Diagnostics of Mediterranean Explosive Cyclogenesis Using the Pressure Tendency Equation †

: The objective of this study is the evaluation of the physical processes responsible for the genesis and evolution of an explosive cyclone in the central Mediterranean with the aid of the surface pressure tendency equation. For this reason, the equation is solved numerically, providing the opportunity to quantitatively specify the relative signiﬁcance of the diabatic processes in Mediterranean explosive cyclogenesis, contrary to the qualitative approach of previous studies. Our approach allows for the ﬁrst time a direct comparison of the physical mechanisms between the cyclogenesis over the northern and the southern part of the central Mediterranean. The results demonstrate that the interaction between the upper level baroclinic and low-level diabatic processes triggered the development of the explosive cyclone, but low-level baroclinicity and diabatic processes prevailed during the cyclone evolution.


Introduction
Mediterranean explosive cyclogenesis has been systematically studied during the last decades, regarding both its climatological characteristics and the dynamic processes evolved [1][2][3][4][5][6].In the above studies, both the baroclinic and diabatic processes and their relevant importance on cyclones' rapid deepening were examined, but the approach was in all cases from the qualitative point of view.
In this study, the modified version of the pressure tendency equation (hereafter, PTE) is employed based on the study of [7] and applied to the ERA-5 1hr reanalysis dataset in order to quantitatively assess the contribution of the diabatic processes to the deepening of a case of explosive cyclogenesis over the central Mediterranean, during the period 12-16 November 2017, and more specifically during the first hours of the 15 November 2017, where the western parts of Athens were affected by strong flash floods which led to 21 human life losses [8,9].

Materials and Methods
The new ECMWF/ERA5 dataset [10] is employed, while the atmospheric fields used at surface and on pressure levels are on an hourly time step and on 0.25 • × 0.25 • regular latitude-longitude grid.The diagnostic approach is based on the surface PTE [7] which considers an air column from the surface up to an upper boundary with pressure equal to p 2 following the equation: Dp Dϕ ITT EP where p sfc is the surface pressure, ρ sfc is the respective air density at surface, ϕ p2 is the geopotential height at the pressure level equal to p 2 , R d is the gas constant for dry air, T v is the virtual temperature, and g is the gravitational acceleration.The terms of the above equation from the left to the right denote the rate of surface pressure tendency (Dp), the rate of geopotential change at the upper boundary of the air column (Dϕ), the vertically integrated virtual temperature tendency (ITT), the mass loss (increase) by surface precipitation P (evaporation E) (EP), and a residuum due to discretization (RES PTE ).
The ITT term of Equation ( 1) was further analyzed as follows [7]: where T is temperature, v and ω the horizontal and vertical wind components, respectively, c p the specific heat capacity at constant pressure, and Q the diabatic heating rate.The first and second terms on the right-hand side describe the effect of horizontal temperature advection (TADV) and vertical motions (VMT) on the column-integrated temperature tendency.DIAB contains the influence of diabatic processes such as radiative warming/cooling, latent heat release due to phase changes of water, diffusion, and dissipation.The term RES ITT represents errors due to discretization in time and space.The ITT term also includes a small term arising from changes in the humidity content in the column, which is neglected for reasons explained in [7].The surface PTE is evaluated over a 3 • × 3 • latitude-longitude box extending from the surface to 100 hPa centered on the position of the cyclone, as derived following the minimum mean sea level pressure (MSLP) from the ECMWF/ERA5 dataset.DIAB had to be calculated as the residuum of the equation determining the ITT and is therefore termed DIAB RES , which almost coincides to the DIAB term [7].Finally, the relative contribution of DIAB RES to the total pressure tendency, DIAB ptend , is defined by DIAB ptend equation of [7] (Equation (3) of Fink et al. 2012 [7]).

Application of the PTE for the First Phase of the Case of Explosive Cyclogenesis in the Gulf of Genoa
The explosive cyclone phase includes the time period between 12/00 UTC and 13/11 UTC (Figure 1a), namely the period where the upper-level cyclonic circulation in NW Europe begun to develop until the formation of surface explosive cyclogenesis in the Gulf of Genoa [11].However, surface MSLP analysis shows one cyclone center is formed in the Ligurian Sea, while a secondary center is located over northern Italy, both with a pressure of about 990 hPa (Figure 1b).Since the calculation of the physical parameters considers an area (box), both the implication of the ''reference" cyclone center in the Ligurian Sea and of the secondary cyclone over northern Italy is included.
sidering that the 100 hPa isobaric level descends towards lower isentropic surfaces, which implies upward motions in the lower troposphere [12].The respective ITT term (Figure 1c) presents negative values and differential warming during the greatest part of the cyclone evolution, which proves that the variations in the upper-level dynamics result in the rapid deepening of the surface cyclone.According to [7], such an interaction between the Dφ and ITT terms can be observed in cases where the explosive deepening occurred within the left exit region of the polar front jet streak (Figure 1b) [13].Figure 1d shows that the ITT term significantly contributes to the surface deepening.Although at isolated hourly time steps the ITT term contributes to the surface rise, the RESPTE term is also enhanced, which is probably related to the discretization of the precipitation simulation [7].Moreover, negative VMT values were calculated during the time period between 12/00 -13/01 UTC.It should be noted that if downward motions are strong in the upper and the middle troposphere due to positive potential vorticity anomalies (not shown), they can balance the effect of low-level unstable conditions [14].Also, one of the primary characteristics which was also observed by [7] is that the TADV term presents an opposite sign from the respective VMT term, with similar absolute values.Actually, this cancellation results from the upward motions of the air over the isentropic surfaces to the east (downstream) of a mid-latitude frontal depression [15], where low-level warm air advection dominates.Moreover, the positive values of TADV imply that the differential The numerical simulation of the PTE has a theoretical basis only if the Dϕ term is significantly smaller than the respective ITT term [7].Indeed, according to Figure 1c, the Dϕ values are significantly smaller than the ITT values.RES PTE is almost negligible during the incipient stage, although it strengthens during the rapid deepening stage, strongly implying that even with the advanced ERA5 dataset, deficiencies arise when the quantitative precipitation simulation is performed on an hourly time step, in accordance with the results of [7].The Dϕ term is negative almost throughout the cyclone evolution until the explosive cyclogenesis, which denotes a positive effect on the pressure tendency, considering that the 100 hPa isobaric level descends towards lower isentropic surfaces, which implies upward motions in the lower troposphere [12].The respective ITT term (Figure 1c) presents negative values and differential warming during the greatest part of the cyclone evolution, which proves that the variations in the upper-level dynamics result in the rapid deepening of the surface cyclone.According to [7], such an interaction between the Dϕ and ITT terms can be observed in cases where the explosive deepening occurred within the left exit region of the polar front jet streak (Figure 1b) [13].
Figure 1d shows that the ITT term significantly contributes to the surface deepening.Although at isolated hourly time steps the ITT term contributes to the surface rise, the RES PTE term is also enhanced, which is probably related to the discretization of the precipitation simulation [7].Moreover, negative VMT values were calculated during the time period between 12/00 -13/01 UTC.It should be noted that if downward motions are strong in the upper and the middle troposphere due to positive potential vorticity anomalies (not shown), they can balance the effect of low-level unstable conditions [14].Also, one of the primary characteristics which was also observed by [7] is that the TADV term presents an opposite sign from the respective VMT term, with similar absolute values.Actually, this cancellation results from the upward motions of the air over the isentropic surfaces to the east (downstream) of a mid-latitude frontal depression [15], where low-level warm air advection dominates.Moreover, the positive values of TADV imply that the differential temperature advection in the middle and upper level surpasses the surface and low-level warm air advection.The DIAB RES term presents small values, although larger during the period of the explosive cyclogenesis, denoting the effect of diabatic heating during the rapid deepening.It should be also noted that the DIAB term is closely related to the VMT term, considering the latent heat release due to condensation.After all the above, Figure 1d shows that during almost all the time period, the DIAB RES term is negative and thus the DIAB ptend term simulates the quantitative effect of the diabatic processes in the surface cyclone deepening.Thus, during the initiation of the surface cyclogenesis where the cyclone was located to the lee of the Alps, the effect of the diabatic processes was relatively small with a contribution between 10 and 30% of the total surface pressure fall, while the frontal depression begun its rapid deepening, the degree of influence of the diabatic processes enhanced, and DIAB ptend presented values between 60 and 90%, demonstrating that diabatic processes dominated over the baroclinic ones.

Application of the PTE for the Second Phase of the Case of Explosive Cyclone Evolution
The analysis of the PTE and ITT equations for the period between 13/12 UTC and 16/23 UTC is presented in Figure 2c,d, while Figure 2a shows the respective cyclone track.Figure 2b presents the formation of a secondary surface cyclogenesis in the Gulf of Syrte with a pressure of about 1008 hPa, which is distinct from the explosive depression.The specific surface cyclone propagated E-NE towards the southern Ionian Sea without tendency of further deepening.
Figure 2c shows that Dϕ values are significantly smaller than the respective ITT values.It should be noted that the Dp curve includes the influence of the cyclogenetic activity over the southern central Mediterranean parts.The ITT term is dominant during the largest part of the explosive cyclone phase.The RES PTE term presents relatively large values in those stages where ITT values are also enhanced and is always with an opposite sign compared to the ITT, in accordance with [7].Dϕ is also negative throughout the cyclone evolution, which implies the positive response in the surface cyclone deepening and the fact that the upperlevel dynamics continued to contribute.The ITT term presents positive values over the longest time period, indicating a differential cooling in the atmospheric layer.Nevertheless, the above synoptic behavior would not be so important if the cyclogenetic activity in the Gulf of Syrte would not have been triggered.The low-level warm air advection above the extended area of the Gulf of Syrte reaching the southern Ionian Sea, combined with the cold air advection from the N-NW parts of the area, enhanced the low-level baroclinicity and the tendency for surface frontogenesis over the southern parts of the central Mediterranean area (Figure 2b).
The behavior of the ITT term in Figure 2d strongly demonstrates that during the time period between 13/13 UTC and 15/04 UTC, including thus the time period where the strong phenomena occurred over the western parts of Athens, the ITT term contributes to the ascending motions and the surface deepening of the explosive cyclone.Nevertheless, considering the integration procedure performed for the calculations, the above temporal variations are affected from the contribution of the successive surface cyclogenetic events over the southern parts of the central Mediterranean.Although during the onset of the explosive cyclogenesis the middle and upper air descending motions managed to dominate over the low-level ascending motions, considering the positive VMT values during the next stage, the low-level environment with the occurrence of pre-existed warm and moist air (Figure 2b) enhanced the ascending motions, although the upper-level dynamics were reduced.The TADV term presents an opposite sign to the VMT term with similar absolute values.Actually, these two terms tend to cancel the effect due to the ascending motions downstream of a surface depression, namely in areas where a typical mid-latitude frontal depression or a surface of low-level temperature discontinuities with orientation of the isotherms from S-SW to N-NE and warm air advection, prevail over these areas [16].The DIAB RES term presented small values in general, but it is stronger during the initiation of surface successive secondary cyclogenesis in the Gulf of Syrte implying the effect of the diabatic processes in the area between S. Italy, Sicily, the Tyrrhenian Sea, the South Adriatic Sea, and the Gulf of Syrte.Finally, the quantitative evaluation of both the baroclinic and diabatic processes is presented in the gray bars of Figure 2d.During almost all of the period except the time between 15/10 and 16/10 UTC, the DIABptend term presents significant values and seems to be dominant, with values between 70 and 90%.Considering that the DIABRES term is negative, the DIABptend term imprints the quantitative effect of the diabatic processes in the sustainment of the ascending motions at the surface and the lower troposphere.On the contrary, the minima of DIABptend during the time period between 15/10 and 16/10 UTC implies that about 70-90% of the surface pressure deepening is the result of the TADV term, since this time period coincides to the formation of a new upper-level cyclonic disturbance from the west parts of the almost stationary closed cyclonic circulation (not shown) [17].

Conclusions
In this study, a case of explosive cyclogenesis in the central Mediterranean was examined, accompanied by severe weather over the central and southern parts of the Greek area including the western parts of Athens.The new dimension presented in this work is the numerical solution of the PTE, which provided the opportunity to quantitatively specify the relative significance of the diabatic processes.
All the analyses in this work showed that although surface cyclogenesis over the southern parts of the central Mediterranean basin might not be as strong as the respective Finally, the quantitative evaluation of both the baroclinic and diabatic processes is presented in the gray bars of Figure 2d.During almost all of the period except the time between 15/10 and 16/10 UTC, the DIAB ptend term presents significant values and seems to be dominant, with values between 70 and 90%.Considering that the DIAB RES term is negative, the DIAB ptend term imprints the quantitative effect of the diabatic processes in the sustainment of the ascending motions at the surface and the lower troposphere.On the contrary, the minima of DIAB ptend during the time period between 15/10 and 16/10 UTC implies that about 70-90% of the surface pressure deepening is the result of the TADV term, since this time period coincides to the formation of a new upper-level cyclonic disturbance from the west parts of the almost stationary closed cyclonic circulation (not shown) [17].

Conclusions
In this study, a case of explosive cyclogenesis in the central Mediterranean was examined, accompanied by severe weather over the central and southern parts of the Greek area including the western parts of Athens.The new dimension presented in this work is the numerical solution of the PTE, which provided the opportunity to quantitatively specify the relative significance of the diabatic processes.
All the analyses in this work showed that although surface cyclogenesis over the southern parts of the central Mediterranean basin might not be as strong as the respective of the northern central Mediterranean parts [18,19], in fact the low-level baroclinic and diabatic processes over the warm Mediterranean Sea can be connected to severe weather.

Figure 1 .
Figure 1.(a) Track of the explosive cyclone during the first phase (12/00 UTC-13/11 UTC) following the minimum MSLP, (b) MSLP (continuous lines; per 2 hPa), 300 hPa windspeed (shading; K), and winds at 13/06 UTC, (c) the results of the PTE.At the bottom is depicted the temporal evolution of the MSLP (in hPa) of the explosive cyclone, and (d) the respective numerical results of the ITT term.Gray bars (in %) at the bottom depict the DIABptend term.The vertical bold lines delineate the interval of explosive deepening.

Figure 1 .
Figure 1.(a) Track of explosive cyclone during the first phase (12/00 UTC-13/11 UTC) following the minimum MSLP, (b) MSLP (continuous lines; per 2 hPa), 300 hPa windspeed (shading; K), and winds at 13/06 UTC, (c) the results of the PTE.At the bottom is depicted the temporal evolution of the MSLP (in hPa) of the explosive cyclone, and (d) the respective numerical results of the ITT term.Gray bars (in %) at the bottom depict the DIAB ptend term.The vertical bold lines delineate the interval of explosive deepening.

Figure 2 .
Figure 2. (a) Track of the explosive cyclone during the second phase (13/12 UTC-16/23 UTC) following the minimum MSLP, (b) MSLP (continuous lines; per 2 hPa), 850 hPa wet-bulb potential temperature (shading; K), and winds at 14/22 UTC, (c) the results of the PTE.At the bottom is depicted the temporal evolution of the MSLP (in hPa) of the explosive cyclone and (d) the respective numerical results of the ITT term.Gray bars (in %) at the bottom depict the DIABptend term.

Figure 2 .
Figure 2. (a) Track of the explosive cyclone during the second phase (13/12 UTC-16/23 UTC) following the minimum MSLP, (b) MSLP (continuous lines; per 2 hPa), 850 hPa wet-bulb potential temperature (shading; K), and winds at 14/22 UTC, (c) the results of the PTE.At the bottom is depicted the temporal evolution of the MSLP (in hPa) of the explosive cyclone and (d) the respective numerical results of the ITT term.Gray bars (in %) at the bottom depict the DIAB ptend term.