Although ionospheric perturbations such as traveling ionospheric disturbances have a strong impact on Global Navigation Satellite Systems (GNSS) and other space-based radio systems, the description of individual perturbations is difficult. To overcome this problem, it is suggested to use a disturbance ionosphere index (DIX) that describes the perturbation degree of the ionosphere in a less specific form as a proxy. Although such an index does not describe the exact propagation conditions at the measurement site, the estimated index number indicates the probability of a potential impact on radio systems used in communication, navigation, and remote sensing. The definition of such a DIX must take into account the following major requirements: relevance to practical needs, objective measure of ionospheric conditions, easy and reproducible computation, and availability of a reliable database. Since the total electron content has been shown in many publications to act as an outstanding parameter for quantifying the range error and also the strength of ionospheric perturbations, we propose a DIX that is based on GNSS measurements. To illustrate the use of the index, recent storms monitored in 2011 and the Halloween storm are discussed. The proposed index is a robust and objective measure of the ionospheric state, applicable to radio systems which are impacted by a highly variable perturbed ionosphere.
 Ionospheric perturbations may cause serious propagation errors in modern radio systems such as Global Navigation Satellite Systems (GNSS) and space-based remote sensing radars. Hence, information on the behavior of crucial ionospheric parameters describing the perturbation degree is helpful to estimate potential degradation of the performance of these systems. In general the description of the concrete ionospheric perturbation at the radio link is difficult. This is due to the fact that our knowledge on the spatial and temporal variations of the ionosphere is incomplete. A pragmatic solution to overcome this problem is the use of information that describes the perturbation degree of the ionosphere in a general form, i.e., as an index. Although such an index will not describe the exact propagation conditions at the measurement site, the derived quantity (index value) indicates the probability of a possible impact on the radio system from which the risk of violating required accuracy bounds or protection levels may be derived.
 Activity indices such as the Zurich sunspot number Rz and the 10.7 cm radio flux index F10.7 for the solar activity (e.g., for solar radio flux, see http://www.spaceweather.gc.ca/sx-eng.php) or the indices Kp, Ap, Dst for geomagnetic activity [e.g., Campbell, 1996] are often used in space weather modeling and forecast. Since an activity index provides a quick and proxy measure of a complex behavior of a specific subject, the index has usually a great practical value in particular in operational applications. The complex information is condensed in a simple number which can easily be fed into user algorithms and models. Furthermore, knowing the relationship between such an index and space weather drivers, the index should be predictable by using early space weather information.
 As stated by Jakowski et al. , a quick evaluation of the current signal propagation conditions in the ionosphere by an index might help to inform users on the development of an ionospheric storm in their region. In this paper we follow this idea by introducing the disturbance ionosphere index (DIX).
2. Space Weather Indices
 Well established space weather indices such as the solar activity index or geomagnetic indices play an important role in modeling and characterizing the perturbation degree of the geospace. The solar radio flux at 10.7 cm wavelength characterizes the level of solar activity in a similar way as the Zurich sunspot number does. Due to the close relationship of the radio flux with the solar EUV radiation, F10.7 is well suited to describe the level of the total ionization of the ionosphere [Jakowski et al., 1991].
 Whereas the daily averaged F10.7 index provides the ionospheric ionization level in a climatologically sense, geomagnetic indices are usually used to indicate the strength of ionospheric distortions in the vertical and horizontal plasma distribution [e.g., Jakowski et al., 1999]. Since the geomagnetic field reacts very sensitive to solar wind changes, absolute measurements of the geomagnetic field referenced to the mean or by estimating the dynamics of geomagnetic field fluctuations provide valuable information on the perturbation degree of the geospace. Most frequently used planetary indices are Kp and apwhich are derived from 3-hourly measurements of the geomagnetic field fluctuations provided by 12 globally distributed magnetometer stations [e.g.,Menvielle and Berthelier, 1991]. The ring current index Dst provides a direct measure of the strength of the ring current in the equatorial plane at distances of about 3–5 Earth radii as a consequence of enhanced solar wind and interplanetary magnetic field changes. Although geomagnetic indices such as Kp, Ap, and Dst characterize the planetary perturbation quite well, they cannot give a correct description of the perturbation degree of the local or regional ionosphere [Förster and Jakowski, 2000].
 Furthermore, the temporal resolution of these geomagnetic indices in the order of 1–3 h is far away from being sufficient to fulfill customer needs. It can be stated that geomagnetic indices do not really match to customer needs to receive correct ionospheric weather information in near real time. In particular, safety of life (SoL) applications require an actual and reliable index which describes the local or regional ionospheric state for estimating system threats.
3. Suggestion of a Disturbance Ionosphere Index
 The definition of any activity index describing the perturbation degree of the ionosphere depends on the purpose of using the index. For studying the physics of perturbation processes, the activity index might be postprocessed in a comprehensive manner after collecting comprehensive data sets. However, as indicated already in the previous section, operational radio systems which may be sensitive to current space weather conditions need reliable information as fast and as good as possible. The definition of a perturbation index having a potential to be used in operational applications must take into account the following major requirements: relevance to practical needs, objective measure of ionospheric conditions, easy and reproducible computation and availability of a reliable database.
 In an earlier paper by Jakowski et al. we found that GNSS-based total electron content (TEC) and/or its derivatives are outstanding candidates for defining new ionospheric perturbations indices.
 GNSS applications are in particular sensitive to spatial gradients and temporal variability of TEC. Hence, a TEC-based index is in particular relevant for the transionospheric radio link, i.e., for a broad user community operating space-based radio systems in communication, navigation and remote sensing.
 To fulfill user needs we focus on ionospheric perturbations which are characterized by a high spatial and temporal variability. This is a dynamic approach ignoring smooth large scale and slowly developing deviations from the average behavior. Although slow temporal and large spatial scale ionospheric perturbations may be a result or expression of a severe ionospheric storm, they commonly do not cause serious problems in transionospheric radio systems. Hence, an index definition based on deviations of a selected ionospheric parameter from its mean behavior [e.g., Gulyaeva and Stanislawska, 2008; Mielich and Bremer, 2010] is not considered here. Being aware of the sensitivity of GNSS measurements to temporal as well as spatial changes, we focus on a definition which includes both aspects.
 In the earlier papers by Jakowski et al. [2005, 2008] we suggested to derive spatial gradients and temporal changes from TEC maps and their temporal variation, respectively. This procedure provides reasonable results but has the disadvantage that gridded values of vertical TEC are usually smoothed during the mapping procedure and furthermore, require calibration of biases.
 The calibration of TEC or determination of the interfrequency biases is a challenging task resulting in different results by different groups due to different approaches. Although a good accuracy in the order of 1 TECU may be achieved nowadays, spatial gradients at distances in the order of 100 km and less react very sensitive to calibration errors even below 1 TECU. Thus, a perturbation index definition based on calibrated TEC is only useful at large scales [e.g., Yu et al., 2009].
 To avoid the calibration problem, we suggest using noncalibrated differential GNSS phase measurements as input data. The computation of differential phases including removing cycle slips in GNSS data preprocessing is common standard, the signal noise due to multipath is rather low. Therefore, we suggested defining the disturbance ionosphere index (DIX) on the basis of dual frequency carrier phase measurements as first described by Jakowski et al. .
 The simplified observation equation of GNSS carrier phases can be written as:
carrier phase (m);
carrier frequency (s−1);
distance between receiver and transmitter (m);
receiver and transmitter clock offsets (s);
velocity of light (m/s);
instrumentation offset (m);
carrier phase noise (m);
phase ambiguity integer;
slant TEC along the ray path (m−2).
 Dual frequency GPS measurements, e.g., at L1 and L2, enable the computation of differential phases according to:
where bΔ refers to a constant or very slowly varying bias value and εΔ is the residual phase noise.
 We have to be aware that these measurements are usually made along slant raypaths.
 To avoid estimating the bias term, we suggest using the time derivative of slant TEC. Ignoring the noise term we get
Equation (3)provides a reliable measure of the TEC rate of change along the considered radio link between GNSS satellite and ground-based receiver. All subsequent computations are based on the TEC rate of change as a fundamental parameter.
 To achieve independence from elevation angle, slant measurements have to be projected to the vertical and vice versa by the mapping function M. This is commonly done by assuming a spherically stratified single layer ionosphere. This simple assumption provides the possibility to locate the measurement at the Ionospheric Piercing Point (IPP) of the radio link with the ionospheric layer.
 For reasons of simplicity, the nonindexed abbreviation TEC means always vertical TEC. The conversion can be approximated by the commonly used single layer mapping function M(ε) according to:
Earth radius (km);
height of ionosphere single-layer approximation (km);
elevation angle (rad).
 Furthermore, applying this simple assumption, the slant measurement can easily be transformed to the vertical and vice versa. So we get:
 As Figure 1 shows, mapping function change is less than 3 × 10−4s−1 at elevation angles >30°. Since TEC rate of change during severe perturbations may about 1 magnitude higher, we ignore the second term of equation (6) in our approach.
 This leads to the following simplified equation for the vertical TEC rate.
 Let us now consider the motion of the piercing point at the ionospheric layer. The total differential for TEC at the single ionosphere layer is given by:
 This leads to:
where vPP means the velocity of the piercing point at the ionosphere shell. Since the piercing points move in horizontal direction, even static gradients will usually be detected. Only in case when the ionization front is parallel with the IPP motion there is no response. In a spherically stratified layer the first term on the right side is zero, independently from vpp. Typical IPP velocities are expected to range from 100 up to about 500 m/s (see Figure 2). Since these velocities are in the order of TIDs [e.g., Borries et al., 2009], the ionospheric impact depends on the directions of perturbation propagation and IPP motion.
 Let us now consider two radio links indexed by l and k having ionospheric piercing points at geographic coordinates IPPl (φl; λl) and IPPk (φk; λk). The IPPs are separated by the distance s at the ionospheric shell height. Since temporal variations are often due to changes of large-scale forces such as solar radiation, e.g., solar flares, the temporal variation at observation points is similar within a circle in the order of some 100 km. Thus, consideringequation (10), the temporal term cancels out when computing the difference according to:
 The remaining spatial terms provide information on the horizontal structure of TEC. Depending on the extension of horizontal gradients and the velocity vector of IPPs the difference will grow or reduce compared with the individual values at IPPl and IPPk. When considering such data pairs in a statistical way as pointed out later, the derived quantity grows up in case large TEC gradients appear.
 The temporal term is defined by the expression
 This term does not exclude spatial information but compared with equation (11), large-scale temporal variations are well pronounced.
 The location of the average term is defined by the center IPPc of the IPP pair, i.e., by half the distance at the big circle between both points.
 Considering equation (11), a spatial disturbance ionospheric index DIXS could be defined as the arithmetic average (or median) of the difference of TEC rates computed for all IPP pairs within a predefined region.
 Here NP designs the number of IPP pairs and SFS means a scaling factor which can be fixed according the convenience of users. This concerns both the unit as well as the range of DIX numbers.
 So the scaling factor can convert the computed quantity into an appropriate dimensionless number. If users prefer to keep the physical meaning, DIX can be given, e.g., in TECU/min via the scaling factor. Considering only center points located within the selected area, the index can be specified to concrete user needs by defining the area and/or by defining the distance range between the data pairs.
 If the index shall include also temporal information as defined in equation (12), we suggest extending the definition of the total DIX as follows.
 The tuning factor η can be used to balance temporal and spatial terms according to concrete user needs. Since GNSS reference networks are mostly sensitive to horizontal gradients, a high tuning factor η should be useful. The scaling factor SF might be used to create a dimensionless index which could optimize the range of values for practical use.
 If calibrated vertical TEC is available, i.e., if bΔ is known, spatial gradients and temporal changes can be included individually in the determination of the perturbation index. Although not discussed in this paper and not recommended for characterizing ionospheric perturbations at shorter distances than 100 km, calibrated TEC could be used to formulate a DIXcal in analogy to equation (11) according to:
 Here Δs designates the distance between considered IPPs. This disturbance index separates stronger between temporal and spatial TEC variations than it is done in equations (13) and (14). Nevertheless, we favor the definition of DIX given in equation (14) because this procedure does not require calibration procedures of instrumental biases. Therefore, this approach is simple and robust and can better characterize ionospheric gradients at lower horizontal scales, e.g., of less than 100 km. Since no TEC calibration is needed, there is no impact of instrumental bias errors which may become crucial at short distances.
 To further specify the index, we suggest selecting a critical length Lc which is of interest for the user. After fixing the critical length, only those pairs of radio links are considered whose IPP distance is less than Lc. In this study we fixed the range by using those IPP pairs which are closer than 1000 km.
 At the lower end we recommend the condition: LC ≥ 2000· Δt in SI units. Since precise differential GNSS networks are sensitive to horizontal TEC gradients at scales of up to about 100 km, the critical length Lc should not exceed 200 km in such applications.
4. Application of DIX Approach at Storm Test Cases
 To give a first impression how DIX behaves during a storm, here we present a computation of the DIX at well defined areas over Europe during four ionospheric storms.
 During the severe Halloween storm from 28–30 October 2003 the global ionosphere was strongly disturbed, in particular also over Europe [e.g., Yizengaw et al., 2005; Jakowski et al., 2008]. This storm is well suited for demonstration because it includes both flare as well as solar wind induced perturbations [Tsurutani et al., 2005]. To compute DIX according to equation (14), we used data from numerous GPS stations, most of them belonging to IGS and EUREF geodetic networks. The elevation cutoff angle was 10° and the GPS sampling time interval was Δt = 30s. The TEC rate of change is always measured in TECU/min (1 TECU = 1016 m−2). Since the scaling factor was fixed in these computations at SF = 1, DIX is provided here in units of TECU/min. In the same way as SF, also the tuning parameter η can be adapted to practical needs of customers as mentioned before.
 Further studies shall reveal the optimal presentation of DIX including fixation of the scaling factor SF and the spatiotemporal tuning factor η.
 As discussed earlier, the first term under the square root in equation (14) focuses on temporal variations. Thus, the flare effect on 28 October 2003 is well pronounced by a sharp peak that reaches more than 4.5 at the selected scale whereas remaining variations at day time are well below 0.3. Since the second term under the square root in equation (14) focuses on spatial variations, the flare which occurred at 11:05 UT on 28 October is practically not visible in Figure 3 (left) except for a few outliers in the vicinity of the flare. Visible are instead some temporal and spatial changes due to plasma redistribution processes as a consequence of the flare event and subsequent CME.
 To get a complete index description, temporal and spatial terms may be combined thus forming the total index (cf. equation (14)). As mentioned before, depending on user needs, the balance between both terms may be tuned by the parameter η in equation (14); here we fixed η = 5. This explains why we see both effects in the presentation of the total DIX in Figure 4 on 28 October 2003.
 The DIX computations for the Halloween storm period are based on 30s GPS RINEX data. Although the input data were cycle slip controlled, some outliers obviously still remained in the processed data sets. Due to recent achievements in GNSS observation techniques such as the Real Time Pilot Project (RTPP) of IGS, 1 Hz sampled data can be used in streaming mode, enabling a more reliable data quality of data processing. Taking advantage of the availability of 1 Hz data via the Federal Agency for Cartography and Geodesy (BKG) Frankfurt (http://www.bkg.bund.de/nn_147094/EN/Home/homepage:node.html:nnn=true) we subsequently present DIX computations made for some recent ionospheric storms in 2011.
 We start the discussion of the ionospheric storm on 26 September 2011 (Dstmin = −103 at 24:00 UT). Considering Figure 5, it becomes clear that DIX will represent medium- to large-scale perturbations (50 < Lc < 1000 km is used) in this example. If more dense GNSS networks are available, also small-scale perturbations can be characterized by DIX. Taking into account the medium- to large-scale spatial range restriction, 30 s samples are used for the DIX calculations shown inFigure 6.
 It can be seen that DIX reflects the geomagnetic storm characterized by global indices such Dst in the ionosphere quite different. Whereas the onset phase shows a more pronounced effect in the 40°N latitude range around 13:00 UT, the ionospheric response to the main phase starting at about 16 UT is restricted to the higher latitudes at 60°N where simultaneously also phase scintillations can be observed. This obvious difference which cannot be described by a global geomagnetic index underlines the necessity of a separate ionospheric perturbation index. This conclusion is confirmed by the storm characteristics observed on 5 August 2011 (Dstmin = −113 at 4:00 UT on 6 August). Here, as Figure 7 shows, significant storm pattern appear both at high latitudes (60°N) and midlatitudes (40°N) in the evening hours.
 As DIX map at 22:05 UT shows, the regionally averaged values show a strong effect over Southwest Europe, whereas mid-European area is less impacted at this moment. It is evident that the DIX map is very dynamic depending on generation, dissipation and propagation of perturbation processes in the course of a storm. The maximum number of sectors in which a region of interest may be subdivided, depends on the data coverage. To ensure a reliable statistics within the individual sectors, the sector size must be large enough. A subdivision is not needed if the perturbation degree of the entire region shall be characterized by one representative DIX value.
 As mentioned before in the introduction, an acceptable perturbation index must reflect the objective state of the ionosphere independent from observation techniques. To check this requirement, DIX was computed by using completely independent data sets for the ionospheric storm on 18 February 2011 (cf. http://swaciweb.dlr.de/news/solar-storm-15-18feb2011/?no_cache=1&L=1). The first data set is given by the public available GNSS data streams offered by the geodetic community such as IGS or EUREF via BKG Frankfurt. The other is the GPS receiver network of the European Geostationary Navigation Overlay Service (EGNOS). The GNSS Monitor stations for deriving ionospheric corrections (RIMS) provide also 1Hz sampled data, comparable with IGS.
 Although the GNSS receiver distribution is quite different, it is remarkable that both DIX plots agree very well as shown in Figure 8. The different noise level is due to the different number of data. This result is very important, demonstrating that an augmentation service like EGNOS could be supported by external monitoring services like SWACI (http://swaciweb.dlr.de).
5. Summary and Outlook
 A new disturbance ionosphere index (DIX) has been suggested for characterizing the current state of the ionosphere. This index is based on dual frequency GNSS carrier phase measurements. The availability of such data is permanently increasing which improves the conditions for estimating DIX on regional and global scale with a good performance.
 It has been shown that the ionosphere reacts quite different on space weather factors depending on time and geographic/geomagnetic location. This underlines the practical need for an ionospheric perturbation index as suggested.
 In particular, the proposed index is useful for GNSS customers. Following the same computational rules, the proposed DIX may be defined on local, regional and global scale depending on user needs. The proposed index does not require any calibration procedure and can easily be calculated. The index is applicable to radio systems which are impacted by a perturbed ionosphere characterized by a high variability in space and time. Taking into account that real time measurements are already performed at sampling rates of 1s on global scale as the Real Time Pilot Project (RTPP, http://www.rtigs.net/pilot/index.php) of the International GNSS service (IGS) demonstrates, DIX can provide selected spatial information from 2 to more than 1000 km characteristic length. The definition of distance range depends on user needs. It has been shown that DIX provides an objective measure of the ionospheric state. Hence, studying space weather relationships of DIX, it should be possible to forecast DIX and related performance changes in GNSS applications.
 The robust, objective and easy adaptable index should have a great potential for being used in operational ionospheric weather services and GNSS augmentation systems.
 To provide operators and users of radio systems in telecommunication, navigation or remote sensing with valuable information about the ionospheric state, DLR is establishing a Space Weather Center Ionosphere (SWACI, http://swaciweb.dlr.de). It is planned to release a regional perturbation index (DIX) over Europe in 2012 to learn more about relationships between the perturbed ionospheric structure and DIX. Further work has to be done to tune the DIX approach in an optimal way in close cooperation with customers.
 The authors thank the International GNSS Service for operating the IGS Real Time Pilot Project (RTPP); the Federal Agency for Cartography and Geodesy, Frankfurt, for distributing the measured geodetic data; and the EGNOS Project Office for making available GPS observation data from RIMS. This research is essentially supported by the Ministry of Education and Science of the German State Government of Mecklenburg-Vorpommern under grant AU 07 008.