New global electron density observations from GPS-RO in the D- and E-Region ionosphere

Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

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New global electron density observations from GPS-RO in the D- and E-Region ionosphere Dong L. Wu Goddard Space Flight Center, Greenbelt, MD, USA

A B S T R A C T

A novel retrieval technique is developed for electron density (Ne) in the D- and E-region (80–120 km) using the high-quality 50-Hz GPS radio occultation (GPS-RO) phase measurements. The new algorithm assumes a slow, linear variation in the F-region background when the GPS-RO passes through the D- and E-region, and extracts the Ne profiles at 80–130 km from the phase advance signal caused by Ne. Unlike the conventional Abel function, the new approach produces a sharp Ne weighting function in the lower ionosphere, and the Ne retrievals are in good agreement with the IRI (International Reference Ionosphere) model in terms of monthly maps, zonal means and diurnal variations. The daytime GPS-RO Ne profiles can be well characterized by the α-Chapman function of three parameters (NmE, hmE and H), showing that the bottom of E-region is deepening and sharpening towards the summer pole. At high latitudes the monthly GPS-RO Ne maps at 80–120 km reveal clear enhancement in the auroral zones, more prominent at night, as a result of energetic electron precipitation (EEP) from the outer radiation belt. The D-/E-region auroral Ne is strongly correlated with Kp on a daily basis. The new Ne data allow further comprehensive analyses of the sporadic E (Es) phenomena in connection with the background Ne in the E-region. The layered (2–10 km) and fluctuated (<2 km) Es components, namely Ne_Layer than Ne_Pert, are extracted with respect to the background Ne_Region on a profile-by-profile basis. The Ne_Layer component has a strong but highly-refined peak at ~105 km, with an amplitude smaller than Ne_Region approximately by an order of magnitude. The Ne_Pert component, which was studied extensively in the past, is ~2 orders of magnitude weaker than Ne_Layer. Both Ne_Layer and Ne_Pert are subject to significant diurnal and semidiurnal variations, showing downward progression with local time in amplitude. The 11-year solar cycle dominates the Ne interannual variations, showing larger Ne_Region and Ne_Layer but smaller Ne_Pert amplitudes in the solar maximum years. Enhanced Ne profiles are often observed in the polar winter, showing good correlation with solar proton events (SPEs) and geomagnetic activity. The new methodology offers great potential for retrieving low Ne in the D-region, where radio propagation and communication blackouts can occur due to enhanced ionization. For space weather applications it is recommended for GPSRO operations to raise the top of high-rate data acquisition to ~140 km in the future.

1. Introduction The E-region (90–140 km) acts as a dynamical, chemical, and electrical interface between the lower atmosphere and the upper ionosphere. Ionization in the E-region is mainly due to photodissociation of atomic/ molecular oxygen (O/O2) and nitric oxide (NO) by short-wave (<150 nm) solar radiation (e.g., Banks and Kockarts, 1973). The E-region electron density (Ne) can reach ~1011 e
/m3 at 100 km during the day but diminishes at night due to lack of incident radiation. The E-region is known for its vital role in radio communication since its first observation by Appleton and Barnett (1925). As a weakly-ionized plasma, the electrons and ions in the E-region are transported in different velocities and controlled by different processes. The ratio of electron gyrofrequency vs. electron-neutral collision frequency is high while such a ratio for ions is low, implying that the electrons tend to move along the geomagnetic field lines while the ions are dragged along with the neutrals. This leads to an important process called the E-region dynamo, which can result in currents and polarization electric fields. The E-region polarization electric fields can map along equipotential geomagnetic field lines to the F-region, affecting the F-

region ionosphere (e.g., Heelis, 2004). In addition, conductivity in the Dand E-region has an important implication for the surface-ionosphere potential under the global electrical circuit (GEC) framework (e.g., Hays and Roble, 1979). The 70–100 km altitude is the region where most sprite halos occur (Wescott et al., 2001) and a higher electron density would favor sprite initiation (Qin et al., 2011). The ionospheric dynamo processes are highly variable and coupled to each other because the ionospheric conductivity at ~100–140 km altitudes can be strongly affected by photochemistry, atmospheric planetary and tidal waves, and other sources such as polar energetic particle precipitation (EPP), including electrons and protons from the magnetosphere (Kelly and Heelis, 1989; Rees, 1989). For example, the tidal modulation on the E-region dynamo is not limited to the regional Ne enhancement. Its effects can be found in the higher ionospheric layers in a coupled electrodynamical system (England et al., 2006). On the other hand, magnetospheric disturbances allow energetic electrons in the outer radiation belt to precipitate down to the lower polar ionosphere, enhancing the E-region ionization and upper-atmospheric ozone chemistry (Thorne, 1977; Verronen et al., 2011). Enhanced Ne in the auroral E-region has been observed during both quiet and geomagnetic storm

http://dx.doi.org/10.1016/j.jastp.2017.07.013 Received 12 February 2017; Received in revised form 27 June 2017; Accepted 20 July 2017 Available online xxxx 1364-6826/Published by Elsevier Ltd.

Please cite this article in press as: Wu, D.L., New global electron density observations from GPS-RO in the D- and E-Region ionosphere, Journal of Atmospheric and Solar-Terrestrial Physics (2017), http://dx.doi.org/10.1016/j.jastp.2017.07.013

D.L. Wu

Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

periods (e.g., Mayer and Jakowski, 2009; Tsai et al., 2010; Zhang et al., 2010; Mannucci et al., 2015). The ionosphere is also known for frequent, irregular small-scale variability and instability. In the E-region, for instance, sporadic E (Es) is a transient disturbance to the background Ne profile at 90–120 km altitudes (Mathews, 1998). The wind shear is thought to play a critical role in Es formation by converging the plasma density via the v  B motion in this region (Whitehead, 1960; Haldoupis, 2011). Global distribution and seasonal variation of Es have been obtained and studied extensively with Global Positioning System (GPS) radio occultation (GPS-RO) measurements (e.g., Wu et al., 2005; Arras et al., 2009; Chu et al., 2014). These sporadic layers can even occur in the D-region ionosphere (Hoppe et al., 1999). Observations of the E-region ionosphere have been relying primarily on the global routine ionosonde network (e.g., Reinisch and Galkin, 2011) and the research network of very low frequency (VLF) and extremely low frequency (ELF) (e.g., Cummer and Inan, 2000). From a limited number of stations worldwide, ionosonde measurements provide critical near-real inputs to the International Reference Ionosphere (IRI) model (Bilitza et al., 2014) and ionospheric research in general. Observations of the E-region Ne from space remain a great challenge. GPS-RO emerges as a promising technique for profiling Ne in the ionosphere (Hajj et al., 1994; Hajj and Romans, 1998; Schreiner et al., 1999; Syndergaard, 2002; Nicolls et al., 2009; Yue et al., 2013), but the uncertainty and systematic errors of retrieved Ne in the E-region remain quite large (Yue et al., 2010; Wu et al., 2015; Pedatella et al., 2015). In this study a novel technique is developed to retrieve the E-region Ne from the high-quality GPS-RO 50-Hz phase measurements. The new algorithm is able to obtain accurate Ne profiles at 80–130 km by removing F-region contributions with a linear fit to the data at 50–80 km. This bottom-up approach is quite promising, yielding the E-region Ne climatology in good agreement with the IRI model. The rest of the paper is divided in five sections, starting with the physical principle of GPS-RO excess phase measurements in section 2 and a description of the retrieval algorithm in section 3. The retrieval results and E-region Ne climatology are presented in section 4. Finally, a summary and future work are given in section 5. Additional technical details and description of theoretical basis on the retrieval algorithm, including uncertainty evaluation, can be found in the Appendices.


 40:3  1016 τp ¼
∫ 1
np ds ¼ hTEC f2 LOS

where hTEC is horizontal total electron content (TEC), along the light of sight (LOS) of RO path, τp is in meter, and np is phase refractive index. In this study it is convenient to break τp down further by contributions from the F- and E-region as follows

τp ¼ τp

F

þ τp

E

¼

40:3  1016 ðhTECF þ hTECE Þ f2

(3)

where hTECF and hTECE are the F- and E-region contributions, respectively, as illustrated in Fig. 1. The bending-induced excess phase (τbend ) is caused by vertical gradient of np , which is a function of electron density Ne profile in the ionosphere and neutral atmospheric density in the lower atmosphere. Depending on the sign of Ne vertical gradient in the ionosphere, as illustrated in Fig. 1, the refracted occultation path can bend towards and downwards from Earth (Hajj and Romans, 1998). The bending effects increase the path length of radio propagation and thus increase τex . The bending from a very sharp layer can reach as high as 0.01 –0.02 near the tangent point (Wu et al., 2005), but is reversed between the radio propagation into and out of the layer. The typical vertical gradient of a Chapman-layer ionosphere, τbend is found to be 1–2 m (Hoque and Jakowski, 2011), or 0.001 –0.002 equivalent in bending angle (Appendix B). The bending in the lower atmosphere, τbend T , has been used to retrieve atmospheric density, temperature and water vapor. In summary, the key contributions to τex can be expressed as

τex ¼ τbend

T

þ τbend

F


τp

F


τp

E

(4)

where τbend T and τbend F are the bending delay from the troposphere/ stratosphere and the F-region respectively. All variables in Eq. (4) are a function of tangent height (ht). Bending is proportional, as a first order approximation, to the Ne vertical gradient. Hence, the bending from the E-region τbend E is negligible, compared to τbend F from the F-region, due to a weaker E-region Ne. Effects of τbend E are also small, compared to τp E , because of the short path length near the tangent point (i.e., tangent height layer). In fact, spherically homogeneous stratification is often assumed for Ne, which means Ne is constant in the tangent height layer with little bending. The contribution to τex from the tangent height layer is mainly due to phase advance (τp ) of wave propagation in the plasma. In addition, τbend appears to be a slow function of ht, compared to τp . As ht decreases, τbend tends to vary gradually as a result of accumulated effects above ht, whereas τp responds immediately to the change of Ne in the tangent height layer. The accumulated effects above the E-region ht,

2. GPS-RO excess phase measurements The standard level-1b GPS-RO data, such as the COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate) atmPhs data archived at University Corporation for Atmospheric Research (UCAR), contain profiles of L1 and L2 excess phase (τex) and amplitude (i.e., signal-to-noise ratio, or SNR) measurements sampled at a rate of 50 Hz. Unlike the 1-Hz POD (precise orbit determination) data, the 50-Hz RO data are more precise since they are measured with a highgain antenna. In determining the excess phase, clock errors have been removed using a double differencing method (Schreiner et al., 2011). The excess phase (τex) is defined as the distance difference between the observed and straight-line paths. In the ionosphere, radio propagation can have a phase speed faster than light speed, resulting an apparent phase advance (τp ) in τex (Appendix A). Thus, τex can be expressed as a sum of the component due to bending (τbend ) of the path and the component due to phase advance, namely

τex ¼ τbend
τp

(2)

(1)

where the negative sign in front of τp is set explicitly to reflect phase advance. The bending cause phase delay whereas the ionospheric electron density induces phase advance. The differences between bendinginduced phase delay and propagation phase advance are discussed in further details in Appendix A. Neglecting higher-order terms, the ionospheric phase advance can be written as

Fig. 1. A Schematic to show the radio propagation between GPS (G point) transmitter and LEO (L point) receiver during radio occultation (RO). The radio propagation can deviate from the G-L straight line due to the bending in the F- and E-region (grey curve). In addition, the ionospheric electron content also causes phase advance in the G-L link. The net effects from bending delay and phase advance in the plasma determine the excess phase measured in the G-L link. The tangent height of G-L link is denoted by ht.

2

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

the fitted function is extrapolated to all ht above 80 km. The difference between the extrapolated background (containing most of the F-region contributions) and observed excess phase, τbg
τex , yields the E-region contribution (τp E ). The bottom-up scheme produces a sharp weighting function of electron density in the E-region with a rapid tapering-off of contributions at heights above the tangent height (Appendix C). This weighting function is much sharper than the Abel function used in conventional algorithms. The long tail of Abel function in the F-region makes the E-region retrieval very sensitive to the F-region residual and variability, which has been the fundamental issue in a number of Ne retrieval schemes (Hajj and Remans, 1998; Lei et al., 2007; Hysell, 2007; Nicolls et al., 2009; Yue et al., 2010; Wu et al., 2015; Pedatella et al., 2015). The Ne retrieval in this study uses the sequential estimation approach formulated in Rodgers (1976) and the weighting functions as calculated in Appendix C. The measurement vector y is the horizontal total electron content in the E-region as a function of tangent height ht as derived from Eqs (3) and (4), i.e., y≡fhTECE ðht Þ; ht ¼ h1 ⋯hn g. The state vector x is Ne profile, i.e., x≡fNE ðzÞ; z ¼ 80; ⋯; 140 kmg. They are related through the weighting function K, or the Jacobians as in K ¼ ∂y/∂x, in the linear equation as follows

dominated by τbend F and τp F , manifest themselves as a slow drifting in τex with respect to ht, whereas the τp E contribution to τex varies at the rate of Ne with height. Thus, by carefully separating scale–dependent τex variations with respect to ht, it is feasible to extract the τp E and associated E-region Ne (Fig. 2). 3. Retrieval algorithm of E-region electron density Retrieving the E-region electron content from GPS-RO requires accurate estimation of F-region contributions in the τex profile because the radio wave in GPS-RO must propagate through the F-region before reaching the E-region. Because F-region effects on the τex measurement are often much larger than those from the E-region, a small residual after the removal of F-region contributions will lead to a relatively large error in the E-region Ne. This has been a major challenge for the top-down onion-peeling approach whereby the Abel inversion in the E-region must deal with a significant weight function tail in the F-region (e.g., Nicolls et al., 2009; Yue et al., 2013; Pedatella et al., 2015). Here a new approach is developed to remove the unwanted F-region contributions in a RO profile. As shown in Fig. 2, the F-region contributions (τbend F
τp F ) vary approximately linearly with ht at ht < ~80 km where there is little ionospheric contribution from the tangent point. This forms the basis of a key assumption made in this study to extract the E-region electron content. The new method assumes that the linear variation of τex at ht ¼ 50–80 km is mostly due to the F-region contributions and this linear dependence is valid as well at ht ¼ 80–130 km because the E-region contributions are much smaller than the F-region ones. The new algorithm, called the bottom-up approach, estimates the Fregion background (τbend F
τp F ) by fitting the τex measurements at ht ¼ 50–80 km to a linear function with respect to ht , namely, τbg ¼ a0 þ a1 ht , where a0 and a1 are the coefficients from the fit. Then,

y ¼ K⋅x þ εy

(5)

where εy is the measurement uncertainty of y. The inversion of x is based on the standard optimal estimation approach formulated by Rodgers (1976).

h i
1 h i T
1 T
1 S
1 x0 ¼ S
1 a þ K Sy K a a þ K Sy y

(6)

where x′ is an optimal solution to x in Eq. (5) and a is the a priori estimate of x, which is set to zero in this study. Sa and Sy are covariance matrices

Fig. 2. (Left): An example of COSMIC τex and SNR profiles from January 1, 2008; (Right): derived hTEC profiles for the E-region background (hTECE_Reg) and thin layers (hTECE_Lyr). The Fregion contributions are approximated with a linear function of ht fitted from the τex measurements at ht ¼ 50–80 km. The 50 km is chosen as the lower ht limit to avoid the bending due to the neutral atmospheric density (τbend T ). The difference between L1 τex and the linear fit yields τp E , which is inverted to obtain the Ne profile shown in the right panel, using Eq. (5). Layered structures (namely hTECE _Lyr) are extracted using a high-pass filter. In this case the hTECE _Lyr features are correlate well with an U-shape scintillation in the SNR profile as described in Zeng and Sokolovskiy (2010). 3

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

for a and y respectively. The inversion algorithm has been tested with simulated data for the Ne retrieval (Appendix C), showing promising results at 80–120 km altitudes. In summary, the bottom-up approach takes advantage of the slowlyvarying F-region components (τbend F þ τp F ) at tangent heights < 80 km. As the first order approximation, the F-region components of GPS-RO τex vary linearly with ht in the E-region and below. Using the τex measurements at ht below the E-region, the new algorithm is able to retrieve Ne at 80–130 km by removing the F-region contribution with a linear function on a profile-by-profile basis. The bottom-up fit appears to remove most of the F-region contributions at heights > ~140 km and produce a sharp weighting function for the Ne retrievals in the E-region. The new method has several merits over the top-down onion peeling approaches associated with the Abel inversion:

distributed GPS-RO satellites, together producing as high as 2000 daily occultations since its launch in April 2006 (Anthes et al., 2008). Since the initial deployment period (2006–2007), the six satellites have raised their altitudes from 500 km to 700–800 km, spreading out from their original orbital plane, to provide a full diurnal coverage from pole to pole. The daily number of RO observations fluctuates largely, and since 2010 the number has been decreasing as the satellites age (Appendix D). The GRACE mission was launched in March 2002 with two formation-flying satellites (GRACE-A and GRACE-B), but its GPS-RO observation was not part of regular operation till March 2007 (Wickert et al., 2005). Since then, GRACE has been steadily producing ~180 daily occultation profiles. TerraSAR-X was launched in June 2007 with routine RO observations (~300 daily occultations) since August 2008 (Yoon et al., 2009; Zus et al., 2014; Appendix D). The IRI-2016 model is employed here to provide a first order validation of the GPS-RO Ne retrieval. It is a data-based empirical model that describes monthly-mean Ne and other ionospheric properties at 60–2000 km altitudes, using available ground-based and spaceborne observations. The IRI-2016 is the latest version in which improvements were made for the F1- and F2-region Ne profiles and real-time representation (Bilitza et al., 2014). Several attempts were made to extend the IRI model to include the storm-time E-region using FUV measurements (Zhang et al., 2010) and NOþ emission (Mertens et al., 2013a,b), these extensions are the indirect approaches for the E-region Ne with limited local time coverage at a given time. Therefore, these extended storm-time IRI models are not used for the comparisons here. Fig. 3 is an example of Ne map from COSMIC at 100 km for January 2008, to compare with the IRI map. For a fixed UTC, the longitudinal variation in fact is a manifestation of local time variation. Both COSMIC and IRI Ne maps show a similar pattern in the longitudinal (or local time) variation as a function, with a distribution biased towards the summer hemisphere. No meridional bands are found in this retrieval when compared to the IRI, which suggests the banded structures from the Abel retrieval revealed by Wu et al., (2015) and Pedatella et al., (2015) are likely the F-region residual errors. The COSMIC peak at noon is located to the south of the geomagnetic equator, more so than that in the IRI model. Overall, the COSMIC daytime Ne values at 100 km are slightly lower by 20–30% than the IRI model. However, the mean Ne at 90 km is similar to the IRI model and the retrievals at 80–86 km are larger than the model (not shown). The estimated uncertainty of Ne retrievals, 0.6–1.4  1010 e
/m3 at 90–120 km (Appendix C), enables to detect weak Ne features and variability in the E-region. In a monthly average there are typically 150–400 samples in an 8  4 longitude-latitude gridbox at the equator and high latitudes. Thus, it improves the detection limit to 3–11  109 e
/m3 with monthly averaging. Some of the patchy features in Fig. 3 are likely due to the E-region variability insufficiently sampled in space and time. Despite the continuing demands for more spatiotemporal coverage, COSMIC observations perhaps have the best coverage of the ionosphere at present. In the Jan-2008 map, the enhancements from energetic particle precipitation (EPP) in the auroral ovals are clearly evident in the COSMIC map, particularly in the nighttime sector of the auroral ovals. Although the auroral features exist during the day, the elevated daytime Ne prevents them from standing out of the background. As described above, the storm-time features are not included in the basic model of IRI-2016. Various approaches, mostly using the indirect E-region measurements, are being developed to improve the storm-time E-region ionosphere. Therefore, the direct, self-compliant Ne measurements from GPS-RO in the E-region will play an essential role in advancing our understanding of the ionosphere and its coupling with the thermosphere and magnetosphere as a whole. Fig. 4 compares COSMIC and IRI Ne distributions for July 2008. Both COSMIC and IRI maps show the noon peak is closer to the geomagnetic equator than what appears in the January case. The COSMIC noon maximum spreads slightly wider in latitude than IRI, and exhibits asymmetry about noon in longitude or local time. As seen later, tidal

1) Unlike the Abel inversion, the bottom-up method is less sensitive to the F-region ionosphere and its variability because of its sharp vertical weighting function. As shown in a validation study (Wu et al., 2015), the Abel inversion produces many unphysical Ne features as large as 100% in the E-region, compared to the IRI model. Despite some recent improvements with the Abel approach (Pedatella et al., 2015), the F-region residuals can be still seen in the lower part of Ne profile with large effects on the E-region Ne retrievals. 2) The new technique described here is self-compliant. It does not rely on any auxiliary data/models or a priori profile in inferring the E-region Ne. The bottom-up fitting in the new algorithm copes with a wide range of F-region variability, including 3-D effects due to horizontal Ne gradients. Ionospheric inhomogeneity and auxiliary data about the F-region could lead to a significant bias in the E-region Ne retrievals, depending on the a-priori used or how the a-priori is developed (e.g., Nicolls et al., 2009; Yue et al., 2013; Pedatella et al., 2015). 3) The new approach needs only L1 50-Hz τex , the best measurement among the published RO data in terms of data quality, measurement precision, and SNR. Without relying on the slightly-noisy L2 data, the number of Ne retrievals is significantly higher. 4) The high-quality L1 50-Hz τex data also allow small Ne fluctuations in the E-region (aka. Sporadic-E or Es) to be detected, because of the high precision of the phase measurement. As seen in Fig. 2, layered structures and fluctuations are often embedded in the E-region background with weak amplitudes. These structures can exist during both day and night. Previous studies have shown that these Es features have strong tidal modulation and seasonal variations (e.g., Wu et al., 2005; Arras et al., 2009). But these studies were not able to relate Es variability to the background Ne and compare its amplitude with other large-scale layered E-region variability in e
/m3 unit. 4. Morphology of E-region electron content 4.1. Monthly means and seasonal variations For the global E-region Ne, the new methodology is applied to the GPS-RO atmPhs data archived at UCAR CDAAC (University Corporation for Atmospheric Research COSMIC Data Analysis and Archive Center). The atmPhs is a level-1b data set that contains RO τex profiles for L1 and L2 channels. Among the CDAAC archives, only CHAMP (Challenging Minisatellite Payload), COSMIC, GRACE (Gravity Recovery And Climate Experiment), and TerraSAR-X missions produce regular 50-Hz τex measurements up to 130 km. Thus, this E-region study is limited to these data sets at present. The CDAAC level-1b data statistics and data reduction procedure are detailed in Appendix D. The CHAMP mission was launched in July 2001, producing ~220 daily occultations (Wickert et al., 2001; Appendix D). Initially, its receiver acquired the 50-Hz RO data up to ~100 km, but raised the top to ~150 km starting January 2002 (Wu et al., 2005). The CHAMP RO observation was ended in October 2008 before the mission was eventually terminated in September 2010. The COSMIC mission has six 4

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 3. COSMIC (left) and IRI-2016 model (right) Ne maps at 100 km for January 2008, respectively. The UTC (Coordinated Universal Time) for these maps is given in the bottom. The lower panels are the polar projections of the same map. The white line is the geomagnetic equator. During January, the northern hemisphere (NH) of 60 poleward is mostly in the dark with lower Ne, but the enhancement from EEP in the auroral oval is still significant. In fact, the EEP enhancement around the auroral over is evident in both poles.

The new Ne retrieval algorithm allows small-scale features to be extracted in the E-region since it retains the original vertical resolution of the τex profile. In this analysis a retrieved Ne profile is divided into Ne Region , Ne Layer and Ne Pert , based on the vertical scale of variability as

modulation of the E-region Ne, which is also not represented in the IRI model, can produce such asymmetry. The migrating and non-migrating tides as well as other planetary waves are thought to play a significant role in the ionospheric dynamo (e.g., Immel et al., 2006; Forbes and Wu, 2006; Forbes et al., 2008). The low and mid-latitude nighttime Ne does not vanish completely in the COSMIC maps for both January and July cases, but they are absent in the IRI model. The nighttime D- and E-region Ne at lower and mid-latitudes have been a research interest for a number of groups (e.g., Smith and Gilchrist, 1984; Han and Cummer, 2010). Although the daytime conductivity is essential for the E-region dynamo, the evening-time conductivity and the gradient of sunset conductivity in the E-region have been the center of debate on what cause the evening pre-reversal enhancement (PRE), which is an enhanced vertical ion drift in the evening equatorial F-region (Eccles, 1998; Heelis et al., 2012; Richmond and Fang, 2015).

Ne ¼ Ne

Region

þ Ne

Layer

þ Ne

Pert

(7)

where Ne_Layer is the E-region background Ne as in Figs. 3 and 4, Ne_Layer is the layered component with a vertical scale between 2 and 10 km, and Ne_Pert represents the perturbations at scales <2 km. The rate of vertical sampling is ~2 km/s during both rising and setting occultation profiles. Hence, the 50-Hz L1 τex data are effectively sampling the E-region at a high (~40 m) vertical resolution. A high-pass filter, from the difference between the original and 51-point-smoothed profiles, is employed to extract the small-scale (<2 km) component. For the 2–10 km component, a band-passed filter is developed from combination of a 31-point lowpass filter and long-wave background filter (Appendix E). In this approach a long-wave background is empirically determined from an annealing algorithm that applies the 31-point smooth iteratively. In each iteration the algorithm checks the difference between the original and smoothed profiles, rejects positive outliers (enhanced layers), and interpolates to fill the rejected points. The final profile represents a background (i.e., the long-wave background) without enhanced layers (i.e., Ne_Region), and the difference between the 31-point smoothed and the long-wave background yields Ne_Layer. The filter characteristics of the 51point high-pass and the band-pass filters are detailed in Appendix E. Fig. 5 shows the zonal mean Ne_Region from COSMIC observations and the IRI model for January and July 2008, along with the Ne Layer and Ne Pert components and the perturbation (or scintillation) component in the L1 SNR. The E-region background Ne (Ne_Region) rises sharply above

4.2. Sporadic E (Es) Global characterization of Es was previously investigated with recent GPS-RO observations (e.g., Wu et al., 2005; Arras et al., 2009; Chu et al., 2014), primarily focusing on small-scale (<2 km) vertical oscillations in the phase and SNR measurements. However, the variation and formation of Es remains as active research subjects. Particularly lacking is how various Es components are excited and connected to the background Ne and instability in the ionosphere. There is evidence in observations that suggest a possible coupling between mesoscale spread F and Es layers (Haldoupis et al., 2003). While different theories on this coupling have been proposed, the polarization electric fields generated by Es are viewed as the key mechanism for interactions between the E- and F-region (e.g., Shalimov and Haldoupis, 2005; Tsunoda, 2008). 5

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 4. As in Fig. 3 but for July 2008.

include the contributions from both Ne_Layer and Ne_Pert, which are difficult to separate between each other in the SNR measurement. The SNR scintillation is very sensitive to vertical gradient of electron density, not necessarily proportional to electron content of the Es layer. By having the two distinct components, Es can be comprehended in a more thorough framework.

80 km, but biased toward the summer hemisphere as seen in Figs. 3–4. The wintertime high-latitude Ne_Region band comes mostly from the auroral oval. There is a significant latitudinal variation at the bottom of COSMIC zonal mean Ne_Region, showing a gradually deepened E-layer ionosphere towards the summer pole. This latitudinal variation disappears at higher altitudes, replaced by a strong enhancement in the equatorial region. A similar deepening tendency is seen in the IRI model but appears at a slightly higher altitude. The Ne_Layer enhancement, residing mostly between 95 and 105 km, is also biased towards the summer hemisphere with the deepening slope as in Ne_Region. Although overall smaller than Ne_Region in amplitude, Ne_Layer can significantly modulate the E-region electron content, particularly in the summer mid-latitudes (~40 ) where it peaks. The layered (2–10 km) Ne enhancement in the E-region is part of the Es phenomenon, but its global distribution and properties have not been studied in the past with the GPS-RO data. The Es morphologies derived from GPS-RO were mostly from smaller vertical scales (<2 km) (e.g., Wu et al., 2005; Arras et al., 2009; Chu et al., 2014). Therefore, in this study the Ne_Layer features are treated separately from the smaller-scale component (Ne_Pert) that was investigated in the past. Representing fluctuations of vertical scales less than 2 km, the distributions of Ne_Pert and SNR_Pert resemble each other. The Ne_Pert and SNR_Pert morphology is similar to that reported in previous studies (e.g., Wu et al., 2005; Arras et al., 2009), except that Ne_Pert shows a much smaller amplitude in e
/m3 than Ne_Layer and Ne_Region. The Ne_Pert amplitude is approximately 2 orders of magnitude weaker than Ne_Layer, but measurable by the GPS-RO technique because of the high precision of 50Hz L1 τex data. Ne_Pert and SNR_Pert have a strong peak in the summer midlatitudes (~40 ). There is a second peak near the equator in July and in the subtropics (~20 N) in January. A high-latitude peak from the auroral oval is more evident in the NH during January than one in the southern hemisphere (SH) during July. Broadly speaking, the Es phenomena

4.3. Characterization of Ne_Region with the α-Chapman function The Chapman-layer ionosphere is a simplified mathematical model of ionization profile as a result photoionization from solar radiation (ion production) and recombination from collisions with neutrals (ion loss) (Chapman, 1931). In this simplified model, radiation from the sun is monochromatic and attenuated exponentially by a stratified atmosphere with density decreasing exponentially with height. Ionization potentials and reaction rates are proportional to the available sunlight at each altitude, while the loss from electron-ion recombination is proportional to (Ne)2 for charge neutral plasma. The Chapman layer/function is the solution when the production and loss processes reach the equilibrium. The actual ionospheric (D-, E-, and F-) layers may deviate from the ideal Chapman model, depending on detailed radiation, recombination, transport processes in each specific region. As a result, the morphology of Ne profiles may vary in altitude, time of day, and latitude. In fact, none of the layers disappear totally at night, because of scattered radiation and transport mechanisms. In the E-region, the bottom of daytime Ne profile is in close agreement with the Chapman description. Studies have shown that the bottom can be characterized by the α-Chapman function (e.g., Shume et al., 2005), which is expressed by 0

0
z Ne ðzÞ ¼ NmE ef0:5⋅ð1
z
e Þg

6

(8)

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 5. Zonal mean structures of Ne components from for January (left) and July 2008 (right) as described in Eq. (6), from top to bottom: IRI-2016, COSMIC Ne_Region, Ne_Layer, Ne_Pert, and SNR_Pert. SNR_Pert is the L1 signal power (i.e., SNR) fluctuation derived using the same high-pass filter as for Ne_pert.

the Chapman function at 80–90 km, which is not evident in this study. Fig. 7 displays the fitted three Chapman-layer parameters as a function of latitude and local time for four nominal season months in 2008. As expected, NmE depends strongly on solar local time or solar zenith angle (χ), and so are the daytime hmE and H. During the daytime as the sunlight path length shortens towards noon, χ decreases, and so do hmE and H. In other words, the E-layer penetrates deeper into the atmosphere at noon with a sharper tapering-off at the bottom. The deepening trend in daytime hmE and H with latitude towards the summer pole is consistent with the slope and vertical gradient seen in Fig. 5. July has the lowest daytime NmE. For all four months the daytime NmE is slightly asymmetric about noon in local time, showing a small residual

where NmE is the E-region peak density, z0 ¼ ðz
hmE Þ=H, H is the effective scale height, and hmE is the characteristic peak altitude. At the bottom of the E-region, the height dependence of Ne profile is dominated by the last term in the exponential in Eq. (8), namely,
z0

Ne ðzÞ≈NmE ef
0:5⋅e g . Therefore, parameters hmE and H serve as the key variables to characterize structural variations of the diminishing E-layer. Fig. 6 show the fit of monthly Ne_Region profiles at 75–130 km to the α-Chapman function (Eq. (8)). All three parameters (NmE, hmE, and H) are used in the fitting. In both cases in Fig. 6, the α-Chapman function represents the retrieved E-region Ne profiles quite well. In a dataassimilation-aided retrieval, Nicolls et al., (2012) found that their retrieved Ne_Region profiles for January 2008 deviated significantly from 7

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 6. Examples of monthly zonal mean COSMIC Ne profiles (solid line) at the equator for January 2008 and fitted Chapman functions (dashed line). The local time of the mean profile, as well as the fitting parameters, is indicated in each panel.

dynamo during daytime map to the F-region, driving plasma there upward and poleward via the E  B drift, causing equatorial ionospheric anomaly (EIA) (Farley et al., 1986; Heelis, 2004). Thus, modulations of the E-region wind dynamo, especially in the wind field, will cause the similar variations in the F-region EIA (e.g., England et al., 2006; Immel et al., 2006; Forbes et al., 2008). Vertically propagating tidal waves are known to reach very large (tens of m/s) amplitudes in the E-region (Hagan and Forbes, 2002). Multiple tidal components exist, including both migrating and non-migrating tides in various wave modes (e.g., Forbes and Wu, 2006). To highlight the diurnal cycle and potential tidal impacts on Ne, the time-height section plot is used for each latitude bin. Fig. 8 shows the time-height variation of Ne components at four southern latitudes in January 2008. Although tidal modulations are not obvious in the Ne_Region component, there exists a clear semidiurnal variation in Ne_Layer and Ne_Pert, especially at summertime mid-to-high latitudes. The semidiurnal tidal signature in Es, which is equivalent to the Ne_Pert component, has been analyzed extensively by Arras et al., (2009). They showed that the tilted Es enhancement at 50–55 N was closely in line with the zero zonal wind of the tidal oscillation. The new Ne_Layer component extracted in this study exhibits diurnal and semidiurnal variations similar to Ne_Pert, but on the top of a strong diurnal variation as in Ne_Region. At 16 S there appears a stronger diurnal variation than the semidiurnal, compared to other

extending into the early evening. The local time NmE gradient appears larger in sunrise than sunset. The nighttime scale height H is generally long, suggesting more influences from the F-region ionosphere and up. For example, the EPP in the auroral zones can penetrate deep into the atmosphere from the magnetosphere, providing an extraordinary production of ions and electrons in the E- and D-region (Barabash et al., 2004) and effects in the middle atmosphere through transport (e.g., Holt et al., 2012). Such particle precipitation in the auroral zone is irregular in nature. The sporadic enhanced E-layer due to EEP has been studied semi-quantitatively using GPS-RO data (Mayer and Jakowski, 2009; Mannucci et al., 2015), and the storm-induced enhanced E-layers are generally confined in the vicinity of the auroral oval and may last a few days. 4.4. Diurnal and semidiurnal variations One of the most powerful impacts of the E-region conductivity on the ionosphere above is through the so-called “E-region wind dynamo”, whereby polarization electric fields are generated from a current induced by ions and electrons moving in different directions. In the E-region ions tend to move with neutral winds through collisions while electrons travel along with geomagnetic field lines due to their high gyro-/collision-frequency ratio. The polarization electric fields generated by the E-region 8

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Fig. 7. Fitted Chapman parameters NmE, hmE, and H as a function of geographic latitude and solar local time, for the January, April, July and October 2008. The white line denotes χ ¼ 90 .

2005). As seen in the previous section, this poor sampling will affect Ne_Region and Ne_Layer than Ne_Pert because of the stronger diurnal variations in the former components. Fig. 10 compares the time series of monthly Ne for three different Ne_Region, Ne_Layer and Ne_Pert components at 100 km for 2002–2016. The data prior to the COSMIC era are solely from CHAMP, and therefore produce a noisier variation due to poor local time sampling. The monthly averages are computed with equal weight on each 2-hourly local time bin, to take into account the presence of strong diurnal variations in these variables. A higher Ne_Region during the solar maximum years (2002–2005 and 2012–2015) is clearly seen in the time series at all latitudes. For the Ne_Layer component, the solar cycle variation is weak and the CHAMP observations may not be very useful to extract the weak variation. There is an indication in the Ne_Pert component that the Es amplitude is slightly larger during solar minimum years (2007–2009). To highlight the solar-cycle variations, Fig. 11 compares the equatorial Ne_Region means with F10.7 for the COSMIC era. The interannual variations of the 100-km Ne_Region are dominated by the solar 11-year cycle, as expected for increases in the soft X-ray irradiances and the resulting photoelectron flux (Richards, 2013). Despite very little sunlight at night, the solar-cycle variation is evident in the night mean. On the top of the 11-year modulation is a strong semiannual variation with the peaks near the equinoxes. The fall peaks are often larger than the spring ones in the daytime means, but nearly equal in the nighttime. The semiannual variations appear to be greater during the solar maximum years, more so in the nighttime means.

latitudes. Although it peaks near noon at 120 km, this diurnal component produces enhanced Es amplitudes in the late afternoon and early evening hours at 110 and 100 km, respectively. Fig. 9 shows the diurnal and semidiurnal variations of Ne_Region, Ne_Layer and Ne_Pert components at four northern latitudes for July 2008. Like the January mean, there exists a distinct enhanced layer at ~105 km in the background electron density Ne_Region. This layer is roughly symmetric around the noon, more regularly varying with local time than the density above 110 km. Although the Ne_Region amplitudes are generally weaker than January 2008, the Es components (Ne_Layer and Ne_Pert) have larger amplitudes. The Es at summertime mid-to-high latitudes has a strong semidiurnal modulation that appears from a semidiurnal tide. Again, the subtropical (16 N) Es components contain a strong diurnal variation that leads to the late afternoon and early evening enhancement at 100–110 km. 4.5. Interannual variations and solar influences Solar activity has strong influences on the E-region ionosphere (Kelley and Heelis, 1989). Solar-cycle variations and a significant secular trend exist in the long-term ionosonde data (Bremer, 2008). The foE measurements from global 71 stations show generally higher foE during the solar max years with an increasing trend between 1955 and 2005. The corresponding h’E has been decreasing during this period. Cooling and contraction of the upper atmosphere are thought to have a net effect of increasing ionization rate in the E-region (Qian et al., 2008). GPS-RO sensors have been observing the global E-region continuously since 2002. Due to the strong diurnal and semidiurnal variations of electron density, monthly averaged measurements from these sensors may fluctuate due to insufficient sampling in local time. For example, CHAMP was not able to sample all local times within a month (Wu et al.,

4.6. Auroral particle precipitation in the E-Region At shorter time scales (minutes to days), external forcing from solar 9

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Fig. 8. Solar local time variations of the three components of E-region electron density: Ne_Region, Ne_Layer and Ne_Pert, for latitudes of ±60 , ±16 and 0 in January 2008. Semidiurnal variations with a vertical wavelength of 35 km (dashed lines) are drawn to aid the comparisons.

these two SPEs at 80 and 100 km in the polar NH. It is readily to identify the SPE-induced Ne enhancement in the nighttime data at high latitudes where the EPP sources dominate its variability. In these proton event cases, the Ne enhancement stands out significantly at 80 km, but diminishes quickly with height. At 100 km no Ne enhancements from the SPEs can be found. Larger Ne enhancements at lower altitudes are expected because of the deeper penetration of high energetic particles and electrons (Rees, 1989; Kirkwood and Osepian, 1995; Verronen et al., 2015). Belova et al., (2005) reported an enhanced polar Ne down to 60 km during the October 29–30 2003 SPE.

UV and soft X-ray radiation, electron and proton precipitation, and galactic cosmic rays can affect the polar E-region ionization and the upper atmosphere through energetic particle precipitation (EPP) along the magnetic field line (e.g., Rees et al., 1988; Randall et al., 2005; Rodger et al., 2007; Turunen et al., 2009; Verronen et al., 2011). EPP includes both solar proton event (SPE) and energetic electron precipitation (EEP). For instance, the 24 January and 8 March 2012 SPEs, the two largest in solar cycle 24, caused ozone depletion as much as large 20% in the northern polar mesosphere for several days (Jackman et al., 2014). The left panels in Fig. 12 show the nighttime Ne_Region enhancement from

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 9. As in Fig. 8 but for July 2008.

Zawedde et al., 2016). It was further suggested that the solar-controlled energetic particle forcing has a comparable effect on the polar winter atmosphere as the solar irradiance variations (Sepp€al€a and Clilverd, 2014). There is a strong correlation between electron density and geomagnetic activity. During the periods without major SPEs, as seen in the right panels of Fig. 12, the polar Ne_Region at 80 km has significant fluctuations that appear to correlate well with the Kp index, as expected for the enhanced particle precipitations from geomagnetic disturbances. Fig. 13 shows that the solar cycle variation remains evident in the GPS-RO Ne at 86 km in the polar region. Although the background Ne at 86 km (i.e.,

In addition to SPEs, energetic electrons (>100 keV) stored in the radiation belt are capable of penetrating down to the upper atmosphere and the lower ionosphere during geomagnetic disturbances (e.g., Strickland et al., 1993; Rodger et al., 2007; Verronen et al., 2015). It has been argued that frequent EEP events from the outer radiation belt could play as an equally important role as SPEs in modulating ozone chemistry in the middle/upper atmosphere (Andersson et al., 2014), especially with precipitation of auroral electrons (300 eV–20 keV) and medium-energy electrons (30 keV–2.5 MeV) (Codrescu et al., 1997). The 100–300 keV EEP events were found to be closely associated with ozone-destroying hydrogen species (e.g., OH) in the mesosphere (Verronen et al., 2011;

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Fig. 10. Time series of E-region Ne_Region, Ne_Layer and Ne_Pert at 100 km as a function of geographic latitude, derived from CHAMP (January 2002 – April 2006) and COSMIC (May 2006 – present), GRACE (March 2007 – present) and TerraSAR-X (August 2008 – present). The white line indicates the beginning of the COSMIC era. CHAMP suffers from insufficient sampling in solar local time, which causes more fluctuations than the COSMIC data. The CHAMP data prior to 2002 are excluded here because the RO top altitude was not high enough for the E-region study (e.g., Wu et al., 2005).

Auroral electron precipitation is a main source of electrons produced in the polar D-region. Because of its low density, the amount of auroral electron precipitation to the D- and lower E-region relies primarily on the models that are based on the electron flux spectra measured at satellite altitudes or the UV-VIS emissions in the upper E-region where most of the auroral light is produced (Hardy et al., 1985; Roble and Ridley, 1987; Zhang and Paxton, 2008). Particles with higher energy tend to penetrate deeper into the polar atmosphere (Basu et al., 1993; Strickland et al., 1993) and the Kp index is often used as the control parameter for particle fluxes. In general, these models produce a midnight maximum in auroral intensity, but significant uncertainty remains in particle energy flux distributions as well as attributions to electron/proton precipitation. As seen in Figs. 15 and 16 for the January and July climatology, GPSRO observations reveal an interesting transition of auroral Ne from the

Ne_Region) peaks in the summer solstice at high latitudes, the transient layer component Ne_Layer peak in the winter months. Overall, the solar cycle variation of Ne at 86 km is stronger in the NH than SH, which seems to be consistent with wintertime polar ozone variability on a similar timescale (Andersson et al., 2014). Fig. 14 further shows the Ne-Kp correlation of short-time-scale variability as a function of geomagnetic latitude and height for 2006–2016. The correlation is found generally consistent from year to year, higher in the polar region and at lower altitudes. The high correlation in the polar region is indicative of storm impacts of magnetospheric disturbances on the E-region ionization as seen in Figs. 3–4. The correlation in the SH auroral region appears to extend to a higher altitude than one in the NH, which both peaks at ~65 of geomagnetic latitude. Very weak correlation with Kp is found at low latitudes.

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

electrons precipitate into the lower polar ionosphere. The transition appears to be universal, occurring in both January and July as well as in other months in the NH and SH, with the daytime maximum peaks around ~10–11 in SLT at 80 km, 1–2 h earlier than the SLT noon. The locations of the maximum/minimum Ne appear to rotate gradually with local time as height increases. There is tendency that the auroral oval is thickened as height decreases. Nevertheless, the variability of auroral Ne in the lower ionosphere remains as a key scientific interest because of catalytic ozone loss in the mesosphere through ionization and odd hydrogen chemistry (Andersson et al., 2014). Validations and observations of the precipitating electron fluxes in this region are still lacking (Verronen et al., 2015; Tyssoy et al., 2016). 5. Summary and future work A new algorithm is developed to retrieve the E-region Ne using the only GPS-RO 50-Hz L1 excess phase (τex ) measurements. The new methodology assumes a slow, linear variation of the F-region background when GPS-RO pass through the E-region, and applies a linear fit to the τex measurements at 50–80 km to remove the F-region contributions at 80–130 km. Unlike the conventional Abel function, this bottom-up approach produces a sharp Ne weighting function and enables a reliable Ne retrieval in the E-region. Initial evaluations of the GPS-RO Ne reveal good agreement with the IRI model in the E-region. For January and July 2008, the GPS-RO observations produce a consistent morphology with IRI, in terms of monthly

Fig. 11. Time series of monthly mean 100-km Ne_Region at the geographic equator (10 S10 N) from COSMIC, GRACE and TerraSAR-X. The curves from top to bottom are daytime Ne mean, all-time Ne mean, nighttime Ne mean, and daily F10.7 index.

midnight maximum at 120 km to the midday maximum at 80 km. Thanks to the high vertical resolution of RO sounding technique, this is the first evidence from space that the auroral Ne distribution shifts as energetic

Fig. 12. Time series of daily mean Ne_Region from geomagnetic latitudes of 65 poleward at 80 and 120 km, with the Kp index in color. Only nighttime data are used to compute these daily averages. On the left are the daily means of the polar NH during the first 100 days in 2012 when two major SPEs occurred in 24 January (Day 24) and 8 March (Day 68). On the right are the daily means of the polar SH during a period of 100 days in mid-2012 when there was no major SPE. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 13

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 13. As in Fig. 10 but for 86 km.

magnitude weaker than Ne_Layer. Both Ne_Layer than Ne_Pert are considered as the Es components in this study. Their diurnal and semidiurnal variations show downward progression with local time in amplitude, as expected from the tidal wave modulation of Es. There are significant annual and interannual variations in the three Ne components as observed by GPS-RO, with larger amplitudes in the summer hemisphere. The 11-year solar cycle dominates the interannual variations, showing larger Ne_Region and Ne_Layer amplitudes but smaller Ne_Pert amplitudes in the solar maximum years. Impacts of solar proton events (SPEs) are evident in the daily mean Ne_Region, showing significantly enhanced electron density at 80 km, especially in the polar nighttime measurements. The new Ne measurements at the bottom of the ionosphere will be able to provide observational constraints on the storm-time ionization from auroral and medium-to-high energy electrons, as well as one from solar protons. Initial results from this simple retrieval algorithm are shown to be promising. Further improvements are planned after carrying out more

maps, zonal means and diurnal variations, despite a slightly lower (~30%) bias with the GPS-RO Ne. The daytime Ne profiles can be well characterized by the α-Chapman function of three parameters (NmE, hmE and H), showing an expected diurnal variation in NmE. The daytime hmE and H parameters indicate that the bottom of E-region is deepening and sharpening towards the summer pole. At high latitudes the monthly maps of GPS-RO Ne at 90–120 km reveal clear enhancement in the auroral zones, more prominent at night. The nighttime auroral Ne is highly correlated with Kp and the correlation increases as altitude decreases. The new E-region Ne measurements allow further comprehensive analyses of the sporadic E (Es) phenomena in connection with the background Ne in the E-region. The layered (2–10 km) and fluctuated (<2 km) Es enhancements, namely Ne_Layer than Ne_Pert, can be extracted from the background Ne_Region. The Ne_Layer component has a strong but highlyrefined peak at ~105 km, but its amplitude is smaller than the background Ne_Region by an order of magnitude. The Ne_Pert amplitude, which was previously studied with GPS-RO phase and SNR data, is ~2 orders of

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Bilitza et al., 2014; Zhang et al., 2010; Mertens et al., 2013a,b). It is found that strong bending from sharp vertical Ne gradients in the E-region can cause a low bias in the retrieved Ne at and above the gradient height (Appendix C), for which a more sophisticated fitting technique may be used to correct the bending effect. In addition, the new methodology has great potential of extending the Ne retrieval to the D-region, where radio propagation and communication blackouts can occur due to enhanced ionization. In addition, the enhanced ionization in the polar D-region also has an important implication for atmospheric ozone balance. The retrieval algorithm can be modified to retrieve the D-region Ne by accounting for the bending from the neutral atmosphere and 30–60 km, which requires use of both L1 and L2 τex measurements. It is recommended that the top of high-rate data acquisition should be raised to ~140 km for all operational GPS-RO missions, given their invaluable information about the E-region ionosphere. Several missions, with focus on stratospheric and tropospheric sounding, do not have the top in GPS-RO reaching the E-region. For example, MetOp GPS-RO acquires the high-rate data only up to 85 km. Because of the diurnal sampling is critical for studying the E-region ionosphere, it is highly desirable for all GPS-RO missions to contribute the ionospheric measurements. By increasing the number of the E-region GPS-RO observations collectively, it is feasible to achieve a 3-hourly update globally, including the stormtime auroral zones, which will lead to a substantial advance in space weather prediction. As the satellites are operated beyond their design lifetime, the number of daily RO from COSMIC is steadily reduced. As a

Fig. 14. Correlation coefficient between daily “nighttime” Ne_Region and Kp index for 2006–2016. The “nighttime” data include all solar elevation angles below 45 and are aggregated into 4 bins in geomagnetic latitude.

validations of GPS-RO retrievals against ionosonde observations (Reinisch and Galkin, 2011), the IRI model and its storm-time extensions (e.g.,

Fig. 15. Auroral electron density at 80–120 km for January of 2007–2016 as a function of geomagnetic latitude (30 poleward) and solar local time (SLT). The top and bottom panels are for NH and SH, respectively. SLT noontime is on the topside (bottom-side) of the NH (SH) maps. 15

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Journal of Atmospheric and Solar-Terrestrial Physics xxx (2017) 1–24

Fig. 16. As in Fig. 15 but for July.

Center (CDAAC) services for data processing and distribution, as well as the F10.7 data from the Laboratory for Atmospheric and Space Physics, University of Colorado, are acknowledged. The author thanks X. Yue for providing the GPS-RO simulation data from University Corporation for Atmospheric Research (UCAR) and the anonymous reviewers for valuable suggestions that led to an improved paper. He is also grateful for enlightening discussions with W. Wang and J. Yue on ionospheric sciences, and with D. Bilitza on the IRI model.

result, the monthly means become noisier due to poorer local time sampling. The upcoming COSMIC-2 mission hopefully will improve the local time sampling in the E-region, especially during the solar minimum years when the ionospheric Ne trends can be best detected. Acknowledgments The work is by supported by NASA's Sun-Climate research at Goddard Space Flight Center (GSFC). UCAR COSMIC Data Analysis and Archive

Appendices.

Appendix A. Phase Delays and Advances in GPS-RO The GPS-RO carrier phase measurements can be written as

τðλi Þ ¼ R þ τbend

T

þ τbend I ðλi Þ
τp ðλi Þ þ Ni λi

(A.1)

where i ¼ 1 or 2, denoting for the GPS L1 or L2 channel. All variables in Eq. (A.1) are positive with the explicit sign in front of them: τ carrier phase measured at L1 or L2 frequency λi L1 or L2 wavelength R straight-line distance between GPS and LEO τbend T phase delay due to atmospheric bending

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τbend I ðλi Þ phase delay due to ionospheric bending τp(λi) phase advance in the ionosphere Ni carrier phase bias or ambiguous number Receiver/transmitter clock error, multipath delay in code measurements as well as other delay/error in code measurements at L1 or L2 frequency are neglected. The ionospheric bending (τbend I ) in the radio propagation path will cause phase delay, but radio propagation in the plasma causes phase advance (τp ). Phase advance means that the phase speed is faster than the light speed, although the group velocity of radio waves still does not exceed the light speed. The excess phase (τex ) is defined as

τex ðλi Þ ≡ τðλi Þ
R

(A.2)

In the atmPhs data processing, the 50-Hz τex profile uses the measurement at the top tangent height (ht) as the reference and sets the carrier phase bias (Ni) to zero. Hence, τex ðλi ; ht Þ is also a function of ht and can be written as

τex ðλi ; ht Þ ¼ τbend T ðht Þ þ τbend I ðλi ; ht Þ
τp ðλi ; ht Þ

(A.3)

where τp ðλi ; ht Þ is the accumulated difference of radio propagation between vacuum and the plasma with phase refractive index np,

τp ðλi ; ht Þ ¼


 1
np ds

∫

(A.4)

straight line

The phase (vp ) and group (vg ) velocities of radio propagation in plasma are different and related through the first-order approximation of the ionospheric dispersion relation

ω2 ¼ c2 k 2 þ ω2p

(A.5)

where ω is the angular frequency, k is the wave number, c is the light speed in vacuum, and ωp is known as the critical plasma frequency. In the pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ionosphere, ωp ¼ e Ne =ε0 me where Ne is electron number density (e.g., Davies, 1965; Crawford, 1968). Using electron charge e ¼ 1.6  10
19 C, mass
31 me ¼ 9.11  10 kg and vacuum permittivity ε0 ¼ 8.85  10
12 F/m, one has

ωp ¼ 56:4⋅Ne1=2 rad=s

(A.6)

From the definition of velocities vp ≡ω=k, vg ≡dω=dk, the refractive index np ≡c=vp ng ≡c=vg can be approximated by

np ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1
ðfc =f Þ2 ≈1
40:3⋅Ne f 2

(A.7)

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1
ðfc =f Þ2 ≈1 þ 40:3⋅Ne f 2 ng ¼ 1

(A.8)

where fp ≡ ωp =2π, f ≡ ω=2π,, and f ≫ fp is assumed. The approximation in Eqs. (A.7-A.8) is resulted from Eq. (A6) and

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ω . 2
 2ffi
 2  p f ≈1
40:3⋅Ne f 2 1
fp f ≈1
0:5⋅ fp f ≈1
0:5⋅ 2π Eqs. (A.7-A.8) neglect higher orders of frequency dependence. From Eq. (A.4) the ionospheric advance is proportional to total electron content along the GPS-RO path, or hTEC, i.e.,

 τp ðλi ; ht Þ ¼ 40:3  1016 ⋅hTECðht Þ fi2 where hTEC≡

∫

(A.9)

Ne ⋅ds, fi ¼ c=λi is the GPS L1 or L2 frequency in Hz, hTEC is in TEC unit (or TECu), and τp is in meter. For L1 frequency

straight line

(1575.42 MHz), 1 TECu ¼ 1016 e
/m2, or 0.162 m in τp . The ionospheric bending τbend I ðλi ; ht Þ is also proportional inversely to fi2 because of the same frequency dependence in the plasma refractive index, i.e.,

 τbend I ðλi ; ht Þ∝1 fi2 Different from the phase delay τp ðλi ; ht Þ, the bending is induced by a vertical gradient in the refractive index. The bending can be upward and downward in the F-region, depending on where wave propagation is in the top and bottom side of the ionosphere. For a typical Chapman-layer ionosphere, Hoque and Jakowski (2011) found that the net τbend I in GPS-RO is about 1–2 m. Because both τbend I ðλi ; ht Þ and τp ðλi ; ht Þ are dependent on 1/fi2 , their effects cannot be separated using L1 and L2 measurements. Because the neutral atmospheric bending τbend T ðht Þ is independent of radio frequency, its effect can be extracted using the L1 and L2 measurements. However, for the ionospheric Ne retrieval, their effects need to be considered carefully. Neglecting τbend I ðλi ; ht Þ contributions will lead to a significant error in the τp ðλi ; ht Þ and subsequent TEC retrievals, which many inversion techniques fail at the bottom of the ionosphere where is Ne relatively low and very sensitive to the residual error from the retrieved profile above. The new methodology described in Section 3 assumes that the τbend I ðλi ; ht Þ and τp ðλi ; ht Þ from the Fregion vary nearly linearly with ht in the E-region, such that their effects can be removed accurately using the measurements below the E-region. This technique and assumption are verified with simulated GPS-RO data and approve to be quite promising.

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Appendix B. Relationship of Bending Angle and Phase Delay There is a simple analytical relationship between bending angle (α) and excess phase (τbend ). As shown in Fig. B1, the bending angle can be expressed as

α ¼ δG þ δL ≈ x

1 1 þ rG cosθG rL cosθL

(B.1)

On the other hand, the excess phase due to bending (τbend ) can be approximated as the distance difference between the bended and straight-line path, fGB
GAg þ fLB
LAg, or mathematically

τbend ≈

≈

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðrL cosθL Þ þ x2
rL cosθL ðrG cosθG Þ þ x2
rG cosθG þ



x2 1 1 þ 2 rG cosθG rL cosθL

(B.2)

Substituting Eq (B.1) to Eq (B.2), it yields

τbend ≈

2  α 1 1 þ rG cosθG rL cosθL 2

(B.3)

This is the first-order approximation between bending angle and bending-induced excess phase. Assuming typical orbital parameters, rG ¼ 20,200 km and rL ¼ 7100 km, a 0.001 bending at ht ¼ 100 km produces ~1 m delay in phase. In the troposphere, the bending near the surface can be as large as 1 , or 1 km in phase delay. Although the net ionospheric bending is often small, the local bending can be very large in the presence of a sharp electron density layer. Wu et al., (2005) reported a ~150 m lag between L1 and L2 phase oscillations when radio wave propagates through a strong Es layer. Because the bending is proportional to 1=fi2 , L2 will have more bending than L1. In other words, a 0.01 in L1 bending is equivalent to 0.016 in L2 for the same electron density gradient. This bending separation will lead to a lag of ~160 m in GPS-RO.

Fig. B1. GPS-RO geometry with bending relative to the straight line between GPS transmitter (G) and receiver at LEO (L). Point A is the tangent point of the straight line, whereas point B is the intersection of two lines asymptotic to the bended ray between transmitter and receiver. The angles between the straight line and the line asymptotic to the bended ray are δG and δL at transmitter and receiver, respectively, whereas the angles between the straight line and the line to the Earth center are θG and θL . x is the distance between A and B, namely, x≡AB. Point O is the center of Earth.

Appendix C. Simulated Data and Retrieval Errors The bottom-up method produces a much sharper weighting function in the E-region than the Abel function used in conventional algorithms. Fig. C1 compares the two weighting functions calculated from a daytime IRI Ne profile. The Abel functions have a long tail in the F-region, which makes Abelbased onion-peeling approaches very sensitive to the F-region residual and variability. In contrast, the weighting function from this work tapers off sharply at altitudes above the tangent height, allowing retrieval of the E-region Ne more accurately. The weighting function of the new removal procedure for F-region contributions is similar in different Ne profiles.

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Fig. C1. Comparison of the weighting functions between the detrended τex (black) from this work and the Abel function (red) at ht ¼ 80, 90, 100, 110, and 120 km, based on a daytime IRI Ne profile (right). The sharp peak and little F-region residual of the de-trended τex weighting function makes the new technique very promising to profile the E-region electron density.

The bottom-up retrieval scheme for the E-region Ne retrieval is tested using simulated GPS-RO τex data. A total of 920 simulated profiles, randomly distributed in space and time, are generated using IRI Ne profiles, and they cover a wide dynamic range of ionospheric variability in both E- and F-region. A comparison of the retrieved Ne and the true values is shown in Fig. C2, in which the simple algorithm is able to capture the small D- and E-region Ne variations reasonably well. Statistically, the retrieval algorithm with the bottom-up approach shows overall good performance when compared against the truth at most altitudes in the D- and E-region (Fig. C3). While the linear function appears to work well in most cases, retrievals appear to underestimate the large (Ne > 1011 e
/m3) values at all levels. As shown in Fig. C4, these underestimated cases are associated with sharp Ne vertical gradient in the E-region where the bending effect needs to be taken into account. A significant E-region bending would create a challenge to the assumption of the bottom-up method, i.e., nearly-linear dependence of τbend I ðλi ; ht Þ and τp ðλi ; ht Þ with respect to ht at ht ¼ 50–80 km. For these enhanced cases where the E-region reaches strongly to lower altitudes, there is a significant E/F-region bending τbend I ðλi ; ht Þ that can offset the phase advance τp ðλi ; ht Þ, as described in Eq. (A3), causing an underestimated τp ðλi ; ht Þ at ht > 80 km with a linear function correction. In other words, the fit to the τex profile will overcorrect the F-region contributions at ht ¼ 50–80 km and lead to an underestimated Ne retrieval in the E-region. Further improvements of the bottom-up Ne retrieval can be made from several aspects by 1) allowing a quadratic function fitting, and 2) developing empirical correction for profiles with large Ne vertical gradients. The current algorithm does not use the quadratic fitting, which may be employed to remove the nonlinear dependence due to strong bending in the E-region. Since the bending is proportional to the vertical gradient of Ne profile, the retrieval biases in Fig. C3 are examined against the τex vertical gradient at 90 km, as shown in Fig. C4. As expected for the bending-induced error, the biases at 100–120 km increase substantially when the gradient exceed ~0.15 m/km. It is noted that the biases at 100–120 km are more sensitive to the gradients at 80–90 km than those at 100–120 km. Thus, it is feasible to improve the Ne retrieval by developing a correction scheme based on the τex gradient. Finally, more sophisticated inversion can be carried out by using the realistic weighting function (Fig. C1), instead of the simple conversion in Eq. (5). However, it requires more analyses and tests to optimize the retrieval performance for the cases where Ne enhancement and large gradients occur in the lower E-region and D-region ionosphere. For the current algorithm configuration, uncertainty of the Ne retrieval can be estimated from the simulation results in Figs. C3 and C4. Excluding the cases with large gradients (dτex =dz > 0.15 m/km) cases where significant underestimation is found, the single-profile uncertainty of Ne retrievals is approximately 0.4–1.9  1010 e
/m3 at 90–120 km (Table C1).

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Fig. C2. (a) The simulated L1 τex profile (thin line) with an atmospheric bending effect at lower tangent heights, and a linear fit (thick solid line) to the bending-free L1 τex profile (thick dashed line). (b) The retrieved Ne profile (dashed) from the simulated GPSRO data, compared to the true Ne profile (solid).

Fig. C3. The retrieved Ne vs. truth from simulated GPS-RO data. The 1:1 line is plotted to guide comparisons.

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Fig. C4. Residuals between the truth and the Ne retrieved from simulated GPS-RO data as shown in Fig. C3, as a function of the vertical gradient of exL1 profiles. The bias becomes large for the gradients >0.1 m/km, and can be corrected empirically using the gradient on a profile-by-profile basis.

Table C.1 Estimated Ne Retrieval Uncertainty Height (km)

Uncertainty (1010 e
/m3)

90 100 110 120

0.6 1.1 1.7 1.9

Appendix D. GPS-RO Data Reduction and Statistics The atmPhs data used in this study are from the archive published at UCAR CDAAC using only essential variables including tangent height, longitude, latitude, UTC, distance between GPS transmitter and receiver, and L1 excess phase measurements. Four GPS-RO missions archived in CDAAC produce the 50-Hz data up to 120 km, and they are CHAMP (January 2002 – September 2008), COSMIC (May 2006 – present), GRACE (March 2007 – present) and TerraSAR-X (August 2008 – present). The number of occultations in the atmPhs files is shown in Fig. D1 from 2001 to present. CHAMP is the only available source before COSMIC for studying the E-region, but did not provide enough spatiotemporal sampling. Despite successful operations in the early period of the mission, the number of COSMIC occultations has been steadily decreasing from 2000 in 2007 to ~600 per day in 2016. The RO data acquisition from GRACE and TerraSAR-X missions has been quite stable, producing ~180 and ~280 profiles per day. The high-rate RO data from other archived missions, Metop-A, –B and SAC-C, do not reach high enough to the E-region, and therefore are excluded in this study. For data quality control the Ne retrieval algorithm screens the 50-Hz measurements in atmPhs such that they meet the following requirements:

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Fig. D.1. Daily numbers of occultation profiles, after quality-screened for the E-region retrieval, from CHAMP, COSMIC, GRACE and TerraSAR-X on CDAAC.

1. 2. 3. 4. 5. 6.

The The The The The The

number of occultation measurements above 80 km is greater than 100. number of occultation measurements below 50 km is greater than 5. average L1 SNR above 50 km is greater than 100. average L1 τex above 50 km is less than 20 m and great then 0. average L1 τex increases with decreasing tangent height, i.e., τex (ht ¼ 45–55 km) > τex (ht ¼ 75–85 km). height difference of adjacent measurements is always less than 2 km.

Appendix E. High-pass and band-pass filters To extract small-scale oscillations in Ne profiles, a simple boxcar-smoothing function is used. Because the vertical rising/setting rate of GPS-RO is ~2 km/s, the 51-point smooth corresponds to a ~2 km truncation in wavelength. For estimating the Ne_Pert variance, the difference between the original and the 51-point smoothed profiles is used. As seen in Fig. E1, this high-pass filter has a half-maximum wavelength of ~2.5 km. Different from the small-scale perturbations that oscillate randomly about the mean, the layered enhancements with a vertical scale of 2–10 km show a distinct positive (negative) bump in Ne (τex ) (e.g., Fig. 2). To extract this component, a special band-passed filter is needed. At the short wavelength end, a 31-point low-pass filter is used, which is simply a 31-point smooth function. At the long-wave end, an empirical background is needed to account for large-scale variations in the background. This long-wave dynamic background is empirically determined using an iterative annealing algorithm. It starts with the 31-point smoothed profile and checks the difference between the original and smoothed profiles in each iteration. The algorithm rejects positive outliers (enhanced layers) and uses interpolation to fill the rejected points. The final profile usually converges in 5–10 iterations and represents a background without enhanced layers, which is Ne_Region. The difference between the 31-point smoothed and the long-wave background yields Ne_Layer. The filter characteristics of this band-pass filter are shown in Fig. E1 with half-maximum truncations at 2 km and 12 km.

Fig. E1. Response functions of the 51-point high-pass filter (solid) and the 2–10 km band-pass filter (dashed).

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