Artificial Intelligence-Based Methods and Algorithms in Fog and Atmospheric Low-Visibility Forecasting

Abstract

The accurate prediction of atmospheric low-visibility events due to fog, haze or atmospheric pollution is an extremely important problem, with major consequences for transportation systems, and with alternative applications in agriculture, forest ecology and ecosystems management. In this paper, we provide a comprehensive literature review and analysis of AI-based methods applied to fog and low-visibility events forecasting. We also discuss the main general issues which arise when dealing with AI-based techniques in this kind of problem, open research questions, novel AI approaches and data sources which can be exploited. Finally, the most important new AI-based methodologies which can improve atmospheric visibility forecasting are also revised, including computational experiments on the application of ordinal classification approaches to a problem of low-visibility events prediction in two Spanish airports from METAR data.

1. Introduction

Fog events have important impacts on different natural and human systems [1,2,3]. In some cases, fog can provide valuable water resources of fresh water for arid zones [4,5], or it can be exploited in agriculture [6,7] and ecosystem management [8]. Fog may affect other human systems, such as telecommunications [9] or solar energy exploitation [10] for instance, and fog-related low-visibility events may deeply affect transportation systems [11]. In this sense, low-visibility conditions due to dense fog, mist, haze, or their combination provide highly unsafe scenarios on roads [12,13], presenting numerous challenges to drivers and increasing the risk for passengers and pedestrians [14], including strong visual effects, and decreasing the ability to see through the air [15,16]. Fog-related low-visibility events can also affect deeply to airports and related facilities [17,18].

The accurate prediction of fog events, and their associated low-visibility and extreme low-visibility episodes [19], is therefore a very important problem, with major consequences for road and aviation safety (and therefore with important economic impacts), and other applications in agriculture and ecosystems. It is, therefore, a topic in line with the Sustainable Development Goals-UN 2030 agenda, in which remote sensing plays a fundamental role [20]. Different computational methods have been applied to fog and low-visibility forecasts. Numerical weather prediction (NWP) systems have often been applied for low-visibility events forecasting. The mesoscale characteristics of many fog events have led to the use of high-resolution NWP models to improve the accuracy in the forecast of fog events [1,21,22,23,24]. However, the local physics mechanisms of fog formation [25,26,27] are difficult to model with mesoscale NWP, and thus, in recent years, there has been a major interest in advanced statistical and artificial intelligence-based (AI) approaches [28], able to process different types of measured and simulated meteorological variables, and time-series data. In particular, the application of AI-based approaches has been massive in recent years, including data-driven methods, machine learning (ML), deep learning (DL) and hybrid algorithms [29,30].

In this paper, we provide a comprehensive literature review and analysis of AI-based methods applied to fog and low-visibility events forecasting. We also discuss the main issues found, open questions, novel AI approaches and data sources which can be exploited to improve future forecasting systems based on AI algorithms. Finally, we will show some computational experiments on the application of novel AI-based methods, ordinal classification approaches in this case, for fog events prediction at two airports in Northern Spain.

The rest of the paper has been structured in the following way: Section 2 provides a detailed literature review, with analysis of the AI-based methodology used, and the results obtained in each case. Section 3 discusses the most important characteristics of the published works on AI-based atmospheric visibility prediction, and it also includes the most important challenges and open questions for working with AI-methods on these problems. Some of these challenges and open problems discussed here are imbalanced data, data quality and measurements, and new methodological approaches. Section 4 shows the performance of different ordinal classification algorithms in the prediction of low-visibility events at two Spanish airports from reanalysis and METAR data. Finally, Section 5 closes the paper with some conclusions and future remarks on this research work.

2. Literature Review

Dealing with a good literature review on a hot topic such as ML/DL for fog or low-visibility event prediction is not an easy task. There are several possibilities to structure the review, which may highlight different aspects of the previous works, such as the type of algorithm involved, or the fog characteristics, etc. Instead, we think that a temporal perspective may help understand the evolution of the topic, from the first works published in the mid 1990s to the boom of AI approaches in the last 5 years.

Maybe the first serious attempt to apply ML to a problem of fog prediction was carried out in [31], where a model output statistics (MOS) scheme, using a stepwise-selection multiple linear regression approach was proposed. The approach was focused on the estimation of daily fog probability in data from the North Pacific Ocean summer season. Also, one of the first attempts to apply more advanced ML algorithms to fog prediction, again to marine fog, was [32], where a classification tree approach (C4.5) was tested over different data including weather ship observations and also buoy measurements taken off the coast of California. The C4.5 classification tree obtained different rules for the occurrence and no-occurrence of marine fog in both testing datasets considered.

In [33], artificial neural networks (ANNs) were used to provide accurate forecasts at Canberra International Airport employing a 44-year database of standard meteorological observations. Predictions were made with a time horizon of 3, 6, 12 and 18 h. This is one of the first AI-based models focused on predicting fog and visibility conditions at airports. In [34], neural networks were applied to problems of ceiling and visibility condition prediction at different aerodromes in the Northwest United States. Specifically, a total of 39 such neural networks were developed for each of 39 terminal aerodrome forecast stations. The results obtained were compared to alternative algorithms, including logistic regression and MOS, showing superiority in most cases.

In [35], a fuzzy logic fog forecasting model based on outputs from a high-resolution operational NWP model was proposed. In this case, the fuzzy logic was employed to deal with the inaccuracy of NWP prediction and uncertainties associated with relationships between fog predictors and fog occurrence. In [36], good results were obtained with a multi-layer perceptron with a back-propagation learning technique in the forecasting of 3 h visibility intervals during winter at Kolkata airport (India). The work in [37] also used a very similar artificial neural network to predict the occurrence of fog events at the Academia da Força Aérea (Brasil). Bayesian decision networks were applied in [38] in a real problem of low-visibility conditions at Melbourne airport. In [39], ML-based decision-tree algorithms were applied to nowcasting fog events in the coastal desert area of Dubai, AUE. The ML approach was tested in a problem of fog prediction with up to six hours of prediction time-horizon, and its performance was compared against the coupled Weather Research and Forecasting (WRF) model and the PAFOG fog numerical model. In [40], different ML regression approaches were tested in a problem of low-visibility event prediction due to radiation fog at Valladolid airport, Spain. ML models such as support vector machines or extreme learning machines were the best performing algorithms in this problem of fog prediction. In [41] discussed for the first time the application of DL approaches to problems of fog events prediction. Specifically, deep neural networks were tested in a problem of regression associated with visibility due to fog in Urumqi International Airport, the hub of the Xinjiang region, China. In [42], a visibility prediction problem due to fog in airports of Northern Morocco was carried out. In this case, the outputs of the operational NWP model AROME served as inputs for different ML regression algorithms, such as gradient boosting and deep neural networks, obtaining good results in the prediction of low-visibility events in the zone. In [43], a multi-objective evolutionary neural network was applied to the same problem, obtaining improvements over alternative ML algorithms. In [44], a hybrid prediction model for daily low-visibility events at Valladolid Airport was proposed, which combines fixed-size and dynamic windows and adapts its size according to the dynamics of the time series, using ordinal classifiers as the prediction model. In [45], a deep hybrid convolutional neural network (DHCNN) was applied to a problem of visibility range prediction from camera images, in situations of strong foggy weather conditions. In [46], a nowcast prediction problem of low-visibility states due to fog was tackled, based on tree-based statistical models and using highly-resolved meteorological observations at Vienna International Airport. The forecasting prediction time horizon was set to a maximum of 1 h, and input variables such as the current visibility state, ceiling, and horizontal visibility were considered to implement the system. In [47], a problem of low-visibility classification with ML models was tackled. In this case, the problem was modeled as a multi-class classification task, where five classifiers were developed and successfully tested over visibility data in Florida, USA. In [48], a hybrid approach formed by a numerical weather model and ML regressors based on gradient boosting (XGBoost and LightGBM) was proposed for a problem of visibility prediction and successfully tested in meteorological observation stations in the Beijing–Tianjin–Hebei region (China), with data from 2002 to 2018.

From 2020 to nowadays, the applications of ML and DL models to problems of fog and visibility prediction have been massive. In [49], different ML models (tree-based ensemble, feed-forward neural networks and generalized linear methods) were applied in a problem of horizontal visibility prediction, using hourly observed data at 36 synoptic land stations over the northern part of Morocco. In [50], an Auto Regressive Recurrent Neural Network was considered for a problem of low-visibility prediction at airports. A comparison with an alternative recurrent neural network was carried out. In [51], a problem of low-visibility prediction with ML/DL algorithms at Wamena airport, Indonesia, was considered. Specifically, the problem was encoded as a binary prediction problem from meteorological variables up to 6 h in advance. Five ML algorithms, distributed random forest, deep neural networks, gradient boosting, Generalized Linear Model, and Extreme Randomized Tree, were considered. In [52], an analysis of the persistence in low-visibility time series due to radiation fog at Valladolid airport was considered. The work includes a binary prediction of fog event occurrence with different ML approaches. There are other works which deal with the persistence of fog events, and their analysis for improving fog prediction, such as [53] or [54], with results at the Prakash Narayan International Airport in Patna, India. In [55], a problem of short-term fog event prediction at Anhui region, China, was considered. The application of long short-term memory (LSTM) deep networks is considered, based on meteorological inputs. A comparison with alternative ML and DL algorithms was carried out.

In [56], a statistical analysis of the time series data from orographic fog at Mondoñedo, Lugo, Northern Spain, was carried out, with the objective of improving the prediction of extreme fog events at the area. In [57], a problem of visibility prediction over South Korea was tackled, by using a random forest (RF) model based on ground observations and air pollutant data from the ECMWF model. A comparison with a numerical model from Korea Meteorological Administration showed a better performance of the ML-based approach. In [58], a problem of fog detection at Korea Peninsula was tackled, based on an ML-based logistic regression model (LRM), at three time points throughout the day (daytime, nighttime, and dawn/dusk). Detection results between 83% and 94% of accuracy were reported in that study with the LRM method. In [59], a hybrid DL/ML approach to estimate visibility range under foggy weather conditions was proposed. Specifically, a deep convolutional neural network (DCNN) trained with raw image data is considered for feature extraction, and a support vector machine (SVM) is then applied to obtain the visibility range estimation. In [60], a fog prediction problem in the Istanbul strait was tackled, by means of ML methods. The visibility in the strait was estimated with different ML techniques, with the gradient boosting as the most accurate method, based on input characteristics such as wind speed/direction, humidity, pressure and time indicators. In [61], a fusion of ML models was proposed over multi-source data, for a problem of visibility prediction in Eastern China. Extreme gradient boosting techniques were applied as regression methods in this case. In [62], a scSE-LinkNet model for daytime sea fog detection was proposed. The approach leverages residual blocks to encoder feature maps and an attention module to learn the features of sea fog data by considering spectral and spatial information of nodes. Satellite radar data from Cloud-Aerosol Lidar with Orthogonal Polarization were used as input variables.

In [63], a fog forecast system at Poprad-Tatry Airport using ML algorithms (support vector machines, decision trees and k-nearest neighbors) was proposed. The forecast models make use of information on visibility obtained through remote camera observations in this case. In [64], shallow ML classification and regression algorithms were used to forecast the orographic fog in the A-8 motor road. In [65], ML techniques are applied to classify low-visibility events in Chengdu, China. Very recently, alternative approaches based on tree-based ML algorithms have been discussed in [66]. In [67], the relationship between airport visibility and meteorological elements at different potential heights were investigated. Specifically, the hourly visibility of different Chinese airports is predicted by applying nine AI-based algorithm models, including, among others, Bayesian Ridge Regression, LASSO or Elastic-Net Regression algorithms. In [68], ML approaches have been proposed to estimate visibility in Seoul, one of the most polluted cities in Asia. Input data considered were meteorological variables (temperature, relative humidity, and precipitation) and particulate matter (PM10 and PM2.5), which were acquired from an automatic weather station. Observational data were considered as target. In [69], an RF approach was applied to a problem of visibility estimation in South Korea. The model was trained for the whole Korean Peninsula, with visibility inputs and meteorological and air pollution variables. In [70], linear regression and RF algorithms were successfully applied to a problem of fog prediction, using data from FM-120 instruments, which continuously measured liquid water content in the air in the Monterey area, California (USA). In [71], an analysis of the fog generation characteristics at different sites of the Korea Meteorological Administration in Sejong and Busan was carried out. Additionally, three ML-based models, including RF and deep neural networks, were tested for estimating visibility using meteorological input variables. In [72], nine ML approaches were tested for a problem of low-visibility event prediction at 47 international airports in China, in the period 2010–2020. Input variables from the National Meteorological Data Science Center of China are used in the study. The work showed that the random forest-based approaches were the techniques which performed the best in this prediction problem. In [65], six different ML approaches were tested in a problem of atmospheric visibility prediction, from ground observation target data at Chengdu, China. As input data, ERA5 reanalysis from the ECMWF was considered. A Principal Component Analysis was applied to the data as a pre-processing step. The results obtained showed that neural networks obtained the best results among all ML methods tested in this particular problem. In [73], a multi-modal learning approach based on DL methods to improve the forecasting accuracy of sea fog was proposed. Specifically, a convolutional neural network (CNN) and gated recurrent unit (GRU) models were tested over images from closed-circuit television (CCTV) and multivariate time series data, respectively, taken at Daesan Port (South Korea) with good results in predicting sea fog events. In [74], a problem of visibility classification in airports was tackled by means of data-driven DL approaches and multiple nonlinear regression analysis. The runway visual range (RVR) was selected as objective, and surface meteorological variables were included into DL techniques (CNNs models) to obtain a prediction. In [75], three statistical and ML models based on discriminant analysis, logistic regression analysis, and SVMs were considered in a problem of radiation fog prediction in Japan. Input variables such as temperature, humidity, wind speed, precipitation, sunshine, and visibility data were considered, and feature selection for the problem was carried out by using the Akaike information criterion (AIC).

In [76], three DL techniques (CNN, Unet and ConvLSTM) were applied to a problem of fog and low stratus prediction (short-term, night-time) forecasting in Morocco. The results were compared to that of hourly observations from Meteorological Aviation Routine Weather Reports (METARs) at different Moroccan airports. In [77], different ML methods (SVM, k-nearest neighbors, and RF, as well as several DL methods) were tested in a visibility forecasting problem in China. The input data considered were the main factors related to visibility, such as wind speed, wind direction, temperature and humidity, among others. In [78], different ML methods were applied to solve a problem of atmospheric visibility in five topographical regions: hills, basins, plains, alluvial plains, and rift valleys of Taiwan. Four air pollution factors and five meteorological variables were selected as independent inputs. Support vector machines, multilayer perceptron model, and an extreme gradient boosting model were applied to solve the low-visibility prediction problem. In [79], a problem of low-visibility prediction for Jay Prakash Narayan International Airport, Patna, India, was tackled using a historical synoptic dataset and ML approaches with boosting, bagging and stacking versions. A related work [80] by the same authors further discussed the application of a hybrid CNN-LSTM algorithm for visibility prediction at Patna Airport. In [77], different ML (SVM) and DL (LSTM, recurrent neural networks and GRUs) techniques were applied to a problem of low-visibility event forecasting due to haze in China. In [81], a discussion on the application of DL models to low-visibility event prediction was carried out, with tests at different locations in Florida. In [82], a further study of DL ensembles for low-visibility events due to fog prediction were carried out, with experimental evaluation on orographic fog events at Northern Spain. In [83], a prediction problem focused on extreme low-visibility events was tackled, based on inductive and evolutionary-based decision rules, in which the explicability of prediction is the main conducting thread. In [84], a recursive neural network (RNN) was applied to a problem of hourly atmospheric visibility prediction in central and eastern China, with a prediction time-horizon of 12 h. A comparison with other DL approaches based on CNNs was also carried out. In [85], an ensemble learning approach was developed to tackle a short-term prediction model of low-visibility on freeways using meteorological data. RF and XGBoost were employed to obtain the visibility prediction models, and back-propagation neural network and logistic regression were used for comparison and evaluation purposes. Experiments with data from Guanyinyan service area, on the G50S freeway in Chongqing, China, showed the goodness of this approach. In [86], an ensemble approach formed by the merge of two base learners (XGBoost and LightGBM) was proposed in a problem of atmospheric visibility prediction in different Chinese cities due to pollution. A study on feature importance and feature selection was also applied to optimize the prediction accuracy in different seasons with different pollution sources. In [87], two techniques based on ML and DL methods (RF and LSTM) were applied to estimate visibility in Sofia airport (Bulgaria) using 11 meteorological input parameters.

In [30], a review on the application of different deep learning models (convolutional neural networks (CNNs), recurrent neural networks (RNNs), Generative Adversarial Networks (GANs), and Transformer networks) in visibility estimation, prediction, and enhancement was proposed. This review was not only focused on atmospheric low-visibility events due to fog, but it had a broader scope, including analysis of visibility in images and image quality with DL techniques. In [88], an ML-based prediction model for atmospheric visibility in China using multiple independent variables was recently proposed. XGBoost and RF models have been used to predict the visibility in different regions of the country, in the majority of cases affected by high levels of pollution and smog, and to evaluate the extent to which the visibility changes can be explained by individual factors. In [89], a system called FogFusionNet is proposed as a multi-modal sea fog prediction model, which uses CCTV images and multivariate time series observation data to predict marine fog and visibility in a given zone. The system is focused on classification problems tackled with a deep LSTM network, where three visibility classes are defined—normal visibility, low-visibility, and sea fog—at different prediction time horizons from 1h to 6 h. In [90], different ML methods were applied to evaluate marine fog visibility conditions and nowcasting of visibility based on the data from fog and turbulence interactions in the marine atmosphere campaign observations, collected in Northeast territories of Canada. Support vector regression algorithms, least-squares gradient boosting and DL techniques have been applied to this specific problem. In [91], three ML models (RF, XGBoost and categorical boosting) were tested in a problem of low-visibility event prediction associated with sea fog in Beibu Gulf (China). The XGBoost approach demonstrated the best performance among all of them, obtaining an extremely good match between predictions and observations of visibility in the considered location of study. In [92], an advanced approach for the ocean fog prediction model at the Yellow sea region based on ML techniques is proposed. The system leverages satellite measurements and high-performance data-driven methods. Specifically, satellite data related to ocean fog are used, and ML algorithms are integrated with NWP outputs and sea surface temperature (SST)-related variables to obtain a high-performance fog prediction system. In [93], a modified XGBoost algorithm has been applied to the prediction of radiation fog at Linden-Leihgestern, Germany. The modifications of XGBoost include a pre-processing of temporal data into the model training, and also to consider a weighted moving-average filter in the algorithm. These modifications were reported to improve the performance of XGBoost algorithms in fog prediction. In [94], a gradient boosted trees ML model was applied to a problem of fog detection and low stratus at different locations across Europe. The algorithm was trained with ground truth observations from METAR stations and the SEVIRI observations from satellites. In [95], a CNN-type algorithm was applied to a problem of detecting fog top over eastern Taiwan mountains. The training data consisted of the three visible bands observed at 8 a.m. local time from the Himawari-8 satellite between the years 2019 and 2021, with the fog edges (in the case of fog occurrence) serving as the training labels. In [96], a spatiotemporal self-attention-based U-Net approach with a multi-task learning module was introduced. That approach was applied to a case study of low-visibility prediction on the Korean Peninsula, using data from 155 automatic weather stations all over the country. In [97], a fog monitoring algorithm based on the lightweight DL model ABNet was proposed. The system works by processing different images, to finally fully extract fog concentration and high-frequency information, obtaining a final high-performance classification model, which showed excellent prediction accuracy. This system has been tested on real images from Guizhou region highways (China). In [98], another study with data from Guizhou region was presented, where three DL Unet-based visibility forecasting models were proposed, based on different inputs and meteorological variables. In [99], a problem of low-visibility event prediction at King Khalid airport in Riyadh, Saudi Arabia, due to air pollution and particles was conducted. The problem was codified as a binary classification task, and two ML classifiers (RF and K-nearest neighbors (KNN)) were evaluated. Different models based on feature selection methods were also discussed. In [100], a Graph Convolutional Network (GCN) and GRU was proposed for a problem of short-term visibility prediction in Jiangsu province, China. The system was trained with meteorological input variables collected in 2017 and 2018 in 10 measurement stations in the zone. In [101], different ML models such as RF, adaptive boosting, gradient boosting, XGBoost, LightGBM, and categorical boosting were evaluated in a problem of visibility prediction at Bangkok airport during the dry season (November–April), considering different air pollutants, meteorological variables, and time-related variables as inputs. This work also introduces a study on explicability of the ML outputs by means of the Shapley Additive exPlanation (SHAP) method. In [102], a hybrid ML-based algorithm for a problem of low-visibility prediction was proposed. The approach combined a back-propagation neural network and a LightGBM classifier to obtain a robust prediction system for low-visibility events. Results of the prediction system at Montgomery, USA, were reported. In [103], a problem of low-visibility event simulation due to haze impacts was tackled. Decision trees and RF algorithms were tested, using atmospheric boundary layer meteorological data, pollutant concentrations, and ground observations. A case study with data from Donghai, Jiangsu province, China, was discussed. In [104], a visibility prediction algorithm based on CNNs and GCNs was proposed. The algorithm works based on different inputs such as ERA5 reanalysis data and ground observations. The proposed DL-based prediction model was trained with multi-site data, so it was able to learn spatiotemporal visibility patterns across various sites, improving the prediction capability in all of them.

3. Discussion, Analysis and Challenges

3.1. Discussion and Analysis

The evolution of the publications related to fog and low-visibility events, including their detection, prediction and analysis, can be better appreciated by observing Figure 1. It shows the number of published papers versus publication year, for works on ML/DL algorithms in fog and low-visibility-related problems. As can be seen, the topic started to receive some attention from the scientific community in 2015, with a boom from 2020 onward, when the number of applications and algorithmic proposals were increasing every year. Studies before 2015 are scarce, and they mainly apply ML techniques to specific low-visibility events, mainly in airports. The graph shows up to the year 2024.

In recent years, the number of works dealing with DL techniques has been much larger than those applying ML algorithms, which seems to highlight a change in the type of AI algorithms applied, in consonance with the trend in AI field.

Regarding the analyzed publications, we have detected an important variety in the input data used, from direct measurements, to satellite data, airport data (METAR), camera images and inputs from numerical models such as ERA5 models. On the other hand, a large variety of ML/DL algorithms have been applied, including different types of shallow and deep neural networks, RF, logistic regression, tree-based algorithms, SVMs, XGBoost, CNNs, LSTMs, etc. Figure 2 shows an histogram of the most applied algorithms in problems of atmospheric low-visibility and fog forecasting in the literature, during the analyzed period. As can be seen, the tree-based approaches (including RF) have been greatly used, due to their good performance and easy implementation. Classical ML approaches such as artificial neural networks (shallow) or support vector machines have also been successfully tested in different problems related to fog and visibility prediction in the literature. In recent years, deep neural network and gradient boosting algorithms have also been massively applied to this type of prediction problems. Other type of algorithms such as fuzzy logic-based, ordinal classification approaches, recurrent networks or LSTM approaches have been much less explored in the literature.

3.2. Challenges

3.2.1. Imbalanced Data

As other problems related to meteorology, fog and low-visibility events are in general rare events, this means that situations of very low visibility can be considered similar to extreme events, i.e., characterized by a very low frequency of occurrence. As such, if we tackle the problem as a classification task, those classes associated with low-visibility will contain, in general, much less samples than classes associated with situations of high visibility. In other words, fog and low-visibility event prediction usually lead to classification problems that are very imbalanced in terms of the number of samples among classes [105]. This is an inherent characteristic of any problem related to fog and low-visibility forecasting which must be taken into account in ML/DL approaches, usually by including specific data augmentation schemes or other data balance algorithms.

Recent studies in the literature have proposed various strategies to mitigate the strong impact of class imbalance. These strategies can be broadly categorized into three different groups: undersampling, oversampling, and hybrid methods. The first group is composed of undersampling techniques, which are designed to mitigate the predominance of majority classes by removing some of their samples. For example, in [106], a method that clusters borderline noise and outlier samples from the majority class to distinguish between ‘safe’ and ‘rare’ instances was introduced. Similarly, in [107], a method for removing majority-class samples with a high degree of overlap, thereby simplifying the problem while preserving informative data, was proposed. The second group, made by oversampling methods, prioritize the enrichment of minority classes. For instance, [108] presented LoRAS (Localized Random Affine Shadowsampling), which addresses the over-generalization issues of classical approaches such as the Synthetic Minority Over-sampling TEchnique (SMOTE) [109] by providing a more accurate estimate of the local mean in minority-class regions. Likewise, in [110], a scalable SMOTE variant for large datasets, replacing the costly k-nearest neighbors search with computations of the mode, minimum, and maximum values to generate synthetic samples was developed. Finally, the third category groups hybrid approaches, which combine undersampling and oversampling to balance classes while reducing the risk of overfitting. For instance, [111] integrated Tomek links [112] with Borderline SMOTE [113] to achieve well-structured balancing, and in [114], a two-step method was proposed: first by discarding majority-class samples far from the SVM decision boundary, and secondly by applying safe-level SMOTE [115] if imbalance persists.

3.2.2. Data and Quality of Observations

One of the most important challenges when dealing with fog and low-visibility event prediction is the lack of data and good-quality observations related to fog. Since fog is a local or mesoscale meteorological event, though conditioned by the synoptic conditions, it requires global numerical models and reanalysis. METAR data from airports are a good option in some cases [116], but they do not cover large parts of the territory. Observation campaigns [117,118,119] are then the only way of obtaining good-quality data, completely covering specific zones. However, there is a lack of public databases for research with good-quality observations and data to help develop better prediction algorithms for fog and low-visibility events. Within these conditions, it seems reasonable to bet for a fusion of information sources when applying ML/DL techniques to fog and low-visibility forecasts.

Fog phenomena are strongly dependent on local conditions and factors, such as terrain form, orography and topography, altitude, close location of water reservoirs, etc. In fact, local characteristics of fog depend much on the complexity of the terrain, as recognized in different recent works [120]. Also, some local physical processes such as turbulence, radiation, land-surface coupling, and microphysics are key for obtaining an accurate prediction of some low-visibility events associated with radiation fog [22]. An important challenge in the forecasting of fog and low-visibility events with ML/DL algorithms is to include these local conditions and phenomena in the algorithms, as physically-informed ML/DL approaches. However, the development of some fog events also depends on synoptic conditions and atmospheric circulation types. This fact is well known, and there are classical works on synoptic conditions leading to different fog types and events from over a century ago [121], as well as very recent studies with a similar objective of relating synoptic conditions with fog types, such as [122], which presents a study at Incheon airport (Republic of Korea), or more recently [123], which dealt with synoptic conditions of fog in the Namib desert. Circulation types and patterns have also been studied in fog formation problems such as [124], for consecutive fog events in the United Arab Emirates. Closely related to synoptic analysis of fog events, some studies have dealt with teleconnections of fog episodes, such as [125], where the teleconnections associated with water collection from fog events on the east coast of Spain are analyzed. In spite of these previous works on synoptic conditions and teleconnections, these topics are usually not included in fog and low-visibility forecasting systems with ML/DL.

3.2.3. New Methodological Approaches

In the analyzed literature, the problems of fog and low-visibility prediction with ML/DL algorithms have been both approached as classification and regression tasks. In the case of classification, either binary or multi-class. As can be seen, alternative methodologies such as ordinal classification have been used very little in this context, except occasional works validating the approach in some specific cases [44]. However, the real value of ordinal classification (intrinsic order in the problem’s classes) has not been fully exploited in the literature, and it is one of the proposals of this work.

Multi-task learning is another novel AI paradigm, barely tested in fog and low-visibility event prediction. Only very recent works have dealt with multi-task learning to improve prediction systems for fog events [104].

Explainable AI (XAI) [126] is a promising AI line to be explored in fog and low-visibility prediction problems. Very few works have applied XAI concepts to explain the decisions taken by AI methods in problems related to fog prediction. Only very recent papers, such as [101], where the SHAP method has been applied, or [127], focused on feature selection, have tried to include some kind of explainability in ML results. This line of research is promising, since it can help understand which are the most important physical processes (data) that AI relies on to obtain robust and accurate fog or low-visibility event predictions.

4. Computational Examples

In this study, a minimal computational example is provided to demonstrate the potential of ordinal classification, alongside the interpretability of the proposed models. This interpretability enables researchers and practitioners to understand the reasoning behind each prediction. This section begins with an introduction to the field of ordinal classification. Subsequently, the datasets used are described, defining two different case studies. The ordinal approach used and the experimental design are then presented. Following this, the results of the employed model are presented and thoroughly analyzed. Finally, this section offers an in-depth interpretive analysis of the models, highlighting the significance of the variables used and illustrating the process by which the models generate predictions.

4.1. Ordinal Classification

Nominal classification (or standard classification) tries to predict a label from a vector of characteristics defining the pattern. The label to be predicted belongs to a set of possible categories, among which no specific relationship is assumed. However, there is another field, known as ordinal classification (also known as ordinal regression) that involves predicting categories within an ordinal scale [128]. Consequently, these categories can be arranged based on a natural order relationship determined by the characteristics of the real-world problem. This implies that the costs of classification errors vary based on the distance between the predicted and target classes within the ordinal scale. This differs from regression (in which the target variable is of a real and continuous type), since we have a finite set of possible values (labels), between which we cannot establish a distance. The other approach, which is equally incorrect, is to tackle these problems using a standard nominal approximation, i.e., ignoring the natural order relationship between the categories. This implies a loss of crucial information that could improve its performance and/or accelerate the learning process when incorporated into the classifier. Therefore, ordinal classification is an intermediate problem between classification and regression.

If we analyze the literature, ordinal classification problems are often addressed through a nominal approximation, i.e., ignoring the natural order between the categories analyzed. In addition, the very nature of the ordinal classification task means that standard performance metrics should be avoided and therefore, specific error measures adapted to the ordinal problem should be used. Hence, we believe it is vitally important that specific ordinal classification methods are considered for this type of problem. For example, let us imagine a problem of low-visibility prediction in an airport, where the categories can be clear, mist, fog, as in [44]. The prediction of fog events is of crucial importance, given that poor visibility can have a significant impact on aeronautical safety. In this sense, confusing fog situations with clear ones should be far more penalized than confusing them with mist ones. This is why specific error measures are used to consider the different costs.

The field of ordinal classification has experienced significant growth in recent years, in part due to the development of open-source libraries such as ORCA [129] and dlordinal [130], among others. ORCA is a MATLAB-based framework that offers an extensive number of ordinal classification techniques and performance metrics included in the experimental study of [128]. Conversely, dlordinal is a Python library that includes recent deep learning approaches for ordinal classification.

Despite its advantages, ordinal classification also presents some limitations. A significant challenge arises when the probability distributions of the observations and forecasts exhibit a substantial shift. In such cases, the predefined class thresholds may no longer correspond to meaningful separations between categories, making the assignment of instances to classes ambiguous. In addition, ordinal methods, as with most ML approaches, remain sensitive to class imbalance, which can disproportionately bias predictions toward majority classes while under-representing extreme categories. These limitations underscore the necessity of incorporating adaptive strategies for class definition and distance measurement when applying ordinal classification in real-world scenarios [131].

4.2. Data Description

To demonstrate a practical application of ordinal classification for visibility prediction, we consider a case study involving two Spanish airports in Galicia, located in the northwest of the country (Santiago de Compostela, LEST, and Vigo, LEVX). Figure 3 illustrates the location of both airports in Spain. In both cases, we consider METAR data at the airport, which provide hourly estimation of visibility in the airport. Data spans from January 2010 to December 2023, with a total 122,712 patterns. For these two case studies, we have reserved the first $75\%$ of the samples for training the models (92,034 patterns, from January 2010 to June 2019, both included), while the remaining $25\%$ of them are used for testing purposes (30,678 patterns, from July 2019 to December 2023, both included). Note that low-visibility operations (LVOs) in an airport or aerodrome refer to the specialized procedures and technologies that enable aircraft to operate safely in conditions of reduced visibility, such as fog, heavy rain, or snow. These operations are critical for maintaining the efficiency and safety of air travel in adverse weather conditions. Typically a runway visual range below 550 m, general VISibility (VIS) under 800 m or a cloud base below 200 feet will trigger LVOs.

With these figures in mind, let $\mathcal{V}$ be a measure of visibility at the airport (obtained from METAR data in this case), and four classes are considered for this prediction problem, established as follows:

• ${\mathcal{C}}_0\to \mathcal{V}\le 500$ m,
• ${\mathcal{C}}_1\to 500$ m $<\mathcal{V}\le 1000$ m,
• ${\mathcal{C}}_2\to 1000$ m $<\mathcal{V}\le 5000$ m,
• ${\mathcal{C}}_3\to 5000$ m $<\mathcal{V}<\infty$.

This ordinal categorization covers a range of visibility scenarios, from extremely low-visibility to optimal clear conditions. In fact, class ${\mathcal{C}}_0$ represents low-visibility situations, ${\mathcal{C}}_1$ indicates reduced visibility, ${\mathcal{C}}_2$ corresponds to medium visibility, and finally class ${\mathcal{C}}_3$ stands for clear conditions. Using this discretization, the distributions of patterns per class for the two case studies are shown in

Table 1. Number of training and testing patterns per class.

Case Study	Class	Training Set	Testing Set
LEST	${\mathcal{C}}_0$	1407 (1.53 %)	386 (1.26 %)
	${\mathcal{C}}_1$	939 (1.02 %)	230 (0.75 %)
	${\mathcal{C}}_2$	9588 (10.42 %)	2957 (9.64 %)
	${\mathcal{C}}_3$	80,099 (87.03 %)	27,105 (88.35 %)
LEVX	${\mathcal{C}}_0$	4506 (4.89 %)	1853 (6.04 %)
	${\mathcal{C}}_1$	1904 (2.07 %)	634 (2.07 %)
	${\mathcal{C}}_2$	8979 (9.76 %)	2128 (6.93 %)
	${\mathcal{C}}_3$	76,644 (83.28 %)	26,063 (84.96 %)

. It is important to highlight that these distributions correspond specifically to the task of predicting visibility at the next time step ($t+1$).

As can be observed, for classes ${\mathcal{C}}_0$ and ${\mathcal{C}}_1$, the number of samples is highly reduced with respect to the number of patterns in other classes, making the correct prediction of patterns belonging to these classes a real challenge.

Regarding the input variables, we consider a set of five variables, along with the observed visibility, $\mathcal{V}$ at t, which serves as an autoregressive variable.

Table 2. Predictive meteorological variables collected at the airports.

Acronym	Description	Units
D	Wind direction	Degrees
S	Wind speed	m/s
T	Temperature	Celsius
De	Dew point	Celsius
P	Pressure	hPa
$\mathcal{V}$	Visibility	m

presents this set of input variables as well as their units. The prediction time horizon is one hour, corresponding to $t+1$.

4.3. Logistic All-Threshold (LAT)

In this work, we consider one of the first approaches in ordinal classification: the ordinal logistic regression [132,133]. This methodology stands out for obtaining excellent performances across a wide range of applications, and at the same time, it offers models that are straightforward to interpret and explain, thus aligning well with the principles of XAI. This approach belongs to threshold-based methodologies [128], as it employs $Q+1$ thresholds ($\theta$) for a problem with Q classes. These thresholds must satisfy the constraint ${\theta }_0\le {\theta }_1\le \dots \le {\theta }_Q$, used to divide the real line on which patterns are projected into Q intervals, each associated with an ordinal category, such that a projected pattern between thresholds ${\theta }_{q-1}$ and ${\theta }_q$ belongs to category $C_q$. Note that ${\theta }_0=-inf$ and ${\theta }_Q=+inf$. Two variants of this method have been presented in the literature: 1) the Logistic Immediate-Threshold (LIT) approach, which uses only the adjacent thresholds ${\theta }_{q-1}$ and ${\theta }_q$ for the given class ${\mathcal{C}}_q$ to compute the class probabilities; and 2) the Logistic All-Threshold (LAT) variant, which incorporates all thresholds to capture the whole ordinal structure. In this study, we use the LAT approach to better account for the entire ordinal hierarchy as well as the significant class imbalance present in the LEST and LEVX datasets.

4.4. Experimental Settings

The LAT approach is compared against a well-known nominal classifier, the Ridge Regression classifier [134], serving as baseline approach. It has demonstrated outstanding performance across a wide range of applications [135,136], including its application to imbalanced problems [137]. Both LAT and Ridge classifiers share the same hyperparameter, the regularization strength. The cross-validation of this hyperparameter is performed using a grid search strategy over the values $\{{10}^{-3},{10}^{-2},\dots ,{10}^3\}$, following a 3-fold procedure and employing the Average Mean Absolute Error (AMAE) metric for optimization [138]. Note that all the input variables presented in Table 2 have been standardized before training the models.

To evaluate the performance of these models, a comprehensive set of six metrics is employed. These include three nominal metrics—Correct Classification Rate (CCR) [139], Minimum Sensitivity (MS) [140], and Balanced Accuracy (BA) [141]—as well as three ordinal measures—Quadratic Weighted Kappa (QWK) [142], AMAE, and Maximum Mean Absolute Error (MMAE) [143]. Specifically, QWK penalizes misclassifications proportionally to the distance between the predicted and true classes on the ordinal scale, reflecting a more accurate evaluation of classifier performance. Additionally, AMAE and MMAE address class imbalance more effectively, making them particularly suitable for this problem. AMAE represents the average of the mean absolute errors (MAEs) across classes, whereas MMAE is the maximum of the MAE across classes, i.e., it represents the error for the worst-performing class. It is important to note that both AMAE and MMAE are minimization metrics, while the remaining metrics (CCR, MS, BA, and QWK) are maximization metrics.

4.5. Results

The results obtained for both case studies are presented in

Table 3. Results achieved by LAT and Ridge in terms of six different performance metrics.

Case Study	Classifier	CCR (↑)	MS (↑)	BA (↑)	QWK (↑)	AMAE (↓)	MMAE (↓)
LEST	LAT	0.8372	0.2783	0.5696	0.6162	0.5263	0.8000
	Ridge	0.8792	0.0174	0.5647	0.5969	0.6088	1.1478
LEVX	LAT	0.8251	0.2571	0.5482	0.7327	0.5776	0.8297
	Ridge	0.8712	0.2240	0.5295	0.7174	0.6586	1.0000

. For the LEST case study, the LAT classifier demonstrates superior performance across five out of six evaluated metrics. Focusing first on the nominal performance measures, i.e., CCR, MS, and BA, the Ridge classifier achieves a higher CCR ($0.8792$) than LAT ($0.8372$). However, CCR, being a nominal metric, does not account for the ordinal structure of the classification problem, potentially overestimating performance when errors involve large distances in the ordinal scale. Furthermore, due to the extreme class imbalance in the dataset (as detailed in Table 1), CCR should be interpreted cautiously and considered alongside other metrics such as MS or BA. For instance, while Ridge achieves an impressive CCR, it performs poorly in MS ($0.0174$ compared to $0.2783$ for LAT), indicating its poor ability to accurately classify the worst-performing class. This suggests that Ridge focuses on optimizing accuracy for the majority class ($C_3$) at the expense of minority classes ($C_0$ and $C_1$). When the CCR is balanced according to the class distribution, as reflected in the BA metric, LAT ($0.5696$) outperforms Ridge ($0.5647$), demonstrating a more equitable classification performance across all classes.

Now, focusing on the ordinal metrics, i.e., QWK, AMAE, and MMAE, the LAT classifier exhibits a closer alignment with the ordinal nature of the problem. Specifically, in terms of QWK, LAT outperforms Ridge by a considerable margin ($0.6162$ vs. $0.5969$). Moreover, LAT achieves lower values for both metrics ($0.5263$ for AMAE and $0.8000$ for MMAE) compared to Ridge ($0.6088$ for AMAE and $1.1478$ for MMAE). Notably, the difference between LAT and Ridge is more pronounced for MMAE, highlighting the poor performance of Ridge on the most difficult class to be learned. These results demonstrate the robustness of LAT in addressing the complexities of ordinal classification.

For the LEVX case study, the observations are consistent with those from the LEST case study. Examining the nominal metrics, the Ridge classifier once again achieves a higher CCR, reflecting superior nominal accuracy. However, as previously discussed, CCR must be interpreted alongside other metrics that consider the main characteristics and issues of this imbalanced ordinal problem. While Ridge demonstrates an improvement in MS ($0.2240$) compared to its performance in the LEST case study, it still does not outperform LAT ($0.2571$). Moreover, the difference in BA is bigger in favor of LAT, achieving $0.5482$ compared to $0.5295$ for Ridge. These results again show that, although Ridge excels in nominal accuracy, LAT offers a more balanced and reliable performance for imbalance classification.

Regarding the ordinal metrics, the LAT classifier consistently outperforms Ridge, showcasing its robustness in capturing the ordinal relationships inherent in the data. The superior QWK score of $0.7327$ for LAT, compared to $0.7174$ for Ridge, highlights its better handling of ordinal misclassifications. Similarly, LAT achieves lower AMAE ($0.5776$) and MMAE ($0.8297$) values than Ridge ($0.6586$ and $1.0000$, respectively), indicating that LAT provides not only a more equitable performance across all classes but also greater accuracy for the worst-performing class. These findings demonstrate the effectiveness of the LAT classifier in addressing the challenges of ordinal classification, particularly in imbalanced scenarios.

Table 4. Confusion matrices obtained in the testing set by the LAT and Ridge classifiers in the LEST case study.

	LAT				Ridge
	${\mathit{C}}_{\mathit{0}}$	${\mathit{C}}_{\mathit{1}}$	${\mathit{C}}_{\mathit{2}}$	${\mathit{C}}_{\mathit{3}}$	${\mathit{C}}_{\mathit{0}}$	${\mathit{C}}_{\mathit{1}}$	${\mathit{C}}_{\mathit{2}}$	${\mathit{C}}_{\mathit{3}}$
$C_0$	247	74	42	23	308	10	22	46
$C_1$	110	64	38	18	160	4	28	38
$C_2$	180	728	1408	641	622	73	1526	736
$C_3$	78	290	2771	23,966	287	46	1637	25,135

and

Table 5. Confusion matrices obtained in the testing set by the LAT and Ridge classifiers in the LEVX case study.

	LAT				B
	${\mathit{C}}_{\mathit{0}}$	${\mathit{C}}_{\mathit{1}}$	${\mathit{C}}_{\mathit{2}}$	${\mathit{C}}_{\mathit{3}}$	${\mathit{C}}_{\mathit{0}}$	${\mathit{C}}_{\mathit{1}}$	${\mathit{C}}_{\mathit{2}}$	${\mathit{C}}_{\mathit{3}}$
$C_0$	1237	298	241	77	1268	284	83	218
$C_1$	281	163	135	55	321	142	64	107
$C_2$	358	530	813	427	552	318	552	706
$C_3$	299	323	2342	23,099	473	197	629	24,764

present the confusion matrices obtained from both approaches for the LEST and LEVX case studies, respectively. As can be observed, for the LAT classifier, misclassification errors generally occur between adjacent classes on the ordinal scale, and they decrease as the predicted class gets further away from the observed class. In contrast, the Ridge classifier behaves differently, as it does not penalize the distance between the observed and predicted classes. It is important to note that in ordinal classification problems, if a classification error occurs, it is preferable for it to involve an adjacent class rather than one further apart. In this context, minimizing one particular type of error is especially critical: misclassifying a low-visibility event as a clear event, which may have significant repercussions. Notably, the LAT classifier commits only 23 and 77 such errors for the LEST and LEVX case studies, respectively. By comparison, the Ridge classifier produces two and nearly three times that amount of errors, respectively, for the two case studies.

The other type of error that should be minimized is misclassifying a clear event as a low-visibility one. While this type of error does not carry the critical repercussions of the previous type, such as air collisions caused by low-visibility, it can result in substantial economic losses. These may arise from canceled flights or other operational decisions made by staff based on prediction systems indicating low-visibility when, in reality, conditions were entirely clear. In this case, the number of errors made by the Ridge classifier is significantly reduced by the LAT classifier, decreasing from 287 and 473 to 78 (a reduction of $72.8\%$) and 299 (a reduction of $36.8\%$) for the LEST and LEVX case studies, respectively.

4.6. Explainability of LAT Models

Another interesting characteristic of LAT is its ability to generate explainable models, aligning with the XAI paradigm [126], which emphasizes the importance of both performance and interpretability. As the LAT classifier is a linear approach, interpreting the trained models is relatively straightforward. Equations (1) and (2) present the mathematical expressions for the LAT models learned for the two case studies, LEST and LEVX, respectively. Note that while the input variables are measured at t, the prediction $\widehat{y}$ is made at $t+1$.

$$\widehat{y}=0.0251·\mathrm{D}+0.5895·\mathrm{S}+\mathbf{1}.\mathbf{2080}·\mathrm{T}-0.8659·\mathrm{De}-0.0597·\mathrm{P}+\mathbf{1}.\mathbf{1393}·\mathcal{V}$$

(1)

$$\widehat{y}=0.0105·\mathrm{D}+0.0830·\mathrm{S}+\mathbf{2}.\mathbf{9560}·\mathrm{T}-\mathbf{2}.\mathbf{2868}·\mathrm{De}-0.1045·\mathrm{P}+1.1608·\mathcal{V}$$

(2)

Each input variable (as detailed in Table 2) has a weight assigned, which can be either positive or negative. A positive weight indicates a direct relationship with the predicted variable (visibility at the airport), while a negative weight signifies an inverse relationship. The magnitude of the weights reflects the relative importance of each variable in the final prediction. For the LEST case study (Equation (1)), the most important variables are temperature (T) and the visibility ($\mathcal{V}$), with respective weights of $1.2080$ and $1.1393$. As mentioned, the observed visibility is incorporated as part of an autoregressive approach, meaning that the visibility measurement at time t is utilized to predict the value at $t+1$. Conversely, in the LEVX case study (Equation (2)), while temperature (T) remains the most critical variable, with a higher weight of $2.9560$, the dew point (De) is now the second most important variable, though with a negative influence, with a weight of $-2.2868$. It is also noteworthy that wind-related variables, namely direction (D) and speed (S), exhibit relatively small weights in both models, suggesting they have a limited impact on the predictions.

Figure 4 illustrates the reliability of the LAT classifier by comparing its predictions (blue) with the observed values (orange) for both case studies (LEST and LEVX) over the last month of the testing dataset, December 2023. This particular month was selected due to its high variability in visibility conditions. As shown in Figure 4, the LAT classifier accurately captures the general trends of the visibility time series for both case studies. In general terms, all class changes are successfully identified by the LAT approach. For the LEST case study, six significant transitions to the low-visibility class ($C_0$) occur, and all are accurately detected by LAT. Similar observations are made for LEVX, where the number of transitions to $C_0$ is higher. Furthermore, LAT effectively handles abrupt changes in the time series, such as the ones observed around 16 December 2023, and around 24 December 2023 in the LEST and LEVX cases, respectively. It is also important to highlight that LAT also predicts low-visibility events ($C_0$) in some additional instances, particularly during transitions from $C_3$ to $C_1$, as observed around 9 December 2023 in the LEST case. However, in general terms, when LAT misclassifies, it predicts an adjacent class rather than a distant one, as demonstrated in the LEST case study around 23 and 24 December 2023.

To further illustrate the reliability of the LAT approach, Figure 5 presents the projections of the patterns, again over the last month of the testing dataset (December 2023), made by LAT onto the real line (represented in the x-axis), along with the set of thresholds, which have been learned from the data. The thresholds split the real line into Q intervals, each associated with an ordinal class, such that a projected pattern between thresholds ${\theta }_{q-1}$ and ${\theta }_q$ is classified as class $C_q$. As shown, the thresholds are similar for both case studies, although some differences are evident. Notably, the thresholds for LEST are larger, indicating differences in visibility levels between the two case studies.

Although the LAT classifier accurately predicts the majority of patterns, it produces some misclassifications. For instance, the patterns within rectangle 1 show cases where clear events are misclassified as low-visibility. Such errors may lead to unnecessary costs, such as flight cancellations, caused by a considerable misjudgment. Similarly, rectangle 3 highlights another critical type of error, where low-visibility conditions are misclassified as clear events. These errors are particularly severe, as they could result in dangerous situations, such as improper flight landings or takeoffs under extremely difficult conditions. Notably, during December 2023, LAT made only 5 of these critical errors in the LEVX case study and none in the LEST case study.

However, most misclassifications occur near the thresholds, as can be observed by the patterns included in rectangle 2. This indicates that errors made by the LAT classifier generally are borderline examples close to the thresholds, indicating its ability to consistently follow the ordi1nal structure of t2he problem while ma3intaining high performance.

5. Conclusions

Fog events have extremely important impacts on different human systems, mainly related to road and air transportation. The accurate prediction of atmospheric low-visibility events, in many cases associated with fog, is key to manage potentially dangerous situations in these systems. In this paper, we have discussed a comprehensive review about published literature on AI-based methods and algorithms applied to fog and low-visibility event forecasting. We have also discussed the general main issues related to this kind of problem, open research questions and novel AI-based approaches on the field. We have also reviewed some important new AI-based methodologies which can improve atmospheric visibility forecasting. To illustrate them, we have shown a case study on the application of ordinal classification algorithms for low-visibility event prediction due to fog in two Spanish airports, using METAR data. We have shown that ordinal classification is a novel methodology able to obtain excellent results in classification problems associated with low-visibility event prediction problems.