PARAFOG v2.0: a near real-time decision tool to support nowcasting fog formation events at local scales

Laboratoire de Météorologie Dynamique, Ecole Polytechnique, 91128 Palaiseau, France. Institut Pierre Simon Laplace, Ecole Polytechnique, Centre National de la Recherche Scientifique, 91128 Palaiseau, France. 10 Institut Pierre Simon Laplace, Université Versailles Saint Quentin-en-Yvelines, 78280 Guyancourt, France. Laboratoire de Météorologie Dynamique, Ecole Polytechnique, Centre National de la Recherche Scientifique, 91128 Palaiseau, France.

The difficulties of NWP fog forecasting can be explained by the fact that fog events are driven by complex land-atmosphere interactions in the atmospheric boundary layer, where vertical resolution of NWP models is still not high enough. To simulate more detailed information, 1D high-resolution numerical models have been used to 70 complement the classical NWP setup, which allows specific local observations to be incorporated (e.g. Bergot et al., 2005). More recently, Large-Eddy Simulations (LES) have been used to explicitly resolve small-scales processes at play within the fog cloud (Bergot et al., 2016;Mazoyer et al., 2017;Waersted et al., 2019). Still, LES modelling is computationally very expensive, and both microphysical and chemical parametrizations 75 are still needed.
Another approach to forecast fog events is based upon ground-and/or space-based observations. From its top perspective, satellite imagery allows to monitor fog by combining different bands with relatively good space-time resolutions. With this regard, https://doi.org/10.5194/amt-2021-99 Preprint. Discussion started: 23 April 2021 c Author(s) 2021. CC BY 4.0 License. Cermak and Bendix (2008) developed an operational fog/low stratus daytime scheme 80 based on Meteosat data. Cermak and Bendix (2011) extended this approach to only discriminate ground radiation fog by introducing some microphysical hypotheses, before being adapted by Egli et al. (2017) to make it suitable for several meteorological conditions encountered over Europe. Egli et al. (2018) proposed a hybrid diurnal fog product based on the combination of satellite images and ground-based observations. In 85 addition, Kneringer et al. (2019) and Dietz et al. (2019) developed probabilistic fog nowcasting systems to forecast different low-visibility procedures from standard meteorological measurements available at Vienna international airport for lead times of +30 min to +120 min.
While both the aforementioned satellite-and learn-based studies do not intend to track 90 the evolution of particular physical processes driving fog formation, ground-based observations may provide valuable key information by monitoring their true values in complement to NWP models. Ground-based observations allow to accurately measure key variable at play in a fog cloud at high temporal resolution (~ every minute). For instance, radiation fog formation results from an aerosol-particle hygroscopic growth 95 process illustrating the vapor-to-liquid phase change before fog onset. Based on attenuated backscatter analysis, Automatic Lidar and Ceilometer (ALC) data provide key information portraying this physical process. Haeffelin et al. (2016) developed the nearreal time fog analysis tool PARAFOG (hereafter referred to as PFG1), with the objective to predict radiation fog formation based on ALC measurements together with classical 100 meteorological observations. During the pre-fog condition (usually 1 to 3 hours before fog), PFG1 determines a reference ALC-attenuated backscatter profile based on which the rate of change of aerosol-particle hygroscopic growth can be assessed. PFG1 retrieves pre-fog alert levels with a vertical resolution of about 15 m ranging from 0 to 400 m a.g.l.
and time resolution of one minute. PARAFOG is experimentally used at Paris 105 international airports (Roissy-Charles de Gaulle and Orly) where it provides valuable information supporting the decision making of both weather forecasters and air traffic controllers that affect scheduling of airplanes. Several years of experience with PFG1 have highlighted some limitations, such as the monitoring of stratus lowering fogs, its capabilities to monitor the entire fog life cycle, or even its anticipation for shallow 110 radiation fog events near the surface. In this study, we present PARAFOG v2 (hereafter referred to as PFG2), which is an improved and extended version of PFG1 allowing to discriminate between radiation and stratus-lowering fog formation, respectively.
• Radiation fog events (RAD) refer to fog that forms during radiative cooling at the 115 ground surface, usually at night, in presence of anticyclonic, low wind speed, and clear-sky conditions (Gultepe et al., 2007). Due to the radiative cooling, the air just above the ground is affected by a progressive hygroscopic growth of fog condensation nuclei, turning water vapor into liquid after reaching supersaturation, whereby reducing the surface visibility.

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• When radiative cooling coincides with large-scale subsidence, the cloud base height of stratus clouds can gradually decrease down to the surface, defining stratus lowering fog events (STL). Indeed, stratus cloud top radiative cooling acts to transport larger cloud droplets downwards (while strengthening the cloud top inversion), and permits the cloud base to subside until reaching the ground at times 125 (Dupont et al., 2012).
This article is organized as follows: Sect. 2 introduces the measurements used as input to PFG2 and measurement sites where evaluation studies are conducted. Sect. 3 presents the new methodology developed in PFG2. Section 4 presents the PFG2 results obtained at different European sites. The quantitative assessment of PFG2 and its relative 130 performance is presented in Sect. 5. Finally, a summary of the both main developments and results is given in Sect. 6, along with some thoughts for potential improvements.

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The data used in this study are mainly based on observations collected at SIRTA  (Haeffelin et al., 2010;Waersted et al., 2019). PFG1 field experiments 145 took place at SIRTA from 2006 to 2014, where a synergistic suite of instruments was designed to document the entire fog life cycle in correlation with dynamical, thermodynamical, optical and microphysical properties (e.g. Elias et al., 2009;Dupont et al. 2012;Dupont et al., 2016).
Complementing the SIRTA observations, data from major European airports regularly 150 affected by fog are considered to test the robustness of PFG2 in a range of local environments and meteorological conditions. The present study considers the following four airports: Paris Roissy-Charles de Gaulle, Zurich, Munich and Vienna ( Figure 1).

b) Instruments and fog event statistics
155 Among all the instruments deployed at SIRTA, the present study makes use of a Vaisala CL31 ceilometer (generation CLE321) providing attenuated backscatter profiles at ~910 nm as well as cloud base height using the operating procedures recommended by Kotthaus et al. (2016). In addition, scatterometers (Degreane DF20/20+/320) provide horizontal visibility at 4 m a.g.l., whereas both temperature and relative humidity observations are 160 recorded by an automatic weather station at 2 m a.g.l. All airports considered in this study are equipped with a Vaisala CL31, automatic weather station and visibilimeters ( Table   1). The present study considers 9 years of measurements at SIRTA from 2011 to 2019, and up to two fog seasons at the Paris-Roissy, Vienna, Munich and Zurich airports between 2014 and 2017 (Table 1).

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The number of fog events for each site is derived using the Tardif and Rasmussen (2007) analysis procedure. analysis. In this study, we only focus on fog events that correspond to RAD or STL, which represent more than 90% of cases regardless of the sites considered. Note also that fog events retrieved following the Tardif and Rasmussen (2007) algorithm are not considered when data are missing from either the CL31 or the meteorological station measurements as these are required input data to PFG2. The total number of fog events considered in  (Table 1).

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PFG2 has been designed to operate with relatively standard instruments, which are commonly found at national meteorological service sites, airports, and/or research observatories. The rationale for this approach is to develop a fog decision tool widely and easily applicable that enables to track the evolution of both physical and key parameters in near-real time for fog formation. In the same way as PFG1, PFG2 makes use of ALC 185 measurements together with visibility and relative humidity from a meteorological station. The current version of PFG2 retrieves fog alerts at a vertical and temporal resolution of 15 m and 1 min, respectively. PFG2 has also been entirely upgraded to Python 3 and the main advances (compared to PFG1) are:

i)
A more efficient memory management.
iii) An assessment of the fog life cycle (discriminating between formation and mature stages).
iv) New output visualization options (operational and reanalysis mode). Note that 195 we only present PFG2 outputs visualizations in reanalysis mode in this study.
The operational mode corresponds to a simplified version with the visibility, attenuated backscatter profiles between 0 and 400m, alert levels and fog type retrieved from PFG2 together with the status of the algorithm.
The methodology of the PFG2 algorithm ( Figure 2) is divided into three main steps: 200 a) PFG2 is "turned ON" when the relative humidity measured at ground level exceeds a value of 85 % for a period of at least 10 min.
b) The visibility allows to discriminate between the formation and mature fog stages. If the visibility is greater than 1000 m for a period of at least 10 min, a fog formation module is activated.

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c) The distinction between RAD and STL fog type during the formation stage is based on the cloud fraction analysis deduced from the ALC measurements. If the two-hour averaged cloud fraction between 0 and 1000 m a.g.l. is greater (lower) than 50 %, the STL (RAD) formation calculation is activated. To reliably distinguish between RAD or STL fog situation, the cloud fraction calculation is 210 updated every hour.

b) Radiation fog module
PFG1 was initially designed to monitor the early stages of RAD fog events by analysing the rate of change of the aerosol-particle hygroscopic growth derived from ALC 215 measurements in near real time. An in-depth analysis of the performance of PFG1 (see Section 5a for details about the methodology and Figure 9) gave useful insights. Overall, PFG1 performance at SIRTA over 128 RAD fog events between 2011 and 2019 had a hit rate of 70 %. At the Paris-Roissy, Vienna and Zurich airport sites, hit rates of about 90 % were achieved, while the performance was markedly lower than 50 % at the airport of 220 Munich (37%) and Zurich (31%). This analysis reveals that a substantial number of RAD fog events were not detected at SIRTA and the Munich and Zurich airports using the PFG1 algorithm. Figure  visibility can fluctuate at the scale of minute, the visibility measured at 4 m is lower than 1000 m for hit (missed) RAD fog events for ~ 90% (~ 75%) of the time. At 20 m, this situation is different since it represents 80% (25%) for hit (missed) RAD fog events. This discrepancy can be explained by the fact that RAD missed events correspond to shallow radiation fog layers, while RAD hit events are associated with thick radiation fog layers.

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The distinct distributions of the attenuated backscatter profiles related to hit/missed RAD fog events, respectively confirm this conclusion ( Figure 3 c-d). Attenuated backscatter profiles associated with missed RAD events are on the order of 1 x 10 -6 sr -1 .m -1 , except for the first range gate near the surface with values around 1 x 10 -5 sr -1 .m -1 ( Figure 3d).
In contrast, the attenuated backscatter profiles associated with the thick RAD fog layers 235 that resulted in PFG1 "hits" show high values ranging from 1x10 -3 sr -1 . m -1 at the surface to 1 x 10 -6 sr -1 .m -1 at 100m, and are around 1 x 10 -7 sr -1 .m -1 for higher altitudes ( Figure   3c). These two regimes are typical of thin and thick RAD fog events, respectively . The thin RAD fog events occurred near the surface in a very shallow hydrated layer, where the ALC measurements are not able to monitor the aerosol 240 hydration. According to Kotthaus et al. (2016), observation in the first range gate of the Vaisala CL31 measurement is of poor quality due to incomplete optical overlap.
Therefore, PFG1 has difficulties to provide alerts for shallow radiation fog layers. Thin RAD fog events occur frequently at Munich and Zurich airports.
To incorporate also very shallow fog layers, a new approach based on a fuzzy logic 245 algorithm has been implemented in PFG2. Here, the fuzzy-logic algorithm (Mendel, 1995) transforms non-linear data into scalar outputs referring to low, moderate and high fog alerts (hereafter referred to as LOW, MOD, HIGH, respectively). The fuzzy-logic algorithm has been selected due to its simple implementation and its low computational cost. Here it relies on a combination of visibility measurements and attenuated backscatter 250 ratio gradient (RG in Haeffelin et al., 2016). RG allows to monitor the aerosol activation process and is derived from a reference ALC-attenuated backscatter profile determined during pre-condition-fog conditions. For each considered alert, a typical range of values is assigned to the visibility and RG variables. Each range of values is expressed as a membership function (MBF) and finally combined in a process called aggregation (A).

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The fuzzy logic method employed in the PFG2-RAD module uses one dimensional trapezoidal MBFs (F) to calculate the aggregation score that describes how well the observations characterize the imminent fog formation. The general expression of the aggregation score A level (t) as a function of MBFs and alerts is given in equation 1: where level refers to the considered alert and Fvisi (resp. FRG) represents the MBF associated with the visibility (resp. RG).
The MBFs are assumed to have trapezoidal shape and are described as follows: where x is the considered variable, x1 and x4 (resp. x2 and x3) the lower (resp. upper) corners of the trapezoid. Note that the complete parameters associated with the trapezoidal functions for fog formation in PFG2 are given in The PFG2-STL module is again based on a fuzzy logic algorithm. Since low stratus clouds can be close to the ground for hours before their cloud base height starts to descend whereby causing a fog event, exploiting the attenuated backscatter ratio gradient as for PFG2-RAD does not provide useful insights. Hence, the PFG2-STL fuzzy logic algorithm relies on a combination of visibility and cloud base height (CBH) observations ( Figure   285 4). The PFG2-STL module uses one dimensional trapezoidal MBFs (F) together with weights (w) to calculate the aggregation score as described in equation 2: where level refers to the respective alert, Fvisi (resp. FCBH) represents the MBF associated 290 with visibility (resp. CBH) and wvisi (wCBH) is related to the weight given to the visibility (resp. CBH).
The weights are determined empirically from the temporal gradient of both visibility and CBH variables, considering the 60 min prior to STL fog events that occurred at SIRTA between 2011 and 2019. The weights are standardized with a linear scaling as follows: , where x is the original value of the considered variable (temporal evolution of visibility or CBH), and xmin (xmax) is the minimum (maximum) bound of x. The boundaries employed in this study are 0 to -2500 m.h -1 for the visibility gradient, and 0 to -50 m.h -1 300 for the CBH gradient, respectively (Figure 4 a-b)). Note that these thresholds may need to be adapted for sites with very different fog characteristics. The final score A level (t) in equation 3 is converted to a STL fog alert level (LOW, MOD, or HIGH) by assigning the alert with the highest score (i.e. maximum rule value).

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Here we present the ability of the PFG2 algorithm to anticipate the alert level for three different meteorological situations prior to fog formation at Munich airport, SIRTA observatory, and Zurich airport.  As shown in Figure 6, the temperature (relative humidity) decreased (increased) from ~13 °C to 8 °C (from ~80 to 99 %), in presence of low-wind (< 4 m.s -1 ) and clear sky conditions during the first part of the night. As a result of the radiative cooling, the visibility was reduced, leading to a fog onset at 01:40 UTC. Overall, the PFG2-RAD module performs well for this fog event since it has gradually delivered low to high alerts about 6 hours before the fog onset. The reference attenuated backscatter profile is on the order of 1 x 10 -7 sr -1 .m -1 , with a reference RHref of 68 %. The aerosol activation started in altitudes ranging from 50 to 200 m a.g.l. For this RAD fog case, the first HIGH alert occurred ~100 min before fog onset, and the PFG2-RAD algorithm correctly identified 340 the fog type as a thick radiation fog layer. and then from MOD to HIGH (15h42 -18h32 UTC), with HIGH alert reported more than 25 min prior to the fog onset.

-Quantitative assessment of PFG2 performance
The performance of the PFG2 algorithm is evaluated at 5 European sites, namely SIRTA, 355 and the airports at Vienna, Munich, Zurich, and Paris-Roissy.

a) Assessment methodology
A specific assessment methodology has been designed to evaluate alerts provided by the PFG2 algorithm. The corresponding diagram of the PFG2 assessment methodology is shown in Figure 7, while the overall assessment framework is described hereafter: o The successive sub-periods presenting the same alarm levels are gathered in a single alarm (e.g. two consecutive HIGH alarms are counted as one). alarm. Note that the LOW and MOD alarms are not considered for the quantitative 395 assessment of PFG2 performance. These alarms are intended as indicators of conditions favourable for fog formation, but without specific lead times.

b) Application to SIRTA and European airport sites
The quantitative assessment of PFG2 algorithm performances at the European sites is 400 presented in Figure 9. It is based on a contingency table analysis and the two following  Roissy (26%), whereas it becomes 10 % at Munich, 40 % at Vienna, and 43 % at Zurich.
However, these results must be strengthened with a more substantial database for the different airports which only present a few cases of STL over one or two fog seasons (Table 1).

c) First high alerts characterization at SIRTA
Another important parameter of the statistical PFG2 assessment relies on the characterization of the first HIGH alert that results in a subsequent fog event during periods of hits. Here, the first high alert in the longest block of high alerts since the start of a fog event is analysed over a 180 min period. Figure 10 shows the distribution of these 430 first HIGH alerts for both RAD and STL fog events at SIRTA. Each hour is characterized by a different regime. The probability that a first "true" high alert occurs more than 2 hours before a fog event is relatively low, representing about 20% (5%) for RAD (STL) events. These probabilities are doubled between -120 and -60 min (RAD ~ 40 %; STL ~ 10%), while it sharply increases (until to reach 100%) over the last hour prior to a RAD / 435 STL fog event. Here, the discrepancies between the first HIGH alerts for the PFG2-RAD and -STL modules highlight the difference in terms of dynamics between the two fog types. Radiative fog events occur most of the time during night-time radiation cooling, characterized by low winds and high-pressure conditions. The hygroscopic growth of condensation nuclei is progressive and allows PFG-RAD to anticipate well the related fog 440 events by combining the visibility and the RG measurements. However, STL fog events may oscillate a few tens of meters above the surface before lowering and leading to a fog.
This more "sudden" character is found in the first HIGH alerts of PFG2-STL which sometimes starts to retrieve them only a few minutes before the fog onset. As a result, PFG2 has already 40 % (against 25 %) chance to have delivered the first HIGH alert for Overall, the pre-fog alert levels retrieved by both the PFG2-RAD and -STL modules at SIRTA, and both Munich and Zurich airports are found to be consistent with the local weather analysis. Pre-fog alert level gradually rises from LOW to MOD, and then from MOD to HIGH as one gets closer to a fog event and the visibility decreases. The HIGH 465 pre-fog alerts are found to occur between 30 and 60 minutes prior to fog formation regardless of the fog type considered, whereas the associated thin/thick discrimination matches well with RAD fog events.
An original approach to assess the performance of the pre-fog alert levels retrieved by both the PFG2-RAD and -STL algorithms has been subsequently proposed to support

Acknowledgements
The contribution of the first author and the PFG2 project were supported by the "Direction  Tables   Table 1: Main characteristics of the different sites and instruments used in this study.   whereas STL refers to stratus lowering fog events. RH stands for relative humidity and CF0-1000m refers to the cloud fraction between 0 and 1000m.

Figure 2:
Flow chart of PARAFOG-v2 algorithm. RAD stands for radiation fogs, whereas STL refers to stratus lowering fog events. RH stands for relative humidity and CF0-1000m refers to the cloud fraction between 0 and 1000 m.