⇦Chinese Physics Letters, 2018, Vol. 35, No. 10, Article code 109401⇨ Global Statistical Study of Ionospheric Waves Based on COSMIC GPS Radio Occultation Data * Xuan-Yun Zeng(曾炫云)1,2, Xiang-Hui Xue(薛向辉)1**, Xin-An Yue(乐新安)3,4, Ming-Jiao Jia(贾铭蛟)1, Bing-Kun Yu(于秉坤)1, Jian-Fei Wu(吴建飞)1, Chao Yu(于超)1 Affiliations 1CAS Key Laboratory of Geospace Environment, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026 2The Open University of Guangdong, Guangzhou 510091 3Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029 4College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049 Received 17 May 2018, online 15 September 2018 ^*Supported by the National Natural Science Foundation of China under Grant Nos 41774158, 41474129 and 41704148, the Chinese Meridian Project, and the Youth Innovation Promotion Association of the Chinese Academy of Sciences under Grant No 2011324.
^**Corresponding author. Email: xuexh@ustc.edu.cn Citation Text: Ceng X Y, Xue X H, Le X A, Jia M J and Yu B K et al 2018 Chin. Phys. Lett. 35 109401 Abstract Extracting and parameterizing ionospheric waves globally and statistically is a longstanding problem. Based on the multichannel maximum entropy method (MMEM) used for studying ionospheric waves by previous work, we calculate the parameters of ionospheric waves by applying the MMEM to numerously temporally approximate and spatially close global-positioning-system radio occultation total electron content profile triples provided by the unique clustered satellites flight between years 2006 and 2007 right after the constellation observing system for meteorology, ionosphere, and climate (COSMIC) mission launch. The results show that the amplitude of ionospheric waves increases at the low and high latitudes ($\sim$0.15 TECU) and decreases in the mid-latitudes ($\sim$0.05 TECU). The vertical wavelength of the ionospheric waves increases in the mid-latitudes (e.g., $\sim$50 km at altitudes of 200–250 km) and decreases at the low and high latitudes (e.g., $\sim$35 km at altitudes of 200–250 km). The horizontal wavelength shows a similar result (e.g., $\sim$1400 km in the mid-latitudes and $\sim$800 km at the low and high latitudes). DOI:10.1088/0256-307X/35/10/109401 PACS:94.20.-y, 94.20.Vv, 94.20.W- © 2018 Chinese Physics Society Article Text The deviation of ionospheric structure from its drastic changes in its regular form, known as ionospheric disturbance, can be caused by mutations in ionization sources, non-equilibrium dynamic processes, unstable magnetic flow processes, and some human factors. Through a wide range of experiments, modeling, and theoretical efforts, ionospheric waves have been studied in depth. The analyses of ionospheric waves were focused on many aspects, including the parameterization and the mechanism of generation and propagation. For example, on October 18, 1985, observations of ionospheric waves at observatories in Greenland, eastern North America, and Europe were obtained.[1] The gravity wave (GW) sources are related with the occurrence of ionospheric electro jet current surges as shown in Ref. [2]. The results shown in Ref. [3] (downward propagation, productivity correlated to magnetic field, compatibility to neutral atmospheric periods, Coriolis effect traces) are compatible with the initial assumption of atmospheric gravity wave (AGW) as the main origin of the studied ionospheric waves. Ionospheric waves with spatial wavelengths from hundreds to a thousand kilometers are detected most frequently.[4] The satellite observations can provide the total electron content (TEC) data well for studying ionospheric fluctuations. However, due to the limited spatial coverage of satellite observations, the extraction of spatial parameters for ionospheric waves (especially horizontal wavelengths) becomes difficult. In recent years, the maximum entropy method (MEM),[5] a good method used for extracting parameters of ionospheric waves, has successfully been applied.[6,7] The multichannel maximum entropy method (MMEM) was firstly applied to yield the main frequency and phase differences among TEC perturbation series observed by different stations, and successfully obtained the propagation parameters of ionospheric waves in Ref. [8]. Although there are a large number of case studies of ionospheric waves in certain regions, global research on ionospheric waves remains rare. Based on the above-mentioned work, we decide to combine the wavelet analysis method and the MMEM to derive ionospheric waves from the constellation observing system for meteorology, ionosphere, and climate (COSMIC) global positioning system (GPS) radio occultation (RO) TEC observations to obtain global statistics. The COSMIC mission was launched in April 2006 via cooperation between the United States of America and Taiwan, China. It provides ionospheric and atmospheric profile observations through the RO technique.[9] An important feature of the COSMIC constellation is that immediately after launch, the six satellites were clustered together in one orbit. Right after the launch the separation between each pair was about 1–2 s in time (about 10 km along the orbit) and is gradually increasing with time.[10] This small separation allows for closely collocated occultation from one GPS satellite with almost parallel occultation planes. It took almost a year for the six satellites to completely separate on the track from each other. As a result, the calibrated occultation TEC below the low Earth orbit (LEO) derived from COSMIC level2 ionPrf data product from June 2006 to May 2007 were used. We calculated the height resolution distribution of the original COSMIC electron density profile in the range of 150–350 km. It was found that the height resolution was basically from a few tenths of a kilometer to about 3 km, thus the height resolution of 1 km was selected for interpolation between 150 and 350 km for each profile before analysis. The limitation of the height resolution of electron density is observed by COSMIC, and our method of extracting vertical wavelengths allows us to observe fluctuations in the vertical wavelength range from 10 to 200 km.

Fig. 1. (a) Schematic of the arrangement of radio occultation triples for the determination of the absolute horizontal wave number $k_{\rm h}$. The purple lines represent the wave phases, and $x_{i} y_{i}$ denotes the position. (b)–(f) Example for data analysis. (b) Three TEC fluctuation profiles satisfying the spatiotemporal conditions. (c) Derived ionospheric wave amplitude and (d) vertical wavelength from a wavelet analysis for each TEC fluctuation profile. (e) Phase shift between two TEC fluctuation profiles from a cross-spectral analysis for the three combinations (1–2, 1–3, and 2–3) of TEC fluctuation pairs. (f) The resulting horizontal wavelength after Eq. (2).

We followed the method of extracting electron density perturbation from the vertical profile mentioned, shown in Ref. [11]. First, we used the fourth-order polynomial fittings and subtracted the background. Secondly, the sixth-order Butterworth band-pass filter was used to filter the residuals. Taking into account that the vertical resolution of the data is around 1 km, we chose the wavelength range of the band-pass filter as 10–20 km. The ranges of spatial and longer temporal sampling are usually 180–600 km and 900–1200 s.[12-14] Larger spatial and longer temporal sampling can contain more triples and more ionospheric waves can be observed. To observe more ionospheric waves, our co-located RO triple profiles was chosen within 1200 s and 600 km. Figure 1(a) shows the observing geometry for a triple of measurements in a constant altitude $z$. The positions of the three ROs (red, orange, and blue points) are denoted with $x_{1} y_{1}$, $x_{2} y_{2}$, and $x_{3} y_{3}$, and the purple lines represent lines of constant phase (wavefronts) of the ionospheric waves. The distances between each of those three points at a constant altitude from ROs are required to be less than 600 km. Figures 1(b) to 1(f) show an example of each step (after detrending) from TEC fluctuations (Fig. 1(b)) to horizontal wavelengths (Fig. 1(f)). Wavelet methodology is useful in identifying and analyzing ionospheric disturbances.[15] We followed the method of wavelet analysis used in Refs. [14,16] to obtain the amplitude and vertical wavelength of ionospheric waves for each single profile between 150 km and 350 km. The results of vertical profiles are shown in Figs. 1(c) and 1(d). The profile pairs with the vertical wavelength difference less than 6 km for each altitude were chosen to ensure that the wave structures in the single profile are caused by the same ionospheric waves, similar to the description of Ref. [14]. Here we introduce the MMEM to obtain the horizontal parameters of ionospheric waves. We selected every two of those three co-located RO profiles, and applied a vertical running window of 80 km at intervals of 1000 m for the MEM analysis. The different frequencies (i.e., vertical wavelengths) and phase differences between each pair of those profiles were obtained. Based on the main frequency obtained before, the corresponding phase difference was chosen from the cross-power spectrum. The results of phase differences obtained from the RO example are shown in Fig. 1(e) (the red, orange or blue lines represent a combination of 1–2, 1–3, or 2–3, respectively). The phase difference between two fluctuation profiles at a constant altitude neglecting the time and with the same vertical wavenumber is given[17] by $$\begin{align} \Delta {\it \Phi}_{ij} (z)=k\cdot ({x_{i} -x_{j}})+l\cdot ({y_{i} -y_{j}}),~~ \tag {1} \end{align} $$ where $\Delta {\it \Phi}_{ij}$ is the phase shift between two of those three co-located RO profiles at the constant altitude $z$, $k$, and $l$ denote the $x$ and $y$ components of the horizontal wave number, and $x_{i}y_{i}$ denotes the position of the three ROs. Each point of the measurement triple serves as a reference point; i.e., Eq. (2) is solved three times.[16] For example, if $x_{1} y_{1}$ (Fig. 1(a)) is the reference point, the following linear equation system is given and solved for $k$ and $l$, $$\begin{align} \Delta {\it \Phi}_{12} (z)=\,&k\cdot ({x_{1} -x_{2}})+l\cdot ({y_{1} -y_{2}}), \\ \Delta {\it \Phi}_{13} (z)=\,&k\cdot ({x_{1} -x_{3}})+l\cdot ({y_{1} -y_{3}}).~~ \tag {2} \end{align} $$ The result was marked as $k_{1}$ and $l_{1}$. When changing the reference point, we obtained three groups of horizontal wave numbers ($k_{1}$, $l_{1}$), ($k_{2}$, $l_{2}$), and ($k_{3}$, $l_{3}$). We calculated the horizontal wavelength from those three groups of values and considered the middle wavelength as the result of those three co-located RO profiles. The horizontal wavelength $\lambda_{\rm h}$ can be expressed[16] as $\lambda_{\rm h} =\frac{2\pi}{|{\boldsymbol k}_{\rm h}|}$, where ${\boldsymbol k}_{\rm h}$ is the horizontal wave number. The vertical profiles of $\lambda_{\rm h}$ obtained from the RO example are also shown in Fig. 1(f). To analyze the latitudinal features of ionospheric waves, we averaged the parameters of ionospheric waves in different latitudes at intervals of 2$^{\circ}$, and the height range used for averaging is divided into four parts (i.e., 150–200 km, 200–250 km, 250–300 km, and 300–350 km). Figures 2(a)–2(d) show the zonal mean number of triples based on the four seasons from June 2006 to May 2007. The number of triples increased in the middle and high latitudes and decreased in the equatorial and polar regions, which is related to the geometry of satellites. To ensure the credibility of the statistics, we removed latitudes with the number of triples below 100 (i.e., a portion of the polar region over 85$^{\circ}\!$ in the whole year and the region between 5$^{\circ}\!$N and 5$^{\circ}\!$S in DJF 06/07) when averaging the parameters of ionospheric waves. Figures 2(e)–2(p) show the zonal mean ionospheric waves amplitude ($\hat{I}$), vertical wavelength ($\lambda_{z}$), and horizontal wavelength ($\lambda_{\rm h}$) for different altitude intervals based on the time period June 2006 to May 2007, respectively. The maximum $\hat{I}$ (around 0.15 TECU) was observed in the tropics in the whole year, and in the southern hemisphere (SH) and northern hemisphere (NH) polar region from September 2006 to November 2006 (SON 2006). The parameter $\hat{I}$ with a second maximum (around 0.1 TECU) appeared around 30$^{\circ}\!$S from June 2006 to August 2006 (JJA 2006) and around 30$^{\circ}\!$N from December 2006 to February 2007 (DJF 06/07). Another maximum shows around 60$^{\circ}\!$S and 60$^{\circ}\!$N all the year. The value of $\lambda_{z}$ in the equatorial and polar regions (i.e., around 40 km) was smaller than in the mid-high latitudes (i.e., around 80 km) at all different heights. Moreover, $\lambda_{z}$ at 250–300 km was much larger than other heights. An interesting phenomenon is that there was a local minimum of $\lambda_{z}$ near 30$^{\circ}\!$S and 30$^{\circ}\!$N in the middle and high latitudes in the whole year. Similar to the results of $\lambda_{z}$, $\lambda_{\rm h}$ in the equatorial regions and polar region (around 800 km) was smaller than in the mid-high latitudes (around 1200 km). The value of $\lambda_{\rm h}$ did not change significantly with height. There was also a local minimum of $\lambda_{\rm h}$ near 30$^{\circ}\!$S and 30$^{\circ}\!$N in the middle and high latitudes in the whole year.

Fig. 2. (a)–(d) Zonal number of profile triples ($\Delta d\leqslant 600$ km and $\Delta t\leqslant 20$ min) in JJA 2006, SON 2006, DJF 06/07, and MAM 2007 for all triples. (e)–(h) Zonal mean ionospheric wave amplitude $\hat{I}$ for different altitude intervals based between June 2006 and May 2007. (i)–(l) For the vertical wavelength $\lambda_{z}$. (m)–(p) For the horizontal wavelength $\lambda_{\rm h}$. JJA: June, July, and August; SON: September, October, and November; DJF: December, January, and February; MAM: March, April, and May.

Here we took the altitudes from 200 to 250 km as an example, and averaged the parameters of these altitudes to study the global distribution of ionospheric wave parameters. The months of JJA 2006, SON 2006, DJF 06/07, and MAM 2007 were selected to show seasonal changes. Figures 3(a)–3(d) show the global number of profile triples ($\Delta d\leqslant 600$ km and $\Delta t\leqslant 20$ min) in JJA 2006, SON 2006, DJF 06/07, and MAM 2007 for all triples. The gray area is marked as the place with the number of triples below 3 in each bin and we removed these places when averaging parameters (shown in Figs. 4(a)–4(d), 5(a)–5(d), and 6(a)–6(d)). Figures 4(a)–4(d), 5(a)–5(d), and 6(a)–6(d) respectively show the global $\hat{I}$, $\lambda_{z}$, and $\lambda_{\rm h}$ derived from 3 points of COSMIC RO TEC profiles during 2006/2007 varying with seasons at 200–250 km. The locations without any triples are not shown. One interesting phenomenon is that in the tropics, the maximum parameters of ionospheric waves (especially $\hat{I}$, $\lambda_{\rm h} $) appeared in the junction of land and sea in South America and Africa, as well as India, Indonesia, while in the polar regions, $\hat{I}$ increased in SON 2006, MAM 2007 and decreased in JJA 2006, DJF 06/07. In addition, the maximum $\hat{I}$ located in the southern Andes in JJA 2006, MAM 2007, and in the Tibetan Plateau in SON 2006 and DJF 06/07. The local maximum of $\lambda_{z}$ appeared in the Tibetan Plateau, the Antarctic Peninsula, Madagascar, and the Rockies. The local maximum of $\lambda_{\rm h}$ located in the Rocky Mountains and Eastern Pacific Ocean in SON 2006, in the west of Scandinavia in DJF 06/07, and in the east of Brazil and Japan and the south side of Africa in MAM 2007.

Fig. 3. The global number of profile triples ((a) $\Delta d\leqslant 600$ km and (b) $\Delta t\leqslant 20$ min) for the globe in JJA 2006, SON 2006, DJF 06/07, and MAM 2007.

Fig. 4. (a)–(d) The values of $\hat{I}$ derived from 3 points of COSMIC RO TEC profiles for the globe in JJA 2006, SON 2006, DJF 06/07, and MAM 2007.

Our results show that the ionospheric wave amplitude in the polar region and the equator is particularly strong, similar to the results shown in Ref. [18]. The observed vertical wavelength increases with height to a maximum at heights of 250–300 km and then begins to decrease. A possible explanation is to take into account the changes of GWs when propagating upward. The vertical wavelengths of dissipating GWs, $\lambda_{z} ({z_{\rm diss}})$, increases exponentially with altitude, although with a smaller slope for $z$ over 200 km.[17] The horizontal wavelength $\lambda_{\rm h}$ and wave period spectra also change with altitude for dissipating GWs.[17] A GW spectrum excited from convection shifts to increasingly larger $\lambda_{z}$ and $\lambda_{\rm h}$ with altitude in the thermosphere that are not characteristic of the initial convective scales was also shown in Ref. [17]. Additionally, a lower thermospheric shear shifts this spectrum to even larger $\lambda_{z}$, consistent with observations.

Fig. 5. (a)–(d) The values of $\lambda_{z}$ derived from 3 points of COSMIC RO TEC profiles for the globe in JJA 2006, SON 2006, DJF 06/07, and MAM 2007.

Fig. 6. (a)–(d) The values of $\lambda_{\rm h}$ derived from 3 points of COSMIC RO TEC profiles for the globe in JJA 2006, SON 2006, DJF 06/07, and MAM 2007.

Seen from our global distribution of ionospheric wave parameters, the ionospheric waves are particularly active in the polar region and at the sea-land junction in the low-latitude regions. One interesting area of those regions is Japan. The source of the large-scale ionospheric waves over Japan appeared to be auroral processes at high latitudes.[19] Considering the inclination of the geomagnetic field over Japan, both the damping and growing large-scale ionospheric waves could be explained by the upward and downward propagating AGWs, respectively.[20] We also compared the ionospheric wave parameters obtained with the results of others. For example, the large-scale ionospheric wave during the period of strong solar activity in the middle of July, 2000 with the amplitude of about 2 TECU and the wavelength of 2200 km.[21] The ionospheric waves over Japan derived from OI 630-nm nightglow observations were characterized, and the meridional components of wavelengths determined from ionospheric data are 930–5250 km.[22] COSMIC provides the vertical profile of the electron density (in units of per cubic centimeter) that varies from one hundred kilometers to several hundred kilometers, and TEC (in units of TECU) after the integration covering the same height range and varying with the height. We used the wavelet analysis method to extract the vertical wavelengths of the ionospheric waves, and we found that either the electronic density file (unit: per cubic centimeter) or the TEC file (unit: TECU), shows the same results of the vertical wavelength. As a result, we used the TEC profile to extract the vertical wavelength using the wavelet analysis method. We calculated the height resolution distribution of the original COSMIC electron density profile in the range of 150–350 km. It was found that the height resolution was basically from a few tenths of a kilometer to about 3 km, thus the height resolution of 1 km was selected for interpolation. The limitation of the height resolution of electron density observed by COSMIC, and our method of extracting vertical wavelengths allow us to observe fluctuations in the vertical wavelength range from 10 to 200 km. We only kept the triples with a small difference in vertical wavelength between each of the three profiles to ensure that the disturbances of the three profiles in one triple are from the same ionospheric wave, which can also reduce the impact of different combinations of occultation observation points on the results of parameters of ionospheric waves. Comparing the global distribution of the number of triples with the amplitude, vertical wavelength, and horizontal wavelength of ionospheric waves, we found that there is no corresponding relationship between the number of triples and the parameters of ionospheric waves, and the distribution of those parameters of ionospheric waves was more related to the geographical location (e.g., some hot spot regions of ionospheric waves). This shows that the effect of the combination of different observation points on the parameters of ionospheric waves is at least not obvious on the global distribution. We also found that the number of triples has a slight effect on the results of the parameters of ionospheric waves from the zonal distribution (Fig. 2). In addition, due to the relatively uniform distribution of the global scanning orbits of six satellites COSMIC, the distribution of the latitude and longitude positions of the occultation observation points in each grid are basically uniform, and the impact on the final results should be small. It is difficult to interpret GW and ionospheric wave data obtained by various observation techniques since it is often uncertain whether the observed wave characteristics are due to properties and positions of the dynamical AGW sources, or to interactions of the propagating GWs with the mean flow (tides, planetary waves, and convection).[23] The application of ionospheric tomography from TEC data is a further tool to determine the spatial source and wave properties.[23] The work to be carried out in the future includes further research on the difference between daytime and nighttime ionospheric waves, as well as the relationship between AGW and ionospheric waves. For example, the study shown in Ref. [24] concentrated on the problem of how to infer, as comprehensively as possible, AGW information from measured ionospheric waves. In summary, we have taken full advantage of the COSMIC ionospheric TEC data from June 2006 to May 2007 and obtained the complete seasonal and spatial variations of parameters for ionospheric waves. The ionospheric waves are very active in low latitudes and polar regions. The amplitude and horizontal wavelength of the ionospheric waves show similar rules at heights of 150–350 km, while the vertical wavelength has a large difference. The global distributions of ionospheric waves' amplitude, vertical wavelength, and horizontal wavelength from our analysis show that ionospheric waves are usually very strong at the sea-land junction. We acknowledge the data used in this study from the COSMIC data provided by the UCAR/CDAAC scientific team (http://cdaac-www.cosmic.ucar.edu/cdaac/). References Gravity wave studyA new magnetic coordinate system for conjugate studies at high latitudesIncoherent scatter radar observations of AGW/TID events generated by the moving solar terminatorRecursive Multichannel Maximum Entropy Spectral EstimationInterpretations of observed climatological patterns in stratospheric gravity wave varianceInterpretations of observed climatological patterns in stratospheric gravity wave varianceDirect radar observations of TIDs in the D- and E-regionsCOSMIC GPS observations of topographic gravity waves in the stratosphere around the Tibetan PlateauComparative analysis of radio occultation processing approaches based on Fourier integral operatorsThe COSMIC/FORMOSAT-3 Mission: Early resultsIntercomparisons of HIRDLS, COSMIC and SABER for the detection of stratospheric gravity wavesObservation and analysis of a large amplitude mountain wave event over the Antarctic PeninsulaGravity wave activity in the lower atmosphere: Seasonal and latitudinal variationsStudy of ionospheric disturbances over Mexico associated with transient space weather eventsOn the determination of gravity wave momentum flux from GPS radio occultation dataAn apparent ionospheric response to the passage of hurricanesA study of atmospheric gravity waves and travelling ionospheric disturbances at equatorial latitudesRecherches sur la raie 6300 de la luminescence atmospherique nocturneObservation of large-scale traveling ionospheric disturbances of auroral origin by global GPS networksInternal atmospheric gravity waves at ionospheric heightsCharacteristics of medium- and large-scale TIDs over Japan derived from OI 630-nm nightglow observationEISCAT progress 1983-1985

[1]	Rice D D et al 1988 Radio Sci. 23 919
[2]	Bristow W A, Greenwald R A and Samson J C 1994 J. Geophys. Res. 99 319
[3]	Hernández M et al 2006 J. Geophys. Res. 111 11
[4]	Galushko V G et al 1998 Ann. Geophys. 16 821
[5]	Morf M et al 1978 IEEE Trans. Geosci. Electron. 16 85
[6]	Preusse P et al 2002 J. Geophys. Res. 107 8178
[7]	Ern M 2004 J. Geophys. Res. 109 D20103
[8]	Ding F et al 2011 J. Geophys. Res. 116 A09327
[9]	Zeng X Y et al 2017 Sci. Chin. Earth Sci. 60 188
[10]	Schreiner W et al 2007 Geophys. Res. Lett. 34 L04808
[11]	de la Torre A et al 2014 J. Geophys. Res. 119 2046
[12]	Wright C J, Rivas M B and Gille J C 2011 Atmos. Meas. Tech. 4 1581
[13]	Alexander M J 2015 Geophys. Res. Lett. 42 6860
[14]	Schmidt T, Alexander P and de la Torre A 2016 J. Geophys. Res. 121 4443
[15]	Romero-Hernandez E et al 2017 Adv. Space Res. 60 1838
[16]	Faber A et al 2013 Atmos. Meas. Tech. 6 3169
[17]	Vadas S L 2007 J. Geophys. Res. 112 305
[18]	Balthazor R L and Moffett R J 1997 Ann. Geophys. 15 1048
[19]	Kubota M et al 2000 Geophys. Res. Lett. 27 4037
[20]	Tsugawa T 2004 J. Geophys. Res. 109 A06302
[21]	Zhang D H et al 2002 Chin. J. Geophys. 45 469
[22]	Kubota M, Fukunishi H and Okano S 2001 Earth Planets Space 53 741
[23]	Hocke K and Schlegel K 1996 Ann. Geophysicae 14 917
[24]	Kirchengast G, Hocke K and Schlegel K 1995 Radio Sci. 30 1551