The typical feature of the vertical ionogram, which is produced by local enhancements of electron density (patches and arcs), is investigated. The polar patches drift from the dayside of the Earth across the magnetic pole in accordance with convection flow patterns at speeds of a few hundred meters per second. Patches are typically about 500 km in length in the dawn-to-dusk direction, but they range from 200 to 1000 km and exhibit electron density enhancements of up to a factor of 10 above background. A model of the ionosphere with irregularities (midlatitude trough, auroral oval, polar cap patches, and Sun-aligned arcs) was developed in collaboration with the University of Leicester (UK). Based on this model, the vertical ionograms for different time and geophysical conditions were simulated. The ionograms were classified by types of the trace shapes. The results of simulation are very reminiscent of the main characteristics of the ionograms observed in high latitude. It is believed that the variations of the model parameters may be employed to estimate the real parameters of the high-latitude ionospheric inhomogeneities.
 There are a number of radio science methods for monitoring high-latitude ionosphere. Among them are the following: satellite measurements of the total electron content, coherent high-frequency (HF) radar data, and vertical and oblique sounding by ionosondes [Weber et al., 1989; Alfonsi et al., 2008; Carter et al., 2012]. The interpretation of these experimental data is complicated by the considerable intricacy of the high-latitude ionosphere structure and dynamics.
 The complexity and variability of the high-latitude ionosphere structure are induced by the presence of the localized regions of enhanced electron density in the F region, namely, patches and arcs. Monitoring of the high-latitude ionosphere reveals the stochastic rather than the regular nature of patches and arcs formation and evolution.
 Most patches are formed by transient magnetic reconnection events. They drift from the dayside of the Earth across the magnetic pole in accordance with convection flow patterns at speeds of a few hundred meters per second [Weber et al., 1989; Ma and Schunk, 1997]. Parameters of the patches of enhanced electron density (number, speed, trajectory, and intensity) strongly depend on the geophysical conditions. Patches are typically about 500 km in length in the dawn-to-dusk direction, but they range from 200 to 1000 km and exhibit electron density enhancements of up to a factor of 10 above background [McEwen and Harris, 1996; McDougall et al., 1996]. The period of the patch appearance is about half an hour. In winter, especially in the period of maximum solar activity, patches are observed most frequently. They have been observed also at sunspot minimum [McEwen and Harris, 1996] but were less detectable. There is evidence that they can retain their form as they traverse the whole polar cap [McEwen, 1998].
 Electron density gradients associated with large-scale structures within the ionosphere (midlatitude trough, auroral oval, patches, and arcs) form tilted reflection surfaces for HF (high-frequency) radio waves. Consequently, HF radio signals propagating through this region often arrive at the receiver over paths well displaced from the great circle direction. Deviations of a few degrees are associated with tilts due to the solar terminator and travelling ionospheric disturbances [Jones and Reynolds, 1975]. Very large deviations are particularly prevalent in the high-latitude regions, where signals often arrive at the receiver with bearings displaced from the great circle direction by up to ±100° or more. These large deviations from the great circle path are due to the electron density depletion and the associated ionospheric tilts within the midlatitude trough at subauroral latitudes [Rogers et al., 1997; Stocker et al., 2002; Warrington et al., 1997; Siddle et al., 2004a, 2004b] and in the polar cap, where they are attributed to the presence of convecting patches and arcs of enhanced electron density [Warrington et al., 1997].
 In addition to the large-scale tilts, which cause large deviations of the signal from the great circle direction, irregularities in the electron density distribution may be considered as providing a rough reflecting surface for HF radio waves. As a result of this roughness, signals associated with each propagation mode arrive at the receiver over a range of angles in both azimuth and elevation. The directional spread of the received signal energy is an important parameter to be considered in the design of multielement receiving arrays and the associated signal processing methods used, for example, in radiolocation or adaptive reception systems.
 The model of the ionosphere with irregularities was developed in collaboration with the University of Leicester (UK) [Zaalov et al., 2003, 2005]. The background ionosphere is modeled on the basis of the vertical sounding data. This model of the high-latitude ionosphere is oriented to application for wave propagation problem. A number of vertical ionograms for different time and geophysical conditions were simulated based on this model.
2 The Model
 There are a number of different models of ionosphere [Chasovitin et al., 1987] that describe the ionosphere under undisturbed conditions. However, none of them can reproduce the ionospheric profile in the high-latitude region with sufficient accuracy [Egorova et al., 1995]. In addition, the majority of the existing models do not reflect the day-to-day variations of the real ionosphere.
 Our original model consists of models of the background ionosphere, midlatitude trough, auroral oval, patches, and Sun-aligned arcs.
 An adjustable model of an electron density profile was constructed based on vertical sounding data, which are now available via the Internet (http://spidr.ngdc.noaa.gov/spidr/index.html). The F and E layer parameters (critical frequencies, maximum height, and half-thickness of the layer) retrieved from vertical sounding data are used for constructing the background ionosphere model. These data are smoothed and converted to longitude and latitude dependencies.
 At present, there is no reliable self-consistent model of F layer patches and Sun-aligned arcs of enhanced electron density in the polar ionosphere. Nevertheless, ray-tracing simulation requires continuous, three-dimensional distribution (with derivatives) of electron density in the area of calculation. The computational model of the electron density irregularities affecting the HF propagation must be in accordance with the general understanding of the structure of the high-latitude ionosphere, but on the other hand, it must be simple enough to be incorporated into the ray-tracing code.
 Since the north ionosphere is a disturbed region containing irregularities of various scales and amplitudes, it is difficult to construct an acceptable homing algorithm due to the very complicated structure of the rays. As an alternative, the calculation of a number of rays falling in the area close to the receiver produces reasonable results [Zaalov et al., 2005].
 A quasi-statistical approach has been adopted in modeling F layer patches and arcs. Their distributions inside the polar cap were determined by one of a number of different scenarios. The shape, size, speed, and maximum of the patch plasma frequency were defined by parameters, which depend on the scenario.
 The size of the region in which the patches and arcs are located is a function of Kp. The Sun-aligned arcs move slowly across the polar cap in the direction of the By component of the interplanetary magnetic field (IMF), while the trajectories of the patches are formed according to the convection flow patterns given by Lockwood .
 Each patch in the convection flow patterns is composed of an arbitrary number of three-dimensional Gaussian fractions with an approximately equal scale in both horizontal directions. The position of each component of the internal structure of the patches is defined as a random function with a specific spatial scale around the regularly distributed “nodes” in the area surrounding the geomagnetic pole. The temporal evolution of the patches depends on the movement of the component forming the patch coupled with the rotation of the Earth beneath the convection flow patterns. The numbers of the nodes (i.e., the number of patches) in Sun-to-Earth and dawn-to-dusk directions can be changed depending on the scenario.
 The model is illustrated for 14 January 2011. The distribution of the plasma frequencies in megahertz at the height of 180 km is shown by color in Figure 1. The daily average Kp index was 1.7, the sunspot number was 14, the Bz component of the IMF was −0.3 nT (http://omniweb.gsfc.nasa.gov), and the critical frequency of the F layer of the ionosphere was 3.9 MHz. This model is described in detail in Zaalov et al. .
3 The Ionograms
 A number of vertical ionograms in the polar cap region for different time and geophysical conditions were simulated. The ionosonde located in Thule/Qaanaaq (77.5°N, 69.2°E) was exploited for comparison of simulated and measured ionograms. The vertical sounding data were acquired from the Lowell Digital Ionogram Data Base via the Internet (http://car.uml.edu/common/DIDBYearListForStation?ursiCode=THJ77).
 The structure (i.e., ionogram trace shape) of the high-latitude ionograms is very complicated. The directions of arrival characteristics are even more complicated. The Digisonde 4D system uses a very advanced technique for determining the angle of arrival of signals. The beams of the angle of arrival are marked by color, as shown in Figure 2. The ray-tracing technique allows us obtain directional patterns as well. However, the problem of comparing simulated and measured directional characteristics is quite difficult. It requires defining of the precise spatial distribution of the ionosphere electron density in the presence of patches. In reality, the determination of patch fine structure seems to be practically impossible. Besides, the measurements show that signals having equal delay at the same frequency do arrive from different beams. In the following, we will focus our considerations solely on the shapes of the trace, but not on angles of arrival.
 The approach of this paper is to employ the scenario with a single patch in order to interpret the observed ionograms (Figure 3). The size, shape, and intensity of the patches are varied in the simulations. The choice of the scenario corresponding to a specific set of parameters defines the structure of the ionograms. It is believed that the variations of the model parameters may be employed to estimate the real parameters of the high-latitude large-scale ionospheric inhomogeneities.
 It is well known that the high-latitude ionograms are rather complex. Very different structures of ionograms are observed during a day.
 The first goal of this paper is an attempt to classify the large variety of high-latitude vertical ionograms. In our view, all experimental ionograms could be categorized into a number of main types as follows: (1) “simple” (Figures 4a and 4b) ionogram typical for middle latitude, (2) “fork” (Figures 5a and 5b) ionogram with single splitting, (3) “complex” (Figures 6a and 6b) ionogram with multiple splitting, (4) “U-shaped” (Figures 7a and 7b) ionogram with arc shape trace, (5) “spots” (Figures 8a and 8b) ionogram with detached spot, and (6) “multiple U” (Figures 9a and 9b) structures.
 Figures 4a–9a represent the data recorded at the ionosonde located in Thule (http://car.uml.edu/common/DIDBYearListForStation?ursiCode=THJ77). The ionograms depicted in Figures 4b–9b correspond to the Thule ionosonde data, which are adjusted for the convenience of the analysis and comparison with simulations. Curves automatically generated by Digisonde software were removed to make the ionogram structure simpler, as shown in Figures 4a–9a. More solid lines were added in order to highlight the main feature of the ionogram structure that seems to be more important for comparing with the simulated ones. Vertical axis labels were converted from virtual heights (km) to delays of the signals (ms).
 In the case when the patch does not affect the ionogram structure, the ionogram is named simple (Figure 4b). The main trace marked by a solid line (arc-shaped structure without any splitting) corresponds to vertical O-mode (ordinary) echoes. The X-mode trace (extraordinary) is indicated by a dotted-solid line. The upper separated curves correspond to multiple reflections from the ground. It is necessary to note that only the O-mode echo traces are under consideration. In the following sections, only the O-mode traces are marked by a solid line to make the ionogram structure more convenient for analysis.
 The structure presented in Figure 5b is characterized by the splitting of the main trace. Three different traces start from the single specific frequency. Another structure is demonstrated in Figure 6b, where splitting occurs from a number of frequencies, forming a complex structure of the ionogram. An ionogram with a U-shaped structure is presented in Figure 7b. This type of the ionogram structure was first described and simulated by James and MacDougall . The ionograms depicted in Figures 5b–7b are rather typical. These ionogram structures are observed almost every day.
 The ionogram structures with spots shown in Figure 8b occur more rarely in observations. Such a structure has a noticeable U-shaped trace with detached spots above it. The ionogram shown in Figure 9b could be called a multiple U structure. On this ionogram, a number of U-shaped structures are observed. Multiple U ionograms were detected relatively seldom.
 In the interval of 15 min, the structure of the ionogram may change considerably. The assessments of the plasma frequencies of the patches immediately from the ionogram (i.e., maximum frequency of the trace) show that their values may change by a factor of 2 or 3 in 15 min. However, it is reasonable to suppose that in reality, the patch shifts significantly, while the electron density of the patches has changed only slightly during this time.
 In order to estimate the real parameters of the patches, the ionogram simulations were employed. A number of ionograms were calculated based on the developed model of the high-latitude ionosphere. The variation of the patch parameters (size, location, speed, and maximum of the plasma frequency) and the comparison of simulated and measured ionograms make the assessment of real parameters of the patches possible.
3.1 Plasma Frequency of the Patch
 The estimation of the critical frequency of the ionosphere directly from the ionogram is not a straightforward task. Usually, the critical frequency is associated with the length of the main trace of the ionogram. However, this is correct only in the case of stratified media (i.e., without horizontal gradient of electron density).
 As an example, the ionogram represented in Figure 10a (Thule on 20 January 2006, 19:00 UT) is examined. The adapted ionogram is shown in Figure 10b. The structure of this ionogram corresponds to the fork type. The splitting frequency is about 5 MHz, and the trace continues up to 8 MHz. The simulated ionogram best fitted to the observed one is presented in Figure 10c. The relative power of the propagation modes in decibels is shown by gray scale in all simulated ionograms. It is calculated for the background ionosphere parameters corresponding to 20 January 2006, 19:00 UT (the Kp index was 3, the sunspot number was 16, the Bz component was about zero, and the critical frequency of the F layer of the ionosphere was 3.2 MHz). The maximum of the patch plasma frequency, which is embedded into the background ionosphere, is 7 MHz. The size of the patch is 600 km along and 400 km traverse to the direction of motion of the patch. The center of the patch is located at 100 km away from the receiver.
 Another ionogram with the same structure (fork) is shown in Figure 11a (Thule on 14 January 2011, 19:00 UT). In the corresponding ionogram (Figure 11b), the splitting frequency is about 5 MHz, and the trace continues up to 7 MHz. In order to simulate the ionogram with the similar structure (Figure 11c), the plasma frequency of the modeled patch of about 5 MHz is required. This ionogram is calculated for the background ionosphere parameters corresponding to 14 January 2011, 19:00 UT (the Kp index was 2.2, the sunspot number was 14, the Bz component was about zero, and the critical frequency of the F layer was 3.9 MHz). As was expected, the decreasing of the patch plasma frequency results in the diminishing of the splitting frequency and the shortening of the main trace. The signature of the patch of enhanced electron density with the maximum of the plasma frequency of 2 MHz and less is not detectable in the simulated ionograms.
3.2 Patch Speed Evaluation
 In order to estimate the speed of the patch, it is necessary to examine a number of ionograms in a row. The ionograms recorded on 14 January 2011 were selected for this purpose.
 The ionogram structure was very variable in that day. A number of major types of the ionograms were observed in spite of the geomagnetic activity being moderate in this period. The Kp index was between 2 and 3, and the sunspot number was about 14. The Bz component of the IMF changed its sign varying between −2 and 2 nT during the day. After 16:00 UT, the Bz component was about zero (http://omniweb.gsfc.nasa.gov), and the critical frequency of the F layer decreased from 4.7 to 3.9 MHz.
 The first pair of ionograms corresponds to 19:00 UT (Figure 11a) and 19:15 UT (Figure 12a). In 15 min, the ionograms structure has changed from a fork structure (Figure 11b) to a U-shaped one (Figure 12b). The ionograms presented in Figures 11c and 12c were simulated for the background ionosphere parameters corresponding to 14 January 2011. The size of the patch was about 600 km along and 400 km traverse to the direction of motion of the patch. The patch plasma frequency was set to 5 MHz. The simulations show that the fork structure is typical for ionograms in the case when the patch is located near the receiver. As soon as the edge of the patch passes over the receiver, the structure of the ionogram is changed to a U-shaped one. In order to simulate the transformation of the fork (Figure 11c) ionogram structure to the U-shaped one (Figure 12c), it was necessary to shift the center of the patch from 100 to 400 km away from the receiver.
 The resemblance between experimental (Figures 11b and 12b) and simulated (Figures 11c and 12c) ionograms confirms the validity of the parameters. In this case, the patch speed was about 300 m/s. It is a rather typical drift velocity of the patch that may vary from hundreds of meters per second up to 1 km/s [Ma and Schunk, 1997].
 The second set of ionograms displays the evolution of a complex ionogram structure (Figures 13a and 13b) to the transitional phase between complex and U-shaped structures (Figures 14a and 14b). This type of ionogram structure is discernible for slightly splitting long main trace with an arc near the end of the trace. These two ionograms (Figures 13a and 14a) were recorded in a 15 min interval. Simulated ionograms were calculated for the patch size of 600 km along and 400 km traverse to the direction of motion of the patch and the plasma frequency of 7 MHz. The center of the patch was shifted from 350 to 550 km (Figures 13c and 14c, respectively) away from the sounder. In this particular case, the speed of the patch was approximately 200 m/s.
3.3 Size of the Patch
 The next task is the assessment of the size of the patch of enhanced electron density. First of all, it is necessary to take into account that the location of the ionosonde (Thule/Qaanaaq 77.5°N, 69.2°E) is in a vicinity of the geomagnetic pole. In this area, the size of the patches is usually rather small. Their size and shape can change significantly in the process of the further drift.
 In the cases shown in Figures 11c and 12c, it was accepted that the patch size was 600 km × 400 km, with the plasma frequency of 5 MHz. Similar ionogram structures (fork and U shaped) occur also for larger patches. The size of the patch shown in Figures 15 and 16 was 1200 km × 600 km. All ionograms depicted in Figures 11c, 12c, 14, and 15 were calculated for the background ionosphere parameters corresponding to 14 January 2011 and the embedded patch with the plasma frequency of 5 MHz. However, it is evident that the similarities of the ionograms (Figures 15 and 16) with the ionosonde data (Figures 11b and 12b) are observed only in ionogram structures, but not in the length of the main trace and the value of the splitting frequency. On the contrary, simulated ionograms (Figures 11c and 12c) are similar to the measured ones (Figures 11b and 12b). Hence, the conclusion that the observed ionograms (Figures 11b and 12b) correspond to the patch of enhanced electron density, the size of 600 km × 400 km, and the plasma frequency of 5 MHz seems to be quite consistent.
 In contrast to fork and U-shaped ionograms, the simulation of a complex structure (Figure 13b) usually requires accepting the larger patch size.
3.4 Uncommon Ionogram Structures
 The ionogram structures discussed before were observed frequently. Simple, fork, complex, and U-shaped ionograms occur in measurements rather often, while the ionograms with detached spots were observed quite rarely. The ionogram recorded on 5 January 2012, 19:00 UT, is shown in Figure 17a. The simulated ionogram presented in Figure 17c corresponds to the parameters of the background ionosphere on 5 January 2012. It was accepted that the size of the patch was 1200 km × 600 km, with the plasma frequency of about 9 MHz. The variation of the patch size shows that only large patches can produce a U-shaped with spot structure. The center of the patch is located about 800 km away from the receiver, i.e., the distance between the edge of the patch and the receiver is about 200 km.
 The multiple U–type ionograms occur only at a particular date, but they are rather typical during that day. The ionogram recorded at Thule (THJ77) on 9 September 2011, 17:00 UT, is presented in Figure 18a. The multiple U structure is highlighted in Figure 18b. A geomagnetic storm occurred on that day. After 12:00 UT, the value of the Kp index exceeded 3, and after 15:00 UT, it rose up to 5.5. During this period, the southward Bz component of the IMF reached a minimum of about −9 nT. The sunspot number was 47 (http://omniweb.gsfc.nasa.gov). The critical frequency of the F layer at 17:00 UT was 4.1 MHz. At least three U-shaped structures are evident on this ionogram.
 It was not possible to simulate such structures using the current model of the patches. This is a matter for further investigation to improve the model.
 The structure of the high-latitude F region ionosphere and the occurring processes are quite different from the middle-latitude ionosphere due to the presence of the localized regions of enhanced electron density, namely, the polar cap patches and Sun-aligned arcs. In a period of about 15 min, the structures of the ionograms can change significantly, and the length of the ionogram traces varies by a factor of 2–3.
 The model of the ionosphere with irregularities (polar cap patches and Sun-aligned arcs) has been used to simulate the vertical ionograms in the polar cap area. There is a good resemblance in shape between simulated and observed ionogram traces for high latitude. Adjustment of model parameters may be employed to estimate the proper characteristics of the high-latitude large-scale ionospheric inhomogeneities.
 Various shapes of traces on the ionograms were classified by types (simple, ionogram typical for middle latitudes; fork, ionogram with splitting at the end of the trace; complex, ionogram with multiple splitting; U shaped, ionogram with an arc shape trace; spots, ionogram with detached spot; and multiple U structures). The model enables us to simulate the majority of ionogram structures.
 The ionogram structures evolve from fork to simple via complex, spots, and U-shaped types, while patches travel in the vicinity of the receiver.
 The influence of a patch on the ionogram structure is getting weak if the distance between the edge of the patch and the receiver exceeds 400 km. There is no dependence on the patch size.
 The maximum of the plasma frequency of the patch in the polar region is not associated directly with the length of the ionogram main trace. However, the simulations show clear correlation between the patch plasma frequency and the value of the splitting frequency of the ionogram traces and the length of the traces as well.
 The assessment of the patch speed requires considering a number of ionograms consecutively observed in a relatively short time. An analysis of the sequence of the simulated ionograms allows us to evaluate the patch speed, making the assumption that in this interval, the main parameters of the patches (plasma frequency, speed, and size) do not change significantly.
 Simulation of ionograms provides the interpretation of vertical sounding data and the estimation of the plasma frequency, speed, and size of the patch of enhanced electron density.
 The authors are grateful to the University of Massachusetts Lowell Center for Atmospheric Research for the Digisonde data.