Western Mediterranean Precipitation Extremes, the Result of Quasi-Resonant Sea–Atmosphere Feedbacks

Abstract

The Mediterranean region has been identified as a climate change hotspot, and 13 case studies of extreme rainfall events (EREs) make it possible to categorize convective systems according to whether they are tropical-like or extratropical cyclones. This study, which focuses on the western Mediterranean basin from 2000 to 2021, is based on the cross-wavelet analysis in the period range of 11.4 to 45.7 days of (1) the height of precipitation at a particular place representative of the deep convective system used as the temporal reference and (2) the amount of precipitation in the western Mediterranean basin, as well as the sea surface temperature (SST) in the Mediterranean, the Adriatic, the Aegean Sea, the Black Sea, the Baltic, the North Sea and the Atlantic Ocean. Extratropical cyclones result from quasi-resonant atmospheric water and SST feedbacks, reflecting the co-evolution of the clustering of lows and the harmonization of thermocline depths and a relative stability of the atmospheric blocking circulation. When the SST anomaly in the western Mediterranean is greater than 0.5 °C, in its paroxysmal phase, the deep convective system is centered both over the southeast of France and the Mediterranean off the French coast. However, when the SST anomaly is weaker, deep convective systems can develop in different patterns, depending on SST anomalies in the peripheral seas. They can produce a low-pressure system extending from the Pyrenees to southern Italy or Sicily when the SST anomaly in the western Mediterranean is in phase opposition with EREs. In some cases, partial clustering of Atlantic and Mediterranean low-pressure systems occurs, producing a large cyclonic system. Tropical-like cyclones develop in the absence of any significant SST anomalies. Like extratropical cyclones, they occur in autumn or even winter, when the thermal gradient between the sea surface and the upper atmosphere is greatest but, this way, non-resonantly. Their return period is around 2 to 3 years. However, due to the gradual increase in the SST of the western Mediterranean in summer resulting from global warming, they can now lead to an ERE as happened on 21 January 2020.

1. Introduction

Mediterranean countries are particularly affected by extreme rainfall events (EREs) and catastrophic flooding. In some specific cases, up to 800 mm of rainfall [1] and up to 1000 deaths [2,3] have been recorded in a single day. An increase in the frequency of heavy rainfall in Mediterranean Europe has been demonstrated [4]. Climate projections show a strengthening of this trend for the coming years [5,6,7,8,9,10,11,12], thus the Mediterranean region has been defined as a hotspot for climate change because of an expected increase in the torrential rains that frequently affect this densely populated area.

Based on the combination of sea level pressure and geopotential height at 500 hPa, the clustering of lows clearly demonstrates the prevalence of distinct synoptic-scale atmospheric conditions during the occurrence of EREs for different locations within the region [13,14]. The extent to which EREs are connected to other regions outside the western Mediterranean has been studied in [15]. Moisture transport from extremely distant sources, including the tropics, may play an essential role as a precipitation enhancer. The authors conclude that “in the context of climate change, a global perspective must be taken, considering that alterations in remote regions, for example, of sea surface temperature, can have a direct influence on these potentially catastrophic events”.

Although occurring at mid-latitudes, cyclonic systems initiated in the Mediterranean may have similarities to tropical cyclones [16,17]. Like cyclonic systems forming in the Gulf of Mexico or the China Sea, Mediterranean subtropical cyclones result from baroclinic instabilities in the atmosphere and the potential instability and water vapor content above a warm enclosed or semi-enclosed sea associated with the development of severe convective systems. In particular, the western Mediterranean is a deep and almost closed sea surrounded by high mountain ranges. EREs mainly develop in late summer when the temperature gradient between the sea surface, which can reach temperatures of 30 °C, and the upper atmosphere is maximum while sea–atmosphere exchanges of heat and moisture can potentially destabilize air masses travelling over the sea.

In [18], the effect of sea surface temperature (SST) in torrential rains has been demonstrated from three heavy precipitation events affecting the Valencia region in Spain. Simulations with perturbed sea surface temperature in different areas of the Mediterranean along the air mass path were run to compare results with unperturbed states. The variation of sea surface temperature in certain areas caused significant changes in rainfall amount and its spatial distribution. The authors concluded the existence of areas that to a greater extent favor air–sea interaction, leading to the development of torrential rainfall. These results could be extended to the whole Mediterranean basin to look for such potential recharge areas, showing that SST could be a relevant indicator for forecasting and/or monitoring EREs.

However, like cyclonic systems forming at mid-latitudes, the most intense Mediterranean events result from quasi-resonant phenomena. They simultaneously involve the clustering of mesoscale depressions, the availability of a latent heat flux over warm seas whose surface temperature is peaking, the deepening of a cut-off low, and a relative stability of the atmospheric blocking circulation [19]. The simultaneity of these phenomena is not fortuitous. It necessarily presupposes their concerted development during the slow maturation processes of the cyclonic system. This maturation phase occurring in a particular frequency band, although broad, presents a characteristic of quasi-resonance.

As such, the genesis of extreme Mediterranean events has similarities with tropical cyclones when they landfall while migrating poleward. Here again, the initiation of the cyclonic system over the warm sea does not necessarily occur when the SST reaches a maximum. On the other hand, the available latent heat flux must be relayed by the surrounding seas for the cyclone to develop, which occurs when the SST anomalies peak there in the period range of quasi-resonance. In this way, SST is not only an indicator of torrential rain recharge areas when measured in the western Mediterranean, but its monitoring in the central and eastern Mediterranean as well as in the Black Sea, the Baltic Sea, the North Sea, and the Atlantic Ocean shows that the recharge involves much larger areas than what was commonly accepted until now.

The complexity of dynamic systems that occur in the characteristic period ranges result from the conjunction of interactions that occur in a large range of period scales, when they lead to a very heavy large-scale rainfall on an almost-stationary convergence zone. The characteristic periods, expressed from the available data of precipitation in harmonic modes with respect to the declination of the sun, generally range from 1/12 year for the uniformity of the phase of SST anomalies to 1/24 year for the clustering of lows and to 1/384 year for the deep convective system [19]. In some cases, phase homogenization of SST anomalies occurs in the same harmonic mode as the clustering of lows, that is 1/24 year. These two modes are distinct in the case of Mediterranean events.

The methodology followed in this study was developed in two previous studies focusing on mid-latitude EREs. It consists of breaking down the precipitation height and SST anomalies into characteristic period ranges; their coherence and their phase highlight the different dynamic systems involved in the genesis of EREs. However, the Mediterranean has two peculiar characteristics. On one hand, the height of precipitation can reach extremely high values—an event reaching 817 mm in one day is documented [20]—and on the other hand, the sea–atmosphere interactions imply distant closed or semi-closed seas whose role is essential in the development of EREs. Large scale moisture transport is a more important factor than evaporation over local sources [15]. From the observation of 160 extreme precipitation events with an atmospheric model enabled for state-of-the-art moisture tracking, the authors demonstrated that more than 50% of the average precipitation fraction comes from distant source regions. This particularity indicates direct connections of the Mediterranean basin with multiple locations on the western, central, and eastern Europe and a global scale energy redistribution.

Here, because precipitation is used as an indicator of remote connection with the torrential rainfall event, the study of the coherence and the phase of the precipitations resulting from convective systems while being distant is made possible thanks to the GPM (Global Precipitation Measurement) satellite constellation using microwave sensors. This equipment provides a reliable and quantitative description of the precipitation (instantaneous and on the daily scale) throughout the evolution of the precipitation systems in the Mediterranean region [21]. As such, the study presented here could not have been conducted with the same representativeness without the inclusion of GPM.

2. Materials and Methods

2.1. Data

Daily (1/4° × 1/4°) SST data are provided by the NOAA: https://www.ncei.noaa.gov/data/sea-surface-temperature-optimum-interpolation/v2.1/access/avhrr/ accessed on 1 May 2023 [22,23,24,25]. The daily optimum interpolation SST is a blend of in situ ship and buoy SSTs with satellite SSTs derived from the Advanced Very High-Resolution Radiometer (AVHRR). The data are averaged on grids (1° × 1°) to obtain a resolution adapted to the needs of the present study. Indeed, here the representativeness and the precision of the SST take precedence over the spatial resolution.

Version 06 of daily (0.2° × 0.2°) data of precipitation (2000 to present) combines information from the GPM satellite constellation using microwave sensors to estimate precipitation over the majority of the Earth’s surface: https://www.ncei.noaa.gov/data/global-precipitation-climatology-project-gpcp-daily/access/ accessed on 1 May 2023 [26].

2.2. Decomposition of SST and Precipitation Depth in Period Ranges

The coevolution of atmospheric and marine processes is highlighted from the cross-wavelet analysis of precipitation height and SST and a common time reference [27,28]. When the latter is chosen where the ultimate concentration of precipitation occurs, the phases of both precipitation height and SST anomalies are expressed in relation to the date of occurrence of the western Mediterranean precipitation extreme. SST anomalies referring to the Mediterranean and peripheral seas, as well as the Atlantic Ocean, according to 12 regions are represented in Figure 1.

The cross-wavelet spectrum of both precipitation height and SST and the time reference is performed within a period range characteristic of harmonic modes of the declination of the Sun. Each time series, whether it is SST or rainfall height, is first represented as a time-period spectrum. Then, this spectrum is sampled so as to characterize each series by an amplitude and a phase, both in a predetermined period range and for a specific date. To obtain that, the spectrum is scale-averaged within the prescribed period range and time-averaged within a time interval framing the date. Instead of a wavelet spectrum, a cross-wavelet spectrum is preferred here so that the series to be processed is “compared” to a reference series. This reference series is one of the most representative rainfall series of EREs, where precipitation is torrential. The time interval is defined in such a way as to frame the date of appearance of the ERE, its width being equal to the period in order to optimize the representativeness of the results. All of this is to ensure that the phase represents the elapsed time relative to the date of occurrence of the ERE. The same reference is used for all regionalized time series, whether they are SST or rainfall height. SST data are centered in order to express SST anomalies.

Three period ranges are used, 0.71 to 1.43 days, 1.43 to 2.9 days, and 11.4 to 45.7 days whose mean periods within the logarithmic scales are 0.95, 1.9, and 21.5 days, respectively; the low and high limits of the period ranges are equal to 3/4 and 3/2 times the mean period, respectively. The first two period ranges refer to the 1/384 and 1/192 harmonic modes to display the depth of precipitation over 1 and 2 days, respectively. The third period range reflects the merging of 1/24 and 1/12 harmonic modes characteristic of both the clustering of lows and harmonization of SST anomalies in the present case of Mediterranean events [19]. This considers the possible overlap of the two characteristic period ranges of the two phenomena.

Mediterranean rains are characterized by precipitation amounts that can exceed 200 mm in a few hours, over areas of only a few km². The problem of representativeness and accuracy of their measurement therefore arises. However, these problems are bypassed here by choosing the upper class of precipitation amounts greater than 60 mm per day. As will be shown, precipitation anomalies higher than this threshold form compact spots. The compactness of the amplitude of precipitations, which is observed for all classes, shows that the temporal and spatial resolution of the data, as well as their accuracy, fulfill the requirements of the present study. Otherwise, anomalies would be scattered. On the other hand, any biases resulting from the calibration of satellite measurements in relation to terrestrial gauges are of little importance in the quantitative representation of torrential rains at daily intervals whose height is well above this threshold.

2.3. Coherence and Phase of Rainfall and SST Anomalies According to Harmonic Modes

The region most frequently affected by the western Mediterranean EREs is located in the southeast of France (region in blue in Figure 1). It results from upper-level flow anomalies in the form of troughs and cut-offs and low-level flows that are subject to orographic uplift, that is the Cevennes to the north, the Pyrenees to the west, and the Alps to the East [29].

The precipitation $P_m$ averaged over the region representative of the most frequent EREs is used as a temporal reference from 2000 to 2021 in the expression of the coherence and phase of the pairs $\left(P_m,{\mathrm{SSTA}}_i\right),$ where ${\mathrm{SSTA}}_i$ is the average SST anomalies over the region i. The possible causal relationships between the average precipitation observed in this region of interest and the average SST anomalies in the 12 marine regions are established from the coherence and the phase of the pairs considered one by one (Figure 2). We can then consider that the concomitance of SST and precipitation anomalies reveals a causal relationship with a confidence level of the coherence higher than 95% and the phase included between 0 and 2 days (Figure 2c). In the opposite case, any phase shift reflects the independence of the phenomena.

2.3.1. Exceptional Rainfall Episodes in the Period Range of 11.4 to 45.7 Days

The eleven most significant events with the highest amplitude in the period range of 11.4 to 45.7 days are represented in Figure 2b. Defining EREs from this criterion amounts to hypothesizing that they result from the co-evolution of the clustering of mesoscale lows and the harmonization of SST anomalies, that is to say the formation of the synoptic convective system. This period range is therefore representative of the amount of atmospheric water conveyed by the cyclonic system. In contrast, the concentration of precipitation resulting from the deep convection that occurs in faster period ranges depends on local factors such as orography and the temperature gradient between the sea and the land.

As shown in Figure 2c and

Table 1. SST anomalies associated with rainfall events.

Event	SST1	SST2	SST3	SST4	SST5	SST6	SST7	SST8	SST9	SST10	SST11	SST12
1					x	x	x	x
2					x	x	x		x	x
3	x	x	x						x	x
4			x				x
5	x				x			x		x	x	x
6		x	x				x		x	x
7							x	x
8			x				x
9	x		x					x		x
10	x		x	x					x	x
11	x	x		x				x	x			x
1′		x	x		x	x	x
2′		x	x						x
3′		x			x		x	x

, each of these 11 events, whose return period is close to 2 years, correspond to one or more SST anomalies. However, events 1′ to 3′ have an infra-annual return period despite the presence of SST anomalies coherent and in phase with the precipitation event.

The most influential SST anomalies (more than 2 occurrences) when the cyclogenesis leads to EREs 1 to 11 come from the region 2 of the Mediterranean and the regions 7 to 10, i.e., the western and eastern Black Sea, the Baltic Sea, and the North Sea.

2.3.2. Exceptional Rainfall Amount for One Day

EREs in the period range of 11.4 to 45.7 days generally give rise to high return period events that occur in one day (Figure 2a,b). EREs defined both in the period range of 11.4 to 45.7 days and in one day have nearly the same return period equal or higher than 2 years, except ERE 1 that produced numerous precipitation events of relatively low intensity. In this case, the convective system did not develop in a deep convective system since the precipitation events spread over time. It can therefore be considered that, with very few exceptions, an ERE defined in the period range of 11.4 to 45.7 days results in an ERE at daily intervals and vice versa.

3. Results

During the 22 years of observation, 14 Mediterranean precipitation events have occurred in southeastern France in coordination with SST anomalies over western European seas (Figure 2b). A total of 11 EREs (numbered from 1 to 11) were identified from precipitation anomalies in the wavelet spectrum scale-averaged over the period range of 11.4 to 45.7 days, the amplitude of which is higher than the 95% confidence level.

On the other hand, three events (numbered from 1′ to 3′) occurred in conjunction with SST anomalies without however producing an ERE (Figure 2b,c). This is because, indeed, the conditions of quasi-resonance of the atmospheric water, SST feedbacks, require the co-evolution of the low-pressure system and the SST anomalies. However, these necessary conditions are not sufficient. Without the stabilization of the atmospheric blocking circulation the clustering of mesoscale lows cannot take place to completion.

The questions that now arise are (1) how EREs develop when a quasi-resonance occurs, which implies the co-evolution of atmospheric water, SST feedbacks, as well as a relative stability of the atmospheric blocking circulation and (2) how EREs develop in the absence of coherent SST anomalies.

In order to identify the different facets of the co-evolution of precipitation and SST anomalies over the different European closed or semi-closed seas, as well as on the Atlantic Ocean, each of the 11 EREs occurring in the southeast of France as well as EREs occurring exclusively in Italy (ERE 12) or Spain (ERE 13) are represented synthetically.

For each ERE, two figures represent the ultimate concentration of precipitations, one for the amplitude of precipitation occurring during a single day (period range, 0.71 to 1.43 days) and the other during two successive days (period range, 1.43 to 2.9 days). Two pairs of figures represent the precipitation and SST anomalies within the period range of 11.4 to 45.7 days. For each pair, one figure is the amplitude of the anomalies independently of their date of occurrence and the other is the phase with respect to the time reference. The same time reference is used for both rainfall and SST anomalies, that is a time series of daily precipitation reflecting at best the ERE.

Each figure therefore represents the complete evolution of the low-pressure system in its paroxysmal phase on a daily and bi-daily basis (only the amplitude of the precipitation matters because the phase would be very imprecise) as well as in the period range of 11.4 to 45.7 days representative of the clustering of mesoscale lows. On the other hand, the amplitude and the phase of SST anomalies in the same period range of 11.4 to 45.7 days reflect the harmonization of these anomalies. The joint representation of the amplitude and the phase of the SST and precipitation anomalies, in the same period range and with the same time reference, highlights the co-evolution of the anomalies. Indeed, low-pressure systems are associated with convergence, cyclonic vorticity, and upward water vapor motion to the mid-troposphere levels, hence atmospheric water–SST feedbacks [30]. A quasi-resonance phenomenon occurs when positive SST anomalies have a high amplitude and are in phase with EREs. This methodological approach defines a typology of the co-evolution of precipitation and SST anomalies.

3.1. The Western Mediterranean SST Anomaly Is Strong, in Phase with EREs

A quasi-resonance phenomenon occurs when the positive SST anomalies of the western Mediterranean and the Adriatic Sea, as well as most of the enclosed or semi-enclosed European seas, have a high amplitude and are in phase with EREs. EREs 3 and 10 (Figure 3 and Figure S1) exhibit these characteristics.

According to Figure 3, the Baltic Sea is strongly involved in the co-evolution of oceanic and atmospheric phenomena. SST anomalies in phase with ERE 3 exceed 0.5 °C along the arc following the coasts of Spain, France, and Italy, as well as in the Adriatic and Baltic seas (Figure 3e,f). Clustering of lows occurs on a large scale; the precipitation anomaly in the period range of 11.4 to 42.7 days, in phase with EREs, largely covers the Gulf of Lion as well as the French territory located north of the Gulf of Lion (Figure 3c,d). The rainfall depth averaging over 0.2° × 0.2° meshes greater than 60 mm/day is located in the Nimes region (the main anomaly is centered at 44°N, 4°E) both in the daily and bi-daily period ranges (Figure 3a,b); precipitation height reaches 431 mm/day locally.

The SST anomaly of the western Mediterranean in phase with ERE 10 follows the French coast, then the coast at the north of Italy, exceeding 0.5 °C (Figure S1e,f). The SST anomaly in the Adriatic Sea in phase with EREs exceeds 0.7 °C, extending to the South in the Central Mediterranean. The eastern Black Sea, the Baltic Sea, and the North Sea off the Scandinavian peninsula are also involved in the quasi-resonance since they exhibit strong SST anomalies in phase with EREs. The rainfall anomaly in the period range of 11.4 to 42.7 days, in phase with EREs, is a wide south–west–north–east strip that follows the Spain and French coasts (Figure S1c,d). The rainfall depth greater than 60 mm/day is located off the Toulon region (the main anomaly is centered at 42°N, 6°E) in the daily period range (Figure S1a,b); precipitation height reaches 326 mm/day locally.

3.2. The Western Mediterranean SST Anomaly Is Weak, in Phase with EREs

A weak SST anomaly of the western Mediterranean in phase with EREs reflects a phenomenon of quasi-resonance proven by the coherence of this anomaly with those of the enclosed and semi-enclosed European seas. The low-pressure system is more extensive than in the previous cases so that it may partially merge with a low-pressure system formed over the Atlantic. Such a phenomenon is highlighted thanks to the amplitude and the phase of the precipitation anomalies in the period range of 11.4 to 42.7 days.

3.2.1. Partial Clustering of Atlantic and Mediterranean Low-Pressure Systems

EREs 7, 8, and 9 (Figure 4 and Figures S2 and S3) are the outcomes of such a partial clustering of Atlantic and Mediterranean low-pressure systems. In the three cases, the SST anomalies of the western Mediterranean are weak, around 0.3 °C, in phase with EREs. Strong SST anomalies in phase with EREs occur in the Adriatic, Black, and Baltic Seas, exceeding 0.5 °C (Figure 4e,f and Figures S2e,f and S3e,f). The eastern Mediterranean and the North Sea off the Scandinavian peninsula are also in phase with ERE 7; the Aegean is in phase with ERE 8; the Central Mediterranean and the North Sea are in phase with ERE 9.

In Figure S2c,d, the clustering of the Atlantic and Mediterranean lows is reflected by the phase homogenization where the amplitude of the precipitation anomalies is peaking. Precipitation anomalies off the Gulf of Lion on one hand and off the southwest coast of France on the other hand are in phase with ERE 7. The clustering of the Atlantic and Mediterranean lows occurs in the same way for ERE 8 (Figure S3c,d). As for ERE 9, a narrow strip that follows the Spanish border links the Mediterranean and the Atlantic lows (Figure 4c,d).

In each of these three cases, the Atlantic and Mediterranean depressions result in precipitation anomalies nearly in phase with EREs. These anomalies are more or less disjointed, the gap reflecting the presence of cloud/water vapor. The main precipitation anomalies are essentially concentrated over the Mediterranean, extending very little over the continent (Figure 4c and Figures S2c and S3c).

In its paroxysmal phase, the deep convective system of ERE 7 is concentrated off the Gulf of Lion near the Mediterranean coast of France (Figure S2a,b); precipitation height reaches 520 mm/day locally. For ERE 8, the convective system extends in the north–south direction with a strong penetration into French territory, reaching the German border, while zigzagging (Figure S3a,b); precipitation height reaches 288 mm/day locally. For ERE 9, several anomalies are on either side of the southeast coast of France, with a strong penetration to the west into French and Spanish territories along the Pyrenean (Figure 4a,b); precipitation height reaches 260 mm/day locally.

3.2.2. The Atlantic Ocean Does Not Contribute Significantly to the Co-Evolution of the Extratropical Cyclone

EREs 2, 4, and 6 (Figure 5 and Figures S4 and S5) exhibit these characteristics. In each of the three cases, a phase-shifted precipitation anomaly is interposed between the Mediterranean and Atlantic anomalies, which highlights the absence of continuity and therefore of a link between the two depressions (Figure 5c,d and Figures S4c,d and S5c,d). The SST anomalies of the western Mediterranean are weak, around 0.3 °C, in phase with EREs 4 or 6 (Figures S4e,f and S5e,f) or partly out of phase with ERE 2 (Figure 5e,f). Strong SST anomalies in phase with EREs occur in the Black and Baltic Seas, exceeding 0.5 °C. Although of lesser amplitude, the anomalies of the Adriatic, the Aegean, the eastern Mediterranean, and the North Sea off the Scandinavian peninsula are in phase with EREs, which shows that these seas are also involved in the quasi-resonance.

The deep convective system of ERE 2 covers more than half of the French territory with precipitation heights exceeding 60 mm forming a south–east north–west tongue overlapping the sea and the land off the coast within the daily and bi-daily period ranges (precipitation height reaches 678 mm/day locally). As for EREs 4 and 6, the convective systems develop mainly above the Mediterranean (precipitation height reaches 342 and 286 mm/day locally).

3.3. SST Anomalies in Western Mediterranean out of Phase with EREs

EREs 1, 12, 5, and 11 (Figure 6 and Figures S6–S8) exhibit these characteristics. The extension of SST anomalies in the western Mediterranean varies significantly from one ERE to another. Anomalies exceeding 0.5 °C are located off the French coast for EREs 1, 5, and 11, and are more extensive for ERE 12 (Figure 6e,f and Figures S6e,f–S8e,f). They are all out of phase, behind EREs 1, 12, and 5 or ahead of ERE 11 (this phase shift mainly concerns the Adriatic, the central Mediterranean, and the Mediterranean off the Spanish coast). This phase shift also concerns the Adriatic Sea, either in its northern part (EREs 1, 12, 5) or as a whole (ERE 11).

As for ERE 1, SST anomalies exceed 0.5 °C off the southwestern coast of Turkey and in the Black Sea. The southern part of the Adriatic, the central part of the Mediterranean, and the Black Sea are in phase with EREs. However, the Baltic is out of phase and the anomaly in the Atlantic off the southwestern coast of France as well. These same characteristics apply to ERE 12 with the exception of the Baltic Sea, which is in phase with EREs.

The Adriatic, the Atlantic off the southwestern coast of France, and the Black Sea are partially out of phase with ERE 5. However, the Aegean, the Baltic, and the North Sea off the Scandinavian coast are in phase with ERE 5.

Like the Adriatic and the central Mediterranean, the Atlantic anomaly off the southwestern coast of France is out of phase with ERE 11 (ahead of the ERE). However, the Mediterranean off the Gulf of Lion, the Black Sea, the Baltic, and the North Sea off the Scandinavian peninsula are in phase with EREs.

Due to the phase shift of the SST anomaly, the western Mediterranean is not involved in the sea–atmosphere quasi-resonance. In this way, mainly depressions resulting from baroclinic instabilities induced by SST anomalies of closed and semi-closed seas intervene in the clustering of lows, which is shifted to the east. This is clearly displayed in Figure 6c,d and Figure S6c,d, referring to EREs 1 and 12, respectively. As for EREs 5 and 11, homogenization of the phase is not complete (Figures S7c,d and S8c,d). For ERE 5, the clustering of lows occurs over two distinct regions, in southeastern France on one hand and in southern Italy and western Croatia on the other. For ERE 11, the clustering of lows occurs off the eastern coast of Spain, off the southeastern coast of France, and off the west coast of Italy; the phase of the anomaly shifts from west to east.

It follows that the deep convective system is moved towards the north of Italy, Corsica and Sardinia for EREs 1 and 12 (Figure 6a,b and Figure S6a,b); precipitation height reaches 222 and 259 mm/day locally, respectively. For ERE 5, the deep convective system moves in 3 days from the southeast of France towards the south of Italy while intensifying (Figure S7a,b). The anomaly exceeds 60 mm/day in Italy for both the daily and bi-daily period ranges (precipitation height reaches 256 mm/day locally). For ERE 11, the deep convective system moves in 2 days from the coasts of the northeastern Spain and the southeast of France towards Sicily while mitigating (Figure S8a,b). The anomaly in the Gulf of Lion exceeds 60 mm/day for both the daily and bi-daily period ranges (precipitation height reaches 283 mm/day locally). Such a shift in the deep convective system has only occurred in the two cases studied during the 22 years of observation.

3.4. Non-Resonant Mediterranean EREs

Such events occur non-resonantly in the western Mediterranean, i.e., without an SST anomaly in the period range of 11.4 to 45.7 days. ERE 13 occurring on 21 January 2020 (Figure 7) exhibits this characteristic, producing precipitation anomalies that exceed 60 mm/day off the northeastern coast of Spain (precipitation height reaches 428 mm/day locally). Among EREs of this type, ERE 13 is the one with the greatest amplitude observed during the 22 years of observation.

4. Discussion

4.1. Typology

These 13 cases studies (EREs 1 to 11 occurring in the southeast of France, ERE 12 occurring in Italy, and ERE 13 occurring in Spain) highlighted the driving role of SST anomalies in the western Mediterranean as to the evolution of EREs in southwestern Europe. The discriminating criterion is the amplitude and the phase relative to the ERE of the SST anomaly in the period range of 11.4 to 45.7 days. A quasi-resonance phenomenon occurs when the SST anomaly is in phase with EREs, whatever its amplitude. In this case, an ERE is the outcome of co-evolution of the low-pressure system, SST anomalies of the enclosed and semi-enclosed seas of Europe, as well as the deepening of a cut-off low over the western Mediterranean off the western coasts of Italy.

Atmospheric water–SST feedbacks in the period range of 11.4 to 45.7 days lead to concerted evolution of the clustering of lows and the homogenization of SST anomalies, in phase with EREs. This supposes a relative stability of the atmospheric blocking circulation. Otherwise, the maturation time of the clustering processes of mesoscale depressions, as well as the harmonization of the depth of the thermoclines, is not sufficient to allow the formation of an ERE. The western Mediterranean, the enclosed and semi-enclosed seas of Europe, and possibly the narrow strip of the Atlantic along the southwest coast of France are concerned. The interruption of such a budding rainfall event has occurred three times during the 22 years of observation (events 1′, 2′, and 3′ in Figure 2b,c).

Partial clustering of Atlantic and Mediterranean low-pressure systems may occur, in phase with EREs in the period range of 11.4 to 45.7 days. A transfer of cloud/water vapor occurs between the two low-pressure systems, independent of SST anomalies in the Atlantic off the French or Spanish coasts. Such SST anomalies may however be involved in cyclogenesis over the western Mediterranean as well as the enclosed or semi-enclosed seas when they are in phase with EREs, as for EREs 5 and 11 (Table 1).

EREs may develop wherein the SST anomaly of the western Mediterranean is out of phase in the period range of 11.4 to 45.7 days, whether it is ahead or behind the ERE. This shows that the Mediterranean is not resonantly involved in cyclogenesis. Such events occur mainly through the contribution of the peripheral enclosed or semi-enclosed seas, so much so that the depression is shifted eastward, in the direction of the Aegean and the Black seas. The deep convective system may even extend from the Pyrenees or northeastern Spain towards Italy within 2 to 3 days. This happened twice during the observation period (EREs 5, 11). The daily rainfall amount of ERE 5 reached an unequaled amplitude both in Italy and in Croatia.

Finally, some EREs may occur non-resonantly, similar to tropical cyclones. When no SST anomaly is in phase with EREs, the low-pressure system remains confined to the western Mediterranean. Most Mediterranean events of this type occur in late summer, with a return period of a few years. However, ERE 13 with a return period much greater than the observation period occurred on 21/01/2020 (Figure 7). Mainly the northeast of Spain was impacted near the coast.

4.2. Incidence of Global Warming

While northern and western Europe, due to its oceanic influence, is moderately impacted by anthropogenic warming [31], it experiences severe droughts or torrential rains, the frequency of which is increasing. The Mediterranean basin is no exception to this rule. Indeed, as mentioned in the introduction, numerous studies show an increase in torrential rains over the Mediterranean basin in recent decades, which is one of the reasons why this heavily populated basin has been declared a hotspot.

Unlike the EREs observed at mid-latitudes, which essentially result from baroclinic instabilities of the atmosphere induced by SST anomalies of the oceans, they are mainly influenced by the Mediterranean Sea as well as the enclosed or semi-enclosed seas of central and northern Europe. This property gives the Mediterranean basin a particular behavior due to the rapid warming of the seas involved (Figure 8).

EREs are potentially impacted by global warming whether sea–atmosphere feedbacks occur resonantly or non-resonantly (

Table 2. Increase in SST and moisture during the observation period (1996–2022). Moisture variations are deduced from ΔSST by using the Clausius–Clapeyron relationship.

	Δ SST (°C)	Δ Moisture (%)
Western Mediterranean	1.46	10%
Adriatic	2.16	15%
Black Sea	1.34	9%
Baltic	1.73	12%

). Indeed, the latent heat released by water vapor is an important energy source of developing cyclonic eddies. Consequently, non-resonant events (tropical-like cyclones whose genesis cannot be linked to a precise SST anomaly) are favored by an increase in the surface temperature of the western Mediterranean. Quasi-resonant events (extratropical cyclones whose genesis is clearly linked to a coherent SST anomaly), for their part, are favored by an increase in the surface temperature of peripheral closed or semi-closed seas, especially the Adriatic.

5. Conclusions

Based on the decomposition in the period range of 11.4 to 45.7 days of precipitation depth in the western Mediterranean basin and SST from European seas as well as the Atlantic Ocean, 13 case studies of extreme rainfall events made it possible to categorize the convective systems according to the amplitude of the anomalies as well as their phase relative to the occurrence of the extreme event. Two low-pressure systems are highlighted, tropical-like and extratropical cyclones.

Extratropical cyclones result from the co-evolution of the low-pressure system and the SST anomalies in the Atlantic off the coasts of France and Spain and the enclosed and semi-enclosed seas of Europe, mainly the western Mediterranean, the Adriatic, the western Black Sea, the Baltic, and the North Sea off the Scandinavian peninsula. Quasi-resonant atmospheric water–SST feedbacks occur, resulting in the uniformization of the phases of the precipitation and SST anomalies, concomitantly with the extreme event, which reflects the co-evolution of the clustering of lows and the harmonization of thermocline depths. However, the development until its term of the extreme event supposes a relative stability in the atmospheric blocking circulation. Otherwise, the event does not occur, even in the presence of coherent SST anomalies.

When SST anomalies in the western Mediterranean are greater than 0.5 °C, the deep convective systems are centered over the southeast of France and the Mediterranean off the French coast. On the other hand, when SST anomalies in the western Mediterranean are weaker, deep convective systems can develop in different patterns, depending on SST anomalies in the peripheral seas. They can move towards northern Italy or even produce a low-pressure system extending from the Pyrenees to southern Italy or Sicily when the SST anomaly in the western Mediterranean is in phase opposition with EREs. In some cases, partial clustering of Atlantic and Mediterranean low-pressure systems occurs, producing a large cyclonic system.

Tropical-like cyclones may develop in the absence of significant SST anomalies in the period range of 11.4 to 45.7 days, both in the western Mediterranean and the peripheral seas. Like extratropical cyclones, tropical-like cyclones occur in autumn or even winter, when the thermal gradient between the sea surface and the upper atmosphere is greatest but, this way, non-resonantly. Such convective systems are frequent and the return period is around 2 to 3 years. However, to the increase in the temperature of the western Mediterranean in summer resulting from global warming can lead to an ERE, as happened on 21 January 2020.

To summarize, the classification of EREs according to the SST anomalies observed in the period range of 11.4 to 45.7 days shows that Mediterranean events can behave either as extratropical cyclones or as tropical-like cyclones. The latter occurring in a non-resonant way, EREs appear in autumn or at the beginning of winter when the subsurface temperature of the western Mediterranean is still high, generally exceeding 30 °C, without however revealing any localized SST anomaly. Such cyclones remain confined to the western Mediterranean and can very severely impact the eastern Spanish coast and/or the southeastern French coast.

Extratropical cyclones are more frequent and more extensive. They happen in October–November resulting from an SST anomaly in the western Mediterranean, coherent with EREs. When this SST anomaly overreaches 0.5 °C while being in phase with EREs, the extratropical cyclone generally remains confined to the western Mediterranean regardless of the peripheral seas contributing to the recharge. When the western Mediterranean SST anomaly is weaker while being in phase with EREs, the Atlantic may contribute to the recharge, in addition to the peripheral closed or semi-closed seas. The extratropical cyclone moves along the northwestern coast and possibly the southwestern coast of Italy when the western Mediterranean SST anomaly is out of phase with EREs.

In any case, the increase in the frequency of EREs with global warming, as evidenced by numerous studies quoted in the introduction, is globally explained by the warming of the Mediterranean as well as the enclosed or semi-enclosed seas of Europe. However, there is still much to do to better anticipate them and to improve future projections of Mediterranean precipitation extremes, which must involve feedback between the thermal anomalies of the European seas and the stability of the atmospheric blocking circulation, the subject of future works.