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Analysis of the ionosphere irregularities in E region based on COSMIC occultation data
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research xxx (2015) xxx–xxx www.elsevier.com/locate/asr
Analysis of the ionosphere irregularities in E region based on COSMIC occultation data Jun Niu a,b, Han-xian Fang a,b,⇑, Xi-xi Wang a,b, Li-bin Weng a,b, Lan Guo c a
Institution of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China b State Key Laboratory of Space Weather, Chinese Academy of Science, Beijing 100190, China c Meteorological Center of Air Force, Beijing 100061, China Received 17 November 2014; received in revised form 8 April 2015; accepted 10 April 2015
Abstract Sporadic-E layer is a usual phenomenon in ionosphere which has an important impact on the satellite navigation, communication, radar system and so on. In this paper, by using a wavelet decomposition and reconstruction technique, fluctuation of slant total electron content have been obtained which shows a strong enhancement at the Es layer altitude. The COSMIC data during year 2007 have been calculated by using this method; global distribution and seasonal variation both show well agreement with the Es layer feature which confirm the validity of the method. Linear and non-linear empirical formulas between TEC fluctuation and Es critical frequency are built and these formulas indicate that it may be better in inversing the strong Es. Ó 2015 Published by Elsevier Ltd. on behalf of COSPAR.
Keywords: Ionospheric sporadic-E; COSMIC occultation; Wavelet decomposition and reconstruction
1. Introduction With the development of science and technology, the radio occultation technique has became a new technology to detect the Earth space, GPS occultation technique has became an effective measurement to detecting the ionosphere for its global distribution, high vertical resolution and low cost (Lei et al., 2001). In recent years, occultation data have been applied to investigate the global distribution and variation of Sporadic-E (Es) (Wu et al., 2005; Wu, 2006; Arras et al., 2008; Yeh et al., 2012), which solved the issue that the ground-based observation can only obtain the local variation of Es. The occultation techniques not only provide a method to investigate the global ⇑ Corresponding author at: Institution of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China. Tel.: +86 13813863008. E-mail address: [email protected] (H.-x. Fang).
distribution and variation, but also make it possible for further study on its physical mechanism and modeling. At present, the most accepted mechanism is the wind shear theory proposed Whitehead (1961, 1989) which has been verified by a lot of studies and experiments. But this theory does not fully explain the observed phenomena of Sporadic-E, and also needs more validation with large number of measured data. Other researchers also made some meaningful conclusions and conjecture on the study of Sporadic-E, for instance, (Hocke et al., 2001; Hocke and Igarashi, 2002; Garcia-Fernandez and Tsuda, 2006) analyzed characteristics of Es-layer during solar maximum and minimum with the data of CHAMP and GPS/MET, they pointed out that the Sporadic-E is a kind of phenomenon with obvious geographical distribution and seasonal variation; (Nygren et al., 1984; Basu et al., 1973) pointed out that the formation mechanism of larger scale Es may be caused by electron density gradient drift instability; (Farley, 1985; Smith and Royrvik, 1985) used
http://dx.doi.org/10.1016/j.asr.2015.04.014 0273-1177/Ó 2015 Published by Elsevier Ltd. on behalf of COSPAR.
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
2
J. Niu et al. / Advances in Space Research xxx (2015) xxx–xxx
gradient of plasma instabilities and two-stream instability to explain the formation mechanism of smaller scale Es. Since the controversy still exists, so we still need detail observation data. There have been some research on analysis of Es by occultation data (Wu et al., 2005; Wu, 2006; Arras et al., 2008; Yeh et al., 2012), but these research mostly use the signal–noise data, which is based on the assumption that the noise is caused by the Es layer, to verify the occurrence of Es. In this paper, we proposed a method based on wavelet analysis and slant TEC data not only to detect the occurrence of Es, but also to inverse the critical frequency of Es. To validate this method, we present the Es occurrence global distribution and inversed critical frequency compared with the known global distribution feature and ground-based Es critical frequency observation.
2. Data and methods The main data in this paper are occultation data (download from COSMIC centre) and the Es critical frequency data (download from Space Physics Interactive Data Resource, SPIDR). COSMIC occultation system is launched by Taiwan and USA, which is widely used by researchers; it has the largest observation data currently. In this article, second-level occultation data (ionprf files) during 2007–2008 is used which includes GPS, LEO satellite orbit data, TEC, electron density, etc. During the occultation process, GPS signal path scans the entire ionosphere from high altitude to low altitude, including the Es layer height range from 90 km to 120 km. In the ionospheric occultation event, the slant TEC, which is refer to the ”horizontal” TEC between GPS satellite and LEO satellite in the entire paper instead of the vertical TEC of the entire ionosphere, can be inversed from the phase delay. In addition, the electron content above the LEO orbit height have been removed in these TEC data. The electron density irregularities that exist in ionosphere would cause the disturbance of slant TEC, which can be used to inverse the Es critical frequency, is rather small respect to the ionosphere background. So we applied a wavelet analysis method to obtain this small STEC perturbation. The wavelet analysis is an effective time–frequency analysis methods. The essence of the wavelet transform is to perform convolution on a translation and narrow wave weight function which has localized nature both in a time domain and frequency domain, so that the signal can be decomposed into the individual components at different time and frequency. _
Set wðtÞ 2 L2 , its Fourier transform is wðwÞ, so that when allowed to meet the conditions: Cw ¼
Z
þ1
1
_
2
j wðwÞj dw < þ1 jwj
ð1Þ
wðwÞ is called a basic wavelet or mother wavelet. After the dilation and translation of wðwÞ, we can get: 1 tb wa;b ðtÞ ¼ pffiffiffi w a; b 2 R; a–0 ð2Þ a a We call it a wavelet series, the a is scaling factor or scale factor and the b is translation factor. The wavelet transform is defined for arbitrary signal as: Z þ1 1 t b dt W f ða; bÞ ¼< f ; wa;b >¼ pffiffiffi xðtÞw ð3Þ a a 1 W f ða; bÞ is the wavelet transform coefficient. The reconstruction (inverse) transformation is: Z þ1 Z þ1 1 1 tb f ðtÞ ¼ W ða; bÞw dadb ð4Þ f C w 1 1 a2 a We can divide the STEC to two parts as low frequency part Ltec and high frequency part Htec, which stand for the ionospheric background and fluctuation caused by ionospheric irregularities, by applying this wavelet decomposition and reconstruction method. In this paper, a 3-rd sym wavelet is used in the wavelet decomposition and reconstruction method. 3. Results Fig. 1 shows a typical inversion result with the method discussed above, the left panel is the slant TEC variation with altitude and the middle panel is the Ltec variation with altitude and right panel is the Htec variation with altitude. Here the TEC refer to the slant TEC between the GPS satellite and LEO satellite instead of the usually vertical TEC. As we know, the existence of Es layers would result in an additional phase delay which means an enhancement in TEC. But this enhancement is rather small than the regular TEC, so we can only distinguish this small enhancement as a perturbation in the Htec profile. The perturbation in Htec profile may be also caused by solar flares which can cause a ionosphere disturbance including the E region but we do not consider this because we only use the data in the period with rather low solar activity. This result is obtained from an occultation event in 2009.182, the file name is ionPfr_C001.2009.182.00.07. G10_2009.2650_nc. It is obviously that the TEC profile is quite similar with the Ltec profile especially above the 200 km with the Htec value nearly zero. Between the height rang from 140 km to 200 km, the Htec profile has a small fluctuation but not varies largely, this may be caused by the small electron density in the “valley” region. Under 140 km, the absolute value of this fluctuation dramatically increase with the maximum value about 1.4 TECU at 100 km, this perturbation may indicate the occurrence of Es. Fig. 2 shows another variation of the Htec with altitude which is obtained from a occultation events near UK station (FF051, 51.7°N, 1.5°W) at 18 o’clock on the July
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
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Fig. 1. Variation of TEC (left), Ltec (middle) and Htec (right) with altitude. Notice that all TEC in this paper refer to the slant TEC between the GPS satellite and LEO satellite instead of the usually vertical TEC.
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4th, 2009 (UT). As shown in the figure, the fluctuation of Htec from 800 km to 200 km is similar with the example above, but the maximum value is 1 TECU at 100 km. At the same time, the ground observation shows a Es critical frequency 4.5 MHz at 102 km. This may indicate, at least, that we can predicate the occurrence of Es and we would validate this method further in the latter section. 4. Validation To validate the method we have proposed, we present the global distribution of DTEC (for simplification purpose, we use DTEC standing for maximum absolute Htec value) to validate that if a large DTEC can indicate the occurrence of Es. Furthermore, we select more than 500 sets occultation data, which is compared with the ground-based observation, to verify the correlation between DTEC and Es critical frequency. 4.1. Global distribution and seasonal variation With the method proposed in the previous section, we analyzed the COSMIC occultation data during the full year
2007 and the seasonal distribution of DTEC. The results shown in Fig. 3. The location of DTEC which were greater than 2 TEU had been identified in Fig. 3. As we can see from Fig. 3, the distribution DTEC was in well agreement with the observations of Es-layer (Wu et al., 2005; Arras et al., 2008; Yeh et al., 2012). Both of them present a significant seasonal variation and global distribution. The large DTEC have a high occurrence rate in the summer and winter, but low rate in the spring and autumn. The occurrence rate is extremely high in the mid-latitude region of the summer hemisphere. This figure also shows a series of large DTEC value in the high latitude which can be seen in all seasons, this is consistent with the result in the Antarctica (Zhao et al., 2012) which found that Es in Antarctica has a weaker seasonal variation than the mid-latitude region and there is no dramatic difference in different season. This region is in accordance with the aurora region so these large values may also be caused by the particle precipitation. Since the well agreement between DTEC and Es distributions and variations, we can definitely conclude that large DTEC represents the occurrence of Es. 4.2. Comparison of DTEC and Es critical frequency Since a Es with high electron density would cause a strong perturbation in TEC data, so we may inverse the Es critical frequency (foEs) from the DTEC data. Therefore, we should verify, first of all, the correlation between them. Because of the randomness of the global distribution of occultation data, we need to match the data before we compare it with the ground observation data. The matching principles in this article are, 1. Space matching: the difference between the average position of the occultation tangent point and the ground station is within 2°; 2. Time matching: the difference between the occultation time and the observation data from ground-based observatories is within one hour. We choose a lower space resolution to
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
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Fig. 3. Seasonal distribution of parameter DTEC (TECU) in year 2007.
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
J. Niu et al. / Advances in Space Research xxx (2015) xxx–xxx
5
obtain enough occultation data for the comparison. While the ground based observation have well time continuity, so we can choose a higher time resolution. In accordance with the matching principles, we match 530 sets of foEs data and the occultation data from 2007 to 2008 in the Europe region. The comparison result is shown in Fig. 4. As shown in Fig. 4, the variation of DTEC and foEs is basically the same, and the correlation coefficient between the two sets data is 0.85. This means that there is a well linear or quasi-linear relation between DTEC and foEs. By using a least square fitting method, we derive a linear relation shown as following: foEsin ¼ 3:24 DTEC þ 1:89
ð5Þ
The foEsin is the inversed Es critical frequency (unit: MHz). In this formula, we can find that a DTEC about 1 TECU equals to a 5 MHz Es critical frequency. This indicates that this method may be better in strong Es critical frequency inversion since a small DTEC may not be caused by Es layer but other factors in the ionosphere. The average relative error is about 10%. 5. Discussion As we have proposed a simple linear formula between DTEC and foes, we also put forward a non-linear formula between them. Considering a simple occultation event model as shown in Fig.5, we assume that the electron density in the Es layer is the same everywhere and the electron content along with the GPS signals above the Es layer is the same, therefore we can define the TEC fluctuation as a line integral of Es electron density along GPS signals. By considering the distribution of electron density is symmetrical, so we can obtain the DTEC as following: Z DTEC ¼ 2 ne dL ð6Þ L
Es critical frequency(/MHz) / ΔTEC(TECU)
The ne is the electron density in the Es layer. As we have assumed that the electron density a constant in the Es layer, so the formula can be written as:
7
foEs smoothed foEs Δ TEC smoothed Δ TEC
6 5
DTEC ¼ 2ne L ¼
2 foEs2 L 80:6
ð7Þ
The value of L is relate to the Es thickness, Es altitude, electron density distribution and so on. The thickness of Es layer is about several kilometers, so here we may take L as 15 km since it is obvious longer than several kilometers to estimate the coefficient. In this non-linear formula, foEs equals to5 MHz represents a TEC fluctuation about 1 TECU, just the same with the observation in the previous section. So we may obtain a new formula by using a least square method from the observation, this non-linear formation is displayed as following: DTEC ¼ 0:038foEs2
ð8Þ
The units of DTEC and foEs respectively are TECU and MHz. However, these formulas are just empirical formulas in simplification conditions. The electron density distribution and GPS signal paths in realistic are rather complicate, so we still need more observation data and more accurate model to investigate this correlation. But we still have two problems in this paper. One of them is the low resolution of the ionprf files (only 1 Hz which means about 2 km resolution in altitude), which means we can only detect the Es layers with thickness larger than 2 km. The other problem is that the DTEC is not only affected by the amplitude but also the tilt angle (Zeng and Sokolovskiy, 2010). This indicates that our formulas may have significant errors in some cases, so we should give more attentions on this problem in the later research. 6. Conclusion
4 3 2 1 0
Fig. 5. Schematic diagram showing the simple model.
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Fig. 4. Comparison between DTEC and foEs obtained from the selected data.
In this paper, we analyze the TEC data obtained from the occultation data of COSMIC by using the wavelet decomposition and reconstruction method. We extract the maximum fluctuation DTEC of the high-frequency component between 90 km and 120 km and take it as new parameters characterizing the Es layer. The TEC fluctuation increases dramatically at the Es layer altitude. We consider this large DTEC as the occurrence of Es. We
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
6
J. Niu et al. / Advances in Space Research xxx (2015) xxx–xxx
analyze the COSMIC occultation data during the full year 2007 and obtain the seasonal global distribution of DTEC. The global distribution and seasonal variation is in quite well agreement with the known Es feature; this confirms the validity of our method. We also compare the DTEC with the Es critical frequency, they show a well correlation and we obtain a linear formula by the least square method. This formula indicates that it may be better in inversing the strong Es. In the discussion section, we build a simple model and derived a non-linear formula. Both formulas present well agreement with the observation. In a word, we propose a new method to detect the Es layer with the occultation data, linear and non-linear formulas are built to inverse the Es critical frequency. Since the lack of data sets in the same location and time, this method still needs further study. Acknowledgements Thanks COSMIC for providing ionospheric occultation data and SPIDR (Space Physics Interactive Data Resource) for its foEs data. References Arras, C., Wickert, J., Beyerle, G., et al., 2008. A global climatology of ionospheric irregularities derived from GPS radio occultation. Geophys. Res. Lett. 35, L14809. http://dx.doi.org/10.1029/ 2008GL034158. Basu, S., Vesprinti, R.T., Aarons, J., 1973. Field aligned ionospheric and e-region irregularities and sporadic E. Radio Sci. 8, 235–246.
Farley, D.T., 1985. Theory of equatorial electrojet plasma waves: new developments and current status. J. Atmos. Terr. Phys. 47, 729–744. Garcia-Fernandez, M., Tsuda, T., 2006. A global distribution of sporadic E events revealed by means of CHAMP-GPS occultations. Earth Planets Space 58, 33–36. Hocke, K., Igarashi, K., 2002. Structure of the Earth’s lower ionosphere observed by GPS/MET radio occultation. J. Geophys. Res. 107 (A5). Hocke, K., Igarashi, K., Nakamura, M., et al., 2001. Global sounding of sporadic E layers by the GPS/MET radio occultation experiment. J. Atmos. Sol. Terr. Phys. 2001 (63), 1973–1980. Jiuhou, Lei., Syndergaard, S., Burns, A.G., et al., 2001. Comparison of COSMIC ionospheric measurements with ground-based observations and model predictions: preliminary results. J. Geophys. Res. 112, A07308. http://dx.doi.org/10.1029/2006JA012240. Nygren, T., Jalonen, L., Oksman, J., et al., 1984. The role of electric filed and neutral wind direction in the formation of sporadic E-layer. J. Atmos. Terr. Phys. 46, 373–381. Smith, L.G., Royrvik, O., 1985. Electron-density irregularities in the daytime equatorial ionosphere. J. Atmos. Terr. Phys. 41, 813–824. Whitehead, J.D., 1961. The formation of the sporadic-E layer in the temperate zones. J. Atmos. Terr. Phys. 29, 49–58. Whitehead, J.D., 1989. Recent work on mid-latitude and equatorial sporadic-E. J. Atmos. Terr. Phys. 51, 401–424. Wu, D.L., 2006. Small-scale fluctuations and scintillations in high resolution GPS/CHAMP SNR and phase data. J. Atmos. Sol. Terr. Phys. 68, 999–1017. Wu, D.L., Ao, C.O., Hajj, G.A., et al., 2005. Sporadic E morphology from GPS-CHAMP radio occultation. J. Geophys. Res. 110, A01306. http://dx.doi.org/10.1029/2004JA010701. Yeh, W.H., Huang, C.Y., Hsiao, T.Y., et al., 2012. Amplitude morphology of GPS radio occultation data for sporadic-E layers. J. Geophys. Res. 117, A11304. http://dx.doi.org/10.1029/2012JA017875. Zeng, Z., Sokolovskiy, S., 2010. Effect of sporadic E cloud on GPS radio occultation signal. Geophys. Res. Lett. 37. http://dx.doi.org/10.1029/ 2010GL044561. Zhao, H.S., Xu, Z.W., Wu, J., 2012. Sporadic E morphology in Antarctica. Chin. J. Polar Res. 24, 129–135.
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
ScienceDirect Advances in Space Research xxx (2015) xxx–xxx www.elsevier.com/locate/asr
Analysis of the ionosphere irregularities in E region based on COSMIC occultation data Jun Niu a,b, Han-xian Fang a,b,⇑, Xi-xi Wang a,b, Li-bin Weng a,b, Lan Guo c a
Institution of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China b State Key Laboratory of Space Weather, Chinese Academy of Science, Beijing 100190, China c Meteorological Center of Air Force, Beijing 100061, China Received 17 November 2014; received in revised form 8 April 2015; accepted 10 April 2015
Abstract Sporadic-E layer is a usual phenomenon in ionosphere which has an important impact on the satellite navigation, communication, radar system and so on. In this paper, by using a wavelet decomposition and reconstruction technique, fluctuation of slant total electron content have been obtained which shows a strong enhancement at the Es layer altitude. The COSMIC data during year 2007 have been calculated by using this method; global distribution and seasonal variation both show well agreement with the Es layer feature which confirm the validity of the method. Linear and non-linear empirical formulas between TEC fluctuation and Es critical frequency are built and these formulas indicate that it may be better in inversing the strong Es. Ó 2015 Published by Elsevier Ltd. on behalf of COSPAR.
Keywords: Ionospheric sporadic-E; COSMIC occultation; Wavelet decomposition and reconstruction
1. Introduction With the development of science and technology, the radio occultation technique has became a new technology to detect the Earth space, GPS occultation technique has became an effective measurement to detecting the ionosphere for its global distribution, high vertical resolution and low cost (Lei et al., 2001). In recent years, occultation data have been applied to investigate the global distribution and variation of Sporadic-E (Es) (Wu et al., 2005; Wu, 2006; Arras et al., 2008; Yeh et al., 2012), which solved the issue that the ground-based observation can only obtain the local variation of Es. The occultation techniques not only provide a method to investigate the global ⇑ Corresponding author at: Institution of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China. Tel.: +86 13813863008. E-mail address: [email protected] (H.-x. Fang).
distribution and variation, but also make it possible for further study on its physical mechanism and modeling. At present, the most accepted mechanism is the wind shear theory proposed Whitehead (1961, 1989) which has been verified by a lot of studies and experiments. But this theory does not fully explain the observed phenomena of Sporadic-E, and also needs more validation with large number of measured data. Other researchers also made some meaningful conclusions and conjecture on the study of Sporadic-E, for instance, (Hocke et al., 2001; Hocke and Igarashi, 2002; Garcia-Fernandez and Tsuda, 2006) analyzed characteristics of Es-layer during solar maximum and minimum with the data of CHAMP and GPS/MET, they pointed out that the Sporadic-E is a kind of phenomenon with obvious geographical distribution and seasonal variation; (Nygren et al., 1984; Basu et al., 1973) pointed out that the formation mechanism of larger scale Es may be caused by electron density gradient drift instability; (Farley, 1985; Smith and Royrvik, 1985) used
http://dx.doi.org/10.1016/j.asr.2015.04.014 0273-1177/Ó 2015 Published by Elsevier Ltd. on behalf of COSPAR.
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
2
J. Niu et al. / Advances in Space Research xxx (2015) xxx–xxx
gradient of plasma instabilities and two-stream instability to explain the formation mechanism of smaller scale Es. Since the controversy still exists, so we still need detail observation data. There have been some research on analysis of Es by occultation data (Wu et al., 2005; Wu, 2006; Arras et al., 2008; Yeh et al., 2012), but these research mostly use the signal–noise data, which is based on the assumption that the noise is caused by the Es layer, to verify the occurrence of Es. In this paper, we proposed a method based on wavelet analysis and slant TEC data not only to detect the occurrence of Es, but also to inverse the critical frequency of Es. To validate this method, we present the Es occurrence global distribution and inversed critical frequency compared with the known global distribution feature and ground-based Es critical frequency observation.
2. Data and methods The main data in this paper are occultation data (download from COSMIC centre) and the Es critical frequency data (download from Space Physics Interactive Data Resource, SPIDR). COSMIC occultation system is launched by Taiwan and USA, which is widely used by researchers; it has the largest observation data currently. In this article, second-level occultation data (ionprf files) during 2007–2008 is used which includes GPS, LEO satellite orbit data, TEC, electron density, etc. During the occultation process, GPS signal path scans the entire ionosphere from high altitude to low altitude, including the Es layer height range from 90 km to 120 km. In the ionospheric occultation event, the slant TEC, which is refer to the ”horizontal” TEC between GPS satellite and LEO satellite in the entire paper instead of the vertical TEC of the entire ionosphere, can be inversed from the phase delay. In addition, the electron content above the LEO orbit height have been removed in these TEC data. The electron density irregularities that exist in ionosphere would cause the disturbance of slant TEC, which can be used to inverse the Es critical frequency, is rather small respect to the ionosphere background. So we applied a wavelet analysis method to obtain this small STEC perturbation. The wavelet analysis is an effective time–frequency analysis methods. The essence of the wavelet transform is to perform convolution on a translation and narrow wave weight function which has localized nature both in a time domain and frequency domain, so that the signal can be decomposed into the individual components at different time and frequency. _
Set wðtÞ 2 L2 , its Fourier transform is wðwÞ, so that when allowed to meet the conditions: Cw ¼
Z
þ1
1
_
2
j wðwÞj dw < þ1 jwj
ð1Þ
wðwÞ is called a basic wavelet or mother wavelet. After the dilation and translation of wðwÞ, we can get: 1 tb wa;b ðtÞ ¼ pffiffiffi w a; b 2 R; a–0 ð2Þ a a We call it a wavelet series, the a is scaling factor or scale factor and the b is translation factor. The wavelet transform is defined for arbitrary signal as: Z þ1 1 t b dt W f ða; bÞ ¼< f ; wa;b >¼ pffiffiffi xðtÞw ð3Þ a a 1 W f ða; bÞ is the wavelet transform coefficient. The reconstruction (inverse) transformation is: Z þ1 Z þ1 1 1 tb f ðtÞ ¼ W ða; bÞw dadb ð4Þ f C w 1 1 a2 a We can divide the STEC to two parts as low frequency part Ltec and high frequency part Htec, which stand for the ionospheric background and fluctuation caused by ionospheric irregularities, by applying this wavelet decomposition and reconstruction method. In this paper, a 3-rd sym wavelet is used in the wavelet decomposition and reconstruction method. 3. Results Fig. 1 shows a typical inversion result with the method discussed above, the left panel is the slant TEC variation with altitude and the middle panel is the Ltec variation with altitude and right panel is the Htec variation with altitude. Here the TEC refer to the slant TEC between the GPS satellite and LEO satellite instead of the usually vertical TEC. As we know, the existence of Es layers would result in an additional phase delay which means an enhancement in TEC. But this enhancement is rather small than the regular TEC, so we can only distinguish this small enhancement as a perturbation in the Htec profile. The perturbation in Htec profile may be also caused by solar flares which can cause a ionosphere disturbance including the E region but we do not consider this because we only use the data in the period with rather low solar activity. This result is obtained from an occultation event in 2009.182, the file name is ionPfr_C001.2009.182.00.07. G10_2009.2650_nc. It is obviously that the TEC profile is quite similar with the Ltec profile especially above the 200 km with the Htec value nearly zero. Between the height rang from 140 km to 200 km, the Htec profile has a small fluctuation but not varies largely, this may be caused by the small electron density in the “valley” region. Under 140 km, the absolute value of this fluctuation dramatically increase with the maximum value about 1.4 TECU at 100 km, this perturbation may indicate the occurrence of Es. Fig. 2 shows another variation of the Htec with altitude which is obtained from a occultation events near UK station (FF051, 51.7°N, 1.5°W) at 18 o’clock on the July
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
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100
100
0
0 0
50 100 TEC(/TECU)
0
50 100 Ltec(/TECU)
3
0 −2
0 Htec(/TECU)
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Fig. 1. Variation of TEC (left), Ltec (middle) and Htec (right) with altitude. Notice that all TEC in this paper refer to the slant TEC between the GPS satellite and LEO satellite instead of the usually vertical TEC.
800 700
Altitude(/km)
600 500 400 300 200 100 0 −2
−1.5
−1
−0.5
0 0.5 Htec (/TECU)
1
1.5
2
Fig. 2. Variation of TEC fluctuation with height.
4th, 2009 (UT). As shown in the figure, the fluctuation of Htec from 800 km to 200 km is similar with the example above, but the maximum value is 1 TECU at 100 km. At the same time, the ground observation shows a Es critical frequency 4.5 MHz at 102 km. This may indicate, at least, that we can predicate the occurrence of Es and we would validate this method further in the latter section. 4. Validation To validate the method we have proposed, we present the global distribution of DTEC (for simplification purpose, we use DTEC standing for maximum absolute Htec value) to validate that if a large DTEC can indicate the occurrence of Es. Furthermore, we select more than 500 sets occultation data, which is compared with the ground-based observation, to verify the correlation between DTEC and Es critical frequency. 4.1. Global distribution and seasonal variation With the method proposed in the previous section, we analyzed the COSMIC occultation data during the full year
2007 and the seasonal distribution of DTEC. The results shown in Fig. 3. The location of DTEC which were greater than 2 TEU had been identified in Fig. 3. As we can see from Fig. 3, the distribution DTEC was in well agreement with the observations of Es-layer (Wu et al., 2005; Arras et al., 2008; Yeh et al., 2012). Both of them present a significant seasonal variation and global distribution. The large DTEC have a high occurrence rate in the summer and winter, but low rate in the spring and autumn. The occurrence rate is extremely high in the mid-latitude region of the summer hemisphere. This figure also shows a series of large DTEC value in the high latitude which can be seen in all seasons, this is consistent with the result in the Antarctica (Zhao et al., 2012) which found that Es in Antarctica has a weaker seasonal variation than the mid-latitude region and there is no dramatic difference in different season. This region is in accordance with the aurora region so these large values may also be caused by the particle precipitation. Since the well agreement between DTEC and Es distributions and variations, we can definitely conclude that large DTEC represents the occurrence of Es. 4.2. Comparison of DTEC and Es critical frequency Since a Es with high electron density would cause a strong perturbation in TEC data, so we may inverse the Es critical frequency (foEs) from the DTEC data. Therefore, we should verify, first of all, the correlation between them. Because of the randomness of the global distribution of occultation data, we need to match the data before we compare it with the ground observation data. The matching principles in this article are, 1. Space matching: the difference between the average position of the occultation tangent point and the ground station is within 2°; 2. Time matching: the difference between the occultation time and the observation data from ground-based observatories is within one hour. We choose a lower space resolution to
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
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Spring 18
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o
Longitude( )
Fig. 3. Seasonal distribution of parameter DTEC (TECU) in year 2007.
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
J. Niu et al. / Advances in Space Research xxx (2015) xxx–xxx
5
obtain enough occultation data for the comparison. While the ground based observation have well time continuity, so we can choose a higher time resolution. In accordance with the matching principles, we match 530 sets of foEs data and the occultation data from 2007 to 2008 in the Europe region. The comparison result is shown in Fig. 4. As shown in Fig. 4, the variation of DTEC and foEs is basically the same, and the correlation coefficient between the two sets data is 0.85. This means that there is a well linear or quasi-linear relation between DTEC and foEs. By using a least square fitting method, we derive a linear relation shown as following: foEsin ¼ 3:24 DTEC þ 1:89
ð5Þ
The foEsin is the inversed Es critical frequency (unit: MHz). In this formula, we can find that a DTEC about 1 TECU equals to a 5 MHz Es critical frequency. This indicates that this method may be better in strong Es critical frequency inversion since a small DTEC may not be caused by Es layer but other factors in the ionosphere. The average relative error is about 10%. 5. Discussion As we have proposed a simple linear formula between DTEC and foes, we also put forward a non-linear formula between them. Considering a simple occultation event model as shown in Fig.5, we assume that the electron density in the Es layer is the same everywhere and the electron content along with the GPS signals above the Es layer is the same, therefore we can define the TEC fluctuation as a line integral of Es electron density along GPS signals. By considering the distribution of electron density is symmetrical, so we can obtain the DTEC as following: Z DTEC ¼ 2 ne dL ð6Þ L
Es critical frequency(/MHz) / ΔTEC(TECU)
The ne is the electron density in the Es layer. As we have assumed that the electron density a constant in the Es layer, so the formula can be written as:
7
foEs smoothed foEs Δ TEC smoothed Δ TEC
6 5
DTEC ¼ 2ne L ¼
2 foEs2 L 80:6
ð7Þ
The value of L is relate to the Es thickness, Es altitude, electron density distribution and so on. The thickness of Es layer is about several kilometers, so here we may take L as 15 km since it is obvious longer than several kilometers to estimate the coefficient. In this non-linear formula, foEs equals to5 MHz represents a TEC fluctuation about 1 TECU, just the same with the observation in the previous section. So we may obtain a new formula by using a least square method from the observation, this non-linear formation is displayed as following: DTEC ¼ 0:038foEs2
ð8Þ
The units of DTEC and foEs respectively are TECU and MHz. However, these formulas are just empirical formulas in simplification conditions. The electron density distribution and GPS signal paths in realistic are rather complicate, so we still need more observation data and more accurate model to investigate this correlation. But we still have two problems in this paper. One of them is the low resolution of the ionprf files (only 1 Hz which means about 2 km resolution in altitude), which means we can only detect the Es layers with thickness larger than 2 km. The other problem is that the DTEC is not only affected by the amplitude but also the tilt angle (Zeng and Sokolovskiy, 2010). This indicates that our formulas may have significant errors in some cases, so we should give more attentions on this problem in the later research. 6. Conclusion
4 3 2 1 0
Fig. 5. Schematic diagram showing the simple model.
0
50
100
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200 250 300 350 Number of selected data
400
450
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Fig. 4. Comparison between DTEC and foEs obtained from the selected data.
In this paper, we analyze the TEC data obtained from the occultation data of COSMIC by using the wavelet decomposition and reconstruction method. We extract the maximum fluctuation DTEC of the high-frequency component between 90 km and 120 km and take it as new parameters characterizing the Es layer. The TEC fluctuation increases dramatically at the Es layer altitude. We consider this large DTEC as the occurrence of Es. We
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014
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J. Niu et al. / Advances in Space Research xxx (2015) xxx–xxx
analyze the COSMIC occultation data during the full year 2007 and obtain the seasonal global distribution of DTEC. The global distribution and seasonal variation is in quite well agreement with the known Es feature; this confirms the validity of our method. We also compare the DTEC with the Es critical frequency, they show a well correlation and we obtain a linear formula by the least square method. This formula indicates that it may be better in inversing the strong Es. In the discussion section, we build a simple model and derived a non-linear formula. Both formulas present well agreement with the observation. In a word, we propose a new method to detect the Es layer with the occultation data, linear and non-linear formulas are built to inverse the Es critical frequency. Since the lack of data sets in the same location and time, this method still needs further study. Acknowledgements Thanks COSMIC for providing ionospheric occultation data and SPIDR (Space Physics Interactive Data Resource) for its foEs data. References Arras, C., Wickert, J., Beyerle, G., et al., 2008. A global climatology of ionospheric irregularities derived from GPS radio occultation. Geophys. Res. Lett. 35, L14809. http://dx.doi.org/10.1029/ 2008GL034158. Basu, S., Vesprinti, R.T., Aarons, J., 1973. Field aligned ionospheric and e-region irregularities and sporadic E. Radio Sci. 8, 235–246.
Farley, D.T., 1985. Theory of equatorial electrojet plasma waves: new developments and current status. J. Atmos. Terr. Phys. 47, 729–744. Garcia-Fernandez, M., Tsuda, T., 2006. A global distribution of sporadic E events revealed by means of CHAMP-GPS occultations. Earth Planets Space 58, 33–36. Hocke, K., Igarashi, K., 2002. Structure of the Earth’s lower ionosphere observed by GPS/MET radio occultation. J. Geophys. Res. 107 (A5). Hocke, K., Igarashi, K., Nakamura, M., et al., 2001. Global sounding of sporadic E layers by the GPS/MET radio occultation experiment. J. Atmos. Sol. Terr. Phys. 2001 (63), 1973–1980. Jiuhou, Lei., Syndergaard, S., Burns, A.G., et al., 2001. Comparison of COSMIC ionospheric measurements with ground-based observations and model predictions: preliminary results. J. Geophys. Res. 112, A07308. http://dx.doi.org/10.1029/2006JA012240. Nygren, T., Jalonen, L., Oksman, J., et al., 1984. The role of electric filed and neutral wind direction in the formation of sporadic E-layer. J. Atmos. Terr. Phys. 46, 373–381. Smith, L.G., Royrvik, O., 1985. Electron-density irregularities in the daytime equatorial ionosphere. J. Atmos. Terr. Phys. 41, 813–824. Whitehead, J.D., 1961. The formation of the sporadic-E layer in the temperate zones. J. Atmos. Terr. Phys. 29, 49–58. Whitehead, J.D., 1989. Recent work on mid-latitude and equatorial sporadic-E. J. Atmos. Terr. Phys. 51, 401–424. Wu, D.L., 2006. Small-scale fluctuations and scintillations in high resolution GPS/CHAMP SNR and phase data. J. Atmos. Sol. Terr. Phys. 68, 999–1017. Wu, D.L., Ao, C.O., Hajj, G.A., et al., 2005. Sporadic E morphology from GPS-CHAMP radio occultation. J. Geophys. Res. 110, A01306. http://dx.doi.org/10.1029/2004JA010701. Yeh, W.H., Huang, C.Y., Hsiao, T.Y., et al., 2012. Amplitude morphology of GPS radio occultation data for sporadic-E layers. J. Geophys. Res. 117, A11304. http://dx.doi.org/10.1029/2012JA017875. Zeng, Z., Sokolovskiy, S., 2010. Effect of sporadic E cloud on GPS radio occultation signal. Geophys. Res. Lett. 37. http://dx.doi.org/10.1029/ 2010GL044561. Zhao, H.S., Xu, Z.W., Wu, J., 2012. Sporadic E morphology in Antarctica. Chin. J. Polar Res. 24, 129–135.
Please cite this article in press as: Niu, J., et al. Analysis of the ionosphere irregularities in E region based on COSMIC occultation data. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.04.014