Predictor Variables Influencing Visibility Prediction Based on Elevation and Its Range for Improving Traffic Operations and Safety

Low visibility condition hinders both air traffic and road traffic operations. Accurate forecasting of visibility condition helps aircraft operators and travel-ers to make better decisions and improve their safety. It is, therefore, essential to investigate and identify the predictor variables that could influence and help predict visibility. The objective of this study is to identify the predictor variables that influence visibility. Four years of surface weather observations, from January 2011 to December 2014, were collected from the weather stations located in and around the state of North Carolina, USA for the model development. Ordinary least squares (OLS) and weighted least squares (WLS) regression models were developed for different visibility and elevation ranges. The results indicate that elevation, cloud cover, and precipitation are negatively associated with the visibility in visibility less than 15,000 m model. The elevation, cloud cover and the presence of water bodies within the vicinity play an important role in the visibility less than 2000 m model. The chances of low visibility condition are higher between six to twelve hours after the rainfall when compared to the first six hours after the rainfall. The results from this study help to understand the influence of predictor variables that should be dealt with to improve the traffic operations and safety concerning the visibility near the airports/road transportation network.

wind affect the air and road traffic operations. From the year 1982 through the year 2013, inclement weather condition contributed to 35% of the general fatal aviation incidents in the United States [1]. Low ceiling, fog, and clouds were among the top three variables which contributed to the weather-related fatalities in air traffic operations. According to the Federal Highway Administration (FHWA), from the year 2005 to the year 2014, around 28,533 road crashes occurred per year due to fog, resulting in over 495 fatalities and 10,448 injury crashes [2]. From the year 2002 to the year 2012, there were 19,188 reported fog-related crashes in North Carolina alone [3]. A recent study also quantified the effect of rainfall and visibility conditions on road traffic travel time reliability [4]. Therefore, it is necessary to alert the aircraft operators and motorists beforehand to improve safety and mobility during low visibility. However, fog is a localized phenomenon. It would be expensive to install visibility sensors at every few miles along roads. Hence, identifying the predictor variables associated with low visibility not only helps predict visibility but also helps disseminate potential risk associated with low visibility condition.
In the past, researchers used several statistical and numerical modeling techniques for fog assessment. Vislocky and Fritsch [5] developed linear regression models to predict ceiling height and visibility. The threshold values for visibility were less than 1.61 km, 4.83 km, 8.05 km, and 11.27 km, which were based on aircraft operations. Surface observation parameters such as opaque cloud amount, cloud cover, precipitation occurrence, wind direction and speed, sea level pressure, dewpoint, and dewpoint depression were considered as the predictor variables. Hilliker and Fritsch [6] developed models to forecast visibility at the San Francisco International Airport for 1 -6 hour lead times. They observed that the inclusion of upper-air predictor variables can reduce prediction error by 3% than models solely from surface data.
A detailed literature review related to the fog prediction methods is presented by Gultepe et al. [7]. Several research studies documented the parameters in fog assessments. Meyer et al. [8] showed that visibility in foggy conditions is a function of droplet number concentration. On the other hand, Jiusto [9] suggested that visibility is a function of both droplet size and liquid water content, concluding that liquid water content is directly related to the droplet size.
Tardif and Rasmussen [10] analyzed meteorological factors and scenarios leading to the occurrence of precipitation fog in the New York City area. Their study indicates that 18% of the analyzed precipitation events corresponded with fog events and that the majority of fog events occurred during light precipitation.
Most of the fog events occurred at high elevation stations due to upslope flow and lowering of the cloud base. Since relative humidity is a function of temperature, they divided fog events into those that occurred due to moistening, cooling, moistening and cooling, or static conditions. An analysis of all fog events based events, respectively. Studies such as by Pulugurtha et al. [11] have explored the influence of surface weather observations and meteorological predictor variables on visibility. However, the visibility could be influenced by time-of-the-day, rainfall in past hours, wind speed, and the presence of water bodies within the vicinity. The contribution of the aforementioned predictor variables for different visibility and elevation ranges could vary and has not been explored in the past. Therefore, this study focuses on identifying the meteorological and temporal predictor variables which could influence the visibility with respect to change in the elevation and its range.

Methodology
The methodology adopted in this study includes the following steps.

Identify the Weather Stations and Collect Surface Weather Observations
National Oceanic and Atmospheric Administration (NOAA)/National Centers for Environmental Information (NCEI) collects hourly meteorological data from over 20,000 locations across the world [12] [13]. This Integrated Surface Database (ISD) includes visibility, 2-m air temperature, dew point temperature, wind speed, atmospheric pressure, precipitation, and current weather conditions. Some stations also collect snow depth and snowfall information. The ISD database undergoes a meticulous quality control process before distribution [14] [15]. However, data quality issues still remain in the database [15]. These issues are dealt with effectively through additional quality assurance algorithms.
Data for four years, from January 2011 to December 2014, for 238 ISD locations in and near the state of North Carolina, USA were collected and processed for this study.

Process Data
The collected surface weather observations were processed by deleting the missing values and outliers using Microsoft SQL server. Further, precipitation in previous hours and time-of-the-day could influence the formation of fog. Therefore, binary variables such as the occurrence of rainfall and time-of-the-day were added to the database.
Oliver [3] stated that crashes related to the low visibility conditions (49%) are more likely during morning hours. In addition, the literature review indicated that precipitation is a governing factor in low visibility conditions. Therefore, Typically, fog forms when the dewpoint depression is roughly less than 2.5˚C -4.0˚C.
According to the NOAA, fog is formed by the collection of suspended water droplets or ice crystals near Earth's surface, which reduces the horizontal visibility below 1 km [16]. The water bodies in the vicinity of the weather station could influence the formation of fog. Therefore, the presence of water bodies within a 1.61-km buffer of each weather station was captured using ArcGIS and was represented as a dichotomous variable.

Develop and Compare the Regression Models
Ordinary least squares (OLS) and weighted least squares (WLS) regression models were developed to investigate the effect of predictor variables on the visibility.

Validate the Developed Models
Among all the developed models, the best-fitted model was selected based on the statistical tests. Two months ( (1).
where, V observed(i,j) is the observed visibility at a weather station "i" during an hour "j", V predicted(i,j) is estimated visibility at the same weather station "i" during the same hour "j", and, N is the total number of hours.

Results
The developed models are discussed next.

Visibility Less than 10,000 m
The developed OLS and WLS regression models for visibility less than 10,000 m are summarized in Table 2. The WLS regression models outperformed the OLS

Visibility Less than 5000 m
The developed OLS and WLS regression models for the visibility less than 5000 m are summarized in Table 3

Visibility Less than 2000 m
The developed OLS and WLS regression models for visibility less than 2000 m are summarized in Table 4. The elevation, cloud cover, and the presence of wa-    In addition, both the aforementioned models are observed to be best-fitted models with higher R-square and adjusted R-square values and lower AIC, and lower RMSE values.

Validation of the Selected Model
The WLS regression model for visibility less than 15,000 m and the WLS regres-

Conclusions
This study focuses on identifying predictor variables associated with different visibility and elevation ranges. Based on the application/mode of transportation,  Based on the findings, implementing dynamic message sign-boards/communicating the information through radio/phones or the Internet to the motorists in the mountainous areas, near the water bodies and between six to twelve hours after the rainfall about the possibility of low visibility condition could improve the safety for motorists.
Comparing the visibility from weather stations, numerical models, satellite data, and for regions with different climatic and topographical conditions warrant further investigation.