Micro-Scale Properties of Different Bora Types

atmosphere

Article Micro-Scale Properties of Different Bora Types

Vinko Šoljan 1,* ID , Andreina Belušić 2 ID , Kristina Šarović 3, Irena Nimac 4, Stjepana Brzaj 4, Jurica Suhin 1, Martin Belavić 4, Željko Veˇcenaj 2 and Branko Grisogono 2 1 Croatia Control Ltd., 10410 Velika Gorica, Croatia; [email protected] 2 Department of Geophysics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia; [email protected] (A.B.); [email protected] (Ž.V.); [email protected] (B.G.) 3 EKONERG—Energy and Environmental Protection Institute, 10000 Zagreb, Croatia; [email protected] 4 Meteorological and Hydrological Service, 10000 Zagreb, Croatia; [email protected] (I.N.); [email protected] (S.B.); [email protected] (M.B.) * Correspondence: [email protected]; Tel.: +385-98-891-555

Received: 24 January 2018; Accepted: 16 March 2018; Published: 21 March 2018

Abstract: In this paper we use 20 Hz wind measurements on three levels (2, 5, and 10 m) to investigate the differences in micro-scale properties of different bora types, i.e., deep and shallow bora with further subdivision to cyclonic and anticyclonic bora cases. Using Fourier spectral analysis, we investigate a suitable turbulence averaging scale and bora gust pulsations. The obtained data set is further used to test the Monin–Obukhov similarity theory, the surface layer stratification, the behavior of the terms in the prognostic turbulence kinetic energy equation, and the wind profiles. One of our main goals is to identify possible micro-scale differences between shallow and deep bora types because of the possible different mountain wave dynamics in those flows. We found that a turbulence averaging scale of 30 min is suitable for this location and is in agreement with previous bora studies. The wind speed power spectral densities of all selected bora episodes showed pulsations with periods of 2–8 min. This suggests that mountain wave breaking was present in all cases, regardless of flow depth and synoptic type. The stability parameter analysis confirmed the near-neutral thermal stratification of bora; a consequence of intensive mechanical mixing. No significant differences related to bora type were observed in other micro-scale parameters.

Keywords: bora; turbulence; micro-scale; pulsations; wind proﬁles; surface layer; mountain wave

1. Introduction Bora is a gusty downslope wind blowing from the northeast in the lee of the Dinaric Alps and other dynamically similar parts of the world [1]. It is dynamically generated by the interaction of airflow and orography [2]. Bora macro-scale characteristics have been investigated since the middle of the 20th century [3]. Early mesoscale research focused on the katabatic model of bora [4], which was later shown to be deficient in explaining stronger bora events. A major breakthrough in bora mesoscale research started with the ALPEX (Alpine Experiment) project in 1981 [5] and the subsequent findings by Smith [2], which showed that bora is essentially a dynamically generated wind, best explained by the hydraulic and wave breaking theory [6,7]. In recent years, bora’s mesoscale characteristics have been extensively studied during the Mesoscale Alpine Programme (MAP) project [8–10]. A recent review of bora mesoscale properties at the northeastern Adriatic can be found in [11]. With respect to the synoptic setup, three types of bora have been identified in the past: cyclonic, anticyclonic [3], and frontal [12]. The typical setup for cyclonic bora is when a mid-latitude cyclone moves to the southern Adriatic, pulling colder air from the continent to the eastern Adriatic coast. Anticyclonic bora blows when there is an anticyclone situated over Central Europe, extending over the

Atmosphere 2018, 9, 116; doi:10.3390/atmos9040116 www.mdpi.com/journal/atmosphere Atmosphere 2018, 9, 116 2 of 25

Dinaric Alps [3]. Frontal bora is characterized by a sudden increase in wind speed and short duration, following the passage of a cold front [12]. Both cyclonic and anticyclonic bora can be either deep or shallow, depending on the depth of synoptic flow over the mountains (e.g., [13]). For example, a common feature above a mature mid-latitude cyclone is the southwesterly flow in the divergent (eastern) flank of the upper-level trough (i.e., the flow from positive vorticity maximum to negative vorticity maximum at 300 hPa). This is why most cyclonic boras are shallow [2,4,14,15]. However, in the case of an occluded cyclone, there is usually a cut-off low in the upper levels, sometimes favorably aligned with the surface cyclone, thus providing deep NE (northeasterly) to N (northerly) flow throughout the troposphere. Anticyclonic deep bora occurs when a deep positively tilted trough passes and the upper N or NE flow in its western flank is above the southeastern quadrant of a surface anticyclone. Alternatively, the northwestern quadrant of a cut-off low can also provide deep NE flow above the surface anticyclonic bora. Anticyclonic deep bora seems to be the most frequent among deep bora types [16] because its synoptic setup is more common than that of cyclonic deep bora. Since strong anticyclones can persist for days, it is not uncommon for this type of bora to last up to a week. Deep bora is associated with vertically propagating mountain waves [2], while shallow bora is associated with wave breaking and violent downslope windstorms [7]. Shallow bora does not allow significant vertical propagation of wave energy, thus generating strong downslope windstorms in the lee. Vertical wind shear plays a significant role in the vertical propagation of waves in deep bora. In the case of positive wind shear (wind speed increasing with height), wave breaking does not occur at least until tropopause, because of the linearizing effect of the increasing wind speed [11]. In the case of weak vertical shear or wind speed decrease with height, wave breaking is likely to happen in the lower or middle troposphere, again reflecting mountain wave energy to lower levels and generating violent downslope windstorm. Regardless of more than a century of intensive research of bora climatology (e.g., [17–19]) and bora macro- and mesoscale properties (e.g., [11,20–22]), some important details about bora micro-scale properties are not yet known. One of them includes detailed characteristics of severe bora episodes. The most severe bora episodes (downslope windstorms), with gusts reaching up to 70 m·s−1, are caused by wave breaking when there is a critical level above the mountaintop [7]. The critical level is usually marked by strong inversion [23] and a decrease in wind speed or change in wind direction by height, thus acting as an efficient reflector of wave energy. The critical level can be imposed by synoptic scale or generated by wave breaking itself—caused by wave amplitude increasing with height [24]. Severe bora typically induces shooting flow in the lee of coastal mountains [24] that may extend out over the sea in the form of multiple low-level jets behind mountain passes, while lee wakes (weaker flow regions) occur behind mountaintops [9]. Sea surface SAR (Synthetic Aperture Radar) data analysis by Kuzmićet al. [13] revealed the existence of secondary bora jets—caused by smaller mountain and island features (gaps and flanks)—that are only a few kilometers apart and several kilometers long. Moreover, they documented fine-scale convective cells pertaining to cold bora outbreak over relatively warm sea. Bora pulsations with periods of 3–4 min were first mentioned in the work of Watanabe [25], based on the experience of local fishermen. The first confirmation of those observations in the measured data was in the work of Petkovšek [26,27], who found pulsations with periods between 3 and 11 min. Although the existence of pulsations has been known for a long time, the detailed physics behind the gustiness and pulsations of bora has been addressed only recently. Belušićet al. [28] also found that the pulsations occur with periods between 3 and 11 min in the town of Senj, a location well known as a bora maximum site (Figure1). Furthermore, this was also confirmed by using fine-scale numerical modeling [29], and measurements at the Pometeno Brdo (in a free translation, Pometeno Brdo means Swept Away Hill) [30]—a bora site upwind of the city of Split (Figure1) that is about 200 km southeast from Senj. The former study found that the generation of gust pulsations was associated with mountain wave breaking and Kelvin-Helmholtz shear instability (KHI) above Atmosphere 2018, 9, x FOR PEER REVIEW 3 of 25 Atmosphere 2018, 9, 116 3 of 25 gust pulsations was associated with mountain wave breaking and Kelvin-Helmholtz shear theinstability bora shooting (KHI) above flow. the This bora mechanism shooting wasflow. first This demonstrated mechanism was by Peltierfirst demonstrated and Scinocca by [ 31Peltier] for mountainand Scinocca windstorms [31] for in mountain Boulder, CO,windstorms USA. Measurements in Boulder, andCO, numerical USA. Measurements modeling studies and numerical [28,29,32] alsomodeling showed studies that the [28,29,32] pulsations also disappear showed that in the the presence pulsations of positivedisappear vertical in the wind presence shear of above posit theive mountaintopvertical wind (e.g.,shear the above presence the mountaintop of an upper-tropospheric (e.g., the presence jet stream). of an upper-tropospheric jet stream).

(a) (b)

(c)

FigureFigure 1.1. ((aa)) TheThe AdriaticAdriatic coastcoast withwith locationslocations ofof previousprevious borabora studiesstudies markedmarked (Senj(Senj andand PometenoPometeno BrdoBrdo near the city city of of Split). Split). The The Zadar Zadar and and Zagreb Zagreb Maksimir Maksimir sounding sounding stations stations are also are alsomarked. marked. The Thebox boxrepresents represents the thearea area of this of this study. study. (b ()b shows) shows the the zoomed zoomed in in view view of of that that area, area, while while ( c) showsshows thethe zoomedzoomed inin viewview ofof thethe measurementmeasurement sitesite atat thethe MaslenicaMaslenica BridgeBridge (shown(shown asas thethe boxbox inin bb).). TheThe VelebitVelebit MountainMountain isis mostlymostly northnorth ofof thethe site.site.

Micro-scaleMicro-scale characteristicscharacteristics of severesevere turbulenceturbulence in thethe wavewave breakingbreaking regionregion areare thethe focalfocal pointpoint ofof current current bora bora research. research. In order order to to improve improve turbulence turbulence parameterization parameterization schemes schemes in in numerical numerical models,models, VeˇcenajetVečenaj et al.al. [[33]33] evaluatedevaluated turbulenceturbulence kinetickinetic energyenergy (TKE)(TKE) andand itsits dissipationdissipation raterate forfor aa borabora eventevent inin thethe towntown ofof Senj.Senj. VeˇcenajetVečenaj et al.al. [[34]34] estimatedestimated thethe turbulenceturbulence dissipationdissipation raterate alongalong thethe AdriaticAdriatic seasea coast,coast, usingusing 44 HzHz aircraftaircraft andand dropsondedropsonde datadata obtainedobtained duringduring thethe MAPMAP project.project. ForFor thethe PometenoPometeno BrdoBrdo site, site, Lepri Lepri et et al. al. [35 [35]] analyzed analyzed bora bora wind wind speed speed profiles profiles from from 5 Hz 5 dataHz data and foundand found that theythat they agreed agree withd with commonly commonly used used empirical empirical power-law power and-law theand logarithmic-law the logarithmic profiles.-law profiles. They They also foundalso found that thermalthat thermal stratification stratification of the of surface the surface layer is layer near is neutral near neutral due to strongdue to mechanical strong mechanical mixing. Usingmixing. the Using same the data, same Lepri data, et al. Lepri [1,36 ]et further al. [1,36] investigated further investigated turbulence intensity,turbulence Reynolds intensity, shear Reynolds stress andshear turbulence stress and length turbulence scale profileslength scale for the profiles mentioned for the location. mentioned location. WithoutWithout such such high high-frequency-frequency in in situ situ measurements measurements of wind of wind speed speed in space in (e.g., space aircraft (e.g., aircraftmeasurements) measurements) and in and time in time (single (single-point-point ground ground-based-based measurements measurements on on,, e.g., e.g., meteorological towers/masts),towers/masts), the the exploration exploration of of bora micro-scalemicro-scale properties would not not be be possible. possible. For a a more more comprehensivecomprehensive insight into into the the nature nature of of bora bora turbulence, turbulence, even even higher higher sampling sampling frequency frequency (e.g., (e.g., >10 >10Hz) Hz)measurements measurements are areneeded. needed. This This also also hints hints at the at thegoal goal of this of thisstudy. study. Bora has a major influence on all forms of transportation, engineering structures, electrical and telecommunication grids, agriculture, sea dynamics, air pollution, tourism, and firefighting.

Atmosphere 2018, 9, 116 4 of 25

Bora has a major influence on all forms of transportation, engineering structures, electrical and telecommunication grids, agriculture, sea dynamics, air pollution, tourism, and firefighting. Engineering structures in areas prone to severe downslope windstorms must be strong enough to withstand these hurricane force winds. Agriculture in those areas must also be adapted to such harsh conditions. Transportation is the most vulnerable human activity, since severe bora episodes can completely shut down all road traffic to and from the coast. In some extreme cases, even the air traffic at the whole eastern Adriatic coast can be completely suspended. The Maslenica Bridge is a very important transportation route, connecting the southern and central Croatian coast—the northeastern Adriatic coast—with inland parts of Croatia. The purpose of this study is to test whether some of the previous results obtained for different measuring sites apply to the Maslenica Bridge location. Namely, the turbulence averaging time scale, bora pulsations, thermal stratification, TKE budget, and wind speed profiles. Furthermore, we aim to identify possible differences in those micro-scale properties of different bora types. As this has not been attempted before, it could give new insights into the turbulence characteristics of bora wind. For this purpose, we classify bora episodes by the flow depth and the synoptic type. As already mentioned, the flow depth is important in defining the mountain wave dynamics. We think that the synoptic type (i.e., cyclonic, anticyclonic or frontal) can influence the micro-scale properties of bora mainly because of different wind speeds, but also with different vertical wind and temperature profiles (e.g., stronger inversions in anticyclones), which additionally define mountain wave dynamics. The maximum wind speeds depend on the synoptic type because anticyclones have horizontal pressure gradient limit (inertial instability) and thus can never have wind speeds as high as very deep cyclones. Finally, the flow depth itself is also dependent on synoptic situation. In the following sections, we will explain all the methods and data used, show and discuss the obtained results, summarize the main findings, and provide conclusions.

2. Methods and Data

2.1. Measurement Site and Instruments The measurement site (15.53◦ E, 44.24◦ N, 78 m ASL) is settled ≈30 km northeast of the city of Zadar and ≈200 m northeast from the Maslenica Bridge on the A1 section of the Croatian motorway (Figure1). High-frequency data were collected on a 10 m mast. WindMaster Pro ultrasonic anemometers (Gill Instruments Ltd., Lymington, UK) measured the 3D wind speed and sonic temperature at 2, 5, and 10 m levels above the ground during the period from 8 October 2015 to 11 February 2016. The data were sampled with a frequency of 20 Hz. This is the highest sampling rate for any prolonged bora in situ measurements that exist today. The anemometers were connected to a CR3000 data logger (Campbell Scientiﬁc Inc., Logan, UT, USA) and the whole system was powered by two 60 W solar panels. The ground in the immediate vicinity of the mast is characteristic for the Adriatic coastline, with prevailing bare rocks and some herb cover in the form of garrigue (low, shriveled, light scrub) and maquis (dense hard-leaf shirk).

2.2. Data Quality Check The measured data were quality checked and despiked using two methods described in [37]. Unrealistic data values were detected by using absolute limits (100 m·s−1 for the wind speed and 100 ◦C for the temperature) and linearly interpolated. Spikes were identified as three or fewer consecutive points in the time series with an amplitude larger than 3.5 standard deviations from the moving mean with a window length of 6000 data points (5 min). Spikes were also linearly interpolated and the process was repeated after increasing the standard deviation factor by 0.1 until no more spikes were detected. While interpolating the removed unrealistic data values and spikes, we kept a record of where those missing data points were located. We did this because we noticed that the interpolated continuous blocks of missing data had a negative influence on the spectral analysis (random missing data did not Atmosphere 2018, 9, 116 5 of 25 have such large influence). After despiking, we downsampled the data to 10 Hz by averaging two consecutiveAtmosphere data 2018, points9, x FOR inPEER order REVIEW to reduce the number of missing data points. After these procedures,5 of 25 the missing1% for all data analyzed were episodes, reduced with to less an exception than 1% of for one all episode analyzed where episodes, there was with 3.9% an of exceptionmissing data of one episodeat the where 5 m level. there was 3.9% of missing data at the 5 m level.

2.3. Criteria2.3. Criteria forBora for Bora Episode Episode Detection Detection and and Selection Selection To identifyTo identify bora bora episodes episodes in in the the recorded recorded data, data, we we used used 10 10-min-min averages averages of u of andu andv windv wind componentscomponents from from the 10 the m 10 level. m level.The wind The direction wind direction distributions distribution of differents of different wind speed wind speed categories visualizedcategories as the visualized wind rose as the (Figure wind2 )rose clearly (Figure indicate 2) clearly the dominantindicate the wind dominant directions wind ofdirections stronger of bora eventsstronger during bora the events measurements. during the measurements.

FigureFigure 2. The 2. The wind wind rose rose from from 10-min 10-min wind wind averages averages of all all data. data. The The wind wind speed speed catego categoryry limits limits are in are in − m·s m1,· ands−1, and the the numbers numbers on on the the plot plot indicateindicate the the relative relative frequency frequency of occurrence. of occurrence.

TheThe highest highest relative relative frequency frequency of of wind wind speed speed >10 >10 m· ms−1· sis− 1 fromis from directions directions 15°–60°. 15 Thus,◦–60◦ . we Thus, we decideddecided toto setset the wind wind direction direction criterion criterion to 40° to 40± 40°.◦ ± The40◦ .lowest The lowestwind speed wind limit speed was limit set to was 4 set to 4 mm··s−1 1inin order order to tofilter filter out outweaker weaker katabatic katabatic or other or thermally other thermally driven flows driven, while flows, still being while able still to being −1 able tocatch catch certain certain feeble feeble onsets onsets of bora. of bora. A similar A similar threshold threshold (5 m (5·s m) · wass−1 ) used was usedby Lepri by Lepri et al. et [35]. al. [35]. Furthermore, the detection algorithm required that these conditions must be satisfied for at least 6 Furthermore, the detection algorithm required that these conditions must be satisfied for at least h, with an allowed discontinuity of 1 h. This is to allow for possible weaker periods or even wind 6 h, with an allowed discontinuity of 1 h. This is to allow for possible weaker periods or even wind reversals within the bora episodes caused by lee rotor formation or low-level flow separation reversals[22,38,39]. within Bora the episodes bora episodes detected caused in this by way lee were rotor also formation visually orchecked low-level (not flowshown). separation We also [tried22,38 ,39]. Boravarying episodes the detected detection in settings, this way which were confirmed also visually that checkedthe stated (not settings shown). were Weoptimal also triedbecause varying they the detectioncaused settings, minimal which fragmentation confirmed of thatseemingly the stated whole settings bora episodes. were optimal because they caused minimal fragmentationUsing ofthese seemingly criteria, wholea total of bora 14 bora episodes. episodes were detected. For each of these episodes, the Usingsynoptic these situation criteria, was a analyzed total of using 14 bora surface episodes analysis were [40], detected. 500 hPa geopotential For each of and these mean episodes, sea the synopticlevel pressure situation analysis was [41 analyzed] (NCEP GDAS/FNLusing surface—National analysis Centers [40], 500 for Environmental hPa geopotential Prediction and mean sea levelGlobal pressure Data Assimilation analysis [41 ] System/Final (NCEP GDAS/FNL—National 0.25° × 0.25° analysis), Centers and soundings for Environmental from Zadar Prediction and Zagreb stations [42] (University of Wyoming database). Figure 1 shows the position of the sounding Global Data Assimilation System/Final 0.25◦ × 0.25◦ analysis), and soundings from Zadar and Zagreb stations in relation to the measurement site. According to this analysis, we classified all bora stations [42] (University of Wyoming database). Figure1 shows the position of the sounding stations episodes and selected the ones that unambiguously fell into one of the main bora type categories in relation(Table to1). the measurement site. According to this analysis, we classified all bora episodes and selected the ones that unambiguously fell into one of the main bora type categories (Table1). Table 1. The main bora type categories. Table 1. The main bora type categories. Bora Type Abbreviation shallow cyclonic SC Bora Type Abbreviation shallow anticyclonic SA shallowdeep cyclonic DC SC shallowdeep anticyclonic DA SA deep cyclonic DC frontal F deep anticyclonic DA frontal F

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To emphasize the relevance of the flow depth in defining the mountain wave and bora dynamics, in this work, we propose a classification of bora episodes first by flow depth and then by its synoptic setup. The criterion for determining the depth of bora flow from sounding data was that the upper wind direction must be from the direction 40◦ ± 45◦, which is similar to the one used by Smith [2]. An episode was classified as deep if this criterion was satisfied at least up to 500 hPa. Since the sounding data were available only at 00 UTC (Coordinated Universal Time) and 12 UTC, a 500 hPa geopotential height analysis was also used to subjectively assess the flow depth. Many episodes are transitional, and so may include change from cyclonic to anticyclonic (e.g., SC to SA; see Table1). In some cases, this is also accompanied by change of the flow depth (e.g., SC to DA). In transitional episodes with one dominant type, that type is emphasized with bold font (see Table2 in the Results and Discussion Section).

2.4. Bora Turbulence Spectra Before analyzing the turbulent characteristics of the selected bora episodes, an appropriate averaging time scale needs to be determined. The averaging time scale is needed to separate turbulent perturbations from the mesoscale and synoptic atmospheric motions. To separate the signals into mean and ﬂuctuating components, we used Reynolds decomposition. The basic assumption of Reynolds decomposition is the existence of a local minimum (spectral “gap”) in the power spectral densities of various turbulence quantities, such as wind speed or potential temperature [43,44]. Before Reynolds decomposition, the mean wind direction was determined for each bora episode and the coordinate system was rotated, so the x-axis points downstream of this mean wind speed. The power spectral densities were calculated for the horizontal components (u and v) of wind speed using the Welch algorithm [45] and then smoothed using the frequency window that expands in width with frequency [46]. This frequency smoothing is needed to obtain representative spectral curve from the estimates, which exhibit excessive crowding and large scatter at the high-frequency end on a logarithmic scale. Since datasets of bora episodes contain blocks of missing data, the calculation of power spectral densities was not simple. For blocks of missing data shorter than 1 s (10 data points), the missing data were replaced by linearly interpolated values. If an episode contained blocks of missing data larger than 1 s, the episode was split into smaller segments with a minimum length of 3 h and without missing data. Then the power spectral densities were calculated for every segment using a window length equal to half the length of the smallest segment of one bora episode. Finally, a spectrum for a single bora episode was created by averaging spectral estimates of every segment in the episode.

2.5. Taylor Hypothesis After ﬁnding a suitable averaging period by spectral analysis, the time series was divided into non-overlapping block intervals with the length of the mentioned period. All intervals were checked for missing data, which may corrupt the time series. Sporadic and random missing data do not appear in groups and therefore do not corrupt the time series after interpolation. If any of those intervals had more than 50% of data missing, the interval was excluded for all measurement levels. The remaining intervals were tested for Taylor’s hypothesis (TH), which allows us to transform from the space domain (wavenumber, k) to the time domain (frequency, f ). The criterion for the validity of TH is σ < 0.5U, where U is the mean horizontal wind speed and σ is the standard deviation (e.g., [44]). If the ratio of the standard deviation to mean horizontal wind speed was greater than or equal to 0.5, the corresponding intervals were omitted. Atmosphere 2018, 9, 116 7 of 25

2.6. Stability Parameter and Friction Velocity In order to analyze thermal stratiﬁcation of each bora episode, dimensionless height ζ, or stability parameter (e.g., [44]) was calculated for each block interval using the following equation: z ζ = (1) L Here, z represents the height of the observation level and L is the Obukhov length deﬁned as the height where dynamical-mechanical turbulence generation is approximately equal to the thermal-buoyancy contribution to the turbulence generation or destruction:

3 −θu∗ L = (2) gk(w0θ0) where k = 0.4 is the von Karman constant (e.g., [47]), g = 9.81 m·s−2 is acceleration due to gravity, θ is the mean virtual potential temperature, w0θ0 is local (at each measurement height) vertical kinematic heat ﬂux, and u∗ is the local friction velocity calculated as: q 4 0 0 2 0 0 2 u∗ = (u w ) + (v w ) (3)

Since the relative humidity measurements were not available, we used ultrasonic temperature values instead of potential virtual temperature for determining turbulence heat flux. According to some authors [30,48,49], the ultrasonic temperature is a good approximation of the potential temperature. The negative stability parameter implies statically unstable stratification; a positive stability parameter implies stable stratification, while the stratification is neutral when the stability parameter is equal to zero. Here, we took block intervals with absolute values of the stability parameter less than 0.02 as near-neutral, which is the same criterion that was used in [30].

2.7. Monin–Obukhov Similarity Functions Due to the intensive mechanical mixing during bora episodes, the thermal stratiﬁcation of the atmosphere is generally very close to neutral (ζ ≈ 0)[35]. However, there are periods when the value of the stability parameter deviates from zero, which means that in those periods the atmosphere is not neutrally stratiﬁed. According to the Monin–Obukhov similarity theory, during those periods, the wind shear should satisfy the following relationship

∂U u∗ = Φ (ζ) (4) ∂z m kz where U is the mean value of the streamwise wind speed (u = U + u0) and Φm(ζ) represents the following similarity function: Φm(ζ) = 1 + 4.7ζ for ζ > 0 (5) −1/4 Φm(ζ) = (1 − 15ζ) for ζ < 0 (6) In order to check the applicability of the similarity theory in bora wind cases, the block intervals were divided according to the thermal stratiﬁcation of the atmosphere into stable and unstable intervals. The experimental value of the similarity function appropriate for each block interval was calculated using the measurement data as follows:

∂U kz Φm, exp(ζ2) = (7) ∂z u∗2 where Φm, exp is the experimental value of the similarity function, ζ2 is the stability parameter at the 2 m height, and u∗2 is the friction velocity, also at the 2 m height. Since the measurement data were Atmosphere 2018, 9, 116 8 of 25 available at measurement heights of 2, 5, and 10 m, two layers were analyzed: 2–5 m and 5–10 m. The height (z) was calculated as the arithmetic mean for each layer and the wind shear (∂U/∂z) was calculated with ﬁnite differences.

2.8. Turbulence Kinetic Energy Budget TKE is a measure of turbulence intensity. Therefore, it is one of the most important variables in micrometeorology. The equations needed to examine the TKE budget and individual terms are implemented following Equations (1) and (2) in [49]. The individual terms in the TKE budget equation (e.g., [44]) describe the physical processes that generate, transport, or suppress turbulence. After rotating the coordinate system in the mean wind direction, V is globally zero for each episode. The standard assumption is that there is no subsidence (W = 0). We checked and confirmed that W was small compared to U and could be neglected. The one-dimensional, nearly horizontally homogeneous TKE budget equation can be written as (hereafter in the text e¯ will be referred to as TKE for simplicity): 0 ∂e g ∂U ∂ w e = + w0θ0 − u0w0 − − ε + Rs (8) ∂t θ ∂z ∂z IIIIIIIV where U is the mean value of the streamwise wind speed, u’ and w’ are the corresponding turbulent values. Variable ε represents the dissipation of TKE into heat by molecular viscosity, and Rs is the residual. In theory, the overbars represent suitable spatial (instead of ensemble) averaging. Since we require the validity of TH, in practice, the overbars are considered as time averaging on block intervals. Term I represents a local storage of TKE, which is equal to the increase or decrease of TKE in time at a given location due to all of the TKE production, transport, or redistribution and destruction terms. The production and destruction terms include the buoyant production/consumption (term II), which depends on the sign of the heat flux; the mechanical (shear) production (term III), which is typically positive in the surface layer because of opposite signs of the horizontal momentum fluxes and vertical wind shear; the vertical turbulent transport or redistribution of TKE by turbulent eddies (term IV); the dissipation of TKE into heat by molecular viscosity (ε); and the residual Rs containing term that describes the pressure transport of TKE. All the TKE terms, besides the dissipation rate (ε), can easily be calculated directly from the measured u, v, and w components. The local change of TKE is calculated using the central finite difference scheme. Term II is calculated for 2 m, 5 m, and 10 m separately, and the middle level (3.5 m and 7.5 m) values are obtained by averaging between the two heights. Similarly, all terms that require values from upper and lower levels are calculated for the corresponding middle level using the central finite difference scheme. In order to evaluate ε, the inertial dissipation method (IDM)—provided by Kolmogorov’s 1941 hypothesis—can be employed following Equations (7)–(9) in [50]. The same method was used by Veˇcenajin [33,34]. Finally, the residual term is calculated using all known terms by assuming the balance between the left- and right-hand sides of Equation (8).

2.9. Wind Profiles In order to investigate the agreement of the experimental data with the logarithmic-law approximation for neutral wind speed vertical profiles in the surface layer [44], statically near-neutral block intervals during bora episodes were studied. These intervals are defined as the intervals during which |ζ| < 0.02 is valid for all three levels [30]. For every interval the profile friction velocity u∗p and roughness length z0 are calculated as follows:

k(U10 − U2) u∗p = (9) ln z10 z2 Atmosphere 2018, 9, 116 9 of 25

U2 z10 z0 = z2 exp − ln (10) U10 − U2 z2 where z10 and z2 are the heights, while U10 and U2 are time-averaged mean wind speeds in the x-direction at the highest (10 m) and the lowest (2 m) levels. The vertical wind proﬁle is reconstructed with mean and median values of these parameters as: u∗p z u(z) = ln (11) k z0

Equations (9)–(11) are derived from the Equation (3), using certain approximations and parameterizations [51]. Thus, they are related to the mean, low-frequency measurements, in contrast to local friction velocity, which is related to high-frequency measurements.

3. Results and Discussion

3.1. Selected Bora Episodes Table2 shows all the detected bora episodes, classified by their types. Synoptic maps and soundings analyses indicate that four episodes are transitional with respect to flow depth (B02, B07, B08, and B11 in Table2), while in two episodes (B03 and B12) the synoptic flow changes from cyclonic to anticyclonic without significant change of the flow depth. Three episodes (B05, B10, and B14) also include passages of occluded or warm fronts, but none of the episodes exhibit typical characteristics of frontal bora type. Episode B05 is very short and partially caused by cold air advection as the surface cyclone progressed southeast, but the surface analysis did not show the corresponding surface cold front. The shortest and also the weakest episode (B10) has some characteristics of frontal bora, although surface analysis did not show a typical cold front passage, but merely a slow transition of a quasi-stationary front, as the cold air mass slowly advected from the northwest. Due to the low wind speeds and untypical character of these episodes, they were not included in our micro-scale turbulence analysis.

Table 2. All detected bora episodes. Times are in UTC. “Avg U” is the average 10-min wind speed at 10 m, “max U” is the maximum 10-min wind speed value, and “max G” is the 1-s maximum gust. All wind speeds are in m·s−1. The chosen episodes and dominant bora type are marked with bold font.

Episode Start End Duration Avg U Max U Max G Type B01 10 October 2015. 09:20 11 October 2015. 07:10 0 days 21:50 12.16 18.21 27.94 SC B02 21 October 2015. 16:00 23 October 2015. 01:40 1 day 09:40 13.35 20.12 35.68 SC/DC B03 23 October 2015. 11:30 24 October 2015. 00:30 0 days 13:00 8.08 13.53 24.18 DC/DA B04 30 October 2015. 03:30 1 November 2015. 12:30 2 days 09:00 7.16 12.88 21.02 SA B05 21 November 2015. 15:50 22 November 2015. 00:40 0 days 08:50 10.31 16.77 26.34 F/SC B06 22 November 2015. 08:20 22 November 2015. 20:10 0 days 11:50 7.44 12.26 18.60 SC B07 26 November 2015. 01:30 28 November 2015. 04:00 2 days 02:30 17.69 31.05 45.47 SC/DC B08 10 Decemebr 2015. 01:40 10 Decemebr 2015. 12:00 0 days 10:20 16.57 25.66 36.10 SA/DA B09 30 Decemebr 2015. 10:10 30 Decemebr 2015. 21:40 0 days 11:30 9.58 16.46 26.90 DA B10 3 January 2016. 12:40 3 January 2016. 19:00 0 days 06:20 5.92 9.62 16.35 SC/F B11 15 January 2016. 23:30 17 January 2016. 04:10 1 day 04:40 18.02 28.40 40.18 SC/DC B12 17 January 2016. 14:50 18 January 2016. 07:30 0 days 16:40 20.82 28.78 39.68 SC/SA B13 21 January 2016. 13:00 22 January 2016. 06:40 0 days 17:40 7.25 10.91 17.42 SA B14 3 February 2016. 22:40 4 February 2016. 16:50 0 days 18:10 19.17 25.83 37.27 F/SC

Bora B14 was predominantly of a shallow cyclonic (SC) type with a warm front passage and cold air advection following the cyclone. Non-transitional deep cyclonic (DC) bora was not detected in the recorded data. Thus, for further micro-scale analysis, we chose the following episodes: B01 (SC), B09 (DA), and B13 (SA), because they represent typical cases throughout the episode. Although B04 (SA) was longer and had a higher maximum wind speed than B13 (SA), the sounding data were missing for part of the episode, so B13 (SA) was chosen instead. Episode B13 actually had a higher Atmosphere 2018, 9, 116 10 of 25 average wind speed than B04. Additionally, note from Table2 that 1-s gust maxima are usually two to three times larger than the related 10-min speed averages at 10 m. Figure3 shows the surface analysis (NCEP GDAS/FNL) at 12 UTC on 10 October 2015, whichAtmosphere represents 2018, the9, x FOR synoptic PEER REVIEW situation after the beginning of the B01 (SC) episode. 10 of 25

Figure 3. The surface analysis (NCEP GDAS/FNL) mean sea level pressure (solid line) and geopotential Figure 3. The surface analysis (NCEP GDAS/FNL) mean sea level pressure (solid line) and height at 500 hPa (dashed line) for 12 UTC on 10 October 2015. The bora episode B01 (SC). geopotential height at 500 hPa (dashed line) for 12 UTC on 10 October 2015. The bora episode B01 The measurement(SC). The measurement site is marked site is marked with the with orange the orange star. star.

The surfaceThe surface cyclone, cyclone, with with its its center center situated situated over the the Tyrrhenian Tyrrhenian Sea, Sea, influences inﬂuences the theeastern eastern AdriaticAdriatic coast coastwith its with northeastern its northeastern quadrant. quadrant. A more A detailed more detailed analysis analysis of the surface of the surface and upper-level and featuresupper reveal-level strong features surface reveal pressure strong gradientssurface pressure over the gradients Dinaric over Alps the and Dinaric an upper-level Alps and trough an at 500 hPaupper with-level winds trough from at 500 the hPa south. with This winds is from a typical the south. situation This foris a SCtypical bora situation type. for SC bora type. The ZagrebThe Zagreb 12 UTC12 UTC sounding sounding for for the the samesame dayday (Figure 4a)4a) is is not not ideally ideally upstream upstream from from the the measuringmeasuring tower tower (it is(it more is more to to the the north north compared compared to low low-level-level wind, wind, which which is more is more from from the e theast), east), but it still reflects the vertical structure of upstream bora conditions in lower levels. At the same but itbut still it reﬂects still reflects the vertical the vertical structure structure of upstream of upstream bora bora conditions conditions in in lower lower levels. levels. At At the the same same time, time, the Zadar sounding (Figure 4b) shows that the bora layer ends above 850 hPa, which the Zadar sounding (Figure4b) shows that the bora layer ends above 850 hPa, which corresponds to corresponds to an inversion visible at around 800 hPa. an inversion visible at around 800 hPa.

(a) (b)

FigureFigure 4. The 4. The skew-T skew- log-PT log-P graph graph ofof soundingsounding data data from from the the Zagreb Zagreb (a) and (a) Zadar and Zadar (b) stations (b) stations at 12 at 12 UTCUTC on on 10 10 October October 2015. 2015. BoraBora episodeepisode B01 B01 (SC). (SC). The The vertical vertical axis axis (pressure) (pressure) is in is hPa in hPaand andhorizontal horizontal axis (temperature) is in °C. axis (temperature)axis (temperature) is in is◦ inC. °C.

AtmosphereAtmosphere 20182018,, 99,, 116x FOR PEER REVIEW 11 of 25 Atmosphere 2018, 9, x FOR PEER REVIEW 11 of 25

Figure 5a shows the time series of 10 Hz streamwise wind speed (u) at the 10 m level for the FigureFigure5 a5a shows shows the the time time series series of of 10 10 Hz Hz streamwise streamwise wind wind speed speed ( (uu)) atat thethe 1010 mm levellevel forfor thethe bora B01. borabora B01.B01.

Figure 5. (a) Bora episode (B01) streamwise wind speed (u) downsampled to 10 Hz. The white line is FigureFigure 5.5.( (aa)) BoraBora episodeepisode (B01)(B01) streamwisestreamwise windwind speedspeed ((uu)) downsampleddownsampled to to 10 10 Hz. Hz. TheThe whitewhite lineline isis the 10-min moving average. (b) The zoomed 60 min of the same data with 1-min moving average is thethe 10-min10-min moving moving average. average. ( b(b)) The The zoomed zoomed 60 60 min min of of the the same same data data with wit 1-minh 1-min moving moving average average is in is in red color. redin red color. color.

TheThe zoomedzoomedzoomed wind windwind speed speedspeed data datadata with withwith a 1-min aa 11--minmin moving movingmoving average averageaverage (Figure (Figure(Figure5b) shows 5b)5b) showsshows the pulsations thethe pulsationspulsations with −1 anwithwith amplitude anan amplitudeamplitude of more ofof more thanmore 10 thanthan m· 10s10− 1 mmand··ss−1 andvaryingand varyingvarying periods periodsperiods on a on scaleon aa scalescale of around ofof aroundaround 5 min. 55 min.min. ForFor episodeepisodeepisode B09 B09B09 (DA) (DA)(DA) surface surfacesurface analysis analysisanalysis at 12atat UTC1212 UTCUTC on 30 onon December 3030 DecDecemberember 2015 (Figure20152015 (Figure(Figure6) features 6)6) featuresfeatures a strong aa anticyclonestrongstrong anticycloneanticyclone (1045 hPa (1045(1045 at thehPahPa center) atat thethe center) inﬂuencingcenter) influencinginfluencing most of mostmost Europe ofof EuropeEurope (a larger-area (a(a largerlarger surface--areaarea surfacesurface analysis analysisanalysis can be foundcancan bebe at foundfound [40]). atat [40][40]).).

FigureFigure 6.6. AsAs withwith FigureFigure3 3,3,, but butbut for forfor B09 B09B09 (DA); (DA);(DA); 12 1212 UTC UTCUTC on onon 30 3030 December DecDecemberember 2015. 2015.2015.

At the same time, which is approximately 2 h after the beginning of the B09 episode, 500 hPa AtAt tthehe samesame time,time, whichwhich isis approximatelyapproximately 22 hh afterafter thethe beginningbeginning ofof thethe B09B09 episode,episode, 500500 hPahPa geopotential height (Figure6) shows the western ﬂank of an upper-level trough, passing over the geopotentialgeopotential heightheight (Figure(Figure 6)6) showsshows thethe westernwestern flankflank ofof anan upperupper--levellevel trough,trough, passingpassing overover thethe BlackBlack SeaSea region.region. ThisThis combinationcombination ofof thethe surfacesurface andand upperupper levellevel feafeaturestures providesprovides N/NEN/NE windswinds throughoutthroughout thethe troposphere.troposphere.

Atmosphere 2018, 9, 116 12 of 25

BlackAtmosphere Sea 2018 region., 9, x FOR This PEER combination REVIEW of the surface and upper level features provides N/NE winds12 of 25 Atmospherethroughout 2018 the, 9, x troposphere. FOR PEER REVIEW 12 of 25 DeepDeep N/NE N/NE flow ﬂow can can also be seen in the Zagreb sounding sounding (Figure7 7a),a), together together with with strong strong Deep N/NE flow can also be seen in the Zagreb sounding (Figure 7a), together with strong subsidencesubsidence inversion inversion at at 800 800 hPa—a hPa— typicala typical signature signature of such of a such strong a anticyclone. strong anticyclone. The Zadar The sounding Zadar subsidence inversion at 800 hPa—a typical signature of such a strong anticyclone. The Zadar (Figuresounding7b) (Figure features 7b) a similar features wind a similar proﬁle, wind with profile, somewhat with weakersomewhat subsidence weaker subsidence inversion. inversion. sounding (Figure 7b) features a similar wind profile, with somewhat weaker subsidence inversion.

(a) (b) (a) (b) Figure 7. As with Figure 4, but for the bora episode B09 (DA); 12 UTC on 30 December 2015. FigureFigure 7. As 7. withAs withFigure Figure 4, but4, butfor the for bora the bora episode episode B09 B09(DA); (DA); 12 UTC 12 UTC on 30 on Dec 30 Decemberember 2015. 2015. Figure 8 shows the time series of streamwise wind speed (u) at the 10 m level for bora B09. Figure 88 showsshows thethe timetime seriesseries ofof streamwisestreamwise wind wind speedspeed ((u)) atat thethe 1010 mm levellevel forfor borabora B09.B09.

Figure 8. As with Figure 5, but for the bora episode B09 (DA). Figure 8. AsAs with with Figure 55,, butbut forfor thethe borabora episodeepisode B09B09 (DA).(DA). The bora episode B09 has somewhat lower wind speeds in the middle and higher wind speeds The bora episode B09 has somewhat lower wind speeds in the middle and higher wind speeds after the beginning and before the weaker end of the episode. The zoomed data (Figure 8b) with after the beginning and before the weaker end of the episode.episode. The zoomed data (Figure 88b)b) withwith 1-min moving average shows the superposition of pulsations with varying periods (around 3–5 1-min1-min movingmoving average average shows shows the the superposition superposition of pulsationsof pulsations with with varying varying periods periods (around (around 3–5 min). 3–5 min). Some of the pulsations have estimated amplitudes over 10 m·s−1. min).Some Some of the of pulsations the pulsations have estimatedhave estimated amplitudes amplitudes over 10 over m· s10−1 m. ·s−1. The surface analysis at 00 UTC on 22 January 2016 (Figure 9), 11 h after the beginning of the B13 The surface analysis at 00 UTC on 22 Jan Januaryuary 2016 (F (Figureigure 99),), 1111 hh afterafter thethe beginningbeginning ofof thethe B13B13 episode (SA), shows a weak anticyclone with the center over Central Europe. episode (SA), shows a weak anticyclone with the center over Central Europe.

Atmosphere 2018, 9, 116 13 of 25 Atmosphere 2018, 9, x FOR PEER REVIEW 13 of 25 Atmosphere 2018, 9, x FOR PEER REVIEW 13 of 25

Figure 9. As with Figure 3, but for B13 (SA); 00 UTC on 22 January 2016. Figure 9. As with Figure 33,, butbut forfor B13B13 (SA);(SA); 0000 UTCUTC onon 2222 JanuaryJanuary 2016.2016.

A more more detailed detailed analysis analysis shows shows that that the thestrongest strongest surface surface pressure pressure gradients gradients are over are the over Dinaric the Alps,Dinaric while Alps, the while 500 hPathe 500 NW hPa (northwesterly) NW (northwesterly) winds at winds the western at the western ﬂank of flank the upper-level of the upper trough-level dominatetrough dominate the area. the area. The Zagreb sounding at 00 UTC on 22 JanuaryJanuary 2016 (Figure 1010a)a) displays a shallow NE wind layer, cappedcapped by an inversioninversion at 850 hPa, with NW NW winds winds throughout throughout the the rest rest of of the the troposphere. troposphere. Zadar sounding (Figure 1010b)b) also shows a shallow NE wind layer, capped by a very stable layer and with NWNW windswinds above.above.

(a) (b) Figure 10. As with Figure 4, but for B13 (SA); 00 UTC on 22 January 2016. Figure 10. As with Figure 44,, butbut forfor B13B13 (SA);(SA); 0000 UTCUTC onon 2222 JanuaryJanuary 2016.2016.

The time series series of of streamwise streamwise wind wind speed speed (u (u) )at at the the 10 10 m m level level for for this this episode episode can can be beseen seen in inFigure Figure 11. 11 .

Atmosphere 2018, 9, 116 14 of 25 AtmosphereAtmosphere 2018 2018, 9,, 9x, FORx FOR PEER PEER REVIEW REVIEW 1414 of of25 25

FigureFigureFigure 11. 11.11. As As with with Figure Figure 55, 5,but, but but for for for the the the bora bora bora episode episode episode B13 B13 B13 (SA). (SA). (SA).

AsAsAs in inin the thethe previous previousprevious two twotwo episodes, episodes,episodes, a aa1 - 1-min1min-min moving movingmoving average averageaverage of ofof the thethe zoomed zoomedzoomed data datadata (Figure (Figure(Figure 11b) 1111b)b) also alsoalso showsshowsshows pulsating pulsatingpulsating behavior behaviorbehavior with withwith estimated estimatedestimated amplitudes amplitudesamplitudes around aroundaround 5 55m mm·s·−1·ss− −1and1 andand periods periods periods around around around 5 5min. 5 min. min.

3.2.3.2.3.2. Bora Bora Spectra SpectraSpectra FrequencyFrequencyFrequency weighted weightedweighted power powerpower spectral spectralspectral densities densitiesdensities were werewere calculated calculatedcalculated and andand smoothed smoothedsmoothed (Section (Section(Section 2.4) 2.42.4) )for forfor horizontalhorizontalhorizontal wind windwind components componentscomponents at at levels levels 2, 2, 5, 5,5, and andand 10 1010 m mm for forfor all allall episodes. episodes.episodes. In In Figure Figure 12, 1212, the, thethe spectra spectraspectra are areare shownshownshown for forfor three threethree selected selectedselected bora borabora episodes episodesepisodes (B01, (B01,(B01, B09, B09,B09, and andand B13). B13).B13).

FiFigureFiguregure 12. 12. 12. A A log log-linearlog-linear-linear representation representation of of the the the frequency frequency-weighted frequency-weighted-weighted power power spectral spectral spectral densities densities densities of of of the the the longitudinallongitudinallongitudinal (u (()u component)) componentcomponent (a (,ac,,ec,),e and) and lateral lateral (v ()v component) componentcomponent (b (,bd,,df), fof) of the the wind wind speed speed at atlevels levels 2, 2,5, 5, andandand 10 1010 m, m,m, for forfor the thethe three threethree selected selectedselected bora borabora episodes episodes;episodes; (;a ((,aba,,)bb B01)) B01B01 (SC); (SC);(SC); (c (,(cdc,,)dd )B09) B09B09 (DA); (DA);(DA); (e ((,efe,),f f)B13) B13B13 (SA (SA).(SA). )Thick. ThickThick dasheddasheddashed black blackblack vertical verticalvertical lines lineslines indicate indicateindicate the thethe 30 30-min30-min-min and andand 5- 5-min5min-min periods. periods.periods.

ItIt Itis isis clearly clearlyclearly visible visible visible that that thethe the uu component ucomponent component contains contains contains more more more energy energy energy than than than the thev thecomponent v vcomponent component for allfor for three all all threetypesthree types oftypes bora of of (notebora bora (note the (note y-axis the the y ranges), -yaxis-axis ranges), ranges), which waswhich which expected was was expected expected due to thedue due initial to to the rotationthe initial initial ofrotation rotation the coordinate of of the the coordinatecoordinate system. system. Additionally, Additionally, as as expected expected, the, the data data at at 10 10 m m contain contain a ahigher higher amount amount of of energy energy thanthan the the data data at at 5 5and and 2 2m m at at the the lower lower frequency frequency band. band. Howe However,ver, the the data data at at 2 2m m contains contains a ahigher higher

Atmosphere 2018, 9, 116 15 of 25

Atmosphere 2018, 9, x FOR PEER REVIEW 15 of 25 system. Additionally, as expected, the data at 10 m contain a higher amount of energy than the data at 5amount and 2 mof at en theergy lower at a frequency higher frequency band. However, band than the the data data at 2 at m contains10 and 5 am. higher Differences amount in of spectra energy atbetween a higher the frequency u and v components band than the are data larger at 10 for and the 5 bora m. Differences episodes with in spectra stronger between winds the (B01u and vB09),components depending are on larger a frequency for the band bora episodesin which withthe energy stronger is observed. winds (B01 and B09), depending on a frequencyThe appropriate band in which turbulence the energy averaging is observed. time scale had to be estimated in order to proceed with the analysisThe appropriate (Section 2.4). turbulence In this study, averaging we have time chosen scale had to do to beit in estimated a subjective in order way, tolooking proceed only with at the analysispower spectral (Section densities 2.4). In and this study,bearing we in havemind chosen some most to do rece it innt a bora subjective turbulence way, lookingresearch only [1,30]. at theA minimum power spectral of energy densities (energy and “gap bearing”) in infrequency mind some-weighted most recent power bora spectra turbulence for bora research episodes [1 ,B0130]. A(SC) minimum and B09 of (DA) energy is located (energy near “gap”) the infrequency frequency-weighted corresponding power to the spectra 30-min for period. bora episodes Spectra B01for (SC)bora and episode B09 (DA) B13 (SA) is located do not near show the a frequency clear minimum corresponding like they to did the 30-min for B01 period. and B09 Spectra or, more for boraprecisely, episode the B13energy (SA) from do not large show-scale a clear motions minimum (the left like side they of did thefor spectrum) B01 and is B09 missing. or, more Regardless precisely, theof the energy missing from energy, large-scale there motions is a significant (the left side difference of the spectrum) in the energy is missing. between Regardless periods of of the 30 missing and 5 energy,min, and there we can is a significantsay that there difference is also an in theenergy energy gap between in the spectra periods for of bora 30 and episode 5 min, B13. and we can say that thereSince is the also energy an energy gap gap is located in the spectra between for 15 bora and episode 40 min, B13. we may use a 30-min time period followingSince the the instructions energy gap provided is located in between Section 2.5. 15 andThis 40is in min, accordance we may wi useth a[52] 30-min for the time nocturnal period followingstable boundary the instructions layer in the provided Croatian in Sectionlowland 2.5 (town. This of is Kutina), in accordance while withBabić [52 et] al. for [30] the nocturnalfound an stableenergy boundary gap at the layer 15- inmin the period Croatian for lowland bora episodes (town of at Kutina), Pometeno while Brdo, Babićet northeast al. [30] from found the an energycity of gapSplit. at Hence, the 15-min all further period analyses for bora wer episodese performed at Pometeno on block Brdo, intervals northeast of 30 from min the length. city of Split. Hence, all furtherThere analysesis an energy were peak performed in both on the block u and intervals v component of 30 min of length.the given power spectral densities, betweenThere the is anperiods energy of peak ≈2 and in both 8 min. the u Theand venergycomponent peaks of are the most given likely power related spectral to densities, bora pulsations between the[11,28,29] periods, which of ≈2 can and also 8 min. be The seen energy in the peaksu time are series most (Figures likely related 5, 8, and to bora 11). pulsations The power [11 spectral,28,29], whichdensity can of also bora be episode seen in B09 the u showstime series a large (Figures peak between5,8 and 11 periods). The power 104 s and spectral 103 density s. This isof at bora the episodelowest end B09 of shows the pulsations a large peak similar between to that periods in [53]. 104 Spectral s and 103analysis s. This did is not at theshow lowest any endsignificant of the pulsationsdifference in similar power to spectral that in [densities53]. Spectral between analysis bora did episodes not show B01 any (SC) significant and B13 (SA). difference Other inthan power the spectralpeak in the densities B09 (DA) between spectra, bora which episodes could B01 be (SC) related and to B13 different (SA). Other flow than dynamics the peak (deep in the bora), B09 there (DA) spectra,is no clear which connection could be between related the todifferent power spectral flow dynamics densities (deep of different bora), therebora episodes is no clear and connection the type betweenof bora. the power spectral densities of different bora episodes and the type of bora.

3.3. Friction Velocity and Stability Parameter Time series of friction velocity calculated from turbulent ﬂuxesfluxes (Section 2.62.6,, Equation (3)), for all three levels of bora B01 (SC) are shown in Figure 1313.. The friction velocity time series is closely related to the TKE time series (not shown).shown).

Figure 13. The time series of friction velocity (푢∗) for bora B01 (SC). The blue line is 푢∗ at 2 m, the Figure 13. The time series of friction velocity (u∗) for bora B01 (SC). The blue line is u∗ at 2 m, the green green line is at 5 m, and the magenta line is at 10 m. line is at 5 m, and the magenta line is at 10 m.

Figure 13 shows that lower values of friction velocity appear at the beginning and at the end of the bora episode. Comparing this figure to Figure 5, it can be seen that the friction velocity is closely related to the streamwise wind speed (u). It should also be noted that the friction velocity values are

Atmosphere 2018, 9, 116 16 of 25

Figure 13 shows that lower values of friction velocity appear at the beginning and at the end of the bora episode. Comparing this ﬁgure to Figure5, it can be seen that the friction velocity is closely Atmosphere 2018, 9, x FOR PEER REVIEW 16 of 25 relatedAtmosphere to 2018 the, 9 streamwise, x FOR PEER windREVIEW speed (u). It should also be noted that the friction velocity values16 of are 25 generally highest at the 5 m level. In total, the bora B01 (SC) has 43 30-min30-min blocks, with all blocks generally highest at the 5 m level. In total, the bora B01 (SC) has 43 30-min blocks, with all blocks satisfying Taylor’s hypothesis (TH, Section 2.52.5).). satisfying Taylor’s hypothesis (TH, Section 2.5). The B09 bora (DA) (Figure 1414)) is relatively short,short, and thus has only 23 30-min30-min blocks,blocks, of which The B09 bora (DA) (Figure 14) is relatively short, and thus has only 23 30-min blocks, of which three blocks at the end of the episode did not satisfy TH (Section 2.5).2.5). Such Such invalid invalid blocks blocks are are usually three blocks at the end of the episode did not satisfy TH (Section 2.5). Such invalid blocks are usually located at the beginning or the end of t thehe episode, where turbulence intensity seems to be the highest located at the beginning or the end of the episode, where turbulence intensity seems to be the highest (i.e., large large standard standard deviation deviation of relativelyof relatively low low wind wind speed). speed). Nevertheless, Nevertheless, Figure Figure 14 shows 14 that shows friction that (i.e., large standard deviation of relatively low wind speed). Nevertheless, Figure 14 shows that velocityfriction velocity is closely is related closely to related the wind to speedthe wind for thisspeed episode for this as wellepisode (Figure as well8). This (Figure also explains8). This also the friction velocity is closely related to the wind speed for this episode as well (Figure 8). This also lowerexplains friction the lower velocity friction values velocity in the values middle in of the this middle episode, of this as the episode, wind speed as the was wind also speed lower was in also that explains the lower friction velocity values in the middle of this episode, as the wind speed was also partlower of in the that episode. part of the episode. lower in that part of the episode.

Figure 14. As with Figure 13, but for the bora episode B09 (DA). Figure 14. As with Figure 13, but for the bora episode B09 (DA). Interestingly, for this episode, the friction velocity at the 5 m level is also higher than at the Interestingly, forfor this this episode, episode the, the friction friction velocity velocity at theat the 5 m 5 levelm level is also is also higher higher than atthan the at other the other two levels. twoother levels. two levels. Bora B13 (SA), in Figure 15, has 35 30-min blocks, of which one block near the end of the episode Bora B13 (SA) (SA),, in Figure 15, has 35 30 30-min-min bloc blocks,ks, of which one block near the end of the episode was discarded. was discarded.

Figure 15. As with Figure 13, but for the bora episode B13 (SA). Figure 15. As with Figure 13, but for the bora episode B13 (SA). Figure 15. As with Figure 13, but for the bora episode B13 (SA). As with the other two episodes (B01 and B09), a close relation between wind speed (Figure 11) As with the other two episodes (B01 and B09), a close relation between wind speed (Figure 11) and friction velocity can easily be seen. For this episode, the friction velocity at 5 m is also higher and friction velocity can easily be seen. For this episode, the friction velocity at 5 m is also higher than at the other two levels. than at the other two levels. The distribution of friction velocity for each bora episode at different vertical levels is shown in The distribution of friction velocity for each bora episode at different vertical levels is shown in Figure 16. For the bora episode B01 (SC), two maxima occur at the lower levels. The first one (located Figure 16. For the bora episode B01 (SC), two maxima occur at the lower levels. The first one (located around 0.7–0.8 m·s−1) probably corresponds to the moderate wind speeds at the beginning and the around 0.7–0.8 m·s−1) probably corresponds to the moderate wind speeds at the beginning and the

Atmosphere 2018, 9, 116 17 of 25

As with the other two episodes (B01 and B09), a close relation between wind speed (Figure 11) and friction velocity can easily be seen. For this episode, the friction velocity at 5 m is also higher than at the other two levels. The distribution of friction velocity for each bora episode at different vertical levels is shown in AtmosphereFigure 16 2018. For, 9 the, x FOR bora PEER episode REVIEW B01 (SC), two maxima occur at the lower levels. The ﬁrst one (located17 of 25 around 0.7–0.8 m·s−1) probably corresponds to the moderate wind speeds at the beginning and the end of the episode, while the other one, which is larger (located around 0.9–1 m·s−1), could be a result end of the episode, while the other one, which is larger (located around 0.9–1 m·s−1), could be a result of the wind speed increase during the more developed part of the episode. of the wind speed increase during the more developed part of the episode.

Figure 16. Frequency distribution of friction velocity for: the B01 (a–c), B09 (d–f), and B13 (g–i) bora Figure 16. Frequency distribution of friction velocity for: the B01 (a–c), B09 (d–f), and B13 (g–i) bora episodes; at three different vertical levels: 2 m (a,d,g), 5 m (b,e,h), and 10 m (c,f,i). episodes; at three different vertical levels: 2 m (a,d,g), 5 m (b,e,h), and 10 m (c,f,i). This bimodality is less pronounced at the highest level, where the friction velocity distribution This bimodality is less pronounced at the highest level, where the friction velocity distribution tends to look more near-normal with similar mean and median values (Table3). This shift towards tends to look more near-normal with similar mean and median values (Table 3). This shift towards near-normal distribution is in better agreement with the results found in [35]. near-normal distribution is in better agreement with the results found in [35]. –1 TableOther 3. twoThe anticyclonic summary statistics bora ofepisodes the friction seem velocity to haveu∗ (m such·s ) distribution for each bora types episode shifted at selected towards lowervertical values levels. of friction velocity (maximum located around 0.5 m·s−1) compared to bora B01 (SC). A slight negative skewness can be noticed for those bora episodes, and is also evident as somewhat larger mediansEpisode compared Height to the (m) corresponding Mean mean Med friction Max velocity. Min SD 2 0.782 0.830 1.051 0.384 0.177 –1 Table 3.B01 The (SC) summary statistics5 of the 0.838 friction velocity 0.832 푢∗ (m 1.118·s ) for each 0.465 bora episode 0.171 at selected vertical levels. 10 0.739 0.737 1.051 0.299 0.186

Episode2 Height 0.580(m) Mean 0.592 Med 0.892Max Min 0.247 SD 0.177 B09 (DA) 5 0.656 0.681 0.999 0.246 0.214 102 0.4350.782 0.421 0.830 0.6791.051 0.384 0.171 0.177 0.154 B01 (SC) 5 0.838 0.832 1.118 0.465 0.171 2 0.454 0.477 0.673 0.106 0.138 B13 (SA) 510 0.4970.739 0.530 0.737 0.7011.051 0.299 0.153 0.186 0.135 102 0.4190.580 0.451 0.592 0.6220.892 0.247 0.171 0.177 0.120 B09 (DA) 5 0.656 0.681 0.999 0.246 0.214 Other two anticyclonic bora episodes10 seem0.435 tohave 0.421 such distribution0.679 0.171 types 0.154 shifted towards lower values of friction velocity (maximum2 located0.454 around 0.477 0.5 m ·s−0.6731) compared 0.106 to0.138 bora B01 (SC). A slight negative skewnessB13 can (SA) be noticed for5 those bora0.497 episodes,0.530 and0.701 is also0.153 evident 0.135 as somewhat larger medians compared to the corresponding10 mean0.419 friction 0.451 velocity. 0.622 0.171 0.120 The stability parameter distribution is shown in Figure 17. In order to compare the stability parametersThe stability between parameter different distribution bora episodes, is theshown width in of Figure the bin 17. was In order kept the to same compare (0.02). the stability parameters between different bora episodes, the width of the bin was kept the same (0.02).

Atmosphere 2018 9 Atmosphere 2018,, 9,, 116x FOR PEER REVIEW 18 of 25

Figure 17. The stability parameter ζ distribution for the B01 (a–c), B09 (d–f), and B13 (g–i) bora episodes Figure 17. The stability parameter ζ distribution for the B01 (a–c), B09 (d–f), and B13 (g–i) bora at three different vertical levels: 2 m (a,d,g), 5 m (b,e,h), and 10 m (c,f,i). episodes at three different vertical levels: 2 m (a,d,g), 5 m (b,e,h), and 10 m (c,f,i). The largest number of stability parameter values is grouped around zero, in accordance with The largest number of stability parameter values is grouped around zero, in accordance with the near-neutral thermal stratification of bora due to intensive mechanical mixing. This was also the near-neutral thermal stratification of bora due to intensive mechanical mixing. This was also found for a summer bora episode in [35] and is especially visible at two lower levels, where most found for a summer bora episode in [35] and is especially visible at two lower levels, where most of of the ζ are between −0.02 and 0.02. At the 10 m level, the frequency of those quasi-neutral cases the ζ are between −0.02 and 0.02. At the 10 m level, the frequency of those quasi-neutral cases is is lower compared to the 2 and 5 m level distributions, because more statically stable cases appear. lower compared to the 2 and 5 m level distributions, because more statically stable cases appear. Stable cases occur during nights when the heat flux is negative and the dynamical effects are either not Stable cases occur during nights when the heat flux is negative and the dynamical effects are either well developed or weakened [54]. The mean values of stability parameters are in general larger than not well developed or weakened [54]. The mean values of stability parameters are in general larger the corresponding medians for the selected bora episodes (Table4). No significant difference related to than the corresponding medians for the selected bora episodes (Table 4). No significant difference the bora type was observed in the stability parameter distribution. related to the bora type was observed in the stability parameter distribution. Table 4. The summary statistics of the stability parameter ζ for each bora episode at selected verticalTable 4.levels. The summary statistics of the stability parameter ζ for each bora episode at selected vertical levels.

EpisodeEpisode Height Height (m) (m) Mean Mean MedMed Max Max Min MinSD SD 22 0.0030.003 0.0030.003 0.011 0.011 0.000 0.0000.002 0.002 B01 (SC)B01 (SC) 55 0.0080.008 0.0080.008 0.024 0.024 0.000 0.0000.005 0.005 10 0.025 0.020 0.147 −0.010 0.028 10 0.025 0.020 0.147 −0.010 0.028 2 0.007 0.003 0.026 0.000 0.008 2 0.007 0.003 0.026 0.000 0.008 B09 (DA) 5 0.018 0.001 0.126 −0.003 0.038 B09 (DA) 105 0.1980.018 0.0450.001 0.126 1.160 −0.003− 0.0040.038 0.307 10 0.198 0.045 1.160 −0.004 0.307 2 0.027 0.004 0.617 −0.021 0.106 B13 (SA) 52 0.0390.027 0.0090.004 0.617 0.401 −0.021− 0.0170.106 0.093 B13 (SA) 105 0.0990.039 0.0280.009 0.401 0.815 −0.017− 0.3010.093 0.223 10 0.099 0.028 0.815 −0.301 0.223 3.4. Monin–Obukhov Similarity Functions 3.4. Monin–Obukhov Similarity Functions The experimental values of the similarity functions (Φm, exp) and the values obtained using the theoreticalThe experimental Equations (5)values and (6)of the in Sectionsimilarity 2.7 functions are shown (훷 in푚,푒푥푝 Figure) and 18 the with values respect obtained to the using stability the parametertheoretical ζEquations. (5) and (6) in Section 2.7 are shown in Figure 18 with respect to the stability parameter 휁.

Atmosphere 2018, 9, 116 19 of 25 Atmosphere 2018, 9, x FOR PEER REVIEW 19 of 25

Figure 18. The experimental similarity function values averaged over 30-min30-min intervals. The The blue, magenta, and black markers denote the intervals from episode B01, B09, B09, and and B13 B13,, respectively, respectively, compared toto thethe theoreticaltheoretical values values of of the the similarity similarity functions functions (red (red lines), lines), for thefor staticallythe statically unstable unstable (a,c) (anda,c) stableand stable (b,d) ( surfaceb,d) surface layer. layer.

The intervalsintervals withwith unstable unstable thermal thermal stratification stratification are are shown shown in thein diagramsthe diagrams on the on left, the andleft, those and withthose stable with stratification stable stratification on the right. on There the right. is a significant There is discrepancy a significant between discrepancy the experimental between and the the theoretical values, especially for ζ2 > 0 in the higher layer (5–10 m layer; Figure 18d). Furthermore, experimental and the theoretical values, especially for 휁2 > 0 in the higher layer (5–10 m layer; theFigure diagrams 18d). Furthermore, on the right (Figurethe diagrams 18b,d) on showing the right stable (Figure intervals 18b,d) show showing relatively stable high intervals dispersion show ofrelatively the experimental high dispersion values, of especially the experimental in the higher values, level. especially Unfortunately, in the higher the diagrams level. Unfortunately, showing the unstablethe diagrams intervals showing do not the contain unstable enough intervals data points do not for contain dispersion enough evaluation. data points Nevertheless, for dispersion it can beevaluation. noticed thatNevertheless, the experimental it can b valuese noticed of the that similarity the experimental functions values are generally of the similarity close to 1. functions This is to beare expected,generally sinceclose althoughto 1. This theis to stability be expected parameter, since is although positive the or negative,stability parameter its absolute is valuepositive stays or low—meaningnegative, its absolute that the value stratification stays low is— mostlymeaning close that to the neutral. stratification is mostly close to neutral. In the lower layer (2–5(2–5 m), the experimental values have lower dispersion (Figure (Figure 18a,b)18a,b).. Furthermore, they show a reasonable trend of increase when the lowest part of the atmosphere becomes more statically stable, and decrease when it become becomess more unstable, which is in accordance with the theoretical expressions. This trend is not so obvious in the upper layer (5–10(5–10 m). It can be concluded that that the the universal universal similarity similarity functions functions are arerelatively relatively successful successful at describing at describing the wind the profile wind inprofile the lower in the part lower of thepart surface of the layer,surface but layer, fail to but give fail reliable to give results reliable above results a certain above height. a certain Therefore, height. theTherefore, use of thethe universaluse of the similarity universal functionssimilarity should functions probably should be probably avoided be in avoided case of bora in case wind of orbora at leastwind usedor at withleast caution.used with caution. The reason reason the the similarity similarity functions functions do notdo notgive give good good results results in the incase the of casebora windof bora most wind probably most liesprobably in the lies failure in the of failure the main of the assumptions main assumptions on which on the which similarity the similarity theory is theory based—that is based the—that surface the layersurface is quasi-stationary,layer is quasi-stationary, horizontal, horizontal, and homogeneous. and homogeneous. For a more For detailed a more analysis, detailed it analy wouldsis, be it necessarywould be necessary to look at ato larger look at number a larger of number bora episodes. of bora episodes. 3.5. Turbulence Kinetic Energy Budget 3.5. Turbulence Kinetic Energy Budget Figure 19 represents the TKE budget terms as defined in Equation (8) (Section 2.8) for the three Figure 19 represents the TKE budget terms as defined in Equation (8) (Section 2.8) for the three selected bora episodes: B01 (SC; Figure 19a), B09 (DA; Figure 19b) and B13 (SA; Figure 19c). selected bora episodes: B01 (SC; Figure 19a), B09 (DA; Figure 19b) and B13 (SA; Figure 19c).

Atmosphere 2018, 9, 116 20 of 25 Atmosphere 2018, 9, x FOR PEER REVIEW 20 of 25

(a)

(b)

(c)

Figure 19. The turbulence kinetic energy (TKE) terms calculated on the two middle levels: 3.5 m (left) Figure 19. The turbulence kinetic energy (TKE) terms calculated on the two middle levels: 3.5 m (left) and 7.5 m (right). Term III (mechanical production) in the solid black line, term II (buoyant and 7.5 m (right). Term III (mechanical production) in the solid black line, term II (buoyant production) production) is the solid blue, dissipation is the solid red line, and the residual term is in dashed red. is the solid blue, dissipation is the solid red line, and the residual term is in dashed red. (a) B01 (SC), ((ba)) B09 B01 (DA), (SC), and (b) B09 (c) B13 (DA), (SA). and The (c) correlation B13 (SA). Thecoefﬁcient correlation between coefficient the mechanical between production the mechanical and dissipationproduction isand ~− dissipation0.9, and between is ~−0.9, the and buoyancy between term the buoyancy and residual term is and 0.8 and residual 0.5 on is the0.8 3.5and and 0.5 7.5on middlethe 3.5 and levels, 7.5respectively. middle levels, respectively.

TheThe shearshear termterm dominatesdominates inin allall three three episodes episodes (with (with a a maximum maximum magnitude magnitude of of 1 1 m m2·s2·−s−33 duringduring thethe mostmost intenseintense phasephase ofof thethe selectedselected borabora episodes)episodes) meaningmeaning thatthat thethe kinetickinetic energyenergy isis extractedextracted fromfrom thethe meanmean ﬂowflow andand transformedtransformed intointo thethe TKE.TKE. ToTo preservepreserve thethe TKETKE balance,balance, thethe residualresidual termterm (with(with aa minimumminimum magnitudemagnitude ofof −−0.30.3 m m22·s·−3s−) 3and) and dissipa dissipationtion term term (with (with a minimum a minimum magnitude magnitude of of−1 m2·s−3) are mostly negative for all episodes, decreasing the TKE in the layer considered here. Negative mechanical production (and the positive residual term), which is visible in the B09 episode,

Atmosphere 2018, 9, 116 21 of 25

−1 m2·s−3) are mostly negative for all episodes, decreasing the TKE in the layer considered here. Atmosphere 2018, 9, x FOR PEER REVIEW 21 of 25 Negative mechanical production (and the positive residual term), which is visible in the B09 episode, is probably due toto the local non-stationaritynon-stationarity of u’ in the corresponding 30 30-min-min interval [55]. [55]. We also found a minimum in the TKE (not shown) and u∗ time series (Figure 14) corresponding to this block found a minimum in the TKE (not shown) and 푢∗ time series (Figure 14) corresponding to this block interval with a negative mechanical production. The other TKE terms togethertogether contribute with only a small portion (20%) to balancing the TKE equation. Terms Terms II (the buoyant buoyant production/consumption) production/consumption) and and IV IV (vertical (vertical turbulent turbulent transport) transport) are are a fewa few orders orders of of magnitude magnitude smaller smaller than than other other TKE TKE budget budget terms. terms. Term Term II II is is dominantly negnegative,ative, acting as a weak sink, while term IV is dominantly positive. These results results agree agree well well with with the the results results from from [49 ] [49] for a for Mountain-Wave a Mountain-Wave event eventduring during the T-REX the Texperiment.-REX experiment. A new A outcome new outcome is that is the that terms the terms only vary only invary magnitude in magnitude depending depending on the on bora the type,bora whiletype, while the signs the signs of the of terms the terms do not do depend not depend on the on synoptic the synoptic type. type. Comparing thethe twotwo middle middle levels, levels, absolute absolute values values of of TKE TKE terms terms on theon lower,the lower, 3.5 m, 3.5 middle m, middle level levelare larger are larger thanthe than corresponding the corresponding 7.5 m middle-level 7.5 m middle values.-level Thisvalues. is due This to is the due fact to that the turbulent fact that turmotionsbulent are motions more intense are more near intense ground near level. ground The most level. intense The most turbulent intense motions turbulent are for motions B01—shallow are for B01cyclonic—shallow bora type—followedcyclonic bora type by— B09—deepfollowed by anticyclonic B09—deep bora anticyclonic case. bora case. It is is interesting interesting to inspect to inspect the temporal the temporal correlation correlation coefficients coefficients between the between mechanical the mechani productioncal productionterm and dissipation, term and dissipation, and between and the between buoyancy the term buoyancy and residual. term and The residual. first correlation The first coefficient correlation is coefficientlarge and negative is large and (~− 0.9negative on both (~− middle0.9 on both levels), middle which levels) can also, which be seen can inalso Figure be seen 19. Furthermore,in Figure 19. Furthermore,these two terms these dominantly two terms balance dominantly the TKE balance budget the equation.TKE budget This equation. implies This that implies the mechanical that the productionmechanical and production dissipation and are dissipation of a similar are size of and a are similar reciprocal. size andThe secondare reciprocal. correlation The coefficient second correlationmentioned is coefficient positive (0.8 mentioned and 0.5 on is positivethe 3.5 m (0.8 and and 7.5 m 0.5 middle on the levels, 3.5 m respectively); and 7.5 m middle consequently, levels, respectively);for statically stable consequen conditions,tly, for the statically pressure stable transport conditions, is negative, the andpressure for statically transport unstable is negative conditions,, and forit is statically positive. unstable conditions, it is positive.

3.6. Wind Proﬁles 3.6. Wind Profiles The vertical wind speed proﬁles reconstructed with the mean and median values (Section 2.9) are The vertical wind speed profiles reconstructed with the mean and median values (Section 2.9) areshown shown in Figure in Figure 20. Both 20. Both methods methods of reconstruction of reconstruction gave resultsgave results with highwith correlations high correlations (between (between 0.9874 0.9874and 0.9995) and 0.9995) and small and relative small relative errors. errors.

Figure 20. The measured (circle) and reconstructed (line) vertical wind speed profiles in the Figure 20. The measured (circle) and reconstructed (line) vertical wind speed profiles in the x-direction x-direction with a percentage of near-neutral 30-min intervals, relative errors, and correlations. The with a percentage of near-neutral 30-min intervals, relative errors, and correlations. The profiles profiles reconstructed with the mean (median) values of 푢∗푝 (friction velocity estimated from wind reconstructed with the mean (median) values of u∗p (friction velocity estimated from wind profile) and profile) and 푧0 are blue (green). The relative errors and correlations between the measurements and z0 are blue (green). The relative errors and correlations between the measurements and reconstructions reconstructions are given in the corresponding colors. are given in the corresponding colors. In the examples depicted, the reconstructions of the vertical wind speed profiles based on the mean values have slightly better results, but that is not the general case. The efficiency of the method depends on the particular bora episode considered. This seems to be a consequence of wind speed,

Atmosphere 2018, 9, 116 22 of 25

In the examples depicted, the reconstructions of the vertical wind speed profiles based on the mean values have slightly better results, but that is not the general case. The efficiency of the method depends on the particular bora episode considered. This seems to be a consequence of wind speed, rather than bora type (different flow depth dynamics). When the vertical profiles shown in Figure 20 are normalized by the maximum average wind speed (not shown), they have the same shape, regardless of the bora type. This does not confirm the findings from [35], where different vertical profile shapes were observed for different wind speeds. We also tried reconstructing the wind profiles with the measured values of u∗ (calculated from turbulent fluxes using Equation (3)), but since these values are persistently lower than the values of u∗p, such profiles underestimate the wind speed at all levels (not shown).

4. Conclusions We carried out, for the first time, a detailed analysis of high-frequency (20 Hz, downsampled to 10 Hz) wind data for several bora episodes measured at the Maslenica Bridge site in Croatia during autumn and winter 2015/2016 on three vertical levels (2, 5, and 10 m). A total of 14 bora episodes were detected and classified by depth and synoptic type, of which three typical episodes were selected and presented in this study: B01 (shallow cyclonic), B09 (deep anticyclonic), and B13 (shallow anticyclonic). Our results confirm the majority of the previous results [28,33,35]. The minimum energy (energy “gap”) in the frequency-weighted power spectral density graphs for the majority of the episodes is located at 30 min. We could not find clear evidence that it depends only on the bora type. Furthermore, power spectral densities disclose energy peaks at periods between 2 and 8 min for all three episodes, which are most likely related to bora pulsations. This further implies that mountain wave breaking occurred in all analyzed episodes. The thermal stratification during a bora episode is near-neutral due to intensive mechanical mixing, independent of the type of the episode. Deviations from this can be seen at the 10 m height in the nighttime, when the most statically stable bora cases occur. However, these never go beyond weak stratifications. The use of similarity functions in the bora surface layer was also tested. We suggest adopting the similarity theory for bora episodes with caution, since they fail to give reliable results, especially above a certain height. This is probably due to the fact that the main assumptions of the similarity theory are violated (i.e., quasi-stationarity and horizontal homogeneity). The vertical wind speed profiles—reconstructed with mean and median values—agree well with the logarithmic profile for the surface layer during all analyzed bora episodes. In the TKE equation, the shear term dominates in all three episodes extracting the kinetic energy from the mean flow and transforming into the TKE. The shear term is mainly balanced by the pressure transport (residual) and dissipation term. In the small set of typical bora types we analyzed (SC, DA, and SA), we found no evidence that possible differences in micro-scale properties are related to different bora types—which was one of the main goals of the study. The inspected elements that explicitly depend on the wind speed (i.e., friction velocity, TKE, and vertical wind profiles) are different, but that is not necessarily a function of bora type. The friction velocity and TKE budget terms increase with the increase of the mean streamwise wind component. In this paper, we present a novel approach to bora time series analysis, but we are aware of the possible limitations in finding micro-scale differences for different flow depth dynamics. The very sparse time series of sounding data (00 UTC and 12 UTC only) and the one-point measurements at Maslenica are a few of them. In order to further enhance this study (e.g., in the application of the similarity function), future work should aim for a more precise flow depth analysis, and perhaps more complex classification (e.g., by considering vertical wind shear and stability); but above all, more cases and measurements in a denser grid are needed to account for horizontal inhomogeneity. Furthermore, this study showed that the strongest bora episodes are mainly transitional in type (possible change in Atmosphere 2018, 9, 116 23 of 25

ﬂow depth dynamics), so to investigate the micro-scale properties of such cases, episodes should be divided into parts according to ﬂow depth and synoptic type, and then analyzed.

Acknowledgments: V.Š. and J.S. acknowledge Croatia Control Ltd. for their support. The work of A.B. has been supported by the Croatian Science Foundation (VITCLIC) project (PKP-2016-06-2975) which is funded by the Environmental Protection and Energy Efficiency Fund under the Government Program (Ministry of Environment and Energy & Ministry of Science and Education) for the Promotion of Research and Development Activities in the Field of Climate Change for the period 2015–2016. K.Š. acknowledges the EKONERG for their support. I.N., S.B., J.S., and M.B. acknowledge the Meteorological and Hydrological Service for their support. This work started as a project assignment within turbulence course at the Department of Geophysics, Faculty of Science, University of Zagreb. The study was partly funded by the Croatian Science Foundation projects CATURBO, No. 09/151 and HRZZ-IP-2016-06-2017 (WESLO). Author Contributions: All authors made a significant contribution to the data analysis, writing, and revising the manuscript. Vinko Šoljan coordinated the work, while also doing data analysis and writing. Andreina Belušić was responsible for the TKE analysis and writing. Kristina Šarovićtested the Monin–Obukhov similarity theory. Irena Nimac analyzed the surface layer stability. Stjepana Brzaj analyzed the wind profiles. Jurica Suhin was responsible for the spectral analysis. Martin Belavićperformed the data cleaning and quality control. Željko Veˇcenajand Branko Grisogono designed and led the project, performed the wind data collection, and contributed to writing the manuscript. Conflicts of Interest: The authors declare no conflicts of interest.

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