2.1.1 Surface measurement data

A network of surface weather stations was installed in the study domain of SOFOG3D at the vicinity of Charbonnière to document the spatial variability of fog and surface heterogeneities at the local scale (Fig. 1b). Four weather stations were also deployed around the supersite in a northeast–southwest transect (Fig. 1b). These stations were installed at Moustey, Cape Sud, Tuzan, and Noaillan, almost at the same altitude, and operated continuously with very high temporal resolution (0.1 s time interval) during the period from 18 October 2019 to 31 December 2020. In addition to temperature, pressure, relative humidity sensors, and anemometers, a scatterometer provided the visibility used to estimate fog formation and dissipation times at each station. Temperature data are used to characterise the spatial variability of the radiative cooling, and wind speed and direction are used for the local circulations.

In this study, fog occurrence is defined using the visibility at the supersite based on an algorithm developed by Tardif and Rasmussen (2007). This algorithm consists of dividing visibility time series into 10 min blocks. A fog block means that half of the visibility measurements during a 10 min period are below 1000 m. Blocks are characterised by a positive or negative construct. A positive construct indicates that five consecutive blocks of which the central block is fog and at least two other blocks are also fog blocks. The opposite means a negative construct. Thus, the fog formation time corresponds to the first fog block in the first positive construct encountered. The fog dissipation time corresponds to the last fog block in the last positive construct before either a negative construct or three consecutive non-fog blocks are encountered. This algorithm discards fog events shorter than 1 h.

Météo-France installed in a fallow field near the supersite a sonic anemometers to continuously measure the near-surface (3 m a.g.l.) meteorological conditions (air temperature and relative humidity), the three components of the wind, and pressure at 0.3 m a.g.l.). These instruments provided high-frequency data at 20 Hz. In this study, to document turbulence and thermodynamical processes driving fog phases, we use the sensible heat flux (SHF), turbulence kinetic energy (TKE), and vertical velocity variance (${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}$). These variables are estimated using eddy covariance methods (Foken et al., 2004; Mauder et al., 2013) calculated every 30 min after quality control of the data. More details on the data can be found in Canut (2020).

2.1.2 Observation of cloud characteristics

For the monitoring of cloud layers, a BASTA cloud radar (Delanoë et al., 2016) was deployed at Charbonnière, and a CL51 ceilometer was deployed at Tuzan (7.4 km northwest of Charbonnière) (Fig. 1b).

BASTA is a 95 GHz cloud radar manufactured by the Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS) with an absolute calibration method for frequency-modulated continuous wave (FMCW) cloud radars based on corner reflectors (Toledo et al., 2020). From 7 November 2019 to 12 March 2020, the radar was operated continuously with a vertical pointing mode having three vertical resolutions (12.5, 25, and 100 m). It provided radar reflectivity and Doppler velocity. The lowest mode, which has its first available gate at 37.5 m a.g.l. and 12.5 m of vertical resolution, is used to estimate the cloud top height (CTH), which gives the fog thickness at a time resolution of 30 s. It also provides the level of highest concentration of droplets in the fog layer. The CTH is estimated using a radar reflectivity threshold of −34 dBZ.

The CL51 is manufactured by Vaisala and automatically provided three estimates of cloud base height (CBH), allowing the detection of cloud decks every 30 s with a vertical resolution of 15 m from 10 October 2019 to 2 April 2020. In this study, we use the lowest CBH, which corresponds to the base height of stratus cloud lowering or lifting when fog forms or dissipates, respectively. More information on the data provided by the CL51 can be found in Burnet (2021).

2.1.3 Temperature, liquid water content, and wind profiling

A microwave radiometer Hatpro (MWR) manufactured by Radiometer Physics GmbH (RPG) was installed at the supersite to characterise thermodynamic atmospheric conditions during the field campaign. From 4 December 2019 to 9 May 2020, the MWR operated continuously at the supersite using two spectral bands: the K-band (22.24–31 GHz), which was used for the retrieval of humidity profiles, integrated water vapour (IWV) content, and liquid water path (LWP), and the V-band (51–58 GHz), which was used to retrieve temperature profiles. In order to improve the vertical resolution in the boundary layer, the MWR was set up to scan in 10 elevation angles (5^∘ a.g.l.) every 10 min with a zenith pointing each 1 s. Using neural networks, brightness temperatures measured by the MWR at all elevation angles (the lower elevations angles added to measurements at zenith) are inverted to temperature and humidity variables. More details on this method can be found in Martinet et al. (2022). Comparing temperature and humidity profiles retrieved by the MWR with radiosonde data, Martinet et al. (2022) found that air temperature has cold biases below 0.5 K in absolute value below 2 km but increases up to 1.5 K above 4 km altitude. The low biases in the lowest atmosphere allow a good estimation of the lowest temperature inversion under focus in this study. For each case study, the transition from stable to adiabatic fog is estimated using the static atmospheric stability in the lowest atmosphere computed using the temperature profile. The air temperature profiles are also used to characterise the atmospheric conditions linked to the development of fog at Charbonnière. For the absolute humidity, the maximum dry bias of the MWR is around 1.4 g m⁻³ in the lowest troposphere up to 1.7 km and becomes wet above (0.3 g m⁻³). Martinet et al. (2022) showed that the LWP accuracy has been validated in clear-sky conditions and has shown errors between 1 and 14 g m⁻². These error range are in the scope of those defined in the literature (Crewell and Löhnert, 2003; Marke et al., 2016). The LWP is a key parameter to consider for the microphysical characteristics of fog and is used in the conceptual model. More information regarding the data can be found in Martinet (2021).

The WindCube lidar has become a common instrument used in documenting very low atmospheric phenomena such as turbulence (Liao et al., 2020; Kumer et al., 2016). Dias Neto et al. (2023) demonstrated the usefulness of the wind speed and direction estimated using the WindCube V2. Comparing wind from WindCube V2 with GPS radiosonde, they found low biases of 0.52 m s⁻¹ and 0.37^∘ for the wind speed and direction, respectively. To investigate the dynamics of the atmosphere at the supersite, a WindCube V2 lidar manufactured by Leosphere was deployed by Météo-France during the field campaign to provide the wind measurements at 10 levels ranging from 40 m to 220 m a.g.l. from 1 October 2019 to 10 April 2020. The measurements made at a 1 Hz frequency and a 20 m vertical resolution provided the estimation of turbulence parameters such as the turbulent kinetic energy (TKE). The wind components are estimated every 10 min using a carrier-to-noise ratio (CNR) of at least −23 dB and a total data availability of at least 50 %. Note that the CNR depends on atmospheric turbulence characteristics and relative humidity (Aitken et al., 2012). In the presence of fog or low stratus, the lidar vertical range becomes low. The TKE is computed as the sum of the horizontal variances as in Kumer et al. (2016). Velocity variances are estimated every 30 min using the wind components at the high resolution. It is used in this study to analyse the role of turbulence within the foggy layer to further characterise fog formation, evolution, and dissipation. More details on the WindCube lidar data can be found in Canut (2022).

2.1.4 Fog adiabaticity and reservoir

To further understand fog characteristics, it is essential to focus our analysis on several variables related to the formation, evolution, and dissipation of fog. Fog adiabaticity and reservoir are key metrics driving the life cycle of fog. They are estimated using the fog conceptual model (Toledo et al., 2021) developed at SIRTA. This model is a uni-dimensional model inspired by previous numerical models for stratus clouds (Betts, 1982; Albrecht et al., 1990; Cermak and Bendix, 2011). The basic hypothesis is to consider a well-mixed fog layer and to express the increase in height of the fog liquid water content as a function of the local adiabaticity and the negative of the change in the saturation mixing ratio with height (Γ_ad(T,P)) (Eq. A1). Fog liquid water path is parameterised as a function depending on the equivalent fog adiabaticity (α_eq) and the CTH (Eq. A3). The equivalent fog adiabaticity is used to characterise the buoyancy in low clouds. α_eq varies depending on the in-cloud mixing parameter β and is expressed as ${\mathit{\alpha }}_{\mathrm{eq}}=(\mathrm{1}-\mathit{\beta })$ (Betts, 1982; Cermak and Bendix, 2011). For low-level clouds, such as stratus and stratocumulus, α_eq is between 0.6 and 0.9 (Braun et al., 2018), indicating sufficient buoyancy in the cloud layer with an adiabatic profile. To parameterise this parameter in the fog conceptual model, Toledo et al. (2021) used an inversion of Eq. (A3) to define a fog adiabaticity from closure (${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$) given as follows:

${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ depends on the accumulated liquid water content (LWC) at the fog base (LWC₀), the fog thickness (e.g. CTH), the LWP, and the adiabaticity. The adiabaticity lapse rate is a function of air temperature and pressure. Toledo et al. (2021) found that the equivalent fog adiabaticity from closure is negative when the LWP is below 30 g m⁻². They defined the transition phase from stable to adiabatic conditions when the equivalent fog adiabaticity from closure is around 0.5. In the conceptual model, this parameter is estimated only for a CTH below 462.5 m with free cloud above.

The model considers that the fog dissipates when its liquid water path is below a certain threshold depending on the local thermodynamic atmospheric conditions. In case of dissipation by lifting the base height of the fog, Wærsted (2018) found a deficit in LWP in the fog layer. This assertion allows for defining a minimum amount of LWP necessary to maintain the horizontal visibility at surface lower or equal to 1000 m, defined as the critical liquid water path (CLWP). Thus, based on Eq. (A3), the CLWP can be expressed in Eq. (2) considering a critical liquid water content at surface (LWC_c).

Theoretically, the LWC_c corresponds to the LWC that would cause a 1000 m visibility. It is estimated from the parameterisation of Gultepe et al. (2006) based on the horizontal visibility at surface.

Considering that adiabatic fog exists because the liquid water path in its thickness is strictly greater than or equal to its CLWP (Toledo et al., 2021), it is possible to define an associated quantity named the fog reservoir of liquid water path (RLWP). The RLWP is defined as the difference between fog current liquid water path and the critical value as follows:

The RLWP depends on the LWCc (Eq. A4), the adiabaticity, and fog thickness. The calculation of RLWP can be used to anticipate the dissipation or thickening of the fog in the coming minutes or hours. Based on 20 fog cases at SIRTA, Toledo Bittner (2021) found that for a RLWP > 30 g m⁻² in a given time instant, fog does not dissipate within the following 30 min. He also showed that the RLWP trend decreases before fog dissipation time and increases when fog is persisting. This behaviour motivates the analysis of the RLWP trend in this study to improve the characterisation of the different fog phases.

The number of fog events observed during the SOFOG3D field campaign is not sufficient to calibrate the fog conceptual model in southeastern France as it was in SIRTA (Toledo et al., 2021). In this study, we use the model with its parameterisation at SIRTA to further characterise the different phases observed in the lifetime of fog based on identified case studies. The model is performed when the visibility is lower than 1000 m. ${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ is used to characterise the fog transition from stable phase to adiabatic phase. The RLWP gives an estimation of the excess or deficit of liquid water of the fog that enables the fog layer to remain at surface or dissipate. It can be used as a diagnostic of how likely the fog will persist in the coming minutes or hours (i.e. as a nowcasting tool for fog dissipation time). More details on the fog conceptual model are given in Appendix A and can be found in Toledo Bittner (2021).

3.1.1 Case study 1 (IOP 5) analysis

Figure 3a and b indicate the time cross-sections of the radar reflectivity estimated from BASTA cloud radar during case study 1 on 28–29 December 2019 up to 600 and 12 000 m, respectively. They show a clear sky before the fog formation time at 22:40 UTC on 28 December 2019. During fog evolution, cloud-free conditions are observed above the fog top height until 09:00 UTC when sparse thin high-altitude clouds occur above the cloud radar. Figure 3c presents a quasi-homogeneous fog formation time between the three sites and a heterogeneous dissipation time. At Charbonnière, fog dissipated at 11:00 UTC on 29 December 2019 and 2 h earlier at Noaillan. At all sites, low temperatures below 4 ^∘C (Fig. 3e) are observed during the fog period. Near the surface, light winds (<1 m s⁻¹) are recorded at all sites from fog pre-onset to fog stable–adiabatic transition times (Fig. 3d and f).

Figure 3In (a, b) a time–height cross-section is given from the surface up to 600 and 12 000 m, respectively, of the radar reflectivity from BASTA (shaded), the time evolution of the cloud top height from BASTA (red line), and the cloud base height from the ceilometer (CL51) (green line). Time evolution of (c) surface visibility, (d) 10 m wind speed, (e) 2 m air temperature, and (f) 10 m wind direction observed on the 28–29 December 2019 (case study 1, IOP 5) at the five meteorological stations (red, black, blue, green, and pink lines for Moustey (1 m a.g.l.), Charbonnière (3 m a.g.l.), Cape Sud (3 m a.g.l.), Tuzan (3 m a.g.l.), and Noaillan (1 m a.g.l.), respectively) deployed around the supersite. Note that wind was not collected at Tuzan. In (c), the visibility measured at Moustey was interrupted by technical issues. Vertical dashed black lines indicate fog formation (left) and dissipation (right) times. Dashed green lines show the transition time from stable fog to adiabatic fog (fog mature phase). The dashed red line indicates the sunrise.

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The fog pre-onset is marked by a double stratification of the atmospheric boundary layer with a thin inversion from the surface up to 100 m and deep and strong inversion (around 8 ^∘C km⁻¹) above (Fig. 4a). Atmospheric conditions are dominated by an easterly wind that reaches 5 m s⁻¹ above 100 m a.g.l., which is possibly due to a low-level jet (Fig. 4d). The mean cooling rate near the surface is −0.9 ^∘C h⁻¹. The strong decrease in temperature is associated with a negative SHF (−0.23 W m⁻²) (Fig. 4h), near-surface low wind (0.61 m s⁻¹) (Fig. 3d and f), and low turbulence (TKE = 0.11 m² s⁻² and ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}=\mathrm{0.002}$ m² s⁻²). These conditions lead to thermally stable atmospheric conditions that are favourable for radiation fog formation (Table 1).

Figure 4Evolution of fog macrophysical characteristics observed on the 28–29 December 2019 (case study 1, IOP 5) at Charbonnière. Panels (a) and (b) show vertical profiles of air temperature from the Hatpro microwave radiometer (MWR) and radar reflectivity from BASTA radar, respectively. Panel (c) shows a time–height cross-section of air temperature from the MWR (shaded), time evolution of inversion top height (ITH) (open grey squares), inversion base height (IBH) (open grey squares), and cloud top height (CTH) from the cloud radar (open black squares) and the cloud base height (CBH) from the ceilometer (open black circles). Panel (d) shows wind speed (shaded) and direction (arrows) from the WindCube. Arrows in (d) indicate only the direction of the horizontal flow. (e) Time evolution of air temperature at 3 m a.g.l. from the meteorological station (red line) and equivalent adiabaticity of closure from the fog conceptual model (blue line). (f) The mean of the turbulent kinetic energy (TKE) in the layer 40–220 m (solid black line) and 100–160 m a.g.l. (dashed black line) from the WindCube (black line) and the TKE (blue line) and vertical velocity variance (red line) at 3 m a.g.l. from the flux station at Charbonnière. (g) The LWP estimate from the MWR (blue line) and the RLWP from the fog conceptual model (red line). (h) Sensible heat flux (SHF) (red) from the flux station. Vertical dashed black lines indicate fog formation and dissipation times. Dashed green lines indicate the transition period (fog mature phase) from stable to adiabatic fog. The dashed red line indicates sunrise.

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The fog stable phase lasts around 6 h (22:50–05:00 UTC) and is characterised on average by a very low negative near-surface cooling rate (−0.18 ^∘C h⁻¹), an almost zero SHF, an easterly light wind (0.78 m s⁻¹), low turbulence (TKE = 0.07 m² s⁻², ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}=\mathrm{0.01}$ m² s⁻²), negative ${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ (−1.3) (Fig. 4e), low LWP (2.18 g m⁻²) (Fig. 4g), slight increase in time of the fog thickness up to 50 m, and relatively stable temperature inversion height. These characteristics maintain the thermally stable fog with a horizontal visibility of 736 m on average.

The transition time from stable to adiabatic fog is observed between 05:00 and 07:00 UTC (2 h duration) and associated with the lowest visibility (198 m), a transition in the vertical profiles of air temperature (Fig. 4a) from stable at 05:00 UTC to unstable at 06:00 UTC in the fog layer, a deepening of the cold layer, an increase in the mean SHF reaching 44 and around 10 W m⁻² at the phase end (Fig. 4h), and an increase in the turbulence (TKE up to 0.15 m² s⁻² and ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}$ up to 0.04 m² s⁻²) generated by the strengthening of the wind speed (1.14 m s⁻¹) and its shift in direction from east to southeast. From 05:00 to 06:00 UTC, the coldest temperature shifts from the surface up to 50 m a.g.l., and the vertical profile of radar reflectivity increases with height, indicating a vertical development of fog (Fig. 4b) generated by turbulence processes. At the end of this phase, ${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ reaches 0.5, which is consistent with the threshold obtained at the SIRTA site by Toledo et al. (2021). The ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}$ values observed are higher than the threshold fixed by Price (2019) for a thermally stable surface layer. The LWP (28 g m⁻²) and RLWP (+15 g m⁻²) peak at the end of the transition phase consistently with a decrease in visibility. Due to the simultaneous increase in SHF, TKE, and ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}$, the transition phase is driven by both thermal and mechanical turbulence.

The fog adiabatic phase is observed between 07:00 and 11:00 UTC (4 h duration) at the supersite and characterised by a vertical development of fog up to 187.5 m (Fig. 4b) and the arrival of sparse high clouds (Fig. 3a and b) associated with the lowering of the temperature inversion top height above the fog top (Fig. 4c). Note that these clouds have no effect on the radiative cooling at the top height of the fog. The fog layer becomes warmer (+0.77 ^∘C h⁻¹ on average), and its LWP and RLWP reach 26.16 and +6.38 g m⁻², respectively. The turbulence gradually increases in the fog layer (Fig. 4f) (TKE = 0.23 m² s⁻²) due to an increase in the horizontal wind speed (2.4 m s⁻¹) combined with an increase in the vertical shear and the wind shift from southeasterly to easterly (Fig. 4d). In the same way, ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}$ increases to 0.04 m² s⁻² and is driven both by the vertical wind shear and the increase in SHF (12.9 W m⁻²) (Fig. 4h). For this case study, the moderate mechanical and thermal turbulence causes the vertical mixing in the fog layer, which slightly increases the surface horizontal visibility (370 m) and fog top height (185 m).

At the supersite, in the absence of any cloud above the fog layer, the fog dissipates after sunrise. It is marked by a continued increase in SHF (Fig. 4h) due to solar radiation (daytime atmospheric convection), negative RLWP (−11.39 g m⁻²), an increase in CTH (290 m), LWP (maximum of 43.34 g m⁻²), stable ${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ around 0.63, and more thermal turbulence (${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}=\mathrm{0.06}$ m² s⁻²) allowing more vertical mixing. Based on the RLWP, the fog conceptual model would predict a deficit of liquid water in the fog layer 1 h before the lifting of its base height (Fig. 4g). The fog dissipation phase is induced by the increase in the vertical mixing generated by the thermal (solar heating) and mechanical turbulence associated with TKE values larger than 0.4 m² s⁻² (Fig. 4f).

In summary, for this radiative fog event, the fog conceptual model is consistent with the in situ measurements of turbulence on the timing of the different fog phases. It has provided additional elements for understanding the different phases of the fog life cycle.

3.1.2 Case study 2 (IOP 6) analysis

As in case study 1, case study 2 is a radiation fog that forms under clear skies a few hours after sunset (Fig. 5a and b) under a double stratification of the low atmosphere (Fig. 6a), southerly very low near-surface wind speed (0.2 m s⁻¹), low TKE (0.06 m² s⁻²), and negative surface SHF. The fog lasts 12 h and completely dissipates around 08:40 UTC on 6 January 2020 at the supersite (see Table 1) and at 04:30 UTC at Noaillan, revealing more spatial variability than in case study 1.

Figure 5The same as Fig. 3 but for 5–6 January 2020 (case study 2, IOP 6). In (c) only Charbonnière and Noaillan have valid data. In (c) the visibility measured at Moustey, Tuzan, and Cape Sud was interrupted by technical issues.

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Figure 6The same as Fig. 4 but for 5–6 January 2020 (case study 2, IOP 6). The vertical dashed red line indicates the sunrise.

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The fog stable phase lasts 3 h 20 min (20:40 to 00:00 UTC), half the time of case study 1, with fog characteristics similar to those of case study 1. A 2 h fog transition phase is observed from 00:00 to 02:00 UTC, (2 h duration as for IOP 5) at the supersite (Fig. 6a and b) and characterised by positive SHF (7.76 W m⁻²) and larger values of TKE (0.23 m² s⁻¹) allowing vertical mixing and transition towards adiabatic fog. A significantly longer fog adiabatic phase is observed from 02:00 to 08:40 UTC (twice longer than in IOP 5). The first period from 02:00 to 05:00 UTC is characterised by continued positive SHF (10 W m⁻²) (Fig. 6h) and significant turbulence (TKE > 0.2 m² s⁻² and ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}>\mathrm{0.02}$ m² s⁻²) (Fig. 6f) leading to a deeper fog with relatively high LWP (42 g m⁻²) and a positive RLWP until 04:30 UTC (Fig. 6g). The second period from 05:00 to 08:40 UTC is characterised by continued positive SHF an significant ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}$ (>0.02 m² s⁻²), while the TKE decreases (<0.2 m² s⁻²) associated with the decrease in wind speed in the fog layer. A sharp decrease in LWP, with a reduction in fog top height, leads to RLWP oscillating around 0 g m⁻², and the horizontal visibility increases and then decreases again. During this period, the sharp decrease in LWP (<20 g m⁻²) results in a fog layer that is not very resilient to the significant turbulence, as shown by the very low RLWP values and rapidly changing horizontal visibility (Fig. 5c). The decrease in LWP could be driven by production of drizzle, as reported through droplets freezing on the tethered balloon. Fog dissipation occurred after sunrise (08:40 UTC, under positive SHF (14 W m⁻²) driven by the turbulence associated with mechanical and thermal processes (mean TKE ∼ 0.28 m² s⁻² and ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}\sim \mathrm{0.048}$ m² s⁻²).

3.2.1 Case study 3 (IOP 11) analysis

In spite of different formation conditions for case study 3, compared to case 1 and 2, the stable fog phase of this case is characterised by fog conditions that are similar to those of case 1 and 2 (Fig. 8): slightly negative SHF, low turbulence (TKE = 0.03 m² s⁻²), and low LWP (<10 g m⁻²). Case study 3 differs from the previous case studies as it has a longer duration for the stable-to-adiabatic fog transition (3 h 30 min duration), during which SHF remains slightly negative; TKE remains mostly below 0.03 m² s⁻²; and CTH, LWP, and ${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ increase progressively, while RLWP remains relatively stable (5–10 g m⁻²). In case study 3, the very short fog adiabatic phase (1 h) is characterised by increasing vertical wind shear near fog top height (Fig. 8d) that generates dynamical instability driving the vertical mixing, reducing the temperature inversion above fog top (Fig. 8c) and promoting vertical development of the fog layer. The rapid increase in CTH is not sufficiently compensated for by the increase in LWP, leading to a decrease in RLWP (Fig. 8g) and subsequent increase in near-surface visibility and dissipation of the fog. Increasing wind aloft brings warm drier air over the top of the fog that then mixes into it (TKE = 0.33 m² s⁻² and ${\mathit{\sigma }}_{\mathrm{w}}^{\mathrm{2}}=\mathrm{0.07}$ m² s⁻²), evaporating fog droplets, reducing the RLWP to negative values, and causing the fog to lift into low stratus. The fog dissipation phase is thus driven by the advection of warm air at the supersite (Fig. 7e).

Figure 8The same as Fig. 4 but for 8–9 February 2020 (case study 3, IOP 11).

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Figure 9The same as Fig. 3 but for 7–8 March 2020 (case study 4, IOP 14).

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3.2.2 Case study 4 (IOP 14) analysis

As in case study 3, fog case study 4 starts with a very low stratus fog and subsidence of the cloud layer resulting in a fog. The fog layer is perturbed by the advection from the northwest (captured in Meteosat Second image, not shown) around 00:30 UTC of another stratus with a base height above the fog top height. From 04:00 UTC, the fog becomes intermittent with a first dissipation observed at that time and a definitive dissipation around 07:00 UTC.

The 2 h long fog stable phase is also characterised by a cooling rate near −1 ^∘C h⁻¹, slightly negative SHF and low turbulence (TKE < 0.1 m² s⁻²). The relatively short transition from stable to adiabatic fog (<1 h 30 min) is characterised by an increase in mechanically driven turbulence (wind shear, Fig. 10d) with a southerly wind that likely brings additional moisture, leading to a rapid increase in both CTH and LWP (near 40 g m⁻²).

Figure 10The same as Fig. 4 but for 7–8 March 2020 (case study 4, IOP 14). The LWP, RLWP, and ${\mathit{\alpha }}_{\mathrm{eq}}^{\mathrm{closure}}$ are disrupted between 00:30 and 02:30 UTC because the LWP estimated by the MWR takes into account the liquid water in the advected stratus.

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The fog adiabatic phase is observed from 00:20 to 04:00 UTC (3 h 40 min duration) followed by a temporary dissipation of the fog from 04:00 to 05:30 UTC and a definitive fog dissipation at 07:00 UTC. This adiabatic phase is characterised by a 250–300 m deep fog with 40–50 g m⁻² LWP. The mechanically driven TKE ranges between 0.2–0.4 m⁻² s⁻² (Fig. 10f), which confirms the turbulence that a relatively deep fog layer can withstand. The evolution of RLWP to negative values after 04:00 UTC (Fig. 10g) shows that the conceptual model captures the transition from an adiabatic fog with low near-surface visibility (<300 m) to one with horizontal visibility at or above 1000 m (Fig. 9c). The definitive dissipation is not associated with increasing turbulence but rather with the presence of middle-altitude clouds that likely reduce significantly the fog top radiative cooling, as precisely characterised by Waersted et al. (2017), and hence liquid water content production. Indeed, Fig. 10g reveals a significant LWP reduction after 06:30 UTC that explains the definitive dissipation of the fog before sunrise.