Nighttime and daytime medium-scale traveling ionospheric disturbances (MSTIDs) are detected with dense and wide detrended total electron content (TEC) maps over North America using multiple GPS receiver networks. The TEC maps cover a wide region of 60–130°W and 24–54°N (30–65°N in geomagnetic latitude), and have a spatial resolution of 1.05° × 1.05° in latitude and longitude (0.15° × 0.15° with 7 × 7 pixel smoothing) and a temporal resolution of 30 seconds. The TEC maps reveal, for the first time, that the nighttime MSTIDs propagate southwestward with 200–500 km wavelengths over North America and have wavefronts longer than ∼2,000 km. We also observe that daytime MSTIDs with 300–1,000 km wavelengths propagate southeastward until mid-afternoon and southwestward in the late afternoon. In the mid-to-late afternoon, these MSTIDs propagating in the different directions are superimposed. The TEC maps can be a new powerful tool to investigate the MSTIDs.
 Traveling ionospheric disturbances (TIDs) are wave-like perturbations of the ionospheric plasma. The TIDs have been considered generally as plasma manifestations of atmospheric gravity waves (AGWs) propagating in the ionosphere [Hines, 1960]. The TIDs/AGWs have a significant role in the transfer of energy and momentum in the ionosphere. The TIDs are categorized into two groups: medium-scale and large-scale, according to their wave parameters such as wavelength, velocity, and period [Hocke and Schlegel, 1996]. Medium-scale TIDs (MSTIDs) have horizontal wavelengths of several hundred kilometers, horizontal velocities of 100–250 m/s, and periods of 15–60 minutes.
 Since mid-1990s, several new characteristics of the MSTIDs have been revealed by the ionospheric observations with two-dimensional mapping techniques using multipoint GPS receiver networks and all-sky airglow imagers. Clear spatial structures of the nighttime MSTIDs are first shown by Saito et al.  using the high-resolution mapping of TEC perturbations over Japan. The nighttime MSTIDs are frequently observed in summer and generally have wavefronts along northwest-southeast direction and propagate southwestward [Shiokawa et al., 2003a; Kotake et al., 2007]. The preferred propagation direction cannot be explained by the classical theory of AGWs [Kelley and Makela, 2001]. In contrast with the nighttime MSTIDs, the daytime MSTIDs generally propagate equatorward and appear frequently in winter [Hernández-Pajares et al., 2006]. These different characteristics between daytime and nighttime MSTIDs suggest that mechanisms causing MSTIDs could be different between daytime and nighttime [Kotake et al., 2007].
 Although there have been many studies of MSTIDs, there are still many characteristics, such as the width of their wavefronts and the northern and southern limits of their propagation, that have not been determined. This is because of the limited spatial coverage of ionospheric observations. In this study, we make dense and wide detrended TEC maps over North America using multiple GPS receiver networks. These TEC maps reveal several new characteristics of the MSTIDs. The method used to process the GPS data into the detrended TEC maps will be given, and then the typical nighttime and daytime MSTIDs observed over North America will be presented.
 The GPS data analyzed in this study are obtained via the ftp server of the ontinuously Operating Reference System (CORS), the Scripps Orbit and Permanent Array Center (SOPAC), and the International GNSS Service (IGS). There are more than 1,400 permanent GPS receivers in North America as of December 2006. The distribution of the GPS receivers is shown in Figure 1. Almost all GPS receivers provide the data of carrier phase and pseudo-range measurements in two frequencies (f1 = 1575.42 MHz, f2 = 1227.60 MHz) every 30 seconds.
 Slant TEC, Is, the integrated electron density along the entire line-of-sight (LOS) between receiver and satellite, can be derived using the following equation [Mannucci et al., 1999]:
where L1 and L2 are the recorded carrier phases of the signal (converted to distance units), λ1n1 and λ2n2 are integer cycle ambiguities, and br and bs are satellite and receiver instrumental biases terms. Vertical TEC, I, can be obtained from the slant TEC using the equation, I = Is · S, where S is a slant factor which is a ratio of the ionosphere thickness, 200 km, to the LOS length between 250 km and 450 km altitude. Although the integer cycle ambiguities and the both satellite and receiver biases must be determined to obtain the absolute value of TEC, we do not determine these unknowns because this study is focused on perturbation components of TEC caused by TIDs. In this study, we use the perturbation components of TEC derived by detrending I with one-hour running average for each LOS.
 This simple detrending method is more suitable than other method such as FFT to derive about one-hour TEC variation from a series of GPS LOS TEC whose duration is a few hours, and often used in TID research with a dense GPS network [Saito et al., 1998; Tsugawa et al., 2006b; Kotake et al., 2007].
 The relative change of TEC is obtained theoretically with a precision of 0.01–0.02 TECU (1 TECU = 1016 m−2), which corresponds to ∼1% of the wavelength of GPS signals L1 (0.19 m) and L2 (0.24 m) [Spilker and Parkinson, 1996]. We neglect the TEC data from large satellite zenith angles (60–90°) to reduce cycle slips and errors due to conversion from slant to vertical TEC.
 The two-dimensional maps of the detrended TEC can be obtained from all available GPS LOS TEC every 30-seconds. As shown in Figure 2, the TEC map covers the wide region from 60°W to 130°W longitude and from 24°N to 54°N latitude. The size of each pixel is 0.15° × 0.15° in latitude and longitude. The TEC value for each pixel is an average of perturbations for all LOS which crossed the pixel at 300 km altitude (the approximate F-region peak height). To compensate for the scarcity of the TEC data distribution, the TEC value in each pixel is smoothed temporally with the running average of 10 minutes, during which an ionospheric pierce point (IPP) moves ∼50 km around the zenith of a GPS receiver. Then the TEC map in each epoch is smoothed spatially with the running average of 7 × 7 pixel (1.05° × 1.05°) in latitude and longitude. As a result, the detrended TEC maps over North America can observe TEC variations whose time scale is between 10 and 60 minutes and spatial scale is larger than 1.05° × 1.05° in longitude and latitude.
3. MSTID Observations
Figure 2 shows the time sequence of two-dimensional maps of the detrended TEC over North America in the nighttime between 03:30 UT (21:30 CST) and 06:10 UT (00:10 CST) on July 20, 2006 with a 20-minute interval. Central Standard Time, CST(=UT-6 hour), is referred to here to give a sense of a local time of center of North America. A movie of Figure 2 with 30-second resolution is available through the auxiliary material associated with this paper (see Animation S1). The Kp index during this day keeps between 0+ and 1, indicating that the geomagnetic activity is very quiet. Clear wave-like structures with the wavelengths of 200–500 km and the wavefronts stretching in NW–SE direction gradually appear around 03:50 UT (Figure 2b) in 70–90°W and 30–45°N, and in 110–120°W and 30–40°N. The structures are not elongated along the geomagnetic field line because the declinations of the geomagnetic field at 30°N latitude are 6° west and 12.1° east of the north around 80°W and 120°W, respectively. They have the peak-to-peak amplitudes larger than ∼0.5 TECU. Figures 2b, 2c, 2d, and 2e clearly show that the wave-like structures propagate approximately 500 km in a southwestward direction from 03:50–04:50 UT (1 hour). Therefore their propagation velocity is estimated to be 100–150 m/s. Judging from the wavelengths, propagation velocities and directions, these wave-like structures are identified as the nighttime MSTIDs which have been observed in Japan [Saito et al., 1998] and Southern California [Kotake et al., 2007].
 Focusing on the MSTID structures, it should be noted that their wavefronts can extend longer than 1,000 km as seen at 80–90°W and 110–120°W in Figure 2d. Especially, the longest wavefront at 80–90°W can extend between ∼25–45°N (∼35–55°N geomagnetic latitude (MLAT)), which corresponds to ∼2,000 km. Comparing Figures 2a and 2b, it is also noted that their wavefronts have already been long since their appearance at 80–90°W and 110–120°W. After the MSTIDs propagate southwestward keeping their wave-like structures between 03:50 and 04:50 UT (Figures 2b, 2c, 2d, and 2e), each structure gradually decays around 05:50–06:10 UT (Figures 2h and 2i).
Figure 3 shows the TEC maps for the daytime between 19:20 UT (13:20 CST) and 22:00 UT (16:00 CST) on November 28, 2006, in the same format as Figure 2. A movie of Figure 3 is also available (see Animation S2). The Kp index during this day is between 1 and 2+, indicating that the geomagnetic activity is quiet. Consecutive wave-like structures with the wavefronts stretching in NE–SW direction are seen in the entire field of observation between 19:20–21:00 UT (Figures 3a, 3b, 3c, 3d, 3e, and 3f). These waves propagate southeastward at the velocity of 100–200 m/s. Their wavelengths are 300–1,000 km, wavefronts are longer than ∼2,000 km, and peak-to-peak amplitudes are larger than ∼0.5 TECU. From their wave parameters, the wave-like structures can be identified as the daytime MSTIDs observed in Japan [Tsugawa et al., 2006a] and Southern California [Kotake et al., 2007].
 While the daytime MSTIDs are observed to propagate southeastward over North America until around mid-afternoon, southwestward propagating MSTIDs are also observed in the late afternoon between 21:20 and 22:00 UT (15:20 and 16:00 CST) as shown in Figures 3g, 3h, and 3i. The latter southwestward-propagating MSTIDs have the comparable wavelength and velocity, and relatively small peak-to-peak amplitude to the former southeastward MSTIDs. The two MSTIDs propagating in the different directions are superimposed on each other around mid- to late afternoon (Figures 3e, 3f, 3g, and 3h).
4. Discussion and Conclusions
 Dense and wide two-dimensional mapping of detrended TEC over North America reveals spatial and temporal variations of TEC between the sub-auroral regions and the mid-latitudes. The TEC maps produced here have a temporal resolution of 30 seconds with 10-minute smoothing, a spatial resolution of 1.05° × 1.05° (0.15° × 0.15° with 7 × 7 pixel smoothing) in latitude and longitude, and cover a spatial coverage of 60–130°W longitude and 24–54°N latitude (30–65°N in geomagnetic latitude (MLAT)). Such high-resolution and wide-coverage TEC observations have not been attained in the past.
 Using these TEC maps, we observe clear MSTIDs traveling southwestward with 200–500 km wavelength and 100–150 m/s propagation velocity during the nighttime on July 20, 2006 as shown in Figure 2. The nighttime MSTIDs have been observed over Japan (∼18–36°N MLAT) by the GPS-TEC observations and the 630-nm airglow observations [e.g., Saito et al., 2001; Shiokawa et al., 2002]. The wide-coverage TEC maps over North America reveal, for the first time, that the nighttime MSTIDs can appear from mid-latitudes to sub-auroral regions between 35–55°N MLAT. These results indicate that the nighttime MSTIDs can occur around ∼20–55°N MLAT.
 It is recently reported that the nighttime MSTIDs have polarization electric field inside their structures [Saito et al., 2002; Shiokawa et al., 2003b] and symmetric patterns at geomagnetic conjugate points in both hemispheres [Otsuka et al., 2004; Shiokawa et al., 2005]. These results indicate electrodynamic forces, such as the Perkins instability, could play an important role in the generation of nighttime MSTIDs [Perkins, 1973; Garcia et al., 2000]. To explain the preferred southwestward propagation direction, Kelley and Makela  have proposed a mechanism in which polarization electric fields (Ep) along the horizontal wavefront play an important role, assuming the MSTIDs structures are finite in the direction parallel to the horizontal wavefront. In this study, we reveal that the wavefront of the nighttime MSTIDs can extend longer than ∼2,000 km in the NW–SE direction between 35–55°N MLAT as shown in Figure 2d. Although their NW–SE extending wavefronts could not conflict with the Perkins instability, it is difficult for the Kelley and Makela's model to explain the southwestward propagation of the nighttime MSTIDs whose wavefronts extend from mid-latitudes to sub-auroral regions.
 Previous observational results show the occurrence rate of the nighttime MSTIDs has a longitudinal dependence. Kotake et al.  have shown that the seasonal variation of the MSTID occurrence rate over Southern California has a major peak in summer, similar to that over Japan. On the other hand, the MSTID occurrence rate over Arecibo, Puerto Rico has a major peak in winter [Garcia et al., 2000]. In the wide TEC maps over North America (Figure 2), clear MSTID structure can not be seen around 100°W longitude in contrast with around 80–90°W and 110–130°W longitude. These results suggest that a boundary of the longitudinal dependence of the MSTID occurrence may exist around 100°W longitude. This longitudinal variation may be ascribed to the background conditions causing the plasma instability, such as neutral wind and geomagnetic declination angle. The geomagnetic inclination angle also could affect the amplitude of the nighttime MSTIDs because the horizontal inhomogeneity of the electron density is basically caused by upward/downward E × B drift of the plasma due to the Ep. Consequently, the wide-coverage TEC maps over North America could reveal the longitudinal and latitudinal dependence of the MSTID occurrence, and contribute to studies of the mechanisms for generation and propagation of the nighttime MSTIDs.
 Using the TEC maps, we also observe clear MSTIDs with 300–1,000 km wavelength and 100–200 m/s propagation velocity during the daytime on November 28, 2006 (Figure 3). It is noted that the 300–1,000 km wavelength of the daytime MSTIDs observed in this study is a little larger than the 100–500 km wavelength reported by Hernández-Pajares et al. . This discrepancy would result from the difference of the MSTID periods observed in this study (10–60 minutes) and by Hernández-Pajares et al.  (lower than 20 minutes). The daytime MSTIDs are considered to be caused by AGWs [Kotake et al., 2007]. The MSTIDs propagate southeastward until around mid-afternoon while the MSTIDs propagate southwestward in the late afternoon. This local time variation of the MSTID propagation direction is consistent with previous observations [e.g., Afraimovich et al., 1999], and can be explained by the wind filtering effect of the AGWs [Waldock and Jones, 1986]. In this study, the TEC maps reveal, for the first time, that the two MSTIDs propagating southeastward and southwestward are superimposed on each other around mid- to late afternoon.
 One of new findings using the wide-coverage TEC maps is horizontal wavefronts of the daytime MSTIDs extended straightly for more than ∼2,000 km in the almost zonal direction. Although there have been several studies on the wavefront extension of LSTIDs associated with geomagnetic storms [e.g., Afraimovich et al., 2000], there have been few studies on that of MSTIDs. This plane wave structure of the MSTIDs indicates that the sources of AGWs are located far from mid-latitude ionosphere and/or that their sources are elongated in the zonal direction. We could suspect that the daytime MSTIDs shown in Figure 3 may be caused by the AGWs launched at the two different locations at auroral latitudes, and they propagate over North America in the different directions. To clarify the source location of the daytime MSTIDs, we need to observe their vertical wavelength, which could be achieved with incoherent scatter radars (ISR), such as Millstone Hill ISR [42.6°N, 71.5°W].
 The amplitude of daytime MSTIDs seem to increase as they travel equatorward as shown in Figure 3. This latitudinal variation of the MSTID amplitude could be explained by that of the background TEC which is generally larger at low latitudes than at high latitudes. If the AGWs propagate with a constant amplitude, the total amount of plasma variation caused by the AGWs could be larger at lower latitudes, resulting in the latitudinal variation of the MSTID amplitude. On the other hand, the geomagnetic inclination angle decreases as the latitude decreases, resulting in that the upward/downward plasma variation along the geomagnetic field due to the AGWs decreases as the latitudes decreases. The ion-drag effect can damp the AGWs in the daytime ionosphere [Tsugawa et al., 2003, 2004]. These two effects could cause the decrease of the MSTID amplitude as the latitude decreases. Although we will not discuss these effects or the background TEC conditions further in this paper, the wide-coverage TEC maps over North America can reveal the increase and/or decrease (growth and/or damping) of the MSTID amplitude and contribute to studies of the latitude dependence and temporal evolution of the MSTIDs.
 The GPS data used in this study were obtained via the ftp servers of CORS (ftp://www.ngs.noaa.gov/cors/rinex/), SOPAC (ftp://garner.ucsd.edu/pub/rinex/), and IGS (ftp://cddisa.gsfc.nasa.gov/pub/gps/data/daily/). We acknowledge the IGS, UNAVCO, SCIGN and its sponsors, the W.M. Keck Foundation, NASA, NSF, USGS, SCEC for providing GPS data. A portion of this work was done while T.T. was a Visiting Scientist at the MIT Haystack Observatory supported by a grant of Research Fellowships of the Japan Society for the Promotion of Science (JSPS) for Young Scientists.