Using the Austrian network of 10 two-frequency GPS geodetic reference stations, whose location is known with high precision, a study of mesoscale anomalies in the ionosphere over central Europe has been made (and is still in progress for the following years). From the large number of individual observations during the period from 2000 to 2004, maps of small-scale ionospheric behavior (with a pixel size of 0.5° in latitude and longitude) have been constructed from which local anomalies (at an equivalent height of 250 km) in terms of departure from the model total electron content (TEC) can be recognized. Not all magnetic storms which were most common during the 2000–2002 period of solar maximum showed local effects in the regional ionosphere, but mesoscale ionospheric anomalies which are not (necessarily) associated with space weather were also observed up to 20% of the days of observation, with their highest frequency of occurrence during the winter months (November–February). These anomalies have a typical duration of several hours and seem to be associated with traveling ionospheric disturbances (TIDs) whose origin could lie in gravity waves initiated in the lower atmosphere. Thus TIDs not associated with space weather may play a role in the regional ionosphere but can be detected only by virtue of the dense spatial coverage obtained by a network of GPS stations for precise positioning. From 2000 to 2004, the solar activity and the background ionization decreased considerably. Since TIDs depend on both the properties of atmospheric gravity waves and on the level of ionization, we observed smaller absolute TID amplitudes in 2003–2004 compared with 2000–2001. There is indication that the relative amplitudes have increased slightly, which is consistent with the influence of ion drag on thermosphere dynamics.
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 Radio waves with frequencies above 30 MHz (considered the lower limit of the very high frequency range) are always able to propagate through the ionosphere but are affected by so-called transionospheric propagation effects. These effects depend on the wave frequency and the plasma frequency: The higher the wave frequency in relation to the plasma frequency, the less is the ionospheric influence. This influence is mostly seen as disturbances in wave propagation (propagation errors), and thus users of transionospheric systems try to keep these errors as small as possible. Modern transionospheric applications, like satellite to satellite or Earth to satellite communication, therefore use wave frequencies (much) above 100 MHz, but for frequencies above 10 GHz, the influence of the troposphere (water vapor) will increase rapidly. The best compromise is to use frequencies around 1 GHz. In this case, there is practically no tropospheric influence, and although the ionospheric influence is small, it cannot and must not be neglected. As mentioned above, this ionospheric influence is mostly seen as an annoying disturbance, but since this influence depends mainly on the number of free electrons (electron density), for ionospheric research it is one of the most important data sources for the so-called total electron content (TEC).
2. Ionospheric Influence
 The height distribution of electron density shows several regions with layer shapes based on the so-called Chapman theory of ion and electron production by absorption of solar extreme ultraviolet and X-ray radiation. The most important regions are the so-called D region, E region, and F region. The D region (located between 50 and 90 km) has no distinctive maximum, and a Chapman layer shape does not apply. The E region (90–140 km) has the greatest similarity with a simple Chapman layer. This region plays an important role in geomagnetism because several current systems are located there which influence the geomagnetic field. The F region is the most extended (and main) region of the ionosphere. It is divided into two sublayers, the F1 layer (here we find the maximum of electron and ion production) and the F2 layer in which the ion and electron density maximum is located, the so-called F2 peak (about 300 km in midlatitude). The F2 layer is strongly affected by plasma transport. Besides this regular layering we can find several additional structures with smaller scales in midlatitudes, e.g., the so-called main ionospheric trough, ridges, and other disturbances.
3. TID Traveling Ionospheric Disturbances
 Special types of disturbances are the so-called traveling ionospheric disturbances (TIDs). C. O. Hines was the first to give an explanation for the wavelike disturbances on the basis of similarities in the properties of atmospheric (acoustic) gravity waves (AGWs) and TIDs [Hines, 1959, 1960]: TIDs are the manifestation of AGWs in the thermosphere with the ionization functioning mainly as a passive tracer. Gravity waves change the plasma distribution of (mainly) the F layer, which results in fluctuations of electron density as well as electron content. This hypothesis is now widely accepted. According to their different scales we distinguish between three classes of TIDs: (1) large-scale TIDs (LSTIDs), horizontal wavelengths >1000 km and periods from 30 min to several hours; (2) medium-scale TIDs (MSTIDs), horizontal wavelengths between 100 and 1000 km and periods from 12 min to 1 hour; and (3) small-scale TIDs (SSTIDs), horizontal wavelengths <100 km and periods of a few minutes.
 The AGWs associated with LSTIDs and MSTIDs belong to the gravity branch, while the SSTIDs belong to the acoustic branch but are not measurable because of their smaller scales and amplitudes and are not distinguishable from atmospheric noise. LSTIDs seem to be generated in the auroral region, mainly in connection with geomagnetic activity (storms or substorms), whereas most of the MSTIDs are thought to be generated in the lower atmosphere because of meteorological or topographical effects, such as hurricanes, Föhn phenomena, violent thunderstorms, or cold fronts, but also earthquakes or tides. There are several expected sources [see, e.g., van Velthoven, 1990; Nagpal, 1979], but it is not clear how these tropospherically generated waves reach ionospheric heights; one problem is the mesopause (80 km), which acts like a reflector because of the absolute temperature minimum there. However, there are known correlations between tropospherical activity and MSTID activity [see, e.g., Kelder and Spoelstra, 1987]. Small-scale ionospheric irregularities in the E layer (Es) have been observed by occultation observations of GPS signals with the help of a satellite in low Earth orbit. They imply that these irregularities have their origin in atmospheric gravity waves produced by orography and/or meteorological factors [see Hocke and Tsuda, 2001].
 Since LSTIDs are global phenomena, they are well known, and their influence is recognized in global TEC measurements and models. MSTIDs, however, are often overlooked in global models because of their small scales and only local appearances, so accurate local TEC determination is needed. These local MSTIDs can create problems for accurate surveying or positioning, since for ionospheric corrections, only large-scale models are being used. A major problem is the lack of predictability of MSTIDs. Although it is not possible to predict LSTIDs either, they are indirectly related to so-called space weather. Thus it is possible to provide warnings for the occurrence of MSTID from space weather observations. Our goal was to first gather some general MSTID statistics and to provide some new information on MSTID climatology and furthermore to find possible ionospheric sources over central Europe, leading to improved knowledge about MSTIDs and possibly providing some predictions of MSTID occurrence.
4. Measurements Based on GPS Signals (Phase Differences)
 There are several methods to measure the ionospheric influence on radiowave propagation. Three of the most important are (for further information, see, e.g., Giraud and Petit ) (1) the difference Doppler effect (phase differences), (2) group delay (code differences), and (3) the Faraday effect (polarization shift).
 Because of the high frequencies of the GPS carriers it is not possible to use the Faraday effect, but it is possible to use the other two. Practically, the group delay is used for calibration of ionospheric electron content (TEC) (determination of the ionization level), while the difference Doppler effect gives information on TEC structures and fluctuations. We presently are using phase difference measurements but plan also to use code measurements in the near future to improve our background model which is used to calibrate the measured MSTID fluctuations.
 As mentioned above, here our main interest lies in mesoscale disturbances. For this we need a dense network of receiving stations, otherwise it is not possible to detect MSTID disturbances because of their very local, small-scale, and short-lived appearance. Fortunately, there exists just such a very dense network of dual-frequency receiver GPS stations in Austria. Using the phase data from 10 Austrian stations ensures that there are at least three stations within a radius of 300 km (see Figure 1a). This makes it possible to determine from the phase difference data the variation of the local ionization.
4.1. Difference Doppler Effect
 The basic information from which TID data are derived is the L1–L2 carrier phase difference. Traditionally, the plasma influence which this quantity contains is the so-called difference Doppler effect. (The first use of the difference Doppler effect was made in sounding rocket measurements [Seddon, 1953].) Carrier phase ϕ itself is contained in an electric signal (voltage or current) U which is produced in the receiver by reconstruction of the carrier from the spread spectrum information received by the antenna of the equipment:
Here ε contains the transmitter and receiver errors (from random noise, from the reconstruction process, from time-varying phase shifts, etc.). The phase ϕ is considered to be proportional to the optical path length l from the phase center of the transmitting to the phase center of the receiving antenna:
where f is the transmitted signal frequency, λ is the free space (vacuum) wavelength, and c is the free space velocity of light. If we can obtain the phases on two (reconstructed) carriers with frequencies f1 = pfr, f2 = qfr, with p and q being integers (GPS: p = 154, q = 120) and fr being a reference frequency (fr = 10.23 MHz), the phase difference is given by
where T denotes the position of the transmitter, R denotes the position of the receiver, and n1 and n2 denote the refractive indices (two carriers L1 and L2). Here the ionospheric constant A = 80.6, Ne is the number density of free electrons, and ɛ2,1 contains the errors which survive the combination process. Assuming straight line propagation, both the kinematic and the neutral atmosphere (time-integrated) Doppler effects are compensated precisely.
4.2. Measurement Method
 As mentioned above, we use the GPS phase difference data from 10 dual-frequency GPS receivers located in Austria and operated under supervision of the Space Geodesy Department of the Space Research Institute of the Austrian Academy of Sciences. The downloadable data are stored in the well-known RINEX2 format (W. Gurtner, RINEX: The Receiver Independent Exchange format, version 2, 2000, available at http://igscb.jpl.nasa.gov/igscb/data/format/rinex2.txt). To gain the relative phase differences to be interpreted as differential Doppler, the GPS phase data from the RINEX2 files are prepared in three steps:
 1. Extract and subtract raw data: L1−L2 (carrier phase differences) so we get (Δϕ)0.
 2. Normalize by subtraction to have minimum (Δϕ)0 = 0 so we get (Δϕ)1.
 The output data are the corrected phase difference data and are used to obtain the TID data (only relative data, i.e., deviation of real (disturbed) TEC from a background ionosphere). These phase difference (differential Doppler) data are obtained as follows.
 1. Prepare TID fluctuations by band-pass filtering. This is done by combining a low-pass and a high-pass filter. For the low pass we use the 3RSSH smoother (the nomenclature indicates the span of the running median (3), the splitting operations (S), and the enhancement (H for Hanning); for futher information, see Kleiner and Graedel  or Taubenheim ). This nonlinear filter is capable of removing single or double outliers and otherwise acts like a three-point smoothing procedure. The high-pass filter is based on a cosine square low-pass filter (Hanning window) [Taubenheim, 1969].
 2. Project from slant to vertical (see geometry and example in Figure 1).
 3. Prepare final products for case studies and statistics.
5. Products, Statistics, and Data Interpretation
 For accurate data interpretation, several graphical outputs are produced. The most important ones are the so-called TID plots from which the appropriate TID parameters can directly be read off. In addition we produce so-called bihourly TID maps (pixel maps) which are similar to synoptic weather charts and enable us to see location, dimension, and duration of an MSTID event. These maps are also helpful in selecting possibly interesting cases (TID events) without having to inspect all of the TID plots. Finally, some graphical statistics products in the form of histograms are produced to find possible days of interest.
5.1. TID Plots
 As mentioned above, the deviation data are plotted in the form of so-called TID plots (Figure 2c), which show amplitudes (in 1015 el m−2) and periods (in minutes or hours). Such plots are very useful for determining TID structures but are unsuitable for TID location interpretation and statistics. First, these plots are only two-dimensional amplitudes over local time, enabling accurate interpretation. On the other hand, no information about location is included. Second, since every single satellite-receiver link has to be plotted separately and every station “sees” at least 24 satellites a day (sometimes one of them twice), normally, there are more than 240 TID plots produced per day. Thus there are far too many plots for interpretation, so other graphical products (pixel maps; see section 5.2) have been produced for easier data interpretation.
5.2. Bihourly TID Maps
 For accurate data interpretation we decided to produce sets of six so-called bihourly TID maps (see Figure 3, example for 2001 (high solar flux) and Figure 4, example for 2004 (low solar flux)). In Figure 4, only the most imprortant maps are shown, representing the background ionization (TEC) and the relative deviations/errors due to TID activity. On a map of Europe, shaded pixels (in this paper, gray scale is used) representing TID intensity along the satellite path (measured data) are plotted. The geographic region of interest is central Europe (longitude −5° to 31°, latitude 35° to 56°). The region is divided into rectangles (pixels) with a scale of 0.5° in latitude and longitude. The shading of the pixels denotes the TID intensity level from white (undisturbed) to black (strongly disturbed). The pixel shading of the first map represents the normal background ionization but not the disturbance level; it is used to calibrate the measured disturbances (deviations from normal background). For an accurate interpretation one needs more than one product; therefore primarily four bihourly TID maps have been produced [see Rieger and Leitinger, 2002], whereby the pixel shading represents (1) the level of background ionization given in 1015 el m−2 (since this is the order of the measured deviations, standard TEC units are not used), (2) the absolute deviations of the ionization level from background level given in 1015 el m−2, (3) the relative deviations from background given in percent, and (4) the calculated range errors for one satellite to receiver path given in cm. In addition to these four TID maps, two more TID maps have been produced. These two TID maps illustrate the maximum minus minimum fluctuations within one single pixel, which can be quite large if the wavelength of the TID is comparable with the pixel size. These two pixel maps illustrate (5) the maximum minus minimum level of deviation within a pixel given in 1015 el m−2 and (6) the corresponding range errors for one satellite to receiver path given in cm. These maximum minus minimum maps are useful because they give information about possible TEC variations within such a small area. By inspection of these maps one can recognize that the additional variations within a pixel can be of the same order as the measured mean deviation represented by one pixel.
 For the statistical evaluation, several bar plots have been produced. The heights of the bars represent the number or the average level of disturbed pixels per day. Thereby indicators for disturbed pixels are (1) relative deviations from the background greater than 5% (Figure 5b), (2) absolute (additional) deviations greater than 0.8 × 1015 m−2 (Figure 5a), (3) average absolute deviations (sum of deviations over number of pixels) in 1015 el m−2, and (4) average relative deviations in percent.
 To establish if geomagnetic storms are the generator of the (MS)TIDs or if the generator is other activities like tropospheric weather, two additional bar plots were produced representing (1) the Ap index (Figure 5c) and (2) 10.7 cm solar radio flux (Figure 5d). The relative deviations are not only most important for TID research but are also useful for various other applications. However, for an assessment of the TID influence on surveying results, the absolute deviations are more important. Figure 5 shows the whole set of statistical bar plots. In Figure 6 it is shown that the MSTID activity is (mostly) not correlated to geomagnetic disturbances (represented by the Ap index).
6. Conclusions and Future Work
 TEC observations by means of phase difference data have shown that medium-scale TIDs can influence local and regional GPS applications. Therefore an accurate MSTID determination is important for applications demanding accuracy in the centimeter range, like surveying. Our study has shown that using GPS phase difference data enables one to determine MSTID structures in the ionosphere and to assess MSTID activity on an hourly, daily, and long-term basis. By taking into account MSTID influences, the positioning accuracy of some applications can be evaluated and improved.
 The biggest problem is that TID measurements by means of GPS phase differences cannot be done in real time. TID data are available with a delay of at least 1 hour. Thus nowcasting or forecasting of possible TID events is desired. Possible LSTID events, on the other hand, can be predicted indirectly because they are closely connected to geomagnetic activity and therefore to solar activity (space weather). Although LSTID activity is expected when the level of geomagnetic activity is high, which region of the world is likely to be affected cannot be forecast. However, LSTID warnings could be issued on the basis of recent geomagnetic activity. If LSTIDs have been detected, the probability is high that they will persist for the following hours.
 A more difficult problem is to forecast or nowcast MSTID events. First of all, their nature (i.e., their excitation processes, lifetimes, propagation, and so on) is not as well known as that of LSTIDs. Second, they are often too small to be seen in classical measurements, like ionograms. Therefore one needs a dense network of GPS receiver stations and models/maps with high grid resolution, which is certainly fulfilled in this study. For predicting MSTID occurrence probabilities, a sufficiently good MSTID climatology is needed. This should emerge with a continuation of data collection and production of statistics over some more years.
 Already, the first measurements have shown that there is much more MSTID activity than previously thought. On nearly all days we have seen some activity (mostly below the 5% level). However, most users are only interested if the additional error due to MSTIDs exceeds a given level. Studying the relative TID fluctuations shows that about one fifth of the days are “disturbed” by single MSTID events (see Table 1 for examples for high solar activity (2000), Table 2 for examples of low solar activity (2004), and Table 3 for results for the whole measuring period (January 2000 to December 2004). These disturbances last for 2–6 hours and are quite localized. It is most interesting to see that there are many more disturbances in the winter months. This leads to the assumption that there is a close connection to the lower atmosphere, but the detailed coupling mechanism between the lower atmosphere and ionosphere is still lacking, although suggestions have been made already a long time ago [e.g., Bauer, 1958].
Table 1. Statistics of Mesoscale Ionospheric Disturbances (Larger Than 5% of Background TEC) Based on MSTID Occurrence for the Year 2000, Representing High Solar Activity
Number of days relative to total number of days of observations.
Number of days relative to total number of MSTID days.
Geomagnetic storms (Ap > 50)
Storms with MSTID activity
MSTID days in 2000 (≥ 5%)
MSTID days in first sixth of the year
MSTID days in second sixth of the year
MSTID days in third sixth of the year
MSTID days in fourth sixth of the year
MSTID days in fifth sixth of the year
MSTID days in sixth sixth of the year
 It would be interesting to make comparisons of different geographical regions where good spatial resolution is given (e.g., Europe and Japan). The Japanese GPS Earth Observation Network (GEONET) was created in the mid-nineties to investigate earthquake activities and consists of more than 900 stations (1998). The average distance between receivers is approximately 25 km. Ionospheric investigations by using data of this network have shown disturbances regarding LSTIDs (origin in the auroral zone) [Saito et al., 1998].
 The GPS data from the Austrian network needed for our study were provided by the Space Research Institute of the Austrian Academy of Science (Peter Pesec), Graz, Austria. Our study was partly supported by the Austrian Federal Ministry of Defense (BMLV), Vienna, Austria.