Isolated ionospheric disturbances as deduced from global GPS network

We investigate an unusual class of medium-scale traveling ionospheric disturbances (MS TIDs) of the nonwave type, isolated ionospheric disturbances (IIDs) that manifest themselves in total electron content (TEC) variations in the form of single aperiodic negative TEC disturbances of a duration of about 10 min (the total electron content spikes, TECS). It was found that TECS are observed in no more than 1-2 % of the total number of radio paths. We present the results derived from analyzing the dependence of TECS parameters on local time, and on the level of geomagnetic activity. The TECS amplitude exceeds at least one order of magnitude the TEC fluctuation intensity under"background"conditions. To analyze TECS dynamic characteristics the event of 5 October, 2001 was used.


Introduction
Of the known ionospheric irregularities of a different class, mid-latitude isolated ionospheric disturbances (IIDs) stand out as a highly unusual type. The past 40 years saw a consistent interest in the study of the origin of IIDs that was aroused due to difficulties in determining an adequate mechanism for IID generation in mid-latitudes, as well as by the fact that the IID have a marked effect on amplitude and phase characteristics of transionospheric signals from radio engineering communication and navigation systems (Afraimovich et al., 1992) by causing serious malfunctions of these systems.
A large number of publications (e.g., Karasawa, 1985;Titheridge, 1971), including a review by Bowman (1989) were devoted to the study along this line. IIDs are detected when recording amplitude and phase scintillations of transionospheric radio signals in the form of rarely occurring single aperiodic negative impulses with a duration from a few to several tens of seconds (Karasawa, 1985). To name this uncommon type of scintillation Karasawa (1985) seems to be the first to coin the term "spikes-type" (S-) scintillations. Karasawa et al. (1985) noticed from a long-term recording of the signal from the geostationary MARISAT satellite at 1.5 GHz frequency that synchronous with amplitude S-scintillations, there occur similar-appearing changes of the rotation angle of polarization plane that are proportional to a corresponding disturbance of total electron content (TEC). Anomalous fluctuations, recorded during 13 months of observation, occur predominantly in the night-time and last from 5 s to 2 min. The diurnal dependence of the S-type oscillations shows two distinct peaks: 09:00-15:00 in the daytime, and 20:00-01:00 at night. As far as the seasonal dependence is concerned, however, a tomary to associate the occurrence of S-type oscillations with diffraction or interference from small-scale irregularities, "blobs" and "bubbles", generated in the ionosphere. Titheridge (1971) found that amplitude and phase S-scintillations are caused by refraction and diffraction effects at the propagation of the transionospheric signal in a medium with IIDs and presented the corresponding formulae for estimating these effects as a function of relationship of the wavelength of the radio wave, the irregularity size and the sounding geometry (LOS to the satellite and the distance to the layer with To tackle these questions requires statistically significant sets of experimental data with good spatial and temporal resolution in order to gain insight into not only morphological but also dynamic IID characteristics: the direction of travel, the propaga- The objective of this paper is to study the morphology and spatial and temporal properties of IIDs using data from a global network of GPS receivers. Following Karasawa et al. (1985), the term TECS (total electron content spikes) will be used here to designate the IID-induced TEC disturbances. The sample statistic of the occurrence frequency and morphology used in this study does refer to TECS recorded from GPS data. Within the framework of certain model representations, using these data it is possible to reconstruct amplitude and spatial characteristics of local electron density disturbances, i.e. of IIDs themselves. On this basis, the term IIDs will be used below interchangeably with the term TECS. Section 2 describes the method for detecting the TECS obtained in our study. Section 3 presents the TECS morphology. Section 4 is devoted to a detailed analysis of the spatial and temporal properties of IIDs by considering the most pronounced manifestation of TECS on October 5, 2001 in California, USA. The discussion of results compared with findings reported by other authors is presented in Section 5.
Our comparison of IID characteristics with geomagnetic field variations used data from near-lying magnetic variation stations of the INTERMAGNET network (address: http://www.intermagnet.org).
where L 1 λ 1 and L 2 λ 2 are additional paths of the radio signal caused by the phase delay in the ionosphere, (m); L 1 and L 2 represent the number of phase rotations at the frequencies f 1 and f 2 ; λ 1 and λ 2 stand for the corresponding wavelengths, (m); const is the unknown initial phase ambiguity, (m); and nL are errors in determining the phase path, (m).
Phase measurements in the GPS can be made with a high degree of accuracy corresponding to the error of TEC determination of at least 10 14 m −2 when averaged on a 30-second time interval, with some uncertainty of the initial value of TEC, however (Hofmann-Wellenhof et. al, 1992). This makes possible detecting ionization irregularities and wave processes in the ionosphere over a wide range of amplitudes (up to 10 −4 of the diurnal TEC variation) and periods (from 24 hours to 5 min). The unit of TEC T ECU, which is equal to 10 16 m −2 and is commonly accepted in the literature, will be used in the following.
Primary data include series of "oblique" values of TEC I 0 (t), as well as the corresponding series of elevations θ s (t) and azimuths α s (t) of the LOS to the satellite calculated using our developed CONVTEC program which converts the GPS system standard RINEX-files on the INTERNET (Gurtner, 1993).
Series of the values of elevations θ s (t) and azimuths α s (t) of the LOS to the satellite were used to determine the coordinates of subionospheric points, and to convert the "oblique" TEC I 0 (t) to the corresponding value of the "vertical" TEC by employing the technique reported by Klobuchar (1986) where R z is the Earth's radius, and h max =300 km is the height of the F 2 -layer maximum. All results in this study were obtained for elevations θ s (t) larger than 30 • .
The technology of global detection of TEC disturbances that was developed at the ISTP SB RAS makes it possible to select -in the automatic mode from an extensive amount of experimental material -TEC disturbances which can be classed as TECS.
TECS were selected by two criteria. TEC variations were selected first, the standard deviation (rms) of which exceeded the prescribed level ǫ. The statistic of TECS discussed in this paper was obtained for ǫ = 0.1 T ECU. Then, for each filtered series we verified the fulfilment of the "singleness" condition of the TEC overshoot.  The relative amplitude of such a response A min /I 0 has a significant value, 2%. We used, as the background value of I 0 , the absolute "vertical" TEC value I 0 (t) for the site located at 7.5 • S; 105 • E, obtained from IONEX-maps of TEC (Mannucci, 1998).
It should be noted that the above examples both refer to the same time interval and to the stations spaced by a distance over 1300 km. This indicates a local character of the phenomenon and is in agreement with the overall statistic characterizing its spatial correlation (see Section 3).
For each of the events satisfying the above TECS selection criteria, a special file was used to store information about the GPS station name and geographic latitude and longitude; GPS satellite PRN number; amplitude A min ; time t min corresponding to the minimum value of the A min amplitude; and about the TECS duration ∆T . The sample statistic, presented below, was obtained by processing such files. As is evident, the autumn is represented best statistically. Fig.2b shows the seasonal dependence of the number of TECS, N.    The availability of a large number of stations in some regions on the globe, for instance, in California, USA, and West Europe, furnishes an opportunity to determine not only the temporal but also spatial characteristics of TECS. In order to estimate the radius of spatial correlation of events of this type, the number of cases was calculated where TECS within a single 2.3-hour time interval were observed at any two GPS stations spaced by a distance dR. Fig. 3c presents the histogram of the number of such cases P (dR) as a function of distance dR. It was found that the localization of TECS in space is sharply defined. In 90% of cases the distance dR does not exceed 500 km.

SADM-GPS method
The methods of determining the form and dynamic characteristics of TIDs that are used in this study are based on those reported in (Mercier, 1986;Afraimovich, 1997;Afraimovich et al., 1998;1999;2000c).
We determine the velocity and direction of motion of the phase interference pattern (phase front) in terms of some model of this pattern, an adequate choice of which is of critical importance. In the simplest form, space-time variations in phase of the transionospheric radio signal that are proportional to TEC variations dI(t, x, y) in the ionosphere, at each given time t can be represented in terms of the phase interference pattern that moves without a change in its shape (the non dispersive disturbances): where u x (t) and u y (t) are the displacement velocities of intersection of the phase front of the axes x (directed to the East) and y (directed to the North), respectively.
It should be noticed, however, that in real situations this ideal model (3) is not realized in a pure form. This is because that the TIDs propagate in the atmosphere in the form of a dispersing wave packet with a finite value of the width of the angular spectrum. But in the first approximation on short time interval of averaging compared to time period of filtered variations of TEC, the phase interference pattern moves without a substantial change in its shape.
A Statistical, Angle-of-arrival and Doppler Method (SADM) was proposed by Afraimovich (1997) for determining the characteristics of the dynamics of the phase interference pattern in the horizontal plane by measuring variations of phase derivatives with respect to the spatial coordinates I ′ x (t), I ′ y (t), and to the time I ′ t (t). This permits the determination of the unambiguous orientation of α(t) of the wave-vector K in the for GPS-arrays (SADM-GPS) based on a simple model for the displacement of the phase interference pattern that travels without a change in the shape and on using current information about the angular coordinates of the LOS: the elevation θ s (t) and the azimuth α s (t).
The method SADM-GPS makes it possible to determine the horizontal velocity V h (t) and the azimuth α(t) of TID displacement at each specific instant of time (the wave-vector orientation K) in a fixed coordinate system (x, y): where w Series of θ s (t) and α s (t) are used to determine the location of the subionospheric point, as well as to calculate the elevation θ of the wave vector K of the disturbance from the known azimuth α (see formula (5)).
Since the distance between GPS-array elements (from several tens to a few hundred geometry at the height near the main maximum of the F 2 -layer is identical to that on the ground. We used formula (5)  The phase velocity modulus V can be defined as
An analysis of the distribution of the azimuths P (α) (Figs. 7b, 7e, 8b, and 8e) shows a clearly pronounced northward direction of TECS displacement. The elevation of the TECS wave vector, determined from the aspect condition (5), has mostly a small positive value (Figs. 7c, 7f, 8c, and 8f).

The anisotropy and sizes of IIDs
Let us consider in greater detail the "traces" A, B, C, and D. Fig. 6 (a -d)  The IID anisotropy was analyzed by determining the "contrast" C (Mercier, 1986).
We calculated the ratio C N,E : where σ N and σ E are the standard deviations of the corresponding series of the TECS coordinates N i and E i . These series were obtained by transforming the initial series N ′ i and E ′ i by rotating the original coordinate system (N, E) by an angle β: Mercier (1986) showed that it is possible to find such a value of the rotation angle

Estimating the relative IID amplitude
Let us now obtain the mean estimate of the relative amplitude of a local electron density disturbance typified by the IID of October 5, 2001.
A mean TECS absolute amplitude over California equal 0.1 T ECU (see Fig.1c, f). As the background value of I 0 , we used the absolute "vertical" TEC value of I 0 (t) obtained from IONEX-maps of the TEC (see Fig.10c). These maps with two-hour temporal resolution were constructed using the well-known methods and are placed on the Internet site ftp://cddisa.gsfc.naa.gov/.  Fig.5f).
Comparison of Fig. 10c and d reveals that the greatest TECS occurrence probability corresponds to the night-time hours for which the "vertical" TEC value I 0 (t) does not exceed 10 T ECU.
Hence the relative amplitude of TECS dI/I 0 makes up 1%, that is quite significant for this disturbance period (∆T = 10 min) and exceeds one order of magnitude the amplitude of typical background TEC fluctuations (Afraimovich et al., 2001a).
It is further assumed that the characteristic vertical size of the IID is of the same order as the transverse horizontal size (of about 100 km -see Section 4.3). The vertical extent of the part of the ionosphere that makes the main contribution to the TEC modulation is no less than 500-1000 km. Hence it follows that the relative amplitude dN/N of the local electron density disturbance for IID reaches a considerably large value, 5-10%.

Discussion
What is the nature of the ionospheric irregularities that are responsible for the occurrence of TECS, and Do they differ from the known published ionospheric disturbances?
We shall try to unravel this situation using the sample statistic obtained in Section 3 and the October 5, 2001 event as an example, because for this event it was possible not only to record a large number of TECS but also to obtain estimates of the size, anisotropy and velocity of isolated ionospheric irregularities that are responsible for the occurrence of TECS (Section 4).
It is significant that, according to Internet data for the concerned region of the USA  Fig.5f).
However, most TECS on that day were observed before the launching time.
As far as seismic activity is concerned, we analyzed the data covering not only  (Fig. 5b).
This disturbance was also accompanied by an increase of the H-component fluctuation amplitude in the range of 2-20-min periods (Fig.5c). The variation range of the geomagnetic Dst-index for the selected time interval was also relatively small (no more than 20 nT); however, the period from 08:00 to 15:00 UT showed a clearly pronounced increase in variations of the Dst-index that coincided with the period when the H-component of the magnetic field was increasing (Fig. 5a).
Hence, the data from magnetic-variation stations do not suggest the conclusion that the observed TECSs are associated with magnetic field variations.

Can TECS be caused by the E s -layer ionospheric irregu-
larities that are responsible for S-and QP-scintillations?
As has been pointed out in the Introduction, a large number of publications (e.g., Karasawa, 1985;Titheridge, 1971;etc.), were devoted to the study the "spikes-type"  Thus we did not obtain any direct confirmation of the fact that TECS were caused by intense ionospheric irregularities located in the E s -layer. The question of the origin of the IID that are responsible for TECS remains open.
It should be noted that direct comparison of our results with the data obtained by Karasawa (1985), Titheridge (1971), and Bowman (1989), is made difficult by the fact that the overwhelming amount of earlier data was obtained for amplitude, rather than phase, scintillations. On the other hand, extracting data on amplitude variations of GPS signals from Internet RINEX-files is highly difficult (Gurtner, 1993).
To understand the nature of TECS requires invoking data from different, independent diagnostic tools, including incoherent scatter radars, ionosondes, magnetometers, etc.

Conclusion
Main results of this study may be summarized as follows: 1. TECS constitute a rare event that occurs mainly in the night-time in the spring and autumn periods, in a weakly disturbed or quiet geomagnetic situation.       Fig.6 (a, c, e, g), but for the station longitudes and t min .  Fig.7, but for the "trace" C (on the left; 376 arrays), and for the "trace" D (on the right; 280 arrays).  Figure 9: a, c, e, g { the dependencies of the standard deviation N ( ) of the values of the coordinates of subionospheric points in a topocentric coordinate system, and of the corresponding to t min , on the rotation angle c = 0 + /2 ( stands for the rotation angle of the original coordinate system) for the "traces" A, B, C, and D (Fig. 6); b, d, f, h { the dependencies of the value of the ratio C N;E on c = 0 + /2. The values of the contrast C are shown by the horizontal dashed line.