Understanding the Impacts of Upper-Tropospheric Cold Low on Typhoon Jongdari (2018) Using Piecewise Potential Vorticity Inversion

Typhoon Jongdari (2018) had an unusual looping path before making landfall in Japan, which posed a forecasting challenge for operational numerical models. The impacts of an upper-tropospheric cold low (UTCL) on the track and intensity of Jongdari are investigated using numerical simulations. The storm track and intensity are well simulated in the control experiment using the GFS analysis as the initial and boundary conditions. In the sensitivity experiment (RCL), the UTCL is removed from the initial-condition fields using the piecewise potential vorticity inversion (PPVI), and both the track and intensity of Jongdari change substantially. The diagnosis of potential vorticity tendency suggests that horizontal advection is the primary contributor for storm motion. Flow decomposition using the PPVI further demonstrates that the steering flow is strongly affected by the UTCL, and the looping path of Jongdari results from the Fujiwhara interaction between the typhoon and UTCL. Jongdari first intensifies and then weakens in the control experiment, consistent with the observation. In contrast, it undergoes a gradual intensification in the RCL experiment. The UTCL contributes to the intensification of Jongdari at the early stage by enhancing the eddy flux convergence of angular momentum and reducing inertial stability, and it contributes to the storm weakening via enhanced vertical wind shear at the later stage when moving closer to Jongdari. Different sea surface temperatures and other environmental conditions along the different storm tracks also contribute to the intensity differences between the control and the RCL experiments, indicating the indirect impacts of the UTCL on the typhoon intensity.

Piecewise potential vorticity inversion without far-field response?

Given a flow domain D with subdomains D1 and D2, piecewise potential vorticity inversion (PPVI) inverts a potential vorticity (PV) anomaly in D2 and assumes vanishing PV in D1 where boundary conditions must be taken into account. It is a widely held view that the PV anomaly exerts a far-field influence on D1 which is revealed by PPVI. Tests of this assertion are conducted using a simple quasigeostrophic model where an upper layer D2 contains a PV anomaly and D1 is the layer underneath. This anomaly is inverted. Any downward physical impact of PV in D2 must also be represented in the results of a downward piecewise density inversion (PDI) based on the hydrostatic relation and the density in D2 as following from PPVI. There is no doubt about the impact of the mass in D2 on the flow in the lower layer D1. Thus results of PPVI and PDI have to agree closely. First, PPVI is applied to a locally confined PV-anomaly in D2. There is no far-field ’response’ in D1 if stationarity is imposed. Modifications of boundary conditions lead to “induced” flows in D1 but the results of PPVI and PDI differ widely. This leads to a simple proof that there is no physical far-field influence of PV-anomalies in D2. Wave patterns of the streamfunction restricted to D2 are prescribed in a second series of tests. The related PV-anomalies are obtained by differentiation and are also confined to D2 in this case. This approach illustrates the basic procedure to derive PV-fields from observations which excludes a far-field response.

Nonuniqueness of Attribution in Piecewise Potential Vorticity Inversion

Piecewise potential vorticity inversion (PPVI) seeks to determine the impact of observed potential vorticity (PV) anomalies on the surrounding flow. This widely used technique is based on dividing a flow domain D into subdomains D1 and D2 = D − D1. The influence of PV in D1 on the flow in D2 is assessed by removing all PV anomalies in D2 and then inverting the modified PV in D. The resulting flow with streamfunction ψ1 is attributed to the PV anomalies in D1. The relation of PV in D1 to ψ1 in D2 is not unique, because there are many PV distributions in D1 that induce the same ψ1. There is, however, a unique solution if the ageostrophic circulation is included in the inversion procedure. The superposition principle requires that the sum of inverted flows with PV = 0 in D2 and the complementary ones with PV = 0 in D1 equal the inverted flow for the complete observed PV in D. It is demonstrated, using two isolated PV balls as a paradigmatic example, that the superposition principle is violated if the ageostrophic circulation is included in PPVI, because the ageostrophic circulation cannot be associated with only one of the anomalies. Inversions of Ertel’s PV are carried out using Charney’s balance condition. PPVI is not unique in that case, because many different PV fields can be specified in D1, which all lead to the same inverted flow in D2. The balance condition assumes vanishing vertical velocity w so that uniqueness cannot be established by including w in the inversion, as was possible in the quasigeostrophic case.

Diagnosis of a North American Polar–Subtropical Jet Superposition Employing Piecewise Potential Vorticity Inversion

The polar jet (PJ) and subtropical jet (STJ) often reside in different climatological latitude bands. On occasion, the meridional separation between the two jets can vanish, resulting in a relatively rare vertical superposition of the PJ and STJ. A large-scale environment conducive to jet superposition can be conceptualized as one that facilitates the simultaneous advection of tropopause-level potential vorticity (PV) perturbations along the polar and subtropical waveguides toward midlatitudes. Once these PV perturbations are transported into close proximity to one another, interactions between tropopause-level, lower-tropospheric, and diabatically generated PV perturbations work to restructure the tropopause into the two-step, pole-to-equator tropopause structure characteristic of a jet superposition. This study employs piecewise PV inversion to diagnose the interactions between large-scale PV perturbations throughout the development of a jet superposition during the 18–20 December 2009 mid-Atlantic blizzard. While the influence of PV perturbations in the lower troposphere as well as those generated via diabatic processes were notable in this case, tropopause-level PV perturbations played the most substantial role in restructuring the tropopause prior to jet superposition. A novel PV partitioning scheme is presented that isolates PV perturbations associated with the PJ and STJ, respectively. Inversion of the jet-specific PV perturbations suggests that these separate features make distinct contributions to the restructuring of the tropopause that characterizes the development of a jet superposition.