Explosive Cyclogenesis around the Korean Peninsula in May 2016 from a Potential Vorticity Perspective: Case Study and Numerical Simulations

: An explosive cyclone event that occurred near the Korean Peninsula in early May 2016 is simulated using the Weather Research and Forecasting (WRF) model to examine the developmental mechanisms of the explosive cyclone. After conﬁrming that the WRF model reproduces the synoptic environments and main features of the event well, the favorable environmental conditions for the rapid development of the cyclone are analyzed, and the explosive development mechanisms of the cyclone are investigated with perturbation potential vorticity (PV) ﬁelds. The piecewise PV inversion method is used to identify the dynamically relevant meteorological ﬁelds associated with each perturbation PV anomaly. The rapid deepening of the surface cyclone was inﬂuenced by both adiabatic (an upper tropospheric PV anomaly) and diabatic (a low-level PV anomaly associated with condensational heating) processes, while the baroclinic processes in the lower troposphere had the smallest contribution. In the explosive phase of the cyclone life cycle, the diabatically generated PV anomalies associated with condensational heating induced by the ascending air in the warm conveyor belt are the most important factors for the initial intensity of the cyclone. The upper-level forcing is the most important factor in the evolution of the cyclone’s track, but it is of secondary importance for the initial strong deepening.


Introduction
Explosive cyclones are extratropical cyclones characterized by a strong deepening (a sea level pressure decrease larger than 24 hPa within 24 h at 60 • N or the equivalent [1]) and are often linked not only to extreme weather conditions, including strong winds and heavy rainfall, but also to extreme ocean events such as abnormally high waves [2] and, in some cases, storm surge. Sanders and Gyakum [1] first conducted a study on explosive cyclones in 1980 and demonstrated the importance of the baroclinic instability to this phenomenon; since then, many researchers have identified the development mechanisms of explosive cyclones, including physical and dynamical processes [3][4][5][6][7][8][9][10].
According to Shapiro et al. [11], explosive cyclones initially develop in response to a combination of different mechanisms that include upper-level cyclonic vorticity advection, low-level warm air advection, and latent heat release. This may be influenced by Rossby wave breaking, which contributes to the development of intense cyclones by constraining and intensifying the upper-level jet stream [12][13][14]. Furthermore, the heating and moistening of the atmosphere and the reduced stability due to air-sea interactions are also important prior to and during explosive cyclone development [15][16][17].   Figure 2d shows a cloud band curling around the cyclone center and a dry intrusion forming a hook-shaped cloud pattern, which indicates explosive cyclogenesis [36]. The hook-shaped cloud developed into a spiral cloud, which is characteristic of the mature stage of an explosive cyclone (Figure 2e). Strong winds reaching the surface in the dry air ahead of the hook-shaped cloud head can be produced by a sting jet, which is also present at that time, with the WCB located beneath the PV intrusion [37,38]. The dry intrusion enters the circulation of the surface cyclone, which means that cold, dry air with a high PV intrudes into the lower troposphere from the lower stratosphere and/or upper troposphere. The spiral cloud pattern was associated with the dry intrusion from the upper level and indicates the condition of the upper-level cyclonic circulation (Figure 2f). From synoptic charts, the dry intrusion with a cloudless area is found to descend over the warm and moist sectors, which can lead to potential instability. The spiral patterns developed after the surface deepening had nearly finished, and the upper-level cyclone continued to intensify or maintain its strength.

Data
The following data are employed herein: (1) the analyzed surface weather charts and upper-level weather charts from the Korean Meteorological Administration (KMA) for cyclone   Figure 2d shows a cloud band curling around the cyclone center and a dry intrusion forming a hook-shaped cloud pattern, which indicates explosive cyclogenesis [36]. The hook-shaped cloud developed into a spiral cloud, which is characteristic of the mature stage of an explosive cyclone (Figure 2e). Strong winds reaching the surface in the dry air ahead of the hook-shaped cloud head can be produced by a sting jet, which is also present at that time, with the WCB located beneath the PV intrusion [37,38]. The dry intrusion enters the circulation of the surface cyclone, which means that cold, dry air with a high PV intrudes into the lower troposphere from the lower stratosphere and/or upper troposphere. The spiral cloud pattern was associated with the dry intrusion from the upper level and indicates the condition of the upper-level cyclonic circulation (Figure 2f). From synoptic charts, the dry intrusion with a cloudless area is found to descend over the warm and moist sectors, which can lead to potential instability. The spiral patterns developed after the surface deepening had nearly finished, and the upper-level cyclone continued to intensify or maintain its strength.
tracking, (2) the COMS-1 infrared imagery downloaded from the satellite information service system of the KMA, and (3) the global final analysis (FNL) dataset produced with a resolution of 1.0° and 26 vertical levels for numerical simulations and experiments, which are provided by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR). The NCEP FNL is taken as the initial and 6-hourly forecast files for the initial and boundary conditions.

Model Description
To obtain a comprehensive three-dimensional structure of the explosive cyclone, the Advanced Research WRF (WRF-ARW) model [39] version 3.7 developed by NCAR was used. The model incorporates fully incompressible nonhydrostatic equations in conjunction with terrain-following vertical coordinates. The model was run with two domains starting at 0000 UTC 2 May 2016 and integrated for 72 h to include the entire lifetime of the explosive cyclone. The horizontal resolutions of the outer and inner domains are 20 and 4 km with 218 × 218 and 361 × 361 grids (Figure 3), respectively. Both domains have 40 vertical layers from the surface to the 50 hPa level, and the

Data
The following data are employed herein: (1) the analyzed surface weather charts and upper-level weather charts from the Korean Meteorological Administration (KMA) for cyclone tracking, (2) the COMS-1 infrared imagery downloaded from the satellite information service system of the KMA, and (3) the global final analysis (FNL) dataset produced with a resolution of 1.0 • and 26 vertical levels for numerical simulations and experiments, which are provided by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR). The NCEP FNL is taken as the initial and 6-hourly forecast files for the initial and boundary conditions.

Model Description
To obtain a comprehensive three-dimensional structure of the explosive cyclone, the Advanced Research WRF (WRF-ARW) model [39] version 3.7 developed by NCAR was used. The model incorporates fully incompressible nonhydrostatic equations in conjunction with terrain-following vertical coordinates. The model was run with two domains starting at 0000 UTC 2 May 2016 and integrated for 72 h to include the entire lifetime of the explosive cyclone. The horizontal resolutions of the outer and inner domains are 20 and 4 km with 218 × 218 and 361 × 361 grids (Figure 3), respectively. Both domains have 40 vertical layers from the surface to the 50 hPa level, and the model instantaneous outputs were saved every hour. The Yonsei University (YSU) planetary boundary layer scheme [40], Noah Land Surface Model [41], Kain-Fritsch cumulus parameterization scheme [42], Dudhia short-wave and rapid radiative transfer model (RRTM) long-wave radiation scheme [43], and the WRF Single-Moment 6-Class Microphysics Scheme [44] were applied to both simulations. A summary of the model configuration parameters and physical schemes used is given in Table 1. model instantaneous outputs were saved every hour. The Yonsei University (YSU) planetary boundary layer scheme [40], Noah Land Surface Model [41], Kain-Fritsch cumulus parameterization scheme [42], Dudhia short-wave and rapid radiative transfer model (RRTM) long-wave radiation scheme [43], and the WRF Single-Moment 6-Class Microphysics Scheme [44] were applied to both simulations. A summary of the model configuration parameters and physical schemes used is given in Table 1.

Piecewise PV Analysis
The Ertel PV (EPV) is defined as [45,46] where ρ is the density, η is the absolute vorticity vector, and θ is the potential temperature. The PV is expressed in PV units (PVU; 1 PVU = 10 −6 m 2 s −1 K kg −1 ). The EPV is conserved for the primitive equations given an adiabatic frictionless flow. Considering a given distribution of the PV throughout a domain, an appropriate balance condition, and suitable boundary conditions, the PPVI allows for where ρ is the density, η is the absolute vorticity vector, and θ is the potential temperature. The PV is expressed in PV units (PVU; 1 PVU = 10 −6 m 2 s −1 K kg −1 ). The EPV is conserved for the primitive equations given an adiabatic frictionless flow. Considering a given distribution of the PV throughout a domain, an appropriate balance condition, and suitable boundary conditions, the PPVI allows for the recovery of the mass and momentum fields attributable to discrete PV anomalies. The Davis and Emanuel [31] method, which is used in this study, assumes (1) hydrostatic balance and (2) that the magnitude of the irrotational component of the wind is much smaller than the magnitude of the nondivergent component (i.e., V χ V ψ ). Applying these approximations, the divergence equation and Equation (1) can be rewritten as where Φ is the geopotential, ψ is the nondivergent stream function, λ is the longitude, φ is the latitude, a is the radius of the earth, P is the pressure, and κ = R/c p is the Exner function, which serves as the vertical coordinate. Equation (2) is a nonlinear balance equation by Charney [47], which has been demonstrated by previous studies to be an excellent approximation to observed flows [48], thus validating the application of PV diagnostics to the real atmosphere [49].

Experimental Design
To quantify the impact of various PV anomalies, including the upper-level trough, the stratospheric air intrusion, the LHR, the sensible heat flux, and the enhanced local baroclinicity from differential diabatic heating on the explosive cyclogenesis, PPVI was conducted. PPVI has been discussed in detail by the authors of previous studies [31,[50][51][52]. In order to use the PPVI method effectively, it is necessary to meaningfully partition the perturbation PV [51]. In order to invert particular PV anomalies, a mean state must be defined. The mean state for the present case is defined as the time average between 0000 UTC 1 May and 0000 UTC 6 May 2016. Given the mean state, the whole atmosphere was partitioned into four parts in a domain (10-60 • N, 90-170 • E) according to same approach in Baxter et al. [53]: (1) the upper-level perturbation PV (UP): this anomaly represents the main upper-level forcing and is defined as all of the positive and negative perturbation PVs with an relative humidity (RH) < 70% from 500 hPa to the 100 hPa boundary PV; (2) the moist interior PV (MP): the lower-tropospheric PV anomaly related to condensational heating is defined as all positive perturbation PVs with an RH ≥ 70% from 950 hPa to 400 hPa; (3) the lower boundary (LP): this anomaly represents the low-level baroclinicity and is defined as all positive and negative perturbation PVs from the surface through 925 hPa; and (4) the remaining interior PV (RP): all positive and negative perturbation PVs with an RH < 70% from 950 hPa to 550 hPa, which are likely remnants of the diabatically generated PV. The removal of the UP and MP simulations was designed to isolate the effect of the tropopause undulations associated with upper-tropospheric/lower-stratospheric air and to consider the effect of condensation-related diabatic processes, respectively. The removal of the LP simulation was designed to consider the effect of diabatic heating that was closely related to the baroclinicity and boundary layer processes. The removal of the RP simulation was designed to examine the effect of the diabatically generated PV remnants not included in the above three simulations. To illustrate the effect of the removal of the four partitioned perturbation PVs, four simulations were performed-namely, the removal of UP (RUP), MP (RMP), LP (RLP), and RP (RRP). Figure 4 shows the initial conditions of each simulation for a 500 hPa geopotential height and the sea level pressure after the PPVI procedure. Finally, to gain an accurate understanding of the impacts of the upper-level perturbation PV and moist interior PV on cyclogenesis, two additional simulations were performed, in which UP and MP are doubled; they are denoted as DUP and DMP, respectively.  At 1200 UTC on 2 May, the flow was characterized by a short-wave trough feature at the 500 hPa level near 37 °N, 113 °E. The trough moved northeastward and deepened during the following 24 h. The initial surface cyclone with a CSLP of 1002 hPa formed within a strong baroclinic zone southeast of a short-wave trough aloft (Figure 5a). The short-wave trough with its positively tilted axis over the area east of China is evident at the 500 hPa level. The 500 hPa short-wave trough was located ~10° longitude upstream from the surface cyclone, which was characterized with a strong isotherm gradient and strong baroclinicity. This superposition between the surface cyclone and the short-wave trough provides a favorable condition for the surface cyclone to develop. At 0000 UTC

Control Simulation
At 1200 UTC on 2 May, the flow was characterized by a short-wave trough feature at the 500 hPa level near 37 • N, 113 • E. The trough moved northeastward and deepened during the following 24 h. The initial surface cyclone with a CSLP of 1002 hPa formed within a strong baroclinic zone southeast of a short-wave trough aloft (Figure 5a). The short-wave trough with its positively tilted axis over the area east of China is evident at the 500 hPa level. The 500 hPa short-wave trough was located~10 • longitude upstream from the surface cyclone, which was characterized with a strong isotherm gradient and strong baroclinicity. This superposition between the surface cyclone and the short-wave trough provides a favorable condition for the surface cyclone to develop. At 0000 UTC on 3 May, the surface cyclone rapidly deepened to a CSLP of 982 hPa and moved northeastward to the northern part of the Korean Peninsula (Figure 5b). The 850 hPa potential temperature contour and the 500 hPa isohypse at the leading edge of the trough intersect, suggesting that baroclinicity and warm air advection are intensifying over the region. The warm sector in the WCB's region of strongest ascent was linked with the upper-level PV anomaly. Then, the 500 hPa short-wave trough developed into a cut-off low. A very strong upper-level jet is located at the base of the cut-off, reaching a value of~45 m s −1 . During the following 12 h, the surface cyclone reached its maximum intensity with a CSLP of 972 hPa (Figure 5c). Warm advection enhanced the 500 hPa ridge, and cold advection deepened the 500 hPa trough, which shows a well-developed baroclinic pattern. At 0000 UTC on 4 May, the surface cyclone remained almost stationary with a CSLP of 974 hPa. The system showed evidence of occlusion because the temperature advection weakened and completely lost its vertical tilt (Figure 5d). Although there are slight differences in the position between the observed and model-simulated explosive cyclone from its initial to final stages, the simulation results of the WRF model can be used to examine the development mechanisms of the explosive cyclone.
Atmosphere 2019, 10, x FOR PEER REVIEW  8 of 19 on 3 May, the surface cyclone rapidly deepened to a CSLP of 982 hPa and moved northeastward to the northern part of the Korean Peninsula (Figure 5b). The 850 hPa potential temperature contour and the 500 hPa isohypse at the leading edge of the trough intersect, suggesting that baroclinicity and warm air advection are intensifying over the region. The warm sector in the WCB's region of strongest ascent was linked with the upper-level PV anomaly. Then, the 500 hPa short-wave trough developed into a cut-off low. A very strong upper-level jet is located at the base of the cut-off, reaching a value of ~45 m s −1 . During the following 12 h, the surface cyclone reached its maximum intensity with a CSLP of 972 hPa (Figure 5c). Warm advection enhanced the 500 hPa ridge, and cold advection deepened the 500 hPa trough, which shows a well-developed baroclinic pattern. At 0000 UTC on 4 May, the surface cyclone remained almost stationary with a CSLP of 974 hPa. The system showed evidence of occlusion because the temperature advection weakened and completely lost its vertical tilt (Figure 5d). Although there are slight differences in the position between the observed and model-simulated explosive cyclone from its initial to final stages, the simulation results of the WRF model can be used to examine the development mechanisms of the explosive cyclone. The evolution of the PV on the 320-K isentropic surface from 1200 UTC 2 May to 0000 UTC 4 May is given in Figure 5 to show the necessary conditions for cyclogenesis. At 1200 UTC 2 May, a southward penetration of the PV contours was simulated at approximately 35 °N, 113 °E, with a local maximum of PV greater than 7.0 PVU directly above the positively tilted trough at the 500 hPa level (Figure 6a). During the following 12 h, the PV anomaly core moved northeastward over the Shandong Peninsula near 36 °N, 122 °E (Figure 6b), while the cut-off low was generated by the The evolution of the PV on the 320-K isentropic surface from 1200 UTC 2 May to 0000 UTC 4 May is given in Figure 5 to show the necessary conditions for cyclogenesis. At 1200 UTC 2 May, a southward penetration of the PV contours was simulated at approximately 35 • N, 113 • E, with a local maximum of PV greater than 7.0 PVU directly above the positively tilted trough at the 500 hPa level (Figure 6a). During the following 12 h, the PV anomaly core moved northeastward over the Shandong Peninsula near 36 • N, 122 • E (Figure 6b), while the cut-off low was generated by the deepening of the 500 hPa trough. This was because the negative PV anomaly over the surface cyclone was intensified by cloud diabatic processes in the WCB outflow region and the southern part of the high-PV air stream cut off from the main stratospheric PV reservoir [22,23], as shown in Figure 5b. Then, intense condensational heating and low-level PV production were induced by the ascending air in the WCB. At 1200 UTC 3 May, the PV anomaly core on the 320 K isentropic surface was located very close to the surface cyclone center. A cyclonic rolling-up of the 300 hPa PV anomaly exceeding 5.0 PVU was generated around the center of the surface cyclone, developing the characteristic inverted comma shape that is associated with the lowermost stratospheric dry air intrusion (Figure 6c). The upper-level PV anomaly and the comma-shaped cloud shown in Figure 2e,f were closely associated with the dry air intrusion to the rear of the surface cyclone.  For a better analysis of the three-dimensional aspects of the PV evolution, Figure 7 shows the vertical cross section of the simulated PV from 1200 UTC 2 May to 1200 UTC 4 May along a longitudinal line based on the position of the surface cyclone center. As a result of the gradual tropopause intrusion, the high PV tongue descended from the upper troposphere to the middle troposphere with the 1.6-PVU contour extending downward to the lowest point of 500 hPa at 1200 UTC on 2 May 2016 ( Figure 7a). Meanwhile, there were two lower-level high PVs, one between 500 and 700 hPa and the other between 800 and 900 hPa. This shows that a PV tower is beginning to form through a connection between the upper-level high PVs and lower-level high PVs. At 0000 UTC on 3 May (Figure 7b), the PV tower formed corresponding to the time at which the surface cyclone reached its deepest intensity. It is noted that the increase and upward extension of the lower-level PV reached up to 2.7 PVU, occurring between 500 and 900 hPa, and the upper-level PV moved eastward to the region of enhanced low-level PV ~12 h before the formation of the PV tower. The For a better analysis of the three-dimensional aspects of the PV evolution, Figure 7 shows the vertical cross section of the simulated PV from 1200 UTC 2 May to 1200 UTC 4 May along a longitudinal line based on the position of the surface cyclone center. As a result of the gradual tropopause intrusion, the high PV tongue descended from the upper troposphere to the middle troposphere with the 1.6-PVU contour extending downward to the lowest point of 500 hPa at 1200 UTC on 2 May 2016 ( Figure 7a). Meanwhile, there were two lower-level high PVs, one between 500 and 700 hPa and the other between 800 and 900 hPa. This shows that a PV tower is beginning to form through a connection between the upper-level high PVs and lower-level high PVs. At 0000 UTC on 3 May (Figure 7b), the PV tower formed corresponding to the time at which the surface cyclone reached its deepest intensity. It is noted that the increase and upward extension of the lower-level PV reached up to 2.7 PVU, occurring between 500 and 900 hPa, and the upper-level PV moved eastward to the region of enhanced low-level PV~12 h before the formation of the PV tower. The amplification of the explosive cyclone resulted from the interaction between the upper-and lower-level PV anomalies, inducing strong cyclonic circulation from the surface to the tropopause (Figure 7c). This result is in agreement with the findings in previous studies [15,16,54], which showed the importance of the interaction between the upper-level PV anomalies and the diabatically induced low-level PV anomalies. Therefore, explosive cyclogenesis can be regarded as a result of the PV tower that forms through both adiabatic (upper-level PV) and diabatic (lower-level PV) processes.

PPVI Results
The effects of each of the four perturbation PVs on the CSLP changes during the lifecycle of the explosive cyclone are presented. Figure 8 shows the time series of the CSLP simulated using the initial and boundary conditions from each of the simulations of RUP, RMP, RLP, and RRP during the 36-h period from 1200 UTC 2 May to 0000 UTC 4 May 2016. Compared to other simulations, the RUP and RMP simulations produced apparently weak cyclones (Figure 8a), which clearly shows the reduced influence of the upper-level and moist interior PV anomalies on the surface cyclogenesis.

PPVI Results
The effects of each of the four perturbation PVs on the CSLP changes during the lifecycle of the explosive cyclone are presented. Figure 8 shows the time series of the CSLP simulated using the initial and boundary conditions from each of the simulations of RUP, RMP, RLP, and RRP during the 36-h period from 1200 UTC 2 May to 0000 UTC 4 May 2016. Compared to other simulations, the RUP and RMP simulations produced apparently weak cyclones (Figure 8a), which clearly shows the reduced influence of the upper-level and moist interior PV anomalies on the surface cyclogenesis. The RUP cyclone continued to deepen with a small deepening rate throughout the 48-h simulation, although the initial CSLP was smaller than that of the RMP cyclone. The RMP simulation is similar in deepening rate to the control (CTL) simulation during a +27-h integration (Figure 8b), but it has a weak cyclone because the highest initial CSLP is 1019 hPa. Nevertheless, the RMP cyclone also rapidly developed with a deepening of 27 hPa during the first 24-h integration. Thus, the RMP cyclone develops a 16 hPa weaker CSLP by the 30-h integration, although it begins with a 15 hPa weaker CSLP than that of the CTL. This result implies that the lower-tropospheric PV anomalies associated with condensational heating between 400 and 950 hPa have a greater impact on the initial cyclogenesis. In addition, the upper-level PV anomaly is an important factor in both the initial cyclogenesis and the development of the cyclone throughout the cyclone's lifecycle. Figure 8a also shows that the time variation in the simulated CSLP of RRP is almost equal to that in the CTL throughout the lifecycle. The CSLPs in all simulations represent the maximum intensities of the cyclone: 973.3 hPa at +27 h in the CTL, 992.7 hPa at +45 h in RUP, 984.9 hPa at +30 h in RMP, 973.3 hPa at +30 h in RLP, and 971.7 hPa at +27 h in RRP. Figure 9 shows the cyclone tracks represented by the locations of the CSLP minima simulated using the initial and boundary conditions from each of the four perturbation PVs during the 48-h integration from 1200 UTC on 2 May. There is a clear difference in the cyclone tracks for the RUP and RMP simulations compared to the other simulations due to the initial positions of the cyclones. The RUP cyclone moved northeastward across the Korean Peninsula until its dissipation, while the RMP cyclone moved northward. The results of the RUP and RMP simulations are therefore analyzed in more detail in the next section.  Figure 9 shows the cyclone tracks represented by the locations of the CSLP minima simulated using the initial and boundary conditions from each of the four perturbation PVs during the 48-h integration from 1200 UTC on 2 May. There is a clear difference in the cyclone tracks for the RUP and RMP simulations compared to the other simulations due to the initial positions of the cyclones. The RUP cyclone moved northeastward across the Korean Peninsula until its dissipation, while the RMP cyclone moved northward. The results of the RUP and RMP simulations are therefore analyzed in more detail in the next section.

Upper-Level Forcing
To examine the effect of the upper-level PV structure during the cyclone lifecycle, we performed RUP and DUP simulations; Figure 10 shows the 500 hPa geopotential height, SLP, and 300 hPa PV fields during the lifecycle in the simulations. The upper-level trough located around 37 °N, 113 °E and the surface cyclone in the CTL simulation are found only in weak forms with a CSLP quickly than that of the DUP after the 3-h integration (Figure 11b). As shown in Figure 8b, the RUP cyclone continued to deepen during the 45-h integration, while the DUP cyclone was only developing for the 18-h integration. In particular, the DUP cyclone shows an explosive deepening tendency before the 15-h integration. Therefore, the upper-level dynamics, through the distribution of the PV, played an important role in the formation and development of the explosive cyclone during the initial and developing stages.

Condensational Heating
To examine the effect of the lower-tropospheric PV anomaly related to condensational heating during the cyclone lifecycle, we performed RMP and DMP simulations; Figure 12 shows the 700 hPa geopotential height, sea level pressure, and 700 hPa PV fields during the lifecycle in the simulations. The removal of the moist interior PV anomaly reproduces a short-wave trough at the 700 hPa level to the west of the Shandong Peninsula and a weak surface low near 30 °N, 120 °E (Figure 12a). This trough developed into a cut-off low accompanied by a 1.5 PVU 700 hPa PV anomaly over the Shandong Peninsula, and a surface low developed under the front of the trough. This cut-off low subsequently continued to deepen and traveled northeastward, and the surface low developed to its maximum intensity with a CSLP of 988 hPa and also moved northeastward (Figures 12b-d). When the moist interior PV anomaly is doubled (DMP), the surface cyclone is more enhanced as compared to the CTL during the lifecycle. The CSLP of the initial DMP cyclone was 980 hPa (Figure 11a), which is ~22 hPa lower than that of the CTL cyclone, and the initial position is almost the same as that of the CTL. The deepening rate of the DMP cyclone was weaker than that of the CTL during the 33-h integration, whereas the CTL cyclone deepened more quickly than that of the DMP after the 3-h integration (Figure 11b). The RMP cyclone continued to deepen during the 33-h integration, while the DMP cyclone only developed during the 21-h integration. Between the simulations, the RMP cyclone had a higher deepening rate than the DMP cyclone. An analysis of the influence of LHR on the PV tendency following the method of Heo et al. [5] revealed that the contribution of the latent heating term is almost zero during the 48-h integration, except for a positive contribution of about

Upper-Level Forcing
To examine the effect of the upper-level PV structure during the cyclone lifecycle, we performed RUP and DUP simulations; Figure 10 shows the 500 hPa geopotential height, SLP, and 300 hPa PV fields during the lifecycle in the simulations. The upper-level trough located around 37 • N, 113 • E and the surface cyclone in the CTL simulation are found only in weak forms with a CSLP of 1012 hPa in the RUP simulation at the initial time (Figure 10a). The trough is not developed as a cut-off low and remains a weak trough during the 48-h integration period. Correspondingly, the track of the surface cyclone is shifted to the south, mainly owing to the initial position shown in Figure 9 compared with the CTL. In addition, the 300 hPa PV anomaly core was located to the west of the surface cyclone center, and the cyclonic "rolling-up" of the 300 hPa PV anomaly in the CTL simulation associated with the lowermost stratospheric dry air intrusion is not found during this period (Figure 10b-d). When the upper-level PV anomaly is doubled (DUP), a cut-off low is immediately formed with more extension of the tropopause undulation over the surface cyclone at the initial time ( Figure 10e). Correspondingly, the surface cyclone is 10 hPa stronger than the CTL (Figure 11a). Except for the fact that the DUP cyclone moves slightly faster than the CTL, the doubled upper-level PV anomaly has little effect on the cyclone track. The RUP (DUP) simulation is not only unable (able) to reproduce the deepening of the cyclone but results in a much shallower (deeper) system than that in the CTL simulation. In fact, the RUP cyclone is shifted about 500 km southward from the initial to mature stages. The deepening rate of the DUP cyclone was stronger than that of the CTL during the first 3-h integration, whereas the CTL cyclone deepened more quickly than that of the DUP after the 3-h integration ( Figure 11b). As shown in Figure 8b, the RUP cyclone continued to deepen during the 45-h integration, while the DUP cyclone was only developing for the 18-h integration. In particular, the DUP cyclone shows an explosive deepening tendency before the 15-h integration. Therefore, the upper-level dynamics, through the distribution of the PV, played an important role in the formation and development of the explosive cyclone during the initial and developing stages.
deepened to a CSLP of 964 hPa. Doubling the moist interior PV anomaly strengthened the PV tower through the interaction with the upper-level PV anomaly. Further, the surface cyclone and a cut-off low at 700 hPa level developed unrealistically compared to the CTL simulation, but this system was merged with the system that developed to the north of the Korean Peninsula and propagated northeastward at 0000 UTC 4 May 2016.

Conclusions and Remarks
This study presents the effect of four perturbation PVs on the rapidly deepening cyclone around the Korean Peninsula from 2 to 5 May 2016. This case of rapid cyclogenesis was associated with high winds and waves that caused considerable damage over the east coast of Korea, which was characterized by a significant upper-level PV anomaly and a lower-tropospheric PV anomaly related to condensational heating. The study was based on the output from a numerical simulation of this cyclone performed with the WRF-ARW model and on simulations using PPVI results, which were used to examine the role of the low-to mid-tropospheric PV anomalies on the evolution of the explosive cyclone. This approach seems more realistic than any other techniques in the literature that perform this type of sensitivity experiment [52]. The effect of each partitioned perturbation PV on explosive cyclone development is investigated by integrating the WRF model by removing or doubling the intensity of each partitioned perturbation PV in the initial conditions of the model.
The initial cyclogenesis was found to be the main effect of the condensational heating associated with the mid-tropospheric PV anomaly and the secondary effect of the upper-level forcing associated with the upper-level PV anomaly. For the intensity of the cyclone, the simulation results for the removal of the upper-level and moist interior PV anomalies show a weak cyclone, but the other simulations are not much different from the CTL. Once the upper-level PV anomaly is removed, there is no rapid deepening of the cyclone. When removing the moist interior PV anomaly, the initial CSLP of the cyclone is the highest, but the cyclone experienced a phase of rapid development with a deepening of 27 hPa during the first 24-h integration. Although the initial CSLPs of the cyclones simulated by the removal of the lower boundary PV and the remnants of the diabatically generated PV anomalies were slightly different from the CTL cyclone, they deepened similarly to the CTL.

Condensational Heating
To examine the effect of the lower-tropospheric PV anomaly related to condensational heating during the cyclone lifecycle, we performed RMP and DMP simulations; Figure 12 shows the 700 hPa geopotential height, sea level pressure, and 700 hPa PV fields during the lifecycle in the simulations. The removal of the moist interior PV anomaly reproduces a short-wave trough at the 700 hPa level to the west of the Shandong Peninsula and a weak surface low near 30 • N, 120 • E (Figure 12a). This trough developed into a cut-off low accompanied by a 1.5 PVU 700 hPa PV anomaly over the Shandong Peninsula, and a surface low developed under the front of the trough. This cut-off low subsequently continued to deepen and traveled northeastward, and the surface low developed to its maximum intensity with a CSLP of 988 hPa and also moved northeastward (Figure 12b-d). When the moist interior PV anomaly is doubled (DMP), the surface cyclone is more enhanced as compared to the CTL during the lifecycle. The CSLP of the initial DMP cyclone was 980 hPa (Figure 11a), which is 22 hPa lower than that of the CTL cyclone, and the initial position is almost the same as that of the CTL. The deepening rate of the DMP cyclone was weaker than that of the CTL during the 33-h integration, whereas the CTL cyclone deepened more quickly than that of the DMP after the 3-h integration (Figure 11b). The RMP cyclone continued to deepen during the 33-h integration, while the DMP cyclone only developed during the 21-h integration. Between the simulations, the RMP cyclone had a higher deepening rate than the DMP cyclone. An analysis of the influence of LHR on the PV tendency following the method of Heo et al. [5] revealed that the contribution of the latent heating term is almost zero during the 48-h integration, except for a positive contribution of about 1.0 PVU (6 h) −1 below the 900 hPa level (not shown). Until 0000 UTC 4 May 2016, the intensity of the cut-off low with a 2.5 PVU anomaly at a 700 hPa PV was maintained, and the surface cyclone deepened to a CSLP of 964 hPa. Doubling the moist interior PV anomaly strengthened the PV tower through the interaction with the upper-level PV anomaly. Further, the surface cyclone and a cut-off low at 700 hPa level developed unrealistically compared to the CTL simulation, but this system was merged with the system that developed to the north of the Korean Peninsula and propagated northeastward at 0000 UTC 4 May 2016. The simulation results of the removal and doubling of the upper-level PV anomalies demonstrate that the intensity of the upper-level PV anomalies, and their relative configuration with respect to the explosive cyclone was also very critical to the development of the cyclone during the initial and developing stages. The simulation results of the removal and doubling of the moist

Conclusions and Remarks
This study presents the effect of four perturbation PVs on the rapidly deepening cyclone around the Korean Peninsula from 2 to 5 May 2016. This case of rapid cyclogenesis was associated with high winds and waves that caused considerable damage over the east coast of Korea, which was characterized by a significant upper-level PV anomaly and a lower-tropospheric PV anomaly related to condensational heating. The study was based on the output from a numerical simulation of this cyclone performed with the WRF-ARW model and on simulations using PPVI results, which were used to examine the role of the low-to mid-tropospheric PV anomalies on the evolution of the explosive cyclone. This approach seems more realistic than any other techniques in the literature that perform this type of sensitivity experiment [52]. The effect of each partitioned perturbation PV on explosive cyclone development is investigated by integrating the WRF model by removing or doubling the intensity of each partitioned perturbation PV in the initial conditions of the model.
The initial cyclogenesis was found to be the main effect of the condensational heating associated with the mid-tropospheric PV anomaly and the secondary effect of the upper-level forcing associated with the upper-level PV anomaly. For the intensity of the cyclone, the simulation results for the removal of the upper-level and moist interior PV anomalies show a weak cyclone, but the other simulations are not much different from the CTL. Once the upper-level PV anomaly is removed, there is no rapid deepening of the cyclone. When removing the moist interior PV anomaly, the initial CSLP of the cyclone is the highest, but the cyclone experienced a phase of rapid development with a deepening of 27 hPa during the first 24-h integration. Although the initial CSLPs of the cyclones simulated by the removal of the lower boundary PV and the remnants of the diabatically generated PV anomalies were slightly different from the CTL cyclone, they deepened similarly to the CTL.
The simulation results of the removal and doubling of the upper-level PV anomalies demonstrate that the intensity of the upper-level PV anomalies, and their relative configuration with respect to the explosive cyclone was also very critical to the development of the cyclone during the initial and developing stages. The simulation results of the removal and doubling of the moist interior PV anomalies also demonstrate that the diabatically generated PV anomalies associated with condensational heating were relevant to the surface cyclogenesis at the initial stage of the cyclone. These results revealed that the initial explosive cyclogenesis was largely forced by the diabatically generated PV anomalies associated with condensational heating and that the upper-level forcing is of primary importance to the evolution of the cyclone and is of secondary importance to the initial intensity. These results are in good agreement with the findings of a previous climatological analysis [55], which show that the relative frequency of extratropical cyclones dominated by condensational heating reaches 61% during warmer months. As first described by Schemm and Wernli [22], the warm and cold conveyor belts of an extratropical cyclone are inherently linked. In their idealized study, Schemm and Wernli [22] show that the latent heating inside the WCB amplifies both the upper-level negative PV anomaly and lower-level positive PV anomaly and thereby also amplifies the cyclonic circulation at the surface. The positive low-level PV anomaly generated below the WCB accelerates the cold conveyor belt along the warm bent-back front of the surface cyclone [22]. This is a feedback mechanism between the latent heating and the cold conveyor belt that was later confirmed in a case study by Hirata et al. [56]. The explosive cyclogenesis process is significantly complicated by the involvement of vigorous dynamics, the effects of physical processes, and the interactions between them. Therefore, more case studies are required to examine the relationships among different factors, including the dynamics and physical processes associated with this type of explosive cyclogenesis.
Funding: This research was part of the project titled "Improvements of ocean prediction accuracy using numerical modeling and artificial intelligence technology," funded by the Ministry of Oceans and Fisheries, Korea. This work was also supported by KIOST (Grant PE99742). This work was funded by the Korea Meteorological Administration Research and Development Program (Grant KMI2018-02410).