Based on high-resolution pressure data collected by a microbarograph and Fourier transform (FFT) data processing, a detailed analysis of the frequency spectra characteristics of gravity waves during a hailstone event in the cold vortex of Northeast China (NECV) on 9 September 2021 is presented. The results show that the deep NECV served as the large-scale circulation background for the hailstone event. The development of hailstones was closely related to gravity waves. In different hail stages, the frequency spectra characteristics of gravity waves were obviously different. One and a half hours before hailfall, there were gravity wave precursors with periods of 50–180 min and corresponding amplitudes ranging from 30 to 60 Pa. During hailfall, the center amplitudes of the gravity waves were approximately 50 Pa and 60 Pa, with the corresponding period ranges expanding to 60–70 min and 160–240 min. Simultaneously, hailstones initiated shorter periods (26–34 min) of gravity waves, with the amplitudes increasing to approximately 12–18 Pa. The relationship between hailstones and gravity waves was positive. After hailfall, gravity waves weakened and dissipated rapidly. As shown by the reconstructed gravity waves, key periods of gravity wave precursors ranged from 50–180 min, which preceded hailstones by several hours. When convection developed, there was thunderstorm high pressure and an outflow boundary. The airflow converged and diverged downstream, resulting in the formation of gravity waves and finally triggering hailfall. Gravity wave predecessors are significant for hail warnings and artificial hail suppression.

Two new diagnostic quantities called solenoidal vorticity (SV) and potential solenoidal vorticity (PSV) are defined in this paper for a moist atmosphere based on the generalized moist potential vorticity (GMPV). SV and PSV are introduced to incorporate vorticity information along the isentropic surfaces that GMPV (or PV) has lost. SV is the scalar product of vorticity and the moist solenoidal term ∇ p × ∇ α*, while PSV is the scalar product of vorticity and (∇ p × ∇ α*) × ∇ θ* (a new vector). Application of GMPV, SV, and PSV to a diagnostic study of a heavy rainfall case shows that SV reflects the coupling of vertical wind shear and the baroclinity of the moist atmosphere weighted by the vertical gradient of pressure, while PSV reflects the coupling of vertical wind shear and baroclinity, the static stability, and the vertical gradient of pressure. Although all three quantities exhibit strong signals over the observed precipitation region, SV and PSV are more capable of distinguishing between precipitation and non‐precipitation areas. The following three main factors are concluded to contribute to the very different distribution patterns of GMPV, SV, and PSV: static stability,the vertical gradient of pressure, and different ways of coupling vertical wind shear and baroclinity. These factors are responsible for the good performance of SV and PSV in tracing and predicting heavy rainfall, as demonstrated by the correlation coefficient between SV (PSV) and the rainfall amount obtained from long time series analyses. The results of this study suggest that SV and PSV are good detectors of heavy rainfall and may be used as precipitation prediction parameters.