Mergers as the Maintenance Mechanism of Cutoff Lows: A Case Study over Europe in July 2021

Koryu Yamamoto aAtmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan

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Keita Iga aAtmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan

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Akira Yamazaki bJapan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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Abstract

A cutoff low that covered central Europe in the middle of July 2021 brought heavy rainfall and severe flooding, resulting in more than 200 fatalities. This low was formed by a trough on 11 July and merged with another cutoff low around 12–13 July. Analysis of the energy budget and potential vorticity suggests that the main cutoff low was maintained through the merger with another cutoff low; this was the dominant contributor to maintenance of the main cutoff low around 12–13 July. The results of Lagrangian trajectory analyses support this conclusion. Analysis of diabatic PV modification during the merger indicates that radiation acts mainly to enhance the potential vorticity of the parcels when they move from another cutoff low into the main cutoff low, especially in the upper layer. However, that effect is not pronounced in the lower layer. These results demonstrate that cutoff lows can be maintained through a merger with another cutoff low and underline the need to consider diabatic processes when investigating mergers.

Significance Statement

This study examines an upper-tropospheric cyclone called a cutoff low, which caused a high-impact weather event over Europe in the middle of July 2021, and investigates its maintenance mechanism. This cutoff low merged with another, suggesting a contribution to the maintenance. Diabatic processes during the merger are also investigated. The results of this study suggest that not only do cyclone regions merge, but diabatic modification of the vortex structure can be seen when two cutoff lows merge, and the modification process may differ in different vertical layers of the cutoff low.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Koryu Yamamoto, koryuy@aori.u-tokyo.ac.jp

Abstract

A cutoff low that covered central Europe in the middle of July 2021 brought heavy rainfall and severe flooding, resulting in more than 200 fatalities. This low was formed by a trough on 11 July and merged with another cutoff low around 12–13 July. Analysis of the energy budget and potential vorticity suggests that the main cutoff low was maintained through the merger with another cutoff low; this was the dominant contributor to maintenance of the main cutoff low around 12–13 July. The results of Lagrangian trajectory analyses support this conclusion. Analysis of diabatic PV modification during the merger indicates that radiation acts mainly to enhance the potential vorticity of the parcels when they move from another cutoff low into the main cutoff low, especially in the upper layer. However, that effect is not pronounced in the lower layer. These results demonstrate that cutoff lows can be maintained through a merger with another cutoff low and underline the need to consider diabatic processes when investigating mergers.

Significance Statement

This study examines an upper-tropospheric cyclone called a cutoff low, which caused a high-impact weather event over Europe in the middle of July 2021, and investigates its maintenance mechanism. This cutoff low merged with another, suggesting a contribution to the maintenance. Diabatic processes during the merger are also investigated. The results of this study suggest that not only do cyclone regions merge, but diabatic modification of the vortex structure can be seen when two cutoff lows merge, and the modification process may differ in different vertical layers of the cutoff low.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Koryu Yamamoto, koryuy@aori.u-tokyo.ac.jp

1. Introduction

Cyclonic vortices sometimes detach from a deepened trough of the polar stratospheric reservoir, mainly at mid- and high latitudes, and are called cutoff lows (e.g., Palmén 1949; Palmén and Newton 1969; Nieto et al. 2005; Gimeno et al. 2007; Nieto et al. 2008). They are usually accompanied by the intrusion of a cold and high potential vorticity (PV) air mass from the stratosphere that is advected equatorward into the troposphere through Rossby wave breaking (e.g., Bell and Bosart 1993; Ndarana and Waugh 2010), which reduces stability below the air mass. Thus, the cutoff low is often associated with unstable weather conditions, including heavy precipitation (e.g., Garreaud and Fuenzalida 2007; Tsuji and Takayabu 2019), thunderstorms (e.g., Nikaidou 1986; Tsuboki and Ogura 1999; Mohr et al. 2020), and snowfall events (e.g., Vuille and Ammann 1997; Lillo et al. 2021).

In general, cutoff lows increase the risk of high-impact weather events the longer they stay in one area; therefore, the maintenance mechanism of cutoff lows is a significant issue in terms of the mitigation of the effects of high-impact weather events or improvement of forecast accuracy. Although Hoskins et al. (1985) stated that cutoff lows accompanied by sufficient moisture for convective clouds can decay on a time scale of a few days, other studies have reported that the lifetime of most cutoff lows is several days to weeks (Reboita et al. 2010; Ndarana et al. 2020). Therefore, some cutoff lows can have a relatively long lifetime. Previous works have studied the maintenance mechanism of cutoff lows. For example, Gan and Piva (2013, 2016) considered cutoff lows in the southeastern Pacific and analyzed the eddy kinetic energy (EKE) around them using reanalysis data. Those authors showed that the ageostrophic flux convergence (AFC) term that can be interpreted as the influx of wave packets owing to wave dispersion (Orlanski and Katzfey 1991; Chang and Orlanski 1994; Chang 2000; Gan and Piva 2016) was the main factor in their maintenance. Pinheiro et al. (2022) analyzed a larger area and longer period and investigated cutoff lows using composite maps. They demonstrated that the AFC contributed to onset and development, while the baroclinic conversion (BRC) term played a crucial role in maintaining the system. Fu and Sun (2012) analyzed the EKE of a cutoff low in northeastern China and suggested that interactions with other synoptic eddies were the major factor determining the strength of cutoff lows.

Although these studies are Eulerian based, some have used a Lagrangian approach to examine the maintenance mechanism of cutoff lows. Portmann et al. (2018), who analyzed cutoff lows over Europe, explained that one cutoff low merged with a weak cutoff low, acquiring high PV. Their results suggest that cutoff lows are supplied with energy through mergers with other nearby vortices, which helps to maintain the cutoff lows. In addition, Price and Vaughan (1993) showed that a high-PV air mass from the stratosphere intruded into a cutoff low with cyclonic circulation, which contributed to reintensification of the low.

In the early summer of 2021, Europe was affected by a large-scale circulation including atmospheric blocking and Rossby wave breaking, alongside extreme weather with record-breaking precipitation and prolonged heat waves (Tuel et al. 2022). In July, during the middle of the series of events, Europe was widely affected by heavy rainfall and severe floods, resulting in more than 200 fatalities (Kreienkamp et al. 2021). Kreienkamp et al. (2021) also reported that central Europe was covered by a cutoff low (hereafter “C1”) from 12 to 15 July. As a vast amount of water vapor was supplied to the wide area (Benedict et al. 2022) that had been destabilized by C1, central Europe was affected by persistent heavy rainfall. C1 can be clearly recognized as an isolated area with PV that is equal to or exceeds 2 PVU (PV unit; 1 PVU = 10−6 K kg−1 m2 s−1) on a 330-K isentropic surface from 11 to 19 July (not shown). Just after C1 detaches from the westerlies and forms, around 1400 UTC 11 July, it begins to merge with another cutoff low (hereafter “C2”) located on the northeast side of C1 at 0000 UTC 11 July (Figs. 1a,e). Although the merged cutoff low (i.e., C1 + C2) is absorbed into the polarward high PV area by 0000 UTC 13 July (Figs. 1c,g), C1 detaches again, becoming an isolated vortex by 0000 UTC 14 July (Figs. 1d,h). Cross sections in Figs. 1i–l indicate that C1 is clearly delineated from 11 to 14 July, whereas C2 becomes unclear on 13 July and seems to separate into two main fragments. One of these fragments (marked “C2a” in Fig. 1k) appears to be absorbed into C1, and the other (marked “C2b” in Fig. 1k) is reabsorbed into the polar stratospheric reservoir (Portmann et al. 2021). Therefore, a merger with C2 is easily recognized during the lifetime of C1, and it is suggested that the merger contributes to the maintenance of C1.

Fig. 1.
Fig. 1.

Structures of C1 and C2. (top),(middle) Shading shows PV on (a)–(d) 330- and (e)–(h) 320-K isentropic surfaces. (bottom) Cross sections of PV (shading) and potential temperature (K) (contours) along A–B shown in the top and middle panels as a red dashed line. Blue contours show 320 and 330 K. (a),(e),(i) 0000 UTC 11 Jul, (b),(f),(j) 0000 UTC 12 Jul, (c),(g),(k) 0000 UTC 13 Jul, and (d),(h),(l) 0000 UTC 14 Jul. C1 and C2 are shown by black characters. C2a and C2b are described in the main text. We use ERA5 (Hersbach et al. 2020; see section 2a) for all panels.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

Yamazaki and Itoh (2013a,b) discussed the maintenance of atmospheric blocking based on vortex–vortex interactions, in which vortices (synoptic anticyclones in their context) with the same polarity selectively merge and supply low or anticyclonic PV to a blocking anticyclone (anticyclonic vortex). A schematic of the vortex–vortex interaction or the merger process of binary vortices with the same polarity is illustrated in Fig. 1 of Yamazaki and Itoh (2013a). From their approach, if we assume that PV or vorticity of a cyclone is larger (stronger), the PV or vorticity gradient field of the cyclone becomes steeper and extends farther. In terms of their vortex–vortex interaction concept, a cyclone with higher PV can attract another cyclone more strongly and can receive more PV from the other cyclone. However, they did not investigate the merger process for cutoff lows (cyclonic vortices). Besides, as diabatic processes modify PV (e.g., Hoskins et al. 1985) and can affect the intensity of cutoff lows (e.g., Wirth 1995; Forster and Wirth 2000; Cavallo and Hakim 2009; Ferreira et al. 2016; Portmann et al. 2018), the diabatic processes could also affect the merger process between cutoff lows. For example, the amount of high-PV air drawn into one cutoff low or the merger speed could be changed by a change in diabatic PV. In fact, Yamazaki and Itoh (2013a,b) did not consider diabatic processes when discussing the merger process.

In general, when discussing whether a main cutoff low is maintained by the merger with another cutoff low, Eulerian analyses based on the main cutoff low alone might make it difficult to confirm the energy inflow from the other, whereas it might be difficult to quantify the maintenance mechanism from the Lagrangian perspective alone. Therefore, it is effective to adopt both perspectives.

Thus, adopting both the Eulerian and Lagrangian perspectives, in this paper, we attempt to answer the following questions: (i) when we compare the merger with the Rossby wave energy inflows due to its wave dispersion or with the baroclinic conversion process, what are the relative contributions of the mergers in the maintenance of C1? (ii) Does diabatic PV modification play a significant role in the vortex merger process? Also note that even though there are some useful definitions based on geopotential height when handling cutoff lows (e.g., Nieto et al. 2005; Muñoz et al. 2020; Kasuga et al. 2021), the merger can be seen from the PV perspective in the present case, so we handle C1 and C2 in terms of PV.

The remainder of the present paper is organized as follows. In section 2, we describe the data and methods. We first analyze the intensity of C1 in terms of cyclonic circulation (i.e., EKE) and PV, which are both related to conserved quantities and thus are compatible with our budget and following trajectory analyses. Trajectory analyses are conducted to confirm the merger from the Lagrangian perspective. The diabatic processes that can affect the merger process are also discussed. The results are presented in section 3. Section 4 contains a summary and concluding remarks.

2. Data and methods

a. ERA5

We use isobaric and isentropic data from the fifth major global reanalysis produced by European Centre for Medium-Range Weather Forecasts (ECMWF) (ERA5) (Hersbach et al. 2020). The dataset has 37 pressure levels from 1000 to 1 hPa and four potential temperature levels from 315 to 350 K. The dataset analyzed in this study is hourly with 0.25° × 0.25° longitude–latitude grid cells.

b. WRF

We also use a numerical simulation of C1 and C2 with the Weather Research and Forecasting (WRF) Model version 4.4 (Skamarock et al. 2019) for further examination of the merger. The simulation settings are shown in Table 1, where a single domain is used (Fig. 2) and the initial time is set for 0000 UTC 10 July. The horizontal resolution and time step are 20 km and 1 min, respectively, and the output interval is 10 min. We set 45 vertical layers with the top layer at 50 hPa. Figure 3 shows the results of the simulation; the areas that are 2 PVU and higher and the PV values correspond well to those obtained using ERA5 (Fig. 1), which confirms that the simulation reproduces the merger well.

Table 1.

Simulation settings.

Table 1.
Fig. 2.
Fig. 2.

Schematic of the WRF domain. Red contours show 2-PVU isopleths obtained from the WRF simulation on the 325-K isentropic surface at 0000 UTC 11 Jul.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

Fig. 3.
Fig. 3.

As in Fig. 1, but using the results of the WRF simulation for all the panels. A, B, C1, C2, C2a, and C2b are displayed at the same longitude, latitude, and pressure as in Fig. 1.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

c. Quantitative intensity of C1

We first diagnose how the intensity of C1 evolves based on ERA5 (section 2a). There is no standard metric for the intensity of cutoff lows, but one approach is to adopt EKE, defined as the kinetic energy of perturbations of horizontal wind velocity. EKE gives an estimate of the strength of cutoff lows as cyclonic vortices and is used in studies of the energy of cutoff lows (e.g., Fu et al. 2009; Gan and Piva 2013, 2016; Pinheiro et al. 2022). Another approach is to interpret the intensity in terms of the intrusion of stratospheric air, which is compatible with the PV viewpoint (e.g., Portmann et al. 2018, 2021). Since PV depends on both vorticity and atmospheric stability, PV alone does not necessarily quantify the EKE-based intensity of cyclonic vortices. Therefore, it might be appropriate to discuss the intensity in terms of both EKE and PV, based on the intuitive interpretation of cutoff lows as strong cyclonic vortices with an intrusion of stratospheric air. In this study, we quantify the intensity of C1 with the aid of both EKE and PV.

First, C1 is analyzed with the EKE budget equation as follows (e.g., Orlanski and Katzfey 1991; Chang and Orlanski 1994; Chang 2000):
Kt=(VK)(Vaϕ)ωα[V(V33)V¯V(V33)V¯]p(ωK)p(ωϕ)+RES,
where the overbar denotes the climatological mean defined as an average of June, July, and August 2021 and the prime denotes deviation from the mean. The subscripts “3” and “a” indicate three-dimensional and ageostrophic parameters, respectively. The vectors without the subscript “3” are horizontal. We define V as the horizontal velocity, ϕ as the geopotential, ω as the vertical velocity, α as the specific volume, and K′ as EKE, where K′ ≡ (1/2)V′ ⋅ V′. RES is the residual that includes contributions due to friction, analysis increment, and interpolation (Chang 2000). The left-hand side (lhs) of Eq. (1) represents the tendency of EKE. The first term on the right-hand side (rhs) is the horizontal advection of EKE [EKE flux convergence (KFC)], and the second and third terms are the AFC and BRC, respectively. The fourth term represents barotropic conversion owing to Reynolds stresses (Chang 2000). The fifth and sixth terms are the vertical components of the advective or radiative terms.
Next, we define a two-dimensional area S that is a circle with a radius of 1000 km and a center at the center of C1. We apply the neighbor enclosed area tracking algorithm (Inatsu 2009; Inatsu and Amada 2013; Satake et al. 2013) to 2 PVU contours on the 315-, 320-, and 330-K isentropic surfaces to trace the center of C1. When an enclosed area is recognized on each surface, the center is also detected. The center of C1 across the three surfaces is calculated as the mean of the centers on each surface. A three-dimensional volume V, whose base is S and whose top and bottom are the 100- and 900-hPa surfaces, respectively, is also defined. Note that S and V move along with C1. Equation (1) averaged inside V yields the following (e.g., Chang 2000; Gan and Piva 2013, 2016; Pinheiro et al. 2022):1
Kt=(VK)(Vaϕ)ωαV(V33)V¯V(V33)V¯[ωK]|B+[ωK]|T[ωϕ]|B+[ωϕ]|T+RES,
where the square brackets [⋅] denote values integrated inside S on an isobaric surface and the angle brackets 〈⋅〉 denote values integrated inside V. The terms “T” and “B” indicate 100 and 900 hPa (i.e., the top and bottom of V), respectively.

Second, C1 is analyzed from the PV perspective. The PV values on the 315-, 320-, 330-, and 350-K isentropic surfaces from ERA5 are used for the analysis. For each isentropic surface, we calculate the averaged PV within a circle of radius r km from the center of C1, where we set r = 500 for the 315- and 320-K surfaces and r = 1000 for the 330- and 350-K surfaces. We use the same center of C1 as the EKE budget analysis at each time point.

d. Trajectories

We conduct trajectory analyses in order to discuss the merger between C1 and C2 in detail (i.e., Lagrangian perspective). We use the results of the numerical simulation with WRF (section 2b).

First, we conduct backward trajectory analysis to determine the origin of the air mass that lies inside C1 after the merger ends. Considering that the merger ends before 0000 UTC 14 July (Figs. 1d,h,l), parcels are set inside C1 at 0000 UTC 14 July. Parcels are inserted into C1 three dimensionally, using the following procedures:

  1. A two-dimensional area A is defined as the area exceeding 2 PVU in C1 on the 325-K isentropic surface at 0000 UTC 14 July.

  2. A is set on isentropic surfaces from 315 to 365 K in 5-K intervals at 0000 UTC 14 July. Parcels are set on each surface on all grid points that lie within A and have PV of >2 PVU.

White dots in Fig. 4a show all parcels at the initial time. By placing the parcels on multiple isentropic surfaces, it is possible to use parcels from lower to higher layers of the cutoff low at the initial time. We use 17 890 parcels in total.

Fig. 4.
Fig. 4.

Initial positions of parcels inside (a) C1 at 0000 UTC 14 Jul for the backward trajectory analysis and (b) C2 at 0000 UTC 11 Jul for the forward trajectory analysis. White dots indicate parcels. Semitransparent surfaces represent isentropic surfaces (from 310 to 370 K; every 5 K), and colors show PV according to the scale at right. An interactive version of the figure is available in the supplemental material.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

We calculate parcel positions with a fourth-order Runge–Kutta scheme. The integration time step is 10 min, and the integration period is 3 days backward in time (i.e., back to 0000 UTC 11 July). The parcels are advected by horizontal and vertical winds, where each wind component is interpolated linearly onto each parcel’s position. The present analysis does not calculate trajectories on isentropic surfaces, and diabatic processes that affect the parcels are not excluded from the discussion (section 3c).

Next, parcels are set inside C2 at 0000 UTC 11 July, and we calculate their forward trajectories. The purpose of the forward trajectory analysis is to confirm that some parcels move from C2 to C1 through the merger. Figures 1a, 1e, and 1i show that C1 and C2 can be seen separately at 0000 UTC 11 July, before the merger occurs. We follow procedures 1 and 2 above, but here C2 is the area of interest instead of C1, and 26 097 parcels in total are set off at 0000 UTC 11 July. The initial positions of all parcels are shown in Fig. 4b. The same schemes are used for the calculation, except that the integration period is 3 days forward in time (i.e., up to 0000 UTC 14 July).

e. Diabatic processes

Diabatic processes can strengthen or weaken cutoff lows (e.g., Wirth 1995; Forster and Wirth 2000; Cavallo and Hakim 2009; Ferreira et al. 2016; Portmann et al. 2018). Such processes do not appear explicitly in the EKE budget equation [Eqs. (1) and (2)]. On the other hand, diabatic processes can be evaluated in terms of the change of PV values when friction is ignored. Therefore, a PV-based approach is used for discussion of diabatic processes rather than the EKE that we have introduced as one measure of the intensity of cutoff lows.

The material evolution of Ertel’s PV
Q=1ρηθ
is described as
DQDt=1ρ(ηθ˙)+1ρ(θ×F)
(Hoskins et al. 1985), where η is the absolute vorticity vector, θ is the potential temperature, ρ is the density, and F is the frictional force. The heating term θ˙Dθ/Dt in Eq. (4) can be expanded as
θ˙=θ˙C+θ˙R+θ˙B,
where the first term on the rhs represents the sum of heating from microphysical and cumulus parameterizations and the second and third terms on the rhs represent heating owing to parameterizations of radiation and planetary boundary layers, respectively. Substituting Eq. (5) into Eq. (4) yields
DQDt=1ρ(ηθ˙C)+1ρ(ηθ˙R)+1ρ(ηθ˙B)+1ρ(θ×F).
This explains that the material evolution of PV consists of diabatic and frictional terms, where the first to third terms on the rhs represent the diabatic heating components. For simplicity, each PV tendency due to the diabatic process is hereafter denoted by PVTi(1/ρ)(ηθ˙i), where i ∈ {C, R, B}. The PVTC represents the sum of PV tendency from microphysical and cumulus parameterizations, and PVTR and PVTB represent PV tendency due to parameterizations of radiation and planetary boundary layers, respectively. The total PV tendency from all diabatic processes is described as PVTalli{C,R,B}PVTi.
Some previous studies have reported that diabatic processes due to latent heat release and radiation are the main processes that affect cutoff lows. Where convection is strong and extends through the troposphere, θ˙C reaches a maximum around the middle troposphere (e.g., Cavallo and Hakim 2009). As the corresponding diabatic term in Eq. (6) can be well approximated around the tropopause as
PVTi1ρ(ηθ˙i)1ρ(ζ+f)θ˙iz,
where i = C, ζ is the relative vorticity, and f is the planetary vorticity (Cavallo and Hakim 2009). PV tends to decrease in the upper troposphere owing to latent heat release (Wirth 1995; Cavallo and Hakim 2009; Portmann et al. 2018). In general, because the vertical gradient of water vapor is at maximum near the tropopause, the cooling by longwave radiation is at maximum as well, which means θ˙R reaches its most negative value. Therefore, PV tends to increase in the lowermost stratosphere following Eq. (7) (Forster and Wirth 2000; Ferreira et al. 2016), as Eq. (7) also holds for i = R. If there are convective clouds that reach near the tropopause, because the cloud tops decrease θ˙R there (Price and Vaughan 1993), the PV increase will be more significant.

The analysis of diabatic processes in the present study aims to consider the effect of diabatic processes on the merger process, but first the diabatic field at or around C1 is investigated. Portmann et al. (2018), who studied the life cycles of two cutoff events over Europe in 2015 from the perspective of diabatic processes, calculated only one type of PV tendency [see their Eqs. (2) and (3)], and no quantitative comparison of each process was conducted. In contrast, here we use the output from the WRF to calculate PVTi for each parameterization, allowing us to diagnose the diabatic field at or around C1 in detail. This is similar to the approaches of Cavallo and Hakim (2009) and Spreitzer et al. (2019). We then discuss the effect of diabatic processes on the merger process, which is one of our main objectives. Yamazaki and Itoh (2013a,b) studied the maintenance mechanism of atmospheric blocking in terms of vortex–vortex interactions, and they assumed that adiabatic processes are dominant. However, here we are interested in the connections between the merger of cutoff lows and diabatic processes, so the present study diagnoses PVTi interpolated onto each parcel’s location that was obtained from the forward trajectory analysis, where the parcels are initialized in C2 at 0000 UTC 11 July. In other words, diagnosed PVTi can be interpreted as the diabatic processes that parcels experience while they move around C1.

3. Results

a. Quantitative intensity of C1

1) EKE

Figure 5a shows the temporal evolution of EKE and all terms on the rhs of Eq. (2) from 9 to 16 July, and Fig. 5b shows the temporal evolution of the time derivative of EKE. Figure 5a shows that EKE (black line) reaches a maximum around 0000 UTC 10 July and subsequently decreases until around 1200 UTC 10 July. Then, EKE remains almost constant. The period of this EKE maintenance is indicated by the shaded blue (Figs. 5a,b), and it is suggested that the intensity of C1 is maintained during this period.

Fig. 5.
Fig. 5.

(a) Results of EKE budget analysis for C1. Temporal evolution of EKE (black line) averaged in V, and rhs terms (colored lines) of Eq. (2) (rhs1–9) averaged in V, where, for example, “rhs1” represents the first term on the rhs of Eq. (2). EKE is shown on the left vertical axis and rhs1–9 on the right axis. Line rhs1 is thicker than the others. All lines represent as 7-h running means. (b) The black solid line shows the temporal evolution of the time derivative of EKE averaged in V as a 25-h running mean. Gray dashed lines represent ±6 × 10−5 m2 s−3. Blue shading shows the period from 2300 UTC 10 Jul to 0200 UTC 13 Jul when the black line in (b) is located between the two gray dashed lines around 11 and 12 Jul.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

The sharp decrease in EKE during 0000–1200 UTC 10 July is not discussed in detail in the present study because it is considered an onset phase of C1. However, the deformation of C1 during its onset period (not shown) and the decrease in BRC [green line in Fig. 5a: the third term on the rhs of Eq. (2)], AFC (orange line: the second term), and RES (gold line: the last term) might be the main factors in the EKE decrease. These terms have similar magnitudes.

Figure 5a shows that AFC is dominant at the beginning of the period of blue shading (i.e., when EKE is maintained). AFC has good correspondence with the influx of wave packets due to wave dispersion (Orlanski and Katzfey 1991; Chang and Orlanski 1994; Chang 2000; Gan and Piva 2016). It is clear in Fig. S1 in the online supplemental material that AFC on the northwest side of C1 is mainly positive on 11 July, whereas it is mainly negative on the southwest side, and a dipole structure is clearly seen. Vectors Vaϕ in the northwest side of C1 point from the upstream ridge, whereas those on the southwest point to the southeast (Fig. S1). These features are consistent with the downstream development of baroclinic eddies (Orlanski and Sheldon 1995). As AFC averaged within V is positive in the first half of the period denoted by blue shading in Fig. 5, the energy that C1 receives from the upstream ridge is larger than the energy that dissipates or propagates downstream. This suggests that propagation of energy from the upstream ridge contributes to the maintenance of C1. When focusing on the dipole structure, the northern positive AFC amplifies at 0300 and 0600 UTC compared with 0000 UTC 11 July (Fig. S2), which corresponds with the increase of AFC (Fig. 5a). In Fig. 5a, the residual (RES, gold line) is slightly smaller in magnitude and has an opposite sign to AFC during that period, but its local maxima or minima are far from C1 and the distribution is noisy (Figs. S3d–f). Therefore, this term makes a lesser contribution to C1 than AFC.

KFC [blue line in Fig. 5a: the first term on the rhs of Eq. (2)] then replaces AFC as the dominant term around 0000 UTC 12 July–0000 UTC 13 July. Figures 6a–c depict the horizontal distribution of KFC averaged vertically over 100–900 hPa and high PV (i.e., >2 PVU) on the 330-K surface. The directions of the vectors and cyan contours in Fig. 6a demonstrate that the VK′ flux from upstream and that from the northern side of C1 (around 60°N, 15°W) merge over the northwestern side of C1; the red shaded area on the southwest side implies a positive contribution to EKE development. The cross sections show that the area of maximum positive KFC extends across the area of maximum EKE (jet core) and within the high-PV region along with C1 (around 15°W) and extends vertically from 200 to 400 hPa, suggesting that the intensity of C1 is enhanced by positive KFC over a wide area of C1 (Fig. 6d). KFC explains the convergence associated with the horizontal advection of EKE. Considering that 12–13 July is the period when the merger between C1 and C2 is clearly seen (Figs. 1b,c,f,g,j,k), it is possible that the EKE transport from the northern side of C1 is directly from C2, which is located around 60°N, 10°W at 0000 UTC 12 July due to the merger (see section 3b). At 0000 UTC 13 July, the positive KFC in the southwestern side of C1 is still clearly seen (Figs. 6b,e), but the EKE transport from the northern side of C1 is obscured (Fig. 6b) and the positive KFC region in the southwestern side of C1 becomes unclear toward 0000 UTC 14 July (Figs. 6c,f). These results are consistent with the decrease of KFC (blue line in Fig. 5a) and might also be related to the fact that the merger ends toward 0000 UTC 14 July (Figs. 1c,d,g,h,k,l).

Fig. 6.
Fig. 6.

(top) Horizontal distribution of KFC averaged over 100–900 hPa. Positive values represent EKE sources. Cyan contours give EKE averaged over 100–900 hPa (100, 300, 500, 700, 900, and 1100 m2 s−2), color shading gives KFC averaged over 100–900 hPa, and hatching denotes PV of >2 PVU on 330 K. Vectors and colored arrows denote the direction of vector VK′ and |VK′|, respectively (vectors with size 1.5 × 103 m3 s−3 and larger are drawn), where the depicted VK′ is averaged over 100–900 hPa. Purple circle denotes domain S with a radius of 1000 km. (bottom) Cross sections along the black dashed line in the top panel of PV (shading), potential temperature (K; green and black contours; 330-K isopleths are green and the others are black), EKE (cyan contours; 100, 300, 500, 700, 900, and 1100 m2 s−2), and KFC (red and blue contours; ±0.100, ±0.075, ±0.050, and ±0.025 m2 s−3; red and blue contours show positive and negative, respectively). Purple lines show 1000 km from the center of C1. Panels show 0000 UTC (a),(d) 12 Jul; (b),(e) 13 Jul; and (c),(f) 14 Jul.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

The positive contribution of AFC to the maintenance is consistent with Gan and Piva (2013, 2016), who studied the energetics of cutoff lows with composite maps. In this study, KFC is also a positive factor in the maintenance after AFC becomes dominant, a fact that has not been highlighted in previous studies. One possible reason for the prominence of KFC in this case might be that the impact of C2 on C1 is noticeable. In addition, Pinheiro et al. (2022) reported that the contribution of BRC was also important; however, our results do not confirm this point: the green line that represents the third term on the rhs of Eq. (2) in Fig. 5a is relatively small. This may be due to the absence of noticeable disturbances near the surface around C1 in this case (not shown). Rather, BRC can contribute to the formation of C1 around 9 July before the maintenance period (Fig. 5a).

2) PV

Figure 7 shows the averaged PV inside circles of radii r = 500 (km) and r = 1000 (km). On the 315- and 320-K surfaces, PV gradually increases from 9 to 12 July and then remains almost constant around 12–13 July, before decreasing. The maintenance of PV is consistent with the temporal evolution of EKE.

Fig. 7.
Fig. 7.

Temporal evolution of PV averaged within a circle of radius r km from the center of C1, where we set r = 500 for the 315- and 320-K surfaces and r = 1000 for the 330- and 350-K surfaces. All lines represent 7-h running means. Blue shading is the same as in Fig. 5.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

PV on the 330-K surface decreases from 1200 UTC 9 July to 1200 UTC 10 July, then remains almost constant until around 0000 UTC 13 July, and then decreases. The behavior of PV on the 350-K surface is almost the same as on 330 K until around 0000 UTC 13 July, but thereafter it remains constant. On both surfaces, PV remains almost constant during the period indicated by blue shading, which is consistent with the EKE change. The reason why the PV is maintained after this time on 350 K may be that stratospheric high PV remains on that surface even after C1 decays.

b. Trajectories

The EKE budget analysis (section 3a) indicates the direct transport of energy from C2 to C1 through the merger process, which is visualized by KFC (Figs. 5a and 6a). Trajectory analyses are conducted to confirm the transport from a Lagrangian perspective.

Figures 8a–e show the results of the backward trajectory analysis. Some parcels separate to the north and west over the 3-day period in Figs. 8b–d. This parcel separation to outside C1 coincides with the period when KFC is dominant (Fig. 8f). Figure 8e shows that while most parcels stay in C1 (around 55°N, 20°W), other parcels come from the north side of C2 (around 60°N, 0°E). Of the 17 890 parcels used for the calculation, 3588 are within the purple trapezoid and have PV of >2 PVU at 0000 UTC 11 July. Considering also the results of the EKE budget analysis (section 3a), Figs. 8b–e suggest that C2 is one of the energy sources from both the Eulerian and Lagrangian perspectives. There are also some parcels that originate from the upstream ridge, which is consistent with the horizontal transport of EKE from the upstream ridge visualized by the vectors in Figs. 6a–c.

Fig. 8.
Fig. 8.

(a)–(e) Backward trajectories initialized inside C1 at 0000 UTC 14 Jul. The dots represent parcels with PV shown by color. Red and blue contours show 2-PVU isopleths on the 345- and 325-K isentropic surface, respectively. A purple trapezoid with vertices of (69°N, 15°W), (69°N, 22°E), (40°N, 22°E), (40°N, 15°E), and (60°N, 15°W) is shown in (e). Panels (a)–(e) are snapshots at 0000 UTC 14 Jul, 0600 UTC 13 Jul, 1800 UTC 12 Jul, 0000 UTC 12 Jul, and 0000 UTC 11 Jul, respectively. (f) As in Fig. 5a, but only EKE and KFC are shown and purple letters correspond to the time of the snapshot in each panel.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

The results of the forward trajectories are shown in Figs. 9a–e. The parcels leaving C2 begin to penetrate C1 around 0000 UTC 12 July (Fig. 9b). Figures 9b–e demonstrate that they enter C1 from its northwest side and pass through the south and reach the northeast side of C1 along its edge. Of the 26 097 parcels used for the calculation, 3030 are within the purple circle (Fig. 9e) and have PV of >2 PVU at 0000 UTC 14 July. The inflow with cyclonic circulation along the edge is consistent with the case study of Price and Vaughan (1993). The inflow continues until 14 July, and the timing of the inflow is consistent with the period when KFC is large (Fig. 9f).

Fig. 9.
Fig. 9.

Forward trajectories initialized inside C2 at 0000 UTC 11 Jul. As in Fig. 8, but the purple circle in (e) indicates a distance of 1000 km from the center of C1, and (a)–(e) show snapshots at 0000 UTC 11 Jul, 0000 UTC 12 Jul, 1800 UTC 12 Jul, 0600 UTC 13 Jul, and 0000 UTC 14 Jul, respectively. The dates and times in (a)–(e) correspond to those in Figs. 8e, 8d, 8c, 8b, and 8a, respectively.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

c. Diabatic processes

1) Diabatic field at or around C1

Figure 10 shows the diabatic field at or around C1 at 0000 UTC 12 July, 1200 UTC 12 July, and 0000 UTC 13 July. The diabatic field on the 350-K isentropic surface has two main features (Figs. 10a–c): positive PVTall prevails at all times and the positive PVTall regions are especially prominent around the fringe of C1 but not in the core of C1. On the 330-K isentropic surface (Figs. 10d–f), the diabatic field shows positive PVTall near the core of C1, with larger values than at the periphery. The PVTall at 1200 UTC 12 July (Fig. 10e) is smaller than that 12 h earlier (Fig. 10d) and after (Fig. 10f), and negative PVTall is seen around the edge of C1.

Fig. 10.
Fig. 10.

Diabatic field at or around C1. (a)–(f) Shading shows PVTall, and lime green and yellow contours show 2- and 8-PVU isopleths, respectively, on (a)–(c) 350- and (d)–(f) 330-K isentropic surfaces. (g)–(i) Cross sections along the black dashed lines in (a)–(f) of PV (shading), potential temperature (K; black contours; 330- and 350-K isopleths are the thickest), 2 PVU (lime green contours), and 8 PVU (yellow contours). (j)–(l),(m)–(o) As in (g)–(i), but shading shows PVTC and PVTR, respectively. The left, middle, and right panels are at 0000 UTC 12 Jul, 1200 UTC 12 Jul, and 0000 UTC 13 Jul, respectively.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

We now discuss cross sections along the black dashed line in Figs. 10a–f (Figs. 10g–o). In each panel, there is a latitudinal zone around 45°–50°N where 2- and 8-PVU isopleths descend. Overall, PVTall above the 2-PVU isopleths (Figs. 10g–i) is contributed mainly by PVTR (Figs. 10m–o). In other words, diabatic processes inside C1 are almost exclusively due to the heating or cooling resulting from the parameterization of radiation. On the other hand, Fig. 10l suggests that strong convective clouds overshoot into the stratosphere around 47°–51°N (Price and Vaughan 1993; Garreaud and Fuenzalida 2007; Grams et al. 2014). In fact, negative PVTC spreads across the 2-PVU isopleth, with a few small wiggles of the isopleth there. This suggests that C1 is locally eroded by latent heat release (e.g., Hoskins et al. 1985; Price and Vaughan 1993; Wirth 1995; Bourqui 2006; Cavallo and Hakim 2009); Portmann et al. (2018) referred to this as direct diabatic effects. These convective clouds remain in the north side of C1 after 0000 UTC 13 July (not shown). The PVTB is omitted from Fig. 10 and the following figures because it is almost zero in the upper troposphere and above, but it is included in the calculation for PVTall by its definition (section 2e).

One common feature of the distribution of PVTR at 0000 UTC 12 and 13 July is that PVTR in the layer just above the 2-PVU isopleth tends to be larger in the depression (around 48°N, 315–330 K) than in the vicinity (around 43°N, 350 K). This might be because the vertical gradient of water vapor at the bottom of C1 is stronger than in the surrounding area due to the descent of the 2-PVU surface toward the tropopause near the center of C1, and cooling by longwave radiation is enhanced there (Cavallo and Hakim 2013). Figure 10o shows that the local area with larger PVTR appears around 47°–51°N at 0000 UTC 13 July, combined with strong radiative cooling associated with the presence of the convective clouds above (Cau et al. 2005).

In contrast to the situation at 0000 UTC 12 and 13 July, at 1200 UTC 12 July, there is an area with negative PVTR near the 2-PVU isopleth (Fig. 10n), which may be due to heating mainly in the lower tropopause by shortwave radiation during the daytime and negative PVTR induced in the upper troposphere (not shown). Inside C1, the negative contribution to PVTR due to shortwave radiation offsets the positive counterpart from longwave radiation (Spreitzer et al. 2019).

2) Diabatic processes on parcels moving from C2 to C1

To investigate how diabatic processes relate to the merger between C1 and C2, we focus on two parcel groups out of the 26 097 parcels used in the forward trajectory analysis (section 3b) to discuss PVTi interpolated onto each parcel’s location. The first group, PG350, consists of 375 parcels that are within 350 ± 2.5 K and 1000 km from the center of C1 and that exceed 2 PVU at 0000 UTC 14 July. The second group, PG330, consists of the corresponding 423 parcels within 330 ± 2.5 K. Considering the cross section at 0000 UTC 14 July (Fig. 3l), PG350 can be interpreted as the parcels that move in the upper layer of C1 and PG330 as parcels moving in the middle and lower layer. Figure 11 shows PG350 and PG330 superimposed on PVTall on the 350- and 330-K surface, respectively. The parcels move with the cyclonic circulation along the edge of C1 when they penetrate C1 from C2, as seen in the forward trajectory analysis (Figs. 9a–e), and diabatic processes affect the parcels around the edge of C1.

Fig. 11.
Fig. 11.

PG350 and PG330 superimposed on the diabatic field at or around C1. Shading shows PVTR, and lime green and yellow contours show 2- and 8-PVU isopleths, respectively, on (left) 350- and (right) 330-K isentropic surfaces. Black dots show (left) PG350 (N = 375) and (right) PG330 (N = 423). The purple circle has a radius of 1000 km. Panels show PG350 and PG330 at 12-h intervals: (a),(b) 0000 UTC 12 Jul; (c),(d) 1200 UTC 12 Jul; (e),(f) 0000 UTC 13 Jul; (g),(h) 1200 UTC 13 Jul; and (i),(j) 0000 UTC 14 Jul.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

We diagnose the diabatic processes along each parcel group, and Fig. 12 shows the temporal evolution of the diabatic processes that affect each parcel group. We first consider PG350. Since PG350 passes through the positive PVTall region in the fringe of C1 (Figs. 10a–c and left panels of Fig. 11), positive PVTR is the main component PVTall of PG350 (Figs. 12c–e), and accumulated PVTall tends to increase monotonically (Fig. 12f). This suggests that PV of PG350 continues to increase owing to radiation while the parcels move into C1.

Fig. 12.
Fig. 12.

Temporal evolution of (a) PV of PG350 and PG330, (c)–(h) the diabatic processes that affect PG350 and PG330, and (b) the residual term. The PVTall, PVTC, and PVTR are shown in (c), (d), and (e), respectively. Accumulated PVTall, PVTC, and PVTR from 0000 UTC 11 Jul are shown in (f), (g), and (h), respectively. The residual term in (b) is calculated using (a) PV and (f) the accumulated PVTall. Orange dashed lines, shaded areas, and symbols are from PG350; orange dashed lines show the median, orange shading shows the 12.5th–87.5th percentile range, and orange symbols indicate the time when the proportion of parcels from PG350 that penetrate the purple circle in Fig. 11 first exceeds 25% (Y), 50% (+), and 75% (×). Blue solid lines, shaded areas, and symbols are the same as the orange dashed lines, shaded areas, and symbols, respectively, but for PG330. Black lines in (b)–(h) show 0.0 PVU day−1 or 0.0 PVU.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0024.1

Next, we discuss the diabatic processes along PG330. The PVTall on the 330-K surface differs significantly between 0000 and 1200 UTC due to the presence of daytime shortwave radiation (Figs. 10d–f). The inflow route of PG330 is shown in the right panels of Fig. 11, and the diabatic processes that affect parcels from PG330 are shown in Figs. 12c–e. A diurnal variation of PVTR centered at 0.0 PVU day−1 is shown by the blue line and shading in Fig. 12e, where the lower values may be attributed to the presence of shortwave radiation during the daytime. Accumulated PVTR increases before the symbol “Y,” but thereafter the median is almost constant at around 0.15 PVU with slight fluctuations (Fig. 12h). The distribution is positive at 0000 UTC 14 July. On the other hand, Fig. 12d displays two periods when the shaded area of PVTC becomes negative (i.e., before the “Y” and after the “×”). It is suggested that some parcels of PG330 pass through regions of negative PVTC associated with latent heat release by strong convective clouds. The negative distribution before the “Y” is due to clouds near C2, and the other is due to clouds near C1. Figure 12g shows accumulated PVTC. The median is almost zero throughout the whole period, but the 12.5th percentile decreases. Accumulated PVTall is shown in Fig. 12f. The median is positive before the “Y,” but after that it decreases and becomes almost zero or slightly positive combined with PVTR and PVTC.

Figure 12a shows that the PV supplied to C1 is larger than the PV averaged within a circle of radius 1000 km from the center of C1 (Fig. 7). This suggests that the air mass moving from C2 to C1 is capable of contributing to the maintenance of C1. Figure 12b shows the difference in time evolution of PV and accumulated PVTall for both PG350 and PG330 (e.g., see the period after the “+”). This may be due to the effect of a large number of parcels passing through regions with a large PV gradient, where errors due to linear interpolation may manifest.

4. Summary and concluding remarks

In this study, we have investigated the cutoff low C1 that caused heavy rainfall and severe floods over Europe in July 2021 and discussed its maintenance mechanism from the standpoint of the merger with another cutoff low C2. We analyzed the intensity of C1 with budget analyses and the diabatic processes to address the two questions introduced in section 1: (i) the relative contribution of the merger in the maintenance of C1 and (ii) the role of diabatic PV modification during the merger. The main results from the analyses are as follows:

  1. The analysis of EKE of C1 shows that EKE is maintained around 0000 UTC 11 July–0000 UTC 13 July (Fig. 5). This maintenance of EKE is consistent with the maintenance of PV over the same period (Fig. 7).

  2. KFC is a dominant term during this period of maintenance (Fig. 5a). Considering that the period of KFC dominance around 0000 UTC 12 July–0000 UTC 13 July coincides with the time when the merger between C1 and C2 is apparent (Fig. 1 or Fig. 3) and KFC shows the convergence of the horizontal advection of EKE, this KFC dominance suggests that the merger with C2 maintains the intensity of C1. The good correspondence between KFC and the trajectories (Figs. 8f and 9f) supports this suggestion. Since AFC (the downstream amplification) dominance is not seen around 0000 UTC 12 July–0000 UTC 13 July and no other terms including BRC (the baroclinic conversion) make more contribution to the increase of the intensity of C1 than KFC at this time, it is suggested that the intensity of C1 during this period is maintained mainly by the merger with C2 [in answer to question (i) above].

  3. From a diabatic analysis, parcels moving through the upper layer (∼350 K in this case) have their PV increased (Fig. 12f) mainly by longwave radiation, whereas parcels in the lower layer (∼330 K in this case) move into C1 quasi adiabatically (Fig. 12f) because the negative PV tendency due to shortwave radiation and latent heat release offsets the positive tendency due to longwave radiation. In the merger process between cutoff lows, not only do regions of high PV merge with each other, but PV can be modified diabatically within the vortex, and the modification mechanism may differ between the upper and lower layers [in answer to question (ii) above].

We have stated in section 1 that increased cyclonic PV could promote attraction between cyclonic vortices as suggested by Yamazaki and Itoh (2013a,b). Regarding the above point (3), considering that cutoff lows are associated with high PV, positive diabatic PV modification in the upper layer of C1 has the potential to strengthen the vorticity field induced by C1 and then enhance the merger effects in the maintenance of cutoff lows. However, whether the amount of high-PV air drawn into C1 is increased and the merger process speeds up due to diabatic cyclonic PV production is not fully considered in the present paper. This will be addressed in our future work. The results also suggest that the detailed mechanisms by which diabatic processes contribute to the vortex–vortex interactions differ for the upper-level anticyclones and cyclones (blocking and cutoff lows); we believe this is worth investigating in the near future.

In the present study, since the presence of convection may be temporally and spatially limited, the contribution by negative PVTC is less remarkable. If strong convection was more extensive and sustained for longer, the diabatic field and the PV tendency along the parcels might be different from the present case. The extent to which convection develops may depend on the amount of water vapor in the lower layer (Qi et al. 1999; Benedict et al. 2022) and the influence of terrain (Garreaud and Fuenzalida 2007) in addition to the influence of the cutoff lows themselves.

Additional future work is described below. First, we will conduct numerical experiments under conditions such that C2 is removed or the strength or size of C2 is changed. These experiments are necessary to assess the degree to which merger is sensitive to the vortex strengths and will provide more detailed information on the merger or vortex–vortex interaction between cutoff lows. Second, we will investigate how often mergers between cutoff lows are present on a global and long-term basis. The present case does not rule out the possibility that the merger with C2 and maintenance of C1 are seen because C2 is coincidentally located near C1. Features of vortex mergers will be identified in future work by, for instance, investigating whether they are accidental or occur frequently, or whether they contribute to rapid intensification of cutoff lows. We also note that Hakim et al. (2002) showed in dry three-dimensional idealized experiments that divergent flows induced between cyclonic vortices have the effect of repelling the vortices. The conditions in which cutoff lows merge need to be investigated with more cases.

1

The sign of the fourth term on the rhs of Eq. (2) in Chang (2000) is inverted in the domain-integrated Eq. (3). Similarly, a term with the wrong sign is shown in the domain-integrated EKE budget equation in subsequent papers, namely, Eq. (2) in Gan and Piva (2013), Eq. (1) in Gan and Piva (2016), and Eq. (1) in Pinheiro et al. (2022).

Acknowledgments.

This work was supported by JST SPRING, Grant JPMJSP2108. We thank members of the Dynamic Marine Meteorology Group, Atmosphere and Ocean Research Institute, The University of Tokyo, for their support and valuable comments. We would also like to thank Drs. S. Kasuga, E. Tochimoto, S. Okajima, J. Ito, H. Hirata, T. Ito, Y. Tachibana, and F. Ogawa for stimulating discussions and helpful comments. We would also like to thank Stallard Scientific Editing (https://www.stallardediting.com) for English language review of the manuscript. We are grateful for constructive comments by Dr. T. Galarneau and three anonymous reviewers.

Data availability statement.

The ERA5 data (Climate Data Store: https://cds.climate.copernicus.eu/cdsapp) are provided by ECMWF. The Weather Research and Forecasting (WRF) Model is available at https://www.mmm.ucar.edu/models/wrf.

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  • Nakanishi, M., and H. Niino, 2006: An improved Mellor–Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog. Bound.-Layer Meteor., 119, 397407, https://doi.org/10.1007/s10546-005-9030-8.

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  • Ndarana, T., and D. W. Waugh, 2010: The link between cut-off lows and Rossby wave breaking in the Southern Hemisphere. Quart. J. Roy. Meteor. Soc., 136, 869885, https://doi.org/10.1002/qj.627.

    • Search Google Scholar
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  • Ndarana, T., T. S. Rammopo, H. Chikoore, M. A. Barnes, and M.-J. Bopape, 2020: A quasi-geostrophic diagnosis of the zonal flow associated with cut-off lows over South Africa and surrounding oceans. Climate Dyn., 55, 26312644, https://doi.org/10.1007/s00382-020-05401-4.

    • Search Google Scholar
    • Export Citation
  • Nieto, R., and Coauthors, 2005: Climatological features of cutoff low systems in the Northern Hemisphere. J. Climate, 18, 30853103, https://doi.org/10.1175/JCLI3386.1.

    • Search Google Scholar
    • Export Citation
  • Nieto, R., M. Sprenger, H. Wernli, R. M. Trigo, and L. Gimeno, 2008: Identification and climatology of cut-off lows near the tropopause. Ann. N. Y. Acad. Sci., 1146, 256290, https://doi.org/10.1196/annals.1446.016.

    • Search Google Scholar
    • Export Citation
  • Nikaidou, Y., 1986: Q-map (the potential vorticity maps analyzed on the isentropic surface) (in Japanese). Tenki, 33, 289331.

  • Orlanski, I., and J. Katzfey, 1991: The life cycle of a cyclone wave in the Southern Hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48, 19721998, https://doi.org/10.1175/1520-0469(1991)048%3C1972:TLCOAC%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., and J. P. Sheldon, 1995: Stages in the energetics of baroclinic systems. Tellus, 47A, 605628, https://doi.org/10.3402/tellusa.v47i5.11553.

    • Search Google Scholar
    • Export Citation
  • Palmén, E., 1949: Origin and structure of high-level cyclones south of the: Maximum westerlies. Tellus, 1, 2231, https://doi.org/10.1111/j.2153-3490.1949.tb01925.x.

    • Search Google Scholar
    • Export Citation
  • Palmén, E., and C. W. Newton, 1969: Atmospheric Circulation Systems: Their Structure and Physical Interpretation. Academic Press, 603 pp.

  • Pinheiro, H. R., K. I. Hodges, M. A. Gan, S. H. S. Ferreira, and K. M. Andrade, 2022: Contributions of downstream baroclinic development to strong Southern Hemisphere cut-off lows. Quart. J. Roy. Meteor. Soc., 148, 214232, https://doi.org/10.1002/qj.4201.

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    • Export Citation
  • Portmann, R., B. Crezee, J. Quinting, and H. Wernli, 2018: The complex life cycles of two long-lived potential vorticity cut-offs over Europe. Quart. J. Roy. Meteor. Soc., 144, 701719, https://doi.org/10.1002/qj.3239.

    • Search Google Scholar
    • Export Citation
  • Portmann, R., M. Sprenger, and H. Wernli, 2021: The three-dimensional life cycles of potential vorticity cutoffs: A global and selected regional climatologies in ERA-Interim (1979–2018). Wea. Climate Dyn., 2, 507534, https://doi.org/10.5194/wcd-2-507-2021.

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    • Export Citation
  • Price, J. D., and G. Vaughan, 1993: The potential for stratosphere-troposphere exchange in cut-off-low systems. Quart. J. Roy. Meteor. Soc., 119, 343365, https://doi.org/10.1002/qj.49711951007.

    • Search Google Scholar
    • Export Citation
  • Qi, L., L. M. Leslie, and S. X. Zhao, 1999: Cut-off low pressure systems over southern Australia: Climatology and case study. Int. J. Climatol., 19, 16331649, https://doi.org/10.1002/(SICI)1097-0088(199912)19:15<1633::AID-JOC445>3.0.CO;2-0.

    • Search Google Scholar
    • Export Citation
  • Reboita, M. S., R. Nieto, L. Gimeno, R. P. da Rocha, T. Ambrizzi, R. Garreaud, and L. F. Krüger, 2010: Climatological features of cutoff low systems in the Southern Hemisphere. J. Geophys. Res., 115, D17104, https://doi.org/10.1029/2009JD013251.

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    • Export Citation
  • Satake, Y., M. Inatsu, M. Mori, and A. Hasegawa, 2013: Tropical cyclone tracking using a neighbor enclosed area tracking algorithm. Mon. Wea. Rev., 141, 35393555, https://doi.org/10.1175/MWR-D-12-00092.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2019: A description of the Advanced Research WRF Model version 4. NCAR Tech. Note NCAR/TN-556+STR, 145 pp.

  • Spreitzer, E., R. Attinger, M. Boettcher, R. Forbes, H. Wernli, and H. Joos, 2019: Modification of potential vorticity near the tropopause by nonconservative processes in the ECMWF model. J. Atmos. Sci., 76, 17091726, https://doi.org/10.1175/JAS-D-18-0295.1.

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  • Tsuboki, K., and Y. Ogura, 1999: A potential vorticity analysis of thunderstorm-related cold lows (in Japanese). Tenki, 46, 453459.

  • Tsuji, H., and Y. N. Takayabu, 2019: Precipitation enhancement via the interplay between atmospheric rivers and cutoff lows. Mon. Wea. Rev., 147, 24512466, https://doi.org/10.1175/MWR-D-18-0358.1.

    • Search Google Scholar
    • Export Citation
  • Tuel, A., D. Steinfeld, S. M. Ali, M. Sprenger, and O. Martius, 2022: Large-scale drivers of persistent extreme weather during early summer 2021 in Europe. Geophys. Res. Lett., 49, e2022GL099624, https://doi.org/10.1029/2022GL099624.

    • Search Google Scholar
    • Export Citation
  • Vuille, M., and C. Ammann, 1997: Regional snowfall patterns in the high arid Andes. Climatic Change, 36, 413423, https://doi.org/10.1023/A:1005330802974.

    • Search Google Scholar
    • Export Citation
  • Wirth, V., 1995: Diabatic heating in an axisymmetric cut-off cyclone and related stratosphere-troposphere exchange. Quart. J. Roy. Meteor. Soc., 121, 127147, https://doi.org/10.1002/qj.49712152107.

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  • Yamazaki, A., and H. Itoh, 2013a: Vortex–vortex interactions for the maintenance of blocking. Part I: The selective absorption mechanism and a case study. J. Atmos. Sci., 70, 725742, https://doi.org/10.1175/JAS-D-11-0295.1.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., and H. Itoh, 2013b: Vortex–vortex interactions for the maintenance of blocking. Part II: Numerical experiments. J. Atmos. Sci., 70, 743766, https://doi.org/10.1175/JAS-D-12-0132.1.

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Supplementary Materials

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  • Nakanishi, M., and H. Niino, 2006: An improved Mellor–Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog. Bound.-Layer Meteor., 119, 397407, https://doi.org/10.1007/s10546-005-9030-8.

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  • Ndarana, T., and D. W. Waugh, 2010: The link between cut-off lows and Rossby wave breaking in the Southern Hemisphere. Quart. J. Roy. Meteor. Soc., 136, 869885, https://doi.org/10.1002/qj.627.

    • Search Google Scholar
    • Export Citation
  • Ndarana, T., T. S. Rammopo, H. Chikoore, M. A. Barnes, and M.-J. Bopape, 2020: A quasi-geostrophic diagnosis of the zonal flow associated with cut-off lows over South Africa and surrounding oceans. Climate Dyn., 55, 26312644, https://doi.org/10.1007/s00382-020-05401-4.

    • Search Google Scholar
    • Export Citation
  • Nieto, R., and Coauthors, 2005: Climatological features of cutoff low systems in the Northern Hemisphere. J. Climate, 18, 30853103, https://doi.org/10.1175/JCLI3386.1.

    • Search Google Scholar
    • Export Citation
  • Nieto, R., M. Sprenger, H. Wernli, R. M. Trigo, and L. Gimeno, 2008: Identification and climatology of cut-off lows near the tropopause. Ann. N. Y. Acad. Sci., 1146, 256290, https://doi.org/10.1196/annals.1446.016.

    • Search Google Scholar
    • Export Citation
  • Nikaidou, Y., 1986: Q-map (the potential vorticity maps analyzed on the isentropic surface) (in Japanese). Tenki, 33, 289331.

  • Orlanski, I., and J. Katzfey, 1991: The life cycle of a cyclone wave in the Southern Hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48, 19721998, https://doi.org/10.1175/1520-0469(1991)048%3C1972:TLCOAC%3E2.0.CO;2.

    • Search Google Scholar
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  • Orlanski, I., and J. P. Sheldon, 1995: Stages in the energetics of baroclinic systems. Tellus, 47A, 605628, https://doi.org/10.3402/tellusa.v47i5.11553.

    • Search Google Scholar
    • Export Citation
  • Palmén, E., 1949: Origin and structure of high-level cyclones south of the: Maximum westerlies. Tellus, 1, 2231, https://doi.org/10.1111/j.2153-3490.1949.tb01925.x.

    • Search Google Scholar
    • Export Citation
  • Palmén, E., and C. W. Newton, 1969: Atmospheric Circulation Systems: Their Structure and Physical Interpretation. Academic Press, 603 pp.

  • Pinheiro, H. R., K. I. Hodges, M. A. Gan, S. H. S. Ferreira, and K. M. Andrade, 2022: Contributions of downstream baroclinic development to strong Southern Hemisphere cut-off lows. Quart. J. Roy. Meteor. Soc., 148, 214232, https://doi.org/10.1002/qj.4201.

    • Search Google Scholar
    • Export Citation
  • Portmann, R., B. Crezee, J. Quinting, and H. Wernli, 2018: The complex life cycles of two long-lived potential vorticity cut-offs over Europe. Quart. J. Roy. Meteor. Soc., 144, 701719, https://doi.org/10.1002/qj.3239.

    • Search Google Scholar
    • Export Citation
  • Portmann, R., M. Sprenger, and H. Wernli, 2021: The three-dimensional life cycles of potential vorticity cutoffs: A global and selected regional climatologies in ERA-Interim (1979–2018). Wea. Climate Dyn., 2, 507534, https://doi.org/10.5194/wcd-2-507-2021.

    • Search Google Scholar
    • Export Citation
  • Price, J. D., and G. Vaughan, 1993: The potential for stratosphere-troposphere exchange in cut-off-low systems. Quart. J. Roy. Meteor. Soc., 119, 343365, https://doi.org/10.1002/qj.49711951007.

    • Search Google Scholar
    • Export Citation
  • Qi, L., L. M. Leslie, and S. X. Zhao, 1999: Cut-off low pressure systems over southern Australia: Climatology and case study. Int. J. Climatol., 19, 16331649, https://doi.org/10.1002/(SICI)1097-0088(199912)19:15<1633::AID-JOC445>3.0.CO;2-0.

    • Search Google Scholar
    • Export Citation
  • Reboita, M. S., R. Nieto, L. Gimeno, R. P. da Rocha, T. Ambrizzi, R. Garreaud, and L. F. Krüger, 2010: Climatological features of cutoff low systems in the Southern Hemisphere. J. Geophys. Res., 115, D17104, https://doi.org/10.1029/2009JD013251.

    • Search Google Scholar
    • Export Citation
  • Satake, Y., M. Inatsu, M. Mori, and A. Hasegawa, 2013: Tropical cyclone tracking using a neighbor enclosed area tracking algorithm. Mon. Wea. Rev., 141, 35393555, https://doi.org/10.1175/MWR-D-12-00092.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2019: A description of the Advanced Research WRF Model version 4. NCAR Tech. Note NCAR/TN-556+STR, 145 pp.

  • Spreitzer, E., R. Attinger, M. Boettcher, R. Forbes, H. Wernli, and H. Joos, 2019: Modification of potential vorticity near the tropopause by nonconservative processes in the ECMWF model. J. Atmos. Sci., 76, 17091726, https://doi.org/10.1175/JAS-D-18-0295.1.

    • Search Google Scholar
    • Export Citation
  • Tsuboki, K., and Y. Ogura, 1999: A potential vorticity analysis of thunderstorm-related cold lows (in Japanese). Tenki, 46, 453459.

  • Tsuji, H., and Y. N. Takayabu, 2019: Precipitation enhancement via the interplay between atmospheric rivers and cutoff lows. Mon. Wea. Rev., 147, 24512466, https://doi.org/10.1175/MWR-D-18-0358.1.

    • Search Google Scholar
    • Export Citation
  • Tuel, A., D. Steinfeld, S. M. Ali, M. Sprenger, and O. Martius, 2022: Large-scale drivers of persistent extreme weather during early summer 2021 in Europe. Geophys. Res. Lett., 49, e2022GL099624, https://doi.org/10.1029/2022GL099624.

    • Search Google Scholar
    • Export Citation
  • Vuille, M., and C. Ammann, 1997: Regional snowfall patterns in the high arid Andes. Climatic Change, 36, 413423, https://doi.org/10.1023/A:1005330802974.

    • Search Google Scholar
    • Export Citation
  • Wirth, V., 1995: Diabatic heating in an axisymmetric cut-off cyclone and related stratosphere-troposphere exchange. Quart. J. Roy. Meteor. Soc., 121, 127147, https://doi.org/10.1002/qj.49712152107.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., and H. Itoh, 2013a: Vortex–vortex interactions for the maintenance of blocking. Part I: The selective absorption mechanism and a case study. J. Atmos. Sci., 70, 725742, https://doi.org/10.1175/JAS-D-11-0295.1.

    • Search Google Scholar
    • Export Citation
  • Yamazaki, A., and H. Itoh, 2013b: Vortex–vortex interactions for the maintenance of blocking. Part II: Numerical experiments. J. Atmos. Sci., 70, 743766, https://doi.org/10.1175/JAS-D-12-0132.1.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Structures of C1 and C2. (top),(middle) Shading shows PV on (a)–(d) 330- and (e)–(h) 320-K isentropic surfaces. (bottom) Cross sections of PV (shading) and potential temperature (K) (contours) along A–B shown in the top and middle panels as a red dashed line. Blue contours show 320 and 330 K. (a),(e),(i) 0000 UTC 11 Jul, (b),(f),(j) 0000 UTC 12 Jul, (c),(g),(k) 0000 UTC 13 Jul, and (d),(h),(l) 0000 UTC 14 Jul. C1 and C2 are shown by black characters. C2a and C2b are described in the main text. We use ERA5 (Hersbach et al. 2020; see section 2a) for all panels.

  • Fig. 2.

    Schematic of the WRF domain. Red contours show 2-PVU isopleths obtained from the WRF simulation on the 325-K isentropic surface at 0000 UTC 11 Jul.

  • Fig. 3.

    As in Fig. 1, but using the results of the WRF simulation for all the panels. A, B, C1, C2, C2a, and C2b are displayed at the same longitude, latitude, and pressure as in Fig. 1.

  • Fig. 4.

    Initial positions of parcels inside (a) C1 at 0000 UTC 14 Jul for the backward trajectory analysis and (b) C2 at 0000 UTC 11 Jul for the forward trajectory analysis. White dots indicate parcels. Semitransparent surfaces represent isentropic surfaces (from 310 to 370 K; every 5 K), and colors show PV according to the scale at right. An interactive version of the figure is available in the supplemental material.

  • Fig. 5.

    (a) Results of EKE budget analysis for C1. Temporal evolution of EKE (black line) averaged in V, and rhs terms (colored lines) of Eq. (2) (rhs1–9) averaged in V, where, for example, “rhs1” represents the first term on the rhs of Eq. (2). EKE is shown on the left vertical axis and rhs1–9 on the right axis. Line rhs1 is thicker than the others. All lines represent as 7-h running means. (b) The black solid line shows the temporal evolution of the time derivative of EKE averaged in V as a 25-h running mean. Gray dashed lines represent ±6 × 10−5 m2 s−3. Blue shading shows the period from 2300 UTC 10 Jul to 0200 UTC 13 Jul when the black line in (b) is located between the two gray dashed lines around 11 and 12 Jul.

  • Fig. 6.

    (top) Horizontal distribution of KFC averaged over 100–900 hPa. Positive values represent EKE sources. Cyan contours give EKE averaged over 100–900 hPa (100, 300, 500, 700, 900, and 1100 m2 s−2), color shading gives KFC averaged over 100–900 hPa, and hatching denotes PV of >2 PVU on 330 K. Vectors and colored arrows denote the direction of vector VK′ and |VK′|, respectively (vectors with size 1.5 × 103 m3 s−3 and larger are drawn), where the depicted VK′ is averaged over 100–900 hPa. Purple circle denotes domain S with a radius of 1000 km. (bottom) Cross sections along the black dashed line in the top panel of PV (shading), potential temperature (K; green and black contours; 330-K isopleths are green and the others are black), EKE (cyan contours; 100, 300, 500, 700, 900, and 1100 m2 s−2), and KFC (red and blue contours; ±0.100, ±0.075, ±0.050, and ±0.025 m2 s−3; red and blue contours show positive and negative, respectively). Purple lines show 1000 km from the center of C1. Panels show 0000 UTC (a),(d) 12 Jul; (b),(e) 13 Jul; and (c),(f) 14 Jul.

  • Fig. 7.

    Temporal evolution of PV averaged within a circle of radius r km from the center of C1, where we set r = 500 for the 315- and 320-K surfaces and r = 1000 for the 330- and 350-K surfaces. All lines represent 7-h running means. Blue shading is the same as in Fig. 5.

  • Fig. 8.

    (a)–(e) Backward trajectories initialized inside C1 at 0000 UTC 14 Jul. The dots represent parcels with PV shown by color. Red and blue contours show 2-PVU isopleths on the 345- and 325-K isentropic surface, respectively. A purple trapezoid with vertices of (69°N, 15°W), (69°N, 22°E), (40°N, 22°E), (40°N, 15°E), and (60°N, 15°W) is shown in (e). Panels (a)–(e) are snapshots at 0000 UTC 14 Jul, 0600 UTC 13 Jul, 1800 UTC 12 Jul, 0000 UTC 12 Jul, and 0000 UTC 11 Jul, respectively. (f) As in Fig. 5a, but only EKE and KFC are shown and purple letters correspond to the time of the snapshot in each panel.