The Spectacular Undular Bore in Iowa on 2 October 2007 (2024)

The inversion was also topped by a much less stable layer above about 1 km MSL, which provided a duct for gravity wave energy (e.g., Lindzen and Tung 1976; Nappo 2002). Such a ducting or wave-trapping mechanism may be necessary for a bore to propagate over a significant distance (e.g., Crook 1986). Atmospheric waves may be reflected by layers with large vertical gradients of m² (where m is the vertical wavenumber), and are totally reflected by layers where m² < 0 (e.g., Gill 1982; Nappo 2002). Here m² is related to the Scorer parameter l² (Scorer 1949) through m² = l² − k², where k is the horizontal wavenumber (k = 2π/λ). The Scorer parameter used herein is

where N is the Brunt–Väisälä frequency, U is the component of the background wind in the direction of bore motion (from 300°), and c is the bore speed (12.8 m s⁻¹). So, m² < 0 implies that either the stability is small or negative, or there is significant curvature in the wave-normal wind profile. As defined by Lindzen and Tung (1976), the “reflection coefficient,” r, for an upward-propagating wave incident on a reflecting layer, is the absolute value of A₁/B₁, where A₁ is the amplitude of the reflected wave and B₁ is the amplitude of the incident wave. Following the analysis of Nappo (2002), m² < 0 in the reflecting layer implies that r = 1 for nontrivial cases, meaning that waves incident on the reflecting layer with m² < 0 from below are perfectly reflected, forming a wave duct.

a. Surface observations

One characteristic phenomenon associated with the passage of an undular bore at a surface station is a sudden rise in pressure (e.g., Koch et al. 1991; Karyampudi et al. 1995). This rise is related hydrostatically to the rapid increase in the depth of the low-level cool stable layer, associated with dry-adiabatic lifting below the lifted condensation level (LCL). The initial pressure increase in an undular bore is typically followed by fluctuations in surface pressure, oscillating at the same period as the waves atop the deepened cool layer. However, with a bore, the overall pressure rise is not transient (as with gravity waves or solitary waves); the change in stable-layer depth, and associated surface pressure, remains elevated for a longer period of time. Locatelli et al. (1998) refer to the change in depth as “relatively permanent.”

In the 2 October 2007 case, with 300-hPa divergence and low-level warm advection over Iowa, surface pressures were falling on a synoptic-scale across Iowa during the morning hours. Averaging the observations between 0800 and 1430 UTC at Des Moines (KDSM) shows a background pressure tendency about −0.91 hPa h⁻¹, which continues into the afternoon (Fig. 6). This tendency is removed from the pressure time series to isolate the pressure fluctuations associated with the bore.

The 1-min time series of pressure perturbations (p′) at KDSM from 1415 to 1515 UTC (Fig. 7a) clearly show the pressure jump associated with bore passage. After a small drop in p’ just ahead of the bore, there was a rapid rise in pressure of about 1.5 hPa in 9 min (1432–1441 UTC). Two more pressure oscillations followed the initial pressure jump, both with periods about 8 min and amplitudes of 0.20–0.25 hPa.

Surface winds also rapidly fluctuated with bore passage. The component of the 2-min-averaged surface wind in the direction of observed bore motion (from 300° at 12.8 m s⁻¹) is plotted in Fig. 7b. As is typical for bores, the wind shifted to the direction of bore motion as it passed, increasing to 8.4 m s⁻¹. Oscillations in bore-normal wind also occurred behind the initial wind shift, with periods around 9 min and amplitudes of 2–3 m s⁻¹. It should be noted that the maximum bore-normal wind observed is 8.4 m s⁻¹; even though radar observations show slightly higher values, they are still less than 12.8 m s⁻¹. This provides evidence that this feature is not a density current, since there is typically rear-to-front flow in density currents, which exceeds the speed of movement (e.g., Simpson 1997).

The 1-min surface temperature observations are shown in Fig. 7c. Note that surface temperatures remained basically constant throughout the passage of the bore, with the exception of a slight (0.5°C) temperature rise at the same time as the initial pressure jump. This could be attributed to measurement noise, or it may be associated with the downward mixing of slightly warmer air in the stable boundary layer as the bore and associated gusty winds pass by. The lack of any temperature drop associated with the pressure rise provides strong evidence that this feature is not a density current, since the temperature difference between the cold air behind a density current and the environment ahead of it is what causes the movement of the density current (e.g., Simpson 1997). The 1°C temperature drop just after 1500 UTC was coincident with the onset of heavy rain at the observation site.

b. Radar observations

The initial band of vertical motion associated with the bore produced a “fine line,” with maximum reflectivities >25 dBZ, in plan position indicator (PPI) reflectivity scans from the Des Moines, Iowa (KDMX) Weather Surveillance Radar-1988 Doppler (WSR-88D) Doppler radar (Fig. 8a). This indicates that the bore may have produced some light precipitation. The bore, including three wavelengths of the waves generated behind it, is clearly visible in PPI base velocity scans from KDMX (Fig. 8b).

The 1450 UTC Doppler velocity cross sections at 140° azimuth from the KDMX radar offer a more detailed analysis of the kinematics of the bore (Fig. 8c). Doppler velocities from PPI scans at various elevation angles were gridded (resolution 1 km horizontal, 200 m vertical). The main wind shift at the leading edge of the bore is apparent, with radial velocities shifting from inbound near the 29-km range to outbound, at speeds >10 m s⁻¹, near the 26-km range. The waves behind the leading edge of the bore are also apparent, with at least two more regions of outbound radial velocities centered at ranges of 19 and 12 km, flanked by inbound velocities.

Applying finite differencing (δV_r/δr), where V_r is the radial velocity and r is the range from the radar, to the gridded 1450 UTC Doppler velocity data along 140° azimuth, 2D convergence was estimated. Upward integration of the continuity equation allowed for estimates of vertical motion, assuming that convergence occurred only along the radar beam, which was roughly normal to bore motion. The radar cross-section values of horizontal wind and analyzed vertical motion at 1450 UTC, along with bore speed, were utilized to estimate a time series of vertical displacement of the top of the stable inversion layer through the bore, making the assumption that the bore was in a steady state (Fig. 8d). This analysis was performed using rough trajectory calculations. This analysis indicates that the top of the boundary layer was displaced upward about 400 m in 300 s, then oscillated to about an average height of 958 m after the leading edge of the bore passed.

c. Analysis

The 1-min Automated Surface Observing System (ASOS) data available from Des Moines, along with the high-resolution Doppler radar imagery of the bore, which passed directly over the KDMX WSR-88D radar, allow for excellent analysis of the characteristics of the bore. These may be compared with theory.

As stated in section 2, the height of the prebore stable boundary layer on 2 October 2007 was h₀ = 700 m AGL. The height of the boundary layer after bore passage, h₁, may be estimated using the vertical displacement calculations described in section 3b. These calculations indicate that the average height of the boundary layer behind the leading edge of the bore was 958 m AGL. PPI scans of velocity indicate that oscillations in velocity associated with the bore occurred as high as 900–1100 m AGL. So, using an average from the two methods, h₁ is estimated at 1000 m AGL. This implies a bore strength (h₁/h₀) of 1.43. According to Simpson (1997), when the bore strength is between 1 and 2, the bore is undular, as is the case here.

The observed wavelengths of the waves behind the bore were determined using radar data, and were about 7 km. Laboratory experiments done by Rottman and Simpson (1989) and atmospheric measurements by Clarke et al. (1981) indicate that, for bore strengths between 1.0 and 2.0, the horizontal wavelength of the waves behind the bore should be about 10 (±4) × h₁. In this case, h₁ = 1000 m, so the wavelength should be around 6–14 km. Therefore, the observed wavelength of 7 km is consistent with this theory.