On the Interpretation of Potential Vorticity Variability in Tropical Cyclones in ECMWF High Resolution Operational Forecast Analyses

Curvilinear mesoscale potential vorticity (PV) structures in the upper troposphere / lower stratosphere (UTLS) are a robust feature above tropical cyclones (TCs) in high resolution (9 km grid spacing) European Centre for Medium-Range Weather Forecasting (ECMWF) forecast analyses. UTLS mesoscale PV variability is related to updrafts hitting the base of the stratosphere and is a useful signature of the dynamical adjustment process in forecast models. A statistical approach is used for analyzing ECMWF PV along TC storm tracks, where the standard deviation and mean are calculated in spatial domains following the motion of the center (defined by IBTrACS), at each pressure level every 6 hours. Comparison with satellite cloud-top temperature patterns shows that UTLS curvilinear PV structures in ECMWF analyses are correlated with convective bands seen in satellite data. This technique is useful for investigating the evolution and diurnal cycle of TCs. The formation of PV structures and emission of gravity waves are of interest because they are part of the dynamical adjustment process whereby TCs evolve toward a balanced vortex state. This presentation describes how PV variability is created in the model using scale analysis of terms in the PV conservation equation. Results regarding the evolution and diurnal cycle are described and interpreted in terms of cloud radiative forcing theories.

Results from analyzing 5 TCs in the South Pacific and 15 TCs in the North Atlantic show that, for TCs over open ocean, the diurnal cycle in the standard deviation of 100 hPa PV exhibits a statistically significant maximum near 6 am local time during the development stage, which shifts to near midnight after reaching strength C2, similar to results from satellite studies of gravity wave activity near TCs. The amplitude of the diurnal cycle in the standard deviation of 100 hPa PV in the 6x6 degree domain is abruptly reduced to ~ 1/2 upon reaching C2, while the amplitude of the diurnal cycle in the inner 2x2 degree domain is more steady in time. A peak in the standard deviation of 100 hPa PV often occurs in the inner domain just prior to rapid intensification.

In the inner core at 100 hPa, diurnal variations in the standard deviation of PV and mean PV are strongly negatively correlated, consistent with a midnight peak in cooling and mixing in the UTLS. In the UTLS, the cyclonic inner core strengthens at night when there is a burst of PV variability. Vertical profiles of the standard deviation of Ertel’s PV and of relative vorticity are nearly identical, with their ratio exhibiting an abrupt increase at the tropopause by a factor of 25. This is equal to the jump in the static stability factor in Ertel's PV at the tropopause, which explains the sharp maximum in the standard deviation of PV at 100 hPa.

The evolution and diurnal cycle of PV variability and mean PV at 500 hPa is also discussed. Values of mean PV are related to the Saffir-Simpson intensity scale. TCs often exhibit multiple layers of maxima in PV variability and mean PV in the mid-troposphere. At 500 hPa the correlation coefficient between the standard deviation of PV and of relative vorticity typically exceeds 0.96 and their correlation with cyclonic mean PV is ~ 0.6. This shows that the standard deviation of PV and mean PV in the mid-troposphere are both proportional to cyclone strength.

Vertically coherent temporal maxima in divergence, relative vorticity, and PV support the interpretation that UTLS PV structures are due to updrafts hitting the bottom of the stratosphere and are a useful signature of dynamical adjustment in the model. Investigating the statistical behavior of PV in TCs can contribute toward improved understanding of rapid intensification and the dynamical adjustment process in global forecast models.