**3. Sensitivity Tests**

For the twenty selected cases, ECMWF Re-Analysis (ERA)-Interim datasets of zonal *u* and meridional *v* wind components at the near-surface level (10 m) on a 0.5◦ × 0.5◦ resolution are used [32]. This high resolution was chosen in order to obtain a better representation of the small-scale fronts appearing in the Mediterranean region. The scheme results are compared with the surface analyses produced by the UK MetO ffice, archived by www2.wetter3.de, available every 6 h. Furthermore, for the validation of the results, MSG IR 12.0 μm satellite images, available from the Hellenic National Meteorological Service, are employed. We restrict ourselves here to showing results for the case of 7–10 November 2016 that included two extended tilted cold fronts that travelled across Mediterranean. However, the results were consistently investigated and validated for the other cases. The tests are performed following the rationale described in Section 2.

First, the critical values of the 6 h meridional wind change *dvcrit* was explored. An initial threshold value *dvcrit* = 2ms−<sup>1</sup> was employed, as suggested by [19] in the initial version of FTS. Then, the scheme was employed for di fferent values of *dvcrit* increasing by 1 m s<sup>−</sup>1. Figure 1a shows the synoptic situation of 7 November 2016, 00:00 UTC. In Figure 1b, the identified fronts are depicted (red lines) for the same day and hour for *dvcrit* = 3ms−1. In the same Figure, the light blue regions show the areas where the wind shift criterion is satisfied.

A comparison of Figure 1a,b reveals that the scheme succeeds in identifying fronts over the Atlantic. However, in the Mediterranean, its performance is somewhat lower: although it identifies correctly the main cold front over Italy, this is segmented over the Adriatic Sea while other frontal fragments are produced which do not exist in the synoptic analysis. For larger values of *dvcrit* of 4 and 5 m s<sup>−</sup>1, the erroneous front identifications show a tendency to diminish (Figure 1c). However, when *dvcrit* exceeds the value of 6 m s<sup>−</sup>1, the existing fronts incline to be broken into smaller fragments (Figure 1d). Therefore, moderate values of *dvcrit* ranging between 4–6 m s<sup>−</sup><sup>1</sup> seem to best represent Mediterranean cold fronts. Similar results were derived for the following hours. Figure 2 shows the results for 8 November 2016 at 12:00 UTC.

**Figure 1.** (**a**) Synoptic surface chart over the area of interest at 00:00 UTC 7 November 2016, and identified fronts for (**b**) *dvcrit* = 3ms−1, (**c**) *dvcrit* = 5ms−1, and (**d**) *dvcrit* = 7ms−1. The red lines show the identified fronts, whereas the areas where the wind shift criterion is satisfied are depicted with the light blue color.

Since the analysed Mediterranean fronts are not purely meridionally elongated, but they rather tend to assume a more zonal orientation, the 6 h change of the total wind direction *d*ϕ is explored instead of the change of the meridional wind magnitude. It should be noted that this criterion was found helpful in identifying cold fronts that present zonal orientation in the beginning of their life [31] and the criterion on *dv* might not be able to properly identify them. The scheme was tested for different values of *d*ϕ*crit* starting from 20◦, with steps of 10◦. In Figure 3, the identified fronts are depicted for 7 November 2016, 00:00 UTC, for (a) *d*ϕ*crit* = 30◦ and (b) *d*ϕ*crit* = 50◦. A comparison with the synoptic analysis in Figure 1a shows that the scheme indeed represents the front over Italy when *d*ϕ*crit* = 30◦. However, it can be appreciated that using solely the *d*ϕ criterion, several erroneously identified fronts are obtained. Moreover, for *d*ϕ*crit* = 50◦, the front over Italy is mistakenly broken into smaller fragments. Similar results were obtained for *d*ϕ*crit* > 40◦ and the best representation of fronts was obtained for *d*ϕ*crit* = 30◦ in most cases. To effectively filter out the erroneously identified frontal objects without losing the spatial continuity of the correctly identified fronts, the value *d*ϕ*crit*= 30◦ is adopted.

The use of the *d*ϕ criterion alone is not adequate, since it may lead to mistakenly identified fronts in cases when, at *t* + 6 h, the wind is weak or there is calm. For this reason, another criterion that we apply is that the maximum magnitude of the vector wind is above a threshold value |*U*|*crit*. It should be noted that apart from filtering out mistaken identifications, this criterion also helped in identifying cold fronts entering from North Africa and distorted cold fronts in the Central Mediterranean that rejuvenated when entering the Aegean Sea. To find the optimum value of |*U*|*crit*, values between 0 and 10 m s<sup>−</sup><sup>1</sup> were tested. Figure 4 depicts the results of the scheme on 7 November 2016 00:00 UTC for (a) |*U*|*crit* = 5ms−<sup>1</sup> and (b) |*U*|*crit* = 7ms−1. Red lines represent the identified fronts, whereas colored areas show the magnitude of the total wind |*U*| at the grid points where the *d*ϕ criterion is met. It is

clear that a value of |*U*|*crit* = 5ms−<sup>1</sup> effectively filters out spurious front identifications, while a larger value (e.g., |*U*|*crit* = 7ms–1) erroneously filters out the front over Italy. From the above sensitivity tests, the combination of *d*ϕ*crit* = 30◦ and |*U*|*crit* = 5ms−<sup>1</sup> seems to best represent cold fronts in the Mediterranean at each following synoptic time (Figures 5 and 6). Similar results were derived for the other selected cases under a variety of synoptic environments. It should be noted that based on these dynamic criteria, warm frontal structures are not identified.

**Figure 2.** (**a**) Synoptic surface chart over the area of interest at 12:00 UTC 8 November 2016, and identified fronts for (**b**) *dvcrit* = 2ms−1, (**c**) *dvcrit* = 4ms−1, and (**d**) *dvcrit* = 6ms−1. The red lines show the identified fronts, whereas the areas where the wind shift criterion is satisfied are depicted with the light blue color.

**Figure 3.** Identified fronts at 00:00 UTC 07 November 2016, for (**a**) *d*ϕ*crit* = 30◦ and (**b**) *d*ϕ*crit* = 50◦. The red lines show the identified fronts, whereas the areas where the wind shift criterion is satisfied are depicted with the light blue color.

**Figure 4.** Identified fronts at 00:00 UTC 7 November 2016, for *d*ϕ*crit* = 30◦, (**a**) |*U*|*crit* = 5ms−<sup>1</sup> and (**b**) |*U*|*crit* = 7ms–1. Red lines represent the identified fronts, whereas colored areas show the magnitude of the total wind |*U*| at the grid points where the *d*ϕ criterion is met.

**Figure 5.** (**a**) Synoptic surface chart at 12:00 UTC 08 November 2016, and (**b**) identified fronts for *d*ϕ*crit* = 30◦ and |*U*|*crit* = 5ms–1. Red lines represent the identified fronts, whereas colored areas show the magnitude of the total wind |*U*| at the grid points where the *d*ϕ criterion is met.

**Figure 6.** (**a**) Synoptic surface chart over the area of interest at 00:00 UTC 9 November 2016, and (**b**) identified fronts for *d*ϕ*crit* = 30◦ and |*U*|*crit* = 5ms–1. Red lines represent the identified fronts, whereas colored areas show the magnitude of the total wind |*U*| at the grid points where the *d*ϕ criterion is met.

In summary, in order to identify a front in our MedFTS scheme we require: (a) the zonal component *u* is westerly both at *t* and *t* + 6 h, (b) the meridional wind changes sign from positive to negative, (c) the directional shift of the wind (*d*ϕ) exceeds the threshold of *d*ϕ*crit* = 30◦ and (d) the magnitude of the vector wind |*U*| is greater than |*U*|*crit* = 5ms−1. It should be noted that the initial criterion of *dv*> *dvcrit* used in FTS has been replaced by both the criteria of *d*ϕ > *d*ϕ*crit* and |*U*|>| *U*|*crit*.

In order to check the performance of MedFTS, the results for 19 March 2018 at 12 UTC is demonstrated in Figure 7 which included a cold front that developed over Tunisia and a ffected Greece after rejuvenation and a zonally oriented cold front over the Iberian Peninsula that entered from the Atlantic and moved towards western Mediterranean. Figure 7a,b shows that the surface analysis agrees well with the satellite image for the cold front over Greece. The scheme correctly represents the location and orientation of the fronts at this specific time (Figure 7c), avoiding many erroneous identifications before the use of the |*U*|*crit*. The zonally elongated front over the Iberian Peninsula is also identified correctly by the scheme (Figure 7c) along with its subsequent evolvement. Figure 7d presents the results when the *dv* criterion is solely used. From the comparison between Figure 7c,d becomes evident that the zonal front over the Iberian is not properly identified with the *dv* criterion. Therefore, it is suggested that the successful identification of this front is mainly attributable to the combination of *d*ϕ*crit* and |*U*|*crit* criteria.

**Figure 7.** (**a**) Satellite image (IR 12μm) of the Mediterranean sea at 19 March 2018, 12:00UTC, (**b**) synoptic surface chart over the area of interest at the same time, (**c**) identified fronts for *d*ϕ*crit* = 30◦ and |*U*|*crit* = 5ms–1. Red lines represent the identified fronts, whereas colored areas show the magnitude of the total wind |*U*| at the grid points where the *d*ϕ criterion is met. (**d**) Respective results for the case of solely the *dv* criterion for *dvcrit* = 6ms−1.

## **4. Statistical Validation**

After the above modifications, the new MedFTS scheme was applied for a ten-year period (2007–2016) in order to validate its ability in identifying Mediterranean cold fronts on climatological basis. The number of the cold fronts passing over Greece was counted for the specific synoptic hour

of 00:00 UTC. Then, the results were validated against synoptic analyses obtained from Deutscher Wetterdienst, with the aid of statistical indices (Table 1). It should be noted that the statistical validation handles the occurrence of a cold front as a two-fold categorical variable, and therefore if two fronts appear at the same time over the examined area in the analysis or in the scheme, only one is counted in the total number. Due to the limited geographic area of the examined region, the appearance of more than one front is an extremely rare event and does not a ffect the obtained results.

The total number of the cold fronts identified by the scheme was *a* + *b* = 511, which is slightly lower than the corresponding number identified from the charts (*a* + *c* = 547). From Figure 8 we see that there is excellent agreemen<sup>t</sup> between the monthly frontal frequencies in the two datasets, albeit with a scheme underestimation in spring and summer and overestimation in autumn and winter. Furthermore, the scheme succeeds in capturing the intra-annual variation of the frequency of cold fronts, in agreemen<sup>t</sup> with the results of [22]. The vast majority of the simulated cold fronts is observed during the cold period of the year, from November to March, peaking in February and March. The frequency declines after April with minimum in August due to the predominance of anticyclonic circulation during summer over the Eastern Mediterranean [26].

ϮϬϬϳͲϮϬϭϲ

**Figure 8.** Mean annual cycle of the number of cold fronts identified by the MedFTS (model) and the synoptic charts (analysis) over Greece for the period 2007–2016.

Furthermore, using the indices of Table 1, we calculated the success metrics described in Table 2, taken from [33] and given in Table 3. It can be seen that the scheme succeeded in identifying correctly the bulk of fronts in synoptic charts (hits) while it correctly rejected the vast majority of the fronts that did not appear in the synoptic charts (correct rejection). On the contrary, the number of false alarms and misses are comparatively smaller. It becomes also evident that the false alarms (*b*) are slightly more than the misses (*c*).




**Table 2.** Definition of the statistical metrics used of the validation of the algorithm's capability.

**Table 3.** Values of the indices of Table 1, as they are counted for the decade 2007–2016.


Table 4 gives the values obtained for the metrics of Table 2. It can be seen that the value of FBI is almost equal to the perfect score 1, suggesting that the total number of the fronts in the scheme (*a* + *b*) is almost equal with the total number of fronts appearing in synoptic charts (*a* + *c*). Therefore, the scheme is unbiased, without apparent overestimation or underestimation of the front frequency appearing in the charts. Furthermore, POD was found of 85% and FAR of about 20%, suggesting satisfactory detection of the observed fronts with limited false identifications. Besides, Critical Success Index (CSI) presents high value (0.701), taking into account both incorrectly identified fronts and unidentified fronts. Since CSI is somewhat sensitive to the climatology of the event, the Equitable Threat Score (ETS) is also used, providing comparable value.

**Table 4.** Values of the metrics that are defined in Table 2 for the decade 2007–2016.

