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Variability of the topside thermal plasma parameters during a period of high solar activity for IRI
Advances in Space Research 34 (2004) 1922–1925 www.elsevier.com/locate/asr
Variability of the topside thermal plasma parameters during a period of high solar activity for IRI V. Truhlı´k *, L. Trˇ´ıskova´, J. Sˇmilauer Institute of Atmospheric Physics, Academy of Science Czech Republic, Boe´ni II, 141 31 Praha 4, Czech Republic Received 19 April 2004; received in revised form 24 June 2004; accepted 30 June 2004
Abstract The variability of the electron temperature, ion composition and the upper transition height in the topside ionosphere as given by the IRI models is studied. A variability index based on quartiles is introduced and its global distribution is presented in the form of contour plots for the individual parameters. The obtained global distribution of the variability index described by the associated Legendre polynomials could be used as a complement to the previously developed global models. Ó 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Topside ionosphere; Plasma temperatures; Ion composition
1. Introduction The existing topside global empirical models of the most important thermal plasma parameters (electron density, electron temperature and ion composition) included in IRI (Bilitza, 1990) only describe the main variations of these parameters (depending on local time, latitude, season, longitude, etc.) on the ‘‘climatological scale’’ (e.g. Truhlı´k et al., 2001; Trˇ´ıskova´ et al., 2001, 2003). In many applications the users of models need to know not only the monthly average conditions, but also the expected deviations from the mean or median values. The higher order variations reflecting the temporal influences, caused mainly by ‘‘space weather conditions’’, can be characterized as the variability of the modeled quantities. The scatter of values used to be characterized by standard deviations. In our case, since IRI deals mostly with medians, and since the distribution of values in the individual bins may be nonMaxwellian (the Maxwellian distribution is only a *
Corresponding author. Tel.: +420 6790 3305; fax: +420 762 528. E-mail address: [email protected] (V. Truhlı´k).
special case of the general distribution), the variability parameters analyzed in this paper are the median values, lower and upper quartile, and the corresponding interquartile ranges. The influence of short term events such as storm dynamics as well as of geomagnetic activity is reflected in the magnitude of the variability index.
2. Data used and variability index As the first step to include the variability of the most important ionospheric parameters in IRI models we study the variability of the electron temperature (Te), the relative H+ and O+ ion densities and of the upper transition height (HT) in the altitude range of 550– 2500 km. Satellite data from the ACTIVE mission (Intercosmos 24, perigee 500 km, apogee 2500 km, inclination 83°, time period 1989–1991, i.e. maximum of the solar cycle 22) are used (Truhlı´k et al., 2001; Trˇ´ıskova´ et al., 2003). Since IRI models deal with medians, as a parallel to the usually used standard deviation, which assumes the normal or Maxwellian distribution, the variability index Vind was introduced:
0273-1177/$30 Ó 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2004.06.008
V. Truhlı´k et al. / Advances in Space Research 34 (2004) 1922–1925
V ind ¼
Q3 Q1 100; 2Q2
ð1Þ
where Q1 is the 1st Quartile; Q3, the 3rd Quartile; Q2, the 2nd Quartile (=the Median). Index (1) was expanded into Legendre polynomials in a local time versus latitude grid. The global distributions of the variability index for electron temperature, relative ion composition, and upper transition height for equinox and solstices are shown and discussed in the following paragraphs. 3. Global distribution of the variability index Figs. 1–4 present the global distribution of the variability index (1) for electron temperature Te, for the O+ and H+ ion relative density and for the upper transition height HT. A magnetic local time (MLT) versus modified latitude (invdip) grid is used. The latitude coordinate invdip was introduced by Truhlı´k et al. (2001) to reduce the longitudinal variation to a second-order effect. It is close to the dip latitude near the equator and gets closer to the invariant latitude at higher latitudes. A system of associated Legendre polynomials up to the 8th order for Te and up to the 6th order for the relative density of H+ and O+ and for HT is employed as the modeling function of the variability index. ( 6;8 X log10 V ind ¼ a0l P 0l ðcos hÞ l¼0
) l X m m m al cos mu þ bl sin mu P l ðcos hÞ ; þ m¼1
ð2Þ
1923
where P ml is the associated Legendre function; h, the invdip colatitude (0 . . . p); u, the magnetic local time (0 . . . 2p); Vind, the variability index. Associated Legendre polynomials P ml were used without normalization factors. The coefficients aml and bml in (2) were calculated by a standard least-squares fitting procedure. Before applying this fitting procedure, data (104–105 points for each data group) were binned on a MLT vs. invdip grid. The minimum number of bins in the grid was 7 in latitude vs 14 in local time (or 9 vs 18, depending on the data coverage) to guarantee coefficients fully recoverable and free of the alias effect (Martinec, 1991). Thus the bin width of this grid corresponds to the highest order of the Legendre polynomials (6th or 8th order) in Eq. (2). Examples of the variability index distribution at altitudes of 550 and of 2500 km are shown for equinoxes and solstices in the case of Te and of the O+ and H+ density, and for equinoxes in the case of HT.
3.1. Electron temperature The Te variability index formulated according to (1) and (2) is shown in Fig. 1. For both presented altitudes the variability index reaches values from units of % up to 30%, and we can assume the same for the whole altitude range from 500 to 2500 km due to the continuity of the Te vertical profiles. Its minimum of up to 10% occurs at the equator and at low latitudes both at equinox and solstices, its maximum appears at the winter solstice pole (Southern Hemisphere in June). Equinox and solstice mean the period of ±40 days around the astronomical equinox and solstices, respectively.
Fig. 1. Contour plots of the global distribution of the variability index for Te according to model function (2) based on Intercosmos 24 Te data (e.g., Truhlı´k et al., 2001).
1924
V. Truhlı´k et al. / Advances in Space Research 34 (2004) 1922–1925
Fig. 2. Contour plots of the global distribution of the variability index for the relative O+ density according to model function (2) based on Intercosmos 24 Ion Mass Spectrometer data (e.g., Truhlı´k et al., 2004).
Fig. 3. Contour plots of the global distribution of the variability index for the relative H+ density according to model function (2) based on Intercosmos 24 Ion Mass Spectrometer data (e.g., Truhlı´k et al., 2004).
3.2. Relative density of O+ and H+ The dynamics of the variability index for ion density is much greater than that for Te. For ions, the density of which is dominant in the given region (e.g., O+ at 500 km), the variability index is less than 1%, while the variability index for the density of minor ions (H+ at 550 km) can reach as much as 100%. Fig. 2 shows the case of O+. At altitudes of about 500 km, where the relative O+ density is greater than 90% (Trˇ´ıskova´ et al., 2003), the value of the variability index
reaches at the most 4% at equinox at the poles, in other latitudes it comes to some tenths of percent only. At altitudes of 2500 km, where O+ is not a dominant ion (especially at low and mid-latitudes at night) the variability index increases up to 100% with the minimum at the summer pole and maximum at night mid-latitudes. The variability index of the H+ density is presented in Fig. 3. At low altitudes, where the H+ ions represent only a fraction of percent of the total ion density, the variability index is mostly 40–60%. At the altitude of 2500 km at the equator, where the H+ ion is the dominant component
V. Truhlı´k et al. / Advances in Space Research 34 (2004) 1922–1925
Fig. 4. Contour plots of the global distribution of the variability index for HT according to model function (2) based on Intercosmos 24 Ion Mass Spectrometer measurement (e.g., Trˇ´ıskova´ et al., 2001).
of the ion density, the variability index is 1–3%, at other latitudes it reaches as much as up to 30%. The exception is the variability index of H+ at night mid-laititudes, where it reaches even 100% due to the changing position of the equatorial edge of the light ion trough (e.g., Taylor and Walsh, 1972). 3.3. Upper transition height The distribution of the variability index of the upper transition height HT (the altitude level where the ion gas consists of 50% O+ and 50% light ions) is presented in Fig. 4. Only latitudes up to 50° can be characterized, the transition level at higher latitudes is situated above the Intercosmos24 satellite orbit (Trˇ´ıskova´ et al., 2001). In the latitude range studied the variability index changes with latitude from some percent at the equator to more than 20% at mid-latitudes.
4. Discussion and conclusion The first attempt to represent the variability of the plasma characteristics modeled in the frame of IRI is shown. There are some problems to be solved in a future study. The values of the Vind obtained according to definition (1) seem to be understandable for Te and HT, but in the case of the relative ion density they could be surprising for minor ions. For example, if the amount of
1925
H+ ions at the altitude of 550 km changes between 0.2% and 0.4%, the variability according to (1) is 100%. Another question is the definition of the variability index itself. Instead of the inter-quartile range, the difference between the median and upper and lower quartile separately could be used to characterize the possible range of the modeled values. Nevertheless, the values of the variability index, presented in Figs. 1–4, provide us at least with preliminary information about the possible differences of the real plasma properties from the IRI modeled values. The obtained global distributions of the variability index described by associated Legendre polynomials could be used as a complement to the previously developed global models of the electron temperature (Truhlı´k et al., 2001) and ion composition (Trˇ´ıskova´ et al., 2001, 2003).
Acknowledgements This research was supported by Grant No205/02/ P037 of the Grant Agency of the Czech Republic and by Grants No A3042201 and B3042104 of the Grant Agency of the Academy of Sciences of the Czech Republic.
References Bilitza, D. International Reference Ionosphere 1990, National Space Science Data Center, NSSDC 90-22, Greenbelt, MD, pp. 71–76, 1990. Martinec, Z. Program to calculate the least-squares estimates of the spherical harmonic expansion coefficients of an equally angulargridded scalar field. Comp. Phys. Commun. 64, 140–148, 1991. Taylor Jr., H.A., Walsh, W.J. The light-ion trough, the main trough, and the plasmapause. J. Geophys. Res. 77, 6716, 1972. Truhlı´k, V., Trˇ´ıskova´, L., Sˇmilauer, J. Improved electron temperature model and comparison with satellite data. Adv. Space Res. 27 (1), 101–109, 2001. Truhlı´k, V., Trˇ´ıskova´, L., Sˇmilauer, J. New advances in empirical modelling of ion composition in the outer ionosphere. Adv. Space Res. 33 (6), 844–849, 2004. Trˇ´ıskova´, L., Truhlı´k, V., Sˇmilauer, J. Empirical modeling of the upper transition height for low and middle latitudes. Adv. Space Res. 27 (1), 111–114, 2001. Trˇ´ıskova´, L., Truhlı´k, V., Sˇmilauer, J. An empirical model of ion composition in the outer ionosphere. Adv. Space Res. 31 (3), 653– 663, 2003.
Variability of the topside thermal plasma parameters during a period of high solar activity for IRI V. Truhlı´k *, L. Trˇ´ıskova´, J. Sˇmilauer Institute of Atmospheric Physics, Academy of Science Czech Republic, Boe´ni II, 141 31 Praha 4, Czech Republic Received 19 April 2004; received in revised form 24 June 2004; accepted 30 June 2004
Abstract The variability of the electron temperature, ion composition and the upper transition height in the topside ionosphere as given by the IRI models is studied. A variability index based on quartiles is introduced and its global distribution is presented in the form of contour plots for the individual parameters. The obtained global distribution of the variability index described by the associated Legendre polynomials could be used as a complement to the previously developed global models. Ó 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Topside ionosphere; Plasma temperatures; Ion composition
1. Introduction The existing topside global empirical models of the most important thermal plasma parameters (electron density, electron temperature and ion composition) included in IRI (Bilitza, 1990) only describe the main variations of these parameters (depending on local time, latitude, season, longitude, etc.) on the ‘‘climatological scale’’ (e.g. Truhlı´k et al., 2001; Trˇ´ıskova´ et al., 2001, 2003). In many applications the users of models need to know not only the monthly average conditions, but also the expected deviations from the mean or median values. The higher order variations reflecting the temporal influences, caused mainly by ‘‘space weather conditions’’, can be characterized as the variability of the modeled quantities. The scatter of values used to be characterized by standard deviations. In our case, since IRI deals mostly with medians, and since the distribution of values in the individual bins may be nonMaxwellian (the Maxwellian distribution is only a *
Corresponding author. Tel.: +420 6790 3305; fax: +420 762 528. E-mail address: [email protected] (V. Truhlı´k).
special case of the general distribution), the variability parameters analyzed in this paper are the median values, lower and upper quartile, and the corresponding interquartile ranges. The influence of short term events such as storm dynamics as well as of geomagnetic activity is reflected in the magnitude of the variability index.
2. Data used and variability index As the first step to include the variability of the most important ionospheric parameters in IRI models we study the variability of the electron temperature (Te), the relative H+ and O+ ion densities and of the upper transition height (HT) in the altitude range of 550– 2500 km. Satellite data from the ACTIVE mission (Intercosmos 24, perigee 500 km, apogee 2500 km, inclination 83°, time period 1989–1991, i.e. maximum of the solar cycle 22) are used (Truhlı´k et al., 2001; Trˇ´ıskova´ et al., 2003). Since IRI models deal with medians, as a parallel to the usually used standard deviation, which assumes the normal or Maxwellian distribution, the variability index Vind was introduced:
0273-1177/$30 Ó 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2004.06.008
V. Truhlı´k et al. / Advances in Space Research 34 (2004) 1922–1925
V ind ¼
Q3 Q1 100; 2Q2
ð1Þ
where Q1 is the 1st Quartile; Q3, the 3rd Quartile; Q2, the 2nd Quartile (=the Median). Index (1) was expanded into Legendre polynomials in a local time versus latitude grid. The global distributions of the variability index for electron temperature, relative ion composition, and upper transition height for equinox and solstices are shown and discussed in the following paragraphs. 3. Global distribution of the variability index Figs. 1–4 present the global distribution of the variability index (1) for electron temperature Te, for the O+ and H+ ion relative density and for the upper transition height HT. A magnetic local time (MLT) versus modified latitude (invdip) grid is used. The latitude coordinate invdip was introduced by Truhlı´k et al. (2001) to reduce the longitudinal variation to a second-order effect. It is close to the dip latitude near the equator and gets closer to the invariant latitude at higher latitudes. A system of associated Legendre polynomials up to the 8th order for Te and up to the 6th order for the relative density of H+ and O+ and for HT is employed as the modeling function of the variability index. ( 6;8 X log10 V ind ¼ a0l P 0l ðcos hÞ l¼0
) l X m m m al cos mu þ bl sin mu P l ðcos hÞ ; þ m¼1
ð2Þ
1923
where P ml is the associated Legendre function; h, the invdip colatitude (0 . . . p); u, the magnetic local time (0 . . . 2p); Vind, the variability index. Associated Legendre polynomials P ml were used without normalization factors. The coefficients aml and bml in (2) were calculated by a standard least-squares fitting procedure. Before applying this fitting procedure, data (104–105 points for each data group) were binned on a MLT vs. invdip grid. The minimum number of bins in the grid was 7 in latitude vs 14 in local time (or 9 vs 18, depending on the data coverage) to guarantee coefficients fully recoverable and free of the alias effect (Martinec, 1991). Thus the bin width of this grid corresponds to the highest order of the Legendre polynomials (6th or 8th order) in Eq. (2). Examples of the variability index distribution at altitudes of 550 and of 2500 km are shown for equinoxes and solstices in the case of Te and of the O+ and H+ density, and for equinoxes in the case of HT.
3.1. Electron temperature The Te variability index formulated according to (1) and (2) is shown in Fig. 1. For both presented altitudes the variability index reaches values from units of % up to 30%, and we can assume the same for the whole altitude range from 500 to 2500 km due to the continuity of the Te vertical profiles. Its minimum of up to 10% occurs at the equator and at low latitudes both at equinox and solstices, its maximum appears at the winter solstice pole (Southern Hemisphere in June). Equinox and solstice mean the period of ±40 days around the astronomical equinox and solstices, respectively.
Fig. 1. Contour plots of the global distribution of the variability index for Te according to model function (2) based on Intercosmos 24 Te data (e.g., Truhlı´k et al., 2001).
1924
V. Truhlı´k et al. / Advances in Space Research 34 (2004) 1922–1925
Fig. 2. Contour plots of the global distribution of the variability index for the relative O+ density according to model function (2) based on Intercosmos 24 Ion Mass Spectrometer data (e.g., Truhlı´k et al., 2004).
Fig. 3. Contour plots of the global distribution of the variability index for the relative H+ density according to model function (2) based on Intercosmos 24 Ion Mass Spectrometer data (e.g., Truhlı´k et al., 2004).
3.2. Relative density of O+ and H+ The dynamics of the variability index for ion density is much greater than that for Te. For ions, the density of which is dominant in the given region (e.g., O+ at 500 km), the variability index is less than 1%, while the variability index for the density of minor ions (H+ at 550 km) can reach as much as 100%. Fig. 2 shows the case of O+. At altitudes of about 500 km, where the relative O+ density is greater than 90% (Trˇ´ıskova´ et al., 2003), the value of the variability index
reaches at the most 4% at equinox at the poles, in other latitudes it comes to some tenths of percent only. At altitudes of 2500 km, where O+ is not a dominant ion (especially at low and mid-latitudes at night) the variability index increases up to 100% with the minimum at the summer pole and maximum at night mid-latitudes. The variability index of the H+ density is presented in Fig. 3. At low altitudes, where the H+ ions represent only a fraction of percent of the total ion density, the variability index is mostly 40–60%. At the altitude of 2500 km at the equator, where the H+ ion is the dominant component
V. Truhlı´k et al. / Advances in Space Research 34 (2004) 1922–1925
Fig. 4. Contour plots of the global distribution of the variability index for HT according to model function (2) based on Intercosmos 24 Ion Mass Spectrometer measurement (e.g., Trˇ´ıskova´ et al., 2001).
of the ion density, the variability index is 1–3%, at other latitudes it reaches as much as up to 30%. The exception is the variability index of H+ at night mid-laititudes, where it reaches even 100% due to the changing position of the equatorial edge of the light ion trough (e.g., Taylor and Walsh, 1972). 3.3. Upper transition height The distribution of the variability index of the upper transition height HT (the altitude level where the ion gas consists of 50% O+ and 50% light ions) is presented in Fig. 4. Only latitudes up to 50° can be characterized, the transition level at higher latitudes is situated above the Intercosmos24 satellite orbit (Trˇ´ıskova´ et al., 2001). In the latitude range studied the variability index changes with latitude from some percent at the equator to more than 20% at mid-latitudes.
4. Discussion and conclusion The first attempt to represent the variability of the plasma characteristics modeled in the frame of IRI is shown. There are some problems to be solved in a future study. The values of the Vind obtained according to definition (1) seem to be understandable for Te and HT, but in the case of the relative ion density they could be surprising for minor ions. For example, if the amount of
1925
H+ ions at the altitude of 550 km changes between 0.2% and 0.4%, the variability according to (1) is 100%. Another question is the definition of the variability index itself. Instead of the inter-quartile range, the difference between the median and upper and lower quartile separately could be used to characterize the possible range of the modeled values. Nevertheless, the values of the variability index, presented in Figs. 1–4, provide us at least with preliminary information about the possible differences of the real plasma properties from the IRI modeled values. The obtained global distributions of the variability index described by associated Legendre polynomials could be used as a complement to the previously developed global models of the electron temperature (Truhlı´k et al., 2001) and ion composition (Trˇ´ıskova´ et al., 2001, 2003).
Acknowledgements This research was supported by Grant No205/02/ P037 of the Grant Agency of the Czech Republic and by Grants No A3042201 and B3042104 of the Grant Agency of the Academy of Sciences of the Czech Republic.
References Bilitza, D. International Reference Ionosphere 1990, National Space Science Data Center, NSSDC 90-22, Greenbelt, MD, pp. 71–76, 1990. Martinec, Z. Program to calculate the least-squares estimates of the spherical harmonic expansion coefficients of an equally angulargridded scalar field. Comp. Phys. Commun. 64, 140–148, 1991. Taylor Jr., H.A., Walsh, W.J. The light-ion trough, the main trough, and the plasmapause. J. Geophys. Res. 77, 6716, 1972. Truhlı´k, V., Trˇ´ıskova´, L., Sˇmilauer, J. Improved electron temperature model and comparison with satellite data. Adv. Space Res. 27 (1), 101–109, 2001. Truhlı´k, V., Trˇ´ıskova´, L., Sˇmilauer, J. New advances in empirical modelling of ion composition in the outer ionosphere. Adv. Space Res. 33 (6), 844–849, 2004. Trˇ´ıskova´, L., Truhlı´k, V., Sˇmilauer, J. Empirical modeling of the upper transition height for low and middle latitudes. Adv. Space Res. 27 (1), 111–114, 2001. Trˇ´ıskova´, L., Truhlı´k, V., Sˇmilauer, J. An empirical model of ion composition in the outer ionosphere. Adv. Space Res. 31 (3), 653– 663, 2003.