A PV-gradient related quantity in moist atmosphere and its application in the diagnosis of heavy precipitation

- A PV-gradient related quantity in moist atmosphere called second-order potential vorticity (SMPV) is derived.
- SMPV contains moist static stability, vorticity enstrophy and their vertical gradients.
- SMPV is more capable of diagnosing and detecting strong precipitation than GPV.
- Second-order inhomogeneity of moisture, temperature and wind within precipitation system is highlighted.

In this paper, a PV-gradient related parameter-the second-order potential vorticity (SPV) is generalized into a non-uniformly saturated atmosphere to involve the PV-gradient into precipitation diagnosis, assuming that PV gradient is more capable of describing the whole structure of the air mass boundaries than other single element gradients. The newly derived second-order moist potential vorticity (SMPV), which is defined as the dot product of the generalized vorticity vector and three-dimensional gradient of a conserved form of generalized potential vorticity (GPV), keeps the conserved property as SPV in the frictionless, moist adiabatic atmosphere. Nevertheless, due to the complex calculation of SMPV, a non-conservative form of SMPV (NSMPV) is subtracted from SMPV, which is defined as the dot product of vorticity vector and three-dimensional gradient of GPV by involving the baroclinic vorticity. The capability of the NSMPV on diagnosing and detecting heavy precipitation is examined for a heavy rainfall case, with GPV as a comparison. A typical scale analyses in this case shows that GPV is mainly a coupling of static stability and vertical vorticity, while NSMPV contains static stability, vorticity enstrophy and their vertically inhomogeneity. Due to these information, both GPV and NSMPV show strong anomalies over the precipitation region, by reflecting the cyclonic shear and large vertical variations of temperature and humidity in the lower troposphere. However, GPV also appears strong, wide anomalies out of the precipitation region while NSMPV does not. In addition, due to the vertical gradient of vorticity enstrophy and static stability contained in NSMPV, it also has a reflection on the invasion of cold, dry air in the near-surface layer, which is seen to be a triggering mechanism of the strong precipitation. This indicates that NSMPV perform better than GPV in detecting heavy rainfall and are powerful on distinguishing between precipitation and non-precipitation region. A long time-series analyses over China further verify a steady performance of NSMPV on diagnosing precipitation, which means NSMPV may be used as a precipitation indicator as well as GPV in the future.