Usage of Existing Meteorological Data Networks for Parameterized Road Ice Formation Modeling

Benjamin A. Toms School of Meteorology, and School of Civil Engineering and Environmental Sciences, University of Oklahoma, Norman, Oklahoma

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Jeffrey B. Basara School of Meteorology, and Oklahoma Climatological Survey, University of Oklahoma, Norman, Oklahoma

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Yang Hong School of Civil Engineering and Environmental Sciences, University of Oklahoma, Norman, Oklahoma

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Abstract

A road ice prediction model was developed on the basis of existing data networks with an objective of providing a computationally efficient method of road ice forecasting. Icing risk was separated into three distinct road ice formation mechanisms: hoarfrost, freezing fog, and frozen precipitation. Hoarfrost parameterizations were mostly gathered as presented in previous literature, with modifications incorporated to account for diffusional ice crystal growth-rate complexity. Freezing-fog parameterizations were based on previous fog typological analyses under the assumption that fog formation mechanisms are similar in above- and subfreezing temperatures. Frozen-precipitation parameterizations were primarily unique to the developed model but were also partially based on previous research. Diagnostic analyses use a synthesis of Automated Surface Observing System (ASOS), Automated Weather Observing System (AWOS), and Oklahoma Mesonet data. Prognostic analyses utilize the National Digital Forecast Database (NDFD), a 2.5-km gridded database of forecast meteorological variables output from National Weather Service Weather Forecast Offices. A frequency analysis was performed using the diagnostic parameterizations to determine general road icing risk across the state of Oklahoma. The frequency analyses aligned well with expected temporal maxima and confirmed the viability of the developed parameterizations. Further, a fog typological analysis showed the implemented freezing-fog-formation parameterizations to capture 89% of fog events. These results suggest that the developed model, identified as the Road-Ice Model (RIM), may be implemented as a robust option for analyzing the potential for road ice development based on the background meteorological environment.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Current affiliation: Department of Atmospheric Sciences, Colorado State University, Fort Collins, Colorado.

Corresponding author: Benjamin A. Toms, benatoms@ou.edu

Abstract

A road ice prediction model was developed on the basis of existing data networks with an objective of providing a computationally efficient method of road ice forecasting. Icing risk was separated into three distinct road ice formation mechanisms: hoarfrost, freezing fog, and frozen precipitation. Hoarfrost parameterizations were mostly gathered as presented in previous literature, with modifications incorporated to account for diffusional ice crystal growth-rate complexity. Freezing-fog parameterizations were based on previous fog typological analyses under the assumption that fog formation mechanisms are similar in above- and subfreezing temperatures. Frozen-precipitation parameterizations were primarily unique to the developed model but were also partially based on previous research. Diagnostic analyses use a synthesis of Automated Surface Observing System (ASOS), Automated Weather Observing System (AWOS), and Oklahoma Mesonet data. Prognostic analyses utilize the National Digital Forecast Database (NDFD), a 2.5-km gridded database of forecast meteorological variables output from National Weather Service Weather Forecast Offices. A frequency analysis was performed using the diagnostic parameterizations to determine general road icing risk across the state of Oklahoma. The frequency analyses aligned well with expected temporal maxima and confirmed the viability of the developed parameterizations. Further, a fog typological analysis showed the implemented freezing-fog-formation parameterizations to capture 89% of fog events. These results suggest that the developed model, identified as the Road-Ice Model (RIM), may be implemented as a robust option for analyzing the potential for road ice development based on the background meteorological environment.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Current affiliation: Department of Atmospheric Sciences, Colorado State University, Fort Collins, Colorado.

Corresponding author: Benjamin A. Toms, benatoms@ou.edu

1. Introduction

Throughout the United States, approximately 673 000 people are injured and 7400 people are killed in weather-related automobile crashes every year. One out of every four weather-related crash fatalities is the result of a winter weather phenomenon (Pisano et al. 2008). The detrimental impacts of icy roads have been historically demonstrated through persistent economic and public welfare damages. Although networks of road observation stations, also known as Road Weather Information Systems (RWIS), are limited throughout the United States, surface meteorological observation networks and sophisticated forecast databases—such as those available from the National Weather Service (NWS)—provide an opportunity to improve detection and forecasting of hazardous roadway conditions.

With the assistance of elaborate road-surface observation networks, European nations such as the Czech Republic, Denmark, Sweden, and the United Kingdom have developed diagnostic and prognostic road icing models based on both meteorological parameterizations and roadside observations (Dejmal and Repal 2009; Hewson and Gait 1992; Karlsson 2001; Takle 1990; Sass 1992). Efforts have been characterized by sophisticated RWIS infrastructure but limited forecasting capabilities. However, postevent analyses have resulted in successful meteorological parameterizations of formation mechanisms (Hewson and Gait 1992; Karlsson 2001; Takle 1990). These parameterizations have not been used to their fullest capabilities in the past because of limited spatiotemporal availability of efficiently processed forecast data.

Ice forms on roadways through three primary mechanisms: hoarfrost, freezing fog, and frozen precipitation (Eriksson 2001; Gustavsson 1991; Hewson and Gait 1992). Hoarfrost forms through deposition of water vapor from the ambient air onto the road surface. Freezing-fog-related road icing results from suspended supercooled water droplets freezing on the roadway surface. Continued ice crystal growth may result from either water vapor diffusion or additional suspended droplets contacting the developed crystals and subsequently freezing. Frozen-precipitation-related road icing results from precipitation falling on a roadway with surface temperature at or below 0°C. Of note, all mechanisms of road ice formation require the temperature of the roadway surface to be at or below 0°C (Hewson and Gait 1992).

Hoarfrost requires the saturation vapor pressure with respect to ice corresponding to the temperature of the roadway surface to be less than or equal to the vapor pressure of the ambient air (i.e., the supersaturation of the roadway with respect to ice is greater than or equal to one). This results from conditions favorable for radiational cooling or advection of moist air over a surface with temperature less than the dewpoint of the air (Gustavsson 1991). Numerous studies have attempted to parameterize hoarfrost based on near-surface meteorological variables with reasonable levels of success (Karlsson 2001; Takle 1990; Hewson and Gait 1992).

Meteorologically, fog occurs when suspended water droplets result in visibilities less than 1 km (Roach 1994). Freezing-fog formation results from a variety of environmental conditions, including radiation-induced cooling, advection of moist air masses over a cooler surface, lowering of the base of a cloud deck, and precipitation-induced moistening (Tardif and Rasmussen 2007; Westcott 2007). Additionally, freezing-fog-related icing requires the presence of fog coincident with air and/or road-surface temperatures less than or equal to 0°C. Freezing fog itself has not been parameterized in literature, although Tardif and Rasmussen (2007) parameterized general fog formation via a fog typological analysis of events in the vicinity of New York City.

Frozen-precipitation-related road icing requires either 1) the temperature of the road surface to be below 0°C before precipitation falls, or 2) latent and conductive heat transfer processes associated with frozen precipitation falling on the road surface leading to a decrease of road-surface temperatures to below 0°C (Eriksson 2001; Symons and Perry 1997). Although a well-known phenomenon, parameterization of frozen-precipitation-related road ice formation has not been presented in published literature.

Aside from the three described mechanisms of road ice formation, the foundational prerequisite to road ice is the maintenance of the road-surface temperature at or below 0°C (Hewson and Gait 1992). Quantifying road-surface temperature is the most challenging prospect for models attempting to parameterize road ice without direct measurement of road-surface conditions. The physical processes that contribute to road-surface temperature changes are highly complex and commonly require a numerical model for analysis (Crevier and Delage 2001). To reduce computational demands, numerous other studies have developed models to diagnose road ice formation risk using combinations of RWIS and meteorological parameterizations.

Previously developed models

The majority of previously developed models utilize supplementary road-surface data. Sophisticated models based on heat conduction and energy balance have been explored by Rayer (1987) and Sass (1992, 1997), but these models are dependent upon local vertical profiles of temperature within the roadway. Further efforts to extrapolate road conditions to ambient locations without RWIS have been attempted by Bogren et al. (2001) and Gustavsson (1995).

Shao and Lister (1996) developed a numerical model to solve a road-surface energy balance, but required knowledge of the near-surface profile of static stability. Crevier and Delage (2001) parameterized road-surface temperature using a similar energy balance, but with combined input from the Global Environmental Multiscale (GEM) numerical weather prediction (NWP) model and ambient meteorological observation stations. This model is also dependent upon knowledge of snow coverage and an initial value of road-surface temperatures.

Hewson and Gait (1992) and Takle (1990) overcame a lack of road-surface observations through the development of models dependent primarily upon variables measured by common surface observation stations (e.g., temperature, wind speed, and cloud cover). These models emphasized the effects of radiational cooling on road-surface temperatures to compensate for a lack of reliable road temperature observations. Takle (1990) incorporated both hoarfrost and frozen-precipitation icing mechanisms, with model output being derived from surface thermodynamic and kinematic variables input by a forecaster. Hewson and Gait (1992) combined an intensive literature review with multiple case studies to parameterize hoarfrost formation using data output by weather observation stations throughout the United Kingdom. While these models focused on hoarfrost development, the road-surface temperature parameterizations are applicable to frozen precipitation and freezing fog. As such, the parameterizations of these models were used as the primary sources of hoarfrost and road-surface temperature parameterizations in the current model.

Although a majority of the previously discussed studies focused on hoarfrost as the primary road ice formation mechanism, frozen precipitation and freezing fog also pose a significant risk for road ice formation. Gustavsson (1991, 1995) suggested freezing fog to be a prominent road ice formation mechanism. The results suggested that, given the presence of freezing fog and similar initial road-surface conditions, icing was more significant than that resulting from hoarfrost alone. Parameterizations for freezing-fog formation have not yet been developed, although Tardif and Rasmussen (2007) presented a sophisticated typological analysis for generic fog formation. Their developed fog-formation parameterizations are not directly dependent upon ground or air temperature, and are thus suggested to be applicable to fog formation during subfreezing air surface temperatures.

Eriksson (2001) emphasized the importance of road-surface temperature on the magnitude of frozen-precipitation-related road icing. While Eriksson (2001) suggested the road-surface temperature to be the primary variable relevant to precipitation-related ice formation, the sophisticated RWIS used in the study permits such specific requirements. Alternatively, for instances without RWIS infrastructure, incorporation of previous meteorological conditions conducive to roadway cooling (e.g., nocturnal radiational cooling and/or a preceding period of temperatures below 0°C) may compensate for the lack of road-surface temperature data (Karlsson 2001; Takle 1990). Furthermore, examination of models dependent upon road-surface energy flux supports the idea that, for instances where road-surface temperatures are above freezing, duration and intensity of frozen-precipitation events are the most important variables in precipitation-related icing. Road-surface energy balances developed by Crevier and Delage (2001) and Shao and Lister (1996) suggest road-surface temperatures may fall below 0°C via latent and conductive heat exchange between precipitated water and road surfaces. However, if road-surface temperatures are already below 0°C, ice will readily form (Johnson and Esch 1995; Symons and Perry 1997).

The goal of this study was to synthesize previously developed parameterizations of hoarfrost, freezing fog, and frozen precipitation related to road icing and develop an efficient, comprehensive road ice–forecasting model—hereinafter referred to as the Road-Ice Model (RIM). Unlike previously developed models, RIM uses only preexisting meteorological databases to provide an assessment of road icing risk based on background meteorological conditions. The National Digital Forecast Database (NDFD), Oklahoma Mesonet, and Automated Surface Observing System network are used as the primary data sources, all of which offer high-resolution datasets subject to intensive quality assurance protocol. The development of RIM is sequenced via a discussion of 1) the model structure (section 2), 2) the sources of meteorological data used in the model (section 3), 3) the implemented model parameterizations for prognostic (section 4) and diagnostic (section 5) analyses, and 4) a frequency analysis conducted using the parameterizations of the developed model (section 6).

2. Developed model structure

RIM uses a hierarchical risk assessment structure to evaluate the likelihood of road ice formation. The concept of the hierarchical road icing model established by Hewson and Gait (1992) was expanded upon for RIM. Hewson and Gait (1992) were able to validate their hoarfrost parameterizations with a local RWIS, which asserts the effectiveness of their developed hierarchical structure. The freezing-fog and frozen-precipitation portions of RIM were developed using a similar hierarchical approach, although numerous road icing conditions lead to the output of conditional rather than numerical, scalable risk.

A significant reduction in computational demands results from using a quasi-empirical, parameterized road icing model rather than typical NWP style models. With the proposed data format, prognostic observations are extracted from a database, NDFD (see section 3a), that synthesizes NWP output and human judgment. There are numerous advantages to this approach: 1) the end user can focus on the data output rather than concerning themselves with developing and maintaining NWP model simulations; 2) NWP model output is already validated and modified by experienced meteorologists, increasing the likelihood of forecast accuracy; and 3) the quasi-empirical model can be run efficiently, allowing for high-frequency simulation updates and the efficient communication of icing risk to operational activities.

As of the development of RIM, no sophisticated archival database exists to cross validate the implemented parameterizations within the state of Oklahoma. However, RIM aims to limit the repercussions of this uncertainty through linearized logic (e.g., in the form of hierarchical risk assessment) and usage of parameterizations developed and validated by previous studies [e.g., that of Hewson and Gait (1992), Karlsson (2001), and Takle (1990)]. Future studies will attempt to validate RIM within other regions of the United States where road ice validation data may be available.

3. Data

a. Prognostic

The NDFD is the sole source of data for the prognostic portion of RIM (Table 1). The NDFD is a database of gridded forecasts at a maximum grid resolution of 2.5-km output by NWS Weather Forecast Offices, and combines model output statistics (MOS) data with human judgment (Glahn and Ruth 2003). To analyze NDFD data, the NDFD XML server is accessed via Simple Object Access Protocol (SOAP) on an hourly basis. A query is sent to the NDFD server to acquire geographic coordinates of each grid point throughout Oklahoma. The database is then queried to obtain forecast data for each individual grid point. The data for each individual location are parsed and analyzed for icing risk based on the parameters discussed in subsequent sections using matrix methods available via the Python programming language. Following road ice risk assessment at all grid points, the data are interpolated using a nearest neighbor interpolation method based on Delaunay triangulation (Chew 1989). See Glahn and Ruth (2003) for further details on the NDFD. Figure 1 graphically sequences the initialization of the prognostic portion of RIM.

Table 1.

Data sources and variables used for diagnostic and prognostic analysis.

Table 1.
Fig. 1.
Fig. 1.

Logical sequence for the initialization of the prognostic portion of RIM. Refer to the individually referenced figures for the hierarchical structure of the hoarfrost, freezing-fog, and frozen-precipitation parameterizations.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

b. Diagnostic

The exceptional spatiotemporal availability of surface in situ meteorological observations across Oklahoma is a critical component of RIM. These observations include variables collected via the Oklahoma Mesonet (hereinafter referred to as the Mesonet), Automated Surface Observing System (ASOS), and Automated Weather Observing System (AWOS) networks. The Mesonet consists of 120 surface meteorological observation stations (Brock et al. 1995; McPherson et al. 2007), each of which measure more than 20 environmental variables, including: wind at 2 and 10 m, air temperature at 1.5 and 9 m, relative humidity, rainfall, pressure, solar radiation, soil temperature, and soil moisture (Illston et al. 2008) at various depths. All sensors are mounted on or near a 10-m tower supported by three guy wires and powered via solar energy. Mesonet data are collected and transmitted to a central point every 5 min, where they are quality controlled, distributed, and archived (Shafer et al. 2000; McPherson et al. 2007). The Mesonet was officially commissioned in 1994, and data from the climatological archive consists of over five billion observations.

The ASOS and AWOS networks, in total, consist of 54 additional measurement sites and collect observations of standard World Meteorological Organization defined meteorological variables (e.g., near-surface temperature, wind speed, and air moisture content). Additionally, the sites include observations not collected at Mesonet sites, such as fog presence, precipitation typology, and cloud elevation. Observations gathered by ASOS instruments are subject to a three-stage quality assurance process that spans both automatic and human-based assurance methods. Following an automated raw data processing algorithm that flags any suspect outlier data, the data are subject to review by both local NWS office personnel and the national ASOS Operations and Maintenance Center (AOMC). While ASOS observations are publicly output and subsequently archived every 1 min, the analyses in this study used only 5-min data to align with the temporal resolution of the Mesonet. Refer to the ASOS user’s guide (NOAA 1998) for further details on the ASOS–AWOS cloud detection algorithm and fog presence and precipitation typology indicators. Table 1 details the specific variables used by the Mesonet and ASOS–AWOS stations in this study.

Although both the Mesonet and ASOS–AWOS observation networks provide the necessary variables for diagnosing road ice formation, the higher spatiotemporal resolution of the Mesonet observations supports its utilization as the primary data source for RIM. However, the Mesonet does not measure cloud cover and is limited in its ability to observe frozen precipitation: the Mesonet uses unheated tipping-bucket rain gauges to quantify precipitation, which are inapplicable for immediate analysis of frozen-precipitation events (Brock et al. 1995). Thus, the qualitative ASOS–AWOS precipitation observations are crucial for identification of ongoing frozen-precipitation-related icing events. Further, ASOS–AWOS stations provide additional diagnostic benefit through an internalized, truth-based fog presence algorithm.

To ensure all variables necessary for diagnosing road ice formation are available, each Mesonet station is paired with the nearest ASOS–AWOS station based on simple linear distance. This couples the optimal temporal resolution of Mesonet observations with the supplementary ASOS–AWOS data not available at Mesonet sites. Figure 2 offers a graphical representation of the initialization process of the diagnostic portion of RIM, while Fig. 3 provides a visualization of the observation site coupling process.

Fig. 2.
Fig. 2.

As in Fig. 1, but for the diagnostic portion of RIM.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

Fig. 3.
Fig. 3.

Locations of ASOS stations (stars) and coupled Mesonet (circles) stations. Mesonet stations denoted by the filled circles were used for the frequency analysis conducted using the implemented parameterizations (section 6). The black lines denote the NOAA-designated climate divisions used for the frequency analysis within the current study.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

4. Prognostic parameterizations

Because Oklahoma does not have RWIS infrastructure, the determination of road-surface temperature necessitates meteorological parameterizations of both road ice formation and road-surface temperatures. RIM uses a synthesis of parameterizations developed previously by other studies and logical assertions based on previous research indirectly related to road ice formation. Graphical representations of the prognostic parameterizations and risk assessment decision trees of RIM are offered in Fig. 4 for freezing fog and Fig. 5 for hoarfrost and frozen precipitation.

Fig. 4.
Fig. 4.

Hierarchical risk assessment for the prognostic freezing-fog parameterizations. Solid and dashed lines signify true and false responses, respectively, to the connected conditional statement (parallelograms). For each individual fog type (rectangles outlined by thick lines), the sum of the total arrows intersecting increased risk conclusions (ovals) corresponds to the total icing risk for that fog type. Note that the icing risk for each fog type is not transitive to other fog types, i.e., the icing risk of each fog type depends only on its individual hierarchical tree. Refer to Table 3 for more information.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

Fig. 5.
Fig. 5.

As in Fig. 4, but for diagnostic and prognostic hoarfrost and prognostic frozen-precipitation parameterizations. Refer to Tables 3 and 4 for more information.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

a. Hoarfrost

Hoarfrost occurs when water vapor ambient to the roadway deposits onto the road surface. This provides arguably the most dangerous aspect of road ice formation because of the inability of the driver to visibly observe the gradual process of hoarfrost formation. Furthermore, the complexity of depositional processes leads to complications in the parameterization of hoarfrost formation, which further results in forecast uncertainty. Numerous studies parameterizing hoarfrost using meteorological data have been completed and verified using RWIS, which reduces the uncertainties in the prognostication of hoarfrost formation. A combination of the parameterizations developed by Dejmal and Repal (2009), Hewson and Gait (1992), Karlsson (2001), Shao and Lister (1996), and Takle (1990) was utilized for the development of the hoarfrost portion of RIM (Table 3).

Hoarfrost occurs only when the vapor pressure of the air is greater than the saturation vapor pressure with respect to ice corresponding to the temperature of the roadway [i.e., esi(T) < e(T)] (Hewson and Gait 1992). Two instances exist during which this may occur: 1) periods of prolonged radiational cooling, and 2) advection of moist air over roadways with a road-surface temperature below both 0°C and the near-surface atmospheric dewpoint (Gustavsson 1995; Hewson and Gait 1992; Karlsson 2001). Thus, the parameterizations of hoarfrost formation are based on the satisfaction of one of these two requirements. Contrarily to radiational hoarfrost induction, advectively induced hoarfrost formation has not been extensively parameterized in preexisting literature. This limited the incorporation of such advection relating icing events to a conditional risk based solely on near-surface meteorological variables that typically indicate the risk for rapid low-level moisture advection (e.g., a rapid wind direction change coincident with positive tendencies in near-surface moisture and temperature). The deduction of the actual risk of advection-induced hoarfrost formation is left to the user’s judgment once the precautionary statement has been issued by RIM. Radiationally induced hoarfrost events are, however, numerically parameterized (Fig. 5; Table 3).

1) Influence of radiational cooling

The influences of radiational cooling and near-surface atmospheric conditions are used to parameterize the road-surface temperature (Hewson and Gait 1992). The importance of radiational cooling on hoarfrost formation was indirectly supported by Bogren et al. (2001) and Scherm and Bruggen (1993), who found minimal mid- to upper-level clouds and absent low-level clouds to be the most important factor in determining risk of surface condensation. Lind and Katsaros (1982) similarly determined these conditions to be crucial for rapid radiational cooling of the surface, suggesting surface condensation and radiational cooling to be directly related. Furthermore, the influence of antecedent atmospheric conditions on road-surface temperature was supported by Hewson and Gait (1992), who found antecedent air temperatures at or below 0°C and minimal cloud cover support cooler road-surface temperatures. These influences described by Hewson and Gait (1992) relate to conductive and radiative cooling of the road surface, respectively.

2) Influences of near-surface turbulence

Hewson and Gait (1992) suggested wind speeds greater than 2 m s−1 but less than 9 m s−1 enhance hoarfrost production rate, while Monteith (1957) found similar bounds to constrain dew formation. It is logical to assume wind is not conducive to the development of significant near-surface temperature gradients because of production of turbulent mixing and the resultant breakdown of the near-surface radiational inversion. However, downward mixing of moisture to the road surface is dependent upon the presence of wind-generated turbulence (Hunt et al. 2007; Karlsson 2001). Furthermore, near-surface turbulence does not fully mitigate cooling of the road surface during periods of radiational cooling.

A road-surface thermodynamic energy balance similarly used by Crevier and Delage (2001) was utilized to prove near-surface turbulence does not fully mitigate road-surface cooling. Net thermodynamic energy flux solely due to latent and turbulent energy flux and longwave irradiance may be expressed as
e1
where R is the residual energy, is the emitted infrared radiation flux (where ε is the emissivity coefficient, σ is the Stefan–Boltzmann constant, and Ts is the road-surface temperature), H is the sensible turbulent heat flux, and LαE is the energy flux associated with phase changes of water on the road surface (Crevier and Delage 2001). The turbulent flux terms are expressed as
e2
e3
where ρa is the density of air; cp is the specific heat of air at constant pressure; V is the wind speed at 10 m; Cm and Ch are the surface momentum and moisture transfer coefficients, respectively (Delage and Girard 1992; Zhang et al. 2002); T is air temperature; and q is specific humidity.

A scale analysis was performed on Eq. (1) using the scales provided in Table 2. These scales are as provided by previous studies [e.g., Cm and Ch from Delage and Girard (1992) and Zhang et al. (2002)] or as commonly observed in nature (e.g., ρa, Ta, Ts). The scale analysis results in longwave irradiance on the order of 1 W m−2, sensible turbulent heat flux on the order of 10−3 W m−2, and latent heat flux on the order of 10−3 W m−2 for water sublimation or vaporization. Thus, longwave irradiance dominates road-surface temperature even in the presence of turbulence generated by near-surface winds within the bounds of the hoarfrost wind speed parameterization (2 m s−1 ≤ near-surface wind speed ≤ 9 m s−1). This results in R, the residual energy, being negative, signifying a loss of energy and cooling of the road surface.

Table 2.

Scales used for road-surface energy balance scale analysis.

Table 2.

Additionally, the downward turbulent flux of moisture from the ambient environment toward the road surface enhances hoarfrost production rates (Hewson and Gait 1992; Karlsson 2001). Water content of the air layer directly adjacent to the road is reduced as water vapor deposits onto the road surface. Turbulent mixing rapidly diminishes the resultant near-surface water vapor gradient, which increases the moisture content of the air adjacent to the road surface.

3) Influences of near-surface moisture content

High dewpoint temperature values [e.g., ≥−1°C in the model of Hewson and Gait (1992)] are crucial for rapid hoarfrost formation. Environments characterized by higher dewpoint values, and thus higher water vapor pressure, are able to achieve larger values of supersaturation over the roadway given similar road-surface temperature. However, contradictorily, the maximum diffusional growth rate of an ice crystal occurs well below 0°C, at approximately −15°C (Rogers and Yau 1989; Straka 2009).

As defined by Straka (2009), ice crystal growth rate may be approximated by
e4
e5
e6
where ψ is the vapor diffusivity, T0 = 273.15 K, p0 is the sea level pressure, ρi is the density of ice, D is the diameter of the ice crystal, Si is the saturation ratio (e/), Ls is the latent heat of sublimation, Rυ is the gas constant of water vapor, Ta is the temperature of the ambient environment, and esi is the saturation vapor pressure with respect to ice. As defined by Eqs. (4)(6), the mass growth rate (dM/dt) is dependent upon the supersaturation with respect to ice, the temperature of the ambient environment, and the atmospheric pressure. Thus, parameterizations used by previous studies based solely on supersaturation or near-surface dewpoint are not permissible.

To compensate for this nonlinear relationship between ice crystal growth rate and temperature, a dynamic risk enhancement was incorporated. In RIM, the risk associated with the growth rate of an ice crystal cannot be associated with the state of the road-surface temperature because of a lack of road-surface temperature data. Thus, the maximum ice crystal growth-rate-related risk correlates to the highest possible growth rate associated with the air temperature alone. This is valid under the assumption that the air temperature governs the surface temperature of the ice crystal, which is qualified by the independence of the diffusional growth rate from the surface temperature of the ice crystal [Eq. (5)] (Straka 2009).

4) Additional influences

Hewson and Gait (1992) and Takle (1990) determined the length of night to be critical for hoarfrost development and noted this to be the result of the extended period of radiational cooling during longer nights. However, the temporal specifications for this parameter were arbitrarily defined. Because supplementary research discussing the quantitative significance of nocturnal duration in road ice formation is currently unavailable, this parameter was omitted from RIM.

b. Frozen precipitation

In RIM, icing risk associated with frozen precipitation is limited to the influences of 1) the ambient environmental temperature, 2) the probabilistic risk and quantitative precipitation forecasts (QPF) of frozen precipitation, and 3) parameterization of the road-surface temperature through previous near-surface conditions, similar to the parameterization used for hoarfrost. Table 3 details the prognostic parameterizations of frozen precipitation.

Table 3.

Prognostic parameterizations for freezing fog, frozen precipitation, and hoarfrost.

Table 3.

The risk of precipitation leading to icing of road surfaces initially characterized by above freezing temperatures is largely dependent upon two variables: 1) the latent heat associated with freezing or melting of water in contact with the road surface, and 2) thermal conduction between the frozen precipitation and the roadway (Crevier and Delage 2001; Johnson and Esch 1995; Shao and Lister 1996; Symons and Perry 1997). These two variables are not quantifiable through typical in situ meteorological variables provided by the Mesonet and ASOS/AWOS networks but can be generally accounted for via precipitation intensity and duration (Johnson and Esch 1995). Unfortunately, the current state of the science does not quantify the relationship between precipitation intensity and road ice formation. As such, precipitation duration estimates are not directly incorporated into the assessment of road icing risk but may be added as an additional qualifier.

Precipitation falling on roadways with road-surface temperatures less than 0°C inherently leads to the maximum road icing risk. For cases where road-surface temperatures might be above 0°C, preceding atmospheric conditions are considered. Air temperatures at or below 0°C lead to progressive cooling of the road surface and an enhanced likelihood of precipitation-related road icing (Johnson and Esch 1995; Wood and Clark 1999). Although statically defining the separation between temperatures that are and are not conducive to the cooling of road-surface temperatures to below 0°C is unrealistic, an air temperature of 0°C is the warmest air temperature that could possibly lead to sufficient road cooling through thermal conduction alone. Thus, 0°C was set as the risk threshold to ensure all potential cases are encompassed. This does increase the risk of false positives, but this deficiency is reduced considering the conditional format of the incorporated prognostic frozen-precipitation hierarchy, that is, users will be encouraged to consider the uncertainty in the forecast (Table 3).

c. Freezing fog

The fog typology of Tardif and Rasmussen (2007) was used as the foundation for freezing-fog parameterization. Primarily, fog formation is induced by radiative cooling, morning dew evaporation, precipitation-related moistening, advection of moist air over a cold surface, and cloud-base lowering (Tardif and Rasmussen 2007, 2008). Discussions on basic formation criteria for each fog type are provided within this section. Refer to Table 3 for specific parameterizations of each fog type. The performance of RIM is optimized when the fog parameterizations are used to identify instances of fog formation. Once fog formation has been identified, fog persistence is prognosed as all time periods when the relative humidity stays above the minimum 88% threshold.

Parameterization of fog dependence on air moisture content was derived from a probability density function of relative humidity data from ASOS–AWOS and Mesonet archives from the years 2000–12. All cases of fog were documented and the corresponding relative humidity values were archived. The nonnormal distribution was then normalized through a Box–Cox transformation (Sakia 1992). Using the transformed distribution, relative humidity values within two standard deviations of the mean were set as the requirement for fog formation (≥97.5% of events fell within this range, as defined by the Gaussian model). The resulting requirement of relative humidity being greater than or equal to 88% aligns well with previous research, which has commonly established the minimum relative humidity threshold for fog formation at 90% (Zhou and Du 2010).

Beyond the traditional requirements for freezing-fog formation, diffusional ice crystal growth may also result from the presence of freezing fog, that is, through interaction with suspended water droplets (Straka 2009). Although the minimum relative humidity deemed permissible for fog formation is 88%, diffusional growth is also dependent upon temperature. Therefore, not all surface environments characterized by high moisture content will be conducive to diffusional growth. Similar to the hoarfrost parameterization, freezing-fog-related diffusional ice crystal growth was parameterized through a dynamic risk assessment directly related to diffusional growth rate. Diffusional growth-rate values greater than zero were assigned icing risk, with a linearly increasing risk between the minimum and maximum diffusional growth rates.

1) Radiation fog

Radiation fog occurs only at nighttime when longwave radiation flux from the surface is less than zero, and only when outgoing longwave radiation dominates surface temperature tendencies. Concurrence of minimal cloud cover and cooling surface temperatures is suggestive of such radiational cooling dominance. Additionally, low near-surface wind speeds are correlated with radiation fog formation because of the direct relationship between near-surface wind speed and surface ambient turbulent mixing. Near-surface turbulence tends to diffuse radiational inversions, which allows for thermal conduction between potentially warmer air aloft and the ground surface and reduces the likelihood of radiational fog formation (Baker et al. 2002).

Similar to the derivation of the relative humidity fog formation requirement, a Box–Cox normalization transformation (Sakia 1992) was used in the determination of the maximum wind speed threshold for radiation fog events. The threshold wind speed of 3.3 m s−1 is slightly higher than that established by previous research (a range of 2.03.0 m s−1) (Baker et al. 2002; Tardif and Rasmussen 2007; Zhou and Du 2010). The actual risk value assigned to wind speed decreases linearly from 0 to 3.3 m s−1. While the linear risk function is somewhat arbitrary, research discussing the linearity of the relationship between wind speed and radiation fog formation has not been previously published. Given that minimal wind speeds have been associated with enhanced radiation fog density (Westcott 2007; Zhou and Du 2010), lower wind speeds have been assigned higher risk values.

2) Evaporation fog

The formation mechanisms of evaporation-related fog closely resemble those of radiationally induced fog. The primary differentiating factor between the evaporation and radiation fog types is the development of fog prior to sunrise, which occurs for the latter but not the former (Tardif and Rasmussen 2007). Evaporation fog occurs when the saturation vapor pressure associated with the temperature of the surface of the ground falls to, or below, that of the road ambient air, and dew or frost forms on the ground surface. The dew or frost returns to the vapor state following morning insolation, which increases the moisture content of the near-surface air. This may sometimes lead to high enough near-surface moisture content to induce fog formation. This phenomenon is parameterized through an increase in relative humidity following sunrise with a subsequent decrease in relative humidity. The decrease in relative humidity corresponds to the redevelopment of the planetary boundary layer and turbulent mixing of the near-surface moisture as the surface begins to warm. Parameterization of radiationally induced surface cooling is also crucial to the development of surface dew, and is thus also included (Monteith 1957).

3) Precipitation fog

Using NDFD data, precipitation-related fog can only be forecast following precipitation. The enhanced lower-atmospheric moisture content during precipitation events does not always lead to fog formation, and thus high relative humidity forecasts output by NDFD are not necessarily correlated with precipitation-related fog risk (Tardif and Rasmussen 2008, 2007). Given enhanced surface moisture following a precipitation event with no further precipitation falling, the risk of precipitation-related fog is introduced. During precipitation events, the primary concern resides with frozen precipitation freezing on the roadway surface, so this is not a significant limiting factor in road icing risk assessment.

4) Advection fog

Advection fog is primarily characterized by a significant wind shift associated with a frontal zone and/or thermodynamic boundary. Warm, moist air is advected over a cooler surface, resulting in conductive cooling and eventual saturation of the near-surface air. Low-level cloud cover is indicative of conditions potentially conducive to fog formation during instances of warm, moist advection because of its indication of a progressively lowering moist layer typically associated with warm frontal passages (Baars et al. 2002; Roach 1995).

5) Cloud-base-lowering fog

Cloud-base-lowering (CBL) fog is dependent upon the antecedent presence of a low-level cloud deck (i.e., cloud bases ≤1 km above ground level). CBL fog occurs when large-scale subsidence and/or subcloud-layer moistening (i.e., through cooling or increasing low-level water vapor) leads to the progressive lowering of the cloud deck (Baker et al. 2002; Koracin et al. 2001; Tardif and Rasmussen 2007). This was parameterized through a present cloud deck with progressive moistening of the near-surface layer. Subsidence cannot be parameterized by RIM because of a lack of vertical profiling data within the NDFD, but the progressive moistening of the surface resulting from the lowering of a cloud base would potentially be captured by NDFD relative humidity output.

An increase in near-surface relative humidity to above 88% coincident with persistent cloud cover may be indicative of either advection, CBL, or precipitation fog; however, given that the freezing-fog risks associated with these three fog formation mechanisms are conditional rather than numerical, the capturing of any fog formation type is of more importance than specifying the exact type. In this way, the CBL parameterization serves as a catchall mechanism.

5. Diagnostic parameterizations

The developed diagnostic parameterizations are decidedly simpler than those of the prognostic portion of RIM, given the ability of the ASOS–AWOS stations to directly determine the presence of freezing fog and frozen precipitation. However, a lack of RWIS renders direct interpretation of road ice presence impossible. Therefore, hoarfrost parameterizations used in the prognostic portion of RIM are also used in the diagnostic portion.

a. Hoarfrost application

Unlike freezing fog and frozen precipitation, hoarfrost is not directly measured by surface observation stations. However, hoarfrost formation depends primarily upon meteorological variables frequently measured by Mesonet stations (e.g., temperature, humidity, and wind speed). Mesonet data are therefore utilized as the primary mechanism of hoarfrost diagnosis, with ASOS–AWOS stations providing supplementary cloud-cover data. Cloud-cover observations for each Mesonet station are derived from the output of the closest ambient ASOS–AWOS station (Fig. 3). The implemented parameterizations of diagnostic hoarfrost formation are identical to those of the prognostic portion of RIM because of a lack of diagnostic hoarfrost presence verification (Table 4).

Table 4.

Diagnostic parameterizations for freezing fog, frozen precipitation, and hoarfrost.

Table 4.

b. Freezing-fog and precipitation application

Because of the ability of the ASOS–AWOS networks to indirectly analyze precipitation type and fog presence, the ASOS–AWOS network is used as the primary mechanism for diagnosing freezing-fog and frozen-precipitation events. Should an ASOS–AWOS station observe ongoing fog or precipitation, the Mesonet stations paired with that individual ASOS–AWOS station are checked for 2-m air temperatures at or below 0°C. If the temperature requirement is satisfied, the location of the Mesonet station is flagged for ice occurrence.

For precipitation-related events, if the ASOS–AWOS station categorizes the precipitation to be of frozen nature (e.g., snow, sleet, or freezing rain) but the ambient Mesonet stations determine the temperature to be above freezing, then a cautionary risk is displayed at the above-freezing Mesonet locations. This captures the risk of frozen precipitation progressively cooling the road surface to a subfreezing temperature (a process that is more thoroughly discussed in section 4b). Otherwise, a more significant precipitation-related icing risk is assigned to each respective Mesonet station with surface air temperature at or below 0°C. Table 4 provides the implemented parameterizations for diagnostic freezing-fog and frozen-precipitation risk analysis.

6. Frequency analysis

Frequency analyses were conducted for hoarfrost, freezing-fog, and frozen-precipitation occurrences within Oklahoma using Mesonet and ASOS network data. The ASOS stations were split into seven separate regions based on localized station aggregates within regions of similar precipitation and temperature climatologies, as defined by the National Atmospheric and Oceanic Administration (NOAA) climate regions (Fig. 3) (Guttman and Quayle 1996). Each ASOS station was paired with the closest Mesonet station, and ASOS and Mesonet data were analyzed from 2000 to 2014 for each respective pair. NDFD data were not used for the frequency analysis because of the greater likelihood for observations to accurately resemble atmospheric conditions.

Regionally averaged, 5-min interval annual occurrence rates for the three primary road ice formation mechanisms are provided in Fig. 6. Occurrence rates generally increase from the southeast toward the northwest portions of the state, aside from anomalously high occurrence rates of frozen precipitation within the central region. This positive anomaly is likely a result of the central regions of the state being a climatological transition zone, intermittently experiencing the greater tendency for snowfall in the northwestern portions of the state and freezing rain in the southern and southeastern portions of the state. This aligns with the results of Grout et al. (2012) and White et al. (2013), who found a similar maximum in occurrences of frozen precipitation within central Oklahoma.

Fig. 6.
Fig. 6.

Frequency analyses for the three icing mechanisms for individual NOAA climate divisions. Occurrence rates are annual average 5-min periods of elevated risk in hundreds and are normalized by the number of observations sampled within each region. Bars labeled with an H, a P, or an F correspond to occurrences of hoarfrost, frozen precipitation, or freezing fog, respectively. Background fill within each climate division corresponds to the total annual instances of icing formation risk, with darker shades corresponding to a larger number of icing risk occurrences. Climate divisions were combined in instances of data quantity limitations (in the northeast and southeast portions of the state).

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

Figure 7 displays the frequency analyses for each road ice formation mechanism, and each individual subfigure is discussed in its respective subsequent section. Although there is likely spatial variability in road ice occurrence because of local climatological and topographical factors, the limited temporal range (i.e., 15 yr) diminishes the possibility of capturing localized climatic trends. Data for ASOS locations across the entire of state of Oklahoma were therefore combined for the purposes of the frequency analysis.

Fig. 7.
Fig. 7.

Frequency analyses of (a) hoarfrost, (b) frozen precipitation, and (c) freezing fog for the entire state of Oklahoma. The normalized likelihood of hourly occurrence is color shaded in the left-bottom panel in each section. The annual and diurnal relative frequency distributions are depicted with bar charts in the top and bottom-right section of each panel, respectively. The solid (dashed) black lines on the color-shaded plots delineate the time of sunrise (sunset).

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

a. Hoarfrost

The analysis for hoarfrost events was limited to events that aligned with a 75% or greater likelihood of hoarfrost formation according to Hewson and Gait (1992). As previously discussed in section 4a, the majority of hoarfrost parameterizations implemented in RIM were also used by Hewson and Gait (1992) aside from the parameterizations relating to the influences of nocturnal duration and sublimation growth rate. The threshold hoarfrost risk associated with a ≥75% chance of hoarfrost formation was deduced by summing the mean occurrence rates of each parameter during hoarfrost events, as provided by Hewson and Gait (1992). If a parameter used by Hewson and Gait (1992) was not used in RIM, the associated mean occurrence rate was subtracted from the assumed 75% threshold occurrence rate value. This resulted in a 75% likelihood of occurrence threshold of four.

There is no current robust source of publicly available validation data for road-surface hoarfrost within the state of Oklahoma, which leads to the comparison of the completed frequency analysis with those of previous studies providing the best source of parameterization validation. As expected, the maximum probability of hoarfrost occurrence occurs immediately prior to sunrise (Fig. 7a). This likely results from the parameterizations of supersaturation, cloud cover, and wind speed being related to extended periods of radiational cooling (Hewson and Gait 1992; Hunt et al. 2007; Sass 1992). Radiational surface cooling further saturates the near-surface air given constant or rising surface moisture content, which increases the supersaturation of the air with respect to ice. Such radiational cooling also leads to separation of the near-surface boundary layer from the free atmosphere, which limits downward mixing of momentum, thereby reducing the near-surface wind speed (Wallace and Hobbs 2006). These results are supported by those of Hewson and Gait (1992) and Takle (1990).

The annual probability of hoarfrost occurrence is maximized during December and January. Further study is required to determine the causes of this maximum, which may be the result of 1) longer nights and the resultant longer periods of radiational cooling as suggested by Hewson and Gait (1992) and Takle (1990), or 2) a manifestation of climatologically favorable meteorological conditions not necessarily applicable to other regions. Meteorological variability may be influenced by a multitude of factors, including topography, location relative to the jet streams, and proximity to locations favorable for the generation of differing air masses (e.g., the Gulf of Mexico). A discussion of this meteorological variability is therefore tangential to this paper and is not discussed further.

b. Frozen precipitation

The frozen-precipitation frequency analysis coincides well with the findings of White et al. (2013), whereby a southeast-to-northwest gradient in the occurrence of frozen precipitation is observed. The relative maximum of frozen-precipitation frequency in central Oklahoma (Fig. 6) may be attributed to an enhanced probability of both snow and freezing rain occurring across the central portions of the state (White et al. 2013).

Although the relatively short temporal period of data available for analysis resulted in statistical dominance of widespread and long-lasting events, Fig. 7b appears to provide an adequate general overview of both yearly and daily temporal evolution of precipitation events given the mostly unimodal distributions. Frozen precipitation is most likely to occur in the overnight to morning hours with a frequency minimum in the late afternoon and evening prior to and just after sunset. This pattern is likely in response to the diurnal temperature cycle, whereby surface temperatures generally reach a minimum in the presunrise hours and a maximum in mid-to-late afternoon. A drastic increase in the occurrence of frozen precipitation exists in late November, and a similarly drastic decrease in frozen-precipitation occurrences exists in mid-to-late February. This bimodal distribution may be either the result of climatologically favorable periods for frozen precipitation or an artifact of the short period of record (15 yr).

c. Freezing fog

For the statewide analysis (Fig. 7c), hourly probabilities of freezing-fog occurrence are maximized during the nocturnal and early morning hours. A bimodal distribution in annual occurrences exists coincident with the late-fall and early-spring months, that is, periods of relatively high near-surface moisture content but cooler nocturnal temperatures. The bimodal distribution of freezing-fog events also correlates well with that of frozen-precipitation occurrences, suggesting that the increased frequency of precipitation events may, in turn, lead to an increased frequency of freezing-fog events. Precipitation may increase the likelihood of freezing fog via either evaporation that occurs during or immediately after the precipitation event or prolonged evaporation or sublimation of stagnant surface water.

A typological analysis of all fog types parameterized in RIM (Fig. 8) resulted in temporal trends similar to those depicted in Fig. 7c, but with typological frequency dependent upon climatological region. The parameterizations identified the formation mechanism of at least 89% of ASOS-specified fog events for all climatic regions. To test the sensitivity of the model to relative humidity, the freezing-fog parameterizations were applied to ASOS data for the years 2000–14 on a running 3-h temporal resolution (Fig. 9): that is, each individual observation was compared with the observation from 3 h prior to calculate the tendency terms used in the parameterizations and to determine if freezing fog had already formed during a prior observation. If the model flagged the initiation of a fog event, the subsequent observations at 3-h intervals were also flagged for freezing fog until the relative humidity fell below 88%. Using this method, which is identically used by the prognostic portion of RIM, the model correctly (incorrectly) asserts the presence of fog 70% (20%) of the time for instances when the relative humidity is greater than 88%. The skill of the model improves approximately linearly with increasing relative humidity.

Fig. 8.
Fig. 8.

As in Fig. 6, but for only freezing fog. Frequency analyses are given for each fog formation type for individual NOAA climate divisions, derived from prognostic fog-formation parameterizations. Background fill within each climate division corresponds to the total annual instances of fog formation, with darker shades corresponding to a larger number of fog formation occurrences. Climate divisions were combined in instances of data quantity limitations (in the northeast and southeast portions of the state).

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

Fig. 9.
Fig. 9.

Receiver operating characteristic (ROC) curves showing the sensitivity of the RIM freezing-fog parameterizations to changes in relative humidity. The individual ROC curves of the regions delineated in Fig. 8 are specified by their respective cardinal directions, while the weighted mean of all seven regions is labeled as “Mean.” Increasing circle size corresponds to increasing relative humidity. The smallest (largest) circle denotes instances of >88% (100%) relative humidity, and the intermediate circles denote increases in relative humidity of 2%. True (false) positive rate describes the rate at which the model asserts the presence of fog when fog does (does not) exist. Model skill increases (decreases) toward the upper left (bottom right) of the plot.

Citation: Journal of Applied Meteorology and Climatology 56, 7; 10.1175/JAMC-D-16-0199.1

Using the parameterizations of RIM, evaporation fog formation occurs a negligible proportion of times within Oklahoma and was therefore removed from the analysis. Therefore, while radiational fog events may have been prolonged by continued near-surface dew formation after sunrise (data not shown—confirmed via typological analysis), it appears the evaporation of nocturnally generated dew does not commonly induce significant fog formation following sunrise within Oklahoma. The evaporation fog parameterizations were left in the model, however, to ensure all types of fog events would be captured if RIM were to be implemented in regions that commonly experience such events.

7. Conclusions

Ice-related automobile crashes lead to billions of dollars in financial losses and thousands of lives lost each year (Pisano et al. 2008), but the United States has yet to implement a comprehensive road ice–forecasting model. However, road ice prediction models based on Road Weather Information Systems (RWIS) have been implemented in numerous nations throughout Europe, and, through retrospective analysis, multiple studies have developed meteorological parameterizations of road ice formation. The majority of the developed parameterizations emphasize hoarfrost formation, although numerous studies have also confirmed the risks associated with freezing fog and frozen precipitation.

The goal of this study and the resultant developed model, RIM, was to develop a diagnostic and prognostic model to assist in the prevention of road ice–related impacts on societal infrastructure. Although the United States does not have widespread RWIS infrastructure, the elaborate, national Automated Surface Observing System/Automated Weather Observing System (ASOS/AWOS) surface meteorological networks permit high-resolution diagnostic capabilities. The state of Oklahoma is further unique in that diagnostic data are available through the Oklahoma Mesonet, a mesoscale observational network that is supplementary to typical ASOS–AWOS stations. Prognostic data are available through the National Digital Forecast Database (NDFD)—an archive of forecast data output from NWS offices—which offers numerous variables necessary for parameterization of road ice formation. RIM synchronizes both prognostic and diagnostic data sources to provide a comprehensive risk system for the state of Oklahoma, with the potential for expansion to the entirety of the United States and any region with high-resolution surface observations and prognostic model output. RIM offers a prognostic spatial resolution of 2.5 km within the United States, with a temporal resolution of 1 h for the first 36 forecast hours and a temporal resolution of 3 h thereafter, with a total forecast range of 72 h. While the average spatial (temporal) resolution within Oklahoma is ~40 km (5 min), the diagnostic resolution of RIM is dependent on the surface data network availability within the region the model is implemented.

RIM uses a hierarchical structure to assign road ice formation risk. Parameterizations with numerically assigned risk were derived from previous studies that had quantitatively validated the applicability of the parameterizations to road icing risk. This led to an entirely numerical risk output for 1) all diagnostic icing mechanisms, 2) prognostic radiation-induced hoarfrost formation (Hewson and Gait 1992; Takle 1990; Karlsson 2001; Crevier and Delage 2001), and 3) prognostic radiation and evaporation fog formation. For road ice formation mechanisms that do not have specifically defined numerical risk output, conditional risks are output to communicate the relatively larger forecast uncertainty.

A frequency analysis was performed using the implemented diagnostic parameterizations to 1) attempt to qualify the validity of the implemented hoarfrost and freezing-fog parameterizations, and 2) quantify the frequency of meteorological conditions favorable for road ice formation within Oklahoma. The hoarfrost parameterizations captured a road icing risk similar to that captured by previous studies. The hoarfrost risk validation was limited in scope because of the lack of an available, substantial road ice validation database for the state of Oklahoma. However, the prognostic fog-formation parameterizations were validated using a 15-yr period of archived ASOS data. The fog typological analysis suggested over 90% of fog events would be captured by the implemented prognostic parameterizations. The model correctly asserts the presence of fog 70% of the time for instances when the relative humidity is greater than 88% and incorrectly asserts fog presence only 20% of the time under similar conditions. The skill of the fog portions of the model improves approximately linearly with increasing relative humidity.

Modifications should be made to RIM in the event that additional verification mechanisms become available. Additionally, an RWIS would supplement the implemented meteorological parameterizations and supply a source of road-surface temperature initialization. This would reduce the uncertainty resulting from parameterizing the road-surface temperature based on antecedent conditions. An RWIS would, in turn, limit necessary parameterizations and reduce the risk of false alarms. Admittedly, RIM is limited by the lack of available verification mechanisms for road ice formation and performs most effectively as a tool to assess the background risk of ice formation beyond the temperature of the roadway itself. However, through the indirect verification provided in this study, RIM may confidently be implemented as a robust option for road ice risk assessment based on background meteorological conditions and is applicable across the state of Oklahoma, the United States, and any region with similarly developed near-surface observations and prognostic model output.

Acknowledgments

Funding for this project was provided by ODOT SP&R Item 2249. We thank the three anonymous reviewers for their insightful comments.

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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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  • Fig. 1.

    Logical sequence for the initialization of the prognostic portion of RIM. Refer to the individually referenced figures for the hierarchical structure of the hoarfrost, freezing-fog, and frozen-precipitation parameterizations.

  • Fig. 2.

    As in Fig. 1, but for the diagnostic portion of RIM.

  • Fig. 3.

    Locations of ASOS stations (stars) and coupled Mesonet (circles) stations. Mesonet stations denoted by the filled circles were used for the frequency analysis conducted using the implemented parameterizations (section 6). The black lines denote the NOAA-designated climate divisions used for the frequency analysis within the current study.

  • Fig. 4.

    Hierarchical risk assessment for the prognostic freezing-fog parameterizations. Solid and dashed lines signify true and false responses, respectively, to the connected conditional statement (parallelograms). For each individual fog type (rectangles outlined by thick lines), the sum of the total arrows intersecting increased risk conclusions (ovals) corresponds to the total icing risk for that fog type. Note that the icing risk for each fog type is not transitive to other fog types, i.e., the icing risk of each fog type depends only on its individual hierarchical tree. Refer to Table 3 for more information.

  • Fig. 5.

    As in Fig. 4, but for diagnostic and prognostic hoarfrost and prognostic frozen-precipitation parameterizations. Refer to Tables 3 and 4 for more information.

  • Fig. 6.

    Frequency analyses for the three icing mechanisms for individual NOAA climate divisions. Occurrence rates are annual average 5-min periods of elevated risk in hundreds and are normalized by the number of observations sampled within each region. Bars labeled with an H, a P, or an F correspond to occurrences of hoarfrost, frozen precipitation, or freezing fog, respectively. Background fill within each climate division corresponds to the total annual instances of icing formation risk, with darker shades corresponding to a larger number of icing risk occurrences. Climate divisions were combined in instances of data quantity limitations (in the northeast and southeast portions of the state).

  • Fig. 7.

    Frequency analyses of (a) hoarfrost, (b) frozen precipitation, and (c) freezing fog for the entire state of Oklahoma. The normalized likelihood of hourly occurrence is color shaded in the left-bottom panel in each section. The annual and diurnal relative frequency distributions are depicted with bar charts in the top and bottom-right section of each panel, respectively. The solid (dashed) black lines on the color-shaded plots delineate the time of sunrise (sunset).

  • Fig. 8.

    As in Fig. 6, but for only freezing fog. Frequency analyses are given for each fog formation type for individual NOAA climate divisions, derived from prognostic fog-formation parameterizations. Background fill within each climate division corresponds to the total annual instances of fog formation, with darker shades corresponding to a larger number of fog formation occurrences. Climate divisions were combined in instances of data quantity limitations (in the northeast and southeast portions of the state).

  • Fig. 9.

    Receiver operating characteristic (ROC) curves showing the sensitivity of the RIM freezing-fog parameterizations to changes in relative humidity. The individual ROC curves of the regions delineated in Fig. 8 are specified by their respective cardinal directions, while the weighted mean of all seven regions is labeled as “Mean.” Increasing circle size corresponds to increasing relative humidity. The smallest (largest) circle denotes instances of >88% (100%) relative humidity, and the intermediate circles denote increases in relative humidity of 2%. True (false) positive rate describes the rate at which the model asserts the presence of fog when fog does (does not) exist. Model skill increases (decreases) toward the upper left (bottom right) of the plot.

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