The whole-air inlet was built according to the guideline of the World Calibration Centre for Aerosol Physics (WCCAP) and can sample particles up to 40 µm in diameter at wind speeds below 20 m s⁻¹,. The ambient air at 5.6 m (above ground) was sampled and an isokinetic flow splitter behind the inlet divided the flow into three sub-flows and the make-up flow. In the beginning of the campaign, the inlet was heated to 20 °C, after midday on 19 February to 30 °C. Nafion driers (model MD-700, Perma Pure LLC, NJ, USA) were used to dry the flow before the size distribution, activation, and chemical composition measurements (Fig. S1). Throughout the campaign, the relative humidity in the sampling lines after the Nafion driers was on average (25±9) % (mean ± SD) which follows the recommendation by to keep the sampling RH below 30 %–40 %.

Meteorological parameters (e.g., RH, temperature, atmospheric pressure, precipitation, wind direction, and wind speed) were measured by a VAISALA meteo station (model WXT536, Vaisala, Finland) at about 3.5 m above the ground (anchored over the CNR-container roof to avoid horizontal obstacles and have a free horizon of 360°) with a time resolution of 1 minute. The visibility was measured with a visibility sensor at about 3.35 m above the ground (at λ=880 nm, model 6400, Belfort Instrument, USA) with a time resolution of 1 second.

The GFAS (GFAS-002, after 16:00 UTC on 18 March GFAS-003, Droplet Measurement Tech., USA) measured the ambient particle size distribution in the range between around 0.05 and 72 µm (optical diameter) at approx. 3.7 m above ground with a time resolution of 1 s. It is a single-particle light scattering device and, apart from size distribution, also measures the polarization ratio of the backscattering signal. It samples horizontally at an air speed of (18.3±0.3) m s⁻¹ (GFAS-003 at (17.4±0.2) m s⁻¹) and turns (motor-driven) into the main wind direction to reduce particle sampling losses. During FAIRARI, the threshold for changing the sampling direction was set to a wind direction change of at least 3° at a wind speed above 5 m s⁻¹ for at least 5 s. The size calibration was checked at the end of the campaign using glass beads (Duke standard dry borosilicate glass bead microspheres (20.0±0.1) µm, Thermo Scientific, USA). The ambient particle size distributions were corrected for sampling and impaction losses within the GFAS using the geometries of the instrument and the equations given by based on 1 min time averages. As the wind speeds were generally low, these loss corrections led only to minor changes (4.1 % increase in campaign median effective diameter (ED) and 1.9 % increase in cloud droplet number concentration (CDNC), for Dwet>2 µm). The data were filtered to include only flow velocities between 16.4 and 19.7 m s⁻¹ and laser currents between 87 and 100 mA; however, this filtering did not reduce the size of the measured dataset.

The LWC of the air has been routinely monitored since the early 1990s at the site . During FAIRARI, the LWC was measured by a PVM (model PVM-100, Gerber Scientific, USA), installed on a pole fixed to the ground to measure the LWC at a height of approximately 2 m (above ground) with a time resolution of 1 min. The PVM is based on a forward-scattering laser spectrometer (light source: laser diode, 780 nm; detector: silicon diode) measuring the scattering within a 3 cm⁻³ volume, and LWC is inferred from the calculated scattering flux of the volume. Droplets in between around 3–50 µm diameter range can be detected with the instrument. The PVM was calibrated using a specific light-diffusing calibration disk following the instrument operator's manual.

With the CCNC 1 (model CCNC-100, Droplet Measurement Tech., USA), the aerosol particle activation was measured at the five supersaturation (SS) values that are recommended as standard settings by the Aerosol, Clouds and Trace Gases Research Infrastructure (ACTRIS), 0.1 %, 0.2 %, 0.3 %, 0.5 %, 1.0 % . Measurements of 15 min were conducted at each SS apart from the lowest, where the measurements were conducted for 20 min in a 1 Hz time resolution. This scan time of 80 min was chosen to allow for a stabilization of the temperature after the change in SS and a long enough valid measurement time afterwards. The flow and SS of CCNC 1 were calibrated nine months before the campaign, following the ACTRIS recommendations and checked during the campaign. A sampling flow of about 0.515 L min⁻¹ was measured, which is within the interval of (0.500±0.025) L min⁻¹ as recommended by the manufacturer. To ensure that the temperature had stabilized after a change in set SS, the following 4 min of data were excluded; after a change from the highest to the lowest SS, an additional 5 min were excluded.

A DMPS DMPS 1, 13.3–792 nm, electrical mobility diameter was measuring the dried aerosol size distribution behind the whole air inlet (sample flow 1.2 L min⁻¹, sheath flow 4.55 L min⁻¹, using a custom built medium Vienna type Differential Mobility Analyzer – DMA). It took 12 min to get one full size scan. The size distributions were corrected for multiple charging. A size calibration check of DMPS 1, using (203±5) nm polystyrene latex (PSL) spheres, at the beginning of the campaign showed a good performance of the sizing of the DMPS. We applied loss corrections to the size distribution measurements using the particle loss calculator by , which accounts for particle losses due to diffusion, impaction, and sedimentation. A particle density of 1000 g m⁻³ was assumed. In total, around 3.4 % of the particles got lost in the sampling line until the DMPS 1, while around 10.0 % of the particles got lost until they were counted by the Condensation Particle Counter (CPC) behind the DMA. Regular flow checks and filter tests ensured that no leaks in the sampling lines or pump failures occurred throughout the campaign.

The SP-AMS Aerodyne Research Inc., USA, measured the bulk submicron aerosol composition of the main chemical species, including organic aerosol (OA), nitrates, sulfates, ammonium, chloride, and refractory black carbon (rBC). In addition to the standard tungsten vaporizer, heated to ∼600 °C, it is equipped with an intra-cavity Nd:YAG laser (1064 nm), which provides quantification of rBC. The SP-AMS was operating in different acquisition modes, switching between V-ion mode (laser on), V-ion mode (laser off), and W-ion mode. The data were recorded with a temporal resolution of 1 min and a mass resolution of about 2400 in V-ion mode. The SP-AMS was sampling fog residuals, behind a Counterflow Virtual Impactor (CVI) inlet during fog, and total aerosol, behind the whole-air inlet during non-fog periods.

The chemical composition data from a second high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS, , or interstitial AMS) and MAAP were used to estimate the hygroscopicity of the interstitial aerosol.

The data from both AMS were processed and analyzed using the software packages SQUIRREL 1.66 and PIKA 1.26 . More details on the calibrations, corrections, and analysis using this instrument can be found in .

The MAAP (Model 5012, Thermo Fisher Scientific, USA) estimated the equivalent black carbon (eBC) mass loadings from the optical absorption of aerosol particles collected on a filter, with a time resolution of 1 min. The MAAP also considers multiple scattering effects and absorption enhancement due to reflections from the deposited particles and the filter itself. A mass absorption cross-section (MAC_BC) value of 6.6 m² g⁻¹ was used to determine the eBC mass concentration. Further technical details are given by and .

The κ–Köhler theory is widely used to calculate hygroscopic growth in the sub-saturated regime and aerosol activation based on the particle size and hygroscopicity, with the supersaturation SS defined as : 1SSDwet=Dwet3-Ddry3Dwet3-Ddry3(1-κ)exp⁡4σwMwRTρwDwet-1=RH100-1. Ddry represents the dry diameter of the particle with hygroscopicity κ. ρw is the density of water (997 kg m⁻³), Mw its molecular weight (0.018 kg mol⁻¹), and σw its surface tension (0.0728 N m⁻¹). R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), T the temperature, and Dwet the diameter of the droplet. To estimate κ, we used two approaches.

In the first method to calculate κ, the bulk particle chemical composition, measured by the SP-AMS, was used see e.g.,. For this calculation, several assumptions were needed, including that sulfates came from ammonium sulfate ((NH₄)₂SO₄) and nitrates from ammonium nitrate (NH₄NO₃). These assumptions were justified given the good correlation between the estimated ammonium concentration necessary to achieve an ion balance within the particles and the observed ammonium ion concentrations. With these assumptions and the assumption that the aerosol is internally mixed, the κbulk values were calculated based on the mass concentrations of organic matter, ammonium sulfate, ammonium nitrate, and black carbon (BC). Chloride was not included in this calculation due to its low contribution. The overall hygroscopicity κbulk for a mixture of n different chemical species is expressed as a linear combination of the individual species' κi values (Table S1 and Fig. S2), weighted by their respective volume fractions fi in the dry particle : 2κbulk=∑i=1nfiκiwithfi=miρi∑i=1nmiρi. The volume fractions fi of the individual components were calculated from the measured mass concentrations, mi, and their respective densities, ρi (Table S1 in the Supplement). The same method is employed to obtain the hygroscopicity parameter of the interstitial (κinterstitial) and fog residual (κresidual) aerosol particles.

In the second approach, the bimodal (Aitken and accumulation mode) hygroscopicity parameters were optimized by minimizing the normalized root mean square error (NRMSE) between observed and predicted CCN spectra (i.e., CCN concentration at various supersaturations) measured by the CCNC. The optimization was performed using the Nelder-Mead method implemented in the Python scipy library version 1.15.1,.

To begin, the measured dry aerosol number size distribution was decomposed into two log-normal modes representing smaller Aitken and larger accumulation particles (Fig. S3). Various combinations of organic, inorganic, and BC mass fractions in two modes were then systematically explored to predict CCN concentrations, while conserving the total mass of each chemical species. To simplify the process, the masses of ammonium nitrate and ammonium sulfate were combined and treated as total inorganic mass, while BC was assumed to have the same mass fraction in all aerosol particle sizes. Predicted CCN concentrations were then computed using the κ–Köhler theory . Among all generated combinations of chemical compositions (organic, inorganic, and BC mass fractions) and the associated mode-specific hygroscopicity parameter, the one yielding the lowest NRMSE between observed and predicted CCN spectra was selected as the optimized bimodal composition, described by κoptAitken and κoptacc. We considered a constant ambient temperature of 20 °C for all calculations, which corresponds to the average temperature in the sampling line before the CCNC in our mobile laboratory (see Sect. ).

To estimate the particle number size distribution at a certain relative humidity, and thereby the hygroscopic growth, we applied Eq. (), using κoptacc: every Ddry of the measured dry particle number size distribution was calculated to its corresponding Dwet(Ddry,RH), following . Using Dwet(Ddry,RH) and the measured dry number size distribution, the hydrated number size distribution was calculated: 3dNDMPSdlogDwet=dNDMPSdlogDdrydlogDdrydlogDwet. The hygroscopic growth factor g(RH) is defined as: 4g(RH)=DwetDdry,RHDdry.

Fog events were defined by an RH≥90 % and visibility ≤1 km, and are numbered chronologically, consistent with , where the full list can be found. The criteria had to be constantly met for at least 36 min (allowing for at least 3 size distribution scans of the DMPS) to be counted as an event. Due to the continuity criteria, a night can be split into several fog events if the visibility was above 1 km for short periods. Similar to , we divided the fog events into activated and unactivated fog. When the visibility was below 1 km due to hydrated particles only, i.e. when there was no droplet activation (i.e. absence of a distinct droplet mode observed by the GFAS), we use the term unactivated fog. Once there is droplet activation, we refer to it as activated fog.

Another variable that is often used in the literature to define fog, and especially clouds, is the LWC (see Sect. ). It can be measured directly, e.g. with a PVM or calculated from the measured wet number size distribution, e.g. using a GFAS: 5LWC=ρw∑iπ6Dwet,i3dNGFASdlogDwetidlogDwet,i using the density of water ρw=997 kg m⁻³. To describe the particle sizes in fog, ED is typically used. It is calculated for diameters of a given size range [Dwet,min; Dwet,max] by: 6ED=∑iDwet,i3dNGFAS/dlogDwetidlogDwet,i∑iDwet,i2dNGFAS/dlogDwetidlogDwet,i. Equivalent to ED, the CDNC is calculated by summing the wet number size distribution from Dwet,min to Dwet,max. During fog, the ED typically reflects the size distribution mode, which is dominated by activated particles or fog droplets. However, in practice, it is usually calculated for the entire size range measured by the instrument used in the respective study. With the Fog Monitor (FM) as one of the most commonly used instruments in the literature to measure fog droplet size distributions, this leads to a typically chosen lower diameter of about 2 µm. To explore the impact of varying the lower integration diameter on the resulting ED (using Eq. ) and CDNC, we tested different values for this lower limit. We chose 2 µm as the lower diameter, consistent with the most commonly selected diameter and as a more realistic value for the FAIRARI campaign the calculated activation diameter (Dwet,act_S). In the following, we refer to those variables with ED_>2, CDNC_>2, and ED_act, CDNC_act, respectively. The maximum diameter Dwet,max in this study is given by the detection limit of the GFAS and is therefore 72 µm. Following , the ambient activation diameter, Dact_S, was calculated using the ambient surface size distribution measured by the GFAS and taking its first local minimum from the right. As an illustration, an example number and resulting surface size distribution from DMPS and GFAS is shown in Fig. . The reason behind the significantly lower values shown by the GFAS for the ambient aerosol number size distribution measurements for diameters below about 5 µm (Fig. ) is not fully understood yet and could be due to instrumental issues of the prototype GFAS. A more detailed discussion and comparison to the PVM will follow in the next section.

The ambient peak supersaturation SS_crit was calculated using the wet (measured by the GFAS) and dry (measured by the DMPS) number size distribution and κ–Köhler theory (Eq. ). Assuming that the dry particles activate starting from the largest ones, we used the wet number concentration of activated particles, NGFAS(Dwet>Dwet,act_S)=CDNCact, and summed over the dry number size distribution until the diameter Ddry,act at which a closure was reached with the ambient number concentration: 7NDMPSDdry>Ddry,act=!NGFASDwet>Dwet,act_S=CDNCact. To calculate these number concentrations, we only summed over the measured size range of the instruments and did not fit a curve to the data, thereby potentially missing some of the particles in the coarse mode.

In Sect. , we tested the impact of different fog definitions on the visibility, the LWC, and the ED. For that comparison, we used two different definitions of fog: the visibility-only definition as used in and an additionally added LWC threshold of 0.05 g m⁻³. This threshold was chosen as it corresponds to the previously used threshold of 0.08 g m⁻³, which was originally applied to liquid water content measurements by the PVM that were multiplied by a factor of 1.72 . We also compared the visibility sensor measurements, χm, with the calculated visibility, based on the LWC measurements, χLWC. For that, the Koschmieder equation χ(λ)=constant/be(λ) was combined with the finding by that the light extinction coefficient be can be estimated as be=144.7⋅LWC0.88. However, the coefficients in this power law vary widely, depending on the physicochemical characteristics of the aerosol and the meteorological conditions in the respective environments e.g.,. We therefore calculated the coefficients a and b most appropriate for the winter months in the Po Valley by performing a linear regression on the logarithm of the measured visibility, χm: 8χm(880nm)=!a⋅LWC(780nm)b=χLWC(780nm).

The aerosol and fog parameters were measured with various instruments, which all cover different particle size ranges, have different temporal resolutions, and were measured at slightly different locations around the site.

While our ambient measurements have a temporal resolution of 1 s to 1 min, the dry aerosol number size distributions have a temporal resolution of 12 min. A linear interpolation to a 1 min time resolution, as done for the calculation of N>503 (number concentration of particles with a dry diameter larger than 503 nm), will be small as the variations in the measured dry aerosol number size distributions were small. Moreover, we measured the dry size distribution up to diameters of 792 nm, thereby missing the very largest particles, the coarse mode which can have a profound impact on the aerosol light extinction and thus visibility . In our analysis, a missing coarse mode would decrease the dry activation diameter and thereby decrease the wet activation diameter and increase the critical supersaturation. A comparison between the measurements of the total CPC and the integrated CPC (Nint=(1.033±0.003)⋅Ntot-(183±12) cm⁻³, determined from a weighted bivariate fit, Fig. S4), as well as the method-independent results for κ (see Sect. ), however, suggest that the effect of an undetermined coarse mode is rather small. In addition, the size distribution measurements were binned with rather large bin sizes (up to 85 nm) for large diameters, leading to uncertainties in the determination of the dry activation diameters since the nearest bin diameters were used.

Cloud and fog microphysical parameters are notoriously difficult to measure and thus it is crucial to evaluate the different instruments. We compared the LWC measurements from the GFAS (calculated with Eq. ) with those of the PVM and found that they correlate well (Spearman correlation of 0.82, p≪0.01, Fig. S5a). However, the PVM measures on average (determined from a weighted bivariate fit) about 3 times higher values for the LWC than the GFAS: LWCGFAS=(0.342±0.005)⋅LWCPVM-0.001 g m⁻³. In some fog events (e.g. fog event 15), the LWC measurements demonstrated strong agreement, closely following the 1:1 line (Fig. S5a). These events were characterized by the presence of large fog droplets as can also be seen when comparing the visibility measurements, using the Ground-based Counterflow Virtual Impactor (GCVI), with the calculated visibility, using the GFAS data and Mie theory (Fig. S5b). Moreover, the comparison of the measured and calculated visibility also shows that the GFAS is underestimating the total surface (Fig. S5b): χMie=(2.30±0.02)⋅χm+(27±2) m. Therefore, most likely, the PVM measurements are more accurate, while the GFAS measurements are too low for most of the cases (except when effective droplet diameters were large, see colorcode in Fig. S5b). Potential reasons behind this discrepancy are wrong diameter assignment (Mie wiggles) for smaller particles , underestimation of particle losses for larger particles, and undercounting due to coincidence. Although wind speeds were very low and we corrected for droplet losses in the GFAS using the measured wind speed and direction, we cannot exclude additional minor losses due to misalignment between GFAS and the main wind direction. Further, an underestimation of the droplet concentration could also have been caused by fluctuations in the measured true air speed by the GFAS, although we believe this to be an unlikely cause. As shown in Fig. , the GFAS clearly underestimated particles below 3 µm (in the high gain channel of the GFAS). This could have been caused by a too high rejection rate of the high gain channel (determined from qualifier and sizer) of the GFAS, which would have a more prominent effect when the LWC is less dominated by very large droplets. Moreover, the instruments were measuring about 40 m apart and at different heights (GFAS: 3.7 m, PVM: 1.5 m), which can cause differences in the measurements if the fog is not homogeneous. Furthermore, the instruments were measuring at slightly different wavelengths (780 nm vs. 660 nm, PVM vs. GFAS, respectively), however, if any impact, this should lead to slightly higher values measured by the GFAS than the PVM. Also, the size ranges measured by the two instruments are slightly different; however, even after calculating the LWC for the same size range, the discrepancy remains. The large disagreement in LWC is not unusual, , for example, found that the LWC can differ by up to a factor of 5 between different instruments (before loss corrections).

From the physical and chemical properties of the aerosol described above, we calculated the hygroscopicity parameter (κ) of the particles and parameters related to the droplet activation, namely, wet and dry activation diameter as well as critical supersaturation (Fig. ) using the Köhler theory (Eqs. , , and ). The κ-value is calculated with two different approaches (see Sect. ). κbulk and optimized κ in accumulation mode, κoptacc thus obtained, show very similar distributions, with campaign medians out of fog equal to 0.34 and 0.35, respectively (Fig. a). This implies that particles larger than 1 µm, which are included in the calculation of κoptacc but not in κbulk, are either sparse in number or have a similar hygroscopicity to the smaller particles. The agreement between both methods for calculating κ suggests that the hygroscopicity of accumulation mode particles during winter at SPC can be estimated using the bulk chemical composition measured by the SP-AMS, and hence is also comparable to the inferred hygroscopicities of the residual and interstitial particles (see Fig. a). As expected, the fog residuals represent the most hygroscopic fraction of the aerosol population, while the hygroscopicity of the interstitial particles falls between that of the total aerosol and the residuals. This is explained by the diurnal variability of the hygroscopicity values (see Fig. b), which generally shows higher hygroscopicity values during the day. The increase in the night-time hygroscopicity is due to the enrichment of nitrate . Furthermore, the relatively higher nocturnal increase of the hygroscopicity observed in the residuals as compared with the total aerosol suggests an enhanced uptake of nitrate into the fog droplets in the presence of water. All in all, the hygroscopicity values indicate a highly soluble aerosol, and the difference between the residuals and the interstitial aerosol might suggest some degree of external mixing (Fig. c).

Using the calculated time series of κoptacc, we quantified the hygroscopic growth of dry aerosol particles across all fog events during the campaign (Eq. ). Interestingly, the campaign median of the optimized Aitken-mode hygroscopicity, κoptAitken=0.4, was comparable to κoptacc. This similarity suggests a rather uniform chemical composition across particle sizes. Consequently, κoptacc was adopted as a representative value for all size ranges. As a result, only minor variations in the growth factor at RH=100 % (Eq. ) were observed between events, consistent with the near-constant behavior of κoptacc throughout the campaign.

Particles with a dry diameter of around 13 nm grow by a factor of about 1.60 (IQR: 1.59–1.63), while particles larger than 500 nm grow by more than a factor of 10 (Fig. S7). Under supersaturated conditions, which are needed for droplet activation, these growth factors will be even higher. Using an example fog event, we illustrate the hygroscopic growth of the aerosol particles and their co-existence with activated particles (Fig. ). Already at 100 % RH, some aerosol particles can grow sufficiently to enter the size range typically associated with activated particles or droplets as also shown by e.g.. As a result, the commonly used ambient diameter threshold for fog residual sampling usually around 6–8 µm, see e.g. may be too low, leading to an unintentional sampling of a mixture of unactivated aerosol particles and fog droplets when, for example, using CVI inlets. At the same time, the ambient diameter threshold typically used to analyze interstitial, unactivated aerosol particles (e.g., PM_2.5 or PM₁ inlets) can also be too low in conditions resembling those of the Po Valley, leading to a potential undersampling of interstitial aerosol during periods with high RH.

Analyzing particle activation using the κ-Köhler theory, we find that the median dry activation diameter ranges from approximately ∼370 to ∼710 nm across all fog events (Fig. d). These values, derived from time-resolved κbulk, reflect the temporal variability in aerosol hygroscopicity. In contrast, the DMPS-GFAS closure based on the nearest-neighbour approach gives a comparable range of ∼400–710 nm.

The resulting median wet activation diameter, Dwet,act, and critical supersaturation, SS_crit, range between 5.9 and 13.7 µm and 0.011 % and 0.026 %, respectively (Fig. e and f). The agreement between the wet activation diameter based on the method described in , Dwet,act_S, and the wet activation diameter based on the κ-Köhler theory calculations, Dwet,act, varies (Fig. e). The latter method represents a theoretically accurate definition of the activation diameter but is sensitive to correct number size distribution measurements of both the wet and dry aerosol as input (Eq. ). The former method, on the other hand, relies on the assumption that activation is the main process determining the minimum in the wet aerosol number size distribution and that other size-dependent processes, that simultaneously modify the size distribution, are negligible in this regard.

The LES code MIMICA was used to examine the impact of the dry aerosol number size distribution on the CDNC and LWC during the consecutive fog events 7–9 (Fig. ). In agreement with the high dry activation diameters observed during FAIRARI, we find that the CDNC and LWC are mostly affected by the representation of the largest particles in the dry aerosol number size distribution, while the total aerosol number concentration is of less importance. Optimizing the dry aerosol number size distribution fit to the entire measured distribution results in 55 % and 28 % higher values for the CDNC and LWC, respectively, compared to optimizing the fit to the measured size distribution above a certain diameter threshold larger than 100 nm. This was expected as the calculated dry activation diameter during fog events 7–9 was about 500 nm (Fig. d) and stresses the importance of detailed measurements in this size range.

Furthermore, we analyzed the relative impact of the dry aerosol number size distribution and hygroscopicity on the simulated CDNC and LWC, using parameters of the two fog events that are shown in Fig. S12 (see SI, incl. Figs. S10 and S11). As expected in a polluted region like the Po Valley, where CCNs are abundant, a lower number concentration of large accumulation mode particles (such as in fog events 15–16 compared to fog events 7–9, Figs. S10 and S6), results in fewer activated particles (Fig. S11a). Keeping the hygroscopicity constant but changing the aerosol size distribution, CDNC decreases from 52 cm⁻³ (IQR: 33–66 cm⁻³, m7s7c7) to 22 cm⁻³ (IQR: 18–33 cm⁻³, m7s15c7). Contrary, keeping the size distribution constant but changing the hygroscopicity, CDNC stays almost constant – decrease from 52 cm⁻³ (IQR: 33–66 cm⁻³, m7s7c7) to 51 cm⁻³ (IQR: 33–63 cm⁻³, m7s7c15). Moreover, the slightly higher hygroscopicity of the aerosol particles during events 7–9 compared to 15–16 (0.48 vs. 0.42), led to slightly higher number concentrations of activated particles (using the size distribution of events 7–9 and 15–16, respectively). Changing the dry aerosol number size distribution from a campaign average size distribution to an extreme distribution with respect to the upper tail changed the CDNC by a factor of about 2.5, while exchanging the hygroscopicity of the dry aerosol during those two fog events changed the CDNC only by about 4 %. This is expected, based on the κ–Köhler theory: increasing the hygroscopicity of the particles is related to a lower critical supersaturation needed for the particles to get activated, therefore, decreasing the dry activation diameter for a given ambient supersaturation. The same behavior was observed for the LWC (Fig. S11b). Our results indicate that the microphysical differences between fog events 7–9 and 15–16 are primarily driven by variations in the dry aerosol size distribution, with hygroscopicity playing a comparatively smaller role. These results suggest that while aerosol chemical properties play an important role in determining hygroscopicity and influencing the water vapor budget in fog, the physical characteristics, particularly the size distribution, exert a more primary impact on aerosol activation, thereby shaping fog microphysical development.

The dry and wet activation diameters are expected to be highly variable for different environments and fog types, depending on the dry particle number size distribution, the aerosol hygroscopicity, and the supersaturation. For example, during the ParisFog 2012/2013 campaign, found a mode diameter in the dry particle number size distribution at about 100 nm, similar to us, a much lower κ=0.14 compared to here, and higher peak supersaturations between 0.031 % and 0.046 %, leading to lower wet activation diameters of about 2.6 µm. During WiFEx in the Indo-gangetic Plain region, on the other hand, activation diameters larger than 10 µm were measured . , measuring in the North China Plain, found activation diameters in between (around 4 µm). During the Po Valley experiment in 1989, the supersaturation was about 0.03 % , and two populations of particles with respect to their hygroscopicity were found, using a different method than ours . The dry activation diameter of the more hygroscopic ones was around 425 nm , while the less hygroscopic ones activated at around 775 nm . These past results from the Po Valley are generally in line with our observations, although particularly the supersaturations seem to have decreased over the years. Even though there is a large uncertainty associated with the methods for determining supersaturations, this result could contribute to understanding the factors driving the decrease in the fog occurrence in the Po Valley. Secondly, our results seem to suggest a lower degree of external mixing than reported by the earlier studies - which could be explained by the decrease in local aerosol sources and increase in the contribution of more aged aerosol. Furthermore, the comparison with other environments with abundant fog suggests that the contribution of hygroscopically grown but unactivated particles to visibility reduction and recorded fog properties is likely to be particularly high in the Po Valley environment, which we therefore analyze and discuss in the next subsection.

Comparing the ED and CDNC for minimum diameter thresholds of 2 µm with minimum thresholds of Dwet,act_S (campaign median Dwet,act_S: 10.1 µm, IQR: 9.1–12.1 µm), we find that the ED increases by 81 % (from 11.6 to 21.0 µm, Fig. a), while the CDNC decreases by 87 % (from 97.4 to 12.4 cm⁻³, Fig. b) if only activated particles are considered. These numbers will vary depending on the dry and ambient particle number size distributions, the ratio between unactivated and activated fog times, as well as the droplet growth rate. The mode in the CDNC_>2 histogram around 100 cm⁻³ in Fig. b is caused by a close to constant contribution of hydrated aerosol particles. As the hydrated aerosol particles are small but numerous compared to the activated particles (or fog droplets), they contribute on average with 95.0 % to CDNC₂ (median, IQR: 91.8 %–99.2 %, Fig. c), while their contribution to the LWC₂ is only about 21.3 % (median, IQR: 12.1 %–46.8 %, Fig. d). A key conclusion from these results therefore is that in polluted environments it is likely that, unless the activation is specifically accounted for, a large fraction of the measured CDNC values are actually contributions from the hydrated haze particles. The contribution of these particles to the liquid water path (LWP) can vary substantially.

To illustrate these non-linear relationships and provide clues into factors driving the contribution of hydrated particles to fog microphysics, we analyzed the sensitivity of the LWC of the hydrated aerosol particles to accumulation mode aerosol number concentration and supersaturation in the range of the values observed during FAIRARI. For this, we used κ–Köhler theory (Eq. ) with the median chemical composition and size distribution as inputs (Fig. ). The individual fog events observed during the campaign are also shown, color-coded by the relative difference between water vapor saturation pressure at day-time maximum temperature and night-time minimum temperature as a proxy for local supersaturation. Higher accumulation mode number concentrations lead to a higher LWC, for a constant SS. For a constant accumulation mode number concentration, an increase in the SS first leads to an increase in the corresponding LWC, LWChydr., due to the growth of the hydrated aerosol particles. At an SS of about 0.009 %, however, using κ=0.45, the LWChydr. starts decreasing for increasing SS. This can be explained by the fact that the largest hydrated aerosol particles get activated and, therefore, do not contribute to LWChydr. anymore. Additionally, the sensitivity of LWChydr. to accumulation mode number concentration increases notably as SS decreases. At SS ≈ 0.020 %, increasing the concentration from 1000 to 8000 cm⁻³ raises LWChydr. by about 400 %. This increase grows to roughly 700 % at SS ≈ 0.015 %, and reaches nearly 1000 % at SS ≈ 0.010 %. Using the measured accumulation mode number concentration and the calculated SScrit (see Eq.  and Fig. f), we see that during FAIRARI, the LWChydr. was varying between about 0.006 and 0.027 g m⁻³, the higher values also generally corresponding to the higher accumulation mode number concentrations. Calculated from the GFAS measurements, the quartiles of the event-based LWChydr. vary between 0.001 and 0.021 g m⁻³. However, it should be noted that SScrit, calculated for the fog events, is highly sensitive to the measurements of the GFAS and the DMPS. Given the comparison between the GFAS and the PVM data, the experimental values of LWChydr. probably represent a lower limit – hence we deem the agreement between the prediction based on the dry particle size distribution and the GFAS-based values satisfactory. The observations also show that for a given accumulation mode number concentration supersaturation increases with the relative difference between water vapor saturation pressure at day-time maximum temperature and night-time minimum temperature, as expected – also giving confidence in the methodology for determining SS. For a given SS, on the other hand, the observations show how the number concentration of particles compensates for changes in the relative vapor pressure difference. This also makes sense as for a given amount of condensable water one would expect lower median saturation ratios for higher particle number concentrations.

The relationships between CDNC, LWC, and ED carry fundamental information about fog microphysics, and are useful for e.g. model evaluation and process parameterization purposes. Given the impact of the hydrated vs. activated particles on CDNC and LWC, these relationships are likely to be affected by the way hydrated aerosols are considered in any respective analysis. A clear positive correlation between CDNC and LWC, with the slope depending on the ED, is expected only when the wet number size distribution is monomodal and ED a useful parameter to describe the size distribution (compare Eqs.  and ). Indeed, excluding the hydrated aerosol particles from our data set and focusing solely on the activated particles (Dwet>Dwet,act_S) clearly demonstrates such a correlation (Fig. ). This approach could be applied to any ambient number size distribution dataset to obtain an initial assessment of the impact of hydrated aerosol particles on measured data. The assessment could be particularly useful when in-situ aerosol observations are lacking and a bottom-up calculation of the potential hygroscopic growth of the aerosol particles cannot be performed.

Hydrated aerosols can also impact the actual onset of fog development as, for example, seen in the comparison of the temporal evolution of ED and CDNC (see Fig. S12 for two example fog events). As expected, the ED is mostly affected in the beginning of the fog events (Fig. S12e and f), when activated particles or droplets are still small and few. The CDNC, on the other hand, is affected throughout the whole event, with an approximately constant offset (Fig. S12g and h), caused by the constant contribution of hydrated aerosol particles (as also seen in Figs.  and S13). We therefore analyzed the effect of hydrated aerosol particles on the visibility reduction and thereby the time period defined as fog (unactivated + activated fog). In a first step, we compared the measured visibility with the visibility calculated using the PVM measurements (Eq. , Fig. S14). Including all fog times, both unactivated and activated fog, the visibility can be calculated with χ=17.08⋅LWC-0.71, using the relationship as proposed by . Restricting the fog to periods with LWC > 0.05 g m⁻³, the visibility can be calculated with χ=11.82⋅LWC-0.96. The LWC threshold (>0.05 g m⁻³), therefore, corresponds to a visibility threshold of about 150 m, while the 1 km visibility threshold corresponds to an LWC threshold of about 0.003 g m⁻³.

Next, we compared the effect of a visibility-based vs. an LWC-based fog definition on different fog parameters, such as visibility, LWC, and ED (Fig. ). During FAIRARI, analyzing periods with visibility below 1 km, compared to additionally restricting those periods to an LWC > 0.05 g m⁻³, the median visibility was reduced by 28 %, from about 82 m to about 60 m. The LWC was increased by 52 %, from about 0.11 g m⁻³ to about 0.16 g m⁻³, while the ED was increased by 33 %, from about 11.7 µm to about 15.6 µm. The mode at around 700 m in the histogram of the visibility Fig. a, similar to the results by, the peak at LWC = 0 g m⁻³ (Fig. b), and the low values of ED (Fig. c) for the visibility-based fog definition all suggest the influence of hydrated aerosol particles. Adding an LWC threshold seems to exclude those periods of unactivated fog, decreasing the total in-fog time during FAIRARI by about 36 %.

Choosing an LWC-based fog definition instead of a visibility-based one to exclude periods of unactivated fog raises two additional questions: (1) what LWC threshold should be used? and (2) to what extent are the results affected by the choice of instrument used for the LWC measurements? To answer the first question, we compared the three parameters analyzed in Fig.  with 20 different thresholds for the LWC. We found that the biggest change in resulting campaign average values of visibility, LWC, and ED happens when applying an LWC threshold of around 0.005 g m⁻³ to define fog occurrence (Fig. S15). Most likely, this marks the regime in which droplet activation happens, which leads to a large change in the contribution of hydrated vs. activated particles. To answer the second question, we compared the GFAS with the PVM. As the GFAS most likely underestimates the LWC (Fig. S5), a GFAS-based LWC threshold impacts the analyzed parameters even more (Fig. S16). The visibility decreases by 39 % and the LWC and ED increase by 111 % and 73 %, respectively. The observed decline in fog frequency between 1984 and 2012 in the Po Valley when defining fog occurrence using a visibility threshold versus the approximately constant fog frequency when defining fog occurrence using an LWC-threshold is most likely an indicator of a reduction in the concentration of hydrated aerosol particles as those contribute to the visibility reduction but not so much to the LWC.

In the literature, there is a large spread in defining the presence of fog, combining thresholds for visibility, LWC, and/or CDNC (typically calculated for Dwet>2 µm). A visibility-only fog definition was used by , and , with the difference that chose 2 km as a threshold, instead of 1 km. A CDNC ≥ 1 cm⁻³ definition, measured with a CDP 2, was used by . A combined definition, using CDNC and LWC, was used by and . In their studies, the LWC had to be ≥0.001 g m⁻³ and the CDNC ≥ 10 cm⁻³ and ≥1 cm⁻³, respectively. define fog by a sharp increase in CDNC, but no quantitative criterion for fog occurrence is provided. report the average of a dense fog event with visibility < 200 m. As can be seen in Fig. , the observed key microphysical parameters, LWC and CDNC, cover a large range between the different investigated sites but also show a large temporal variation within each study, ranging from a few tens to several hundreds of fog droplets with LWC-values from around 0.01 g m⁻³ to over 0.3 g m⁻³.

Compared to other fog studies, our CDNC and LWC values align well with those of , who investigated fog in Nanjing, China. This might be due to a similar contribution of hydrated aerosol particles as the wet size distribution and the CDNC vs. LWC relationship suggest. Interestingly, measured more than 25 years earlier at the same site in autumn much higher CDNC and LWC but with higher variability (throughout one month). Studies at more remote locations, such as coastal sites or within rainforests , generally report lower values for CDNC and LWC. Some studies in China , in turn, have observed approximately five times higher values for CDNC and LWC than those found in the current work. This is most likely due to a similar hygroscopicity of the aerosol but larger aerosol number concentrations about 16 000 cm⁻³ for Ddry: 10–700 nm,. Part of the differences in the fog microphysical parameters can be explained by differences in the encountered fog (i.e. temporal, spatial, and seasonal differences among the various studies), as well as e.g. technical reasons and differences within the used fog or cloud probes (incl. data processing and applying or non-applying of loss corrections) . Another important reason is the varying practice in reporting the contribution of hydrated but not activated aerosol particles to LWC and CDNC. During FAIRARI, we saw a contribution of about 85 cm⁻³ hydrated aerosol particles to an average CDNC₂ of about 100 cm⁻³, shifting the values from being close to measurements in Nanjing to being close to values measured at a coastal cite (Fig. ). For comparison, report a contribution of hydrated aerosol particles to CDNC of about 200 cm⁻³, but their total CDNC is much higher (around 600 cm⁻³). In contrast, find a much smaller contribution of about 8 cm⁻³, with a total CDNC of around 61 cm⁻³. Together, these inconsistencies make the comparison of the different studies challenging, impacting the development of numerical models for fog forecasting e.g..

Hydrated aerosol particles also should be accounted for when comparing in situ observations with simulation results (Fig. ). Regarding microphysical properties, MIMICA overestimated both the number concentration of activated particles (droplets) and LWC, as is common in models adopting bulk microphysics schemes. However, the simulated mean droplet diameter aligned well with observations. Accounting for hydrated aerosols formed through hygroscopic growth in the microphysical analysis improved the agreement between simulated and observed droplet number concentrations and droplet diameters.