Seasonality of the dynamical systems metrics
Previous studies have shown that the dynamical systems metrics d and θ, have a strong seasonal dependence (Faranda et al. 2017a, b; Rodrigues et al. 2018). Thus, we remove the seasonal cycle before comparing the various events. The seasonal cycle is estimated by averaging the metrics for a given date and time (e.g., 5th January at 00UTC) over all years, repeating this operation for all timesteps within the year (i.e., from 1st January to 31st December) and finally smoothing the series with a 30-day moving average. The comparison between cold spells and ‘regular’ Cyprus Lows presented in the following sections are all performed using de-seasonalized values of d and θ. The seasonal cycle of d and θ is computed on SLP and Z500 over the Eastern Mediterranean. For the former, d and θ display roughly in-phase winter and summer minima (high intrinsic predictability) and maxima in the shoulder seasons, out-of-phase by 1–2 months (low intrinsic predictability; Fig. 1a). The two minima are comparable for d, while for θ the summer minimum is more pronounced than the winter one. Cyprus Lows are frequent yet not dominant during winter (~ 33% of the winter days; Hochman et al. 2018a). Thus, the wintertime average values of the dynamical systems metrics likely reflect the occurrence of other synoptic classes such as high-pressure systems, which display lower θ and d values than the Cyprus Lows (higher intrinsic predictability; Hochman et al. 2019). Indeed, the median d value for Cyprus Lows is 5.78, while for other days it is 5.39. The same is true for θ (0.81 vs. 0.75). Both differences are significant at the 5% significance level under the Kolmogorov–Smirnov (for the CDFs) and Wilcoxson Rank-Sum (for the medians) tests. On the other hand, the Persian Trough, which dominates the summer months (~ 90% of the summer days; Alpert et al. 2004b), is known to be a relatively persistent and stable atmospheric configuration (Alpert et al. 1990b) and indeed displays very low θ and reasonably low d values (Hochman et al. 2019). Hence, the Persian Trough does account for the bulk of the summertime values of the dynamical systems metrics. A similar pattern is obtained for Z500 (Fig. 1b), although the spring peak in d is shifted towards the summer months, and the d summer minimum is less marked.
The maxima of d and θ in the shoulder seasons, corresponding to high local dimensions and low persistence, reflect that these are periods when a variety of different synoptic systems affect the region (e.g., Alpert and Ziv 1989; Krichak et al. 1997). The coexistence and interaction of both winter and summer systems leads to a high-dimensional, unstable flow. In Faranda et al. (2017b), seasonal maxima in the local dimension of atmospheric flows were interpreted as saddle-like points of the atmospheric dynamics. The above supports the notion that the dynamical systems metrics are modulated by the seasons and reflect synoptic configurations in the Eastern Mediterranean.
Dynamics of cold spells over the Eastern Mediterranean
Virtually all cold spells in the Eastern Mediterranean are associated with Cyprus Lows (96% of the ones considered here). However, it is quite rare for a Cyprus Low to actually lead to a cold spell associated with snow cover in Jerusalem. From an atmospheric dynamics’ viewpoint, the cold spells are associated with a pronounced upper level trough in Z500 and a more eastern cyclone centre than other Cyprus Lows (Fig. 2). This induces a cold northerly flow, occasionally even coming from the Arctic and/or Siberia (Wolfson and Adar 1975; Goldreich 2003). The backward trajectory air parcel analysis illustrates that the flow preceding a cold spell follows a more northerly and continental pathway than the sample for all Cyprus Lows (cf. Fig. 3a and b). The main difference in the air parcels’ physical properties is that the initial potential temperature, temperature and specific humidity of the cold spells’ parcels are lower than the Cyprus Lows’ ones by about 12 K, 10 K and 1 g kg−1, respectively (Fig. 3d–f). The differences in potential temperature between the two groups can mainly be attributed to the poleward origin of the air masses associated with the cold spells.
From a dynamical systems point of view, the cold spells and Cyprus Lows also exhibit substantial differences. Figure 4 shows the CDFs for d and θ computed on SLP and Z500. θ is significantly lower for the cold spells relative to Cyprus Lows, i.e., the snow events are generally more persistent (Fig. 4b, d). We note however that a small number of ‘regular’ Cyprus Lows do display relatively high persistence (low θ computed on SLP), but do not lead to snow in Jerusalem (Fig. 4b). A more complex picture arises for the local dimension. For SLP, there is no significant difference between the two CDFs and their medians according to the Wilcoxson Rank-sum and Kolmogorov–Smirnov tests (Fig. 4a). On the contrary, Z500 shows a significantly lower d for the cold spells than for all Cyprus lows (Fig. 4c).
Next, we test the sensitivity of the dynamical systems metrics to the depth and location of the Cyprus Low using both the Kolmogorov–Smirnov and Rank-Sum tests at the 5% significance level. We find that deeper Cyprus Lows display significantly higher values of d and θ (low intrinsic predictability) computed on SLP (Fig. 5a, b; Hochman et al. 2019). However, Eastern Cyprus Lows show significantly higher d and lower θ relative to Western Cyprus Lows (Fig. 5c, d). This suggests that both the location and depth of a cyclone play an important role in determining its intrinsic predictability. Computing d and θ on Z500 shows a completely different picture. In this case, deep Cyprus Lows show significantly lower d and θ values (high intrinsic predictability) relative to shallow lows (Fig. 5e, f). However, Eastern lows still show significantly higher d and lower θ relative to Western lows (Fig. 5g, h). This again advises that both the depth and location of the Cyprus Low play an important role in determining the intrinsic predictability also at Z500. These results also point to the different ways in which upper and lower level flows reflect on the intrinsic predictability of the atmosphere.
Figure 6 displays the average temporal evolution of d and θ, again computed for both SLP and Z500. The data is centred on 00UTC of the first day of snow or Cyprus Low (0 h in the Figure). Still, precipitation associated with a Cyprus Low event may occur a few hours following the development of the cyclone. Substantial differences are found between the cold spells and ‘regular’ Cyprus Lows. For SLP, cold spells typically display an above-climatology d, which increases up to small negative lags and then decreases rapidly (Fig. 6a). θ shows a similar pattern, but mostly displays near-climatology persistence in the lead up to the event. The ‘regular’ Cyprus Lows display a less pronounced life-cycle, characterised by lower values of d and a slightly lower persistence in the days preceding the onset of the event (Fig. 6b). The build-up to the cold spells is therefore high-dimensional (pointing to a low intrinsic predictability), yet with a near-climatological or even slightly above-average persistence, which is probably a pre-requisite for intense cold air mass transport to the region. Interestingly, the peaks in d and θ occurring in the ~ 48 h prior to the event onset coincide with the time interval for which the majority of the cold-spell air parcels reach the Mediterranean Sea and rapidly increase their potential temperature, temperature and specific humidity at approximately 900 hPa height (Fig. 3). This may point to the role of upward sensible and latent heat fluxes, when cold air interacts with the warm Mediterranean Sea, in affecting the dynamical properties of the atmospheric flow. These fluxes play an important role in the generation and intensification of Cyprus Lows, and may thus conceivably influence their predictability (Stein and Alpert 1993; Alpert et al. 1995). We provide further evidence to support this hypothesis by comparing d and θ computed on SLP for the upper and lower 10% of Lagrangian changes in specific humidity. The changes in specific humidity are calculated along the trajectories of events between − 48 h and 0 h. As shown in Fig. 7, d(θ) is significantly higher (lower) for large changes in the specific humidity. Though this statistical analysis does not demonstrate causal relationship, it does provide a plausibility argument for the important role the rate of moisture uptake, likely due to air-sea fluxes, plays in determining the intrinsic predictability of Cyprus Lows and particularly cold spells.
The dynamical systems metrics computed on Z500 show a radically different picture. The temporal evolutions of d and θ for the cold spells are again in phase with each other, but now show a minimum in the hours preceding the events’ onsets (Fig. 6c). The ‘regular’ Cyprus Lows again display a more subdued life-cycle (Fig. 6d). The apparent contradiction between the SLP and Z500 results may be partly reconciled by considering the vertical structure of Cyprus Lows. We hypothesise that the two flanks of the upper level trough have lower intrinsic predictability (higher d and θ) than the central part of the trough. As the cyclone develops, we therefore expect the dynamical systems metrics to show a minimum in Z500 (Fig. 6c), since the leading flank is the first to enter the domain, followed by the trough centre (see for example Figures S2 and S3 for the ‘Alexa’ cold spell). In addition, the maxima of d and θ computed for SLP occur several hours before the minima calculated for Z500. This likely reflects the westward tilt with height of the low-pressure systems, so that the upper level trough reaches the region later than the surface low (Fig. 2a and an example for the ‘Alexa’ cold spell in Figure S3). Finally, we note that variability in the temporal evolution of the dynamical systems metrics across the different cold spells is smaller in Z500 than in SLP (shading in Fig. 6). The different temporal evolution of the dynamical systems metrics points to the value in using different variables at different levels to obtain a complete picture, but also to the interpretational challenges posed by this analysis approach.
We also assess the sensitivity of the dynamical systems metrics to the size and location of our geographical domain. No qualitative differences are found for shifts or small increases in the domain size (not shown). The only noticeable difference is found for the local dimension (d) distribution computed on SLP and for the largest domain (Sect. 2.3, Figure S4a). For such a large domain, the dynamical systems analysis captures a large part of the subtropical high features alongside the cyclonic features (Figure S2). We therefore conclude that the dynamical systems metrics are in our case largely insensitive to domain size, as long as the main features of the synoptic system of interest are captured within the domain, and that such domain is not extended to the point of including other, concurrent synoptic systems.
We analyse next numerical ensemble forecasts from the GEFS reforecast dataset for both Cyprus Lows and cold spells. Cold spell forecasts typically display a higher spread than other Cyprus Lows at lead times of 69 h (Fig. 8b, f). The spread for both peaks at negative lags, indicating that forecasts initialised prior to the events are more uncertain than forecasts initialised during or after the events (Fig. 8a, e). This agrees with the information provided by the dynamical systems metrics computed on SLP, but contradicts the metrics computed on Z500. No significant differences are found between cold spells and Cyprus Lows in terms of the mean model absolute error (Fig. 8d). However, the two types of events exhibit a different temporal evolution, with the cold spells showing a peak in the absolute error 48 h prior to the event onset (Fig. 8c). The peak at 48 h corresponds to forecasts initialised just before the largest changes in d and θ computed on both SLP and Z500 (cf. Fig. 8c with Fig. 6a, c). This points to the possibility that sharp changes in the values of the two dynamical systems metrics, corresponding to a rapid change in the properties of the atmospheric flow, may indicate lower practical predictability. The corresponding plots for forecast valid time (see Sect. 2.4), are provided in Figure S5. As the spread/skill relation for cold spells is relatively poor, only limited conclusions can be drawn from the ensemble reforecast analysis and from the parallels with the dynamical systems metrics. Generally, the spread/skill at the individual stations is comparable to the average forecast spread/skill (not shown). The largest difference is found for Elat station (Table S1). This station is located at the southernmost tip of Israel and therefore may not be influenced by most Cyprus Lows and cold spells (Figure S1).
A detailed analysis of the ‘Alexa’ cold spell
The evolution of storm ‘Alexa’ is analysed as a case study (Fig. 9). The SLP and Z500 patterns for the first day of ‘Alexa’ are comparable with the average configuration of a cold spell, albeit with a deeper upper level trough and a deeper surface cyclone (cf. Fig. 9a with Fig. 2a, noting the different colour ranges). Moreover, the temporal evolution of ‘Alexa’ from a dynamical systems point of view (Fig. 9b, c) closely resembles the climatological signature of an average cold spell, only with larger absolute values (cf. Fig. 9b, c with Fig. 6a, c). These are not only due to the fact that we are not averaging over several events; indeed, ‘Alexa’ is a cold spell episode with one of the largest ranges of d and θ values over the considered time range. The ‘Alexa’ event is also located in the upper 1% of Cyprus Lows for d computed on SLP (Hochman et al. 2019), and in the lower 5% of d and θ computed on Z500. This suggests that ‘Alexa’ is not only an extreme event concerning its weather and impact, but also from a dynamical systems point of view. The deep Eastern Cyprus Low associated with ‘Alexa’ may have influenced the extreme values of the dynamical systems metrics (see Sect. 3.2).
The air parcel analysis reveals that storm ‘Alexa’ may be considered an archetype for Eastern Mediterranean cold spells. The parcels are embedded in a large-scale “omega” flow pattern over Europe and follow a pronounced continental northerly pathway (Fig. 10a, b). Furthermore, the initial potential temperature and temperature of the air parcels are much lower than the climatology of cold spells by about 8 K and 6 K, respectively (cf. Fig. 10d, e with Fig. 3d, e). The largest d and θ values computed on SLP coincide with the arrival of the majority of air parcels over the Mediterranean (Fig. 10b), and the time at which they substantially increase their potential temperature, temperature and specific humidity (Fig. 10d–f). Indeed, storm ‘Alexa’ is situated in the upper decile of change in specific humidity and potential temperature over the 48 h prior to the event onset, which may reflect on the dynamical systems metrics values for this event (see Sect. 3.2 and Fig. 7).
Figure 11 shows the temporal evolution of the forecast spread/skill for the ‘Alexa’ storm compared to the climatology of cold spells. Throughout the lead up and early phases of the event, the forecast displays a higher error than for other cold spells (Fig. 11b). On the contrary, the spread peaks at 48 h before the event onset, but displays mostly lower values than other cold spells at other times (Fig. 11a, c). The temporal evolution of the SLP ensemble spread mirrors quite closely that of the dynamical systems metrics computed on SLP, peaking in the two days prior to the event’s onset (cf. Fig. 11c with Fig. 6a). Thus, the analysis of the ‘Alexa’ cold spell supports the results for the whole sample of cold spells associated with snow in Jerusalem. The corresponding plots for forecast valid time (see Sect. 2.4), are provided in Figure S6. While we argue (Sect. 2.4) that forecast initial time is closer to the information synthesised by the dynamical system metrics, we note that the picture changes when using forecast valid time, as a dip in SLP spread is present at small negative lags.