Global GNSS-RO Electron Density in the Lower Ionosphere

Abstract

Lack of instrument sensitivity to low electron density (N_e) concentration makes it difficult to measure sharp N_e vertical gradients (four orders of magnitude over 30 km) in the D/E-region. A robust algorithm is developed to retrieve global D/E-region N_e from the high-rate GNSS radio occultation (RO) data, to improve spatiotemporal coverage using recent SmallSat/CubeSat constellations. The new algorithm removes F-region contributions in the RO excess phase profile by fitting a linear function to the data below the D-region. The new GNSS-RO observations reveal many interesting features in the diurnal, seasonal, solar-cycle, and magnetic-field-dependent variations in the N_e morphology. While the D/E-region N_e is a function of solar zenith angle (χ), it exhibits strong latitudinal variations for the same χ with a distribution asymmetric about noon. In addition, large longitudinal variations are observed along the same magnetic field pitch angle. The summer midlatitude N_e and sporadic E (E_s) show a distribution similar to each other. The distribution of auroral electron precipitation correlates better with the pitch angle from the magnetosphere than from one at 100 km. Finally, a new TEC retrieval technique is developed for the high-rate RO data with a top reaching at least 120 km. For better characterization of the E- to F-transition in N_e and more accurate TEC retrievals, it is recommended to have all GNSS-RO acquisition routinely up to 220 km.

1. Introduction

The D- (60–90 km) and E-region (90–150 km) ionosphere play important roles in radio wave propagation because of their effective absorption of short-wave signals (e.g., high-frequency, HF, radio) [1] and reflection of long-wave communication and navigation radios (e.g., very low frequency, or VLF) [2]. It overlaps with the neutral atmosphere, known as the mesosphere, and is associated with large variability. The atmospheric temperature decreases with height in the mesosphere (or the D-region ionosphere), and the atmospheric thermal and density structures can be significantly perturbed by the atmospheric forcings from below (e.g., tides, planetary and gravity waves) [3].

The D-region is arguably one of the most critical interface layers between the lower atmosphere and the ionosphere. It is the layer where the electrical coupling takes place between the ionosphere and the phenomena such as sprites, elves, and blue jets from tropospheric thunderstorms occur. The D/E-region conductivity is important to complete a so-called global electric circuit (GEC), an electrical coupling between the ionosphere and the planetary surface with a DC current driven by tropospheric thunderstorms [4,5]. Because the D/E-layer conductivity can vary substantially between day and night, as well as between solar minimums and maximums over the 11-year cycle, it can short-circuit the F-region dynamo during the day [6,7,8] and modulate the GEC with the atmosphere throughout the day. However, it remains unclear if GEC has a significant feedback effect on thunderstorms, electrified clouds, or even on global cloud cover. If this feedback exists, the coupling between the ionosphere and the troposphere would act an important process to change Earth’s radiation and climate system [9,10,11].

The D-region plasma is weakly ionized during daytime, mainly from photoionization of nitric oxide (NO) by the solar Lyman-α (Ly-α) radiation [12]. When the photoionization is absent at night, the D-region electron density (N_e) decreases substantially but is maintained at a low level from complex sources [13]. During the quiet time, the daytime D-region N_e is balanced largely by positive molecular and cluster ions, where the upper D-layer mostly consists of molecular ions and the lower is dominated by cluster ions [14]. A strong solar activity can bring hard X-rays (wavelength < 1 nm) to ionize mesospheric N₂ and O₂, but even in this situation, the recombination rates are so high in the D-region that the environment tends to relax back to the neutral condition quickly once the ionization sources are gone. Hence, the number concentration in this altitude region is dominant by neutral molecules.

The D/E-region ionosphere can be often perturbed by irregular small-scale dynamic and electromagnetic variability and instability. In the E-region, for instance, sporadic E (E_s) can occur as a transient disturbance to the background N_e profile at 90–120 km altitudes [15]. The wind shear is thought to play a critical role in E_s formation by converging the plasma density via the v × B drift in this region [16,17]. Global distribution and seasonal variation of E_s have been obtained and studied extensively with global navigation satellite system radio occultation (GNSS-RO) [18,19,20] and ground-based observations [21]. These sporadic layers can even occur in the D-layer [22]. At high latitudes, influences on the D/E-region come from magnetospheric disturbances through polar electron precipitation with enhanced ionization. This process is thought to play a role in increasing HO_x and NO_x productions through atmospheric chemical chain reactions involving electrons and positive and negative ions [23,24]. The short-lived HO_x tends to produce direct effects on the O₃ loss that are localized in space (i.e., the mesosphere) and time (i.e., precipitation events) [25,26], whereas the long-lived NO_x can be transported down to the stratosphere to produce indirect effects on the O₃ loss [27,28].

The D/E-region N_e data are rare and limited, largely because of poor instrument sensitivity to low N_e concentration and incapability of remote sensing from space to profile a sharp N_e vertical gradient (i.e., four orders of magnitude over 30 km). Inconvenient and costly access to this altitude region makes in situ measurements infrequent and sparse. Thus, the majority of lower-ionospheric N_e measurements were obtained from sounding rockets (D/E-region) and ionosondes (E/F-region), which constitute the basis of empirical models such as FIRI (Faraday-International Reference Ionosphere) [29] and IRI-2016 (International Reference Ionosphere 2016) [30].

The objective of this study is to develop a robust algorithm to retrieve global D/E-region N_e from the high-rate GNSS-RO data that have been increasing in spatiotemporal sampling from a large number of SmallSat/CubeSat constellations. An improved spatiotemporal coverage is critical for studying the lower ionosphere because of substantial and complex diurnal variations and influences from both the lower atmosphere and upper ionosphere. As in the algorithm developed previously for the E-region by Wu [31], the new retrieval method removes F-region contributions in the excess phase profile with a linear function fit to the data before they are input for the D/E-region N_e retrieval. The GNSS-RO N_e retrievals tend to produce a lower N_e in the E-region compared to the IRI-2016 but in a general agreement with FIRI [32]. Similar results are found in the GNSS-RO N_e retrieval from this study through a brief comparison with ionosonde observations at the Hermanus site. The paper is organized to describe the improved algorithm of N_e retrieval with examples in Section 2, followed by the retrieval results and climatology of the GNSS-RO D/E-region N_e in Section 3. Brief evaluations of the GNSS-RO N_e with ionosonde observations at the Hermanus site and a novel retrieval technique for total electron content (TEC) are discussed in Section 4, before it is concluded in Section 5.

2. Data and Methods

The algorithm developed in this study is an extension of the earlier attempt to retrieve the N_e profile in the lower ionosphere from the GNSS-RO excess phase (${\varphi }_{ex}$) profile [31]. The RO excess phase is the difference between the measured and the free-space straight-line distance of GNSS (transmitter) and LEO (receiver) satellites. In the so-called “bottom-up” technique, a linear function is fitted to the ${\varphi }_{ex}$ profile over a narrow h_t range below the D-region to remove the F-region effects before the data are input for the D/E-region N_e retrieval. The F-region effects need to be removed first as cleanly as possible on a profile-by-profile basis, because a small ${\varphi }_{ex}$ residual from the F-region variability can induce large errors in the D/E-region retrieval. The bottom-up method, self-sufficient in removing F-region effects, is specially designed for retrieving low N_e concentrations in the lower ionosphere (Appendix A). It has several important differences from the conventional onion-peeling or top-down approach.

First, the top-down method assumes spherical homogeneity for all N_e layers along the RO path and requires absolute calibration of the excess phase (${\varphi }_{ex}$) measurements, whereas the bottom-up method assumes only homogeneity in the D/E-region. The homogeneity assumption on the F-region N_e is not required, because it can become problematic for retrieving the N_e below it, as a small error in the F-region N_e retrieval can induce a large effect on the D/E-region N_e. This error propagation is caused by a long tail of the Abel weighting function, which does not vanish even at the RO tangent height (h_t) far below the F-region [31]. As a result, small residual errors of the F-region N_e retrieval can propagate down to the D/E-region N_e in the data inversion process and generate a large error there [33,34]. A manifestation of this error propagation is clearly seen in the N_e profiles retrieved from the onion-peeling approach, which often exhibit large oscillatory, sometimes negative, values in the lower ionosphere [35,36,37]. On the other hand, the bottom-up method shows little contribution from the F-region in its weighting function in the D/E-region, and therefore its N_e retrieval is less impacted by the F-region error. The differences between the Abel and bottom-up weighting functions are detailed in Section 2.3.

Second, the bottom-up method is resilient to complex F-region variability with capability to cope with most of the F-region effects (e.g., inhomogeneity, structural variations) on a profile-by-profile basis. It is a self-sufficient approach, without relying on any auxiliary data. In other words, the algorithm contains a standalone data process using the same ${\varphi }_{ex}$ measurement profile for both E-region N_e retrieval and F-region effect removal. Previous studies found that the E-region N_e retrieval using an auxiliary model or constrained to an assimilated 3D N_e distribution had limited improvements for mitigating unrealistic F-region N_e features [38] and gradient effects on the derived E-region N_e [39]. These model-aided approaches are prone to ionospheric variability and tend to bias towards the quiet-time condition, not working reliably for a disturbed ionosphere.

Third, the bottom-up algorithm does not require absolute ${\varphi }_{ex}$ calibration that is needed to derive a line-of-sight (LOS) or horizontal TEC (hTEC) profile prior to the N_e inversion. It uses a differential ${\varphi }_{ex}$ profile, or the hTEC difference ($\mathsf{\Delta }hTEC$), with respect to a linear function fitted to the ${\varphi }_{ex}$ or hTEC data below the D/E-region. Thus, the linear fit serves a reference of each individual measurement profile, and the derived $\mathsf{\Delta }hTEC$ is used for the N_e retrieval. The algorithm assumes that the F-region contributions to the hTEC in the D/E-region vary linearly over a narrow h_t range, and this linear variation can be estimated and removed using the hTEC measurements below the D-region. As a result, the new algorithm is perhaps more sensitive to residual ionospheric errors (RIEs) and phase scintillations that are uncorrectable with the dual-frequency GNSS RO receivers, but these residual errors are relatively smaller than the systematic error from the spherical homogeneity assumption about the F-region.

Fourth, the bottom-up retrieval should not be used to replace the Abel inversion for the whole ionospheric N_e. Because the linear function used to remove F-region effects is a fit to the lower-ionospheric data, its uncertainty tends to increase with height and causes a large error in the N_e retrieval in the upper ionosphere. Thus, the Abel inversion from hTEC, which requires absolute calibration of the ${\varphi }_{ex}$ profile, still works better for the whole-ionospheric N_e retrieval.

2.1. RO Excess Phase (${\varphi }_{ex}$) Measurements

As a key variable for the N_e retrieval, hTEC(h_t) is the integral of N_e along the RO path at each h_t. It is related to excess phase ${\varphi }_{ex}$ profile by

$${\varphi }_{ex}=\frac{40.3\times {10}^{16}}{f^2}hTEC$$

(1)

Errors in hTEC can come from higher-order dependence (e.g., $f^{-3}$) and multi-path propagation. In the E-region h_t, the hTEC error contains contributions from both the F- and E-region, of which the former is much larger because its residual effects cannot be fully removed. Thus, any small error from the F-region N_e retrieval would cause a large error in the E-region N_e retrieval. The hTEC profile can be derived from the L1 ($f_1$ = 1.57542 GHz) and L2 ($f_2$ = 1.22760 GHz) excess phase (${\varphi }_{exL1}$ and ${\varphi }_{exL2}$ in meters) by

$$hTEC=\left({\varphi }_{exL1}-{\varphi }_{exL2}\right)\frac{f_1^2{f}_2^2}{40.3\times {10}^{16}\left(f_2^2-f_1^2\right)}$$

(2)

In the previous algorithm, Wu [31] used only the ${\varphi }_{exL1}$ measurements to derive hTEC. Therefore, the linear fit for F-region effect removal had to be carried out at h_t = 50–80 km to avoid the atmospheric bending (${\varphi }_{atm}$) at h_t < 60 km. Because the ${\varphi }_{atm}$ contribution is same in the L1 (${\varphi }_{exL1}$) and L2 (${\varphi }_{exL2}$) profiles, Equation (2) uses both L1 and L2 measurements to cancel the ${\varphi }_{atm}$ contribution, such that the linear fit can be carried out from lower h_t. In this study, we fit the hTEC data at h_t = 30–60 km to a linear function and extrapolate it up and subtract it from hTEC to yield $\mathsf{\Delta }hTEC$ for the D/E-region N_e retrieval. Hence, the use of hTEC data at h_t = 30–60 km allows the N_e retrieval extended to the D-region.

To better understand and evaluate error sources and their contributions to hTEC, we broke down ${\varphi }_{ex}$ into the ionospheric and atmospheric components. First, the neutral atmospheric component (${\varphi }_{iono\_free}$) in the ${\varphi }_{ex}$ profile is defined by

$${\varphi }_{iono\_free}=\left(f_1^2·{\varphi }_{exL1}-f_2^2·{\varphi }_{exL2}\right)/\left(f_1^2-f_2^2\right)$$

(3)

Here, ${\varphi }_{iono\_free}$ includes the atmospheric bending ${\varphi }_{atm}$ and the residual ionospheric effect (RIE), or ${\varphi }_{RIE}$, that cannot be accounted for by the assumption from Equation (1):

$${\varphi }_{iono\_free}={\varphi }_{atm}+{\varphi }_{RIE}$$

(4)

Because ${\varphi }_{RIE}$ is not from the neutral atmosphere and is not negligible at h_t > 80 km, it should be considered as a measurement error of hTEC in Equation (2). With the dual-frequency approach, one would hope to correct the $f^{-2}$-dependent ionospheric effects in radio propagation. However, multi-path propagation and higher-order frequency dependence may induce the RIEs at these altitudes [40,41]. In Figure 1a, the ${\varphi }_{atm}$ contribution is obtained from fitting an exponential function to the ${\varphi }_{iono\_free}$ data at h_t = 20–50 km and extrapolated to the heights above.

Furthermore, it is important to understand the contributions to ${\varphi }_{ex\_iono}$ induced by ionospheric bending (${\varphi }_{bend\_iono}$) and phase advance (${\varphi }_{p\_iono}$) effects as radio wave propagates in the ionosphere. The contributions from these processes are significant in the ${\varphi }_{ex\_iono}$ profile shown in Figure 1b, and these components have the opposite sign to each other.

$${\varphi }_{ex\_iono}={\varphi }_{bend\_iono}-{\varphi }_{p\_iono}$$

(5)

This is because bending delay (due to a longer pathlength) and phase advance (due to faster phase speed) in the ionosphere produce the opposite effects in the measured excess phase ${\varphi }_{ex}$. These components are defined by

$${\varphi }_{bend\_iono}={{\displaystyle \int }}_{RO}^{}ds-{{\displaystyle \int }}_{SL}^{}ds$$

(6)

$${\varphi }_{p\_iono}={{\displaystyle \int }}_{RO}^{}\left(n-1\right)ds$$

(7)

where RO and SL in the integral represent the RO and straight-line (SL) path of radio propagation, and n is refractive index of the ionosphere. Although the RO ${\varphi }_{ex\_iono}$ is dominated by $-{\varphi }_{p\_iono}$, ionospheric bending effects are not negligible because of the long pathlength in RO wave propagation. On the other hand, phase advance results from a faster phase speed of wave propagation in the ionospheric plasma, which will shorten ${\varphi }_{ex\_iono}$. The two competing effects both manifest themselves in the GNSS-RO ${\varphi }_{ex}$ profile shown in Figure 1b.

The number of N_e retrievals may decrease with the dual-frequency approach, to some extent, compared to the ${\varphi }_{exL1}$-only approach. Data quality control is obviously more demanding from the joint use of ${\varphi }_{exL1}$ and ${\varphi }_{exL2}$ profiles, because large spikes in either measurement can cause a bad Ne retrieval. Because GNSS-RO ${\varphi }_{ex}$ measurements generally have better signal-to-noise ratio (SNR) for ${\varphi }_{exL1}$ than for ${\varphi }_{exL2}$ from GPS (Global Positioning System), the required ${\varphi }_{atm}$ calculation may be subject to the additional error induced from the ${\varphi }_{exL2}$ profile, which can lead to an unsuccessful N_e retrieval. In addition, the relative signal strengths between L1 and L2 transmitters may vary with the GNSS systems. For example, GLONASS (Global Navigation Satellite System) satellites sometimes transmit stronger signals at the L2 frequency than L1.

The linear fitting for the F-region effect removal is similar between this study and one developed by Wu [31], except for slightly different height ranges. In this study, a linear function is fitted to the hTEC profile at h_t = 30–60 km on a profile-by-profile basis:

$$hTE{C}_{fit}=a_0+a_1·h_t \mathrm{for} h_t=30\text{–}60 \mathrm{km}$$

(8)

The derived linear fit is extrapolated to the heights above at h_t > 60 km, as estimated F-region contributions. By subtracting it from $hTEC$, we can obtain the D/E-region $\mathsf{\Delta }hTEC$ profile (in TECu):

$$\mathsf{\Delta }hTEC=hTEC-hTE{C}_{fit}$$

(9)

where 1 TECu = 10¹⁶ m⁻³. Note that the conversion in Equation (9) neglects higher-order frequency dependence and ionospheric bending effects.

In essence, the bottom-up approach uses the difference $\mathsf{\Delta }hTEC\left(h_t\right)$ with respect to the empirical reference (i.e., a linear function derived from h_t = 30–60 km), instead of absolute $hTEC\left(h_t\right)$ values, for the D/E-region N_e retrieval. As shown in the next section, the $\mathsf{\Delta }hTEC\left(h_t\right)$ at the D/E-region h_t have much smaller contributions from the F-region N_e compared to the Abel weighting functions, which allows to yield a more reliable inversion for the D/E-region N_e.

2.2. Low-Rate (1 Hz) POD and High-Rate (50–100 Hz) RO Data

Both precise orbit determination (POD) and RO antennas can track GNSS signals at negative elevation angles or, in other words, at $h_t$ below the LEO receiver altitude. Generally speaking, the POD antennas have a wider field of view (FOV), lower SNR, and a coarser sampling resolution, compared to the RO antennas. Depending on the POD receiver design, receiver satellite altitude, and data acquisition schedule, the POD 1 Hz occultations usually have a smaller number of profiles (10–30% in COSMIC-1 podTEC) reaching the D/E-region. There are slightly more POD occultation profiles reaching the D/E-region when the satellite is in a lower orbital altitude. Thus, the higher RO cutoff tangent height and noisier hTEC measurements make the POD data less attractive for the D/E-region study.

In this study, we focus mainly on utilizing the high-rate (50–100 Hz) RO data, of which the sampling and spatiotemporal coverage are much higher than the POD data. The dense spatiotemporal sampling is critically needed to characterize the lower ionosphere variability. In addition, the high-rate data have advantages to detect and correct ${\varphi }_{ex}$ measurement errors such as clock time and cycle slips in the presence of ionospheric scintillations [42]. Smaller ${\varphi }_{ex}$ measurement errors help to retrieve a low N_e concentration in the lower ionosphere.

In recognition of the high-rate RO measurements for ionospheric observations, the MetOp-A operation conducted a short experiment with the high-rate RO acquisition up to h_t ~ 290 km during 2020d161–2020d254 (9 June–10 September 2020). The success of the experiment allows the extended acquisition mode to continue from 2021d201 to the decommission in December 2021. As shown later in Section 3, the high-rate provides a significant benefit to the N_e retrievals in the E- to F-region transition and the retrieval of TEC. In addition to the extended high-rate profile from MetOp-A, the Spire GNSS-RO constellation, which NOAA uses to fill the polar latitudes outside the COSMIC-2 coverage, has been routinely acquiring the high-rate RO profile up to h_t ~ 175 km. Among the earlier missions, the C/NOFS (Communications/Navigation Outage Forecasting System) had a frequent high-rate RO data reaching up to h_t ~ 165 km from a low-inclination (13°) elliptical orbit.

The high-rate data in the D/E/F-region also provide a valuable diagnostic for better understanding and quantifying the RIEs of ${\varphi }_{ex}$ measurements in the ionosphere. The high-rate data help to reduce some of the scintillation-induced ${\varphi }_{ex}$ measurement noise, but the high-order frequency dependence and multi-path effects remain as a source of the $\mathsf{\Delta }hTEC$ errors in Equation (9) [31]. As shown in Figure 2, E_s-induced phase scintillation can become a large random error source of $\mathsf{\Delta }hTEC$ at h_t below the E_s layer. An RIE from the F-region can sometimes induce a bias. If the bias is confined in a narrow height region, its impact on the N_e retrieval is generally small. But if the bias is present at all heights, the induced bias can be significant in the retrieved N_e.

RIEs can also have a non-negligible impact on the neutral atmospheric refractivity retrieval. Bending angle ($\alpha$), which is used to derive the atmospheric refractivity, is essentially a vertical derivative of the ${\varphi }_{iono\_free}$ profile, i.e., $\alpha \cong -d{\varphi }_{iono\_free}/d{h}_t$. Therefore, a bias from RIEs would not be a problem for the $\alpha$ retrieval, but a slope or vertical gradient of RIEs would. The RIE-induced $\alpha$ error has been a major issue in the climate-quality data analysis of the upper stratosphere [43,44]. As shown in the second case in Figure 2, a vertical gradient (~1.25 × 10⁻⁷ radians) and bias (~0.03 m) are evident in the RIE profile. For this study, therefore, we simply allow a 0.3 m uncertainty for these RIEs in the D/E-region retrieval algorithm. Full characterization and correction for RIEs is an ongoing area of research and will be reported in a separate study.

2.3. N_e Retrievals

2.3.1. Inversion from $\mathsf{\Delta }\mathrm{hTEC}$

The inversion algorithm for the N_e retrieval in this study uses the optimal estimation inversion method [45]. The measurement vector y is the $\mathsf{\Delta }hTEC$ derived from Equations (3)–(8) as a function of h_t, i.e., y $\equiv \left\{\mathsf{\Delta }hTEC\left(h_t\right); h_t=h_1···h_{max}\right\}$, where $h_{max}$ is the maximum h_t in the RO ${\varphi }_{ex}$ profile. The state vector x is N_e profile, i.e., x $\equiv \left\{N_e\left(z\right); z=60 \mathrm{km}, ···,z_{max}\right\}$. When the measurement vector is changed from $hTEC$ to $\mathsf{\Delta }hTEC$, the weighting functions of the bottom-up algorithm are also transformed from the Abel functions to a new set of functions, as shown in red in Figure 3d. Unlike the Abel function, the new weighting functions for $\mathsf{\Delta }hTEC$ have a very small contribution from higher altitudes, which provide the advantage of minimizing F-region impacts.

The linearized forward model for the measurement vector ($y$) is related to the state vector ($x$) through a weighting function K, or the Jacobians as in $K=\mathbf{\partial }y/\mathbf{\partial }x$, as follows:

$$y=y_0+K·\left(x-x_0\right)+{\mathit{\epsilon }}_{\mathit{y}}$$

(10)

where the linearization is based on the state vector $x_0$ (N_e in m⁻³) and the measurement vector $y_0$ ($\mathsf{\Delta }hTEC$ in TECu). A single N_e profile is used for the $x_0$ in Equation (10), which is a merged profile from the annual mean of IRI-2016 from 2008 for the F-region [30] and the mean FIRI E-region profile for the solar minimum condition [29]. We assume that the weighting function K is invariant with the coefficient $a_1$ (i.e., the slope of the linear function in Equation (8)). The linearization model $x_0$, $y_0$, and K are depicted in Figure 3. The measurement uncertainty of y, or ${\mathit{\epsilon }}_{\mathit{y}}$, is 0.3 m for the ${\varphi }_{exL1}$, or 1.9 TECu for $\mathsf{\Delta }hTEC$, to account for multipath, RIE, scintillation, neglection of ionospheric bending, and other measurement errors. The multipath error from reflections off the spacecraft structure is estimated to <0.2 m for COSMIC-2 [46] and <1 m for COSMIC-1 [38]. The RIE error, as shown in Figure 1, is on the order of ~0.1 m but can be larger in a strong scintillation condition. The $x$ inversion in the optimal estimation method [45] can be expressed by

$$\widehat{x}={\left[S_a^{-1}+K^T{S}_y^{-1}K\right]}^{-1}\left[S_a^{-1}a+K^T{S}_y^{-1}y\right]$$

(11)

where $\widehat{x}$ is an optimal solution to x in Equation 10 and a is the a priori of x, which is set to be same as $x_0$ in this study. $S_a=0.02·\left(5·{10}^8+x_0\right)·I$ and $S_y^{}={\mathit{\epsilon }}_{\mathit{y}}^2·I$ are covariance matrices for a and y, respectively. Note that $S_a$ is a height-dependent parameter, which is empirically determined for stable N_e inversion over a large dynamic range and variability in the D/E-region altitudes. The detailed data flow diagram of the new algorithm and changes can be found in Appendix A.

For computation efficiency of the inversion from $\mathsf{\Delta }hTEC$ to N_e, we employ a variable height range for the state vector such that $z_{max}\le h_{max}$ + 10 km. Because $\mathsf{\Delta }hTEC\left(h_t\right)$ does not have much information on N_e at altitudes above $h_{max}$, it would waste resources to carry out the N_e retrieval at extra levels above $h_{max}$. This adaptive height range in the retrieval helps to reduce the number of N_e levels in the state vector, and therefore save CPU time for the inversion calculation in Equation (11).

2.3.2. D/E-Region

The bottom-up algorithm is developed to enable and optimize the D/E-region N_e retrieval in the situations where the F-region hTEC measurements are unavailable for correcting their effects on the lower-ionospheric retrieval. It is difficult to make this correction with the onion-peeling method when the entire hTEC profile is not available. An example from Equations (9) and (10) is shown in Figure 4, where the N_e profile is retrieved up to the RO top. Since most of the COSMIC 50-Hz RO data have a top height around h_t ~ 125 km (see Appendix B), the D-region and a good portion of the E-region can be resolved, but the number of COSMIC-1 ROs started to decrease after 2017. The sampling reduction creates a problem for uniform local time coverage during the later years of COSMIC-1 mission. On the other hand, the operation from Sun-synchronous MetOp satellites has been stable throughout the mission, acquiring 100 Hz ROs up to h_t ~ 90 km for the D-region. Therefore, the MetOp-A/B/C data are quite useful for studying long-term D-region N_e variations at two Sun-synchronous local times (8–11 h and 20–23 h).

Figure 4 is a relatively quiet case where the RIE component in the ${\varphi }_{iono\_free}$ profile has an amplitude of ~3 cm with a small (~5 cm) E_s residual at h_t ~ 100 km. The D/E-region component (${\varphi }_{p\_D/E}$) in ${\varphi }_{exL1}$ is ~2 m (Figure 4b), significantly greater than the RIE and E_s errors. This ${\varphi }_{p\_D/E}$ corresponds to ~10 TECu in $\mathsf{\Delta }hTEC$ (Figure 4c). Because the observed $\mathsf{\Delta }hTEC$ is larger than the linearization profile ($y_0$) from the state vector ($x_0$), the retrieval yields an inverted N_e greater than $x_0$, as seen in Figure 4d.

The D/E-region N_e. retrievals show a good sensitivity to the diurnal variations (Figure 5), since a constant linearization profile is used in Equation 11 without any a priori information on solar zenith angle (χ). As expected for the low N_e. concentration, the retrieval result is noisier at lower altitudes. More scatters are evident in the early evening hours, especially in the E-region, suggesting the potential impacts from ionospheric scintillations [47]. The local time coverage from the COSMIC-2 is fairly uniform on a single day. By the time of this day (i.e., 1 January 2021), the six-satellite constellation had spread out in local time sampling from their initial launch orbits on 25 June 2019. The low inclination (24°) orbit also helps to cover the tropical diurnal cycle in a relatively shorter period compared to those higher-inclination orbiters.

The diurnal variation of the retrieved D/E-region N_e is generally consistent with FIRI, although it exhibits a large deviation at 60 km (Figure 5). Unlike FIRI, which is symmetric about the local noon, the RO N_e retrievals are skewed slightly toward the afternoon hours. It is clear that the morning-hour onset of the daytime RO N_e lags the FIRI curve, while the retreat from the RO in the evening hours appears lagging behind the noon-symmetric FIRI model. The daytime RO N_e retrievals are slightly higher than the FIRI at 110 km. Given that F10.7 is at 77.7 solar flux unit (sfu) on 1 January 2021, the RO N_e retrievals are generally higher, compared to the FIRI prediction for F10.7 = 75 sfu.

2.3.3. Lower F-Region

The bottom-up algorithm can be extended to retrieve the N_e in the lower F-region if the RO hTEC profile reaches a higher altitude. However, most of the high-rate RO measurements do not go above h_t ~ 120 km in the normal operation. On the other hand, MetOp-A has acquired some high-rate RO data with a top up to ~290 km, allowing to test the new algorithm for the lower F-region retrieval. Figure 6 shows the extended N_e retrievals from the ascending (nighttime) and descending (daytime) orbits in October 2021, revealing the E- to F-region transition across the meridional plane at two local times (8–11 h and 20–23 h). Because the E- and F-region dynamos are electrically connected, this global coverage in the lower ionosphere with a high spatiotemporal sampling is critically needed for studying and understanding their coupling processes.

In addition to MetOp-A, the Spire constellation also produces ROs with a top routinely up to ~175 km, higher than most of the GNSS-RO operations. The Spire’s high-rate data occasionally go up to an even higher altitude for large scintillation cases. As shown in Figure 6, these high profiles provide only sparse sampling at altitudes above 175 km, not enough to produce a reliable climatology. Below that altitude, the Spire sampling seems to be uniform. Different from MetOp-A, the Spire constellation covers all local times. In other words, the Spire zonal mean is truly daytime and nighttime from all local times, whereas the MetOp-A zonal means are from two Sun-synchronous local times (Appendix B). Nevertheless, the Spire daytime and nighttime climatologies below 175 km exhibit the distributions similar to those from MetOp-A.

2.3.4. TEC and Vertical Gradient of $hTEC\left(h_{\mathrm{t}}\right)$

The vertical gradient of $hTEC\left(h_t\right)$ profiles at the lower ionospheric h_t contains quantitative information on TEC and can be used to retrieve TEC without requiring absolute calibration of $hTEC\left(h_t\right)$. In this section we further analyzed the TEC information using the synthetic data from the January 2008 IRI-2016 N_e profiles for different geolocation and solar local time conditions. We compute TEC and $hTEC\left(h_t\right)$ from these N_e profiles and applied the same retrieval algorithm as in Equation (8) to the modeled $hTEC\left(h_t\right)$ and coefficient $a_1$. As illustrated in Figure 7a, the coefficient $a_1$ from the synthetic data and TEC are highly correlated. There is a clear difference between the daytime and nighttime $a_1$-TEC relationships, showing a smaller slope from the daytime profiles. On the other hand, TEC appears to correlate well the hTEC difference or ΔhTEC between h_t = 200 and h_t = 60 km. These sensitivities have an important application for the TEC remote sensing, because the hTEC differencing (ΔhTEC) approach does not require absolute calibration about hTEC measurements. It can be simply achieved by using the $\mathsf{\Delta }hTEC$ with respect to the value at a reference h_t. In a broader sense, it is a similar technique to the measurement vector as formulated in Equations (7) and (8).

The model simulation shows that TEC can be retrieved from the lower-ionospheric $\mathsf{\Delta }hTEC$ measurements with the reference at h_t = 60 km. The technique appears to work best for the $\mathsf{\Delta }hTEC$ measurements with the top reaching h_t = 200 km, the altitude slightly below the F2 peak. Assuming a measurement uncertainty of 1 TECu, we test this idea with the synthetic IRI-2016 data and derive a set of regression coefficients for the TEC retrieval. The synthetic $\mathsf{\Delta }hTEC$ and TEC data represent all variabilities from 2008, and the linear regression is used to develop the retrieval coefficients for $\mathsf{\Delta }hTEC$. Figure 7c,d show two TEC retrieval methods from different five-level $\mathsf{\Delta }hTEC$ data. The regressed coefficients for the five-level $\mathsf{\Delta }hTEC$ data are given by Equations (12) and (13) for the RO top reaching 220 km and 180 km, respectively,

$$\begin{gathered} TE{C}^{\prime }= 0.319·\mathsf{\Delta }hTE{C}_{140}+0.103·\mathsf{\Delta }hTE{C}_{160}-0.071·\mathsf{\Delta }hTE{C}_{180} \\ -0.226·\mathsf{\Delta }hTE{C}_{200}+0.327·\mathsf{\Delta }hTE{C}_{220} \end{gathered}$$

(12)

$$\begin{gathered} TE{C}^{\prime }=0.077·\mathsf{\Delta }hTE{C}_{100}+0.069·\mathsf{\Delta }hTE{C}_{120}+0.015·\mathsf{\Delta }hTE{C}_{140} \\ -0.086·\mathsf{\Delta }hTE{C}_{160}+0.368·\mathsf{\Delta }hTE{C}_{180} \end{gathered}$$

(13)

where TEC’ is the TEC retrieval from the five-level $\mathsf{\Delta }hTEC$ measurements. Figure 7c produces a mean standard deviation of 1.03 TECu of the retrieved TEC from five h_t levels at 140, 160, 180, 200, and 220 km, whereas in Figure 7d the retrieved TEC error increases to 1.75 TECu if the lower levels (100, 120, 140, 160, and 180 km) are used. The $\mathsf{\Delta }hTEC$ measurements near the F2 peak (h_t = 180–220 km) are generally weighted more than those from other heights, as indicated by the regression coefficients in the simulated data. The weight coefficient decreases for the $\mathsf{\Delta }hTEC$ measurements at h_t above the F2 peak (not shown), as expected for the measurements not going through the bulk of the ionosphere.

In summary, the TEC retrieval method demonstrated in Figure 7c is practically useful for the high-rate RO data with the top above 220 km. On the other hand, the method in Figure 7d is applicable to the Spire near-real-time (NRT) data when the top of RO profiles reaches h_t ~ 175 km. For accurate TEC retrievals, these high-h_t RO observations (close to the F2 peak) are more desirable. Thus, it is recommended in future GNSS-RO operations to extend the RO acquisition up to at least h_t = 220 km.

2.4. GNSS-RO Data

Global Navigation Satellite System (GNSS) provides continuous broadcast of positioning and time data from space to the ground and other satellite receivers that can be used to determine their location. There are six major GNSS constellations either in operation or development: U.S. Global Positioning System (GPS), Russian Global Navigation Satellite System (GLONASS), European Navigation Satellite System Galileo (Galileo), Japanese Quasi Zenith Satellite System (QZSS), Chinese BeiDou System (BDS), and Indian Regional Navigation Satellite System (IRNSS). In addition, civil Satellite-based Augmentation System (SBAS) for aviation safety uses geostationary (GEO) satellites to improve the accuracy and reliability of GNSS information by broadcasting the augmentation data with signal measurement error corrections. Each of these GNSS constellations is assigned with a satellite system code: G: GPS, R: GLONASS, E: Galileo, J: QZSS, C: BDS, I: IRNSS, and S: SBAS, which is used in naming every GNSS-LEO link for the RO data.

The GNSS-RO data used in this study are summarized in Appendix B (

Table A1. Summary of GNSS-RO data in this study.

LEO Satellites	Mission Lifetime	Init, Final Alt (km)	Sun-Syn (Asc ECT (1))	Lat Coverage	Top RO Ht (km)	Tracked GNSS	Max No. ROs/day
CHAMP	2001–2008	450,330	varying	90°S/N	140	G	~250
COSMIC-1 (2) constellation	2006–2020	525,810	varying	90°S/N	130	G	~4000
SAC-C	2000–2013	705	10:30	90°S/N	90	G	~300
MetOp-A	2006–2021	820	19:00 (3)	90°S/N	90	G	~720
MetOp-B	2012–	820	19:00	90°S/N	90	G	~700
MetOp-C	2018–	820	19:00	90°S/N	90	G	~650
C/NOPS	2008–2015	850,350	varying	37°S/N	170	G	~320
KOMPSAT-5	2015–	560	06:00	90°S/N	135	G	~600
TSX	2009–	520	18:00	90°S/N	135	G	~320
TDX	2016–	520	18:00	90°S/N	135	G	~320
GRACE	2007–2017	475,300	varying	90°S/N	140	G	~230
FY-3C (4)	2013–	838,850	22:00	90°S/N	135	G	~530
FY-3D	2017–	838	13:30	90°S/N	135	G	~600
FY-3E	2021–	830	05:30	90°S/N	-	G	-
COSMIC-2 (5) constellation	2019–	715,545	varying	44°S/N	90–130	G,R	~6500
PAZ	2018–	520	18:00	90°S/N	135	G	~320
Sentinel-6A	2020–	1336	varying	90°S/N	80	G,R	~830
Spire (6) Constellation	2018–	varying	varying	90°S/N	170–400	G,R,E,J	~4000 (7) ~12,000 (8)
Other (9) Constellations	2020–	varying	varying	varying	varying	varying	varying

⁽¹⁾ Ascending-orbit equator crossing time (Asc ECT). ⁽²⁾ The COSMIC1-3 spacecraft never reached the intended orbital altitude and was operated at 725 km for the rest of its mission. ⁽³⁾ The spacecraft started to drift away from the Sun-sync orbit since ~2021. A scan experiment with the high-rate data up to h_t = 300 km was conducted between 2020.161 and 2020.254. ⁽⁴⁾ The FY-3C spacecraft started to drift away from the Sun-sync orbit (SSO) from 2016 (see Appendix B). ⁽⁵⁾ The COMSIC2 NRT data contain GNSS-RO profiles from GPS and GLONASS. ⁽⁶⁾ The Spire constellation acquires RO profiles from GPS, GLONASS, Galileo, and QZSS before 2021, and BDS since 2022. ⁽⁷⁾ NOAA’s Commercial Weather Data Pilot (CWDP) NRT data published by CDAAC from September 2021 to the present. The daily RO number is from November 2021 statistics. ⁽⁸⁾ NASA’s Commercial SmallSat Data Acquisition (CSDA) data from November 2019 to the present. The daily RO number is from November 2021 statistics, of which approximately 880 are overlapped with the NOAA CWDP profile. ⁽⁹⁾ Other commercial GNSS-RO data include the constellations such as GeoOptics and PlanetIQ.

), which lists different RO missions with information such as operation period, LEO (low Earth orbit) satellite initial and final altitude, orbital precession, latitude coverage, RO top height, and number of daily RO profiles. The majority of GNSS-RO data is obtained from the COSMIC Data Analysis and Archive Center (CDAAC) distribution, which processes the data to Level-2. The Level-1b data are processed with different versions of software, namely, NRT, postprocessing (postProc), and reprocessing (e.g., with subfix “2016”). The satellites that contribute to the global GNSS-RO acquisition include CHAMP (Challenging Minisatellite Payload), SAC-C (Satellite de Aplicaciones Cientifico-C), COSMIC-1/2 (Constellation Observing System for Meteorology, Ionosphere, and Climate 1 or 2), METOP-A/B/C (Meteorological Operational Polar Satellite A/B/C), GRACE (Gravity Recovery and Climate Experiment), C/NOFS, TSX (TerraSAR-X), TDX (TanDEM-X), Korean KOMPSAT-5, Spanish PAZ, and Chinese Fengyun-3 (FY3).

3. Results

3.1. Diurnal Variations

The D/E-region N_e is a strong function of χ as the lower ionosphere is largely influenced by the Ly-α ionization of mesospheric species such as NO. To characterize the N_e morphology, we averaged all the COSMIC-1 RO retrievals from 2006–2020 to generate a monthly climatology for each 2-hourly local time, 4° latitude, and 2 km altitude bin. As shown in Figure 8 for four selected months and four selected altitudes, the new N_e data reveal several interesting features and variations in the lower ionosphere. A complete set of monthly climatology can be found in Figure S1.

Although the D/E-region N_e shows a clear χ-dependence, it exhibits strong latitudinal variations for the same χ. For example, at almost at all altitudes there is an enhanced daytime peak at the summer midlatitude during the solstice months (e.g., June and December). This peak occurs at a late morning hour slightly before noon. For the months near equinox (e.g., March and September), a dip at the magnetic equator is evident in the daytime N_e, especially at 100 and 120 km. This low N_e band, known as the “fountain effect” in the F-region, is likely an imprint of an upward plasma draft induced by the equatorial electrojet (EEJ). As expected for an eastward electric field build-up from EEJ, the E × B force could create an upward plasma drift [48]. Because of the strong vertical gradient in the D/E-region N_e, this vertical drift would manifest itself as a low N_e value compared to those at nearby latitudes without the drift.

Another noticeable feature is the asymmetry of N_e distribution about the noon. The D/E-region N_e climatology clearly shows that N_e arises slightly late in the morning with a lagged decay into the evening. The D-region N_e asymmetry about noon was also reported in ground-based observations [49]. In all monthly climatologies, the extended N_e enhancement from evening to midnight is observed. During the months near the equinox, such a prolonged N_e enhancement in the tropics is punctuated by a short decrease around LST = 19 h.

3.2. D-Region H′ and 𝛽 Parameters

The D-region (60–90 km) ionosphere is poorly characterized due to lack of N_e observations. In situ (e.g., sounding rockets) [50,51], remote sensing from incoherence scattering radar (ISR) [52], and radio wave propagation [53] are the common methods for measuring the D-region N_e [54], but their locations are sparse and the operation cost can be high. In addition, low electron concentrations in the D-region requires high power, large-sized antenna radars to obtain useful N_e measurements, which makes such systems unaffordable for wide deployment. On the other hand, high-frequency radio waves, although useful for the N_e sounding in the E-region and above, tend to pass through the D-region. At very low frequency (VLF, 3–30 kHz) and extremely low frequency (ELF, 0.3–3 kHz), radio waves are completely reflected by the D-layer and the ground surface, of which the two conducting boundaries act as an Earth–ionosphere waveguide (EIWG) to allow a low-loss long-range radio propagation. As a result, the VLF/ELF technique has been increasingly used for remote sensing of the D-region properties, including N_e [55,56,57].

To characterize the D-region N_e, the VLF/ELF observation community often uses a two-parameter D-region N_e model. As described by Wait and Spies [1964], the formula has characteristic reference height H′ (km) and exponential growth rate of N_e with height or 𝛽 (km⁻¹), i.e.,

$$N_e\left(z\right)=1.43\times {10}^{13}{e}^{-0.15H^{\prime }}{e}^{\left[\left(\beta -0.15\right)\left(z-H^{\prime }\right)\right]}\hspace{1em}{\mathrm{m}}^{-3}$$

(14)

The model parameters from fitting to VLF/ELF observations yield a typical H′ value of 65–90 km and 𝛽 of 0.3–0.5 km⁻¹ with a lower H′ value and slightly higher 𝛽 value during daytime [58,59,60,61,62,63,64]. Recently, an update was proposed to characterize a height split in the D-region N_e profiles with a four-parameter scheme, which appears to represent the daytime profiles better [65].

We used the same two-parameter model (Equation (14)) to fit the D-region N_e retrieved from COSMIC-1 (Figure 9). The H′ parameters derived from COSMIC-1 are slightly lower than those derived from the VLF observations [59,60], showing a daytime variation of 70–73 km, compared to 71–77 km from VLF. The COSMIC-1 𝛽 parameters exhibit a little variation around 0.31 km⁻¹ during the day, compared to 0.25–0.4 km⁻¹ reported from the VLF observations. For nighttime, the COSMIC-1 H′ and 𝛽 values are also lower, with H′ varying between 71 and 76 km compared to 82–86 km from VLF, and 𝛽 varying between 0.29 and 0.30 km⁻¹ compared to 0.4–0.6 km⁻¹ from VLF [61,62].

3.3. Magnetic-Field Dependence

In addition to the diurnal variation, the D/E-region N_e can be significantly modulated by the magnetic field. To illustrate the magnetic-field effect, we averaged the COSMIC-1 N_e data from all LSTs and produced a monthly map for each altitude as a function of geographical longitude and latitude. Because the N_e at low and midlatitudes is dominated by the daytime climatology, the all-time averages appear similar to the daytime maps except for high latitudes. Figure 10 shows the 70 km maps, but the N_e distributions at the E-region altitudes are similar. A complete monthly climatology of all-LST maps can be found in Figure S2. The features observed below are generally applicable to the COSMIC-1 data at 70–120 km.

As shown in Figure 10, magnetic-field modulation of the D/E-region N_e is present in all months where the longitudinal variations follow the field line at most latitudes. There is an important distinction between the high-latitude and low- and midlatitude variations on what magnetic fields are in control. At high latitudes, as expected for the domination of auroral electron precipitation, the N_e distribution is correlated better with the magnetic field in the magnetosphere (e.g., at one Earth radius, R_e). As seen Figure 10 (left panels), the correlation appears worse if it is compared to the magnetic pitch angles from the field at 100 km, but the distribution of auroral electron precipitation correlates better with the pitch angle derived from the magnetic field in the magnetosphere. In addition to the direct contribution from electron precipitation, the winter polar vortex is capable of transporting the aurora-produced NO down to the mesosphere and further enhancing the nighttime D-region N_e [66]. The fact that the polar N_e enhancements are closely associated with the magnetic pitch angle implies that such vertical transport from the polar vortex only plays a secondary role in the polar winter anomaly. As shown in the RO observations, the auroral electron precipitation does not produce a very strong polar N_e distribution as simulated under different hypothesized scenarios for the D-region ion chemistry [67].

It is worth noting that the summer-midlatitude N_e distributions in Figure 10 (June and December) bear a striking resemblance to the global E_s morphology reported in the earlier studies with GNSS-RO [18,19,20]. As stressed by Wu [31], the new D/E-region N_e data will allow a more comprehensive study of the E_s formation and its connection to the background E-region N_e concentration. The similar distribution between E_s and N_e suggests that a common process is modulating their longitudinal variations in the summertime midlatitudes.

It remains challenging to fully understand what processes drive large longitudinal variations along the same field pitch angle (Figure 10). Planetary waves, such as the migrating and non-migrating tidal waves, can perturb the D/E-region N_e distribution by modulating the NO density and temperature in the upper mesosphere. In addition, some observations show that the lightning from tropospheric thunderstorms can induce a direct decrease in the D-region N_e [68] or sharpening in the N_e vertical gradient [69,70]. The lightning-induced N_e reduction may explain the relatively lower N_e values (along the same pitch angle) in June over the American and Indian Monsoon regions where deep convection and lightning activity are likely higher than elsewhere. It remains challenging with the GNSS-RO N_e observations to separate the direct lightning effect from others, as the D/E-region N_e is strongly coupled with other processes (e.g., solar radiation, planetary waves).

3.4. Seasonal Variations

To characterize the N_e seasonal variations, we divided the monthly data into daytime, post-sunset (LST = 19 h), and nighttime bins, and plotted these binned data as a function of time and magnetic latitude. Figure 11 shows the time series of N_e at 60, 80, 100, and 120 km. To the first order, the seasonal variation of daytime N_e at these altitudes is driven by solar radiation as the χ maximum moves around the equator with season. The midlatitude maximums near the solstice months are clearly seen in the time series, whereas the seasonal minimums at the midlatitudes appear to be quite different. The minimum in the SH winter is much lower than that in the northern winter. The seasonal asymmetry in N_e is extended to the nighttime time series where the χ effect can still be seen. The nighttime time series provides a better view of the seasonal variation of polar N_e. Similar to the post-sunset result, the polar N_e has a larger concentration in the summer month, as expected for a stronger field-aligned current from the sunlit hemisphere [71,72].

A strong semiannual variation is observed in the nighttime D-region N_e with peaks near the equinox months. Several studies have suggested that the semiannual variation in the D-region could be induced by the NO concentration modulated by dynamic transport processes in the mesosphere and lower thermosphere [73,74]. In this case, the modulated NO concentration and the enhanced nighttime ionization in the D-region are correlated with a peak around the equinox. Consistent with the semiannual variation reported in these earlier studies, the COSMIC-1 observations seem to have two peaks in the tropics, but with a slightly higher concentration in October than that in March.

3.5. E- to F-Region Transition

The onion-peeling approach often produces negative or large oscillatory N_e values in the lower ionosphere [38]. These large errors make the onion-peeling retrieval unsuitable for studying the E- to F-region transition. The new N_e data, such as those with a higher RO top (e.g., Spire), can be used to describe the plasma transition from the E- to F-region with continuous height coverage and high spatiotemporal sampling. Figure 12 presents an example of monthly N_e statistics from such observations where high-RO-top (e.g., Spire) RO data are used. The retrieval covers an altitude range between 60 and 170 km and the data are averaged to 2-hourly bins in local time. More displays of Spire monthly climatology can be found in Figure S3 for the zonal mean and in Figure S4 for diurnal variations at the magnetic equator. One of the interesting features in the 2-hourly zonal mean (Figure 12) is the shift of the daytime N_e maximum from the SH E-region to the NH lower F-region. This shift implies a height-varying χ dependence of the N_e morphology in the lower F-region. Again, the equatorial dip in N_e is obvious in the late afternoon and early evening hours (i.e., LST = 15 h, 17 h, and 19 h), continuing through all altitudes in the E- to lower F-region.

The polar features from auroral electron precipitation are more pronounced in the nighttime zonal mean in Figure 12. It is also known as the polar winter anomaly where ionospheric absorption of radio waves becomes extraordinarily strong [75]. Relatively speaking, they have a nearly uniform concentration in the lower F-region, but with a greater extension to the E-region compared to the low- to midlatitude N_e. The penetration to the D/E-region seems to be deeper around the midnight hours in the NH. Compared to the D/E-region, the nighttime N_e distribution in the lower F-region is less symmetric about the equator. In the early evening hours, the lower F-region appears to have a higher N_e in the winter subtropics, but the distribution peak shifts to the summer subtropics during the predawn hours.

The results presented in Figure 12 are based on the sampling from a subset of the Spire constellation data provided to the NOAA’s CWDP program, which have ~4000 daily RO profiles. Processed by the same COSMIC software to Level-1 and Level-2, these data have only become available on CDAAC for the research community since September 2021. As the constellation continues to expand, it is anticipated that more RO profiles will yield a further improved diurnal coverage on a monthly basis, perhaps to enable one-hour intervals in local time and a spatial resolution better than the 8° × 4° longitude–latitude grid used in this study. One of the advantages with dense spatial sampling is to allow a tomographic retrieval of N_e, which can help to mitigate the horizontal inhomogeneity problem associated with the poor horizontal resolution of the GNSS-RO technique.

3.6. Solar-Cycle Variations

Characterizing the long-term D/E-region N_e variations requires stable satellite operation and uniform sampling/quality in GNSS-RO observations. Because of the strong diurnal variability in the D/E-region N_e, a non-uniform or variable sampling of local times would make the observed N_e variation difficult to interpret and prone to the sampling error from aliasing to the diurnal variation. Although COSMIC-1 had a full diurnal coverage during the early period of mission, its sampling degraded over time as several of its operating satellites stopped working. As a result, the COSMIC-1 data are not ideal for studying the solar-cycle variation. On the other hand, the MetOp observations have been stable with the longest record at two Sun-synchronous local times around 8–10 a.m. and 8–10 p.m. Since the routine GNSS-RO acquisition from MetOp goes up to ~90 km, this long record is only available for the D-region N_e. To fill in the early period (2007–2008) of the MetOp record, we added the SACC data when they had the sampling at the similar equator-crossing time (see Appendix B).

The daytime and nighttime solar-cycle variations at 70 km from the MetOp/SACC observations are highlighted in Figure 13 as a function of magnetic latitude. As expected for the sunlight-driven ionization in the D-region, the D-region N_e correlates well with the Ly-α flux in terms of the solar-cycle variation. In addition, there is a strong semiannual modulation in the magnetic tropics from both daytime and nighttime time series. Because of the presence of the dominating solar-cycle and semiannual variations, it is not straightforward to discern a quasi-biennial oscillation (QBO) modulation in the D-region N_e, which was reported in some of the early studies [76,77].

4. Discussions

4.1. Comparisons with Ionosonde Data at Hermanus

As a preliminary validation effort, the GNSS-RO E-region N_e profiles are compared against ionosonde N_e. The Hermanus (HE13N), South Africa (34.4°S, 19.2°E) ionosonde site was selected for the comparison because of the low f_min (minimum return frequency observed by the ionosondes) values over the period of interest: July 2008–August 2010. A low f_min value in the ionogram measurement is vital to derive the E-region N_e profiles. To collocate the GNSS-RO observations, RO tangent points were required to be within 2° of the Hermanus site and within 30 min of an ionosonde measurement that has an f_min below 1.2 MHz. The ionosonde data were obtained from the Digital Ionogram Database (DIDBASE, accessed 17 January 2022, https://giro.uml.edu/didbase/), and all ionograms were hand-scaled using the SAO Explorer application for ionosondes (https://ulcar.uml.edu/SAO-X/SAO-X.html, accessed 1 March 2022) to eliminate uncertainties caused by automatic scaling and ensure the quality of ionograms used in the comparison. The ionogram with sporadic-E or an uncertain E-region profile was excluded in the comparison. Over this two-year period, a total of 60 ionograms were hand-scaled for the comparison against the RO profiles.

Two examples of the ionosonde vs. RO N_e comparisons are displayed in Figure 14. The vertical line corresponds to the minimum return frequency measured by the ionosonde, f_min. The ionograms show E-region returns from f_min up to f_oE, but no measurements are obtained for the E- to F-region valley. Therefore, this comparison is limited to the altitude range between the f_min altitude and h_mE, which varies with the time of day, location, and ionospheric conditions. As shown in Figure 14, the typical starting height for ionosonde measurements is 90 km, while GNSS-RO is capable of measuring densities at D-region altitudes (see Section 3). The N_mE estimated from the RO and ionosonde techniques are in close agreement for these two examples, and the bottomside E-layer N_e gradients with respect to altitude (dN_e/dz) are also in agreement.

While many of the profiles show agreement in dN_e/dz and N_mE, the profiles are shifted in altitude with RO profiles being slightly higher, by 2 km on average, above the ionosonde profiles. This relatively small altitude difference may be due to the “internal uncertainty of the starting height of the profile” for ionosonde measurements [78]. The ionogram inversion assumptions and uncertainties were described in detail in several studies [79,80,81], revealing challenges in converting measured virtual heights to real heights for N_e. On the other hand, errors from ionospheric bending and derivation of the Earth ellipsoid model may also induce an uncertainty in the GNSS-RO H_SL, but it is expected to be $\le 1$ km.

For this comparison, we show the results obtained for both unshifted (original) and shifted profiles. The shifted profiles are obtained by adjusting the ionosonde N_e altitude to minimize the altitude difference between profiles at f_min. GNSS-RO and ionosonde-derived N_e at each height within the f_min altitude and h_mE for the 60 profiles analyzed in this comparison are displayed in Figure 15. Here, the ionosonde N_e profiles are interpolated at each GNSS-RO altitude for a direct comparison. While the R² and slope values for the linear regressions are nearly equal for the shifted and unshifted profiles, the y-intercept is closer to zero for the shifted profiles, closer to the 1:1 line that represents a perfect match between the two techniques. Overall, the densities show reasonable agreement with a larger variation for elevated densities.

Histograms of the differences in density (N_e,GNSS-RO–N_e,ionosonde) as a function of altitude are displayed in Figure 16. The altitude bias in the unshifted profiles results in an underestimation of the electron densities by the GNSS-RO technique for the altitude range of roughly 90–110 km. However, when the ionosonde profiles are shifted in altitude, this underestimation bias is mostly removed, and the density differences are slightly less than zero for most altitudes. The mean absolute error (MAE) for the unshifted profiles is 1.9 × 10¹⁰ m⁻³, while the shifted profiles’ MAE is reduced to 1.4 × 10¹⁰ m⁻³.

Finally, the averaged daytime N_e for both techniques are displayed in Figure 17 for the shifted and unshifted profiles. Daytime profiles are constrained between 0800–1600 in LST, providing a total of 22 profiles for comparison. The altitude bias is obvious in the unshifted profiles and shifting the ionosonde profiles up in altitude helps to improve agreement. While the shifted ionosonde densities are larger than the RO-derived densities on average, the mean N_e profiles agree within their estimated uncertainty at E-region altitudes. Encouraged by the preliminary comparison, we plan to carry out a further, larger validation study to include more ionosonde sites from different latitudes. The new GNSS-RO N_e data at the altitudes near the ionosonde f_min may provide an alternative pathway for pinning the starting heights during ionogram inversion.

4.2. TEC Comparisons and Maps

The TEC retrieval methods described in Figure 7 are applied to the real RO data and compared with the TEC measurements from ground-based GPS receivers. To validate the TEC retrieval methods, we use the MetOp-A data from 9–18 June 2020 when it acquired the high-rate RO data with the top up to ~290 km. To find collocated RO profiles with ground-based TEC observations, the RO TEC measurements are required within 1° × 1° latitude–longitude and 5 min windows. Figure 18 shows the RO TEC retrievals for the same four methods as illustrated in Figure 7. Similar to the conclusion in Figure 7, the method from Equation (12) works best, showing the lowest bias and standard deviation. The RO-TEC and ground-TEC are in generally good agreement along the 1:1 line. The standard deviations from the MetOp-A retrieval are higher than the simulation from the synthetic data, which may be caused by additional variability and differences in their observing times and spatial averaging where horizontal inhomogeneity can play a role.

To develop a generalized method beyond Equations (11) and (12), we obtained a set of regression coefficients for the TEC retrieval from the RO profiles with different top cutoffs, using the synthetic IRI-2016 data. This method uses all $\mathsf{\Delta }hTEC$ measurements below the RO top, and the retrieval coefficients for different RO top cutoffs are stored in a lookup table. For the RO $\mathsf{\Delta }hTEC$ profiles with the top below 180 km, the TEC retrieval error tends to increase. We found that the RO profiles with a top above 120 km can still produce a scientifically useful TEC retrieval, but the retrieval error becomes too large if the top reaches only to 90 km, such as in the normal operation with MetOp-A/B/C.

One of the advantages with the high-rate RO data is to provide a better spatiotemporal coverage for the TEC measurement. Spatiotemporal sampling is critical for characterizing the ionosphere with large diurnal and geographical variabilities. Because of the recent high number of high-rate RO profiles (see Appendix B), the 2-hourly sampling of global TEC maps can be obtained on a monthly basis from GNSS-RO observations. Figure 19 demonstrates the latest capability of dense sampling from the combined Spire and COSMIC-2 constellations, plus a few additional GNSS-RO satellites in October 2021. More examples of monthly TEC maps can be found in Figure S6. While the daily sampling from the GNSS-RO observations is still sparse, the monthly sampling from these RO observations can provide nearly global coverage over a 4° × 8° latitude–longitude grid every 2 h. Thanks to the COSMIC-2 constellation, there is little data gap in the tropical/subtropical latitudes (<45°N/S). In addition, a small number of gaps are found in extratropical and polar latitudes largely because of the coverage from the Spire constellation. FY3D helps to fill in a small sampling gap in the Spire constellation around noontime at mid- to high latitudes (Appendix B). Further reduction in data gaps at high latitudes is a benefit from other polar-orbiting satellites (MetOp-A, TSX, Kompsat-3, FY3C, PAZ).

Compared to the recent large number of RO profiles, the sampling from the COSMIC-1 constellation plus a few additions still had many regional data gaps in the 2-hourly maps for August 2008 when they were in a mission prime time (Figure 20). The unsampled regions are clearly more than in the case for October 2021. The regions with missing data appear to be randomly distributed, as the COSMIC-1 constellation had been fully deployed and spread in local time coverage. More “apparent” data gaps in the polar region are partly due to the reduced equivalent area from the 4° × 8° latitude–longitude grid.

A few salient features emerge from the 2-hourly TEC maps from October 2021 (Figure 19). First, there appears to be a trough in the NH mid-latitude that evolves with time. October 2021 was generally a quiet month, but this trough feature is absent in the background TEC model [82]. Second, an auroral contribution to TEC is evident in the nighttime SH during UTC = 11Z–17Z. The auroral contribution is generally too weak to observe in TEC except from the enhancement during substorms [83]. Third, there is UTC-dependent symmetry in the subtropical TEC about the magnetic equator. Asymmetric distributions are more pronounced for the UTC time before 07Z.

Current global TEC nowcast and forecast rely primarily on the data analyses from ground-based measurements at the International GNSS Service for Geodynamics (IGS) stations. Because the ground stations are mostly over lands, the IGS-associated analysis centers, including GFZ (GeoForschungsZentrum), JPL (Jet Propulsion Laboratory), and USNO (U.S. Naval Observatory), use various interpolation-filtering methods to fill the data-sparse regions in producing a global TEC map [82,84,85]. Thus, a large TEC uncertainty is expected over the data-sparse regions. Over oceans, satellite altimeters may fill sampling voids with a better sensitivity to TEC measurements [86]. Nevertheless, dense spatiotemporal sampling is needed to provide globally uniform quality for the TEC measurement. As demonstrated in this study, the high-rate RO data can provide such sampling and contribute to the Global Ionosphere Map (GIM) analysis for improved accuracy over data-sparse regions.

4.3. Further Improvements for the Bottom-Up Inversion

As described Section 2, in the N_e inversion the modified measurement vector is a differential hTEC profile relative to its linear variation determined from h_t = 20–50 km. This change yields two advantages: (1) significantly reducing the impact of F-region residuals on the D/E-region N_e retrieval; and (2) making the D/E-region N_e retrieval less dependent on absolute error or accuracy of the hTEC measurement. Apart from these changes, the core inversion formulation (i.e., Equation (11)) is the same in both approaches.

The same principle is applied to the TEC retrieval using hTEC differences between the measurement at h_t = 60 km and those at h_t < 220 km (Section 2.3.4). This ΔhTEC-based TEC retrieval will allow a full use of the high-rate RO data for both neutral atmospheric and ionospheric applications, and the retrieved TECs agree reasonably well with the ground-based observations in the case where the RO profile top reaches 220 km. Because the number of RO profiles is generally greater and the RO data quality (i.e., SNR and hTEC) is better than POD measurements, the high-rate RO profiles with a higher top will attract more attention in the dual applications for atmospheric and ionospheric sciences.

The bottom-up inversion algorithm has several similarities to the Abel inversion in formulation. A further development with this algorithm will be to apply the inversion technique to the 1 Hz POD measurements, some of which have the RO profile reaching to h_t = 100 km or lower. Although these hTEC profiles may not have the same quality as the high-rate RO data, they can serve as a surrogate to verify the D/E-region N_e and TEC retrievals from the bottom-up method. If both POD and RO data can be used independently for the TEC retrieval, it will increase the sampling and coverage by a significant amount. Previous N_e retrievals from the POD hTEC have been struggling in the lower ionosphere, showing large oscillations in the N_e profile [38]. Preliminary results show that the sequential optimization inversion performs better than the onion-peeling approach for retrieving N_e retrieval without artificial oscillations in the lower ionosphere.

Although it is feasible to jointly retrieve the N_e profile from the 1 Hz POD and high-rate RO hTEC measurements, the LEO–PRN pair in both observations needs to be consistent. For COSMIC-2, there are ~50% of the POD profiles that can be paired to the high-rate RO profile. Out of these matches, approximate 50% are overlapped in tangent heights. As a result, there are only ~25% of the RO profiles that may be used for jointly retrieving N_e from the D-region to F-region.

5. Conclusions and Future Work

We have extended the bottom-up N_e retrieval to the D-region (60–90 km) using the ΔhTEC measurement derived from high-rate GNSS-RO data. The new algorithm can produce an N_e profile up to 180 km if the high-rate RO top reaches this height. The optimal estimation inversion has been updated to handle both measurement vectors hTEC with the Abel weighting function and ΔhTEC with the “bottom-up” weighting function. This flexibility allows the algorithm to process the podTEC data, if needed, for the N_e retrieval. In addition to the D/E-region N_e, a new TEC retrieval technique was developed using the high-rate RO data with a top above 120 km. For better characterizing the E- to F- N_e transition and the novel TEC retrieval, it is recommended to have the routine GNSS-RO acquisition up to h_t = 220 km.

The RO N_e retrieval was compared briefly with the ionosonde observations at the Hermanus, South Africa site. A generally good agreement was found in the E-region, with the RO N_e profile being lower in density and shifted upwards slightly in altitude. Encouraged by the preliminary comparison, a greater validation effort is planned to include more ionosonde sites from different latitudes.

The morphology of new GNSS-RO N_e data revealed many interesting features in the diurnal, seasonal, solar-cycle, and magnetic-field-dependent variations. While the D/E-region N_e is a strong function of solar zenith angle (χ), it exhibits strong latitudinal variations for the same χ, and its distribution is asymmetric about noon. The magnetic-field modulation of N_e varies from month to month. There are large longitudinal variations along the same pitch angle of magnetic field. The summer-midlatitude N_e distributions in June and December closely resemble the global E_s morphology, suggesting that the same processes likely drive these geophysical variations. In the polar region, the N_e distribution correlates better with the pitch angle derived from the magnetic field in the magnetosphere than from the 100 km, as expected for the magnetosphere-driven auroral electron precipitation. There is a clear semiannual variation in the nighttime zonal mean N_e in the D-region with peaks near the equinox months. We were able to derive the daytime and nighttime solar-cycle variations in the D-region N_e from the MetOp RO data that had stable operation and uniform sampling at ~9 a.m. and ~9 p.m. local times. There is a good correlation between the long-term N_e variations and the F10.7 flux during 2007–2021.

Spatiotemporal sampling is critical to characterize large diurnal and geographical variabilities in the ionosphere. Because there are more high-rate RO measurements than podTEC, it provides a clear advantage to sample the D/E-region ionosphere better with the high-rate RO observations. The combined spatiotemporal observations from COSMIC-2 and Spire constellations have provided an unprecedented coverage for studying the ionosphere since 2021. As the constellation continues to expand, it is feasible to improve the diurnal sampling to one-hour intervals and a spatial sampling better than the 8° × 4° longitude-latitude grid, as used in this study. The dense spatial sampling will perhaps allow a tomographic retrieval of N_e, to improve the horizontal resolution of the GNSS-RO technique.

For future algorithm developments, we plan to apply the retrieval to the podTEC and ionPhs data to obtain a full N_e profile in the ionosphere. The podTEC data from CDAAC contain the hTEC profile with absolute calibration that can be readily processed with the algorithm developed in this study for an Abel inversion of N_e. The Abel inversion can be further improved to include the podTEC data from both positive and negative elevation angles, making it less dependent on the orbital altitude of the RO receiver. It is also feasible to develop an algorithm for the joint retrievals of TEC and N_e using the $\mathsf{\Delta }hTEC$ profile, which should work in the cases where the absolute hTEC calibration is challenging. Finally, we will conduct a retrieval exercise for the tomographic inversion of TEC and N_e once the GNSS-RO constellations begin to provide a sufficient sampling density.