Favourable and Unfavourable Scenarii of Radiative Fog Formation Defined by Ground-Based and Satellite Observation Data

An innovative set of six observed predictors of fog formation by radiative cooling is proposed, which describes: 1) one of the main processes of fog formation that is the water uptake by aerosols at surface level; 2) the fog development along the vertical up to 30 meters, as well as the cloud cover; and 3) the temporal evolution of the parameters describing the water uptake by aerosols and the cloud cover. The visibility is used as a signal of atmospheric and surface processes affecting the water uptake by aerosols. The vertical fog development is described by the vertical thermal gradient along a 30-m meteorological mast. The cloud cover is described using a ceilometer for low and middle clouds above the instrument, and satellite data for clouds in a pixel and in a larger 9 × 9-pixel region around the site. The set of predictors can be observed in operational conditions, such as on airport fields. Data acquired at the SIRTA platform (Paris, France) during two autumns and two winters were analysed, and the cloud cover classification derived from the SEVIRI instrument on the METEOSAT Second Generation satellite by the EUMETSAT/NWCSAF program was also utilized. The training data set was acquired in November 2011 while the validation data set extended over 12 months. All situations were discriminated between favourable and unfavourable scenarii of radiative cooling fog formation, with a factor of 10 in probability. 246 moderate visibility events (with visibility between 5 and 10 km) were observed under a clear sky in 12 months at SIRTA. While developed fog formed according to one scenario, thin fog formed according to six scenarii. On the contrary to thin fog, developed fog did not form when cirrus clouds were observed above moderate visibility situations. The fog formation probability varied from 12 to 43%, and even reached 100% for one thin fog. As the training data set was acquired in autumn, the predictor set seems more appropriate to nowcast fog in humid autumn conditions, when the fog formation probability was multiplied by ~2. The predictive set could be enriched by predictors proposed in literature, and tests suggest that relative humidity would improve the fog formation probability in winter. Five predictors identify 65 of the 217 no-fog events counted in 12 months, with ~3 h anticipation time. If visibility decreased below 5 km, 88 additional no-fog events were identified. In this case, the formation probability was 35% for developed fog, and 24–60% for thin fog, but with an anticipation time reduced to ~1.5 h. Only one fog, which represents 3% of the fog events, would be missed with such a predictive scheme.


INTRODUCTION
Numerical weather prediction models are usually not able to forecast the fog life cycle (formation, development, dissipation) at satisfying spatial and time resolution (e.g., Clark et al., 2008;Zhou and Ferrier, 2008;Román-Cascón et al., 2015).It is indeed difficult to model the processes at several spatial and time scales.Fog can start as a local scale phenomenon with very fast developments, the most obvious feature being the local visibility drop within few minutes (Elias et al., 2009) due to aerosol activation (e.g., Hammer et al., 2014), with possible high spatial heterogeneities.Also, at larger spatial and time scale, the fog may last for tens of hours and cover entire regions of several tens of km (Cermak and Bendix, 2008).
The fog specific features as the sudden visibility decrease, its potential long duration and large spatial extent, its spatial heterogeneity, all impair severely transport activities, with possible human injuries.Real time observation allows to improve the forecasting results by not only defining initial conditions of the fog formation, but also as a basis of nowcasting.Nowcasting consists in extrapolating observed recent evolution of critical parameters within a few minutes to a few hours, which is a lead-time not covered by numerical weather prediction models (e.g., Vislocky and Fritsch, 1997;Golding, 1998;Wright and Thomas, 1998).Moreover this time window is important, as Valdez (2000) calculated that describing the low visibility event 30 minutes in advance could save $500 million annually at an airport.
We show how several predictors and adapted criteria allow to increase the fog formation probability during scenarii defined as favourable, a few hours in advance.The atmospheric supersaturation is necessary to the fog formation, i.e., relative humidity (RH) has to be larger than a threshold.The threshold can vary in function of various parameters (e.g., Hammer et al., 2014), but is always larger than 100%.Several processes can be responsible for RH increase and fogs can be classified in function of the main processes responsible for the RH increase (Tardif and Rasmussen, 1997).As predictors witness processes in action, they are dependent on the fog type, and we choose to focus on fogs formed by radiative cooling.Jacobs et al. (2008) advised to combine local measurements and satellite observation as well as to process high resolution data.Indeed, ground-based observation is representative of local impact of various atmospheric phenomena at short time resolution, while satellite observation can be used to survey the fog development at a regional scale, as well as the 3D structure of the cloud cover top.Consequently, predictors of the fog formation, and associated criteria, are defined from observations collected at the SIRTA platform and jointly by the SEVIRI instrument onboard the METOSAT Second generation (MSG) satellite platform.The cloud cover classification provided by the EUMETSAT/SAFNWC program (Derrien and Gléau, 2005) is used.SIRTA deploys an impressive instrumental payload to survey atmosphere since early 2000s (Haeffelin et al., 2005), where around 45% of the fogs are formed by radiative cooling (Dupont et al., 2015).
Several studies proposed different predictors of the fog formation.Vislocky and Fritsch (1997) tested observationbased forecast of ceiling and visibility, with superior success than persistence climatology in a few hours lead time.They delivered several suggestions to improve the forecast performance, as adding data satellite imagery and incorporating motion in the observations.We present six predictors derived from three main parameter types: -The atmospheric visibility is used as a signal of atmospheric and surface processes affecting the water uptake by aerosols.Such a signal was always observed before the fogs of November 2011 at SIRTA by Elias et al. (2015), while for example the events of rain or drizzle with reduced visibility were not followed by fog formation.Indeed, before activating into droplets (e.g., Hammer et al., 2014;Mazoyer et al., 2016), aerosols grow up by uptaking water when RH increases, the particle surface which interact with radiation in the visible spectrum increases, and consequently the visibility decreases.To provide enough anticipation time before the fog formation event, we choose to set the first alarm when visibility is included between 5 and 10 km, the mist occurring between this moderate visibility event (mv) and the fog.
The duration of both mv and mist events was ~3 h in average at SIRTA, which is thus considered as the horizon/anticipation time, even if it was highly variable.Moreover, the visibility evolution before, during, and after the moderate visibility event provides a further predictor.-As two radiative cooling fog types are observed at SIRTA with contrasted physical processes (Dupont et al., 2015), and defined by their vertical development (Elias et al., 2012), the vertical thermal gradient over the first 30 m is used to identify the fog type and also as a predictor.-The cloud cover provides several predictors.Indeed, to ensure being in conditions of radiative cooling, it is important to check if the sky is free of clouds before the fog formation.However, the fog could first form not at ground level but at ~100 m above, while visibility at surface level is still larger than a few km, and consequently low cloud cover was observed during the mist preceding the fog formation (Elias et al., 2015).However it is not sure when this elevated fog layer appears, either at beginning of mist, or before mist.Eventually, the cloud cover both over the site and in the region, as well as its time evolution before the mist, all provide several predictors.Measurements made in November 2011 at SIRTA are exploited to define the predictors and the set of criteria, which are then applied to 12 months of data to compute the fog formation probabilities.The paper starts with the presentation of the data and the methodology in Section 2. The predictors and criteria are presented in Section 3. The application of the criteria on observed predictors result in scenarii favourable and unfavourable to fog formation, presented in Section 4. Discussion and conclusion are given in Sections 5 and 6.

The Data Set
The ground-based data set was built from observations made at the SIRTA Observatory (Site Instrumental de Recherche en Télédétection Atmosphérique) (Haeffelin et al., 2005), located in the suburbs of Paris, 20 km South-West from city centre.Analysed measurements were made during 2 autumn and 2 winter seasons from October 2011 to March 2013.We call autumn the three months of October, November and December and winter the three months of January, February and March.The training data set was acquired in November 2011, and the application data set was acquired during the 12 months.
Details about the observations made during the fog seasons at SIRTA are given by Dupont et al. (2015).Visibility was measured by a Degreane DF20+ diffusometer set up at 3 m above ground level (agl).The archive of observed visibility at SIRTA extends over many years.The vertical thermal gradient was measured by thermometers (PT-100 and nonventilated sensor) set up along a 30-m meteorological mast, running since September 2011.Relative humidity was measured (by Rotronics sensors) aside the temperature.The cloud cover below 6 km agl was sounded by a Vaisala CL31 ceilometer, set up at SIRTA in December 2010, providing a 1-min data set.
We also use the cloud type index derived from measurements made by the SEVIRI instrument onboard the METEOSAT Second Generation satellite (MSG, the list of acronyms are given in Table 11), to be complementary with the ceilometer, above 6 km and also in the region around the SIRTA.The EUMETSAT/SAFNWC algorithm processes MSG/SEVIRI data to classify the cloud cover scene into 20 categories which are aggregated into 8 classes pertinent for our study (Section 3.3).The pixel dimension of the SEVIRI instrument is 4.5 × 4.5 km 2 at nadir.All ground-based data are averaged over 15 minutes to 1) keep the best details on the physical processes, as it is a finer time resolution than the 1-hour recommended by Jacobs et al. (2008); and 2) be consistent with MSG/SEVIRI time resolution.

The Methodology: Defining Scenarii with Six Predictors
Six predictors are identified from the observation data set to define scenarii of contrasting probability of developed and thin fog formation by radiative cooling.Firstly, the moderate visibility events (mv) of November 2011 are selected, with visibility included between 5 and 10 km.Secondly, no-fog and pre-fog events are distinguished according to the visibility evolution after the mv event.Then, the observed parameters are averaged during the nofog and pre-fog events (Fig. 1), and the no-fog averages are compared to the pre-fog averages.When sufficient differences are observed, then the parameter is kept as a predictor, as well as the associated criteria to distinguish between no-fog and pre-fog events.Many observed parameters were tested.Identified predictors are presented in detail in Section 3.
Scenarii are defined by a series of criteria applied on the observed predictors, and can be shown in a decision tree (e.g., Fig. 2).Each box of the decision tree represents one scenario, and arrows between the boxes indicate that a further criterion is applied.The top box gives the count of mv events in the validation data set respecting criteria on both predictors of visibility and visibility change in time.The second row shows scenarii defined by three predictors, the third row by four predictors, the fourth row by five predictors and the bottom row by six predictors.The validation data set is composed by 12 months of observation, and tests are also performed selecting only one of the four seasons.
All mv events respecting the different scenarii are counted, and we compute the proportion of no-fog and pre-fog events in each scenario.The number ratio of pre-fog events over all events provides the probability of fog formation, similarly to Veljovic et al. (2015), and according to the definition given in Section 3.2, as: The scenario is called 'favourable to fog formation' when the probability was larger than a threshold, and on the contrary it is said unfavourable when the probability was smaller than this threshold.The background colour of the decision tree boxes is grey for favourable scenarii while it is white for unfavourable (Fig. 2).The contour line is thin for scenarii with 0% fog formation probability.When no observation respect the scenario, the box is not drawn.Sequences giving thin fogs are drawn in red colour, developed fogs in green, and intermediate fogs in blue.Sequences are kept in black when it is not possible to distinguish the fog type.
We mainly comment scenarii at end of branches.One unfavourable scenario was defined by three predictors only, and 17 scenarii with six predictors.The criteria are applied on 15 data sets (Table 1) and we could consequently draw 15 decision trees.Each data set is composed of mv events (Section 3.2) occurring in one of the five time periods and for one of the three visibility sequences.Decision trees for two data sets are shown here, and probability values are provided for seven data sets.Fig. 1.Different types of moderate visibility (mv) events (5 < visibility < 10 km), according to the visibility evolution before, during, and after the mv event.Mist is found below 5 km, clear-air above 10 km, and fog after droplet formation at around 1 km.

Fig. 2.
The first 3 rows of the decision tree for the A2011_all (top) and the 4s_all (bottom) data sets (Table 1).Here no-fog includes no-fog AND no-mist, and the probability is computed as Eq. ( 1).The U1 unfavourable scenario is defined here: middle and high level thick clouds in the pixel (MHTCP) according to the satellite but not detected by the ceilometer above the SIRTA.CS stands for clear-sky, SC for scattered cloud cover and OC for overcast conditions.CF stands for cloud-free sky from bottom to top, CIR for thin cirrus above the clear-sky column (Table 6).

Seasonal Variability in Meteorology
Meteorological parameters are briefly commented to show that our study wiped a large variety of atmospheric conditions.Temperature and relative humidity presented contrasts between mv events of March and November (Table 2).Temperature was in average smaller in November (6-8.5°C)than in March 2012, but larger than in March 2013, exceptionally cold.Standard deviation was smaller in November than in March.Indeed the temperature varied by around 10°C in November while it varied by around 20°C in March.During the four months, the temperature could be smaller than 5°, but temperature was rarely larger than 13°C in November while it reached 20°C in March 2012.
Averaged relative humidity (RH) was smaller in March than in November, with also a larger standard deviation (Table 2).Indeed RH could reach 100% in mv events during the four months but only in March RH could frequently be smaller than 75%.Observation of RH can not be used as a fog predictor here, as relative humidity was always high during the training month of November 2011, whatever the mv event was pre-fog or no-fog (defined in Section 3.2).March shows a contrast with November, with no-fog RH significantly smaller than pre-fog RH (Table 2).
Unlike both temperature and RH, wind conditions did not present significant differences between months.The monthly average of the horizontal wind speed was around Table 1.Fifteen data sets are defined, according to both the time period and the visibility sequence.Only the 7 data sets mentioned in the text and used in Fig. 2 and 8 and in Table 10 are named here._excmc stands for (all events) except clearmv-clear sequences (Fig. 1), and _v5km for mv events followed by mist.The 4s_all data set is the main validation data set.1.5 m s -1 .However the standard deviation was large, around 1.0 m s -1 , meaning that significant variability was observed within each month.The main mode in the wind direction was included between 30 and 90° in both March and November.

Inventory
The predictors and the criteria are listed thereafter.The predictive pertinence of observed parameters and the chosen thresholds are commented in Sections 3.2 to 3.5.
The first predictor of the fog formation by radiative cooling is the visibility and criteria are applied on both the visibility level and its time evolution.The first criteria constrain the visibility range between 5 and 10 km, defining the mv event, which can last from 15 minutes to several hours.The second predictor is the visibility level before or after the mv event (Section 3.2).
Three predictors concern the cloud cover (Sections 3.3 and 3.4): 1) The cloud fraction (CFr) is defined as the proportion of hits, which are detected clouds by the CL31 ceilometer, during 15 minutes, and CFr is averaged for the duration of the mv event.<CFr> is not only a predictor but also defines the fog formation type.Three cloud cover categories are defined: -clear-sky (CS), with <CFr> < 30% and standard deviation < 30%; -overcast condition, with <CFr> > 70% and standard deviation < 30%; -scattered cloud cover, with 30 < <CFr> < 70% or standard deviation > 30%.
2) The cloud cover above the SIRTA is also provided by the cloud type product delivered by EUMETSAT/NWCSAF, in case clear-sky conditions are identified by the ceilometer.The cloud cover proportion is computed as N clear-sky/cirrus /N mv , where N clear-sky/cirrus is the number of times the specific scene is detected in the SIRTA pixel during the mv event, and N mv is the mv event duration in terms of 15-minute time step.Three categories are defined: -cloud-free sky from bottom to top (CF): N cirrus /N mv < 50%, and N clear-sky /N mv ≥ 50%; -only thin cirrus above the site (CIR): N cirrus /N mv ≥ 50%, and N clear-sky /N mv ≤ 50%, -middle and high level thick clouds in the SIRTA pixel but not observed by the ceilometer (MHTCP): N cirrus /N mv < 50% and N clear-sky /N mv < 50%, 3) The regional cloud cover change, in terms of clearsky and low cloud cover, is computed as a change in N clear-sky/low cloud in a 9×9-pixel zone around the SIRTA.Four categories are defined.The most common situation is a 3% increase of low cloud cover per time step, replacing clear-sky.Details are given in Section 3.4.
The sixth predictor is the vertical thermal gradient ∆Tv (Section 3.5): where T is the temperature at two heights (2 and 30 m agl).∆Tv is also used to define the fog type: -not stratified atmosphere (NS) for developed fog: ∆Tv < 0.035 °C m -1 ; -strongly stratified (Str) for thin fog: ∆Tv ≥ 0.060 °C m -1 ; -moderately stratified (MS): 0.035 ≤ ∆Tv < 0.060 °C m -1 .Distinction between thin and developed fog is based on their vertical development.A developed fog produces low visibility condition simultaneously at 4 and 18 m agl at SIRTA (Dupont et al., 2015), while a thin fog produces low visibility condition at 4 m only.The visibility vertical gradient is correlated to the thermal vertical gradient (Elias et al., 2012).Indeed an atmosphere strongly stratified does not permit the transport of cooling, though dynamical interactions with surface generate enough turbulence to form a thin fog.

Moderate Visibility as a Signal of Water Uptake by Aerosols
Horizontal atmospheric visibility at surface level is the most pertinent parameter to observe when dealing with the fog phenomena, because 1) visibility describes the adverse impact of fog on human activities; 2) visibility informs about the progress in the clear air-fog life cycle, marked by the presence of hydrated aerosols and droplets; and 3) visibility can be considered as a signal of atmospheric and surface processes affecting the water uptake by aerosols.Visibility was already used by Vislocky and Fritsch (1997) as a fog predictor.
Several events were defined by Elias et al. (2015) according to the presence of aerosols and droplets (Table 3): fog was defined by the droplet formation, usually occurring at visibility between 1 and 3 km, and the mist was defined by visibility smaller than 5 km, caused by hydrated aerosols, with absence of fog droplets and drizzle and rain drops.The mv event is defined by a visibility included between 5 and 10 km, and clear-air is defined by visibility > 10 km (Table 3).
The mv events are chosen for predicting the fog formation, because significant anticipation time is provided before the fog formation.Indeed, pre-fog mist lays between the end of the mv event and the time of formation of the first fog droplets.Moreover first prediction can be made as soon as the mv event starts, which give further anticipation time.The mean anticipation time is consequently included between the pre-fog mist duration and the added pre-fog mist and mv durations.The averaged mist duration was 1.1 h for developed fog and 2.1 h for thin fog, and the mv event duration was 1.8 h for both fogs.The mean anticipation time was 3 h at the start of the mv event and 1.5 h at the end of the mv event.This is the usual horizon for nowcasting, as Vislocky and Fritsch (1997) studied 1, 3 and 6 h lead times, and classification was applied to period of 4 to 6 h before fog onset by Veljovic et al. (2015).We must keep in mind that these anticipation times are approximates, as mist and mv pre-fog durations were highly variable, with 70 to 120% standard deviation per month, and that they are not predicted here.
As the further condition of clear-sky is set (Section 3.3), only aerosols were responsible for such a low visibility, and neither drizzle neither drops.Visibility decreasing because of aerosols growing up by uptaking water can be considered as a predictor as Elias et al. (2015) showed that such an aerosol presence always preceded fogs in November 2011 at SIRTA.Consequently visibility included between 5 and 10 km is the first condition to predict fog formation, and the first alert is fired at the start of the mv event.
Another parameter to check for fog formation nowcasting is the visibility evolution.Three main types of mv events are defined according to the chronological sequence of events before and after the mv event.Three situations were observed according to the events following the mv event: mv-mist-fog, mv-mist-mv, and mv-clear.Moreover two situations were observed according to the event preceding the mv event: mist-mv or clear-mv.The combination provides three main types of mv events according to the visibility evolution before, during and after the event (Fig. 1): -the pre-fog mv event: the mv event is followed by mist and eventually by fog.The sequences are mist-mv-mistfog and clear-mv-mist-fog.-the no-fog mv event: the mv event is followed by mist when visibility increases back to reach 5 km, and is then followed by another mv event.The two sequences are mist-mv-mist-mv and clear-mv-mist-mv.-the no-mist mv event: the mv event is followed by an event of larger visibility.The two sequences are mistmv-clear and clear-mv-clear.
Table 1 shows that a series of data sets concern all visibility sequences ("_all"), the second series is defined assuming that the clear-mv-clear sequence could be rapidly distinguished to other mv events ("_excmc" for except clear-mv-clear sequences).A third series is composed exclusively of mv events followed by mist ("_v5km").
A significant variability was observed with the month, in terms of event numbers and event cumulated duration (Tables 4 and 5).November 2011 was indeed an exceptional month for fog occurrence with an accumulated duration of almost 5 days of visibility smaller than 1 km (Table 4).According to Elias et al. (2015), eleven developed fogs occurred in November 2011 (by both radiative cooling and stratus lowering), which is similar to the exceptional foggy days at Belgrade airport commented by Veljovic et al. (2015).Moreover visibility also decreased because of thin fogs (Menut et al., 2014).The seasonal contrast in fog occurrence probability was important as the duration of situations with visibility < 10 km was little varying from 300 to 441 hours during four months representative of the four seasons, but the fog duration was divided by four from November 2011 to March 2012 and by 20 to March Table 3. Definition of four observed events at SIRTA.The only criterion on visibility is used to define clear-air and the moderate visibility events.According to Elias et al. (2015), criteria on both visibility and particle presence are used to define mist and the only criterion on particle presence is used to define fog.

Event:
Visibility  1) including the training month, and 1048 mv events were observed during the four seasons (the 4s_all data set).15 pre-fog mv events were counted during in the A2011_all data set and 63 in the 4s_all data set, giving a 9 to 6% probability that fog formed after any mv event, as indicated in the first row of the decision tree (Fig. 2).Almost half of the mv events were not followed by mist and consequently probability increased from 6 to 12% for the 4s_v5km data set.

The Cloud Cover above the SIRTA
The observation of cloud cover above the site by a ceilometer and also by a satellite is an efficient predictor of fog formation.Indeed, the cloud cover can influence the main processes responsible for fog formation, and it was proposed as a fog predictor by Vislocky and Fritsch (1997).According to Dupont et al. (2015), two main fog formation processes occur at SIRTA: radiative cooling (RAD) and stratus lowering.Following Elias et al. (2015), the cloud cover sounded by the CL31 ceilometer during the mv events allows differentiating between both processes, as radiative cooling of the surface occurs under clear-sky.We checked that two main populations were observed in the distribution of the cloud fraction (CFr) during the mv event: <CFr> ~0% in clear-sky and <CFr> ~100% in overcast conditions.Consequently, three categories of cloud cover could be defined according to the mean CFr and its standard deviation (Table 6).At SIRTA, radiative cooling was stronger under clear-sky, with an averaged observed net radiative infrared flux of -60 W m -2 (not shown), and of only -20 W m -2 in overcast conditions.Fig. 2 shows the three top rows of the decision tree for both the autumn 2011 season (A2011_all) and the four seasons (4s_all) data sets.Two main groups of situations are distinguished as the scattered cloud cover was rare, observed during less than 5% of the mv events in all seasons.Fig. 2 also shows that moderate visibility was observed less often under clear-sky than in overcast conditions.Indeed, clear-sky was observed during 246 mv events during the four seasons (54 mv events during the autumn 2011), while overcast conditions were observed during 745 mv events (111 mv events in autumn 2011, second row in Fig. 2).However, equal number of pre-fog events were observed in clear-sky and in overcast conditions during all seasons.Consequently, the probability of RAD fog formation increased by a factor of ~2 thanks to the ceilometer, reaching 20% during the autumn 2011 season and 12% in 4 seasons, while the probability of fog formation was around 4% during the overcast mv events.The two branches of scattered clouds and overcast sky are not processed here, and we deal with the 246 clear-sky mv events (Fig. 2).By selecting clear-sky situations, we also disregard cases of visibility decrease caused by precipitation drops.
The clear-sky definition by the ceilometer is limited to the lowest atmospheric layers between surface level and 6 km agl, and cirrus clouds are not detected by the CL31 ceilometer.Though Anthis and Cracknell (1999) identified the presence of higher clouds as parameters affecting the fog duration.Satellite instruments are consequently complementary to the ceilometer to check the impact of cirrus.Eight cloud type indexes (cti) are defined according to the EUMETSAT/SAFNWC cloud type product (Table 7).Fog is included into the very low and low cloud cover classes (cti = 2 and 3) (Guidard and Tzanos, 2007), clearsky is defined as cti = 1 and thin cirrus as cti = 6.The cloud detection by satellite agreed with the ceilometer, showing a contrast between clear-sky and overcast conditions: as expected, cti = 1 was mostly observed for the ceilometerderived clear-sky and cti = 2 to 4 mostly for the ceilometerderived overcast conditions (Fig. 3 for November 2012).High thick clouds (cti = 5) were rare and observed only in overcast conditions in November 2012.On the contrary, detection of thin cirrus (cti = 6) was not contrasted, and thin cirrus were observed above both clear-sky and overcast conditions.During mv events of November 2011/2012, cirrus were detected above ~25/15% low clouds and ~above 25/10% clear-sky.Similarly, Guidard and Tzanos (2007) Table 5. Number of mv events and fog formation probability after a mv event, during 4 months representative of autumn and winter at SIRTA.Probability was computed as N pre-fog /N all mv events .No-fog and no-mist definitions follow Fig. 1.The difference between N all mv events and the sum of other events is caused by mv events occurring during precipitation events.mentioned that 19% of fogs in France may be hidden under medium and high clouds.Radiative cooling also occurs under thin cirrus, with an averaged net radiative flux close to -60 W m -2 , around 5 W m -2 larger than under cloud-free sky, which is the cirrus radiative effect (Dupont and Haeffelin, 2008).
In case the ceilometer identified clear-sky, three categories of cloud cover were defined by associating the satellite detection: cloud-free from bottom to top (CF), only thin cirrus (CIR), mid and high thick clouds in the pixel (MHTCP) (Table 6).During the 12 months, cirrus were observed during only 9% of the CS mv events (third row of the decision tree in Fig. 2), but interestingly, the fog formation probability under cirrus increased up to 23% for five of the 29 fog events.The further criteria on the vertical thermal gradient show that cirrus clouds during the mv events were predictors of exclusively thin fog formation (Section 3.5), and cirrus presence was not favourable for the formation of developed fogs.The MHTCP situation was also observed during 9% of the mv events, but it never preceded fog formation, probably because of the heating impact of thick clouds.This is consequently defined as the U1 unfavourable scenario.The probability level changed little from CS (only ceilometer) to CF (ceilometer + satellite), and other predictors are required to distinguish between no-fog and pre-fog events.

The Regional Cloud Cover Change during the Moderate Visibility Events at SIRTA
Section 3.3 shows that the cloud cover observed at a local scale (pointed by a ceilometer or averaged over one pixel by the satellite) informs about the fog formation type and can be used as a RAD fog formation predictor.In this Section, we extend the information on cloud cover at a larger scale, detected by the satellite.Moreover, we also consider the changes in the regional cloud cover extent.The satellite 1) is complementary to ceilometer in the SIRTA pixel; 2) surveys the cloud cover evolution in nearby pixels, and 3) increases the anticipation time in case fog would form earlier in a close pixel.Vislocky and Fritsch (1997) advised to incorporate motion in the observation to improve the forecast performance, and Anthis and Cracknell (1999) showed that the fog dissipation follows a specific spatial pattern above Greece, with sharp fog edges, and dissipation progressing from the outer edges inwards.Similarly above the SIRTA but for the fog formation, low and very low cloud cover can appear before formation of developed fog in November 2011 (Elias et al., 2015).However, it is not sure when appeared these clouds, during pre-fog mist or mv events.
As previously mentioned, the satellite cloud type mainly agreed with the ceilometer in the SIRTA pixel, showing a contrast between the ceilometer-derived clear-sky and overcast conditions.Fig. 4 shows that they both agreed to 1) identify mostly clear-sky during mv events preceding RAD fog formation, but 2) low cloud cover in mist events preceding developed fog formation, and on the contrary 3) clear-sky during mist events preceding thin fog formation.Consequently clear-sky is constantly observed before thin fogs, from mv to mist events, while low and very low clouds appeared at some time before the developed fog Table 6.Five categories of cloud cover during the moderate visibility event, detected by: 1) the CL31 ceilometer vertically above the SIRTA and 2) the MSG/SEVIRI satellite instrument in the pixel including the SIRTA.CFr stands for the cloud fraction.7) during mv events, and for two cloud covers defined by the ceilometer in November 2012: clear-sky (left) and overcast (right).
formation (as mentioned in Section 3.3).Moreover thin cirrus were detected in November 2011 before thin fogs but not before developed fogs.The thin and developed fog type distinction is substantially commented in Section 3.5.The satellite is not only able to detect the formation of the fog or of the elevated fog layer, but also the geographical pattern of such a formation.For example, low clouds were progressively replacing clear-sky, westwards, at 02:00 on 15 November 2011, in a 25 × 25-pixel zone around the SIRTA (Fig. 5).Low clouds (cti = 3, green) completely covered the region at 06:00 (middle in Fig. 5).Fog started at 02:45 at the SIRTA (Elias et al., 2015).Low clouds were progressively replaced by very low clouds (cti = 2, blue-grey) and then clear-sky (cti = 1, dark blue) at 10:45 (right in Fig. 5), northwards.We compute a simple spatial heterogeneity indicator in a 9 × 9 pixel zone around the SIRTA as: SH cs = N pixels (cti = 1)/81 (3a) SH lc = (N pixels (cti = 2) + N pixels (cti = 3))/81 (3b) N pixels (cti) is the number of pixels with the same cloud type index cti.The proportion of clear-sky pixels in the 9 × 9-pixel zone, SH cs , and the proportion of low cloud (and very low cloud) pixels, SH lc , are plotted in Fig. 6 between 0:00 and 14:00 on 15 November 2011, as well as the cloud type index in the only SIRTA pixel.Around two hours before the fog formation at SIRTA, when visibility was already below 10 km, the low cloud cover started to increase from 0% in the region, and simultaneously the clear-sky proportion started to decrease down from 100%.In 1.5 hour, 50% clear-sky and 50% low cloud cover was reached in the region, and when fog was observed at SIRTA, more than 80% low cloud cover was observed in the region.Half an hour later, the low cloud cover proportion was 100%.In summary, in around 2.5 hours, the situation reversed in the 9 × 9-pixel zone, from 0/100% to 100%/0 low cloud cover/clear-sky, with around 10% change per time step of no-mist mv event (only 1 point).The low cloud cover increased by 5% per time step during pre-fog mv, and simultaneously the clear-sky decreased by 5%, while in no-fog conditions, no changes occurred in average.The distinction between pre-fog and no-fog conditions was even stronger in mist events.According to November 2011 data, the threshold was fixed at 3% to define four categories during mv (Table 8).Decision trees with application of criteria on the regional cloud cover changes are plotted in Figs.8(a) and 8(b) for the 4 seasons, and for the "cloud-free bottom to top" (CF) and "cirrus above SIRTA" (CIR) branches, respectively.4)) in function of visibility for several 'clear-sky mv' sequences of November 2011: 1) for the sequence with RAD developed fog formation (pre-fog mv, pre-fog mist, and RAD fog); 2) for the no-fog sequence (clear-sky no-fog mv, overcast no-fog mist); 3) for the only event of clear-sky no-mist mv.Month averages in visibility, ∆SH cs and ∆SH lc are plotted as well as the standard deviations in ∆SH cs and ∆SH lc .
Situations with changes in mid and high clouds (MHD and MHI) were not frequent (21 events), with 20% probability of thin fog formation in MHI situation.Strong contrast is observed in the case of regional decrease of mid and high clouds, with 100% probability under cirrus (CIR-MHD) but 10% in cloud-free sky (CF-MHD).The most frequent situation is a regional increase of low cloud cover (LCI), with significant probability: 13% probability in CF-LCI and 20% in CIR-LCI.Most fogs are formed under such situations of low cloud cover increase: 59% of the thin fogs and 100% of the developed fogs.The regional increase of clear-sky (CSI) is not a rare situation (53 events), only observed under cloud-free sky, but with an expected low fog formation probability of 9%.

The Vertical Thermal Gradient
At SIRTA, the vertical development of the RAD fog followed two schemes: 1) fog developed little in a strongly stratified atmosphere and visibility decreased at 4 m agl but not at 18 m agl (Elias et al., 2012;Dupont et al., 2015).The strong stratification indicates no turbulence and no vertical transport of the cooling; 2) fog did develop along the vertical in an atmosphere not too stratified, and visibility decreased at both heights and usually even higher.The vertical thermal gradient over 30 m (Eq.( 2)) is used here as a criterion to distinguish between thin and developed fog (Elias et al., 2012).Averages and standard deviations of the vertical thermal gradient are plotted in Fig. 9 in function of visibility during several sequences of decreasing visibility of November 2011.One plot concerns the developed fog formation (similar to Fig. 7) while the other plot concerns the thin fog formation.In the thin fog sequence clear-sky is observed in both mv and mist events, while in the developed fog sequence, low cloud cover appeared during mist.∆Tv was large in thin fog (+0.10 °C m -1 ), while it was close to 0 in developed fog.Consistently Dupont et al. (2015) showed a temperature change of more than 3°C over 29 m in a thin fog and no changes in a developed fog.Fig. 9 also shows that ∆Tv was large not only in thin fog but also during the preceding mist and mv, and that ∆Tv was small not only in developed fog but also during the preceding mist and mv.Dupont et al. (2015) also showed that the 29-m temperature difference before the fog was smaller in the developed fog sequence than in the thin fog sequence.Moreover a significant contrast was observed between the nofog and pre-fog sequences, with intermediate averaged values around 0.4 °C m -1 in no-fog and no-mist events.While the variability of ∆Tv was large in no-fog conditions, the standard deviation was small in the developed fog sequence.Consequently, ∆Tv was chosen as a predictor of both RAD fog formation and vertical development, and three categories were defined according to the value of ∆Tv (Table 9).
∆Tv is an efficient formation predictor for 9 thin fogs: the probability increased from 9% to 16% for 4 fogs, 10 to 25% for 1 fog, 20 to 33% for 1 fog, and 20 to 43% for 3 fogs (Figs. 8(a) and 8(b)).Also, a correlation was observed between the regional cloud cover change and the thermal vertical gradient, as the developed fog sequence deploys only under cloud-free sky in conditions of regional increase of low cloud cover (CF-LCI).However, the strongly stratified atmospheres were observed under 6 different cloud cover conditions.As previously mentioned, the CF-CSI scenario Table 8.Criteria on the regional cloud cover change (%) detected by MSG/SEVIRI, averaged during the mv event to define 4 categories.The zone covers 9 × 9 pixels around the SIRTA.6), and for the only 4s_all data set (Table 1).For clarity, the image is cut and the left piece is shown at top and the right piece is shown at the bottom (with a common central part).LCI stands for 'regional increase of low cloud cover', MHI 'regional increase of mid and high cloud cover', MHD for 'regional decrease of mid and high level cloud cover', CSI for 'regional increase of clear-sky' (Table 7), NS for 'non stratified', MS for 'moderately stratified' and Str for 'strongly stratified' (Table 8).
was generally unfavourable with 9% probability (row 4 Fig. 8(a)).The ∆Tv predictor not only shows that no developed fogs could be formed in such conditions but also increased the probability to 16% for four thin fogs in one favourable scenario, by generating two unfavourable scenarii of 0-9% probability.Similarly, ∆Tv allowed to distinguish one favourable scenario and two unfavourable scenarii in the CF-MHD situation.On the contrary, ∆Tv could not generate contrasts in the CF-LCI scenario for the 4 seasons data set, but contrasts were observed for nine fogs in the only autumn 2011 season, with probability smaller in MS situation than in both NS and Str.The MS scenario was rather rare, and under cirrus, the probability was contrasted in function of the regional tendency in cloud cover.

Fig. 9.
As Fig. 7 for the vertical thermal gradient, for not only the developed fog but also for thin fog (clear-sky mist following a clear-sky mv).The no-fog 'thin' sequence is: clear-sky no-fog mv, clear-sky no-fog mist.

FAVOURABLE AND UNFAVOURABLE SCENARII
As defined in Section 2, a scenario is said favourable when the fog formation probability was larger than the threshold and unfavourable if the probability was smaller.The probability thresholds are 12% for the _all data sets, 20% for the _excmc data sets, and 24% for the _v5km data sets.Scenarii are listed thereafter, Figs. 2, 8(a) and 8(b) show the scenarii in the decision trees, and Tables 10(a) and 10(b) summarise the probability levels for 7 of the 15 data sets (Table 1).

Unfavourable Scenarii
During the four seasons, 203 mv events occurred in cloud-free conditions from bottom to top of the atmosphere (CF), 22 under thin cirrus (CIR), and 21 events in the U1 unfavourable scenario (Fig. 2).The 22 CIR mv events followed 3 favourable and 2 unfavourable scenarii.The 203 CF mv events followed 6 favourable and 6 unfavourable scenarii.We remind that all scenarii concern mv events under clear-sky, according to the ceilometer.The nine unfavourable condition scenarii are: -U1: middle and high thick clouds observed in the SIRTA pixel by satellite but not detected in the vertical of the SIRTA by the ceilometer (MHTCP) (row 3 in Fig. 2).21 no-fog events were counted.This is mostly a winter scenario as 20 occurred in the only winter 2012 (Table 10(b)).These clouds have a tendency to heat the ground by infrared radiation, with a consequent decrease of RH, which is not favourable to fog formation.-U2-1 and U2-2: cloud-free sky, with low clouds replaced by clear-sky in the 9 × 9-pixel zone, and with ∆Tv < 0.060 °C m -1 (CF-CSI-NS and CF-CSI-MS, row 5, Fig. 8(a)).In the two scenarii, 28 no-fog events were counted, as well as one pre-fog event.U2-2 became favourable in autumn 2012.This cloud cover configuration was favourable for thin fogs, if ∆Tv was large enough (scenario F4, Section 4.2).-U3-1 and U3-2: clear-sky replaced by low clouds in the 9 × 9-pixel zone, under cirrus in the SIRTA pixel, and ∆Tv < 0.060 °C m -1 (CIR-LCI-NS and CIR-LCI-MS, row 5 in Fig. 8(b)).8 no-fog events were counted.
-U4-1 and U4-2: cloud-free sky, and middle and high thick clouds replaced by clear-sky and/or low clouds in the 9 × 9-pixel zone (CF-MHD-NS and CF-MHD-MS, row 5 in Fig. 8(a)), and with ∆Tv < 0.060 °C m -1 .6 nofog events were counted in both autumn 2011 and winter 2012.The presence of low and high thick clouds in the wider zone, even if they tend to disappear, may indicate that RH hardly reached the necessary threshold.-U5-1 and U5-2: cloud-free sky, and decreasing middle and high thick clouds in the 9 × 9 zone (CF-MHI-NS and CF-MHI-MS, row 5 in Fig. 8(a)).Only 2 no-fog events were counted but these scenarii are important as they allow to increase the probability in the CF-MHI-Str scenario from 20 to 33% (F6 favourable scenario, Section 4.2).
To summarise, 35 no-fog events occurred under cloudfree sky with ∆T v < 0.060 °C m -1 , in all cloud conditions except the low cloud increase (CF-CSI, CF-MHI, and CF-MHD).On the contrary under cirrus and in low cloud increase conditions, 8 no-fog events occurred with also ∆Tv < 0.060 °C m -1 (CIR-LCI).In total 65 no-fog mv events were identified in these 9 unfavourable scenarii.One prefog event would be missed with such a predicting scheme, representing only 3% of the pre-fog mv events.Consequently, the fog formation probability was only 1.5% during the unfavourable conditions of all seasons.With the further criterion of visibility smaller than 5 km after the mv event, Table 10(a).Probability levels (Eq.( 1)) during the favourable scenarii of RAD fog formation for different data sets, defined in Table 1 according to the season and the visibility sequence.The 4s_all data set is the main validation data set.Developed (dev) and thin fog formation is indicated for each scenario.The first two rows show the total number of mv events (N mv ) in the data set and for the clear-sky (CS) scenario.The following rows show N pre-fog /probability (%).The last row shows the values for "all favourable scenarii together", calculated as N pre-fog /(N mv minus N no-fog, identified ), N mv in the CS scenario and N no-fog, identified being counted in the last row of Table 10b.For example for the 4s_all data set: 28/(246 -65) = 15%.The bold values indicate the probability levels larger than the threshold of 12% for all visibility sequences ("_all"), 20% for the "_excmc" sequences and 24% the "_v5km" sequences.

Favourable Scenarii
Only one favourable scenario was identified for the developed fog: -Scenario F1: cloud-free sky, with low clouds replacing clear-sky in the 9 × 9-pixel zone, and with no stratification (CF-LCI-NS, row 5 in Fig. 8(a)).Six pre-fog events were counted, as well as 44 no-fog mv events with only 11 followed by mist, resulting in 12% RAD fog formation probability during mv and 35% when mist is observed after mist.These fogs mostly formed in both autumn seasons, with a probability larger than 40%.
The strong stratification was generally favourable, except in CIR-MHD and CIR-CSI situations which never occurred.Consequently six favourable thin fog formation scenarii are defined in strong stratification: -F2 and F5: low clouds replacing clear-sky in the 9 × 9 zone, either in cloud-free sky (CF-LCI-Str, row 5 in Fig. 8(a)) either under cirrus in the SIRTA pixel (CIR-LCI-Str, row 5 in Fig. 8(b)).Seven pre-fog events were counted in cloud-free sky, as well as 51 no-fog events, resulting in 12% probability, increasing to 25% when mv is followed by mist (Table 10(a)).Three pre-fog events were counted under cirrus, as well as 4 no-fog events, resulting in 43% probability, increasing to 60% when mv is followed by mist.-F4: cloud-free sky with low clouds replaced by clear-sky in the 9 × 9 zone (CF-CSI-Str, row 5 in Fig. 8(a)).Four pre-fog events were counted, as well as 21 no-fog events, resulting in 16% probability, increasing to 25% if followed by mist (Table 10(a)).-F6 and F9: increasing mid and high thick clouds in the 9 × 9 zone, either in cloud-free sky (CF-MHI-Str, row 5 in Fig. 8(a)) either under cirrus in the SIRTA pixel (CIR-MHI-Str, row 5 in Fig. 8(b)).One pre-fog event occurred in the F6 scenario with 33% fog formation probability, increasing to 50% if followed by mist.One pre-fog was also counted in the F9 scenario, with 25% fog formation probability, increasing to 33% if followed by mist (Table 10(a)).-F7: decreasing mid and high thick clouds in the 9 × 9 zone, in cloud-free sky (CF-MHD-Str).One pre-fog event was counted, with 25% fog formation probability.Two favourable scenarii were defined in moderately stratified atmosphere: -F3: As for the F1 and F2 scenarii, the cloud situation is cloud-free sky, with low clouds replacing clear-sky in the 9 × 9-pixel zone (CF-LCI), but the stratification is moderate.Four pre-fog events were counted, as well as 21 no-fog events, resulting in 16% probability, increasing to 23.5% when mv is followed by mist (Table 10(a)), then becoming an unfavourable scenario.That makes an ambiguous scenario, with moreover the probability remaining smaller than in the F1 and F2 scenarii in autumn 2011: 57-75% probability in F1-F2 but 29% in F3.CF-...-MS is never favourable except in this situation of LCI.-Scenario F8: under cirrus, with decreasing middle and high thick clouds in the 9 × 9 zone (CIR-MHD-MS, row 5 in Fig. 8(b)).This event was rare, only one pre-fog mv event was counted, resulting in 100% probability.28 pre-fog mv events were identified with these 9 scenarii (Table 10(a)), representing 97% of all the fogs.152 no-fog mv events also belong to these scenarii, and the fog formation probability for all favourable scenarii together for the four seasons was 15%, increasing to 30% if mv is followed by mist, which is ~10 times more probability than in the unfavourable scenarii.The only predictor of visibility generating an initial value of 6%, four predictors multiplied the fog formation probability by more than 2, and the predictor of visibility evolution by a further factor of 2.

The Seasonal Contrast in the Scenarii
We observed a seasonal contrast in RAD fog formation probability and also in fog occurrence (Tables 10(a) and 10(b)).First, 11 fogs formed under clear-sky in autumn 2011, 10 in autumn 2012, and only 8 in both winters 2012 and 2013.With a larger number of mv events in winter, the fog formation probability was larger in autumn (27%) than in winter (< 10%).
Five scenarii were autumn favourable scenario.The fog formation probability of F1 increased from 12% in all seasons to 40-43% in exclusively autumn, with only 0-3% probability in winter (Table 10(a)).F2 was also an autumn scenario with 9-30% probability of thin fog formation in autumn and 0-9% in winter.The same observation was made for F5 with 50% in the only autumn 2012, F7 with 100% in autumn 2011, and F8 with 50% in autumn 2012.For contrast, the only winter scenario was F6, with only 1 fog occurring in winter 2013.F2, F3 and F4 were all-season scenarii, with probability little dependent on the season.
In case a data set covering much more than 2 years was available, it would be possible to add a winter month in the training data set to identify RAD fog formation predictors specific to winter, increasing the averaged fog formation probability.

Alternative Instrumentation
Predictors were defined from data widely available.Indeed ceilometers and diffusometers are instruments usually operated on airport fields, and the EUMETSAT/NWCSAF products are available for the METEOSAT disk Africa, and Middle-Orient).Nevertheless we checked that the proposed instrumentation could be partly replaced.
The cloud cover was characterised over the site with combined ceilometer-cloud fraction and the EUMETSAT/NWCSAF cloud type, but could also be defined from combined downwelling solar and infra-red radiative flux measured by a ground-based station.Tests were performed with the SIRTA data base which were positive.The cloud base height measured by the ceilometer could also be a predictor, but during mist.Indeed Elias et al. (2015) mentioned that the cloud base height of the elevated fog layer in pre-fog mist of November 2011 was smaller than 120 m.Such a parameter could be a predictor in mist, as already proposed by Vislocky and Fritsch (1997).
Also, a meteorological mast can be rare on airport fields.Fortunately, the fog vertical development, defined by the vertical thermal gradient over 30 m in this paper, could be identified by other instruments.Indeed, correlations were found between ∆Tv on one side, and on the other side either the vertical gradient of visibility (Dupont et al., 2015), either the horizontal wind velocity, used as a predictor by Vislocky and Fritsch (1997).
Other measures such as soil water content could also be useful to nowcast RAD fog formation, indeed Bergot and Guedalia (1994) showed a delay of 3h in the fog formation between a very moist soil and a moderately moist soil.However on one hand such probes are not frequently set up on airports fields.On the other hand soil moisture impacts directly surface cooling, then also the temperature evolution and at final relative humidity whose evolution is predicted trough visibility.According to Vislocky and Fritsch (1997), the dew point and the atmospheric pressure could also be used as predictors.
Also, fog may sometimes form without a pre-fog mv is observed.Indeed, Elias et al. (2015) showed that two fog events were not preceded by pre-fog mist events in November 2011 at SIRTA, because the visibility decrease was so fast that no visibility was recorded between 1 and 5 km in the 15 minute time step.Similarly, mv events may not be recorded before fog events at the 15-minute time resolution, with the consequence to miss few pre-fog formation events.These observations suggest that the 15-minute resolution is sometimes too raw for describing the fog life cycle, but it was chosen to be consistent with the MSG temporal resolution.

Aerosol Microphysics and Relative Humidity as Fog Formation Predictors in Winter
Particle properties were studied during the mist-fog cycle in the framework of the PreViBOSS project.However the predictive pertinence of aerosol properties could not be estimated in this paper because measurements were not systematic.As mentioned by Mazoyer et al. (2016), around only 40% of the fogs were sounded by the ambient instrumentation.Moreover hydrated aerosols were so far studied during both the mist and the fog events (Hammer et al., 2014;Elias et al., 2015), but not during the mv events.
Concerning nowcasting, Elias et al. (2015) showed that in November 2011 fogs formed when the optical particle counter counted all aerosols responsible for visibility drop in mist.For example, when some rain or drizzle drops contributed significantly to the visibility decrease, then the fog did not form.Thus the study of pre-fog mist in November 2011 suggested that hydrated aerosols were a pre-requisite to developed fog formation.More precisely than the visibility drop, the predictor could be a parameter directly describing the process of water uptake by aerosols responsible for the visibility drop.The aerosol size observed in ambient conditions is an indicator of the aerosol hydration, as well as the combination of visibility and relative humidity.Veljovic et al. (2015) showed that fog events are characterised by a satisfying correlation coefficient between visibility and RH.
Indeed, such a correlation is not observed for other events of low visibility, as caused by anthropogenic pollution.For example, in March 2014 at SIRTA, visibility could decrease below 10 km not because of aerosols growing up by uptaking water but because the number concentration of relatively dry aerosols increased, at RH < 50% (Dupont et al., 2016).In another location, visibility could reach 6 km with particulate matter concentration PM 10 > 200 µg m -3 (Majewski et al., 2015).
RH is commonly measured at airports and could be used to improve the nowcasting scores.Clark and Hopwood (2001) incorporated local observations into the initial conditions for their one-dimensional model and found humidity data were the most important, though their influence on the forecast lasted no more than about 6 hours.However RH could not be formally used as a predictor here because during the training month of November 2011, averaged RH was larger than 95% in both pre-fog and no-fog mv events.
Anyway, we made a short study of the humidity conditions during both pre-fog and no-fog events to provide a hint on the impact of considering RH as a predictor.2 shows that mean RH was larger than 90% in prefog mv events of March, while RH remained close to 70% in no-fog mv events.Even by examining individual events, RH was larger than 90% in pre-fog events, except during only three pre-fog events when RH was smaller than 80%, but with a large standard deviation indicating the increase of RH.On the other side, RH was smaller than 60% during the no-fog mv events of the developed fog F1 scenario, which were followed by mist and which occurred in March 2012.Thus with the criterion of RH > 70% or RH > 80%, more no-fog mv events could be identified, increasing the fog formation probability.

CONCLUSION
To improve nowcasting of fog formation by radiative cooling, we analysed measurements taken over a 12-month period, when visibility levels were frequently less than 10 km but with contrasted occurrences of fog.The measurements described physical processes occurring at both surface level and along the whole atmospheric column: the aerosol hydration and consequent decrease in visibility; the stratification of the lowest atmospheric layer; and the change in the 3D cloud cover.The physical processes were observed during two autumns and two winters from October 2011 till March 2013 at the SIRTA platform by a diffusometer, a ceilometer, and thermometers set up along a 30-m meteorological mast.We also used data acquired by the SEVIRI instrument on board the METOSAT Second Generation satellite, and processed by the EUMETSAT/ NWCSAF program to derive the cloud classification.The training data set was acquired in November 2011, and the validation data set was composed of 12 months of data.
Six predictors were identified from the November 2011 data set, which allowed us to define favourable and unfavourable scenarii of thin and developed fog formation by radiative cooling.The first predictor was the atmospheric visibility level, which was used to define a moderate visibility (mv) event as having a visibility between 5 and 10 km.Parameters observed during the pre-fog mv events were compared with the same parameters observed during the no-fog mv events to identify fog formation predictors and the corresponding criteria.The other predictors were the change in visibility over time, the change in air temperature from surface level up to 30 m in height, and the state of the cloud cover above SIRTA and the surrounding region.The fog formation probability was increased by a factor of 10 from the unfavourable to the favourable scenarii.
The cloud cover parameters were inferred from complementary ceilometer and MSG/SEVIRI.The ceilometer indicated the height of the local cloud cover up to 6 km a.g.l.above SIRTA while MSG/SEVIRI indicated the height of higher cloud cover above SIRTA and in the surrounding area.In particular, cirrus clouds were not detected by the ceilometer but by MSG/SEVIRI.An unfavourable scenario was defined as clear sky in the vertical above SIRTA according to the ceilometer when middle and high-level thick clouds were detected by MSG/SEVIRI in the pixel.On the other hand, clear sky below cirrus clouds defined a generally favourable scenario with a 23% probability of thin fog formation, while the fog formation probability was 12% under a cloud-free sky from the bottom to the top of the atmosphere.We also studied the influence of changing cloud cover in a 9 × 9-pixel zone around SIRTA.The fog formation probability decreased when clear sky replaced low cloud cover.
The vertical thermal gradient ∆Tv allowed us to distinguish between thin and developed fog, and as a predictor, it allowed us to define the only favourable scenario for the latter: cloudless sky from the bottom to the top of the atmosphere, increasing low cloud cover in the region, and ∆Tv < 0.035 °C m -1 .The fog formation probability was 12% for the 4 seasons, and increased to 35-40% when mv was followed by mist or when mv occurred in autumn.This predictor also showed that any change in regional cloud cover with a cloud-free sky above SIRTA was favourable to thin fog formation, with ∆Tv > 0.060 °C m -1 .The anticipation time was 3 h on average but decreased to ~1.5 h if visibility dropped below 5 km after the mv event.
Also, tests on relative humidity (RH) could improve the fog formation probability in winter.Indeed, visibility could fall below 10 km not only because of aerosol hydration, which is a prerequisite, but because of increasing pollution aerosol number concentration (no-fog).RH could not formally be considered here as a predictor because the training month was November 2011, when RH mostly exceeded 90%.A longer data set composed of these predictors and other meteorological parameters would allow the addition of a winter month in the training data set.Also, independent data sets are needed to define the application limits of the presented scheme.Eventually, the same kind of study can be made with the frequently occurring stratuslowering fog at SIRTA, with other predictors as the cloud base height, precipitation (Vislocky and Fritsch, 1997), and atmospheric water content.

Fig. 3 .
Fig. 3. Frequency distribution of the satellite cloud type index (Table7) during mv events, and for two cloud covers defined by the ceilometer in November 2012: clear-sky (left) and overcast (right).

Fig. 4 .
Fig. 4. The evolution of the cloud type index in the SIRTA pixel, in function of the surface level visibility and the fog type in November 2011: during mv (left) and mist events (right), before thin (top) and developed fog (bottom).

Fig. 5 .
Fig. 5.The cloud cover derived by the satellite during the mv-fog-mv cycle of 15 November 2011, over the 'Ile de France' region (25 pixels).Left image is taken at 02:00, middle image at 06:00 and right image at 10:45.Low clouds (cti = 3) are showed in green, very low clouds (cti = 2) in blue-grey and clear-sky (cti = 1) in dark blue.SIRTA is located in the centre of the image.

Fig. 7 .
Fig. 7. Regional tendency of cloud cover as a predictor: ∆SH cs (left) and ∆SH lc (right) (Eq.(4)) in function of visibility for several 'clear-sky mv' sequences of November 2011: 1) for the sequence with RAD developed fog formation (pre-fog mv, pre-fog mist, and RAD fog); 2) for the no-fog sequence (clear-sky no-fog mv, overcast no-fog mist); 3) for the only event of clear-sky no-mist mv.Month averages in visibility, ∆SH cs and ∆SH lc are plotted as well as the standard deviations in ∆SH cs and ∆SH lc .
Fig.8(a).As Fig.2but for rows 3, 4, 5 and the only cloud-free bottom to top (CF) branch (Table6), and for the only 4s_all data set (Table1).For clarity, the image is cut and the left piece is shown at top and the right piece is shown at the bottom (with a common central part).LCI stands for 'regional increase of low cloud cover', MHI 'regional increase of mid and high cloud cover', MHD for 'regional decrease of mid and high level cloud cover', CSI for 'regional increase of clear-sky' (Table7), NS for 'non stratified', MS for 'moderately stratified' and Str for 'strongly stratified' (Table8).

Table 4 .
Cumulated duration (h) in three visibility ranges during four months representative of autumn and winter at SIRTA.

Table 7 .
Cloud type index (cti) defined according to the SAFNWC/EUMETSAT classification.Cloud categories over sea are not considered, neither above snow/ice.

Table 9 .
Criteria on the vertical thermal gradient ∆T v (°C m -1 ) averaged during the mv event.

Table 11 .
List of acronyms.