Here we study the LLJ characteristics in the Paris region, France. With a population of over 12 million people, the Paris agglomeration is the second-biggest megalopolis and the most densely populated city in Europe. The Paris region has experienced fast and wide urbanization during the last decades but is still surrounded by natural and agricultural areas. Anthropogenic heat emissions and changes in land cover are aggravating the UHI effect . Figure  shows the topography of the Paris region, the land cover classification, and the geographical location of the experimental sites. Paris is located about 150 km from the sea in a valley defined by the Seine River basin and surrounded by plateaus with modest topographic variation, which rise no more than 230 m above sea level (a.s.l.). In the city of Paris, the terrain is relatively flat, the lowest altitude is about 20 m a.s.l. along the river, and the highest altitude is about 130 m a.s.l. on hills in the northern parts of the city. About 20 km southwest of the city is the Paris–Saclay Plateau, which has a mean extension of 10 km and is elevated about 160 m a.s.l. It is an important economic, academic, and industrial area in the region. Due to the distance from the sea, there is no interaction of the sea breeze with the urban area. The long-term prevailing wind direction in the area is southwesterly and has a maritime origin, but winds from the northeast are also often observed .

This study focuses on the summer of 2022 between 15 June and 31 August. The year 2022 was recorded as the warmest observed in France so far, with three reported heat waves between June and August, leading to an exceptional nocturnal mesoscale flow over the Paris region during summertime with a predominant northeasterly flow. Severe conditions were observed especially in the July heat wave, when sea level temperature anomalies above 12 °C were associated with a deficit in precipitation rate of about 80 %, leading to extreme droughts . In general, the summer of 2022 had prevailing winds coming from the northerly to northeasterly directions (0–75°), with speeds below 7 m s-1. The air temperature ranged between 11.8 and 35.2 °C, with a mean value of 20.6 °C. These temperature values for 2022 are high when compared to longer-term averages. Using a comprehensive data set spanning from 2006 to 2022, collected by the Météo-France surface meteorological network and processed by the ReOBS project , the typical synoptic conditions within the study area are analyzed for the summer months of June, July, and August. The prevailing nocturnal winds exhibit a range of directions mostly between 170 and 45°, with average speeds below 8 m s-1. The nocturnal air temperature ranges between 6.6 and 38 °C, with a mean temperature of 18.6 °C.

The Doppler wind lidar (DWL) measurements recorded during the study period (15 June and 31 August 2022) at both the urban and the suburban sites contribute to the wind profile measurement network of the initiative PANAME (PAris region urbaN Atmospheric observations and models for Multidisciplinary rEsearch). The PANAME initiative is an unprecedented program bringing together a collection of multidisciplinary scientific projects that investigate the Paris urban environment in relation to weather, climate, air quality, and impacts on human health. The present study is part of the project called DYNAMICS, which contributes to PANAME with an improved characterization of nocturnal mean flow and turbulence conditions.

The high-power scanning DWL Vaisala WindCube Scan 400S was deployed in the city center of Paris (red dot in Fig. ), on the roof of the Zamansky tower (88 m above ground level – a.g.l.) at the QUALAIR-SU supersite (48.8° N; 2.36° E; 400 m a.s.l.). QUALAIR-SU is a platform dedicated to atmospheric observations and air quality monitoring, which is operated by the Laboratoire Atmosphères, Observations Spatiales (LATMOS) and is hosted by Sorbonne Université at the Jussieu campus . The WindCube Scan 400S is a DWL equipped with a scanning head capable of orienting the laser beam in any direction of the hemisphere . The high energy emitted by the pulse, at 1.54 µm wavelength, allows it to sample the atmosphere at a distance of up to 7 km. Several configurations of pulses are available corresponding to different spatial resolutions (75, 100, 150, or 200 m), with a resolution of 75 m used in this study. A blind zone, spanning twice the spatial resolution (150 m in this study), restricts measurements close to the sensor. Table  provides a summary of the main properties of the instrument. The WindCube Scan 400S can measure under different scanning strategies such as vertical stare, plan-position indicator (PPI), and Doppler beam swinging (DBS). provide a detailed technical description of every scan mode operation and their potential applications. The DBS mode is widely used in urban meteorology to measure vertical profiles of horizontal wind speed and wind direction. It was shown by that DBS operates fast and captures unstable flows well in the urban interface. In this study, a five-point DBS mode is used, with the scanning head successively addressing five lines of sight (LOSs): one vertically oriented LOS (90° elevation angle) and four tilted LOSs (75° elevation angle) pointing north, east, south, and west. Each scanning sequence (one DBS cycle) is completed in approximately 15 s, with 1 s of accumulation time for each LOS and 2 s between two LOSs. The WindCube Scan 400S has been aligned with the geographic north using the hard target method, which has a precision of ±2°.

During the study period (15 June–31 August 2022) the scan strategy was designed to follow an hourly schedule, integrating the DBS scan with the vertical stare and PPI. In the first half of every hour the DBS is performed for 9 min, followed by a 3 min full PPI at 0° of elevation with an angular resolution of 2° s-1, then 5 min of continuous vertical stare at 90° of elevation, followed by another 9 min of DBS and closing with another 3 min full PPI at 0°. The second half of the hour repeats the same schedule. In this study, all vertical profiles of horizontal wind speed observations were derived from the DBS, while the vertical stare data are used to derive the vertical velocity variance (σw2). Observations from the PPI are not used in this study. The implemented scanning schedule was designed to fulfill several objectives but was not specifically optimized for the detection of LLJ. One quality control step is implemented to ensure a high-quality wind profile product: data with a CNR (carrier-to-noise ratio) below -20 dB and above 5 dB are excluded, thereby omitting weak signals and clouds, respectively.

In addition to the observations in central Paris, data collected by a Vaisala WindCube WLS70 at a suburban location on the Saclay Plateau are used in this study. The data recorded with this instrument are used in this study only to highlight the regional scale of the LLJ observed. A detailed analysis of this data collection will be the subject of future studies. This profiling DWL is an instrument specially developed for meteorological applications . The observations are conducted at the SIRTA observatory (Site Instrumental de Recherche par Télédetection Atmosphérique; ), located on the campus of École Polytechnique in Palaiseau, 20 km southwest of Paris (48.713° N, 2.208° E; 156 m a.s.l.; Fig. ). Over the last 25 years, SIRTA has collected a comprehensive data set of atmospheric observations using in situ measurements as well as passive and active remote sensing instruments, characterizing the regional atmospheric background of the Paris region . The WindCube WLS70 uses a 1.54 µm pulsed-fiber laser and a coherent detection system which provides sufficient backscattering signal up to 4 km. Every LOS performed by the WLS70 has a fixed spatial resolution of 50 m (see Table ). The WLS70 performs four-point DBS measurements (10 s) in a way similar to the WindCube Scan 400S, but without the vertical LOS. This study uses 10 min averaged profiles; a previous quality control step is applied to these profiles to ensure 80 % of data availability at each range gate.

Various methods and criteria have been developed to detect a LLJ in a vertical profile of horizontal wind, with techniques depending on the characteristics of the data source (e.g., limitations from measurement sensors) and even the study area. defined a LLJ as any lower-tropospheric wind maximum in the vertical profile of horizontal wind speed that is at least 2 m s-1 greater than speeds both above and below within the lowest 1500 m of the atmosphere. This absolute criterion is widely found in the literature. It was applied to SODAR data collections and radiosonde profiles measured in the USA and even in the Arctic Sea . The threshold of this absolute criterion can be tuned as done by , who used a value of 0.5 m s-1. However, under very weak flow conditions (< 2 m s-1) the performance of the criterion could present limitations in the identification of LLJ events . In such cases, it is possible to use a relative threshold instead, in which a LLJ is detected by a velocity difference of 20 %–25 % between the local maxima and minima. In fact, absolute and relative thresholds have been combined to further improve detection. In different long-term radiosonde campaigns in Sao Paulo, Brazil, the criterion to identify a LLJ event in a single wind speed profile was that the maximum at the LLJ must be greater than or equal to 2 m s-1 and 25 % faster than the minimum above .

Although in other DWL or SODAR-based studies, the same thresholds have been used, the high temporal and spatial resolution of surface-based remote sensing observations allows the incorporation of complementary steps. This enables not only an optimized detection of individual LLJ profiles but also the identification of LLJ events evolving over time . In this study, automatic LLJ detection is an adaptation from the method described by and uses 30 min averaged profiles of horizontal wind speed to best combine the 15 min data products available at QUALAIR-SU and the 10 min data products available at SIRTA. This temporal resolution was previously used in SODAR studies presenting coherent LLJ detection .

Therefore, based on the literature and exploratory tests on the data set, some important conceptual aspects were adapted compared to the original method from .

Daytime LLJ events are negligible in the Paris region. During the day, very few LLJ events are recorded at the urban site. Therefore, this study focuses on the nocturnal periods at times between 18:00 and 09:00 UTC (20:00 and 11:00 local time).

Additionally, technical aspects of the algorithm were also adapted. In the following, a brief description of the implemented adaptations in this study is given, and further details can be found in .

LLJ detection from a single wind profile. We consider every horizontal wind speed profile between the first available gate (238 m a.g.l. at QUALAIR-SU and 105 m a.g.l. at SIRTA) and 1000 m a.g.l. A LLJ is identified in a profile if the local maximum of the horizontal wind speed is at least 1.5 m s-1 stronger than the first local minimum above or below. Note that the minimum below the core height may not be captured correctly by the observations because no information is available < 238 m a.g.l. in the instrument's blind zone. A relative detection criterion was tested, but it produced a high number of false negatives (43 %).

The output parameters of the algorithm are listed as follows. (i) LLJ occurrence is a Boolean value (True [1] or False [0]) given to each profile. (ii) LLJ core height is the height of the maximum in the wind speed profile; in this case, the algorithm can provide it in both meters above ground level (m a.g.l.) and above sea level (a.s.l.). (iii) LLJ core speed is the value of the wind speed at the core height. (iv) LLJ core direction is the wind direction at the height of the wind speed maximum. Additionally, the algorithm identifies the corresponding parameters for the minimum both above and below the jet core in the case that they are recorded by the profile observations.

The UHI intensity (ΔUHI = Turban-Trural) is defined as the difference in air temperature between an urban (Turban) and a rural (Trural) site. Usually, standard meteorological observations at 2 m a.g.l. height are compared. In the current work, the QUALAIR-SU site (red dot in Fig. ) is chosen as the urban site, and a Météo-France station at Melun (48.613° N; 2.679° E; 91 m a.s.l.) is chosen as the rural site (yellow dot in Fig. ).

Data collected at the QUALAIR-SU supersite were used to represent the central urban air temperature (Turban) given that continuous and long-term observations are available. During the intensive observation period (IOP) in the framework of the PANAME 2022 campaign, surface-based meteorological stations were installed by Météo-France to capture the air temperature within the built environment at street level, e.g., at Place de la Madeleine (48.87084° N and 2.32432° N; 79 m a.s.l.) and Boulevard des Capucines (48.87066° N and 2.33175° N; 81 m a.s.l.) on 10 July 2022, i.e., later than the start of the analysis period of the current study (15 June 2022). Hence, data from the QUALAIR-SU meteorological station located at roof level (20 m a.g.l.) are considered here to represent the intensity of the UHI for the Paris region well. ΔUHI is stronger when using the street-level urban measurement sites by about 1 °C when ΔUHI > 6 °C (see Fig. ). Additionally, wind data collected from a 25 m meteorological tower installed at Montsouris Park are used in this study to assess the relationship between ΔUHI and the near-surface wind speed.

The temperature at Melun is measured using a Sterela Opale UME at 2 m a.g.l. and that at QUALAIR-SU using a Vaisala WXT520 automatic weather station at 22 m a.g.l. The mean building height around the QUALAIR-SU site is about 25 m. 30 min averages are calculated for both sites to match the DWL analysis intervals. The average nocturnal UHI intensity is calculated as the mean of the temperature differences recorded during the nocturnal period (sunset to sunrise). Additionally, based on cloud-base height observations from a Lufft CHM15k automatic lidar ceilometer operated at the QUALIR-SU site, nights were classified into cloudy, partly cloudy, and cloud-free periods using the classification approach presented by .

For the performance evaluation of the algorithm the time difference between two consecutive time steps for which a LLJ is detected gives an indication of the persistence of the jet event. The threshold sensitivity and performance analysis by revealed that the time difference threshold has a strong influence on the performance of the algorithm. This may bias the algorithm towards the detection of false positives or very short events, which are not the subject of study in this work. The detection of false positives is further dependent on the quality of the measurements, which in turn depends on factors such as power and sensitivity of the laser system, vertical distribution of the aerosol load (tracers; see Sect. ), and the presence of clouds.

An example of a coherent LLJ detection is presented in Fig. a. The jet core becomes visible in the late evening of 9 August at 19:00 UTC at 550 m a.g.l., with a wind speed of approximately 8 m s-1. After sunset, the core height stabilizes at 500 m a.g.l. and reaches a maximum wind speed between 21:00 and 23:00 UTC. After midnight, the core height increases beyond 550 m a.g.l., followed by a gradual decrease in the core wind speed. The jet persists throughout the night and into the early morning before it dissipates at 08:00 UTC on 10 August. Figure b presents a LLJ detection under weaker flow conditions and lower boundary layer height than the previous example. This LLJ event clearly failed the criterion of four consecutive detections explained in Sect. , and it is not considered in this study.

By classifying LLJs according to their core wind speed magnitude, found that strong jets tend to occur at greater altitudes. studied the relationship between LLJ characteristics and turbulence within the stable nocturnal boundary layer, concluding that the core wind speed and core height can be used to diagnose turbulence effects in the region beneath the jet, considering that strong core wind speeds are usually associated with strong turbulence below and above the core . In this study, both core wind speed and core height were tested as indicators for the classification of LLJs (not shown here); however, it was not possible to identify groups with consistent patterns in the LLJ characteristics. Hence, we found that the vertical velocity variance (σw2) is a more meaningful indicator as it effectively describes the link between the jet winds and surface–atmosphere exchanges. This turbulence quantity approximates the vertical component of the TKE during stable conditions . Here it is assumed that the σw2 observations at the first range gate (238 m a.g.l.) of the DWL at the urban site are representative of the vertical mixing conditions in the nocturnal urban boundary layer. Each LLJ event is classified according to the mean nocturnal average σw2 (between sunset and sunrise). Three classes are defined based on thresholds defined by the median and the 75th percentile of the distribution of σw2 (Fig. ), indicating low (< 0.11 m-2 s-2), intermediate (0.11 m-2 s-2 ≤ σw2 < 0.23 m-2 s-2), and high (≥ 0.23 m-2 s-2) vertical velocity variance.

Based on the 77 d period spanning from 15 June 2022 to 31 August 2022, 55 nights (70 %) exhibit a LLJ event at the urban QUALAIR-SU site. 96 % (53 out of 55 nights) of these LLJ events were also detected over the suburban site at SIRTA, showing that the nocturnal LLJ is a regional phenomenon in the Paris region. A total of 9 out of 55 LLJ events were detected during cloudy conditions, but the complex interactions with cloud dynamics are beyond the scope of this work. Therefore, this study focuses on 46 nights (60 % of the total of 77 nights in the study period) with a LLJ event detected at QUALAIR-SU under cloud-free conditions, in which 830 individual 30 min profiles (i.e., 415 h) were associated with a jet. According to these results, it is possible to say that the LLJ activity during summer Paris 2022 is high, especially when compared to previous studies conducted in Paris during the autumn period or to other European studies of summertime LLJ activity. In the local context, reported a 32 % occurrence of LLJs during the fall of 2014 in Paris by using data collected by a DWL installed at the QUALAIR-SU site. A climatological study at Cabauw, the Netherlands, found that LLJs occurred 32 % of the time during summer, based on 7 years of SODAR profile data . At Utö, Finland, another climatological study reported an average occurrence of LLJs of 28 % for the month of July, based on 2 years of DWL observations . Outside Europe, a long-term study in Florida, USA, reported a 47 % occurrence rate of LLJs during summer, based on 4 years of SODAR data , and another work by also reported a 47 % occurrence rate in a summer study in South Carolina, USA.

During the study period, the LLJ core height (ZLLJ) ranges between 238 and 950 m a.g.l. (Fig. a), i.e., throughout the entire height range considered for detection (Sect. ). Note that for 7 % of the 30 min profiles, when the core height is detected at 238 m a.g.l., the actual LLJ core may at times be located in the instrument blind zone, i.e., below that level. Most jets (64 %) have a core height between 300 and 500 m a.g.l., with 350–400 m a.g.l. being the most common interval (22 %). The median value of the LLJ core height is 388 m a.g.l. These results are similar to previous case study analyses that found the core height of LLJs in the Paris region at 400 m a.g.l. and compare well with observations conducted over Greater London that reported core heights between 300 and 400 m a.g.l. . The analysis carried out at Boulogne-sur-Mer, France (about 200 km north of Paris), reports LLJ core heights < 200 m . At this coastal site, it is likely that land–sea breezes play a role in the formation of the jet, which might explain the occurrence of low-altitude core heights. At other European sites with a coastal influence (Cabauw and Utö), lower ZLLJ values (140 m a.g.l.) were observed during the summer .

The histogram of the LLJ core wind direction (WDLLJ) (Fig. b) shows that LLJs are mostly observed under easterly–northeasterly flow during the study period in summer 2022. 66 % of LLJs have a core wind direction between 0 and 105°, with 30–60° being the most common interval. LLJ profiles with northwesterly flow (300° < WDLLJ ≤ 360°) present an occurrence of 12 %, while southeasterly flow (105° < WDLLJ ≤ 180°) contributes ≈ 14 % of the observed jets. The remaining 8 % of the profiles are distributed in the interval 180 to 300°. To assess how the LLJ over Paris relates to the general regional flow, the overall nocturnal wind direction distribution at 400 m a.g.l. (i.e., the level of the median ZLLJ) is compared to the wind direction occurrence of LLJ events. The wind direction distribution of the LLJ follows a similar pattern as observed for the wind during the entire study period, where the northeasterly–easterly flow is predominant (44 % of 2375 profiles). The likelihood of observing a LLJ is also higher in this sector with a 60 % probability between 0 and 105°, and the highest occurrence (80 %) is in the 30–45° interval. Note that only 2 out of 46 jets (4 %) present a southwest (190–300°) wind direction, a sector that usually has a much larger frequency during summer nights with respect to the long-term climatology (2006–2022; Sect. ).

Figure c shows that the LLJ core wind speed (WSLLJ) varies between 2 and 19 m s-1. For the majority of the jets (85 %), the core wind speed ranges between 4 and 12 m s-1, with a median value of 8.3 m s-1. This is again similar to the modeling results of the 2 d case study in Paris reported by and comparable to a climatological study conducted in Jülich, Germany, a suburban area located 370 km from Paris in the northeasterly direction where the median summer value of WSLLJ is 8.3 m s-1 . Similarities are also found with Cabauw, the Netherlands , which is located in a suburban area 200 km from Paris in the northeasterly direction where the median value of WSLLJ for summer is ≈ 9 m s-1. Given that both Cabauw and Jülich are located roughly upwind of Paris under northeasterly flow, all these sites could be affected by the same LLJ event if the phenomenon has a large enough spatial extent as shown, e.g., by , which could explain these similarities in LLJ wind speed. However, the question of spatial extent goes beyond the scope of the current study. The median WSLLJ found in this study is lower than the wind speeds reported for the summer in Utö, Finland of 11.6 m s-1 and results from a study in Florida, USA, of ≈ 10 m s-1 .

As introduced in Sect. , a σw2-based classification system is used to identify LLJ events with common characteristics and then study their potential impacts on the near-surface atmosphere. Figure  shows that low σw2 is mostly related to jets with a low core height between 238–350 m a.g.l., which in turn present a predominantly east–southeast wind direction (90–180°) and low to intermediate core wind speed < 7 m s-1. It should be noted, however, that LLJ events with core wind speed > 10 m s-1 are also found in the low σw2 class. These outliers are discussed in Sect. . Jets with intermediate σw2 occur mostly in two wind direction sectors: 300–345 and 45–105°. Their core height presents intermediate altitudes between 300 and 450 m a.g.l. and wind speeds between 5–12 m s-1. In the strong σw2 class, the core height tends to be > 450 m a.g.l., with a predominant northeasterly wind direction (30–60°) and wind speeds > 8.3 m s-1.

Figure a presents the mean LLJ horizontal wind speed profile for each σw2 class. Consistent with the histograms (see Fig. ), the low σw2 class presents rather low values of wind speed throughout the profile. The core height of this profile is observed at 350 m a.g.l. and the wind speed at this altitude is 5 m s-1. The minimum wind speed above the core is 3.8 m s-1 and occurs at 1000 m a.g.l.; above this height the wind speed gradually increases. Similarly, the mean wind profile for the intermediate σw2 class presents a core height at a slightly greater altitude of 400 m a.g.l. but with a slightly higher wind speed of about 6.2 m s-1. The minimum above the core is close to that of the low-variance class. The mean profile associated with the strong σw2 class exhibits a distinctly different shape and stronger wind speeds. The core height is located at 475 m a.g.l., i.e., 75 m higher than the moderate σw2 profile. The core wind speed is about 9.2 m s-1, which is 50 % and 30 % stronger than the core wind speed for the low and intermediate σw2 class, respectively. The minimum above the core is about 3.8 m s-1 and located at 1750 m a.g.l., i.e., at greater altitudes than for the other two classes.

The respective median profiles of σw2 for each class are presented in Fig. b, which illustrate that LLJ core height not only influences the horizontal wind speed but also the vertical mixing. For all three median profiles, the strongest vertical mixing is retrieved from data recorded at the first range gate of the lidar (238 m a.g.l.), i.e., closer to ground level. Above this height, the median σw2 values gradually decrease, reaching values close to zero, above the respective jet core shown in Fig. a. As the minimum recorded altitude of the vertical stare depends on the blind zone of the DWL, no information on the vertical velocity variance below 238 m a.g.l. is available. In general, the shape of the three median profiles agrees with those reported in previous studies . In cities, unstable or neutral stratification and higher σw2 are maintained by the added urban heat .

To conclude, the classification system used here in this study allows us to identify the following trends: (i) in the low σw2 class the LLJ profiles are detected in a wind direction sector between 0 and 180°. This class represents all the profiles detected in the southeast sector between 105 and 180° and all the low-altitude cases in the interval between 250 and 300 m a.g.l., and it is the dominant class for profiles with a core wind speed < 6 m s-1. (ii) The intermediate σw2 class is detected in a wide wind direction sector between 300–115° and dominates the northwest sector between 300–360°. The values of core height range between 300–450 m a.g.l., while the core wind speed varies between 5–12 m s-1. (iii) Finally, profiles in the strong σw2 class occur in the wind direction sector between 0–115° but are usually found in the northeast sector between 30 and 60°. LLJs in this category can present core height at high altitudes > 400 m a.g.l. with a strong core wind speed > 8.3 m s-1.

According to , a LLJ typically forms during the night and reaches its maximum wind speed before dawn hours, between midnight and 04:00 local time. Figure a presents an example of a well-defined nocturnal LLJ event observed in Paris during the night between 16–17 July 2022, showing the characteristics of the LLJ core and the minimum above. The WSLLJ is about 7.5 m s-1 before sunset, and then it increases and reaches its maximum (12.5 m s-1) at 2.5 h after sunset (22:30 UTC and 00:30 LT); it then starts to decrease again from about 1 h before sunrise. The ZLLJ is about 750 m a.g.l. at sunset when the convective boundary layer is still collapsing. When WSLLJ starts to increase after sunset (21:00 UTC), ZLLJ decreases to around 400 m a.g.l. and remains around this altitude throughout the night. At sunset, the jet core follows a northeasterly flow that veers toward the east over the course of the night by 90°. The lack of sudden changes indicates that there are no changes in air mass.

The development of the wind speed minimum above the LLJ core (see Fig. a) and the evolution of its characteristics are in accordance with the momentum budget of the atmospheric column in the ABL during a LLJ event . The wind speed is weak (≈ 2.5 m s-1) at sunset and then experiences a slight increase over the course of the night. The height of this minimum is located about 900 m above the LLJ core at sunset and then gradually decreases until it merges with the jet core at the time of the jet dissipation. The wind direction of the jet core and the minimum above differ by about 50° at sunset and then slowly converge over the course of the night before converging again at about 1 h past sunrise. Overall, the wind speed, wind direction and height in the jet core, and the minimum above show distinct contrasts during the time of jet formation and then reach a common point at 07:00 UTC when the jet is completely dissipated and the momentum is distributed evenly over the entire column in the ABL.

This LLJ evolution (Fig. ) suggests that inertial oscillation (IO) is the formation mechanism of this event . At total of 28 out of 46 (61 %) of the cloud-free detections reported in this study have a similar nocturnal evolution, which suggests that IO is highly relevant for jet dynamics in the Paris region. IO is characterized by an oscillation of the wind above the elevated nocturnal temperature inversion with a period of T=2π/f, where f is the Coriolis parameter (f=2Ωsin⁡θ, with Ω and θ being the angular speed of the Earth's rotation and latitude, respectively). At the QUALAIR-SU latitude (θ≈48.84), this gives T≈ 16 h, which is approximately the duration of the most persistent LLJ events observed here, e.g., 7–10 August (see Fig. ). The amplitude of this wind speed oscillation is related to the magnitude of the ageostrophic velocity component and can cause the core wind speed to reach supergeostrophic magnitude. In addition to a gradual increase and decrease (wind speed oscillation hereafter) in the core wind speed, IO is associated with a clockwise change in wind direction, which is clearly evident from the time series (Fig. a) and also illustrated by the hodograph of the meridional and zonal wind components (u,v) (Fig. b).

Fig.  presents the nocturnal evolution of the core wind speed for the 46 jets observed under cloud-free conditions during the study period, classified into three groups of σw2 intensity (Sect. ). In the low σw2 class, 15 out of 19 (79 %) cases do not show the wind speed oscillation, as opposed to 4 visible outliers (16 and 19 July; 11 and 13 August). These outliers do not show common behavior in terms of duration, acceleration, or peak wind speed. These cases are associated with a strong stable atmospheric stratification caused by the advection of hot air masses , but these details are beyond the scope of this study and will be investigated elsewhere. Omitting those outliers, the behavior of the median wind speed curve for the low σw2 class is rather flat with a mean value of 6.23 m s-1. For the events with moderate σw2 values (Fig. b), the median wind speed curve is stronger, with a mean value of 8.07 m s-1. It increases slightly, starting from 2 h after sunset, and reaches its maximum at about 4–5 h later, before starting to slowly decay until dissipation. Finally, for the strong σw2 class (Fig. c) most of the events exhibit a clear oscillation in wind speed. The acceleration starts with the jet formation and lasts until 3 h after sunset. A peak in the core wind speed is observed at around midnight (±2 h), followed by a slow deceleration until dawn hours with a mean value of 10.2 m s-1. The median WSLLJ is 9 m s-1 at 1 h before sunset (i.e., of the same order of magnitude as the peak of the wind speed median in the moderate σw2 class) and then a gradual increase is produced until it reaches the maximum peak at 2 h after sunset, which lasts about 2 h. The WSLLJ gradually starts to decay from about 4 h after sunset until it reaches a minimum right before sunrise, which is associated with the jet dissipation given.

Figure  presents the time series of the nocturnal evolution for the three jet core characteristics (height, wind speed, and wind direction) for each event during the study period, including the cloudy nights. An amplitude in wind speed can clearly be identified for 25 out of 46 (i.e., 54 %) jets, mainly observed for jets with strong vertical velocity variance (as shown in Fig. c) and high core height. This trend is also valid for short-duration cases (< 4 h), for example 16 July. Nocturnal evolution of the core direction (Fig. b) shows that 28 out of 46 (i.e., 61 %) of jets present a persistent clockwise veering with an average change in wind direction of 3.7° h-1. Two cases particularly stand out with a strong veering (> 5° h-1): 28 June and 21 August. They fall into the intermediate and low σw2 class, respectively, and both emerge from a northwesterly direction (322 and 282° respective initial core direction). As discussed (Sect. ), both the wind speed oscillation and the clockwise veering are signatures of the IO formation mechanism. However, not all cases with wind speed oscillation (Fig. a) necessarily present a strong clockwise veering (Fig. b). For example, jets detected between 7 and 9 August show the wind speed oscillation, but their change in core wind direction is less than 1° h-1, remaining almost constant in wind direction.

These time series show the variability in the LLJ duration as well as the timing of both formation and dissipation in detail. Results show that 29 out of 46 (i.e., 63 %) jets last almost the entire night, emerging at sunset ±2 h and dissipating at sunrise ±2 h. However, jets can emerge in the middle of the night and continue even after sunrise. 31 out of 46 (i.e., 67 %) cases last more than 8 h, including cases with a late starting time (up to 4 h after sunset). During the study period, the maximum LLJ duration is 15 h, the minimum duration is 2 h (by conceptual definition), and the mean duration is 9.5 h.

The day-to-day variability highlighted in Fig. a reveals the influence of synoptic conditions for the LLJ characteristics. While some cases appear to be isolated (e.g., 28 June and 10 July), during consecutive LLJ detection the characteristics of their core may vary night after night or may be similar each night. A total of 10 events are detected between 10–19 July (heat wave period) with strong day-to-day variability in terms of σw2 levels and the core characteristics. During this period, jets at high core height and strong wind speeds are associated with strong σw2, while slow and low-altitude jets present weak σw2. A different situation is observed for the seven jets detected between 6–13 August. Persistent synoptic conditions prevail for the first five detections between 6–10 August, with similar nocturnal evolution of core characteristics and vertical mixing. However, the last two detections on 11 and 13 August (outliers in Fig. ) clearly differ from this period as they have short duration, low core height, weaker wind speed, and low vertical mixing.

The persistence of synoptic conditions results in a certain clustering of the LLJ events. For example between 15 and 18 June, four consecutive events have similar durations (10–12 h), with similar speeds (6–9 m s-1), and similar core heights at altitudes < 400 m a.g.l. In the period between 6 and 10 August, the detected events present similar core characteristics with strong wind speed oscillation at high altitudes, occurring in the northeast flow with a wind direction veering becoming more pronounced from one night to the next. These cases present very similar nocturnal evolution and duration, and all of them fall into the same σw2 class (strong vertical mixing). In the period between 3 and 6 July again, after 4 consecutive days with no detection, four short events (< 5 h) are found at medium to high altitudes between 400 and 600 m a.g.l., with wind speeds between 10 and 12 m s-1.

As discussed in Sect. , LLJs in a narrow easterly sector (80–115°) are all associated with low vertical velocity variance. Figure  reveals that these specific LLJ events (18 and 19 July; 11 and 13 August) in fact show the high wind speed outliers detected in Sect.  with a distinct wind speed amplitude (Fig. 7a) and clockwise veering (Fig. b). It is further evident that these easterly jets are found at relatively low altitudes (< 350 m a.g.l.), suggesting that channeling along the low topography of the river Marne basin towards the east of Paris could play a role in the acceleration mechanisms. These processes will be investigated in future studies.

Cloudiness and wind are environmental variables that exert an essential control on the intensity of the UHI and its nocturnal evolution. The UHI of the canopy layer is generally strongest during cloud-free nights and low wind speed conditions, following days with the same characteristics . Figure a presents the relationship between the nocturnal mean surface wind speed at the urban park Montsouris and the nocturnal mean ΔUHI intensity in the Paris region, including only cloud-free nights after fair-weather days to focus the analysis on wind effects only. Wind data at Montsouris Park are collected at a tower 25 m a.g.l., a measurement setting not often available in urban areas. The UHI intensity decreases exponentially with increasing wind speed. Based on observations from different cities in Canada, proposed an empirical formulation where the mean ΔUHI is inversely proportional to the square root of the average regional nocturnal surface wind speed (ΔUHI∝ws‾-κ, with κ being a dimensionless parameter often equal to 0.5). The urban wind direction at Montsouris suggests that weak values of ΔUHI are mostly found under northeasterly flow. This wind direction sector is characterized by LLJs with strong wind speeds and high σw2 values. A best fit to the Paris data following this relation is included in Fig. a and describes a function that follows the drop in ΔUHI due to the increase in wind speed, with an asymptotic shape defined by the threshold ΔUHI ∼ 1 °C, which appears to be the baseline ΔUHI intensity for summertime cloud-free conditions.

The near-surface urban wind speed, sampled at a height (25 m a.g.l.) slightly above the mean building height of 20 m, provides insights on advection processes. However, to assess the role of vertical mixing in spatial contrasts in air temperature, the response of ΔUHI to the vertical velocity variance at 238 m a.g.l. is shown in Fig. b. This relation is even more clearly pronounced as can be seen from the smaller error statistics listed in Table . Given that wind observations above the urban canopy layer (as here at Montsouris Park) are rarely available, the wind speed observations at the rural site Melun were also tested to have a full view of the ΔUHI response to the regional winds. As the rural near-surface wind speeds are associated with a higher uncertainty when predicting the ΔUHI, it is concluded that turbulence observations inside the urban boundary layer show a closer link to the processes that drive the UHI development. The curves in Fig. b represent the best nonlinear model fitted to the data collected during the nights with a LLJ event, using the Tair data collected at QUALAIR-SU. We also add the fit resulting from the data collected by the IOP station at Boulevard des Capucines (see Sect. ). The similarity between the two curves shows that the relationship between ΔUHI and σw2 is preserved even when using QUALAIR-SU data collected at roof level.

These results are consistent with findings by and , who showed that the mixing below the LLJ core can affect the turbulent exchange processes near the surface. Table  presents a summary of the average values of ΔUHI and the LLJ characteristics corresponding to each σw2 class. Weak vertical mixing is associated with strong ΔUHI, calm winds, and shallow core heights, whereas strong mixing relates to weak ΔUHI, strong wind speeds, and greater core heights. Previous studies have shown that jets at low altitudes (up to 300 m a.g.l.) tend to present low to moderate core wind speeds so that weak wind shear only produces little mechanical turbulence. These low-altitude jets are often associated with a strong temperature inversion over the rural surfaces so that the stable stratification of the atmosphere leads to a more effective decoupling from the surface friction. For these conditions of strong atmospheric stratification and weak momentum transport by the LLJ, the cool air remains locally over the vegetated rural surfaces where it was generated through efficient radiative cooling during the cloud-free nights. Both advection and vertical mixing processes are weak and hence support the formation of very strong ΔUHI . Here we demonstrate that σw2, commonly obtained at one measurement location at a height above the roughness sublayer but below the LLJ core, can be considered a representative indicator of the vertical mixing in the nocturnal urban boundary layer and hence a powerful predictor for the UHI intensity.

Note that the relation between ΔUHI and σw2 remains valid even during nights when no consistent LLJ was detected by the automatic procedure (black triangles in Fig. b), and other synoptic processes (such as fronts) are likely to modulate the atmospheric mixing. 53 % of the jet-free nights fall into the low σw2 class (red shading), and all show ΔUHI > 3.5 °C. Future studies will investigate why there is no LLJ detected for some nights although a low σw2 suggests a stable atmospheric stratification that is likely to favor decoupling.