A new global empirical model of the electron temperature with the inclusion of the solar activity variations for IRI
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 17 August 2010
Accepted: 8 October 2011
Published: 27 July 2012
A data-base of electron temperature (Te) comprising of most of the available LEO satellite measurements in the altitude range from 350 to 2000 km has been used for the development of a new global empirical model of Te for the International Reference Ionosphere (IRI). For the first time this will include variations with solar activity. Variations at five fixed altitude ranges centered at 350, 550, 850, 1400, and 2000 km and three seasons (summer, winter, and equinox) were represented by a system of associated Legendre polynomials (up to the 8th order) in terms of magnetic local time and the earlier introduced invdip latitude. The solar activity variations of Te are represented by a correction term of the Te global pattern and it has been derived from the empirical latitudinal profiles of Te for day and night (Truhlik et al., 2009a). Comparisons of the new Te model with data and with the IRI 2007 Te model show that the new model agrees well with the data generally within standard deviation limits and that the model performs better than the current IRI Te model.
Changes of Te caused by solar activity variations are comparable or even below the day-to-day variability and scatter of Te values, which is particularly important in daytime. Thus, the solar activity variation of Te is often hidden in the data scatter.
Frequent inconsistency among various Te data sets especially in regimes of low electron density because most techniques for measuring Te depend critically on the presence of a sufficient number of electrons.
ISIS-1 data were included only above 1500 km and were reduced by 15%. The altitude threshold was introduced because the ISIS-1 data at lower altitudes show discrepancies with several of the other data sets. The reduction factor at high altitudes is a compromise based on the arguments given by Köhnlein (1986) and by Webb and Essex (2003) and also on our own comparisons with data from Intercosmos 24 and 25.
Explorer 31 data were now included but only above 1500 km altitude because the Te probe of this mission is of a similar construction as the Te probe onboard ISIS-1 and the measured Te values indicated similar concerns as for ISIS-1 data.
From Intercosmos 19 only data from altitudes above 750 km were included because the probe produces unrealistically high Te for Ne > 5 · 1011 m−3.
In the case of Intercosmos 24 and 25 the temperature was determined as the median of Tex, Tey, and Tez (identical instruments on both satellites consisted of three Te planar sensors in directions x, y and z; see Truhlik et al. (2001) for more detail).
From the DMSP Te measurements only data for solar activity PF10.7 > 120 (for PF10.7 definition see next section) were taken because the low solar activity (= low density) temperature data are unrealistically high (see Bilitza et al., 2007). Also, we have selected only those data with “quality flag” 1 or 2 as recommended by DMSP SSIES team on http://cindispace.utdallas.edu/DMSP/.
As a new data set we have added the temperature measurements of the Indian SROSS C2 satellite.
Some of the data sets have very high time resolution, much higher than required for our modeling purposes. In these cases we have averaged the data to a 100 second time resolution. The total number of measurements in our database is about 9 million data points across 20 satellites.
3. Model Formulation
Based on the altitude distribution of data in our database (see Fig. 1) and on the need to cover all important height regimes, we have selected the following anchor altitudes for our model: 350, 550, 850, 1400 and 2000 km. Similar to Brace and Theis (1981) and Truhlik et al. (2000) we have averaged data on a local time-latitude grid and modeled global variations using a spherical harmonics expansion to 8th order. In the first step, we have built the core Te model using the Te average in each bin. In the second step, we have created a term describing the solar activity variations in the bins based on the earlier work by Truhlik et al. (2009a). The solar activity variation term is used as an additive term to the core model. After the global models are established for the 5 fixed altitudes they are combined to produce the full altitude profile in the same way as it is done now in the IRI model. The IRI approach is based on the Booker-Epstein formalism (e.g. Bilitza, 1990) which divides the profile into regions of constant gradient with the boundaries given by the 5 fixed altitudes. Epstein-step functions are used to transition from one region to the next thus generating a continuous analytical representation of the Te gradient and integration then results in the final Te formula. For future upgrades of the IRI model physics-based field aligned profile functions as for example deduced by Bilitza (1975), Titheridge (1998), or Truhlik et al. (2009b) could bring further improvement.
3.1 The core model
3.2 The solar activity term
3.3 The full model
4. Model Results and Discussion
4.1 The core model
Te increases with altitude and the altitude gradient during daytime is much larger than during nighttime at low latitudes (±30 deg) during the nighttime the gradient reaches its lowest value.
The morning enhancement (morning overshoot) is well developed at equatorial latitudes and at low altitudes (350, 550 to 850 km).
The latitude dependence is more prominent at lower altitudes (350 to 850 km). Generally the lowest electron temperatures are observed close to the invdip equator. On the other hand the model does not capture small scale spatial and temporal structures like the sub-auroral electron temperature enhancement e.g. Brace (1990), the evening electron temperature crests (Balan et al., 1997) or structures in the high latitude region.
4.2 Comparisons with data
The performance of the model is evaluated in three ways: (i) In the first test we have calculated latitude profiles of Te for the same conditions as in Truhlik et al. (2009a) and then we have compared these profiles with the original data-based profiles. (ii) in the second test we have used the results of the comparison of several models with data in Bilitza et al. (2007) and have added to these our new model values for comparison. (iii) In the last test we have compared the new model, and IRI Intercomos and Brace&Theis models with Te data in our data-base.
4.2.1 Latitude profiles
The latitudinal variation shows the well-known increase of electron temperature towards higher latitudes. During nighttime in all but the highest altitude range the electron temperature is almost constant in the low and middle latitude sector (from −40 to +40 degrees).
Let us first look at the equinox plots (Figs. 5(a)/5(b)) in greater detail. Excluding the 350 and 550 km daytime cases, which will be discussed in the next paragraph, we note that for all other cases the temperature increases from LSA to MSA to HSA across all latitudes. The low altitude nighttime case (right upper panels) shows almost linear behavior. However in all other cases the solar activity variation is not always linear. At 850 km, for example, we note that the MSA and HSA curves are close together and significantly (500–1000 K) above the LSA curve. At 1400 km, on the other hand, the LSA and MSA curves are close together and well below the HSA. The model values show a little bit less range. Overall the shape of the latitudinal curves for the different levels of solar activity is very similar. An exception is the high latitude region where the large data scatter makes an interpretation much more difficult.
The most interesting behavior is seen at 350, and 550 km where the correlation with solar activity is strongly latitude dependent and becomes negative at times. With our data, which is reproduced well by the model, we find that the correlation with solar activity reverses from positive near the equator to negative at middle latitudes, to positive again at high latitudes. The anti-correlation with solar activity at mid-latitudes had been reported earlier with Incoherent Scatter Radar (ISR) observations (see references in Truhlik et al., 2009a).
Figures 6(a)/6(b) show the results for solstices (Northern summer). Data coverage did not allow plotting the complete latitudinal variations of electron temperature for high solar activity at 350 km and for low solar activity at 850 km and at 2000 km for daytime. The largest changes with solar activity are seen in the summer hemisphere (Northern hemisphere in Figs. 6(a)/(b)). Variations of Te with solar activity are more than a factor of two larger in summer than in winter due to the increased photoelectron heating. Again we find mostly linear increase in electron temperature with increasing solar activity except for the low altitude daytime cases (350, 550 and 850 km). At 550 km we find a positive Te response to solar activity in Summer hemisphere and a negative response in the Winter hemisphere. At 350 km the positive response is observed at in the whole range of low latitudes.
Generally, the new model reproduces the original latitude profiles surprisingly well. There is only exception at solstice 2000 km at equatorial latitudes at night. However, the original data shows very large scatter for these conditions (Fig. 6(a) lower right panel).
4.2.2 Comparison with other models and data
The plots at 850 km contain a large number of data points because this is the orbit altitude of the DMSP satellites. The FLIP model and the new Te model represent the data quite well both in terms of the dependence on PF10.7 and of absolute magnitude. The Millstone Hill model, on the other hand, underestimates the data and shows an increase for all seasons. This may be due to the difficulties the ISR techniques has in deducing electron temperatures in region of very low electron density.
For the plasmaspheric altitude range (2000 km) the FLIP model shows the expected increase with increasing solar activity for all seasons. The new Te model shows the expected increase with solar activity for both solstices but for equinox it seems to indicate a “V” type dependence similar to the data averages. But the variation of the data averages is likely due to bins with rather sparse data coverage that are statistically not very reliable.
The comparison of the new Te model with data and other models for nighttime is shown in Fig. 7(b). Temperatures generally increase with solar activity or stay constant as is to be expected from theory (e.g. in Truhlik et al., 2009b). FLIP underestimates the satellite data and the Millstone Hill model values in summer and equinox and clearly requires an additional heat source to elevate electron temperatures above the MSIS neutral temperature background. In winter heating by photoelectrons from the conjugate sunlit ionosphere helps to raise Te above Tn and brings the FLIP temperatures closer to the satellite and radar measurements (Bilitza et al., 2007). Comparing the satellite data with the Millstone Hill model we find similar discrepancies at 850 km as were noted for daytime in the previous chapter. Unfortunately, there was not enough of data for summer at 2000 km where only one data average was available. The new Te model values are for almost all cases in the standard deviations limit.
4.2.3 Comparison with IRI IK and Brace and Theis model
A new Te model for region from the upper ionosphere to the lower plasmasphere is presented. It represents a continuation and improvement of the previous model by Truhlik et al. (2000, 2001) but it is based on bigger volume of data and it also includes a solar activity dependence of the electron temperature based on Bilitza et al. (2007) and Truhlik et al. (2009a, b). The model is available in FORTRAN and IDL on the request from the authors.
We are very grateful to K.-I. Oyama, J. Smi-lauer, M. Hairston, F. Rich, K. W. Min and P. K. Bhuyan for providing data from Hinotori, Intercosmos (19, 24, 25), DMSP (F12, F13, F14, and F15), DMSP (F10 and F11), KOMPSAT-1 and SROSS C2 satellites, respectively. We are also grateful to NASA’s National Space Science Data Center (NSSDC) and Space Physics Data Facility (SPDF) for providing the other satellite Te data and also the Modelweb interface. We also thank Katerina Podolska, BSc., employee of the Institute of Atmospheric Physics for help with processing of the huge amount of DMSP data. This study was supported by grant A300420603 of the Grant Agency of the Academy of Sciences of the Czech Republic, by grant P209/10/2086 of the Grant Agency of the Czech Republic and by NASA grant NNH06CD17C.
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