New Index to Characterize Ionospheric Irregularity Distribution

Characterization of the global ionospheric irregularities as a function of local time, longitude, altitude, and magnetic activities is still a challenge for radio frequency operations, especially at the low‐latitude region. One of the main reasons is lack of observations due to the unevenly distributed instruments. To overcome this constraint, we developed a new spatial density gradient index (DGRI) at two different scale sizes: small scale and medium/large scale. The DGRI is derived from in situ density measurements onboard recently launched constellation of low‐Earth‐orbiting satellites (COSMIC‐2 and ICON) at the rate of 1 Hz. Hence, the DGRI appeared to be suitable parameter that can be used as a proxy to describe the essential features of ionospheric disturbances that may critically affect our radio wave application as well as to identify the “all clear” zone as a function of longitude, latitude, and local time—at a refreshment rate of 30 min or less.

Thus, it is highly essential and critically important for operations to develop an ionospheric index that can accurately characterize the presence and absence of ionospheric irregularities.This is in the same way the geomagnetic indices (e.g., Kp and Dst indices) that are used for describing the level of geomagnetic activity as well as for estimating the perturbation degree of the ionosphere.However, the geomagnetic indices are developed to quantify the global energy input from the space, mainly from the magnetosphere, and may not be always suitable for estimating the level of ionospheric perturbations.Equatorial ionospheric small-scale (sub-km) irregularity patterns may be explained by at least two mechanisms: (a) the changes in Rayleigh-Taylor (RT) instability due to enhance ment of dusk sector E and F region conductivity and hence vertical plasma drift (prereversal enhancement [PRE]) (Sultan, 1996), (b) the forcing from a lower thermosphere (e.g., the gravity wave [GW] seeding) that provide adequate seeds to the bottom side ionosphere to elicit ionospheric irregularity (Fritts et al., 2008;Oberheide et al., 2015;Hysell et al., 2017;Yizengaw & Groves, 2020).This indicates that ionospheric perturbations also occur during geomagnetically quiet period or during the time when geomagnetic indices show no activity at all.This clearly indicates that the ionospheric perturbations cannot be described sufficiently well by only using geomagnetic activity indices, which only describe the forcing from space not from below.Therefore, to quantitatively describe the level of ionospheric perturbation, development of ionospheric perturbation index is essential.Different ionospheric perturbation indices have been developed using ground based GNSS total electron content (TEC) (Jakowski et al., 2012;Pi et al., 1997) and ionosonde (Tsagouri et al., 2000).However, some of these indices only cover certain area where the ground GNSS and ionosondes are available.The two other additional limitations for indices derived from GNSS TEC are (a) lack of properly spaced receivers for the index that requires two closely spaced receivers and (b) the assumption/consideration of the background ionosphere drift and the speed of GNSS ionospheric pierce point as the same.For several decades, different group applied various methods to the in situ plasma density data to automatically detect occurrence of ionospheric irregularities, including ΔN/N (e.g.Huang et al., 2014;Roddy et al., 2010;Smith & Heelis, 2017), root mean square deviation (e.g., Kil & Heelis, 1998), delta log(N) (e.g.Burke et al., 2004), absolute density perturbation after high pass filtration/ polynomial fitting (e.g.Buchert et al., 2015;Xiong et al., 2010), rate of change of density (e.g., Jin et al., 2020), and more sophisticated approaches as bubble index based on combination of magnetic field and plasma density observations (Park et al., 2013).Each method has its own advantages and shortcomings.One of the shortcomings is characterizing the contribution of spatial and temporal variation to the density irregularities detected by the in situ measurement onboard LEO satellites.It is a well-known fact that the in situ density irregularities include both temporal and spatial variability of the ionosphere.The question is-which one is the dominant contributor for the in situ density irregularities?Since the instrument onboard LEO satellite is moving fast (∼7.5 km/s) and does not sample the density of the same region continuously, the major source of in situ irregularities may be due to the spatial variability of the ionosphere not due to temporal variability.Even the density fluctuation from the ground GNSS measurements that samples a confined region represent a mix of the spatial (due to the movement of ionosphere piercing point) and temporal variability of the ionosphere (Jakowski et al., 2005(Jakowski et al., , 2012)).
Therefore, to characterize the spatial gradient contribution to the in situ density irregularities as well as to address all the limitations of ground-based index mentioned above, we present a new and robust ionospheric gradient index that can properly estimates the horizontal density gradient with different scale size using in situ density measurement onboard two new missions-COSMIC-2 and ICON.The new ionospheric disturbance gradient index can overcome several drawbacks, such as global coverage that include over the ocean, large scale (wide) bubble detections, and refreshment rate.Hence, it may be a suitable index to characterize different scale size irregularities/bubbles and identify the global irregularity/scintillation "all clear" zone for operation at the refreshment rate of 30 min or less.The paper also presents important statistical results produced using only 2 years of observations from these two new missions, whereas it required 5-10 years of data accumulation for previous satellite missions with higher orbit inclination to produce similar statistical results.

Data Description and Methodology
The in situ ion density measurement, onboard COSMIC2 and ICON satellites, at the rate of 1 Hz corresponds to a spatial scale of about 7.5 km.The in situ density deviation or irregularities across this spatial scale, which is relevant to cause L-band scintillations at GNSS frequencies in the order of its Fresnel scale.The COSMIC-2 is the constellation of six full-size equatorial orbiting satellites that are deployed onto six evenly spaced circular orbital planes of 24° inclination at an altitude of about 550 km.Each COSMIC-2 satellite orbits with a set of three identical scientific instruments onboard, namely: advanced Tri-GNSS (TGRS) receiver that tracks signals not only from Global Positioning System but from the Russian GLONASS (In Russian: GLObalnaya NAvigazionnaya Sputnikovaya Sistema), the Ion Velocity Meter (IVM), and the Radio Frequency Beacon (Schreiner et al., 2020).The Ionospheric Connection explorer (ICON) is also an equatorial orbiting satellite with an inclination of 27° and at 575 km altitude (Heelis et al., 2022).In addition to several other instruments, ICON also orbits with IVM onboard.The IVM instrument provides in situ density at the rate of 1 Hz, from which we derive the ionospheric perturbation gradient indices.
In this study, we derived spatial in situ density GRaDient Index (GRDI), from IVM in situ density observations at the rate of 1 Hz, to characterize small-and medium/large-scale ionospheric plasma irregularities.Unlike other indices mentioned above, GRDI provide two distinct scale size indices that characterize small and medium-to-large scale irregularities of the low-latitude region.While the small scale GRDI characterizes ionospheric plasma irregularity at the scale of 20 km, the medium-to-large scale GRDI characterizes irregularity at the scale size of 100 km and more.The indices are calculated independently for each space craft.
The first step to estimate GRDI is to calculate the in situ density gradient (GRD) on a sliding window along the satellite track; and can be estimated by taking the difference between in situ density measurement at time (   ) and  ( + Δ) and divided by the distance covered by the satellite during  Δ period.For small and medium-to-large scale irregularity indices the time intervals  (Δ) are different.Hence, to characterize irregularities in the order of 20 km scale size, a satellite with a speed of ∼7.0 km/s needs to travel for at least 3 s.Similarly, to capture irregularities at a scale size of about 110 km or more, the satellite needs to travel for at least 15 s.Therefore, the time intervals required to estimate the small and medium-to-large scale irregularity indices are  Δ = 3s and  Δ = 15s , respectively.The distance,  (), can be estimated in either of the two different ways: (a) the distance between the locations (longitude/latitude) of the satellite at time (   ) and  ( + Δ) or (b) by multiplying the speed of the satellite (  sat ) with the time elapsed  (Δ) .
Where,  GRD is the mean of GRD for   data points.Since the GRD is calculated on a sliding window and has a value for every second, the GRDI has also a time series of 1 second.If data gaps or outliers encountered along the satellite pass, the data will be divided into segments (before and after the data gaps/outliers) and the computation of DGRI along each segment be processed separately.

Results and Discussion
The performance of the gradient indices that we described above have been tested with different type of in situ density irregularity structures and checked if the indices (both small and medium-to-large scale) accurately captured the irregularities detected by in situ measurements.Figure 1 shows different in situ density (second panels), observed at different dates and regions.The top panels indicate the ground tracks (black curve) of the LEO satellites and the precise locations where irregularities (color coded thick curves) are observed.The first example (left panels) exhibited two types of density structures.The first one is large scale structure (LSS) with smooth density peaks, labeled as P1, P2, P3, and P4.The second structure is the small-scale depletions (bubbles) that are imbedded inside the LSS.The middle panels depict an example of a smooth declining background density magnitude, and inside it, small scale density depletions are exhibited.The third example (right panels) represent the type of background density fluctuation without any clear bubbles imbedded in it.In all three different types of in situ density structures, both small (third panels from the top) and medium-to-large (bottom panels) scale indices accurately capture these density dynamics/irregularities.Since ionospheric bubbles tend to form into wedge-like structures along the geomagnetic field line, the in situ density observations at COSMIC-2 or ICON altitudes can be used to map the irregularities back-along the field-to their highest altitude (apex height) at the geomagnetic equator (Mendillo & Tyler, 1983;Sahai et al., 1994).Hence, the pattern of in situ density and the gradient indices, and the geographic locations of irregularities/bubbles (thick curves in the top panels) are color coded with the apex altitudes.
The geolocations of bubbles, as identified through these gradient indices, are also validated with an independent bubble observation, using Global-scale Observations of Limb and Disk (GOLD) ultraviolet (UV) imager onboard commercial communications satellite in geostationary orbit at 47.5°W longitude (Eastes et al., 2020).The top panel in Figure 2 depicts bubbles (dark stripes across magnetic equator in the gray scale contour map) as imaged by GOLD UV spectrometer along with the GRDI irregularity locations along the ground tracks of three different COSMIC-2 satellites (FM2, FM3, FM4).The color coded (with apex altitude) thick curve along each FM curve shows the geolocation of irregularities detected by in situ gradient index with values of small scale GRDI > 0.5  cm −3 ∕km .The apex altitude color index is shown on the right side of the bottom three panels.The two independent observations exhibited excellent agreement.The second panel from the top shows in situ density as a function of local time, and different colors depict in situ density observed by different satellites.The corresponding small and medium/large scale GRDIs are also shown in the third and fourth panels from the top.
The top panel in Figure 2 also presents another important phenomenon-irregularity/bubble coverages over a wide swath of longitudes.Although part of the region was out of GOLD's field of view, the GRDI shows that the bubble coverage in fact extends all the way to west Africa.This indicates that nearly a third of the global equatorial region was covered with ionospheric irregularities, making the region unsafe for radiofrequency operations.This demonstrates the importance of in situ DGRI to identify the global equatorial irregularity coveragewith a refreshment rate of 30 min or less.Unlike the ground-based irregularity index or GOLD images that have limited geographic coverage, in situ gradient indices from seven (ICON and COSMIC-2 missions) LEO satellites allow us to identify the global, including over the ocean, equatorial irregularity coverage.Figure 3 shows a typical two dimensions (longitude/latitude) global irregularity coverages in 30 min (top panel), 60 min (middle panel), and 2 hr (bottom panel) time intervals.The locations of bubbles are indicated by the thick curve, color coded with the magnitude of small-scale DGRI values.The interesting aspect is that within 30-min interval the global equatorial region is at least covered by one or two LEO satellites.The GOLD UV data on the corresponding date and time also detected bubbles in the same region where DGRI indicated the presence of bubbles.GOLD only detected a portion of bubble region (nearly the entire nightside sector at the given universal time) due to its limited field of view.The statistical spatial gradient index distribution pattern can also be used as another method of DGRI validation.
From both ground-and space-based observations as well as from modeling results, equatorial irregularity has a well-established global and seasonal distribution pattern-maximum irregularities occurred near-equinox, where the terminator and field lines are aligned (Tsunoda, 1985;Yizengaw & Groves, 2018).The statistical DGRI, presented in Figure 4, shows similar seasonal and global distribution-DGRI maxima occur along the locations where the solar sunset terminator and geomagnetic field lines are parallel as is depicted by two black curves in the bottom panel.Figure 4 also show two other noticeable patterns.The first one is the DGRI enhancement during June solstice centered in the African and partly in the west Pacific sectors (bottom panel-averaged in 2-days by 5° days/ longitude bin over the given time interval and for all years).Similar observations have been reported before and associated it to the forcing from lower thermosphere (e.g., gravity waves) instead of the conventional plasma physics hypotheses, such as RT instability (Huang et al., 2014;Yizengaw & Groves, 2020).The second phenomena exhibited in Figure 4 is the prominent altitude extension of bubbles in the African sector as shown in the second panel from the bottom, where the data during the given time interval and for all years is averaged in 20 km by 5° altitude/longitude bins.Since high DGRI values refer the steep gradients or deep bubbles, the presence of strong DGRIs at higher apex altitudes (upto 1,050 km), shown between 20°W and 30°E longitudes, indicate strong (deeper) bubbles penetrate to higher altitudes.Otherwise, the bubbles, with low DGRI values, that appear at higher apex altitude could be fossil bubbles (e.g., Kil et al., 2019).Hei et al. (2005) and Burke et al. (2004), using satellite observations also reported similar pattern, and concluded that bubbles in the African region rise to high altitudes (up to 1,000+ km) more often than those in other longitudes.Different driving mechanisms have been suggested for the longitudinal dependence of apex altitude, which is beyond the scope of this paper but will be the subject of a follow up study.
The second panel from the top in Figure 4 shows the local time distributions (averaged in 15-min by 5° loclatime/longitude bins for all years) of DGRI at different longitudes, exhibiting post-midnight bubbles (with significant DGRI but very much weaker than the pre-midnight values) at all longitudes.Multiple previous studies have concluded that post-midnight bubbles are the extension of bubbles generated during pre-midnight local time sector (Huang et al., 2014).Other studies, using ground based passive VHF (Yizengaw et al., 2013) and active backscatter (Patra et al., 2009;Rodrigues et al., 2019) radars, even observed post-midnight strong scintillation and field-aligned irregularity structures, respectively, during the nights when no pre-midnight irregularity pattern observed.All this confirms that the DGRI index can be used as a proxy to characterize ionospheric bubbles/irregularities and identify "all clear" zone at all local times.
The DGRI is also very important parameter to characterize the day-to-day ionospheric bubble global coverage.The top panel in Figure 4 presents global irregularity coverage (averaged in 2° by 5° latitude/longitude bins) in 1 day during pre-midnight (19:00-24:00LT) sector, indicating that nearly the entire equatorial regions were not safe to operate radio wave application during the nightside of 2 October 2022.Thus, the ability to characterize and evaluate the risk of bubble occurrence on a daily basis is also useful for accurate communication and navigation applications.

Advantage of Spatial Gradient Index
Cutting the field-aligned equatorial ionospheric density depletions along LEO satellites (COSMIC-2 and ICON) orbital altitudes characterize the bubbles only in the horizontal direction.This provides an excellent condition to develop spatial gradient index.The possible scenarios of in situ density perturbations in the ionosphere are illustrated in the latitude versus longitude schematic diagram shown in Figure 5.In this scenario, the in situ density captures different size of depletions (black curves), associated with plasma bubbles (blue regions), when the satellite traverse through it along its low-inclination orbit (pink line).The odd and even numbers depict the background density and bubbles with different sizes, respectively.Sometimes bubbles cover wide area (e.g., bubbles #8).It has been observed and confirmed with models that the larger-scale bubbles scenario is believed to be created by a RTI that starts from the bottom side ionosphere and then rise to higher altitude and develop spatial gradients that triggers further instabilities in a cascade from larger to small-scale structures (Abdu, 2005;Retterer & Roddy, 2014).Since the satellite travel fast and cover more distance in a few seconds, such wide bubbles could not be fully captured by the index derived from the time rate of change of in situ density.The satellite requires more than 20 s to cross a wider bubble (e.g., bubble #8) and the time rate of change of in situ density for every two-or five-seconds intervals could not capture the wide bubbles.Because, inside the bubble the in situ density is nearly uniform and the change in density between two points and hence the index derived from it become nearly zero.For example, Jin et al. ( 2020) developed an index derived from the time rate of change of in situ density and characterize plasma irregularities at high-latitude region.Since the satellite is very fast and sweeps large distance in a few seconds, crossing irregularity structures at different scale size, taking the time rate of change of density for every five or 1 second intervals may fail to capture wide bubbles (∼>45 km wide or takes ∼6-s for LEO to cross such wide bubbles).The rate of change of in situ density within a wide bubble become nearly zero, providing wrong index value.However, the index derived from the spatial in situ density gradients, described in Section 2, can capture such wide bubbles-at least using the medium/large scale gradient index.For every 15-s interval at least one of  () or  ( + Δ) , in Equation 1, be outside the bubble.Thus, the spatial DGRI that we introduced in this paper is a convenient method to capture the density depletions/ bubbles that has upto 200 km horizontal width.This demonstrated that DGRIs are in-deed perfect proxies to characterize the spatial density gradients and identify the global "all clear" zone at a refreshment rate of 30-min or less using the near real time data available for operation from COSMIC-2.However, it also has another limitation.Since most of LEO spacecrafts has fixed altitude orbital plane and only samples irregularities in the zonal not in the vertical direction, in situ density sampling could possibly miss capturing the irregularities/bubbles if they are below or above the satellite's orbital altitude.Hence, very low (below threshold value) DGRI values do not necessairly indicate no bubbles/irregularities in the region.This could be considered as a limitation for our spatial gradient index.

Conclusion
Characterization of the global ionospheric irregularity distributions is critically important for the application of radio wave propagation, and also imperative when developing applications and systems.The DGRI we developed from in situ ion density measurements at the rate of 1 Hz appeares to be suitable parameter to characterize ionospheric disturbances.The DGRI not only captures irregularity with different scale size, but also exhibited identical seasonal and global irregularity distribution that has been well accepted from ground-and space-based observations as well as from the model run outputs.Therefore, the gradient index that we introduce in this study can describe essential features of ionospheric perturbations that may critically affect our radio wave application.It also overcome the limited spatial coverage of ground-based observations and provide global bubble characterization and hence "all clear" zone identification map at a refreshment rate of 30-min or less.

Figure 1 .
Figure1.The black thin and color-coded thick curves in the top panels represent the ground tracks of LEO satellites and the location of bubbles, respectively.The in situ density, small and medium-large scales irregularity indices are shown in second, third, and fourth panels from the top, respectively, and all are color coded with Apex altitude.

Figure 2 .
Figure 2. Presents the comparison between GOLD UV imaged bubbles and irregularity locations identified by GRDIs.The top panel shows that both GOLD UV instrument (gray scale contour) and GRDI index (color coded with apex altitude along COSMIC satellite ground tracks), detected bubbles/irregularity at the same region and time.The second panel from top show in situ density as a function of local time-different color depicts different LEO satellites.The corresponding small and medium/large scale GRDIs are shown in the bottom two panels with a threshold values (indicated by horizontal dashed lines) of 0.5  cm −3 ∕km and 0.25  cm −3 ∕km , respectively.

Figure 3 .
Figure3.The two dimensions irregularity coverage in 30 min (top panel), 60 min (middle panel), and 2 hr (bottom panel) time intervals.While different color thin curves represent different LEO satellites, the color-coded thick curves depict the location of bubbles/irregularities.The slightly tilted vertical dashed and solid lines indicate the dusk (left side) and dawn (right side) terminator lines.The dashed lines in all panels represent the terminator lines at the start of time interval, in this case at 00:00 UT.Similarly, the solid tilted vertical lines represent the terminator lines at the end of the time intervals, which is at 04:30 UT (top panel), 05:00 UT (middle panel), and 06:00 UT (bottom panel).

Figure 4 .
Figure 4.The top panel shows 1 day global irregularity coverage during pre-midnight time.The bottom three panels shown the statistical two dimensions GRDI distributions as a function of local time versus longitude, apex altitude versus longitude, and day of the year versus longitude, respectively.The two black curves in the bottom panel indicates the location where the solar sunset terminator and geomagnetic field lines are parallel.The black curve in the second panel from the top shows the integrated (between 19:30 and 23:00 LT) value of GRDI (scale shown at the right side) as a function longitude.

Figure 5 .
Figure 5.A cartoon figure that shows the possible different type of bubbles as detected by in situ (black curve) measurement when the satellite crosses the background (green) and depleted (blue) density structures.