEC and slab thickness derived from it, can be taken to represent the ionosphere.  In any season and year in the declining solar cycle, slab thickness was observed to be substantially constant independent of latitude.  Midday slab thickness is greater in summer than in winter, and greater near sunspot maximum than near minimum.

Acknowledgments

Sincere thanks are expressed to the late John Silby and to Alan Padgham of the Microwave Radar Division, DSTO, for painstakingly providing GPS receiver data from Salisbury, and to Ken Lynn of the Radio Wave Propagation Group, DSTO for the use of Salisbury ionograms.

6. REFERENCES

Almeida, O.G., Garriott, O.K and Da Rosa, A.V. (1970), Determination of the columnar electron content and the layer shape factor of the Plasmasphere up to the Plasmapause, Planetary and Space Science., 18, 159-170.

Bilitza, D. (1990), International Reference Ionosphere 1990, URSI/COSPAR Task Group on the IRI, NSSDC/WDC-A-R&S 90-22, National Space Science Data Center/World Data Center A for Rockets and Satellites, Greenbelt, Maryland, USA, November.

Breed, A.M. (1996), Investigations of the ionosphere over Australia using satellite transmissions, Ph.D. thesis, School of Applied Physics, University of South Australia.

Breed, A.M., Vandenberg, A-M., Goodwin, G.L., Silby, J.H. and Essex, E.A. (1995), Measurement of the Protonosphere in improving position determination using GPS satellites, Workshop on Applications of Radio Science (WARS 95) Digest of Papers, ed. D.Skellern and J.Steel, ISBN No. 1 86408 0302, Australian Committee for Radio Science, Canberra, June.

Daniell, R.E., Brown, L.D., Anderson, D.N., Fox, M.W., Doherty, P.H., Decker, D.T., Sojka, J.J. and Schunk, R.W. (1995), Paramaterized ionospheric model: a global ionospheric paramaterization based on first principle models, Radio Science, 30, 5, 1499-1510.

Davies, K., Fritz, R.B. and Gray, T.B. (1976), Measurements of the columnar electron contents of the Ionosphere and Plasmasphere, Journal of Geophysical Research, 81, 16, 2825-2834.

Davies, K. and Liu, X.M. (1991), Ionospheric Slab Thickness in middle and low latitudes, Radio Science, 26, 4, 997-1005, 1991.

Essex, E.A. (1978), Ionospheric Total Electron Content at southern mid-latitudes during 1971-74, Journal of Atmospheric and Terrestrial Physics, 40, 1019-1024.

Goodwin, G.L. and Breed, A.M. (1999), Solar cycle variations in GPS observations of TEC in southern Australia, paper presented at Workshop on Ionospheric/Atmospheric Effects on Space Based Assets, Defence Science and Technology Organisation, Salisbury, South Australia, January.

Goodwin, G.L. , Silby, J.H., Lynn, K.J.W., Breed, A.M. and Essex, E.A. (1995a), Ionospheric slab thickness measurements using GPS satellites in southern Australia, Advances in Space Research, 15, 2, 125-135.

Goodwin, G.L., Silby, J.H., Lynn, K.J.W., Breed, A.M. and Essex, E.A. (1995b), GPS satellite measurements: ionospheric slab thickness and total electron content presented at the Second South Pacific Solar-Terrestrial Physics (STEP) Workshop, July 1993, Newcastle, Australia, Journal of Atmospheric and Terrestrial Physics, 57, 14, 1723-1732.

Huang, Y-N. (1978), Solar cycle variation in the total electron content at Sagamore Hill, Journal of Atmospheric and Terrestrial Physics, 40, 733-739

Kersley, L. and Klobucher, J.A. (1978), Comparison of protonospheric electron content measurements from the American and European sectors, Geophysical Research Letters, 5, 2, 123-126, February.

Liu, X-M. and Davies, K., Global measurements of the slab thickness of the ionosphere, Proceedings of the International Beacon Satellite Symposium, Tucuman, Argentina, 159-163, June.

McNamara, L.F. and Smith, D.H. (1982), Total electron content of the ionosphere at 31°S, 1967-1974, Journal of Atmospheric and Terrestrial Physics, 44, 3, 227-239.

Titheridge, J.E. (1973), The slab thickness of the mid-latitude ionosphere, Planetary and Space Science, 21, 1775-1793.