The FAIRARI campaign 2021/22 was conducted at the San Pietro Capofiume site (SPC, 44.65° N, 11.62° E) in Italy, which represents a background-polluted continental environment in the eastern Po Valley. The measured quantities and corresponding instruments used in this study are summarized in Sect. S2. We focus on three consecutive radiation fog events that took place during the winter of 2022, labeled as events 7, 8, and 9 (see Fig. a). The series of events began at 18:49 LST (local standard time, UTC+1) on 18 February, and the fog dissipated completely by 07:38 LST on 19 February, with a mean visibility (Vis) ranging between 66 and 151 m. The fog formation was triggered by longwave radiation loss and nocturnal surface cooling, leading to air saturation and aerosol activation. The near-surface layer was stably stratified, characterized by weak turbulence (mean turbulent kinetic energy, TKE ∼0.011 m² s⁻²) and light winds (mean speed ∼ 0.6–0.9 m² s⁻²), predominantly from the southeast to the south (125–200°). The stable conditions favored the accumulation of a high aerosol load (mean number concentration for particles with diameters 13.3–792 nm, Na∼6065 cm-3) and fog droplets (mean number concentration for droplets with diameters 2–60 µm, Nc ∼59 cm-3 and effective diameter, ED ∼ 13 µm) close to the surface and a progressively increasing optical thickness of the fog layer during the evening and early night.

The aerosol chemical composition in terms of mass was dominated by ammonium nitrate, ammonium sulfate, and organics, with minor fractions of chloride and black carbon (Fig. ). The bulk median hygroscopicity parameter κ of the mixture, calculated using the Zdanovskii–Stokes–Robinson (ZSR) method , is approximately 0.45 during the fog events, indicating moderately hygroscopic aerosols. The relatively high κ promoted hygroscopic aerosol growth and the formation of non-activated hydrated particles (hereafter referred to as hydrated particles), which substantially influenced the fog microphysics, particularly droplet number concentration and effective diameter (see further discussion in ). As a result of their hygroscopic growth, hydrated particles also contribute to a bimodal droplet size distribution (Figs. a and a).

In this study, the observed wet critical activation size (i.e., the maximum size of non-activated hydrated particles) was determined using two approaches (see for details). The first approach followed , identifying the ambient activation diameter as the first local minimum from the right side of droplet size distribution; particles larger than this threshold were classified as activated droplets. The second approach employed a closure analysis, comparing the dry aerosol spectrum with the droplet spectrum. Assuming activation starting from the largest aerosols, the dry distribution was integrated until it matched the activated droplet number concentration, the resulting dry particle size was taken as the dry critical activation diameter, and the corresponding wet activation diameter was then calculated using κ-Köhler theory. For fog events 7–9, the wet activation diameters calculated using κ-Köhler theory resulted in a mean value of 9.7 µm , based on which the observed wet particles were categorized into two groups: particles ranging from the typical lower measurement limit of fog monitors (2 µm) up to approximately 10 µm were counted as hydrated particles, while those larger than 10 µm were considered activated droplets. This classification generally agrees with the bimodal size distribution shown in Fig. a.

During the three fog events, two brief interruptions were observed (at 00:14–01:14 and 04:02–04:14 LST), corresponding to periods that did not meet the fog criteria of Vis ≤ 1 km and RH ≥ 90 % . The first interruption was additionally characterized by a temporary disappearance of large droplets and a sharp decrease in LWC, leaving only residual haze particles (Fig. a). We suggest that these interruptions were caused by short-term near-surface warming that led to droplet evaporation, although the precise local meteorological drivers remain unclear (see Sect. ).

The simulations were carried out using the MISU–MIT Cloud and Aerosol model (MIMICA; ), a three-dimensional LES code that solves the equations describing a non-hydrostatic, incompressible atmospheric system. The model employs a 1.5-order subgrid-scale turbulence closure scheme and computes surface fluxes using Monin–Obukhov similarity theory , enabling the representation of the exchange of momentum, heat, and moisture between the surface and atmosphere under specified surface forcing. Warm cloud microphysics is represented using a two-moment bulk scheme , which predicts the mass mixing ratios and number concentrations of hydrometeors. The mass distributions of cloud droplets and raindrops are described by gamma functions. Raindrop terminal velocities follow a power-law relationship , while cloud droplet terminal velocity is computed based on a generalized gamma distribution within the Stokes regime and is incorporated into the prognostic equations for droplet number concentration Nc and liquid mixing ratio Qc (see Sect. S1). Supersaturation is explicitly resolved using the pseudo-analytical approach of , with its effects on condensation and evaporation integrated at each time step.

MIMICA includes an interactive aerosol scheme, where aerosols are described using a two-moment module with all aerosol modes following lognormal size distributions . The aerosol number size distribution with respect to particle radius r in mode k is given by: 1dNa,kdr=Na,k2πrln⁡σkexp⁡-(ln⁡r-ln⁡rg,k)22ln⁡2σk, where Na,k is total aerosol number concentration, rg,k is geometric mean radius and σk is geometric standard deviation for mode k.

In the present study, the aerosol size distribution is represented by one mode, covering the measured size range of 13.3–792 nm. Aerosol hygroscopic growth and activation into droplets are calculated based on κ-Köhler theory (see Sect. S3). Consistent with the lower measurement threshold common in fog monitors , particles with wet diameters larger than 2 µm are typically classified as fog droplets. To further investigate the role of fog droplets with different sizes in fog processes, and similar to the classification of observed wet particles, a detailed classification is applied here to the simulated wet particles: particles that have grown a wet diameter above 2 µm but do not reach the activation size are categorized as hydrated aerosols, whereas those exceeding the activation size (determined by κ-Köhler theory) are counted as activated droplets. Accordingly, the number concentration of total droplets Nc is the sum of hydrated aerosols Nc,hyd and activated droplets Nc,act: 2Nc=Nc,hyd+Nc,act=∫Dmin=2µmDactn(D)dD+∫Dact∞n(D)dD. Radiative transfer is computed using a four-stream scheme , which includes six bands for solar radiation and twelve bands for the infrared part. This scheme accounts for the radiative effects of cloud droplets and raindrops, allowing a dynamic coupling between radiation and cloud microphysical processes. Note that the aerosol particles do not directly affect the radiative transfer, only indirectly by altering the fog microphysical properties.

Based on the above schemes, the diagnosed microphysical quantities of total droplets are used to characterize the fog life cycle and optical properties. Fog periods are defined by a Vis ≤ 1 km and RH ≥ 90 % , where the parameterized visibility Vis is calculated as a function negatively correlated with LWC and Nc : 3Vis=1.002LWC⋅Nc0.6473=1.002ρairQc⋅Nc0.6473, where ρair is the air density and Qc is liquid mixing ratio. This parameterization is applicable for LWC in the range of 0.005–0.5 g m⁻³ and Nc within 1–400 cm⁻³.

The liquid water path LWP and optical thickness τ of the fog layer are calculated following and as: 4LWP=∫fogbasefogtopLWC(z)dz=∫fogbasefogtopρair(z)Qc(z)dz, 5τ=3LWP2ρwreff, where the fog top and base heights are determined from grid cells meeting the criteria: Nc,act≥1 cm⁻³ and Qc≥0.01 g kg⁻¹ ; ρw is the density of liquid water, ρair the air density, and the droplet effective radius is calculated as reff=3Qcρair4πρwNc1/3.

Our reference simulation was initialized at 18:00 LST on 18 February 2022 and continued until 14:00 LST the following day, with a temporal resolution of approximately 1.0 s. Simulation tests showed that this time step optimally balanced numerical accuracy in resolving the supersaturation evolution and computational efficiency. A coarser time step was found to overestimate local supersaturation and droplet activation . The simulation domain was 0.16 km × 0.16 km × 1.6 km, with a grid spacing of 5 m × 5 m × 2 m.

The initial vertical profiles of temperature and humidity were configured using a combination of radiosonde observations at SPC and ECMWF Reanalysis (ERA5, ). The radio sounding and reanalysis both indicated warm-air advection above the fog layer around 22:00 LST. To reproduce this feature, we applied nudging based on the ERA5 profiles between 21:30 and 22:30 LST, primarily for warm advection above 120 m (Fig. S1 in the Supplement). The initial horizontal wind field was set to zero, in agreement with observations and reanalysis that showed weak near-surface winds and wind shear. Since the series of fog events was mainly driven by radiative cooling with negligible vertical motion, the initial updraft was also set to zero. For the surface forcing, the surface skin temperature (SST) was prescribed using 3.5-m temperature observations starting from 18:00 LST (Fig. S2). Due to the absence of soil moisture observations, the baseline surface skin moisture (SSM) was also interpolated based on the 3.5-m data, which were saturated during nighttime. At sunrise, the 3.5-m humidity measurements remained saturated and were thus not representative of the response of soil moisture to shortwave heating. To account for surface heating and subsequent evaporation, we estimated the surface relative humidity RH (in %) after sunrise using the revised Tetens formula : 6RH=ees(T)⋅100=exp⁡17.625TdTd+243.04-17.625TT+243.04⋅100, where the dew point temperature (Td) was approximated by the nocturnal minimum temperature. The influence of surface forcing is further discussed in Sects.  and S6, where sensitivity tests are labeled as SFC_SST and SFC_SSM.

The observed aerosol size distribution showed a relatively large variability during the series of fog events (see Fig. b), with total number concentrations ranging between 4067 and 9927 cm-3. Given the very low aerosol activation rate (<1 %, cf. ), aerosol scavenging and regeneration processes were neglected, and the dry aerosol population was kept close to the fitted observational means during the simulations. In the lognormal distribution fitting, priority was placed on ensuring that the particle size distribution and spectral mean diameter of the accumulation mode matched the observed spectrum, as large particles in these size ranges dominated activation, as suggested by . Specifically, the total aerosol concentration was set to 5000 cm-3, the geometric mean radius to 48.2 nm, and the dimensionless geometric standard deviation to 1.9. The chemical composition of the aerosol mixture was prescribed as constant, based on the observational mean, represented by a molar weight of 49.35 g mol⁻¹, a density of 1618.62 kg m⁻³, and an average κ of 0.45, with its individual chemical components shown in Fig. .

As mentioned in Sect. , the prescribed shape of the droplet size distribution in MIMICA follows a gamma distribution. Figure a shows the observed fog droplet size distribution, together with different idealized gamma distributions using a range of shape parameters. As discussed in , the observations show a clear bimodal droplet size distribution, with one peak around 6 µm, associated with non-activated hydrated particles, and a second peak around 10–40 µm, associated with activated fog droplets. For the reference simulation, we used a distribution with shape parameters α=3 and ν=1, which reasonably captures the observed mean activated droplet spectrum (Fig. ). The peak associated with the hydrated aerosols is predicted in MIMICA by the aerosol module using κ-Köhler theory (see Sect. S3).

Additionally, given the small average droplet size and the correspondingly low collision efficiency and following the recommendation from , the collision-coalescence process was turned off in MIMICA in the reference simulation (tests with collision-coalescence enabled are presented in Sect. S5). The droplet autoconversion term was also excluded due to the absence of precipitation in the observations. Notably, by deactivating these two processes, the droplet size distribution in the model can be maintained largely consistent with that implied by the prescribed shape parameters; otherwise, potential adjustments to the droplet size distribution through collision–coalescence and autoconversion could introduce inconsistencies with the droplet spectrum corresponding to sedimentation rates calculated based on the prescribed shape parameters.

To address the research questions outlined in the introduction and, specifically, to quantify the responses of fog properties to variations in aerosol regimes and droplet microphysical representations, we conducted sensitivity experiments. To systematically evaluate the effects of individual parameters while minimizing parameter interactions, we implemented the one-at-a-time (OAT) sensitivity for the tests. An overview of the experimental design is given in Table. .

The reference simulation (REF, Fig. ) serves as a baseline for our study and is compared to observational data (Figs.  and ) to evaluate the model performance. Figure  shows the time height evolution of in-fog properties. Nocturnal longwave radiative cooling at the surface results in supersaturated air, droplet activation, and fog formation around 19:30 LST. The fog top lifting is mainly attributed to sustained radiative emission by the droplets, with additional contributions from air radiative loss and turbulent diffusion . For the present case, the presence of advected warm air above the fog limits the vertical development. Neglecting the advection, and thus the entrainment of warm, dry air at the fog top, results in a considerably thicker fog layer and an extended fog lifetime compared to the REF simulation (see Sect. S5). As the fog develops and becomes optically thick, the region of strong radiative cooling shifts gradually from the surface to the fog top, where supersaturation and droplet concentrations reach peak levels. During the mature stage (e.g., 00:00–02:00 LST), the negative buoyancy generated by fog-top cooling, together with a weak surface warming (Fig. S2), renders the fog layer thermodynamically unstable and triggers convection. This enhances the mixing within the fog layer and suppresses droplet sedimentation, resulting in relatively high droplet number concentrations and liquid water content. After sunrise, near-surface warming induces droplet evaporation, leading to a decoupling of the fog layer from the surface. In addition, droplet sedimentation is found to play an important role in fog dissipation. If the sedimentation scheme is disabled (see Sect. S5), fog liquid water content, droplet number and geometrical thickness are significantly overestimated, and the dissipation is also delayed compared to observations.

The near-surface microphysics and visibility time series are evaluated against the observations in Fig. . MIMICA simulates the dissipation phase well, but the onset occurs approximately 41 min later than observed. This delay is likely related to uncertainties in the prescribed surface forcing, as the REF simulation relies on 3.5-m air temperature due to the absence of in-situ ground surface temperature measurements. In stable boundary layers, the ground surface is typically colder than the near-surface air and cools at a faster rate, as also reported in early Po Valley field campaigns . Sensitivity experiments with surface temperature perturbations of -0.5 to -3.0 K confirm that lowering the surface temperature results in earlier fog onset (see Fig. S4a), consistent with , who noted that locally cooler or moister surfaces tend to favor fog formation.

The simulated near-surface supersaturation (0.0034 %–0.0294 %, mean 0.0129 %) is in reasonable agreement with observational supersaturation constraints (0.0117 %–0.0238 %, mean 0.0165 %; ), indicating that the REF simulation realistically captures the local microphysical conditions governing droplet activation. The model also reproduces the observed mean droplet size reasonably well but overestimates the number of activated droplets and the liquid water content (Fig. c, a, and b, respectively), which is a common issue when using bulk microphysics schemes . Another potential reason for the overestimate by MIMICA is that the model does not include a detailed parametrization of atmosphere–surface interactions. For example, processes such as droplet deposition at the surface and interception by vegetation are not represented . This overestimation is particularly pronounced for large droplets. As shown in Fig. , the simulated number concentration of droplets larger than 25 µm is substantially higher than observed, except for event 8. These large droplets dominate the total fog water and are most likely the primary reason for the positive modeled bias in liquid water mixing ratio (Fig. ). However, the surface flux of water vapor also plays a crucial role in regulating the liquid water content. A series of sensitivity experiments was conducted, where the surface relative humidity was set to 85 %, 90 %, and 95 % (SSM_085, SSM_090, and SSM_095) and the nocturnal surface warming and evaporation processes based on Eq. () were refined (labeled as SSM_VAR). These adjustments effectively reduce droplet numbers and liquid water relative to REF, and in some cases (e.g., SSM_090 and SSM_085), the model has the potential to capture water loss and non-fog periods between fog events (see Sect. S6).

In contrast to the overestimation of activated droplets, MIMICA reproduces fewer hydrated particles than observed (Fig. ), which is most likely because the hygroscopic growth factor in the model is calculated using a bulk-averaged method, that is, all dry particles take up water vapor with the same factor (see Sect. S3). In reality, due to the Kelvin effect, small particles have a high surface curvature, which increases their equilibrium vapor pressure and inhibits water uptake, whereas larger particles have lower curvature and can absorb water more easily. In other words, the hygroscopic growth factor should increase with particle size, meaning that larger particles should grow more than smaller ones (see the comparison between observed and simulated wet aerosols in Fig. ). Note that when comparing the total number of droplets (i.e., hydrated particles + activated droplets), the model agrees well with observations, indicating that the high bias in activated droplets is partially compensated by the low bias of hydrated particles. Due to their small size, simulated hydrated particles do not contribute substantially to the total fog water content (<1 %). Consequently, and in line with , our simulations show that the development of a well-mixed fog layer is primarily driven by the activated droplets; deactivating the hygroscopic growth scheme in MIMICA has a negligible effect on fog thickness τ and liquid water path LWP (see Sect. S5).

The parameterized visibility from the simulation is generally higher than the observed one (Fig. d). This discrepancy can be partly attributed to the fact that extinction, as a function of wavelength and droplet size distribution (), is not explicitly resolved in MIMICA. Another reason is that in the observations the visibility sensor accounts also for extinction from very fine particles, whereas in the parameterization from , only droplets larger than 2 µm are included. Additionally, neglecting the hydrated particles would result in a further overprediction of visibility (17.80 %–79.03 %, mean 39.64 %) and biases in fog period estimation (Fig. d).

As described in Sect. , to assess the impact of aerosol number concentration Na on fog properties, we conducted the AERO_NA sensitivity experiments, with Na varying from 2000 to 24 000 cm⁻³ in 2000 cm⁻³ increments. With higher Na, the number of both activated and hydrated particles increases, resulting in a higher liquid water content and a decrease in visibility (Fig. c, d, h). At the same time, the longwave radiative cooling is enhanced, which increases negative buoyancy and elevates TKE, thereby promoting stronger fog layer mixing during the mature stage. Under conditions of nearly constant water vapor available for condensation, stronger competition for vapor reduces the mean droplet radius (Fig. e), which is consistent with the Twomey effect in clouds , and was also observed during the field campaign . In addition, enhanced competition suppresses ambient supersaturation, resulting in a smaller fraction of particles that can be activated (i.e., the activation fraction in Fig. a). The droplet conversion fraction, i.e., the ratio of the total droplet number to the aerosol number, also decreases with increasing Na; nevertheless, the relative contribution of hydrated particles to the total droplet population increases and becomes dominant at around Na=12 000 cm-3 (Fig. b). In other words, variations in total Nc are largely attributable to changes in the number of hydrated particles at high aerosol concentrations. Considering the underestimate of the hygroscopic growth factor noted in Sect. , their actual contribution should be higher, and the threshold Na where they start to dominate the total droplet number concentration is likely lower.

For cases with Na<14 000 cm-3, the fog lifetime is generally prolonged with increasing Na, manifested as slightly earlier formation and a more pronounced, delayed dissipation (Fig. a, b). The earlier onset is due to the reduction in visibility caused by the numerous hydrated particles under high Na conditions during the initial stage of the fog, when droplet activation has not yet become dominant. The delayed dissipation can, in our simulations, be attributed to the reduced sedimentation rates that extend the residence time of fog droplets (Fig. g), consistent with the cloud lifetime effect . The amount of shortwave radiation that reaches the surface is also reduced, which, in reality, should dampen surface warming and slow down droplet evaporation . However, in our simulations, the surface forcing was kept identical across all Na cases. Consequently, this type of suppression of near-surface droplet evaporation under high Na is not represented. The case Na=8000 cm-3 appears to stand out from the other cases, with fog dissipating about 7 minutes earlier than in Na=6000 cm-3. However, this difference is not significant. The behavior can be attributed to a slightly faster decrease in Nc and Qc in Na=8000 cm-3 than in Na=6000 cm-3 during the dissipation phase, which accelerates the increase in visibility above the 1 km threshold that is used to identify fog dissipation. The exact timing for when the visibility threshold is passed can be affected by small random perturbations that are used to initialize the model (e.g., in potential temperature). To examine the influence of the random perturbations, we performed duplicate simulations for Na=8000 cm-3 with different random perturbations. These two simulations did indeed show slightly different times for fog dissipation.

For Na>12 000 cm-3, the fog duration becomes almost insensitive to further increases in Na. The reason is that the aerosol activation transitions from an aerosol-limited to a supersaturation-limited regime at high aerosol concentrations. For a constant amount of condensable water vapor, the ambient supersaturation will decline and stabilize as Na increases (Fig. f), meaning that adding more aerosols will not lead to increased activation. This explains the pronounced decline in the relative sensitivity of Nc to changes in Na (Fig. c). Furthermore, since the change in Nc is small, the change in mean droplet size and sedimentation velocity (which is proportional to the square of the droplet size, see Sect. S1) also becomes small (Fig. g). Consequently, the visibility (Fig. h) becomes insensitive to increased Na, and the response of fog lifetime to Na becomes nonlinear.

This result shows that differences in sedimentation rates and the resulting impact on visibility become negligible under extremely high pollution conditions (Fig. g, h). Fig. c also shows that the relative sensitivity of Nc to changes in Na declines sharply at high Na, primarily due to the availability of water vapor and supersaturation.

Figure  shows the fog height and optical properties for the AERO_NA experiments. In contrast to , where halving or doubling the CCN concentration was found to alter fog height by around 35 %, our results show a small influence of changing Na. When Na is doubled, the fog-top height increases on average by no more than 4 %. Even across all AERO_NA cases, the average fog top increase does not exceed 11 %. This suggests that the geometric thickness of the fog layer exhibits a relatively weak sensitivity to variations in Na, when only longwave emission by droplets and subsequent buoyancy-driven turbulent mixing are considered (and no other aerosol-driven radiative effects). By comparison, Na exerts a more pronounced effect on the LWP and fog optical thickness, where the elevated Nc and LWC with increasing Na are a result of not only more activation but also reduced sedimentation that prolongs the droplet residence time.

The response of fog to aerosol chemistry was examined through κ perturbation experiments under different pollution scenarios (see Sect. ). With a higher κ, the number concentration of activated droplets (Fig. a and c) increases, which in turn leads to a decrease in the visibility (Fig. b and d) and an increase in the LWP and optical thickness (not shown) compared to the baseline case. This can be explained by the decrease in the dry activation diameter. However, the sensitivity to κ varies under different pollution scenarios. Overall, the number of activated droplets is more sensitive to κ perturbations under clean conditions, i.e. with lower Na and κ (Fig. a). The case with Na=200 cm-3 is an exception. In this case, only short periods meet the fog criterion (visibility ≤1.0 km) and most data points with large relative changes in microphysical parameters are filtered out, resulting in a weaker statistical response of Nc,act to κ perturbations. Except for Na=200 cm-3, the relative changes in Nc,act range from +6.6 % to +7.8 % when κ is increased by 10 % and from -7.3 % to 5.9 % when κ is reduced by 10 %, which is generally higher than the corresponding changes for polluted conditions (+4.0 % to +5.5 % and -5.5 % to -4.2 %, respectively, Fig. a). The visibility calculated using only activated droplets (Nc,act) in Eq. () shows a similar result (Fig. b). However, when hydrated particles are considered, the sensitivity of the total number concentration of droplets to κ perturbations exhibits a different pattern, with greater sensitivity under polluted conditions. For a +10 % κ perturbation, the relative change in total Nc under clean conditions (baseline κ=0.27) is much lower than that in polluted conditions (baseline κ=0.45), ranging from +18.1 % to +33.6 % (Fig. c), with a corresponding decrease in visibility of -10.7 % to -16.6 % (Fig. d). Under clean conditions, these values are +4.2 % to +15.0 % and -4.4 % to -9.7 %, respectively.

These results partly support previous studies suggesting that the effect of changes in the chemical composition on the activated number of fog droplets is relatively small compared to the effect of changes in the aerosol size distribution e.g.,, particularly under high Na conditions. However, this does not imply that uncertainties in chemical composition can be neglected when hydrated particles are considered; an accurate representation of κ remains crucial, especially for estimating visibility and fog duration. It is also worthwhile to point out that particle composition and size distribution are not decoupled in reality, as both are governed by the sources and atmospheric processing of the emitted particles.

The response in total Nc, and the corresponding visibility, to κ changes is nonlinear, with a much higher sensitivity for positive κ perturbations than for negative ones. This asymmetry arises not only from the nonlinear dependence of aerosol hygroscopic growth and activation on κ perturbations but also from the characteristics of the aerosol size distribution. Taking Na = 12 000 cm-3 as an example, a 10 % increase in κ relative to the baseline reduces the critical activation diameter, resulting in an approximate 4.0 % average increase in activated droplets. At the same time, the hygroscopic growth factor increases by 4.9 %, shifting the wet aerosol spectrum toward larger sizes. Because particles in the accumulation mode are more highly concentrated at smaller sizes, as seen from the lognormal distribution, a large number of fine particles originally just below the 2 µm threshold can exceed it under enhanced hygroscopic growth and are counted into the total Nc. This results in a substantial increase in total Nc (+27.1 %) and, consequently, a sharp decrease in visibility (-14.6 %), given the strong negative correlation between visibility and Nc. In contrast, a 10 % decrease in κ leads to an average reduction in the activated droplets of about 5.3 % and lowers the hygroscopic growth factor by 5.1 %. Given the rapid decline of aerosol number concentration with increasing particle size in the accumulation mode, the wet size distribution resulting from hygroscopic growth scaled by the bulk growth factor retains the same decreasing trend. As the spectrum shifts toward smaller wet sizes with a lower growth factor, only a few particles above the 2 µm threshold fall below it and are excluded from the total Nc. As a result, the reduction in total Nc is relatively limited (-7.8 %), and so is the corresponding increase in visibility (+10.6 %).

As mentioned in Sect.  and shown in Fig. , the generalized gamma distribution exhibits clear limitations in representing the wide spectrum of fog droplet sizes. For simulations with combinations of small shape parameters, such as [1,1], [1,2], [1,3], and [2,1] (hereafter referred to as wide-spectrum cases), the representation of small droplets is reasonable, but the number concentration of large droplets (>30 µm) is overestimated, which increases the bulk mean droplet size and consequently enhances the overall sedimentation rate (Fig. f). In particular, the average sedimentation velocity in cases DROP_A1N2 and DROP_A1N1 is about 1.6 and 2.0 times higher, respectively, than in the narrow-spectrum cases. Additionally, in these wide-spectrum simulations, liquid water is distributed more evenly across droplet sizes, making the fog liquid water more sensitive to sedimentation losses. Together, these two factors lead to a significant reduction in total Nc and Qc, and the post-sedimentation droplet population becomes increasingly dominated by hydrated particles (Fig. b). Consequently, the mean droplet size is reduced, and near-surface visibility increases (Fig. e and g). Fog onset is slightly delayed in the wide-spectrum cases relative to the narrow-spectrum cases, whereas no notable differences are observed among the narrow-spectrum simulations (Fig. a). The model does not show a clear correlation between fog dissipation and the prescribed droplet size distribution (Fig. b). Also, when increasing Na under the same wide-spectrum parameter setting, no delay in the fog dissipation similar to that shown in the AERO_NA experiments (Fig. b) is observed, suggesting that under enhanced sedimentation regimes, the fog lifetime is less sensitive to Na (not shown). Furthermore, in the sensitivity experiments with droplet collision–coalescence enabled, no significant differences are observed across the wide-spectrum cases (not shown). This is likely because the fog droplet sizes are generally relatively small, resulting in very low collision–coalescence efficiency and rendering this process negligible for the overall fog properties.

In terms of vertical structure, for wide-spectrum cases, enhanced sedimentation inhibits fog-top lifting and reduces geometric and optical thickness, and the temporal variability in LWP and τ is smoothed out (Fig. ). In the DROP_A1N1 case, the maximum fog-top height is about 60 m with a mean LWP of 1.57 g m-2, whereas in the narrow-spectrum reference case DROP_A3N1, the maximum fog-top height reaches about 100 m with a mean LWP of 11.87 g m-2.

A comparison among the narrow-spectrum simulations shows that different parameter combinations lead to variations in the fog optical thickness, where a narrower spectrum produces thicker fog layers and some local fluctuations in the near-surface temporal evolution (Fig. ). Nevertheless, the overall near-surface microphysical statistics – such as droplet number concentration, liquid water content, and the relative fraction of hydrated and activated droplets – show only small differences (Fig.  and ). This indicates that merely adjusting the generalized gamma distribution parameters is insufficient to address the positive bias in activated droplet number concentration and the liquid water content of large droplets.