A Mesoscale Gravity-Wave Event Observed during CCOPE. Part IV: Stability Analysis and Doppler-derived Wave Vertical Structure

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Abstract
This paper summarizes the results of a detailed study from the Cooperative Convective Precipitation Experiment (CCOPE) of the vertical structure of mesoscale gravity waves that disturbed a sizable part of the troposphere and that played a significant role in the generation of a mesoscale convective complex. These bimodal waves displayed periods of 148 (50) min, wavelengths of 135 (60) km, and phase speeds of 15.2 (19.8) m s−1. A comparison is made between wave-induced pressure perturbation fields derived from triple-Doppler wind fields within regions of essentially nonconvective precipitation, pressure perturbation fields obtained by bandpass filtering of surface mesonetwork data, and the vertical structure of the pressure eigenfunctions as predicted from a linear stability analysis. It is believed that this represents the first such application of the Doppler radar pressure retrieval technique to the study of gravity waves. In addition, an analysis of the potential for shear instability was performed on all of the special CCOPE soundings taken on this day to determine the representativeness of the chosen soundings for the theoretical analysis and the likelihood that a wave maintenance mechanism endured throughout the 33-h wave event. The analysis of the potential for shear instability and the eigenfunctions both indicate that the bimodal waves were able to efficiently extract energy from the mean flow near several closely spaced critical levels in the 4.0– 6.5-km layer to maintain their coherence for many wave cycles. This result serves as the explanation for the observed ability of the waves to organize precipitation into long convective bands whose axes were along and just ahead of the wave crests. The eigenvalue analysis predicts unstable modes that are hydrostatic, nondispersive, ducted gravity waves characterized by half of a vertical wavelength contained between the ground and the lowest critical level (at z = 4 km). Eigenfunctions of pressure and other variables all display negligible tilt below 2.3–3.3 km, above which a sudden reversal in phase occurs. The vertical structure of the Doppler-derived fields associated with one of these gravity waves agrees in terms of the following respects with the eigenfunction predictions and/or the surface mesoanalyses: (a) the vertical wavelength, horizontal structure, and amplitude of the perturbation horizontal wind and pressure fields, and (b) the in-phase covariance between the pressure and horizontal wind fields at levels below 2.5 km. On the other hand, the theory predicted a much more abrupt vertical transition in phase in the pressure fields and weaker amplitudes aloft than were evident in the Doppler analyses. In addition, the size of the multiple-Doppler analysis domain was too small to capture an entire horizontal wavelength of the 135-km-scale gravity wave, which made direct comparisons difficult. Furthermore, the linear theory predicts much smaller amplitudes and somewhat longer horizontal wavelengths for the vertical motions characterizing both wave modes than those seen in the Doppler winds, which likely also contain nonwave effects. These discrepancies are largely due to the combined effects of weak convection, turbulence, and data sampling problems. Despite these drawbacks, the findings from this and other recent studies using Doppler radars and ground-based radiometers suggest that remote sensing of mesoscale gravity waves that occupy a significant fraction of the troposphere should be exploited further.

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