Particle size distributions were continuously monitored at WOP and WFJ using commercially available scanning mobility particle sizers (SMPS; Model 3938, TSI Inc., US). At both stations, the systems consisted of a differential mobility analyzer (Model 3081, TSI Inc., US), a soft X-ray neutralizer (Model 3088, TSI Inc., US), and a water-based condensation particle counter (Model 3787 at WOP, Model 3788 at WFJ, TSI Inc., US). Running the particle counters in low-flow mode (0.6 L min-1), using a sheath flow of 5.4 L min-1, and applying a total scanning time of 2 min (scan time: 97 s; retrace time: 3 s; purge time: 10 s), particle size distributions between 11.5 and 469.8 nm diameter were monitored.

A Droplet Measurement Technologies (DMT) single-column continuous-flow streamwise thermal gradient chamber (CFSTGC; Roberts and Nenes, 2005) was used to carry out in situ measurements of CCN number concentrations for different supersaturations (SS). The CFSTGC consists of a cylindrical flow tube with wetted walls, inside which SS is developed by applying a linear streamwise temperature gradient between the column top and bottom. Owing to the greater mass diffusivity of water vapor than the thermal diffusivity of air, a constant and controlled SS is generated with a maximum at the centerline of the flow tube. The SS is mainly dependent on the applied temperature gradient, flow rate and pressure (Roberts and Nenes, 2005). An aerosol sample flow is introduced at the column centerline and those particles having a critical supersaturation lower than the instrument SS will activate to form droplets and will afterward be counted and sized by an optical particle counter (OPC) located at the base of the CFSTGC column. The SS developed within the instrument responds linearly to changes in pressure, since its operation relies on the difference between heat and mass diffusivity. Calibration of the instrument, which determines the output supersaturation, was performed by the manufacturer at ∼ 800 mbar, while throughout the campaign the CFSTGC was operating at a lower pressure ∼ 735 mbar, therefore the SS reported by the instrument is adjusted by a factor of 735/800=0.92, which accounts for the difference between the ambient and the calibration pressure (Roberts and Nenes, 2005). CCN concentrations were measured at a specific SS for approximately 10 min; the instrument was cycled between six discrete values ranging from 0.09 % to 0.74 % supersaturations, producing a full spectrum every hour. Each 10 min segment of the raw CCN data is filtered to discount periods of transient operation (during supersaturation changes) and whenever the room temperature housing the instrument changed sufficiently to induce a reset in column temperature (the instrument control software always sets the column temperature to be at least 1.5∘ above the room temperature to exclude spurious supersaturation generation in the column inlet). The CFSTGC was deployed on the mountain-top site of WFJ with the intention of relating the CCN measurements directly to the size distribution and total aerosol concentration data measured by the SMPS instrument at the same station.

In situ observations of the cloud microphysical properties were obtained with the tethered balloon system HoloBalloon (Ramelli et al., 2020). The main component of the measurement platform is the holographic cloud imager HOLIMO 3B, which uses digital in-line holography to image an ensemble of cloud particles in the size range from 6 µm to 2 mm diameter in a three-dimensional detection volume. Note that particles smaller than 6 µm are not detected by HOLIMO, which means that the droplet number concentration may be underestimated. Based on a set of two-dimensional images, information about the particle position, size, and shape can be obtained. The detected particles can be classified as cloud droplets and ice crystals using supervised machine learning (Fugal et al., 2009; Touloupas et al., 2020). The differentiation between cloud droplets (circular) and ice crystals (non-circular) is done for particles exceeding 25 µm diameter based on their shape (Henneberger et al., 2013). From the classification, the phase-resolved size distribution, concentration, and content can be derived (Henneberger et al., 2013; Ramelli et al., 2020). The HoloBalloon platform was flying at WOP and provided vertical profiles of the cloud properties within the lowest 300 m of the boundary layer (BL). The current analysis utilizes the cloud droplet number concentration and liquid water content (LWC) measurements. Note that the LWC is calculated based on the size distribution of the cloud droplets using a liquid water density (ρw) of 1000 kg m-3 and is therefore dominated by large cloud particles.

During the measurement period, meteorological parameters (e.g., pressure, temperature, precipitation, and horizontal wind speed and direction) were continuously monitored by the permanent MeteoSwiss observation station at WFJ. Additionally, a weather station was installed on the OceaNet container (Griesche et al., 2020) deployed at WOP, which also hosted several remote sensing instruments (e.g., cloud radar, Raman lidar, and microwave radiometer) and a particle size velocity (Parsivel) disdrometer (Parsivel2, OTT HydroMet GmbH, Germany; Tokay et al., 2014) to measure precipitation. As there was no wind sensor included in the weather station on the OceaNet container, we utilized the horizontal wind speed and direction measurements from the nearby MeteoSwiss station in Davos, assuming that they provide a good proxy for the wind regime in the valley. Vertical wind speed profiles were obtained with a wind Doppler lidar (WindCube 100S, manufactured by Leosphere) at WOP. Throughout the campaign the wind lidar measured from 200 to 8100 m above ground level (a.g.l.) with high temporal (5 s max) and vertical resolution (50 m). The wind lidar operated following the Doppler beam switching technique with an elevation of 75∘. More information about the remote sensing measurements can be found in Ramelli et al. (2021a).

During the RACLETS campaign, planar and dendritic ice particles were collected from supercooled clouds at WFJ aiming to examine their refreezing ability. A detailed description of the sampling methodology can be found in Mignani et al. (2019). Between 1 and 7 March, images of single dendrites were taken and analyzed visually for the degree of riming (Fig. S4 in the Supplement). The estimated riming degree varies from 1 (lightly rimed) to 4 (heavily rimed) following the categorization of Mosimann et al. (1994). Some representative images of each measured riming degree are shown in Fig. S4b in the Supplement. Although images were captured intermittently, they were taken within all three intense precipitating events occurring during the period of interest (blue shaded areas in Fig. 2). All dendrites captured were at least lightly rimed (i.e., riming degree = 1), which provides direct evidence for the co-existence of supercooled droplets and ice in clouds. Except the indirect evidence of the presence of MPCs over WFJ, Fig. 5 provides an overview of the direct microphysical measurements carried out by the HoloBalloon at WOP (Sect. 2.1.3). Three cloud events are sampled during 7 and 8 March, a more detailed description of which can be found in Ramelli et al. (2021a, b). The observed low-level clouds are likely produced by orographic lifting when the low-level flow is forced to ascent over the local topography from Klosters to WOP producing local updrafts and thus water supersaturated conditions. The cloud LWC measurements from the holographic imager display significant temporal variability that is also related to variations in the altitude of the tethered balloon system, as it tends to follow an adiabatic profile (Fig. 5a, b). Deviations from the adiabatic LWC profile are likely caused by entrainment of dry air within the low-level clouds. During the mixed-phase conditions recorded on 8 March (Fig. 5b), such deviations could also be attributed to the depletion of Nd through riming and depositional growth. These two processes are frequently found to enhance orographic precipitation in feeder clouds. Indeed, a large fraction of rimed ice particles and graupel were observed that day with HOLIMO between 17:00 and 17:40 UTC (Ramelli et al., 2021b). Throughout the two-day dataset presented in Fig. 5, the HoloBalloon system samples at altitudes lower than 300 m a.g.l., providing observations that are representative of BL conditions.

The observed Nd time series collected at WOP are illustrated in Fig. 5c and d. The measurements corresponding to LWC < 0.05 g m-3 are filtered out from the analysis, assuming that they do not effectively capture in-cloud conditions. A similar criterion for LWC was also applied in Lloyd et al. (2015) to determine the periods when clouds were present over the alpine station of Jungfraujoch. Since the measured cloud properties have finer resolution (10–20 s) than the predicted ones, the observed dataset is averaged every 2 min. On 7 March, the balloon-borne measurements were taken in a post-frontal air mass (i.e., passage of a cold front in the morning) and indicated the formation of two low-level liquid layers (Fig. 5c) over WOP, which is attributed to low-level flow blocking (Ramelli et al., 2021a). Note that small droplets (< 6 µm) cannot be detected by HOLIMO (Sect. 2.3.1) and therefore the reported Nd should be considered a lower estimate. However, the influence of small cloud droplets on the reported LWC is minor, since the contribution of the larger cloud droplets dominates. During the first cloud event, an Nd of up to ∼ 100 cm-3 was recorded, while slightly increased Nd in the range of ∼ 50–120 cm-3 is visible during the second cloud event. On 8 March, a small-scale disturbance passed the measurement location Davos, which brought precipitation (Ramelli et al., 2021b). During the passage of the cloud system, the in situ measurements collected at WOP revealed the presence of a persistent low-level feeder cloud confined to the lowest 300 m of the cloud. The mixed-phase low-level cloud that is shown in Fig. 5d turned into an ice-dominated low-level cloud after 18:00 UTC (not shown). Throughout this event, Nd seems to range between ∼ 100–350 cm-3 (Fig. 5d), while the observed ICNC was in the range of ∼ 1–4 L-1 (see Fig. 6b in Ramelli et al., 2021b).

According to Fig. 5e and f, low Naer (< 103 cm-3) and highly variable σw values (∼ 4 times higher σw after 17:00 UTC) are representative of the period throughout which the first cloud formed, while up to 4 times higher Naer is observed during the following two cloud events, with relatively low σw values characterizing the second cloud compared to the third one. On 8 March, the disdrometer recorded rainfall over WOP, starting a few minutes after the development of the observed cloud system, which is reflected in the removal of updraft velocity measurements after 16:15 UTC (Fig. 5f). Note that the concentration measurements presented in Fig. 5 correspond to ambient temperature and pressure conditions. The contrasted aerosol and vertical velocity regimes, in which the observed clouds are formed, offer a great opportunity to test how the proposed methodology performs under a wide range of aerosol and velocity conditions. Indeed, the mean cloud droplet diameters exhibit a wide range of values, which for WOP range between 10 and 17 µm on 7 March and 8 to 12 µm on 8 March (not shown).

The Nd closure performed for the three cloud events observed over WOP during the last two days of the period of interest is presented in Fig. 6. Note that the predicted Nd is evaluated using the updraft velocity PDF calculated for each cloud period, rather than the hourly σw data shown in Fig. 5e and 5f (Sect. 2.3). Owing to the precipitation occurrence during 8 March, we focused on the 15 min time period between 16:00 and 16:15 UTC to determine a relevant updraft velocity from the wind lidar measurements representative of Cloud 3. The Gaussian fit to the updraft velocities gave a distribution with σw=0.24 and 0.16 m s-1 for the first two clouds present on 7 March and σw=0.37 m s-1 for the cloud system observed on 8 March. The w∗ values used to apply the droplet parameterization are therefore between 0.1–0.4 m s-1 (Sect. 2.3). Figure 6 indicates that the parameterization predictions agree to within 25 % with the in situ cloud droplet number concentrations. A similar degree of closure is frequently obtained for other in situ studies (e.g., Meskhidze et al., 2005; Fountoukis et al., 2007; Morales et al., 2011; Kacarab et al., 2020); however, these focused on liquid-phase clouds. Here we show that the methodology can also work for MPCs (i.e., Cloud 3 in Fig. 6). It is important to note here that part of the discrepancy between prediction and measurement could also be related to the underestimation of the measured Nd (Sect. 2.1.3). Hence, an even better degree of closure is likely. Also, the derived σw value used to calculate the predicted Nd for Cloud 1 might be biased low by the lower σw values recorded before 17:00 UTC (Fig. 5e). Nevertheless, the updraft averaging used in the droplet closure study corresponds to the measured Nd averaging time period and, therefore, we do not expect the degree of closure to be affected.

The good agreement between measurements and predictions – even under mixed-phase conditions – reveals that processes like condensation freezing and the removal of cloud droplets through riming and collision coalescence do not disturb the Smax⁡ and hence the Nd predicted by the parameterization, at least for the given clouds. That said, it is known that pre-existing liquid and ice hydrometeors falling to the activation region of clouds can deplete the supersaturation affecting the number of the activated droplets; such supersaturation depletion effects can be included in the droplet activation parameterization (Sud et al., 2013; Barahona et al., 2014) if needed. Furthermore, the parameterization predictions indicate that the best fit is achieved using a κ of ∼ 0.1 (Fig. 6). Naer at WOP is likely dominated by lower κ values, indicating that the particles are getting richer in organic material, compared to WFJ, which supports the aerosol analysis carried out in Sect. 3.1. These results are robust, indicating that for non-precipitating BL clouds the proposed calculation method captures cloud droplet formation at WOP and WFJ.

According to the methodology proposed in Sect. 2.3, using the in situ measured Naer, the estimated chemical composition, and the observed updraft velocity range, we determine the potential Nd and Smax⁡ that would form over both measurement sites. At WOP, clouds are formed locally due to the local topography (Ramelli et al., 2021a, b), supporting the use of surface measured aerosol to estimate the potential Nd over this site. This is further supported by the good agreement between predicted and measured Nd (Sect. 3.2.1). A similar closure study could not be repeated for WFJ owing to a lack of in situ data; however, the air masses sampled (i.e., those given as input to the parameterization) are often in the FT, so they should contain the same aerosol as the one used to form the clouds. This does not apply under perturbed FT conditions, which are, however, accompanied by the presence of less hygroscopic particles over the mountain-top site and are less likely related to cloud formation (Sect. 3.1). Here we assume a κ of 0.25 to calculate the potential droplets for WFJ according to our CCN-derived hygroscopicity values (Table 2) and given that Smax⁡ usually ranges between ∼ 0.1 %–0.3 %. In estimating the potential droplets for WOP, we use a κ of 0.1 given that the aerosol is likely strongly enriched in organics; the good degree of closure supports its selection (Sect. 3.2.1). Figure 7 depicts the potential Nd and the corresponding Smax⁡ time series calculated at ambient conditions for WOP (orange dots) and WFJ (blue dots) using cloud updraft velocities that are indicative of the observed σw range (Sect. 3.4), namely 0.1, 0.3, 0.6, and 0.9 m s-1. The same behavior is seen for all four σw values selected while, as expected, larger values of Nd and Smax⁡ are achieved at higher σw. During the first days of the period of interest, the calculated Nd at WOP (Fig. 7a, c, e, g) is up to 10 times larger than at WFJ, despite the lower κ values characterizing its aerosol population. WFJ tends to have lower Nd due to the lower Naer recorded. It is also important to highlight the anticorrelation between Smax⁡ and Nd values arising from the nonlinear response of droplet number and maximum cloud parcel supersaturation to fluctuations in the available aerosol and CCN concentrations (Reutter et al., 2009; Bougiatioti et al., 2016; Kalkavouras et al., 2019). Higher Naer elevates the potential Nd values. The available condensable water is then shared among more growing droplets, depleting the supersaturation. Even more interesting is the fact that until 28 February the calculated Nd time series at WOP show a pronounced diurnal cycle, similar to the total Naer time series (Sect. 3.1). Lower Nd values are visible after midnight, presumably due to a paucity of BB activities in the valley. Droplet concentrations at WFJ do not follow a diurnal pattern in contrast to the aerosol data (Fig. 1a). However, the activation fraction (i.e., Nd/Naer) at WFJ displays a clear diurnal variability until the end of February (Fig. S5 in the Supplement).

Through comparison with the MeteoSwiss precipitation measurements at WFJ (Fig. 2), it should be emphasized again that during the second sub-period of interest the occurrence of precipitation is followed by a depression in Nd (Fig. 7a, c, e, g) and a concurrent increase in Smax⁡ reaching up to ∼ 1 % (Fig. 7b, d, f, h). Especially at WFJ, Nd drops almost to zero on 1, 4, and 7 March, when precipitation is most intense (blue shaded areas in Figs. 2 and 7). These trends are related to the washout of hygroscopic material observed at WFJ (Fig. 2) leading to the extremely low CCN concentrations (∼ 10 cm-3) measured during these 3 d (Fig. 3). During the first two intense precipitation events, the Naer is relatively high compared to the third event, with concentrations reaching up to ∼ 300 cm-3 at both stations (Fig. 2). The small activation fraction (Fig. S5 in the Supplement) combined with the high Smax⁡ values indicate once more that small particles that activate into cloud droplets only above 0.3 % to 0.5 % of supersaturation are present at both stations. However, this behavior is not seen on 7 March at WFJ.

Combining the potential Nd and the corresponding Smax⁡ with the Naer data yields important information on whether clouds are sensitive to vertical velocity or aerosol changes. Cloud studies (e.g., Jensen and Charlson, 1984; Twomey, 1993; Ghan et al., 1998; Nenes et al., 2001; Reutter et al., 2009) have long recognized the role of water vapor competition on droplet formation, while the success of mechanistic parameterizations for climate models relies on the ability to capture this effect accurately (e.g., Ghan et al., 2011; Morales Betancourt and Nenes, 2014). Twomey (1993) discusses this conceptually and states that competition may be fierce enough to reduce Nd with increasing Naer, which was later demonstrated by Ghan et al. (1998) to occur for mixtures of sulfate aerosol and sea spray. Reutter et al. (2009) did not focus on such extreme conditions of water vapor competition, but rather situations that are consistent with dominance of anthropogenic pollution in clouds. Indeed, for high Naer, droplets in clouds become insensitive to aerosol perturbations, giving rise to the so-called “velocity-limited cloud formation”. Figure 8 displays this by presenting the response of the calculated Nd to changes in Naer for a representative range of updraft velocities prevailing over WOP (top panels) and WFJ (bottom panels). The data are colored by the respective Smax⁡ achieved in cloudy updrafts. For low σw values (Fig. 8a, d) we can identify that above an Naer of ∼ 300 cm-3, the Nd at both stations reaches a plateau where it becomes insensitive to further aerosol changes. At WFJ, the same behavior is seen for intermediate σw values and Naer 1000 cm-3 (Fig. 8f). Kacarab et al. (2020) and Bougiatioti et al. (2020) examined a wide range of ambient size distributions and proposed that clouds became velocity limited when Smax⁡ dropped below 0.1 %. This reflects the increasingly fierce competition for water vapor during droplet formation, which allows only a few particles to activate into cloud droplets.

Building upon these findings, we used the calculated Smax⁡ as an indicator for aerosol- or velocity-limited conditions prevailing over the Alps. The horizontal dashed lines plotted in Fig. 8a, e, and f illustrate a plateau, where Smax⁡ < 0.1 % and the modulation of the Nd is driven mostly by the cloud dynamics, hence the updraft velocity variability, rather than aerosol variations. This plateau is termed the limiting droplet number (Ndlim), following Kacarab et al. (2020), and is essentially the maximum Nd that can be formed under these vertical velocity conditions. The vertical-velocity regime is therefore strictly defined as whenever Smax⁡ drops below 0.1 % and Nd approaches Ndlim. Conversely, when Smax⁡ in clouds exceeds 0.1 %, droplet formation in the BL of both measurement sites is in the aerosol-limited regime, as the Smax⁡ is high enough for clouds to be responsive to aerosol changes.

An alternative way of examining the Ndlim response to changes in σw is shown in Fig. 9. It should be noted that the Ndlim values shown on this figure are determined by calculating the averaged Nd achieved whenever Smax⁡ < 0.1 % for each examined σw value. At WOP, droplet formation is in the velocity-limited regime only for low σw values, namely 0.1 and 0.2 m s-1, when the activated particles have more time to deplete the gas phase and the Smax⁡ reached is that required to activate only the largest particles. At WFJ the prevailing dynamics create velocity-limited conditions even for more turbulent boundary layers when σw reaches up to 0.5 m s-1. Ndlim (cm-3) is linearly correlated with σw (m s-1), which can be described as Ndlim=1137.9σw-17.1 (Fig. 9). As a result, doubling σw from 0.1 to 0.2 m s-1 increases Ndlim by ∼ 60 % for both sites, while transitioning from 0.2 to 0.4 ms-1 further increases Ndlim by ∼ 45 % and finally an additional ∼ 20 % increase in Ndlim occurs for WFJ for the 0.4–0.5 m s-1 velocity range. Remarkable agreement is seen for corresponding trends between Ndlim and σw calculated for marine Stratocumulus clouds formed under extensive BB aerosol plumes over the Southeast Atlantic (SEA) Ocean (Kacarab et al., 2020), along with BL clouds formed in the Southeast United States (SEUS) (Bougiatioti et al., 2020). Both studies have followed the same probabilistic approach for computing Nd as the one followed here. This realization is important as it implies that for regions where velocity-limited conditions are expected (i.e., under particularly high particle loads), Nd∼Ndlim and the Ndlim–σw relationship can be used to diagnose σw from retrievals of droplet number for virtually any type of BL cloud using a number of established methods (e.g., Snider et al., 2017; Grosvenor et al., 2018).

Observations of Nd when compared against Ndlim can potentially be used to deduce if droplet formation is velocity or aerosol limited. This is important because it indicates whether aerosol fluctuations are expected to result in substantial Nd responses in clouds. The strong correlation between σw and Ndlim enables this comparison. From the σw time series together with the linear Ndlim–σw relationship (Sect. 3.2.3; Fig. 9) we obtain estimates of Ndlim for both measurement stations (black dashed line in Fig.  10a, b) and the ratio Nd/Ndlim (magenta dotted lines in Fig. 10a, b). The Nd time series calculated for WOP tend to be approximately one third of Ndlim for most of the observational period (colored circles in Fig. 10a, b), while for WFJ the same ratio is even lower (∼ 1/4). Focusing on the relatively short periods when Smax⁡ values drop below 0.1 %, we estimate that droplet formation over both measurement sites enters a velocity-limited regime when the ratio Nd/Ndlim exceeds a critical value of 0.65, with the most prevalent value being at ∼ 0.9 (Fig. S6 in the Supplement).

Throughout the period of interest, velocity-limited conditions are met at WOP (WFJ) with a frequency of ∼ 0.5 % (∼ 2.5 %) of the total time, again reflecting the sensitivity of droplet formation to aerosol fluctuations. During nighttime, however, when lower σw values (∼ 0.1 m s-1) are recorded at WOP (Fig. 10c), we can observe some short periods characterized by intermediate to high Naer (> 1000 cm-3) when the ratio Nd/Ndlim exceeds ∼ 0.65, indicating that droplet variability is driven by updraft velocity. The σw values calculated at WFJ do not display a clear temporal pattern (Fig. 10d) but are generally higher than those recorded at the valley site. This is expected considering the steepness of the topography than can cause updraft velocities to be higher, especially for air masses approaching the site from the northeasterly directions. Over the high mountain-top site, cloud formation is in the velocity-limited regime (i.e., Nd/Ndlim > 0.65) under high Naer (∼ 1500 cm-3) and higher σw conditions (∼ 0.8 m s-1). These conditions can be created when polluted air masses from the valley site are vertically transported to WFJ.