The results of SPE analyses in Figures 1, 2 indicate a strong tendency of high-precipitation occurrence following arrivals of HSSs from coronal holes. We now examine cases of heavy rainfall events in the context of solar wind disturbances, including HSSs/CIRs (Gosling and Pizzo, 1999; Tsurutani et al., 2006a; Tsurutani et al., 2006b) and interplanetary coronal mass ejections (Gopalswamy, 2016). The solar wind magnetic sector boundaries, where the IMF direction switches its polarity between “away” and “toward” the Sun, that have been identified as heliospheric current sheets (HCSs; Smith et al., 1978; Hoeksema et al., 1983), usually closely precede or are imbedded within CIRs at the leading edge of HSSs. The high-density plasma (HDP) ahead of HCSs/CIRs leads to magnetic field compression, which is another geoeffective solar wind disturbance (Tsurutani et al., 1995). In the absence of IMF data, the magnetic sectors can be estimated from ground-based magnetograms (Svalgaard, 1975).

Figure 4 shows solar wind variables such as the IMF direction longitude (orange crosses) and the Dst index (green line). The symbols on the time axis indicate the times of HSS/CIR arrivals, impacts of ICMEs, and the IMF sector boundary/HCS crossings. Where available, the proxy magnetic field sectors (A: away; T: toward) are indicated below the time axis. Start dates of heavy rainfall events in Canada included in the SPE analysis are marked by symbols at the top. These are examples of events that occurred following arrivals of HSSs/HCSs/CIRs or impacts of ICMEs that caused geomagnetic storms. On 8 June 1999 (Figure 4A), White Rock, BC, experienced a sudden, intense storm with heavy rain that caused flash floods and mudslides. In July 1999 (Figure 4B), heavy snow and rain fell starting on July 2 caused flooding in Clearwater, AB. On September 22–23 (Figure 4C), Prince Edward Island experienced a severe rainstorm, causing flash flooding, damaging eight highways and bridges. The IMERG satellite-based precipitation data for June 2000 are obtained. At the top in Figures 4D, E, the maximum IMERG daily rates at any grid cell over Canada (solid purple line) and the number of IMERG grid cells over Canada with precipitation rates exceeding 50 mm (dotted line) are shown. Figures 4C, D show cases of heavy rainfall events in New Brunswick and Quebec, respectively, and enhanced high-rate precipitation occurrence following HSSs/CIRs. More events in the context of solar wind can be viewed in the Supplementary Material.

Several heavy precipitation events affected eastern Canada in December 2010. Figure 5 shows the maximum IMERG daily rates and the number of grid cells over New Brunswick with precipitation rates exceeding 50 mm. The focus here is on the NB storms (marked by red diamonds) that followed rapid intensifications of extratropical cyclones (marked by open circles scaled by the maximum normalized deepening rate of the central mean SLP). On December 6, the storm that caused strong winds, heavy wet snow, and floods coincided with the arrival of a broad CIR on the leading edge of a moderate HSS that was preceded by high-density plasma adjacent to HCSs. While heavy precipitation and an extreme storm surge that caused floods occurred after the low pressure reached the east coast on December 6, this extratropical cyclone explosively deepened off the East Coast of the United States. Figure 6A shows the daily accumulated precipitation on December 6, overlaid with the storm track. The maximum deepening rate and the minimum central SLP reached are indicated in green and red colors, respectively. Another intense storm during December 13–14 resulted in extensive flood damages in New Brunswick and Quebec. It was caused by a rapidly deepening low-pressure system (Figure 6B) that closely followed the arrival of a major HSS/CIR (Figure 5). The cyclone brought heavy rain, wet snow, and strong winds, causing major power outages in New Brunswick. Heavy rain and floods also occurred in Gaspé, QC, when the high-rate IMERG precipitation peaked. Figure 6B shows the daily accumulated precipitation on December 13, overlaid with the storm track. Similarly, minor HSSs/CIRs on December 20 and 25 were followed by rapid intensifications of extratropical cyclones over the east coast, which brought heavy rain, wet snow, and strong winds to New Brunswick. The December 21 storm also caused a storm surge and flooding. In each case, there was an increase in the IMERG high-rate precipitation occurrence over New Brunswick (Figure 5).

The GOES-13 infrared images (https://www.ncdc.noaa.gov/gibbs/) of an intensifying extratropical cyclone showed “back building” convection cells along squall lines (Bluestein and Jain, 1985) off the East Coast of United States (Figure 7A). The CIMSS data archive (http://tropic.ssec.wisc.edu/archive/) provides overlay data products from wind analysis. The enhanced upper-level (150–300 mb) divergence (Figure 7B) indicates a region with rising air motion. There were strong mid-upper-level southwesterly winds (Figure 7C), low-level winds (Figure 7D) turning southerly over a string of convection cells, and large mid-level wind shear (Figure 7E). Furthermore, low-level winds and vertical wind shears based on the ERA5 reanalysis are also shown in Figure 8, discussed as follows. These conditions are conducive to over-reflection of down-going aurorally excited AGWs with a possibility of amplification (Section 6.3). The over-reflecting AGWs in the unstable frontal zone could contribute to the release of CSI, resulting in a series of convection cells forming the “back building” squall line. Similar cases of intensifying extratropical cyclones were discussed previously (Prikryl et al., 2018; including Supplementary Material).

Several indices are calculated using the ERA5 reanalysis to evaluate the likelihood of slantwise convection in this case. These indices that provide different but Supplementary Material, include SCAPE, fractional SCAPE residual (f _s = (SCAPE—CAPE)/SCAPE), and vertically integrated extent of realizable symmetric instability (Glinton et al., 2017; Chen et al., 2018). A high SCAPE, indicating high convective available potential energy for a slantwise ascending air parcel from low levels, is found but limited to the warm sector of the cyclone (Figure 8A). A closer-to-one f _s indicates the relative dominance of slantwise over upright convection, although such a condition is also scattered mostly in the south (Figure 8B). While the aforementioned two indicate the potential energy, VRS shows the thickness of the air layer (measured in pressure), where CSI, high relative humidity, and vertical motion coexist (Chen et al., 2018). Figure 8C shows that the cold front, where strings of “back building” convection cells (Figure 7A) produced high-rate precipitation co-located well with a high VRS value of above 150 hPa, shows a strong indication that CSI is being released actively there. Such high VRS values well-match the high precipitation band persisted for more than 1 day. As already noted previously, this was co-located with low-level southerly winds and wind shears evaluated between 900 and 1,000-hPa levels (Figure 8D), which is favorable for over-reflection of AGWs.

The extratropical cyclone that caused heavy rain in New Brunswick on December 6 explosively intensified off the east coast (Figure 6A). This coincided with the arrival of the solar wind high-density plasma sheet on the leading edge of a moderate HSS/CIR (Figure 5). Figure 9A shows the GOES-13 infrared images (https://www.ncdc.noaa.gov/gibbs/) of an explosive extratropical cyclone showing development of a “striated delta” cloud in the cyclone vortex and “back building” bands in the cold front. They coincide with regions of high SCAPE and close-to-one f _s (Figure 9B). The resulting latent heat release could have contributed to the explosive development of the cyclone that later brought heavy rainfall to New Brunswick (Figure 6A).

While large SCAPE–CAPE residuals are mostly over the warm sector (to the south) of the extratropical cyclone, the heavy precipitation over New Brunswick on December 6, 00:06 UTC (Figure 10B), is co-located with some locally high VRS values (peak >150 hPa thickness at 03:00 UTC) that lasted more than 6 h over the “bent-back warm front” that wraps around the cyclone center. It should be noted that there exist other low-level forcing mechanisms for heavy precipitation, e.g., frontogenetical lifting and the strong low-level convergence of flows associated with two cyclone centers, which was likely the case when the cyclone was reaching New Brunswick (Figure 10B). Nevertheless, heavy precipitation and a storm surge that caused floods coincided with the arrival of a broad HSS/CIR with a dense HDP at its leading edge on December 6. Furthermore, similar to the observation on December 13, the high-rate precipitation was co-located with high low-level winds and wind shears at 950 hPa (Figure 10D). Equatorward propagating AGWs generated by solar wind coupling to the magnetosphere–ionosphere–atmosphere system could have reached the cyclone and contributed to the release of CSI, leading to cyclone intensification.

At high latitudes, solar wind coupling to the magnetosphere-ionosphere-thermosphere system is the energy source of auroral heating, primarily Joule heating, due to collisions among electrons, positive ions, and neutral molecules (Brekke and Kamide, 1996; Knipp et al., 2004; Thayer and Semeter, 2004; Xu et al., 2013; Richmond, 2021), although its impact on the thermodynamics of the neutral atmosphere is thought to decrease below 100 km (Xu et al., 2013). Auroral heating is highly variable and often driven by ultra-low-frequency (ULF) waves.

The main source of ULF waves are HSSs emanating from coronal holes (Krieger et al., 1973). HSSs from polar coronal holes have speeds of ∼750–800 km/s (Phillips et al., 1994; Phillips et al., 1995; Tsurutani et al., 2006a; Tsurutani et al., 2006b). However, coronal holes that affect the Earth by HSSs are either extensions of polar coronal holes (Phillips et al., 1994) to low latitudes or are self-contained coronal holes forming at low heliographic latitudes (de Toma, 2011). The high-density HCS plasma sheet ahead of CIRs leads to compression of the magnetic field that can cause recurring moderate-to-weak geomagnetic storms (Tsurutani et al., 1995). The high-density plasma sheet impinging onto the magnetosphere results in precipitation of magnetospheric relativistic electrons (Tsurutani et al., 2016). HSSs/CIRs have been shown (Tsurutani et al., 2006a; Tsurutani et al., 2006b) to be associated with high-intensity, long-duration continuous auroral electrojet activity (HILDCAAs) (Tsurutani and Gonzalez, 1987; Tsurutani et al., 1990; Tsurutani et al., 1995). HILDCAAs are caused by trains of solar wind Alfvén waves (Belcher and Davis, 1971) that couple to the magnetosphere–ionosphere system (Dungey, 1961; Dungey, 1995). Coupling produces pulses of Joule heating in the lower thermosphere that can launch AGWs with duration between tens of minutes to hours.

The theoretical understanding of gravity waves and their role in the ionosphere was developed by Hines (1960). The auroral sources of medium- to large-scale gravity waves have been recognized, and AGWs have been observed as traveling ionospheric disturbances (TIDs) for a long time (Chimonas and Hines, 1970; Testud, 1970; Richmond, 1978; Tanaka, 1979; Williams et al., 1993; Balthazor and Moffett, 1997; Oyama et al., 2001; Oyama and Watkins, 2012; Richmond, 2021). Francis (1974) theoretically described and distinguished between direct and Earth-reflected gravity waves and pointed out that the latter appear in the F-region as wave packets of nearly monochromatic waves, while the former induce isolated (nonperiodic) TIDs, which is consistent with the modeling of gravity waves generated by enhancements in the ionospheric electric field (Millward et al., 1993a; Millward et al., 1993b; Millward, 1994). Each electric field enhancement causes a Joule heating pulse, which in turn launches a single gravity wave propagating equatorward and poleward from the source region.

The gravity wave dispersion relation (Hines, 1960) allows both upward (downward phase) and downward group (upward phase) propagation (Hocke and Schlegel, 1996). For clarity, we will refer to downward/upward group (wave energy) propagation as down/upgoing AGWs to distinguish them from upward/downward AGW phase propagation. Yeh and Liu (1974) used the ray theory approach and the WKB approximation and pointed out that a simplified ray tracing procedure based on Snell’s law is applicable for a horizontally stratified atmosphere, e.g., (Bristow et al., 1996; Prikryl et al., 2005; and Prikryl et al., 2009b). A dispersion relation derived from Navier-Stokes equations (Bristow et al., 1996) with temperature gradients included by allowing the scale height to vary with altitude but not considering viscosity, thermal conductivity, and ion drag, showed results suggesting a seasonally dependent reflection of gravity waves due to the temperature gradient at mesospheric altitudes.

Based on a spectral model in terms of spherical harmonics, Mayr et al. (1984a) and Mayr et al. (1984b) described gravity wave response in the atmosphere and showed that propagating waves originating in the thermosphere can excite a spectrum of AGWs in the lower atmosphere, though with much smaller amplitudes. Their transfer function model (TFM), which describes global propagation of acoustic gravity waves in a dissipative and static atmosphere with globally uniform temperature and density variations, was reviewed (Mayr et al., 1990; Mayr et al., 2013). Globally propagating AGWs from sources in the lower thermosphere at high latitudes can be ducted in the lower atmosphere over long distances and reach the troposphere at mid-to-low latitudes. However, the amplitude of AGWs is known to decrease exponentially with decreasing height. At the top of the troposphere, the amplitude in velocity perturbation is 3–4 orders of magnitude smaller than the amplitude of the wave launched in the E-region (Hines, 1965). In the lower thermosphere, large vertical wind velocities with magnitudes of 10–20 m/s are common at high latitudes (Larsen and Meriwether, 2012). Even larger vertical ion motions with amplitudes up to ± 50 m/s have been observed by incoherent scatter radars (Oyama et al., 2005) at altitudes of 95–111 km. Oyama et al. (2008) observed vertical winds exceeding 30 m/s at high-latitude altitudes of 110–120 km during moderately disturbed geomagnetic conditions. Hernandez (1982) observed periodic oscillations of vertical winds with amplitudes up to 50 m/s and a period of 40 min in the mid-latitude thermosphere, which were attributed to the passage of gravity waves from an auroral source. Rees et al. (1984) identified sources at high latitudes of strong vertical winds >100 m/s, resulting from local geomagnetic energy input and subsequent generation of thermospheric gravity waves. In situ measurements of large vertical motions of 100–250 m/s in the thermosphere were attributed to aurora-induced gravity waves (Spencer et al., 1976; Spencer et al., 1982), and vertical winds of 10–20 m/s are commonly observed in the lower thermosphere (Larsen and Meriwether, 2012). Such vertical motions scale down to a few cm/s at the tropospheric level, which is comparable to mean vertical motions in the troposphere (Fukao et al., 1991; Nastrom and Vanzandt, 1994) but less than typical instantaneous vertical motions of up to a few tens of cm/s associated with tropospheric gravity waves (Nastrom et al., 1990).

As already mentioned in Introduction, it has been suggested that aurorally excited AGWs can play a role in the CSI release, leading or contributing to explosive development of extratropical cyclones. When downgoing AGWs over-reflect in the warm frontal zone of extratropical cyclones, even a small lift that they would impart to a moist air parcel already rising over the cold air can initiate slantwise convection, forming a precipitation band. Extreme rainfall events often result from mesoscale convective systems producing convective rainfall regions that are sometimes nearly stationary. Bluestein and Jain (1985) (in Figure 1) introduced a concept of distinct kinds of mesoscale convective line (squall line) developments based on radar reflectivity and satellite observations of squall lines, with the two most commonly identified as “broken line” and “back building” formations. The squall lines form in a conditionally and convectively unstable atmosphere. The “broken line” forms typically along a cold front by probable development of “externally” forced multi-cells appearing at about the same time and transforming “into a solid line as the area of each existing cell expands and new cells develop” (Bluestein and Jain, 1985). The “back building” squall line “consists of the periodic appearance of a new cell upstream, relative to cell motion” and can form along different types of surface boundaries. The other types may include warm frontal bands and wide cold frontal bands (Bluestein and Jain, 1985). Similar to striated delta clouds (Prikryl et al., 2018; their Figure 9), the SPE analysis of solar wind data keyed to dates from the list of squall line cases (Bluestein and Jain, 1985; their Table 1) appears to show a tendency of such mesoscale convective line development to follow arrivals of HSSs/CIRs/ICMEs.

TFM simulations (Prikryl et al., 2018; their Figure 16) of propagation of the gravity wave launched by Joule heating with given vertical heating profiles in the lower thermosphere showed that they can produce vertical wind amplitudes of up to ∼1 cm/s at 10 km altitude. The gravity wave ray tracing examples (Prikryl et al., 2018; their Figure 15) show that AGWs can reach lower troposphere altitudes, where they may at least seed the slantwise convection in a symmetrically unstable environment by providing a small lift to a parcel of air and contribute to the release of instability (Prikryl et al., 2009b; pp. 34 and 42–43). Cases of TIDs and/or their sources in the ionosphere followed several hours later by series of rain bands, or convective cells, indicated an approximately one-to-one correspondence (Prikryl et al., 2009b; Prikryl et al., 2018) that was consistent with the estimated AGW propagation time from the lower thermosphere to the upper troposphere. While even a very small amplitude of these AGWs at tropospheric levels may be sufficient to release the CSI, there is possibility of amplification of AGWs at the reflection point if waves encounter a wind shear or an opposing wind (Jones, 1968; Cowling et al., 1971; McKenzie, 1972; Eltayeb and McKenzie, 1975).

SuperDARN radars (Nishitani et al., 2019) measure the line-of-sight velocity component of E × B drift velocities of ionospheric irregularities in the F-region (at altitudes of ∼350 km), with the electric field E mapping along equipotential magnetic field lines to the lower ionosphere. Velocity measurements are used to map ionospheric convection at mid-to-high latitudes. In addition to ionospheric scattering, the radars also observe the ground scatter power modulated by TIDs, including those that are driven by AGWs. To study the relevant geophysical context of the December 2010 storm event, we now examine in situ measurements of solar wind variables, ionospheric velocity and ground scatter power observed by the SuperDARN, and ground magnetometers sensing ionospheric currents.

On December 12, as in previously studied cases (Prikryl et al., 2009b; Prikryl et al., 2018), pulsed ionospheric flows (PIFs) observed over northern Greenland generated equatorward propagating AGWs/TIDs. Figure 11A shows ionospheric line-of-sight velocity V _los as a function of the magnetic latitude observed by the Iceland Stokkseyri radar beam 15. The ionospheric currents in the E-region at altitudes of ∼110 km flow in the opposite direction to ionospheric convection (PIFs). It is the Joule heating caused by pulses of ionospheric currents that generated AGWs that were observed as TIDs by the Goose Bay radar in Labrador (Figure 11B). Similarly, on December 5, pulses of ionospheric convection/currents at high latitudes generated equatorward-propagating AGWs. Figure 11C shows TIDs in the ground scatter observed by the Pykkvibaer radar beam 7. Figures 11B, C show the ground scatter power focused/defocused by equatorward-propagating TIDs observed by radar beam 12. Rather than showing the ground scatter slant range, the ground scatter range is mapped to reflect the TID location in the ionosphere (Bristow et al., 1994). It is noted that PIFs and the consequent AGWs/TIDs were generated by solar wind Alfvén waves coupling with the dayside magnetosphere/ionosphere by the pulsed magnetic reconnection at the subsolar magnetopause ( Prikryl et al., 1998; Prikryl et al., 2002).

The magnetic reconnection is primarily driven by the southward IMF B _Z component, which is opposite to the Earth’s magnetic field at the subsolar magnetopause. Figure 12A shows the IMF B _Z component in Geocentric Solar Ecliptic (GSE) coordinates (black line) measured by Wind spacecraft in the upstream solar wind. The dotted lines show detrended time series of IMF B _Z (red) and proton velocity V _Z (blue) components that are correlated. The correlation between the respective components of the solar wind magnetic field is the signature of anti-sunward propagating solar wind Alfvén waves (Belcher and Davis, 1971). The normalized fast Fourier transform (FFT) power spectra of the detrended time series of B _Z and V _Z show similar multiple peaks at frequencies of ∼0.25, 0.4, and 0.6 mHz.

The north–south X component of the ground magnetic field (Figure 12B) was measured by a magnetometer on the west coast of Greenland in Upernavik (UPN), located in the field of view of the Stokkseyri radar beam 15. The perturbations of the ground magnetic field are caused by ionospheric currents at altitudes of ∼110 km, with the north–south X component sensing east–west currents. The FFT power spectrum of the detrended time series (red dotted line) is very similar to those of the IMF B _Z and V _Z observed by the Wind spacecraft.

Figure 12C shows the time series of the Goose Bay radar ground scatter power for the range gate 30 showing variations that are due to equatorward-propagating TIDs. The main peak in the FFT power spectrum of the detrended time series (dotted line) is close 0.5 mHz (∼30 min), representing the period of equatorward-propagating AGWs.

Ray tracing of AGWs in a model atmosphere using the dispersion relation has been conducted (Prikryl et al., 2005) to show that downgoing AGWs launched by ionospheric currents at high latitudes can reach the troposphere. They can be ducted in the lower atmosphere to low latitudes, as shown by ray tracing and TFM methods (Prikryl et al., 2018).

Using the MSIS-90 model atmosphere, Figure 13 shows possible group paths from a source at 110 km altitudes of AGWs with a period of 30 min, including the ducted mode in the lower atmosphere. It is noted that group times for rays reaching the troposphere at distances past 3,000 km are greater than 4 h, which is approximately the time from the launch of AGWs to the appearance of “back building” convection cells (Figure 7A). Similar cases have been discussed previously (Prikryl et al., 2009a; Prikryl et al., 2018). Over-reflection of downgoing AGWs in unstable frontal zones could have contributed to the release of the instability, leading to a string of convection cells forming the “back building” squall line shown in Figure 7A.

Theoretical analysis of AGW propagation in the lower atmosphere using an expansion of three-dimensional normal mode functions was performed by Hagiwara and Tanaka (2020). These authors showed that the waves can propagate downward to the troposphere as attenuating gravity waves and “the wave propagations and reflections at the surface create an anti-node of geopotential at the bottom of the atmosphere corresponding to the vertical width of the initial state of the impact.” On the other hand, “standing waves in temperature create a node at the ground surface.” They suggested that standing waves generated in the lower troposphere could affect atmospheric stability through the passage of gravity waves, in turn affecting the development of cyclones.

These theoretical results propose the following question: could the strings of convective cells forming “back building” squall lines, as observed in Figure 7A, be caused by standing waves, as they are generated in the lower troposphere by downgoing AGWs? If so, the nodes (anti-nodes) of a standing wave would be separated by half a wavelength λ/2. While upgoing medium-scale AGWs/TIDs have typically horizontal wavelengths λ ≥400 km, downgoing AGW packets would have shorter horizontal wavelengths λ <300 km (Prikryl et al., 2005; their Figure 2B). Standing waves generated by such AGWs in the lower troposphere, as suggested previously, would have node spacing comparable with the spacing between the convective cells (∼150 km or less). Furthermore, the two “back building” squall lines seem to have formed simultaneously (Figure 7A). This would be consistent with the notion that they were formed by equatorward-propagating AGWs at this time, although the one associated with the main cold front transformed more quickly into a solid squall line, while the convective cells forming the adjacent squall line persisted longer as they expanded.