Fog is one of the major challenges for transportation systems. The economic impact is comparable to that of tornadoes [1
]. For land transport systems, the first impact concerns road safety. In the presence of fog the Meteorological Optical Range (MOR) is reduced. This leads to an increase in the number of accidents at night and doubles the number of fatalities per 100 accidents [2
]. Fog conditions also lead to a reduction in speed, and thus have an impact on mobility. Regarding the study of human perception through fog, only the macroscopic density, defined by the MOR, denoted as V
, is to be taken into account [3
]. Fog is considered to be present for a MOR below 1000 m [3
]. The MOR is the distance through fog for which the luminous flux of a collimated light beam is reduced to 5% of its original value.
With the advent of Advanced Driver Assistance Systems (ADAS), and the development of autonomous vehicles, it is very important to take into account the impact of fog on the sensors dedicated to driving. The MOR is always critical, however, as sensors can use different wavelengths, some of which are beyond the visible; the microstructure of the fog is also critical [4
]. There are indeed many different Droplet Size Distributions (DSD) of fog [1
]. However, fogs with different DSDs do not have the same formation mechanisms and it is therefore difficult to find them in the same place and at the same time. Moreover, although significant measurement campaigns have been carried out [5
], the fog phenomenon is very random and the densest fogs are quite rare [8
]. It is therefore difficult to test the sensors on board vehicles in the natural environment, with real fogs, all the more so as the meteorological sensors must then be located close to the roads.
These different factors led Cerema to propose a test platform that can be used to reproduce fog conditions on demand. Cerema is a state agency of 3000 employees, placed under the supervision of the ministry for Ecology, Energy and Sustainable Development and Energy and the ministry for Regional Equality and Housing. The Cerema acts as a resource center for scientific and technical expertise. Specific features of Cerema are a strong territorial rooting and its capacity to combine many fields of expertise to answer complex questions related to sustainable development. In the field of mobility and transportation, the Research Team, Intelligent Transport System, (Equipe-projet STI) at the Laboratory of Clermont-Ferrand (one of the 17 laboratories of Cerema) conducts research on the mobility and safety in adverse weather conditions as fog and rain. The study of the impact of reduced visibility conditions on driving is addressed both from a technical approach and from driver perception. Tests and analyses are carried out in the platform. That is a research infrastructure, unique in Europe, open to research institutes as well as to private companies in order to evaluate performances of smart system dedicated to transport, or to proceed to any other scientific activities such as model validation, perception tests.
Cerema’s Adverse Weather platform [9
] has been allowing research teams to come and test their system since 1984. A number of studies have been published [10
]. The Adverse Weather platform can reproduce various fogs with two types of DSD and for MORs from 10 to 1000 m. Although initial work has shown a coherence between natural fogs and fogs reproduced in the platform [7
], it is now necessary to validate the DSD of the platform fogs on a larger scale. This is the subject of this article.
Concerning fog DSD analysis, the literature is very extensive. The reader will be able to consult more complete states of the art on this subject [1
]. All the studies show that fog droplet size ranges from a few tenths of a micron to a few tens of microns [1
]. Many of the previous studies use coefficients calculated on the DSD to characterize it. Examples include the liquid water content (LWC) [6
], the total concentration of drops,
] which are systematically calculated, the mean diameter
] or its variants [7
]. Finally, original parameters such as different order moments on the distribution such as standard deviation, skewness and kurtosis, or the autoconversion rate are sometimes used [33
]. Some of these studies attempt to establish a relationship between the above-mentioned parameters:
vs. LWC [38
]. Other studies attempt to characterize the DSD by modeling them. Two main categories of laws are used for fitting: shifted gamma laws [40
] and log normal laws [7
In spite of this very rich bibliography, the classification of fogs is still very complicated. Some works qualitatively discuss the value of coefficients combinations in relation to each other [33
]. Howerver, to our knowledge, there is no quantitative analysis of the relevance of some coefficients to others, nor any systematic method for classifying fogs according to their DSD. This may also be due to small data sets. It is for these reasons that this study is proposed. The main goals are:
to characterize the two types of fogs of the platform. The objective is to show that these fogs are significantly different, over a large amount of data.
to show that these two types of fog DSDs are similar to natural fogs.
4.1. Choice of Parameters by Correlation
The coefficients proposed in the previous section have all been calculated on the database detailed in Section 3.2
. As the coefficients are numerous, and some are highly correlated with each other (Table 2
), only the coefficients that are most representative of the literature, and independent of the others, will be retained for further analysis. It is important to limit the number of parameters to be examined in order to obtain greater clarity, and also to obtain good optimization during PCA.
As shown in Table 2
are highly correlated. In the following only
is retained because it is the most present in the literature. We also find that
is highly correlated with
. This is consistent with previous results from the literature [1
]. The two parameters
are, however, retained because many works in the literature focus on this combination to describe fog.
are directly related to each other. In the following, we preferred to keep
because its relation with the other parameters is closer to a linear relation than for V
(see Equation (3
)). This has the advantage of giving better results in PCA. In the continuation, this parameter selection therefore gives:
Before presenting the results obtained, it is interesting to make a bibliographical review of these different parameters. The
coefficients are clearly the most represented in the literature. Figure 6
shows the data available in the state of the art. The points correspond to natural DSD data, for which the authors have given the values of the parameters mentioned. To these natural DSD point data, the most common models in the literature by Deirmendjian [40
] and Shettle [41
], are added. The data collected as part of the Paris Fog project are also added to Figure 6
shows that there is a wide dispersion of points. This may be due first of all to real variations in natural fogs. It has indeed been established in the literature that fogs can have different particle sizes, depending on the conditions under which they occur.
However, this dispersion is particularly great for the parameter. This can be explained by the fact that the oldest PSAs were not able to distinguish the smallest drops (<1 m). These drops, however, represent a very large quantity in the fogs which greatly skews the average. This limitation of the oldest PSA leads to the same problem on the parameter, the latter being underestimated.
Concerning the models in the literature, Deirmendjian’s DSDs have very high total concentrations compared to natural data. This can be explained by the fact that when designing these models, they were optimized on truncated DSD data for small drops (again due to the limitations of the first PSA). A large number of small drops was neglected when optimizing the model. When resetting the model in the MOR, the number of small diameter drops therefore exploded, because it was initially not included.
As for the Paris Fog DSDs, these are fairly well-positioned in relation to the data in the literature.
This review of the literature provides a basis for comparison of natural and modelled fogs. These comparison points can then be used to validate the fogs produced within the platform. This is the subject of the following sections.
4.2. Descriptive Analysis
All of the DSDs in the database collected have been processed. Four coefficients were calculated for each DSD and are shown in Figure 7
. Figure 7
represents one parameter as a function of another, for all DSDs in the database. In this figure, colored crosses (resp. triangle) represent the data for the MD fog (resp. SD) produced within the platform. A colour scale was added according to the MOR measured by the reference sensor of the platform (completely independent of the PSA). The data represents fog DSDs with MOR values between 10 and 1000 m. In Figure 7
, data from the literature (presented in the previous section) was also added, as a counterbalance. In this representation, the literature data were placed into three groups: radiation (black triangle) or advection (black crosses), where the papers mentioned the type of fog measured, and undefined in the case where the source article does not specify which type of fog it is (black circle). Figure 7
b,e,g show the zoom of Figure 7
provides an initial descriptive analysis of the data. We refer to Figure 9 for the quantitative FCC values. Concerning the qualitative classification, as it is shown in Figure 7
, first of all the two types of fog produced in the platform (crosses vs. triangles) are visibly different, especially for the coefficients
e,f). Secondly, the
coefficients are logically highly correlated with each other (Figure 7
a), but also with the reference MOR value (see the colour gradient). The two types of fogs appear to be more different for high MORs (>500 m) than for low MORs. For example, in Figure 7
e, the mean diameters are very different for light fog (high MOR, low
) and gradually come closer together for dense fog (low MOR, high
): the two groups of dark blue symbols at the lower left of Figure 7
e are clearly distinct (one group with
m] and the second group in
m]), while the orange and red symbols are close together (some crosses are mixed with triangles). This can be explained by the fact that the less dense fogs are only obtained by dissipation of initially denser fog. The regulated production of fog (by nozzles) is possible for MORs up to 200 m maximum. The production must then be totally stopped to obtain fogs for MORs greater than 200 m. The phenomenon of natural dissipation and sedimentation then visibly tends to reduce the largest drops first, as the average diameter decreases as the MOR increases. However, this variation seems much slower for the MD fog than for the SD fog on the platform. This is confirmed by Figure 7
f where it can be seen that the total number of droplets (
) varies much more slowly for MD fogs. The two types of fog produced within the platform, therefore, become more and more similar as the MOR decreases, especially under 200 m. However, this is very consistent with natural fogs, where the same trend is observed (Figure 6
The overall shape of the point clouds obtained in Figure 7
d,f corresponds to what can be found in similar figures in the literature [33
]. It can also be seen that some fog in the bibliography (natural or model) is well-positioned in relation to the fog produced within the platform. It should be noted that the fogs in the literature are covering a very high MOR range (between 100 and 1000 m) compared to the range of fogs measured within the platform (between 10 and 1000 m). There is therefore no data from the literature for the MOR range between 10 m and 100 m (color of the color-bar between green and red). For example LWC can rise above 0.4 g m
, which is not common in literature. However, in the literature, the natural fogs measured are not as dense as the platform fogs. For this reason, Figure 7
b, e.g., zoom in on the areas for which natural fog data from the literature exists. This means that the fogs produced in the platform with visibility between 10 and 100 m cannot be compared to natural fogs, since there are no such data in the literature to our knowledge. Considering the purpose of the platform, that is the evaluation of the performances of vehicle sensors in the most severe conditions, and due to its limited length of 30 m, it is even useful to produce these very dense fog conditions (MOR between 10 and 100 m). Moreover, natural advection fogs have a larger diameter than natural radiation fogs which is perfectly normal, the various references in the literature are therefore consistent. On the other hand, it can be seen that the
of the fogs in the literature is much larger than that of the platform. This can always be explained by the limitation of the oldest PSAs but also by the limitation of our PSA which is limited to 17
m. In addition, the concentrations (
) obtained in the platform are very high compared to those of fogs in the literature. Indeed, it is rare to see fogs with concentrations above 1000 cm
. This is more consistent with data from clouds, and is also related to the fact that the droplets produced in the platform are very small, which would correspond more to radiation fogs, or even haze-like fogs from areas with polluted air. This results is consistent with LWC values obtained, because
is typical for clouds. It suggests that we should work to generate larger droplet sizes in the fogs produced within the platform.
Concerning the models, fog is simulated for MORs between 1000 m and 50 m. Shettle models behave fairly well, with radiation fog having a lower
than advection fog. Both types of fog integrate well with the fogs in the literature. It can be seen that platform fog would assimilate very well with the two models proposed by Shettle for the
parameters. The only limitation is that the
of the fog produced in the platform is smaller than for that of Shettle. In Figure 7
, the Deirmendjian Haze models are not visible because they contain far too many drops, which did not seem valid. The reason for this overestimation was explained in the previous section.
Paris Fog data are interesting in that they are natural data, but also data acquired with the same PSA as those of the platform (PALAS WELAS 2100). These data integrate perfectly with the platform’s data from a global point of view. However, it can be seen that they still have DSDs with a a little larger than that of the platform. Following this observation, we will have to work on the development of the platform in order to be able to produce larger droplets.
As a conclusion to this descriptive analysis, the platform proposes fogs that are quite representative of natural fogs and the literature. On the other hand, the proposed DSD range could be extended, especially with fogs with a higher . Technical solutions are available and are already being considered to meet this new objective.
4.3. Statistical Analysis
The descriptive analysis made it possible to position artificial fogs in relation to natural fogs. However, it is complicated to really classify the two types of fogs, as they are more or less classified according to the parameters analyzed. For example, the parameter pair vs. seems to allow a better classification of fog types than the pairs vs. and vs. . Furthermore, it is difficult to measure how good the classification is. Ultimately, the underlying objective of this study was to clarify which parameters allow better characterization of DSD. As the parameters used are varied, and the literature never uses the same ones, the large database we have at our disposal can help clarify this. In order to answer these problems, a PCA was performed on all the parameters. This allows us to find statistically the best combination of parameters to disperse the available data. In addition, the PCA provides details of the parameter combinations, which makes it possible to know the best parameters for classification of the DSDs. The PCA will, therefore, make reading simpler.
presents the results obtained by the PCA. The first PCA vector is a combination of the four parameters, starting with
. As shown in Figure 8
, the first vector is directly related to the MOR. The second vector is rather related to
is opposed, with very little impact from the other parameters (
). The latter is therefore directly related to the type of fog produced. Indeed for a given MOR, the smaller the drops are, the greater their total number, hence the opposition between
. It is therefore the second vector that best differentiates the two types of fogs produced in the platform for a given MOR.
shows the projected data set for the first two PCA vectors. The dispersion of the data is then visually much clearer. In Figure 8
, the literature models and the Paris Fog data are also projected onto the two PCA vectors. The models are then found at the edge of the data from the platform. On the other hand, the fogs collected in the Paris Fog campaign are perfectly included in the point cloud linked to the platform. This is a major result which shows that the platform fogs are well representative of natural fogs. Although data dispersion is better, a metric should be used to compare the different pairs of parameters proposed quantitatively. The method proposed in Section 3.2
was therefore applied to the database. The method is applied in two cases:
Overall, on all the data.
By sorting the data by MOR packet (this presupposes having the external reference MOR data, given here by the transmissometer).
shows the FCC for each of the two parameters. The pair formed by the first two vectors from the PCA is the one that makes it possible to better classify the data globally, with a differentiation score of
pair is, however, quite close to the PCA result, with a score of
. The other parameters are much less relevant for classifying fogs. This result is very interesting and proposes a new vision, since in the literature the parameters most used to distinguish fogs are often
The overall score allows the parameters to be compared with each other. However, the first descriptive analysis has shown that the DSD coefficients move away from each other when the MOR increases, although this does not mean that the fog would not be differentiated. To verify this, it is possible to go further by applying the method of calculating the FCC on sub-groups of data by classifying them into MOR groups (the reference MOR given by the transmissometer). Figure 9
shows the FCC as a function of MOR. From the figure, it is clear that the
pair is not a good combination for classifying fogs by particle size. The other combinations of parameters all obtain FCCs higher than
for fogs with a MOR higher than 40 m. However, FCCs are worse for fogs of less than 30 m. In the same way, it is generally observed for all parameters that the densest fogs are also the most difficult to differentiate. The best pairs for classifying the fogs for all MORs are the first two PCA vectors and the
pair. By spreading out the densest fogs, with MORs below 40 m, the best couples to differentiate the fogs are
. Finally, the
parameter seems to be the most decisive in the differentiation of fogs, at a fixed MOR. This can be justified, because at a fixed MOR,
depends directly on the size of the droplets, with a third-order factor in relation to the diameter. As the MOR is related to the product of the volume of the drops by their number,
is highly dependent on the particle size at a fixed MOR. In the case of an analysis of the DSD given the MOR (by a sensor different from the PSA), the PCA did not improve the differentiation of the fog compared to the best combination of coefficients. This analysis grouped by MORs must be supplemented by a global analysis, without the contribution of MORs from an external sensor.
This section has therefore shown that PCA can be of interest in the classification of fogs. In addition, it has shown that the parameter pair vs. is the most relevant for classifying fogs of the platform through the use of FCC.
The first objective of this study was to show that the platform has two types of fogs with clearly distinct DSDs. To achieve this, we proposed an innovative method, based on the use of a PCA and the FCC. This method is not restricted to a descriptive analysis but also offers a quantitative analysis. It was used on the conventional coefficients characterising DSD in the literature, namely , , , , , and .
In order to compare the platform fogs to natural fogs, several data sources were proposed. A detailed literature review identified macroscopic data (coefficients) from several hundred DSDs of natural fogs, with data acquisition by different PSAs. In addition, the use of data from the Paris Fog campaign made it possible to compare the platform fogs with natural fogs, whose DSD was measured with the same PSA. The use of the most common fog models in the literature provided a third source of comparison. Given the PSA used and the natural data available to us, this study focused on radiation fogs only.
Many results have been achieved. First of all, the two kinds of fog on the platform are clearly different. Using the most relevant coefficients, the FCC obtained is overall, rising above taking into account the MOR, for MOR fogs above 40 m. In practical terms, this means that we are able to identify which of the two types of fog is reproduced within the platform in of the cases, using only the DSD and the MOR, without any other data. This result, therefore, means that we can confirm that a quantified difference exists between the two types of fog proposed within the platform. Moreover, it appears that the greater the MOR, the more the fogs are identifiable, which may provide development leads to change the DSD of the fogs proposed.
The second result concerns the comparison of the fogs reproduced within the platform with natural fogs: the analysis carried out shows that both types of fogs produced within the platform are included in the range of natural radiation fogs. The fogs proposed are therefore representative of fogs that may exist in nature, both from a macroscopic point of view in terms of MOR, but above all from a microscopic point of view in terms of DSD. In particular, Adverse Weather platform fogs with the smallest drops are at the limit of natural radiation fog or haze-like fog. However, there are examples in the literature of fogs containing much larger droplets and both fogs produced within the platform have quite small droplets, more similar to wet aerosol, and high concentration (closer to polluted fogs or even clouds). Putting aside the fact that older measurements may be skewed due to the use of PSAs that could not measure the smallest droplets and that our sensor cannot measure the largest droplet, it would, therefore, be worthwhile to develop the platform to find means of producing new fogs with larger droplets. This would suggest extending the range of fogs produced within the platform.
At the same time, this study made possible a quantified analysis of the most representative coefficients in the literature according to their ability to differentiate fogs by their DSD. Since PSAs all have very different characteristics, it is very difficult to compare DSDs from two different devices. By using global coefficients, such as , , , etc., it becomes possible to better compare the fogs according to their DSD. Our study shows that the vs. coefficient pair is the best one to classify the fogs produced in the platform. This result is still consistent with the literature; indeed the most highlighted coefficients are the vs. pair, often highlighted for its strong correlation. It would now be very relevant to test this method on a natural fog database.
To conclude, the platform allows systems and sensors to be tested in a large volume of fog (30 m long × 5 m wide × 2.2 m height) in fog and rain conditions. The advantage over competitive facilities of similar dimensions is that it benefits from weather conditions that are finely measured and comparable to certain natural conditions as shown in this study (two clearly different fogs that are representative of a part of natural fogs). On the other hand, The Adverse Weather platform is smaller than others proving grounds that allow vehicle tests in high-speed dynamics. Compared to chambers dedicated to the most accurate reproduction of fog conditions (taking into account thermodynamic phenomena and aerosol composition), the platform has the advantage of being much larger, but also of obtaining faster fog variations on demand. On the other hand, it appears in this study that some ranges of fog are missing, in particular the fogs containing larger droplets (diameter > 10 m), not addressed here.
Then, work will be carried out in order to produce new fogs with DSDs containing larger droplets. The method presented here is entirely reusable for any type of DSD but also for any type of coefficient estimated from the DSD. It can therefore be reapplied: (1) to a set of DSDs from various natural and artificial fogs so as not to be limited to the artificial fogs presented here. In particular, the FCC method would make it possible to check whether fogs can really be differentiated according to the place of occurrence (maritime or continental), the pollution conditions, the climate and the geographical region, or even other artificial or numerical fog simulation platforms; (2) to different parameters, such as extinction coefficients at different wavelengths, or parameters obtained by model optimization on DSDs; (3) to a set of DSDs measured from various PSAs on the same fog. This will be the subject of future work.