In the atmosphere, accurate representation of the orography is crucial for mesoscale climate modelling. Thus, for the observations located over land (i.e. E-OBS and NOAA stations), the first assessment of the AdriSC WRF 3 km model simply consists in looking at the differences in elevation between measurements and model (Fig. 1c and d). For both the NOAA stations and the E-OBS gridded product, these differences are mainly lower than 20 m, except along the Apennines, the Dinarides and the Hellenides, where they can reach up to 300 m. For the NOAA stations, the AdriSC WRF 3 km model orography seems to overall strongly underestimate the elevation along the Apennines (up to 300 m) while overestimating it along the Dinarides (by 100 m on average). However, it should be noticed that the NOAA station locations are extracted from the 3 km model results with a nearest-neighbour methodology; i.e. the closest point of the grid is picked without interpolation. Consequently, these differences do not necessarily imply that the orography used in the AdriSC WRF 3 km model is inaccurate. It simply shows that the location of the extracted point may have a spatial offset of 1 to 2 km compared to the station position. For the E-OBS product, the alternation of strongly positive and negative elevation differences (± 150 m on average) along all the mountains (i.e. Apennines, Dinarides and Hellenides) shows that the orography used to produce the E-OBS dataset is most probably far smoother than the one used in the AdriSC WRF 3 km model. These differences in orography may have some important consequences concerning certain physical processes like precipitation along the mountains.

Another basic assessment of the AdriSC WRF 3 km model is presented with a Taylor diagram. It illustrates, for each variable (i.e. temperature, dew point, rain, pressure, wind speed and wind direction) and each dataset (i.e. E-OBS, CCMP, TRMM, NOAA stations and UWYO soundings), the correlation and the normalised standard deviations between model and observations (Fig. 3). For all the datasets, the worst statistics (correlations lower than 0.5 and normalised standardised deviations of around 0.5 or above 1.5) are obtained for rain, which appears to be poorly captured by the AdriSC WRF 3 km model. Independently of the variable, the best statistics (correlation above 0.9 except for the wind direction and normalised standardised deviations near 1) are reached for the UWYO soundings. This potentially shows a good representation of the atmospheric vertical structure by the AdriSC WRF 3 km model. However, it should be noted that most of the sounding measurements are taken in the higher troposphere (i.e. about 90 % are above 1 km height) where synoptic forcing dominates and hence where climate models generally perform better than in the surface layer. Finally, better statistics (higher correlations and normalised standardised deviations closer to unity) are always obtained with the hourly NOAA station measurements than with the gridded daily or 6-hourly products (i.e. E-OBS, CCMP and TRMM). This is, to some extent, surprising as climate models generally better reproduce the observations at daily rather than hourly scales (e.g. a modelled historical storm shifted by few hours compared to the reality can still be synchronised with the daily averaged observations but would definitely generate big biases if compared to hourly measurements) and provide smoother spatial results than at precise station positions. Even though Taylor diagrams are extremely useful for basic skill assessment of regional climate models depending on various datasets, they may therefore not be precise enough to properly evaluate the hourly results of kilometre-scale models.

For E-OBS daily temperature, rain and pressure over land (Figs. 4 to 6 and Fig. S1 in the Supplement), for CCMP 6-hourly wind speed and direction at sea (Figs. 7, 8 and Fig. S2 in the Supplement), and for TRMM daily rain at sea (Figs. 9 and S2), spatial maps of the median (or MAD-mean for the rain) and MAD of the gridded observations, as well as the median (or MAD-mean for the rain); MAD; and 1st, 25th, 75th, and 99th percentiles of the biases between the AdriSC WRF 3 km results and the observations, are analysed.

For the surface temperature at 2 m height in coastal areas (Figs. 4 and S1), the median of the E-OBS data shows important spatial variations with temperature reaching (a) 15.0 ∘C (± 6.5 ∘C of variations derived from the MAD) on average (up to 18.0 ± 5.5 ∘C) in the south along the Italian coast; (b) 13.0–14.0 ± 6.0 ∘C on average along the Croatian coast; and (c) up to 18.0 ± 6.0 ∘C along the Montenegrin, Albanian, and Greek coasts. Over land, temperatures are lower, on average 10.0 ± 5.5 ∘C (down to 7.0 ± 5.5 ∘C) along the Apennines and 7.0 ± 6.5 ∘C (down to 5.0 ± 6.5 ∘C) along the Dinarides and the Hellenides. Additionally, over the Pannonian plain, temperatures reach 12.0–13.0 ± 7.0 ∘C. Concerning the evaluation, the AdriSC WRF 3 km model overall largely underestimates the temperatures with a negative median bias of -1.5 ∘C in the mountains (± 1.5 ∘C in the Apennines, ± 2.5 ∘C in the Dinarides and ± 2.0 ∘C in the Hellenides), -3.5 ± 1.6 ∘C along the Adriatic coast, and down to -5.0 ± 3.2 ∘C in the Pannonian plain and the Po valley. In terms of extreme conditions, the negative bias reaches down to -4.0 ∘C in the mountains, -6.0 ∘C along the coast and -8.0 ∘C over the Pannonian plain for the 25th percentile and down to -7.0 ∘C in the mountains, -10.0 ∘C along the coast and -15.0 ∘C over the Pannonian plain for the 1st percentile. Concerning the extreme overestimations of the AdriSC WRF 3 km temperatures, on the one hand, the positive bias only reaches up to 1.0–2.0 ∘C for mountains (particularly for the Dinarides) for the 75th percentile, with most of the domain still having a negative bias of about 1.0–2.0 ∘C. On the other hand, it reaches up to 8.0 ∘C in the mountains, 5.0 ∘C along the coast and 6.0 ∘C over the Pannonian plain for the 99th percentile. The AdriSC WRF 3 km model is thus incapable of accurately reproducing the highest surface temperatures captured over land with the E-OBS dataset along the Adriatic. These results are following the work of Varga and Breuer (2020), who studied the sensitivity of simulated 2 m temperature to different WRF 10 km configurations for a 1-year period over a domain that partially covered the Adriatic basin. Specifically, they found that, for any WRF configuration, the spatial distributions of the annual mean temperature bias relative to the E-OBS dataset present a general underestimation of about -4.0 to -3.0 ∘C.

For the daily accumulated rain over land (Figs. 5 and S1), the mean of the E-OBS data reveals that the strongest precipitation occurs mostly along the Croatian coast in the lee of the Dinarides and in Istria, as well as along the Apennines, on average 3.0 ± 3.5 mmd-1 and up to 5.0 ± 5.0–8.0 mmd-1. The AdriSC WRF 3 km model tends to overestimate the daily rain for these places (as well as in southern Italy and in Greece) with a positive mean bias reaching 1.0 ± 3.0 mmd-1 on average and up to 2.0 ± 9.0 mmd-1. In the rest of the domain, the mean bias is slightly negative and reaches 0.5 ± 2.5 mmd-1 on average. Concerning the extreme biases, they reach (a) -1.5 mmd-1 extremely locally in northern Croatia for the 25th percentile, (b) -10.0 mmd-1 on average (up to -40.0 mmd-1) over the entire domain for the 1st percentile, (c) less than 1.5 mmd-1 along the mountains for the 75th percentile and (d) up to 100.0 mmd-1 along the coastal mountains for the 99th percentile. These results in fact present a great improvement compared to the WRF models used within the EURO-CORDEX RCM ensemble (i.e. European domain of the CORDEX community). Indeed, Kotlarski et al. (2014) found that the EURO-CORDEX's WRF models overestimated the mean E-OBS precipitation by more than 100 % over most of the Adriatic region (for both summer and winter), while the biases of the AdriSC WRF 3 km only vary between -40 % in the northern Italy and 50 % along the lee of the highest mountains. Additionally, given the 0.1∘ resolution of the E-OBS dataset, a smoother orography than for the AdriSC WRF 3 km model is used to extrapolate the observed rainfall (Fig. 1). Consequently, the precipitation differences highlighted by the statistical spatial skill assessment (i.e. up to 50 % along the highest mountains) do not necessarily imply that the model is inaccurate and more analyses are needed to reach a definite conclusion.

For the daily sea-level pressure over land (Figs. 6 and S1), an obvious defect of the E-OBS dataset is exhibited by the spatial variations of the median reaching 1024.0–1026.0 ± 6.0–6.5 hPa along the Montenegrin coast and radiating towards the Dinarides and southern Italy with values decreasing to 1018.0 hPa. Similarly, along the northern Croatian coast, another area reaches 1021.0 ± 8.0 hPa at around 45∘ N of latitude. These problems thus cast a doubt on the accuracy of the E-OBS sea-level pressure over the entire eastern part of the AdriSC WRF 3 km domain and in southern Italy. In fact, the issue – linked to an incorrect conversion of the air pressure data to mean sea level at two different stations along the Adriatic coast – has been reported to the data creator and will be fixed in the next release of the E-OBS products. Consequently, the pressure bias is only analysed for the northern Italian peninsula. For this area, the AdriSC WRF 3 km model tends to overestimate the sea-level pressure with a positive median bias below 2.0 ± 2.6–3.2 hPa (1.0 ± 2.8 hPa on average), while the extreme biases reach -2.0 hPa for the 25th percentile, -10.0 hPa for the 1st percentile, 4.0 hPa for the 75th percentile and 10.0 hPa for the 99th percentile. It should be noted that the largest mean sea-level pressure positive biases (about 7 hPa for the 75th percentile) occur over the Pannonian plain (i.e. the northeastern edge of the domain), where the largest 2 m temperature negative biases (about -8 ∘C for the 25th percentile) are also located. Within the EURO-CORDEX ensemble, Kotlarski et al. (2014) found that over the entire European domain, the WRF winter wet biases seemed closely related to distinct negative biases of mean sea-level pressure, indicating a too high intensity of low pressure systems passing the continent. From the limited results analysed here, it thus seems that the AdriSC WRF 3 km is better suited to represent the low pressure systems over the Adriatic region than these RCMs.

For the 6-hourly wind at sea (Figs. 7, 8 and S2), the median of the CCMP wind speed shows that the strongest winds occur in the northern Ionian, southern Adriatic and Tyrrhenian seas reaching 5.5 ± 2.0–2.5 ms-1 on average. In the middle and northern Adriatic, the median of the wind speed is lower than 4.5 ± 2.0 ms-1. The median wind speed bias is positive over the Adriatic Sea and reaches 2.5 ± 1.7 ms-1 in the northern Adriatic and along the Croatian coast. However, it is extremely small (absolute bias below 0.2 ± 1.2–1.7 ms-1 on average, except near the coasts) over the northern Ionian and Tyrrhenian seas. In terms of extremes, on the one hand, the underestimation of the wind speed by the AdriSC WRF 3 km model reaches -1.7 ms-1 over the northern Ionian and Tyrrhenian seas for the 25th percentile and down to -8.0 ms-1 over the northern Ionian and the Adriatic seas for the 1st percentile. On the other hand, the overestimation reaches 4.5 ms-1 in the northern Adriatic Sea for the 75th percentile and up to 15.0 ms-1, also in the northern Adriatic Sea for the 99th percentile. However, the CCMP products are known to underestimate high wind speed events (> 25.0 ms-1). Concerning the wind direction, a qualitative comparison shows that the median, as well as the 25th and 75th percentiles, are similar for the CCMP products and the AdriSC WRF 3 km model within the Adriatic Sea, while the biggest differences are seen within the Ionian and Tyrrhenian seas where the AdriSC WRF 3 km model systematically shifts the directions by 40–120∘ anticlockwise. In more detail, in the Adriatic Sea, the wind is blowing from (a) 220–280∘ N along the Italian coast and 80–120∘ N along the eastern coast for the median, (b) 40–60∘ N in the northern Adriatic and along the eastern coast and 140–180∘ N along the southern Italian coast for the 25th percentile, and, finally, (c) 200–240∘ N in the northern Adriatic and along the eastern coast and 300–360∘ N in the rest of the Adriatic Sea for the 75th percentile. However, it should be noted that the wind directions are much more homogeneous for the CCMP product than for the AdriSC WRF 3 km results, mostly due to both the low spatial resolution and the lack of accuracy of the remote sensing data along the coasts. As an example, the bora – a northern to northeastern downslope wind associated with speeds of 20.0–30.0 ms-1 (Grisogono and Belušić, 2009) – regularly blows along the northern Adriatic and Croatian littoral areas, mostly during winter and spring. The different known bora jets (e.g. Trieste in the northern Adriatic and Senj at about 44.5∘ N latitude) represented by directions lower than 60∘ N in the 25th percentile can be clearly seen with the WRF 3 km model but not with the CCMP products, which uniformly see directions typical of bora storms along the entire northern Adriatic and eastern coast. Therefore, the differences in directions associated with an overestimation of the wind speeds in the northern Adriatic may be linked to the CCMP product and not the inaccuracy of the AdriSC WRF 3 km model.

Finally, for the daily accumulated rain at sea (Figs. 9 and S2), the median of the TRMM data highlights that the heaviest rain (up to 5.0 ± 5.0–9.0 mmd-1) is falling along the northern Croatian coast and the southeastern Adriatic coast. The mean of the rain bias reveals that the AdriSC WRF 3 km model tends (a) to slightly overestimate the rain (0.5–1.0 ± 5.0–9.0 mmd-1) along the Italian coastline of the Adriatic Sea and (b) underestimate it (by up to 1.5–2.0 ± 3.0–4.0 mmd-1) along the eastern coast of the Adriatic Sea and at the boundaries of the WRF 3 km model. This boundary effect is linked to the fact that the WRF 3 km model, which resolves some of the small-scale convective clouds, is nested into the coarser WRF 15 km domain for which the Kain–Fritsch cumulus parameterisation (Kain, 2004) is used. Concerning the extreme precipitation, on the one hand, the negative bias is quasi-null over the entire domain for the 25th percentile and reaches up to -70 mmd-1 along the eastern Adriatic coast for the 1st percentile. On the other hand, the positive bias is up to 1 mmd-1 along the Italian coast for the 75th percentile and up to 40 mmd-1 over the entire Adriatic Sea for the 99th percentile. However, Kolios and Kalimeris (2020) have shown that the TRMM monthly product (3B43) is characterised by an overestimation tendency over the northern and higher-altitude regions of the central Mediterranean, including the Adriatic Sea. They also found that heavy rainfall episodes are underestimated over the marine Mediterranean regions by this product.

In brief, the statistical spatial skill assessment of the AdriSC WRF 3 km model against E-OBS, CCMP and TRMM products has revealed some important discrepancies between the climate model results and the observations. In terms of median (MAD-mean for the rain) and MAD over the entire domain, on the one hand, the model underestimation reaches up to 5.0 ± 3.2 ∘C for the daily surface land temperature and 2.0 ± 4.0 mmd-1 for the daily rain at sea. On the other hand, the model overestimation reaches up to (a) 2.0 ± 9.0 mmd-1 for the daily land rain, (b) 2.0 ± 3.2 hPa for the daily land sea-level pressure and (c) 2.5 ± 1.7 ms-1 for the 6-hourly wind speed at sea. However, except for the temperature, some questions can be raised concerning the quality of these daily (or 6-hourly) gridded products over the Adriatic and northern Ionian domain. Additionally, previous studies (e.g. Bauer et al., 2011; Prein et al., 2013; Warrach-Sagi et al., 2013) have shown that the added value of atmospheric kilometre-scale models compared to RCMs can be cancelled out by spatial and temporal averaging. Consequently, a more precise assessment of the AdriSC WRF 3 km model skills should be done by direct comparison with the ground-based NOAA stations, which provide more reliable observations and can be more easily checked for quality (except for the rain).

In this subsection, the biases between the AdriSC WRF 3 km hourly (6-hourly for the rain) results and the ground-based atmospheric observations are seasonally analysed at each of the 251 NOAA stations with the median and MAD (or mean and MAD-mean for the rain) values for the 2 m temperature, 2 m dew point, sea-level pressure, surface rain, 10 m wind speed and 10 m wind direction (Figs. 10 to 15 and S3 to S7 in the Supplement).

The evaluation of the hourly temperature biases (Figs. 10 and S3) confirms and refines the conclusions reached in Sect. 3.2. First, the AdriSC WRF 3 km model is capable of capturing the observations during winter (DJF) with good accuracy: median values varying between -0.75 and +0.75 ∘C over the entire domain. However, a dozen stations show extreme values reaching -2.50 and +2.50 ∘C and MAD values below ± 1.75 ∘C along the coast and above ± 2.50 ∘C in the mountains in a similar manner to the other seasons (not analysed further). In addition, the model shows no skill in representing the extreme temperatures during summer (JJA), when the median bias is below -3.50 ∘C for the entire domain, except for a few stations where it surprisingly tends to zero. Finally, for spring (MAM) and autumn (SON), the median temperature bias is mostly negative over the entire domain with values varying between -3.00 and -0.50 ∘C, except at some stations along the coast and in the Apennines and Dinarides, where it can be slightly positive with values mostly below 1.00 ∘C. These results are somehow aligned with the previous study of Kotlarski et al. (2014), evaluating climate regional models using WRF at 12 km resolution. In this study, all the WRF models showed a cold bias over the Adriatic basin during summer (about -3.00 to -2.00 ∘C) but also during winter (also about -3.00 to -2.00 ∘C) due to a problem of snowfall and snow cover (Mooney et al. 2013; García-Díez et al. 2015). It is thus interesting to point out that the use of the AdriSC WRF 3 km model largely improves the results in winter but seems to increase the negative biases in summer.

Curiously, the AdriSC WRF 3 km overall shows better skill at capturing the observed dew point at the NOAA stations (Figs. 11 and S4). In winter, the model slightly overestimates the dew point with median biases below 1.00 ± 1.50 ∘C, except along the coast and in the mountains where they can reach up to 3.00 ± 2.50 ∘C and down to -3.00 ± 2.00 ∘C, respectively. In spring, the model seems to even better represent the dew point with positive median biases below 0.75 ± 2.00 ∘C over the entire domain, except at a few stations where either the median biases reach up to 2.50 ± 2.00 ∘C or down to -2.50 ± 1.75 ∘C. In summer and autumn, the model keeps overestimating the dew point along the coast with a median bias of about 1.00 ± 2.00 ∘C (up to 4.00 ± 2.50 ∘C) in summer and 0.75 ± 1.75 ∘C (up to 4.00 ± 2.25 ∘C) in autumn. Additionally, the model underestimates the dew point in the mountains and the plains with a median bias of about -1.50 ± 2.00 ∘C (down to -4.00 ± 2.50 ∘C) in summer and -1.25 ± 1.75 ∘C (down to -4.00 ± 2.00 ∘C) in autumn. As the extreme temperatures are underestimated by the AdriSC WRF 3 km model, particularly in summer, the relatively small bias obtained for the dew point implies that the model also lacks accuracy concerning the relative humidity, which is likely to be overestimated following the approximation from Lawrence (2005).

Contrary to the previous results obtained with E-OBS daily rain and the Taylor diagram, the AdriSC WRF 3 km model seems capable of capturing the observed 6-hourly rain at the NOAA stations (Figs. 12 and S5) with good accuracy independent of the season. Indeed, the absolute mean bias is always below 0.25 ± 0.75 mmd-1 over the entire domain, except at some locations (mostly along the Italian coast) where it can reach 2.50 ± 5.00 mmd-1. However, even though these results are encouraging, the mean and MAD-mean values are not representative of the model's capacity to reproduce extreme rain events for which higher percentiles should be used for further analysis.

Concerning the sea-level pressure evaluation, which could not be thoroughly performed with the E-OBS dataset, the AdriSC WRF 3 km model shows a good agreement with the quality-checked NOAA station observations (Figs. 13 and S6). The best results are obtained in winter when the absolute median bias is below 0.75 ± 0.80 hPa (up to 5.00 ± 1.80 hPa), with a slight overestimation of the model, except for some stations in the mountains. The strongest overestimation of the pressure over the entire domain is, however, found in summer, with a median bias of 3.00–5.00 ± 0.80–1.80 hPa, except in the Apennines and some stations in the coastal Dinarides where it tends to zero. For both spring and autumn, the AdriSC WRF 3 km model tends to overestimate the sea-level pressure for the entire domain, with a median bias below 1.00 ± 0.80–1.80 hPa (up to 4.00 ± 1.80 hPa), except for a few stations where the bias is slightly negative (above -0.75 ± 1.80 hPa). It is worth noticing that, independent of the seasons, the MAD tends to be nearly null along the mountain peaks, small along the coast and higher in the Pannonian plain.

Concerning the wind (Figs. 14, 15 and S7), the overall performance of the AdriSC WRF 3 km model seems satisfactory, independent of the seasons. Indeed, the median speed and direction biases tend towards a 0.0 ms-1 and 0∘ shift in wind direction for nearly half of the NOAA stations. Extreme values are found along the coast, over the Po valley and in the Pannonian plain and reach up to 1.5–2.0 ± 1.5–2.5 ms-1 for the wind speed and ± 30∘ shift for the wind direction. Additionally, despite a strict quality check of the wind measurements, which has eliminated all the stations known to be in sheltered positions, such as three coastal stations (Senj, Rab and Mali Lošinj) in Croatia (Belušić and Klaić, 2004; Klaić et al., 2009; Belušić et al., 2013; Kuzmić et al., 2015), the systematic overestimation of the wind speed by the climate model at certain stations may still be linked to some problems with the observations.

To summarise, the seasonal analysis of the biases between the AdriSC WRF 3 km model and the NOAA stations has highlighted some important results concerning the skills of the AdriSC WRF 3 km model over the land. First, the fact that the model shows no skill to capture the highest temperatures in summer is confirmed. Second, contrarily to the previous results, the 6-hourly rain seems to be accurately enough represented by the model concerning the mean and MAD-mean values, yet the extremes (e.g. 98th to 99.9th percentiles) should also be checked. Third, the atmospheric pressure is relatively well described by the model over the entire domain, even though slightly overestimated, particularly in summer. And finally, the wind speed and direction are found to be reproduced by the model, despite a systematic overestimation at certain stations.

In this section, the differences between the AdriSC WRF 3 km hourly (6-hourly for the rain) results and the ground-based atmospheric observations are first analysed as daily climatology over the full AdriSC WRF 3 km domain and for the entire set of the 251 NOAA stations. The median and associated variabilities (i.e. median ± MAD representing the upper and lower bounds) are used for the 2 m temperature, 2 m dew point, sea-level pressure, 10 m wind speed and 10 m wind direction, while the 98th, 99.5th and 99.9th percentiles are chosen in order to represent the extreme surface rain (Figs. 16 and 17).

For the temperature, dew point and pressure (Fig. 16), the daily climatology analysis confirms the results obtained in the previous sections. First, the AdriSC WRF 3 km model is only capable of representing the 2 m temperature during winter and largely underestimates it by down to -3.0 ∘C in spring and autumn and by more than -5.0 ∘C in summer. Similar results were found by Varga and Breuer (2020) for a WRF model using the same physics than the AdriSC WRF 3 km but coarser horizontal (10 km) and vertical (31 levels) resolutions, particularly in summer (i.e. biases down to -5.4 ∘C in July) but also for all the other seasons (i.e. bias of -4.5 ∘C annually). They also demonstrate that the temperature bias can largely be reduced by using numerical schemes for the planetary boundary and surface layers other than the ones used in this study. Second, the model seems to quite accurately represent the daily climatology of the 2 m dew point, with maximum differences of less than 1.5 ∘C occurring mostly during the winter, when the model overestimates the measurements. Third, the model is also capable of capturing the overall daily climatology of the sea-level pressure, except in summer when it overestimates it by more than 2.0 hPa. Finally, for the 2 m temperature, the 2 m dew point and the sea-level pressure, the daily variability (i.e. upper and lower bounds) of the AdriSC WRF 3 km model is similar to the one obtained with the entire dataset of the 251 NOAA stations.

For the extreme 6-hourly rainfall (Fig. 16), the 98th, 99.5th and 99.9th percentiles of the AdriSC WRF 3 km model overall follow the results obtained with the entire dataset of the 251 NOAA stations. However, for the 163rd, 193rd and 211th days of the year, three peaks recorded by the NOAA stations are not seen by the model. For these 3 specific days, between 39 and 56 occurrences of 6-hourly rainfall above 200 mm were observed at the ground-based stations. If extreme rainfall can occur during severe storms in autumn with rates up to 300 mm(24h)-1 (Davolio et al., 2016), it seems improbable that these occurrences cumulate during 3 specific days in June and July. The three peaks are thus considered to be the result of bad data and are ignored. Concerning the more detailed analysis of the results, the AdriSC WRF 3 km model tends to (a) accurately represent the 98th percentile of the observed 6-hourly rainfall at the daily scale, (b) slightly underestimate (by less than 2 mm(6h)-1) the 99.5th percentile for the entire year, except for a few days in late summer and autumn, and (c) underestimate (by 5 to 20 mm(6h)-1) the 99.9th percentile for the entire year, except for some few days in late summer and autumn when it can overestimate it by up to 40 mm(6h)-1. Overall, this implies that the AdriSC WRF 3 km model is reproducing the extreme rain with a good enough accuracy but not necessarily with the right timing concerning the most extreme events.

Finally, concerning daily climatology of the wind speed and direction (Fig. 17), the AdriSC WRF 3 km model seems to overall overestimate the wind speed by up to 2 ms-1, particularly in winter, while reproducing the wind direction with a good accuracy (slight underestimation by about -15∘ N in autumn and winter). However, the daily observed wind speeds, derived from the entire dataset of the 251 NOAA stations, exhibit a non-continuous behaviour with sharp daily changes between one value to the other for both median and upper or lower bounds. On the contrary, the model results more smoothly transition from one day to the other, with obvious seasonal behaviours (e.g. stronger winds in winter) not observed with the NOAA stations. The quality of the observed wind speeds, including representativeness of station locations, can thus be questioned.

In order to provide an overview of the model behaviour, the probability density functions of the hourly 2 m temperature, 2 m dew point and 10 m wind speed for the entire dataset of the 251 NOAA stations are also analysed in this subsection (Fig. 17). It is important to note that the probability density functions are obtained via a kernel-smoothing method, which presents the advantage of generating continuous distributions but may overestimate the tails of these distributions. Surprisingly, the most important results of this analysis are not related to how the AdriSC WRF 3 km model compares to the observations but instead to the unexpected shape of the distributions of the observed quantities extracted from the NOAA stations. These distributions indeed exhibit a non-continuous behaviour with sharp changes between one value to the other resulting in multiple peaks (i.e. distributions shaped like hedgehogs). It is important to know that the NOAA station temperature, dew point and speed were provided as integer values in the US customary units (i.e. Fahrenheit for temperature and miles per hour for speed). However, the data used in this study were all originally collected by European meteorological stations in metric system units (i.e. degrees Celsius and metres per second) and with their own unknown rounding errors. The presented data thus went through two unit conversions. First, they were converted from the metric system to US customary units with rounding to the closest integer, before integration to the ISD. Second, they were re-converted to degrees Celsius and metres per second before being treated in this study. Consequently, the “hedgehog” shape of the observed distributions is most probably due to these accumulated rounding errors and unit conversions. In light of these results, it is important to understand that the biases between the AdriSC WRF 3 km model and the NOAA station observations may generally be overestimated. For example, the 35 % probability of having 3 ms-1 wind speed in the NOAA station distribution is probably highly exaggerated. Indeed, due to the rounding errors and the unit conversions, this peak is surrounded by underestimation of the other wind speed values (i.e. below 10 % of probability to have 2.25 and 3.75 ms-1 wind speeds). The 18 % probability obtained with the model results for 3 ms-1 wind speeds may thus be more realistic as they come from a smooth and continuous distribution. However, the NOAA station dataset still provides valid comparisons concerning the general behaviour of the model. For example, it shows how the highest temperatures are strongly underestimated by up to 10 ∘C, while the dew points are somewhat better represented except for the extreme values.

The last analysis provided in this subsection is the scaling between precipitation extremes and temperatures. Indeed, under the hypothesis of constant relative humidity, extreme precipitation increases at a scaling rate of 7.00 %∘C-1 following the Clausius–Clapeyron (CC) relationship, which plays a key role in climate studies (e.g. Betts and Harshvardhan, 1987; Held and Soden, 2006; Westra et al., 2014). In this study, the observed and modelled apparent scaling rates – derived from the linear relationship between the logarithm of the extreme precipitation (i.e. 99th percentiles) and the 2 m temperatures (Drobinski et al., 2018) – are thus compared seasonally for the dataset of the 251 NOAA stations (Fig. 18). First, it should be noted that the observed apparent scaling rates are always below the CC scaling rate and can even be negative. This is, however, in good agreement with the results found around the Adriatic basin by Drobinski et al. (2018). Second, the apparent scaling rates extracted from the model results overall follow the tendencies of the observations, independent of the season. Third, in more detail, the scaling rates are reproduced by the AdriSC WRF 3 km (a) most accurately during winter and summer, with underestimations below ± 0.40 %∘C-1 compared to the observed values of 2.66 and -1.83 %∘C-1, respectively, and (b) least accurately during spring and autumn, with an underestimation of 1.61 %∘C-1 (compared to the 1.68 %∘C-1 observed) and an overestimation of 0.89 %∘C-1 (compared to the 3.18 %∘C-1 observed), respectively. Finally, independent of the season, the amount of extreme precipitation (i.e. 99th percentile) depending on the 2 m temperature tends to always be underestimated by the AdriSC WRF 3 km model and shifted by at least 5 ∘C for the lowest temperatures.

In a nutshell, the analysis of the climatologies and distributions has revealed that, except for the summer temperatures at 2 m height and atmospheric sea-level pressure, the AdriSC WRF 3 km model is overall capable of reproducing the observed conditions for the ensemble of the 251 ground-based stations selected in this study. Additionally, the distributions of the NOAA station dataset have been shown to present some non-continuous behaviour most probably linked to the accumulated rounding errors and unit conversions. Finally, the seasonal apparent scaling rates obtained for the entire Adriatic basin with the AdriSC WRF 3 km model are generally in good agreement with those obtained with the observations, except during spring.

The final analysis performed in this study concerns the capability of the AdriSC WRF 3 km model to reproduce the observed vertical structure. Unfortunately, the ERA5 re-analysis cannot be used for this evaluation, following Denamiel et al. (2021), who demonstrated that this product is not capable of reproducing bora events in the northern Adriatic. The only products available for the vertical skill assessment of the AdriSC WRF 3 km model in the Adriatic basin are therefore the four long-term sounding records extracted from the UWYO database. In this section, the seasonal biases between the AdriSC WRF 3 km model and the sounding data recorded twice a day at Rome, Udine, Zadar and Zagreb, are thus presented for the temperature, dew point, pressure and wind speed (Fig. 19).

First (and quite surprisingly), for all the seasons, the vertical behaviour of the AdriSC WRF 3 km model seems to be independent of the location of the soundings. Indeed, for each variable, the median of the vertical biases is overall similarly distributed for the four different stations. Second, the temperature biases are the strongest at the surface (down to -5.0 ∘C in summer as seen before) but tend to rapidly decrease with the height to reach nearly 0.0 ∘C between 2.5 and 10 km height, independent of the season. Between 10 and 15 km, however, the biases present a fast increase (up to 2.5 ∘C) up to 12 km, followed by a fast decrease towards 0.0 ∘C. Third, the dew point biases tend to be small, except in summer, and negative between the surface and 5 km height – on average between -2.0 and -0.5 ∘C, except for Udine where they reach -4.0 ∘C in summer at 2.5 km height. However, above 5 km height, they steadily grow up to 6.0–8.0 ∘C at 15 km height. Following this, independent of the season, the pressure biases are strong at the surface with values between 0.5 and 2.5 hPa, but quasi-null between 1 and 5 km height and steadily increasing up to 3.5 hPa at 12.5 km height. Finally, the wind speed biases show more variability depending on the location of the soundings. However, they are overall strong between the surface and 1 km height, with values up to 2.0 ms-1, a minimum between 1 and 8 km (between -0.5 and 0.5 ms-1, except for Zagreb where they reach -1.0 ms-1 at 2 km), and quite important differences between 8 and 13 km, with negative values reaching down to -1.5 ms-1 at different heights, depending on the location and the season. It should also be mentioned that 7.4 % of the sounding data were recorded below 1 km height, while 33.7 % were taken in the troposphere above 1 km (i.e. 3.7 %km-1) and 16.5 % were taken in the stratosphere up to 15 km (i.e. 3.3 %km-1). The remaining 42.4 % of the sounding data were recorded above 15 km (up to 48 km), beyond the AdriSC WRF 3 km vertical computational limit. This means that biases up to 1 km height have been derived with more data than the ones between 1 and 15 km height. Following these results, the AdriSC WRF 3 km model seems to present the strongest biases in the boundary layer and the stratosphere (above 10 km) but is still capable of properly capturing the dynamics of the troposphere above 1 km height.