Ionospheric F-region patches are 2–10 larger than background electron densities in the polar ionosphere. The EISCAT Svalbard incoherent radar (ESR) observed a sequence of patches between 2000–2200 UT on 12 December 2001. In this paper the source of these structures is investigated using several other data sets, together with a convection-driven trajectory analysis. The data are assimilated into Ionospheric Data Assimilation Three Dimensional (IDA3D). The background model used is the National Center for Atmospheric Research-Thermosphere Ionosphere Mesosphere Electrodynamics General Circulation Model (NCAR TIMEGCM). The trajectory analysis is based on maps of ionospheric convection obtained from the Assimilative Mapping of Ionospheric Electrodynamics (AMIE). In addition to patches, a tongue of ionization (TOI) is investigated. It is shown that patches formed part of the TOI. It is tempting to conclude the TOI and the patches originate at midlatitudes. However, the IDA3D and trajectory analysis suggest that they were transported toward noon from the morning and afternoon sectors near 62° geographic latitude. Thus for this case the TOI and patches did not originate at midlatitudes. This work represents advances in the field of patch research. A new capability to perform an analysis of patch origin and fate, using three-dimensional (3-D) ionospheric assimilation and 2-D trajectory analysis codes, is demonstrated for a sequence of patches observed 12 December 2001. The current resolution of the technique is not able to identify detailed patch formation mechanisms. However, by it can track the plasma back in time to locations and times where patch formation mechanisms operate.
 Ionospheric F-region patches are factor of 2–10 increases over background electron densities in the polar cap, extending 100–1000 km in horizontal extent. They were discovered by Weber et al.  and since then have been studied extensively (see reviews by Crowley , Dandekar and Bullett , and Basu and Valladares ). We still lack a satisfactory explanation of why the plasma density in the polar cap can sometimes be much higher than expected based on solar illumination arguments and, second, why the high densities are often separated by regions of low density. The reason why this is important is to be able to eventually predict the occurrence of patches and their detrimental effects on various technological systems. Several mechanisms have been proposed to explain the formation of the patches but most rely on high-latitude convection to transport ionospheric plasma from the dayside of the polar cap toward the nightside, with or without the effects of particle precipitation. Crowley et al.  showed how patches are transported into the midnight sector, where they are transformed by the sunward convection flow into elongated slivers of plasma called “blobs” in the auroral and subauroral latitudes.
 Practical space weather concerns make it important to understand the formation, transport, and evolution of polar cap patches and blobs. Large plasma structures on scales of >100 km horizontal scales have significant effects on various radar and radio systems, causing degradation in the form of phase advance, time delay, bending, and errors in doppler shift for many practical RF VHF systems, including many military systems. In addition, the sharp gradients on the sides of patches and blobs can be unstable to the growth of smaller-scale ionospheric irregularities, leading to severe scintillation and degradation of satellite communications and navigation signals [Buchau et al., 1985; Basu and Valladares, 1999].
 In order to predict the system effects of large-scale structure, and the formation of ionospheric irregularities in the polar cap and auroral zone, it is necessary to know the ionospheric electron density distribution, including patches and blobs. A major obstacle to progress in this area has been the lack of ionospheric measurements at high latitudes. To predict patch motion, it is also necessary to know the high-latitude convection pattern, which is generally complex and time-varying. As pointed out by Crowley , the sheer size of the polar cap region and the inhospitable polar conditions make it difficult to deploy instrumentation or to obtain sufficient observations of the patch plasma and its motion.
 Colocation of instruments at high-latitude sites has led to some insight into patch formation mechanisms and transport over a limited local area. For example, Valladares [Valladares et al., 1994, 1998] studied patch formation over Sondrestromfjord using the incoherent scatter radar and other instruments located in Greenland. Carlson et al.  developed new observation modes at the EISCAT Svalbard Radar (ESR) to test patch formation mechanisms. Carlson et al.  used colocated optical instruments and the ESR to verify that their mechanism was operating in a particular event.
 In this paper we demonstrate two new tools for specifying plasma enhancements such as patches and blobs throughout the entire high-latitude region and for tracking the evolution of patches as they are transported from the dayside to the nightside of the polar cap. In future papers these tools will be used to study patch formation mechanisms; however, in this paper we focus on the transport of plasma across the polar cap without reference to the formation mechanisms for the patches. In particular, we describe a sequence of patches observed at Svalbard by the ESR, and we show how the patch plasma originated on the dayside and was transported to Svalbard. This study extends and enhances the work on patch evolution reported earlier by Crowley et al. .
 One of the primary new analysis tools used in this study is the Ionospheric Data Assimilation Three-Dimensional (IDA3D) algorithm. IDA3D is an ionospheric spatial analysis algorithm that uses multiple data sources to obtain a global three-dimensional (3-D) specification of electron density [Bust et al., 2004]. In the past the background ionosphere for IDA3D has been provided by the IRI empirical model. However, in this paper for the first time, the background ionosphere was provided by a first-principles, fully coupled, global 3-D ionosphere-thermosphere model. For this study, ground-based GPS data, tomographic data from Alaska and Greenland, ionosonde data, incoherent scatter radar (ISR) data, in situ data from the DMSP and CHAMP satellites, GPS occultation data from the CHAMP satellite and oversatellite electron content (OSEC) from the CHAMP and SAC-C satellites were available to IDA3D.
 The second analysis tool described in this study is the 2-D trajectory analysis code of Crowley et al.  that utilizes realistic high-latitude convection patterns. These patterns are obtained from another assimilation code, called Assimilative Mapping of Ionospheric Electrodynamics (AMIE), which will be discussed in more detail below.
 IDA3D and AMIE are neither models nor simulations but assimilation algorithms that ingest copious amounts of high-latitude data. Both IDA3D and AMIE make use of advanced inverse methods to organize the raw data into images (or maps) of ionospheric structure. However, neither IDA3D alone nor AMIE alone provides complete information on the transport of patch plasma. IDA3D contains no information about convection velocities, while AMIE contains no information about electron densities. What is new here, is the combination of 4-D observations of electron density (through IDA3D) with the transport of the plasma (through AMIE and the trajectory analysis) to investigate and interpret a specific observational case study, a sequence of patches observed by the ESR. We also examine the origin of plasma in a tongue of ionization (TOI) and show how it is related to the patches.
 The rest of the paper is organized as follows: sections 2.1, 2.2, and 2.3 describe the IDA3D technique, the Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model (TIMEGCM) used to provide a background ionosphere for IDA3D, and finally the trajectory analysis package using AMIE potential patterns, respectively. Section 3 presents results obtained from the IDA3D analysis, while section 4 presents the trajectory analysis of the patch events.
2. Description of Tools Used in This Study
2.1. Ionospheric Data Assimilation Three-Dimensional (IDA3D)
 IDA3D is an objective analysis algorithm, based upon three-dimensional variation (3DVAR) data assimilation. This mathematical technique [Daley, 1991; Daley and Barker, 2000] is similar to a least squares fit between the full set of observations and a background specification. As with all analysis algorithms, the observations are interpolated onto a predetermined grid, which allows the measurements to be shown collectively and for larger-scale (larger than a single observation) phenomena to be observed. 3DVAR not only uses the specification and observation errors but also includes the correlation between grid points. In a perfect world the observations would completely span the system, and 3DVAR (and hence IDA3D) would only be an interpolation algorithm. However, such data sets do not exist and a background specification is needed to complete the system.
 IDA3D works by solving the standard 3DVAR equations for ionospheric electron density
where is the analysis electron density at a given time, is the forecast electron density for that time, is the set of electron density and electron content observations, Pa is the analyzed error covariance, Pf is the error covariance matrix for the forecast model, Po is the error covariance matrix for the observations, and the matrix H transforms the predicted electron density to the form and location of the observations. HT refers the the transpose of the matrix H.
 The forecast electron density and error covariance matrix are specified as
where is the specification from a background electron density model, τ is the estimated correlation time, tn is the present time step, tn−1 is the last time step, and Pb is the error covariance matrix for the background electron density model. The analysis, forecast, and background model electron densities are stored as vectors (, , and , respectively) for mathematical elegance and computational efficiency. There are corresponding vectors that associate the electron density with a latitude, longitude, and altitude. The observation vector contains all available data sets that can be incorporated into IDA3D. The transformation matrix H contains the information necessary for predicting the value of the observation from the forecast density vector. The error covariance matrices represent the error between the analysis, observation, or background and the true value of the electron density and the correlation between any two given observations or grid points. It can be separated into an error variance matrix, which is a diagonal matrix, and a correlation matrix between different observations or grid points.
 There are several important properties of equations (1) and (2) that are not immediately obvious. First, it is essentially a least squares weighted fit between the observations and the forecast specification. Second, the covariance matrices contain both the errors and the correlations between grid points. While the observations are usually assumed to be uncorrelated, the background model typically has correlations between grid points. These correlations spread the impact of the observations to a larger region within the model grid. Third, the specification vector depends upon −H rather than H−1−. In words, this means that specification is based upon how well the background model predicts the observations, instead of how well the observations agree with the model. Hence the data is manipulated as little as possible. Finally, any observation that can be predicted from the background model can be ingested. Typically, observations are limited to data sets that can be predicted without major assumptions or complex calculations. These properties make IDA3D a very flexible platform for creating global electron density specifications, but the value of these specifications is dependent upon the amount, the distribution, and the quality of the observations.
 To solve equations (1) and (2), IDA3D needs certain inputs. These include a background climatology with a model grid, electron density specification and correlations, and the set of observations easily related the electron density. The model grid is an input that is chosen for its compatibility with the specific scientific investigation that is planned. It should be noted that IDA3D is not rigidly linked to any background model. The impact of the background model is significantly reduced by application of the Gauss-Markov Kalman filter technique. A Kalman filter [Daley, 1991] is a data assimilation technique that uses the map and error covariances from the previous time step as the background model and error covariances for the present time step. In this way the effects of the background model are reduced from the ionospheric maps after several interactions. Unfortunately, the Kalman filter cannot completely remove the background model effects since the effectiveness of past electron density maps decreases rapidly with time.
 The model correlations are treated as inputs that are independent of the background model. However, as a model input, the correlation values could be based upon the model values. At present, the correlations are treated as correlation lengths in latitude, longitude, and altitude. The model correlations decrease exponentially as the ratio of the distance between the model points and the correlation length. The horizontal and vertical distances are treated separately. In addition, a correlation time τ is given as input. These correlations allow the data to impact a larger region of the specification than just of the grid points affected by the observations and allow past observations to impact the present specification. Using these techniques, IDA3D is able to ingest any available observation of electron density or electron content.
2.2. Global 3-D First Principles Modeling With TIMEGCM
 A family of Thermospheric General Circulation Models (TGCMs) was developed in the early 1980s to study the global temperature, circulation, and chemical structure of the thermosphere and its response to solar and auroral activity. The NCAR model now reaches down to 30 km, includes the mesosphere and upper stratosphere and is known as TIME-GCM [Roble and Ridley, 1994]. It predicts winds, temperatures, major and minor species concentrations, electron densities, and electrodynamic quantities globally from 30 km to about 600 km altitude. The standard NCAR model uses a fixed geographic grid with a 5° × 5° horizontal resolution, and a vertical resolution of a half pressure scale height. The model time step is typically 2–3 min, but rapid changes and storms usually require 1-min time steps to maintain model stability. Recent versions of the TIME-GCM can also be run with a 2.5° horizontal resolution and a quarter scale height vertical resolution; however, the high-resolution version requires shorter time steps and is extremely demanding of computational resources.
 The TIME-GCM codes were originally developed at NCAR for a CRAY Supercomputer environment but have been ported to a workstation environment [Crowley et al., 1999]. The new code can be run on a single PC or on a Beowulf cluster, consisting of a number of high-end PCs. It has been thoroughly tested and validated to ensure it produces the same results as the NCAR codes, given the same inputs, to within numerical accuracy of the personal computers.
 The TIME-GCM has played an important role in understanding the characteristics of the upper atmosphere. An essential part of the TIME-GCM's success is due to its detailed input specification. Among the inputs is the solar ultraviolet flux at 57 key wavelengths, parameterized by the solar 10.7 cm radio flux (F10.7). Properties of the semidiurnal tides propagating up from the lower atmosphere are generally unknown for specific simulation intervals and are specified at the lower boundary using seasonal averages derived from the Global Scale Wave Model of Hagan et al. , although they can be tuned for specific dates if sufficient tidal data are available.
 Other inputs required by the TIME-GCM include high-latitude particle precipitation and electric fields in order to correctly specify the Joule heating and momentum forcing. Roble and Ridley  developed an analytical formulation of the auroral oval and introduced the use of the analytical Heelis convection model [Heelis et al., 1982], including distortions attributable to the interplanetary magnetic field (IMF) By component (see Heelis et al.  for more details).
 The magnitude of the cross polar cap potential difference needed to drive the Heelis potential model can be estimated in a number of ways. In this study, values of the cross-cap potential difference were obtained using the Weimer  empirical model driven by IMF data measured by the ACE satellite. This resulted in reasonable global simulations and was adopted in the present study to provide a background ionosphere for the IDA3D assimilation algorithm. The AMIE convection patterns can be used as a driver for the TIME-GCM but were not used in the present study because of the extra work and because the TIMEGCM is simply being used to provide a starting point for the IDA3D assimilation. This is the first time that the TIMEGCM or any of the NCAR GCMs have been used in an assimilative model, although we emphasize that ionospheric data were not directly assimilated into TIMEGCM here.
2.3. Assimilative Mapping of Ionospheric Electrodynamics (AMIE) and 2-D Plasma Trajectory Analysis
 Ideally, we need to completely define the high-latitude convection pattern in order to specify its effect on plasma transport and its interaction with the neutral thermosphere via momentum transfer and Joule heating. This would require that convection drifts would be routinely measured at high resolution throughout the high-latitude region. In reality, what is available is a sparse collection of single-point measurements irregularly located in space and time. One approach to solving this problem is the use of assimilative techniques, such as the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) procedure of Richmond and Kamide , mentioned above. AMIE is an inversion technique that ingests data from a wide range of sources to produce a realistic representation of the high-latitude electrodynamic state for a given time [Richmond and Kamide, 1988; Richmond et al., 1992]. The data inputs typically include electric fields derived from ion velocities measured using radars and satellites, together with magnetic perturbations from ground- and space-based instruments. Using these data, the distribution of various electrodynamic parameters such as the electric potential and electric field can be derived through the electrodynamic equations. The Northern Hemisphere AMIE patterns used in the present study benefited from several data sets. Direct measurements of ion drifts were available from nine SuperDARN radars (Pykkvibr, Hankasalmi, Kapuskasing, Kodiak, Stokkseyri, Saskatoon, King Salmon, Goose Bay, and Prince George) and the DMSP F12, F13, F14, and F15 satellites (although much of the F12 data were found to be unreliable for this period). The SuperDARN radar and DMSP velocity measurements were binned to the AMIE grid prior to ingestion into AMIE. In addition, magnetic perturbations were ingested from 128 ground-based magnetometers in the Northern Hemisphere. The background electric potential model used by AMIE was the Weimer  empirical model, driven by ACE solar wind data.
 High-latitude potential patterns from AMIE were utilized by Crowley et al.  to drive a trajectory analysis model for ionospheric plasma. The model combines the F-region ion drifts from AMIE together with corotation E-fields to specify the trajectory of plasma in inertial coordinates. Both forward trajectories and back trajectories can be obtained, permitting investigation of the evolution and source of an ionospheric plasma parcel, respectively. Crowley et al.  used their model to study the evolution of patches on the nightside and their subsequent transformation into blobs. In this paper we track patches subsequent to their formation on the dayside until their detection in the midnight sector before they become blobs.
3. Description and Analysis of Experimental Data
Figures 1a and 1b show EISCAT Svalbard Radar (ESR) observations between 1800 and 2300 UT on 12 December 2001. The ESR is located at (78° 09′N and 16° 02′E). The observations were obtained from an observational program with a radar elevation of 30° and two look-directions with interleaved azimuths of 170.0° (Figure 1a) and 185.3° (Figure 1b). The data from the two look-directions are similar, but both are shown to illustrate the spatial variability of the high-latitude plasma. In both Figures 1a and 1b, low electron densities with Ne < 4.0 1011 m−3 at 350 km were observed for several hours followed by a sequence of electron density enhancements between 2000 and 2130 UT, with another broader structure from 2130 to 2215 UT. The enhancements are ionospheric patches: they contained values of 1.0 1012 m−3 or greater, but they were generally short−lived and separated by values of ∼4.5 1011 m−3.
 Simultaneously, the University of Wales tomography array with receivers located on both Svalbard and northern Norway [Kersley et al., 1993] observed ionospheric structure. Their tomographic images (not shown) revealed patch enhancements between 76 and 86 degrees geographic latitude, with the most northern enhancement having densities >1.2 1012 m−3, remarkably similar to the EISCAT observations (E. Pryse, private communication). These observations complement the ISR in several ways: by confirming the overall patchy nature of the ionosphere over Svalbard and Norway and by confirming that the patch structure is extended over a large spatial region and not merely local to Svalbard or the ESR field of view.
Figure 1c presents the interplanetary magnetic field components By and Bz for this time period. The two components are relatively stable and slowly varying except for the reversal of By near 2040 UT (note the IMF data from the ACE satellite have been time-shifted to account for the propagation velocity from ACE to the magnetopause).
 In this paper we investigate the observed high-latitude ionospheric structure and show how the IDA3D and AMIE techniques can be combined to identify the sources and development of structured plasma at high latitudes.
3.2. IDA3D Quasi-Global Analysis
 IDA3D analysis permitted the high-latitude electron density distribution to be mapped for 12 December 2001, based on assimilation of all the available ionospheric data. Data coverage during this period was very good, as described in detail below. Figure 2 shows the availability and distribution of data assimilated into IDA3D for the 2 hour period between 2000 and 2200 UT. Black dots represent 350 km intercepts of GPS TEC data from a large number of stations distributed throughout North America, Alaska, Greenland, and Europe. While the TEC represents a measure of the integrated plasma along the path between the ground receiver and the satellite, the 350 km intercept point represents the location where the measurement most affects the F-region assimilation result. The ARL:UT Greenland tomographic array [Watermann et al., 2002] collected data from numerous satellite passes during this period and provided ground-based beacon “tomography” TEC. Tomography TEC was also available from the Alaska array. Dark blue squares and lines represent tomographic receiver locations and the 350 km satellite track intercept for that receiver. In addition, numerous ionosondes (green triangles) measured NmF2 and HmF2, and electron density profiles were available from the Sondrestrom, Greenland, and EISCAT incoherent scatter radars (red diamonds). Finally, DMSP satellite measurements (orange dots) of in situ electron density at 840 km and space-based GPS occultation TEC (pale blue lines), and oversatellite electron content (OSEC) (pale dashed blues lines) from the CHAMP satellite were also assimilated. Figure 2 reveals that there is a gap in data coverage (except for OSEC data which is >400 km altitude) over the Arctic Ocean between Greenland, and Russia (∼77°−85° geomagnetic latitude and from ∼90° to 180° geomagnetic longitude).
 One of the unique features of global assimilation is that the resulting electron density grid can be sliced in various ways to provide images of the electron density distribution in different formats. We now present various slices to illustrate the state of the high-latitude electron density distribution. In Figure 3 we show a sequence of horizontal cuts through the polar cap electron density distribution for 350 km, obtained from IDA3D. The sequence covers the same interval (1830–2200 UT) as shown in Figure 1. Although IDA3D was run every 5 min, only 30 min intervals are shown here. The plots are drawn with noon at the top of the figure and midnight at the bottom. The latitude–longitude grid, shown as white broken lines represents magnetic coordinates. The terminator is shown as a black line. The continental outlines provide useful reference points. The solid white lines in several of the images show DMSP trajectories that occurred during the same time period. On the dayside, below magnetic latitudes of ∼70°, maximum electron densities occur in the postnoon sector and reach values of >2.5 1012 m−3 (red color).
 At 1830 UT, and subsequent times, there appears to be an extension of these large midlatitude densities into the polar cap. This extension is a manifestation of the well-known tongue of ionization (TOI). TOI have been previously observed [Crowley et al., 2000] and modeled [Sojka et al., 1993]. It is generally accepted that the TOI arises from the transport of midlatitude plasma into the polar cap by antisunward convection in the noon sector, although the evidence for this is still circumstantial at best. To demonstrate this mechanism conclusively requires simultaneous measurements of both the plasma and the convection pattern over a broad spatial extent, and the observations must extend over a sufficient length of time to track the motion and evolution of the plasma enhancements. To our knowledge, these two observational requirements have never been fully met until the present study, in which the IDA3D technique is combined with the parcel trajectory analysis based on detailed AMIE convection patterns. The combination produces some surprising results, as described below.
 Beginning near 1900 UT, the enhanced tongue of ionization in Figure 3 apparently enters the polar cap in the ∼1400 MLT sector and extends toward the geomagnetic pole. However, the TOI does not appear to be completely continuous. Closer observation of Figure 3 reveals that the TOI is highly structured. There is a temptation to view these snapshots as frames in a movie and to interpret the structuring as large patches being pinched off from the TOI. However, it is possible they are not being transported by the convection pattern or that they are artefacts of the IDA3D analysis. Thus only by combining the IDA3D images with a trajectory analysis can their identity as patches and the transport concept be confirmed.
 The (slightly overlapping) orange dots in Figure 3 represent the location of the Svalbard ESR observations at 350 km altitude. Since the ESR was looking south, with a 30° elevation angle, the actual geographic location of the observations (at 350 km altitude) for the 185° azimuth case is at (73.3°,14.5°) geographic latitude and longitude. For the 170° azimuth case, the geographic location of the observations at 350 km altitude is (73.3°,18.7°) latitude and longitude. These observations are between Svalbard and the northern coast of Norway. The IDA3D images indicate considerable variability in this region in the 1830–2200 UT time frame. From 1830 to 1930 (first three images), IDA3D specifies low-density plasma in this region, in agreement with the ESR observations of Figure 1. However, at 2000 to 2230 UT, IDA3D produces a region of high-density plasma between Svalbard and Norway, which corresponds to the observed sequence of patches in Figure 1.
 To show the correspondence between the IDA3D and the ESR observations more clearly, Figure 4 presents a comparison of the ESR observations at 185° azimuth versus the IDA3D electron densities interpolated onto the ESR observation locations. Figure 4a depicts the ESR observations as presented in Figure 1b. Figure 4b illustrates the IDA3D analysis, without the inclusion of the ESR observations in the assimilation, while Figure 4c shows the result of including the ESR data in the assimilation. Figure 4b contains an electron density enhancement similar to that observed by the ESR between 2000 and 2130 UT. Although the large plasma enhancement observed between 2130 and 2230 UT is generally overestimated by IDA3D and extends for about 2 hours, compared with the 1 hour enhancement observed by the ESR, this level of agreement is remarkable considering that only a handful of ground-based GPS TEC observations were available in the Svalbard region. It is much higher fidelity than could be obtained from any empirical or first-principles model of the high latitude region. As expected, when the ESR data is directly assimilated (Figure 4c), IDA3D is able to produce an even better representation of the electron density and matches the observed data very closely, showing what can be achieved with detailed radar data coverage.
 The plasma structures observed by the ESR are clearly patches observed on the nightside of the polar cap, and one might suspect a relationship with the “patchy” TOI development noted in Figure 3. The accuracy of the 4-D ionospheric imaging leads to the question of whether a sequence of IDA3D images can be used to investigate the evolution of the TOI/patch structure. Unfortunately, the lack of data in the critical Arctic Ocean region between Greenland and Norway prevents us from proving a causal connection between the dayside TOI/patches and the nightside ESR observations using IDA3D alone. The current resolution of the IDA3D grid is also a limiting factor because the patches observed by the ESR have a diameter of only about 50 km, as discussed below. To prove this connection therefore, another tool is required that can be used to indicate the patch trajectory in locations where the electron density was not measured.
4. Modeling and Trajectory Analysis
 In order to connect in space and time, the IDA3D evidence for the TOI with the ESR patch observations, we use a trajectory analysis of the plasma flow based on convection patterns obtained using the AMIE technique. Figure 5 shows the electron density distribution from IDA3D for 1800 UT. At this time, the AMIE patterns remained fairly constant and Figure 1 showed that Bz and By remained stable. Superimposed on the figure is the AMIE potential pattern with the effects of corotation added. At lower latitudes, the plasma simply corotates. This AMIE pattern suggests that plasma flows antisunward across the northern face of Greenland near 13 MLT and then on toward Svalbard. A tongue of ionization extends from the dayside over Qanaq, and it is tempting to assume that the entire tongue of ionization, including the portion over Qanaq, originated from the midlatitude noon sector, as has commonly been claimed. Our trajectory analysis permits this hypothesis to be tested.
Figure 6 shows a backward trajectory analysis starting at Qanaq at 1800 UT. The trajectory analysis reveals the location of the ionospheric parcel as it is transported by the changing convection pattern for 5 hours between 1300 and 1800 UT. In our analysis, we ran AMIE at 5 min intervals but computed new parcel locations every minute to achieve high fidelity in the trajectories. Longer time steps or slower cadence in AMIE leads to unacceptable errors in the trajectories, as discussed by Crowley et al. . The trajectory analysis reveals that the ionospheric parcel in this case began its life in the morning sector near 62 degrees geographic latitude. It remained near this latitude for several hours as it was transported toward the noon sector, before being carried into the polar cap. Thus the plasma observed over Qanaq in this case did not come from the midlatitude noon sector but was always poleward of 62 degrees geographic latitude. Trajectories were computed for various locations within the TOI with similar results. Thus the idea that the TOI originates at midlatitudes is shown to be false in this case. In fact, we have examined many AMIE convection patterns, and it is rare for significant convection to extend to middle latitudes, even in the U.S. sector, which is at high magnetic latitude for a given geographic latitude. Thus the TOI and patches cannot generally originate at middle latitudes except in rare cases.
 Using a similar trajectory analysis, it is possible to investigate the source of the patches observed by the ESR in Figure 1. We identified six patches from Figure 4. The center of the first five patches occurred at ∼2005, 2030, 2045, 2055, and 2105. In the case of patch 6, which is much longer-lived, the start and end times are ∼2130 and 2215. For this analysis, each patch was given a radius of 25 km at the ESR observation point, which is approximately the patch size deduced from the radar data, as discussed in more detail below.
 By starting the patches at the Svalbard ESR location and running the trajectories in reverse for several hours, using the appropriate convection patterns, we find that the patches originated in several different locations. We should note that the trajectories shown here are fairly robust, meaning that small changes in the convection pattern introduced by including or omitting single data sets from the AMIE assimilation make small differences to the computed trajectory. Because there are uncertainties in the AMIE convection pattern, the uncertainty in the patch trajectory increases the longer we integrate backward or forward.
Figure 7 summarizes the backward trajectory of the patches arriving at Svalbard at 2005 UT (Figure 7a), 2030 UT (Figure 7b), and 2105 UT (Figure 7c). The plasma in the 2005 patch (Figure 7a) began life in the afternoon sector near 70° and 1500 SLT, where it was transported sunward. Near 1230 MLT, it was carried to higher latitudes, across the polar cap and subsequently out onto the nightside at Svalbard. For the second patch, our analysis indicates that the very small (25 km radius) plasma parcel that arrived at Svalbard at 2030 UT had earlier been stretched across several hours of local time (0800–1130 LT) near 60–65° latitude. As the filament of plasma was convected across the polar cap, its extent reduced significantly, until at Svalbard it was contained in a circular region with a 25 km radius. This figure indicates the large amount of mixing that can occur in the polar cap plasma, and that patches should not generally be thought of as holding their shape for long periods of time as they convect. The analysis again shows that like the TOI analysis in Figure 6, the patches did not originate in the midlatitude noon sector but entered the noon sector already at high latitudes (60–65 degrees). Finally, Figure 7c shows another parcel carried from the morningside 5 hours earlier. In this case the amount of stretching or compression of the parcel was minimal during transport to Svalbard. The choice of 5 hours for the trajectory analysis was somewhat arbitrary, but it provides a typical length of time for plasma to convect from the dayside to Svalbard.
 Although the plasma parcels in Figure 7 arrived at Svalbard within a few minutes of each other, they took very different paths to get there. Figures 8 and 9shows two snapshots indicating the relative locations of all six patches at two different times, superposed on the appropriate IDA3D electron density distribution at 350 km and AMIE equipotentials. Figure 8 shows their locations at 2005 UT, at the time the first patch (1) was observed by the Svalbard radar. At this universal time, the other patches are already in a line as if queueing to be convected into the radar field of view. Our analysis indicates that only a few kilometers separated them from each other. We note that patch 1 has a radius of about 25 km in Figure 8, which is much smaller than the IDA3D resolution. Thus the IDA3D electron densities appear to be smoothly varying compared with the patchiness observed by the ESR (see Figure 1). Nevertheless, the patches do appear to be associated with a region of relatively higher density (pale blue) in the IDA3D image.
Figure 9 shows the relative locations of the six patches at 1715 UT, almost 5 hours before the end of the sixth patch reached Svalbard. At this time, patch 1 that originated in the afternoon sector was already well into the polar cap. Although the plasma parcels all began the backward trajectory at the same place and with the same size and circular shape, Figure 9 shows that they had very different shapes and extents as they crossed the polar cap. For example, patch 2 was still elongated over about 700 km, while patch 5 was only stretched across about 100 km, and patch 1 had already attained its 25 km radius. We again note that the resolution of IDA3D is much coarser than the resolution available in the trajectory analysis of the patches. In this image it appears that patch 1 has entered a region of relatively low electron density, according to the IDA3D image. This could be due either to uncertainties in the IDA3D analysis for this UT or uncertainties in the AMIE convection pattern and resulting trajectory analysis. We also note that the IDA3D analysis suggests a significant depletion of electron density between patch 2 and patches 3–6.
 Unlike Figures 8 and 9, Figure 10 is not a “snapshot” but indicates the shape and location of each patch 5 hours before it was observed by the ESR. Five hours was chosen because this is generally about an hour prior to the plasma entering the noon sector and being swept to higher latitudes. It makes clear that the plasma originated either in the morningside or afternoon sector at geographic latitudes near 60–70°. The figure emphasizes that circular patches of plasma reaching Svalbard on the nightside can originate at very different latitudes and local times on the dayside. The exact location is determined by the convection pattern and its temporal changes during the patch transport. For example, in the present study, patches 3–6 passed close to Qanaq, while patches 1 and 2 remained at lower latitudes as they crossed Greenland (figures not shown).
 The parcel trajectories displayed here are limited in that we cannot yet compute changes in the electron density during transport. As an interim step, it is possible to record the locations of the plasma parcels and then to extract the electron density from the IDA3D analyses. For example, in Figure 11a we show the maximum value of the electron density (NmF2) from IDA3D, for patch 5 as the plasma is transported for 5 hours from its location in Figure 9 on the dayside to its observation by the ESR on the nightside. In the rest of Figure 11, we also show the latitude (Figure 11b), local time (Figure 11c), and solar zenith angle (Figure 11d) at the patch location. The interpolated IDA3D electron density is obtained at the patch location computed from the trajectory analysis. Also shown in the figure are the corresponding values from the background model (TIMEGCM), which are consistently larger than those obtained by data assimilation using IDA3D.
 The plasma density depends on ionospheric production and loss processes during transport. It appears that there are times when the plasma is transported to smaller solar zenith angles, and then the ionization rate is expected to increase and the plasma density will grow. On the other hand, plasma decay will occur during transport from the dayside to the nightside. The background model results exhibited the expected smooth increases and decreases: between 1600 and 1700 UT, when the plasma parcel was convected sunward in the morning sector, solar illumination increased and the plasma density increased. Each patch reached a minimum solar zenith angle (SZA) of about 88 degrees, before being swept to higher latitudes and larger solar zenith angles. The electron density deduced from TIMEGCM along these trajectories generally increased near the lowest solar zenith angles, presumably where production rates exceeded loss rates. At larger solar zenith angles, eventually decay rates exceed production, and a decrease in electron density occurs. The canonical lifetime for F-region plasma is about 1 hour, but this assumes solar illumination ceases. In practice, the plasma lifetime is longer than 1 hour, as shown in this TIMEGCM simulation.
Blelly et al.  attempted to simulate patch formation and transport using a first principles model ionospheric code driven by AMIE convection patterns and using an MSIS neutral atmosphere. Their results showed areas of agreement and disagreement with electron densities measured by the EISCAT UHF radar in Tromso. The quality of their convection patterns was insufficient to provide the detailed agreement sought in their simulations or to provide detailed insight into patch mechanisms. The AMIE patterns used in the present study are based on much more data and are expected to be more accurate. In addition, we found that our trajectories needed to be updated on a 1-min cadence in order to satisfy the Courant condition (Crowley et al. ), whereas Blelly et al. used a 10-min cadence. Nevertheless, they show that plasma can remain in sunlight for extended periods of time, in order to build up the plasma density to levels required for patches and observed by EISCAT. Their analysis of solar zenith angles is similar to those presented here, but they also invoke additional mechanisms for increasing the electron density: namely, compression of the plasma caused by downward transport at a rate that exceeds the loss rate and particle precipitation. Our simple 2-D trajectory analysis is unable to comment on such mechanisms. However, in our analysis, IDA3D provides detailed estimates of the 3-D electron density distribution globally, not just at EISCAT, thereby allowing us to investigate electron densities as they evolve along the patch trajectory. Thus the Blelly et al. paper and approach are complementary to the present paper and both represent an important step toward understanding, simulating, and predicting patch occurrence. Both suffer from our inability to precisely define the high-latitude convection pattern.
 The IDA3D electron densities were much more variable than those from the background model. However, the error bars shown in Figure 10 indicate that much of the variability in IDA3D electron density is within expected uncertainties in the IDA3D assimilation procedure. With a few exceptions, a smooth line can be drawn through the IDA3D error bars that mimics the shape of the background model variation but at 10% lower values, indicating that the IDA3D electron densities in patch 5 behaved much as expected. The other patches exhibited a similar behavior. The error bars shown in Figure 11 arise from three sources: (1) statistical uncertainty in the IDA3D inversion, resulting from uncertainties in the data; (2) an uncertainty ascribed to the background model values; and (3) the quantized grid representation. These error bars are typically ±20%. The maximum value of NmF2 at ∼1830 UT is due to the Qanaq ionosonde. The ionosonde data was manually scaled by the authors. However, there was a large amount of spread-F during this time period, making it difficult to accurately estimate NmF2. The NmF2 was likely overestimated and the error bars underestimated.
 We have examined the IDA3D analysis in more detail at the minimum and maximum values. There are four reasons why unexpected minima or maxima might occur in the analysis. They are (1) lack of data coverage; (2) IDA3D grid size (200 km north-south by 500 km east-west); (3) correlation length (>1 grid cell); (4) uncertainty in AMIE potentials leading to error in trajectory location. In the present case, the minimum electron density near 1930 UT occurs east of Greenland, over the Arctic ocean where we already noted the lack of data for assimilation. Since by definition, a patchy ionosphere contains large gradients, much of the variability of the electron density derived from IDA3D could result from only a few kilometers of deviation from the true patch location. The IDA3D results presented in this paper had a horizontal resolution of 2° of latitude. Thus when there are steep horizontal gradients, such as on the edge of a patch or TOI, IDA3D may misplace the location of the gradient by up to 100 km and therefore misspecify the density along a specific trajectory. In addition, uncertainties in the AMIE potentials (especially in data-poor regions) may contribute to positional uncertainties and variability of the apparent Ne along the patch trajectory.
 The present study provides insight into the scale size of the patches that were observed at Svalbard. Because the velocity of the plasma was measured by the ESR, we can infer that the size of the patches crossing the ESR was on the order of 50 km or less, based on their temporal extent in Figure 1. We have therefore modeled the trajectory analysis based on circular patches with 25 km radius because optical observations of patches often indicate that they are circular in the polar cap and in the nightside, although we have no evidence that they were circular in this case.
 A key question regarding polar cap patches is how they can become circular in the polar cap. Our analysis reveals that it is a natural consequence of their transport by the convection pattern. Patches appear to begin their lives as filaments of plasma that are convected across the polar cap from the dayside. In fact, our analysis indicates that circular patches in the polar cap often originated as narrow filaments on the dayside.
 The IDA3D analysis algorithm provides time-varying images of the ionospheric plasma distribution in the polar cap. They reveal a rapidly varying pattern of high and low densities, including the presence of the tongue of ionization, the trough, and polar cap patches. It is tempting to suppose that the high-density plasma in the tongue of ionization and patches is transported from middle latitudes in the noon sector. However, the associated trajectory analysis presented here suggests that many of the patches (if not all) do not originate at midlatitudes. Plasma parcels that are carried into the central polar cap have generally spent part of their lifetime on the edges of the convection pattern in the noon sector but at high latitudes (62–63 degrees geographic latitudes). Plasma at lower latitudes is not being affected by significant convection electric fields and is not transported into the polar cap.
 Our analysis focused on plasma observed from Svalbard by the ESR. The trajectory analysis showed that the plasma had entered the polar cap on the dayside and convected to the nightside. As mentioned above, the patches were transported along the edges of the convection pattern near 62 degrees geographic and never reached middle latitudes. Similarly, we examined plasma in the tongue of ionization over Qanaq. A backward trajectory revealed that the TOI plasma was never at middle latitudes. The convection patterns used in this study were obtained from the AMIE technique, and are thought to be reasonably reliable. Small changes in the amount of data ingested by AMIE certainly has an effect on the convection patterns and on the trajectories, but this is generally small. The AMIE assimilations are always limited by the lack of electrodynamic data for ingestion. Tests of the sensitivity of the patterns to different data sets revealed limited effect when single data sets such as a DMSP satellite were removed from the assimilation. During very disturbed times, AMIE does sometimes indicate that strong electric fields can occur at latitudes as low as 30 degrees geographic (40 degrees magnetic in the US sector) as shown by G. Crowley and G. Bust (Patch formation during the November 2003 superstorm, submitted to Journal of Geophysical Research, 2007). At such times, it seems possible that high-density plasma could be transported into the polar cap from middle latitudes. This might explain the narrow plumes of large electron density, known as Storm Enhanced Density events, observed over Millstone Hill, Massachusetts, by the Millstone Hill incoherent scatter radar [Foster, 1993; Foster and Vo, 2002; Foster et al., 2005]. However, a trajectory analysis should be performed for such events to confirm or deny the transport hypothesis. Without the trajectory analysis it is difficult to separate temporal and spatial variability in IDA3D images, as we have seen in the present study.
 Finally, the question was asked about whether the patches observed at Svalbard were related to the TOI deduced from IDA3D at 1800 UT (Figure 5). Figure 12 shows a zoomed-in section of the IDA3D electron density for 1800 UT, with the locations of the six patches at 1800 UT superposed. Note that the color scale has been changed from the log-scale of Figure 5 to a linear scale, to provide more detail. The figure reveals that patches 2–6 are following the center of the TOI, while patches 1 and 2 are located in regions of smaller electron density. The figure again emphasizes that the horizontal resolution of IDA3D is too coarse to provide the detail needed to resolve the small patches observed by the ESR.
 Unfortunately, the spatial resolution of the IDA3D electron density distribution is limited by the amount of data for ingestion, and therefore the IDA3D analysis cannot provide detailed information about small-scale mechanisms, such as FTEs [Lockwood and Carlson, 1992] or jets [Ogawa et al., 2001], that might contribute to patch formation. IDA3D has a spatial resolution of 200 km north-south and 500 km east-west and therefore cannot resolve an individual element of the 50 km diameter observed by the Svalbard ESR. Thus it is not surprising that IDA3D does not exactly predict the spatial and temporal variation of the patches observed by the radar. Nevertheless, IDA3D and the trajectory analysis do indicate the path of the patch plasma and therefore where patch formation mechanisms must occur. In the event of plasma-structuring events that are large compared with the IDA3D resolution, perhaps as evidenced by the gap between patches 2 and 3 in Figure 9, then IDA3D may provide more specific information about the location and possibly the mechanism of formation.
 A significant question that has occupied much thought in patch studies is “where does the patch plasma originate?” and a related question: “what mechanism(s) cause the patchy structure?” The IDA3D analysis identifies electron density enhancements but cannot show how they are transported or where they originated. Similarly, the trajectory analysis based on AMIE convection patterns shows where plasma has been but cannot provide information on the plasma density. Thus both IDA3D and the trajectory analysis are required to be able to determine the origin and evolution of the patches observed in the polar cap.
 The combination of trajectory analysis and 3-D ionospheric data assimilation has provided a unique new insight into the structuring of the polar cap ionosphere. The work presented here represents an advance in the field of patch studies.
 It extends and enhances the work on patch evolution reported earlier by Crowley et al. . They used their trajectory analysis to suggest how the disparate observations might be related, and they showed theoretically how patches could be transformed into blobs on the nightside. In particular, the Crowley et al. study used extremely sparse individual electron density data sets, rather than the comprehensive assimilation with multiple data sets performed here. In the present paper we introduced the IDA3D algorithm which allows us to specify the 3-D plasma distribution over the entire high-latitude region for the first time. This is the first time that such maps have been available on a quasi-routine basis. We used a 2-D trajectory analysis based on AMIE convection patterns to explain and understand how the observed plasma distribution evolved. The convection patterns used in the trajectory analysis here were derived by assimilating a much more comprehensive set of electrodynamics data into the AMIE algorithm than that used by Crowley et al. . Thus the current trajectory analysis is expected to be more accurate.
 This study focused on a sequence of patches observed by the ESR on 12 December 2001. Backward trajectory analyses based on AMIE convection potentials revealed where the patch plasma originated, although not the detailed mechanisms of patch formation. We showed that the patches formed part of a TOI, imaged by IDA3D, that extended into the polar cap near 1800 UT. Our analysis revealed that the folklore about how the TOI and patches are formed by the convection of midlatitude plasma into the polar cap is not always correct. In this case we showed that plasma parcels reaching the central polar cap originated near 62–63 degrees geographic latitude. Our study suggests that the origin of plasma for patches that are produced by transport in the convection pattern is determined by the latitudinal extent to which significant convection occurs. In our case, this was about 62 degrees. This threshold latitude is selected simply by the equatorward edge of significant convection. Since the equatorward edge of the convection pattern frequently occurs in this latitude range, our study suggests that patches and the tongue of ionization rarely originate at middle latitudes in the noon sector, thus contradicting a long-held belief in the ionospheric community. In general, significant convection does not reach into midlatitudes, and therefore patches cannot originate at midlatitudes except under exceptional circumstances: under conditions of high magnetic activity with a convection pattern that extends to midlatitudes. If fact, recent analysis of a severe magnetic storm on 30 October 2003 [Stolle et al., 2006] does support a convective origin of the TOI from the dayside midlatitudes during such exceptional circumstances.
 A key question regarding polar cap patches has been how they can become circular in the polar cap. The trajectory analysis presented here reveals that the shape change occurs as a natural result of their transport by the convection pattern. They often start life on the dayside as thin filaments, which may explain the fact that many patches in the literature are described as being cigar-shaped.
 Since the December 2001 data presented here, a much denser network of polar cap observations has evolved. As a result, greater fidelity can now be achieved in mapping the distribution of high-latitude electron densities. Future studies will report other patch events utilizing this denser network of observations. The good agreement obtained between IDA3D and the Svalbard ESR density profiles (Figure 4) even without ESR ingestion lends confidence to the overall accuracy of the IDA3D analysis and suggests that IDA3D might be usefully applied to routinely produce global ionospheric maps for operational purposes.
 In the present study we determined the source of the patch plasma and showed how the plasma was transported and evolved as it crossed the polar cap. In principle, such analyses could be performed for any plasma structure in the polar cap ionosphere, including electron density enhancements caused by precipitation, depleted regions such as troughs and polar holes, scintillating regions, etc.
 Although the trajectory analysis revealed the successive locations of ionospheric plasma, and IDA3D captured the changing plasma densities, what is missing is a description of production and loss processes acting on the parcel of plasma as it is transported. Such work will rely on the development of a first principles coupled ionosphere-thermosphere model capable of high enough resolution to capture the patch structure with high fidelity. The patches observed in the current study appear to have horizontal scales of only about 50 km (0.5° × 0.5°). This is much finer than the current generation of first principles fully coupled global models such as the TIMEGCM.
 The development of IDA3D is a major new achievement, and it offers another approach to data assimilation for ionospheric studies, which is complementary to others being developed in the ionospheric community. The use of a 3-D global first principles ionosphere-thermosphere model to initialize IDA3D offers exciting prospects for the development of a fully operational assimilative nowcasting and forecasting model in the near future. In the future, as the accuracy of our analysis increases with more data and more experience, we plan to permit plasma structure to convect within the IDA3D code. This will allow assimilated data to affect more than just a localized region for the time of observation. The detailed specification of the high-latitude plasma distribution that is beginning to emerge from this work will eventually permit us to quantify the growth and decay of intermediate scale irregularities associated with patches and the location of the irregularities within the patch structure. The smaller-scale phase scintillations that are routinely observed by tomographic receivers and other supplementary instruments will then be used to test our patch specification model.
 This material is based upon work supported by the National Science Foundation under grant ATM-0228467-1. We are indebted to numerous data providers for ionospheric data ingested into IDA3D. These data include the IGS and CORS GPS networks, ionosonde data from SPIDR and from Bodo Reinisch, and ISR data from EISCAT and Sondrestrom obtained through the Madrigal database. The beacon tomography data in Alaska was provided by NWRA and the University of Alaska at Fairbanks. The Greenland tomography array was made possible by work supported by the National Science Foundation under grant ATM-9813864. DMSP in situ measurements of electron density were provided courtesy of M. Hairston, while in situ measurements of electron density from CHAMP were provided by David Cook. OSEC and occultation data from CHAMP and SAC-C were obtained from the GENESIS web site. The Sondrestrom incoherent scatter radar is supported by the national Science Foundation. We are indebted to the Director and staff of EISCAT for operating the facility and supplying the data. EISCAT is an international association supported by Finland (SA), France (CNRS), Germany (MPG), Japan (NIPR), Norway (NFR), Sweden (VR), and the United Kingdom (PPARC). AMIE was developed by Art Richmond at the National Center for Atmospheric Research, Boulder, Colorado, and we are grateful for the opportunity to use the NCAR algorithm. The AMIE technique depends on data provided by many individual experimenters and data centers. We are grateful for SuperDARN radar data from Mike Ruohoniemi (Goose Bay and Kapuskasing), George Sofko (Saskatoon), Jean-Paul Villain (Stokkseyri), and Mark Lester (CUTLASS and Hankasalmi). The Goose Bay and Kapuskasing SuperDARN radars are operated by the Johns Hopkins University Applied Physics Laboratory with support from the National Science Foundation. The Saskatoon HF radar is operated by the University of Saskatchewan with support from the Natural Sciences and Engineering Research Council of Canada. The CUTLASS (Cooperative UK Twin Located Auroral Sounding System) and Hankasalmi radars form part of the SuperDARN (Dual Auroral Radar Network) network and are operated by the Radio and Space Plasma Physics Group at the University of Leicester with support from the Particle Physics and Astronomy Council and additional support from the Finnish Meteorological Institute and the Swedish Meteorological Institute. The Stokkseyri HF radar is operated by CNRS/LPCE (Centre National de la Recherche Scientifique/Laboratoire de Physique Chimie de l'Environnement) and CNRS/CETP (Centre d'etudes des Environnements Terrestre et Planetaires) with support from the Institut National des Sciences de l'Univers. The Defense Meteorological Satellite Program ion velocity data were provided by Fred Rich of the Air Force Research Laboratory and Rod Heelis/Marc Hairston of the University of Texas at Dallas. The following magnetometer data was used in AMIE: CANOPUS (Canadian Space Agency), IMAGE (Finnish Meteorological Institute), Measure (University of California Los Angeles), Greenland coastal chains (Danish Meteorological Institute), MAGIC (University of Michigan), MACCS (Augsburg and Boston University), 210 magnetic meridian (Kyushu University and Nagoya University), and Intermagnet.
 Wolfgang Baumjohann thanks Tony van Eyken and Stephan Buchert for their assistance in evaluating this paper.