Modelling of road surface temperature from a geographical parameter database. Part 2: Numerical

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1 Meteorol. Appl. 8, (2001) Modelling of road surface temperature from a geographical parameter database. Part 2: Numerical Lee Chapman, John E Thornes and Andrew V Bradley, Climate & Atmospheric Research Group, School of Geography and Environmental Sciences, University of Birmingham, Birmingham B15 2TT, UK A new ice prediction strategy is presented based on the numerical modelling of surveyed geographical parameters. This approach enables the thermal projection of road surface temperatures across the road network entirely by model predictions and without the need for thermal maps. The influence of eight geographical parameters (latitude, altitude, sky-view factor, screening, roughness length, road construction, traffic density and topography) is investigated by means of sensitivity analyses. The skyview factor is highlighted as the dominant control on road surface temperature, particularly at high levels of atmospheric stability. A numerical road weather model incorporating all eight parameters was run over 20 nights using forecast and retrospective meteorological data. The model has the ability to explain up to 72% of the variation in road surface temperature purely by thermally projecting surface temperature using geographical variables. Retrospective results produce an average r.m.s. error of 1 ºC which is comparable to existing UK road weather models. 1. Introduction Many countries around the world would benefit from research and investment into methods of predicting (and subsequently preventing) the occurrence of snow and ice on highways. The level of expenditure required in each country depends on the type of climate experienced. At one extreme is that of snowy environments (e.g. Japan and the cold continental interiors); at the opposite end of the spectrum is that of marginal winter environments where the winter air temperature commonly fluctuates around freezing point (e.g. the United Kingdom). Between these two extremes of climate there is a mix of snow and ice hazard as experienced in Scandinavia (Thornes, 2000). The full spectrum of climates is evident across North America. Here, 1.7 billion is spent annually on winter road maintenance approximately 40% of global spending (Boselly et al., 1993). The greatest potential for cost savings in winter maintenance lies in the accurate prediction of ice formation. In snowy environments, ice is insignificant and the winter maintenance budget focuses upon the clearing and melting of snow (approximately 1.1 billion per annum in Japan, which has the snowiest roads in the world). However, countries which are prone to icy roads can make significant annual savings by optimising salt usage. The marginal winter weather experienced in the UK makes for an interesting case study. Currently the UK spends in excess of 140 million on winter road maintenance each year (Cornford & Thornes, 1996), with salt corrosion causing a further 100 million of damage each year to vehicles and structures (Thornes, 2000). Environmental problems are also caused through excessive salt use, which damages groundwater supplies, soils and ecology (Dobson, 1991; Blomqvist, 1998). The high cost of salting means that winter maintenance engineers must decide whether to salt or not a decision which is particularly difficult on marginal nights when surface temperatures may or may not dip below the 0 ºC threshold. Unfortunately, ice is most slippery at 0 ºC (Moore, 1975), and thus an error of judgement on the engineers part can be lethal. Despite a run of mild winters, UK road accident figures directly attributable to snow and ice have steadily increased during the 1990s (Thornes, 1998). This suggests that even with continuing improvements in technology, engineers are still not getting it right, all of the time, and hence the continual need for improvement in ice prediction strategies Ice prediction systems The current approach used for ice prediction is built around RWISs (Road Weather Information Systems). These comprise of several components which are used to predict the variation in RST across a region. The accuracy of road weather forecasts obtained from forecast providers is monitored by automatic weather stations strategically placed on the highway network. These record and monitor meteorological parameters including RST, air temperature, precipitation, dewpoint, wind speed and wind direction. The exact 421

2 L Chapman, J E Thornes and A V Bradley positioning of the outstations varies from country to country. In the UK, they are located at sites where they will measure mesoclimatic variations and not local microclimates. However, it is more common in other countries to locate outstations at sites that are particularly prone to icy conditions (Bogren & Gustavsson, 1989). Data are then transferred from the outstation to a master station computer and combined with regional weather information in a numerical road weather prediction model (Parmenter & Thornes, 1986) Road weather prediction models Numerical road weather prediction models were first developed during the late 1970s and used either a zerodimensional energy balance, a one-dimensional heat conduction model or a neural network approach. Since then many numerical road weather models have been developed around the world (e.g. Thornes, 1984; Rayer, 1987; Shao, 1990; Sass, 1992; Fröhling, 1994; Jacobs & Raatz, 1996; Szymonski & Wojtach, 1996; Best, 1998; Heierli, 1998). All have the same aim of predicting RST and road conditions from a basic forecast of meteorological parameters (Thornes, 1991). In the UK, this is issued at midday in the form of a RST forecast curve from which an early decision is made by the engineers regarding the treating of the roads. Forecast curves are constantly updated throughout the day, often by nowcasting techniques where the forecast is forced by current meteorological data collected at outstations. At least three road weather models are in commercial use in the UK: the Met.Office model (Rayer, 1987), ICEBREAK (Shao 1990) and the PA WeatherCentre model. A retrospective comparison of the first two of these UK models and the Thornes (1984) model was carried out by Thornes & Shao (1991a). The results are shown in Table 1 and are expressed as standard deviation (error variance), r.m.s (root mean square of total error) and bias. Bias is the nature of the error and gives an indication of the reliability of the forecast (Thornes & Stephenson, 2001). To provide a safety net, a small negative bias is preferred, although an accurate model will have small values of standard deviation, r.m.s and bias (Thornes, 1989). Thornes & Shao (1991a) attributed most prediction error in the models to errors in the meteorological input, but also concluded that the ICEBREAK model was the most accurate. Model accuracy was also tested with respect to the start and duration of the freezing period, and ICEBREAK again proved the most accurate. Accuracy is crucial if costs are to be minimised four times more salt is required to melt snow and ice than to prevent its initial formation. Conversely, if salt is spread too soon, it may be dispersed by traffic and precipitation before it has had time to take effect (Thornes, 1991). Components of the Thornes (1984) ice prediction strategy were merged with the Met. Office model in 1986 to produce the OpenRoad service (Rayer, 1987). Improvements were made to this model by streamlining data input with a mesoscale model which was found to reduce bias (Astbury, 1996). Problems have been encountered owing to the coarse scale of the model, resulting in smaller topographical features being disregarded and grid-points of the mesoscale model not coinciding with sensor sites of the original model (Thornes & Shao, 1992). More recently, a site-specific forecast model has been developed which uses landuse data to estimate localised surface fluxes. The incorporation of this site-specific approach has improved road Table 1. Brief description of similarities between the ICEBREAK, Thornes and Met. Office models and summary statistics of model performance (Thornes & Shao, 1991a). 422 ICEBREAK Thornes Met.Office Basic equation Heat conduction Energy balance Heat conduction Road temperature profile Yes No Yes Energy balance Yes Yes Yes Longitude Yes Yes No Sky-view factor Yes No No Influence of traffic Yes No No Inputs T a,t d,w,c a,c t,r T a,t d,w,c a,c t,r T a,t d,w,c a,c t,c 1,R,P Outputs T s and wetness T s and wetness T s and wetness Method of discreterisation Control volume Finite difference Derivation of forecast Solving basic equation Searching for root of Solving basic equation by fully implicit scheme basic equation by iteration by explicit scheme Summary Statistics of Model Performance No. of hours Bias (ºC) Standard Deviation (ºC) r.m.s (ºC) Note: T a = air temperature, T d = dew point, W = wind speed, C a = total cloud amount, C t = dominant cloud type, R = rain period, T s = RST, P = pressure

3 Numerical modelling of RST from a geographical parameter database weather forecasts worldwide (Maisey et al., 2000). Similarly, ICEBREAK has undergone continuous development. It is now fully automated and can be used for three-hourly nowcasting. Tests of the model in several countries indicate that the refinements have further improved performance (Shao & Lister, 1996), though this is largely the result of the reduced forecast interval used for nowcasting. Further improvements have been made with the application of neural networks, resulting in reduced r.m.s values, particularly at geographically complicated sites (Shao, 1998) Spatial thermal projections Road weather models only produce RST forecasts for the outstation from which the meteorological data are obtained. The RWIS therefore requires a means of extrapolating the forecast throughout a road network. The original technique developed for this purpose is thermal mapping the systematic surveying of RST at a set resolution within a road network by using an infrared thermometer connected to a vehicle and measuring RST at a fixed spatial resolution. The extent of RST variation along a route is controlled by atmospheric stability, with the largest temperature difference being recorded in stable conditions (Thornes, 1991). Surveying is undertaken under a variety of synoptic weather conditions to ensure full coverage of different levels of atmospheric stability. The differentials are then presented as thermal maps in a geographical information system and combined with the daily forecast curves to complete the spatial prediction component of the RWIS. Empirical methods provide an alternative methodology to thermal mapping for extrapolation. Since the 1970s work has been ongoing to develop local climatological models for thermal projections between outstations in Sweden (Bogren et al., 1992; Gustavsson & Bogren, 1993). These models are now used commercially and demonstrate that variations in RST can be accurately explained by the influence of several geographical factors (e.g. Bogren & Gustavsson, 1991; Bogren et al., 2000a) and prevailing synoptic conditions (e.g. Gustavsson & Bogren, 1990; Gustavsson et al., 1998; Bogren et al., 2000b). Indeed, the importance of these parameters has been shown in a companion paper (Chapman et al., 2001a) where significant relationships were shown to exist between RST and geographical parameters, with up to 75% of variations in RST able to be explained by a simple statistical model. However, despite extensive empirical research into the role of how geographical parameters control RST, the current format of RWIS in the UK has remained largely untouched for almost a decade and the next generation of models is long overdue. It is proposed that this next generation will comprise dynamic numerical road weather models incorporating synoptic meteorological data and geographical parameters which are used to project RST internally throughout the road network. This paper aims to develop the foundations of a new winter maintenance strategy based upon the numerical modelling of geographical parameters, particularly the sky-view factor (ψ s ). 2. The numerical model 2.1. The Thornes (1984) model An improved road weather prediction model was developed from the Thornes (1984) model to predict local variations in RST over both time and space. The temporal component of the model was first developed by Myrup (1969) and later modified by Outcalt (1971). Based upon the zero-dimensional energy balance approach, the model simulates the surface temperature and energy transfer regime of a selected site by finding the unique equilibrium temperature which balances the flow of energy across the surface (Outcalt, 1971): (1 α)(q + q) + σt 4 sky σt 0 4 R N = LE + H + S (1) where α is surface albedo, Q is direct beam solar radiation, q is diffuse radiation, σ is the Boltzmann constant, T sky is the radiation temperature of the sky hemisphere, T 0 is the surface temperature, R N is net radiation, LE is the latent heat flux, H is the sensible heat flux and S is the heat flux to soil. A full expansion of equation 1 and the FORTRAN program listing is detailed in Outcalt (1971). Thornes (1984) streamlined the model to iteratively predict RST over a 24-hour period, based exclusively on the input of meteorological data at 12 noon. In doing so, Thornes took the opportunity to parameterise some of the constants in the original model. These included changes to the value used for surface albedo (α), development of a coefficient to approximate the impact of rainfall on the latent heat flux and the parameterisation of the impact of cloud upon the radiation budget (cloud top albedo, reflection from cloud sides and reduction of long-wave radiation loss from the surface; Wood, 1978). Finally, for operational purposes, changes were made to the nature of the input data including the use of air temperature and wind speed (measured at heights of 2 m and 20 m respectively), and the use of measured sub-surface temperatures in preference to model-generated temperatures. The scientific value of these changes is assessed in Parmenter & Thornes (1986) where the revised model showed significant forecasting ability. Bradley et al. (2001b) later developed a spatial component to this model to model the impact of the West Midlands surface heat island on RST. Geographical parameters were varied at a 1 km 2 resolution with respect to a landuse classification from a Landsat image. Validation of the model showed that 84% of the varia- 423

4 L Chapman, J E Thornes and A V Bradley tion in RST could be explained at outstations, though results were affected by a positive bias a result of the coarse resolution used. The next section outlines how a high resolution, site-specific spatial component was developed for the original Thornes (1984) model Spatial projection with geographical parameters A summary of the inputs to the new model are shown in Table 2. Meteorological inputs are the same as those used in the Thornes (1984) model, but to enable spatial projections, information regarding geographical parameters is also required. Whereas the original model was designed to be interpolated across a road network by means of thermal maps, this new model is selfcontained and projects RST entirely by means of a geographical parameter database (GPD). The database comprises several geographical parameters; latitude, longitude and altitude (accurately measured at a 20 m resolution with a global positioning system), an empirical cold air pooling index calculated by differentiating altitude data, ψ s and screening calculated from digital fish-eye imagery, and manually determined ordinal classifications of road type and landuse. A full overview of the surveying, development and accuracy of the GPD used in the model is described in more detail in Chapman et al. (2001a). The inclusion of a GPD into a numerical road weather model effectively enables a forecast curve to be produced for every location surveyed in the GPD; in effect, the model is run for each site. The model output is a time/space RST matrix of resolution 20 minutes/20 metres. The output of RST in this format is very dynamic as it enables RST to be displayed for any particular site at any particular time. However, the RST matrix is most powerful when appended with latitude and longitude data, which then allows for the plotting of RST data in a geographical information system. Figure 1 shows hourly thermal projections for the study route shown in Figure 2. RST falls below zero first on the minor roads of rural Worcestershire around 2200h and these ultimately remain the coldest section of the route throughout the night. The city centre remains well above freezing throughout the night whereas RSTs on the M5 motorway are marginal, fluctuating around freezing point between 0300h and dawn. Such a detailed knowledge of cooling rates over a large area is helpful to the winter maintenance engineer, providing detailed information on the optimum time to treat various sections of the road network. Optimisation of salting routes is currently difficult with thermal maps as these provide just a snapshot of forecast minimum temperatures Treatment of geographical parameters in the model Many of the variables are simply used directly from the GPD as parameters in standard physical equations. However, the incorporation of other variables can be more complicated, requiring further assumptions and parameterisation per iteration/site. All the parameters used were measured at a 20 m resolution. (a) Latitude The main impact of latitude is its influence in the laws of radiation geometry and is thus a large-scale control on quantities of incoming solar radiation (Cornford & Thornes, 1996; Thornes, 1991). Latitude is simply read in from the GPD and used to calculate variations in incoming short-wave radiation with respect to the standard laws of radiation geometry (e.g. Oke, 1992). (b) Altitude GPD altitude values are corrected relatively with respect to the height of the forecast outstation before being used to project RST along the survey route in line with the environmental lapse rate. The environmental lapse rate averages around 6.5 ºC.1000 m 1 but is dynamic and frequently changes with respect to atmospheric stability (Tabony, 1985; Thornes, 1991; Oke, 1992). As a consequence, the environmental lapse rate Table 2. Summary of inputs to the numerical model. Temporal data Meteorological data Geographical data Pre-coded constants Angle of declination RST at noon Latitude Thermal conductivity of asphalt Radius vector Air temperature a Longitude Thermal conductivity of concrete Date Dew point a Altitude Thermal conductivity of soil Wind speed a Topographical index Thermal diffusivity of asphalt Rainfall a Sky-view factor Thermal diffusivity of concrete Cloud cover b Screening matrix Thermal diffusivity of soil Cloud type b Landuse Road damping depth Road classification a Nine values at 12:00, 15:00, 18:00, 21:00, :00:00, 03:00, 06:00, 09:00, 12:00. b Eight values averaged over the time periods 12:00 15:00, 15:00 18:00, 18:00 21:00, 21:00 00:00, 00:00 03:00, 03:00 06:00, 06:00 09:00, 09:00 12:

5 Numerical modelling of RST from a geographical parameter database Figure 1. One-hourly time slices of numerically predicted RST along a study route (shown in Figure 2). was parameterised in the model as per Pasquill-Gifford stability classes (Table 3). This was achieved by consultation of upper air data to determine typical values per stability class. (Note that when a temperature inversion was present, a lapse rate of 0 ºC.1000 m -1 was assumed owing to the simulation of temperature inversions in the model by an alternative methodology.) (c) Topography During stable conditions, variations in the form and size of valleys can lead to large variations in air temperature and RST across the mesoscale landscape (Bogren & Gustavsson, 1991; Thompson, 1986; Tabony, 1985; Keen, 1968). This is accounted for in the model by means of an index of surface temperature bias by cold air pooling (CAPI), which is explained in detail in the companion paper (Chapman et al., 2001a). This bias is taken into account at locations in valley bottoms (beneath the thermal belt) between sunset and sunrise on stable nights where it is simply subtracted from the forecasted RST at that site. The strength of the index is exponentially reduced on less stable nights (Table 3) in line with changes in wind-speed and cloud cover (Bogren et al., 2000b). (d) Sky-view factors ψ s is a dimensionless parameterisation of the quantity of visible sky at a location. Represented as a value 425

6 L Chapman, J E Thornes and A V Bradley (e) Screening The impact of screening on RST has been well studied statistically (Gustavsson & Bogren, 1993; Bogren et al., 2000a) and it is anticipated that the use of numerical modelling will enable this parameter to be studied in more detail. However, for this to be achieved it is first necessary to incorporate a measure of screening into the GPD. A simple parameterisation such as ψ s is insufficient to describe the effect of surface geometry on the quantities of incoming radiation at locations with an obstructed sky hemisphere. Instead, the relationship between each individual screening object and the solar beam is required (Bogren, 1991). Figure 2. The study route starts and finishes at the University of Birmingham and passes anticlockwise through the city centre, then through the south-west suburbs of Birmingham and into the north Worcestershire countryside. Major changes in landuse and road type are also marked upon the map. between zero and one, ψ s will approach unity in perfectly flat and open terrain, whereas locations with obstructions such as buildings and trees will cause ψ s to become proportionally less (Oke, 1992; Bradley et al., 2001a). The replacement of a section of the cold sky hemisphere with a warmer surface (Oke et al., 1991) results in increased nocturnal air and surface temperatures at locations with low y s (Bärring et al., 1985; Eliasson, 1996; Postgård & Nunez, 2000). The model accounts for this effect by using ψ s as an extra coefficient on black body emission in the Stefan Boltzmann equation: flux = εσψ s T 4 0 (2) where ε is emissivity (held constant throughout this study at 0.95). ψ s is calculated using the methodology outlined in Chapman et al. (2001b) and are accurate to within ±0.01. Chapman et al. (2001b) discuss a method of rapidly determining the impact of screening at a location throughout the day using the same fish-eye image from which ψ s is derived for the GPD. The image is orientated to the north and divided into 5 segments of which the radius of intrusion (r) of building and trees into the photo is measured (Figure 3a). This process is fully automated and generates 72 values which are appended to the GPD. The radius of intrusion is then converted into the building angle (ζ ) by using equation (3) developed by Steyn (1980): π ζ = r 2r 0 Hence, for any particular azimuth, ζ can be compared with the solar zenith angle (Z) to determine whether a location is receiving direct beam radiation or not at any particular time (Figures 3b & 3c). Once the distinction has been made of the nature of radiation received at the surface, the energy balance (1) is modified appropriately for each model iteration. As the original model splits the incoming solar radiation into direct and diffuse components, the direct component of the model Q can be set to zero if it can be determined that for a certain azimuth, the location is in shade. This method was tested by Chapman et al. (2001b) and was shown to be highly accurate and comparable to other techniques. (3) Table 3 Parameterisation of the environmental lapse rate and topographical bias with respect to Pasquill Gifford stability classes. Class Wind speed (m s 1 ) Cloud cover (octas) Lapse rate Topography (ºC.1000m 1 ) D 5> <4/ /8 9 N/A E 3 5 <4/ /8 6 CAPI/4 F 2 3 <4/8 3 CAPI/2 G <2 N/A 0 CAPI 426

7 Numerical modelling of RST from a geographical parameter database Figure 3. (a) Measurement of r on a fish-eye image. This is repeated for 72 5-degree increments around the image, before being converted into the building angle ζ which is a function of the relative size and distance to the intrusion. This is then compared to the solar zenith Z to determine the nature of incoming radiation. (b) When Z>ζ then incoming radiation will be in the form of direct and diffuse radiation, or (c) just diffuse when the solar beam is blocked. (f) Road construction profiles Variations in the thermal properties of materials used in road construction will result in subtle variations in RST within a road network. The warmest sections of road are often motorways and A-roads owing to their deeper construction (Thornes, 1991; Chapman et al., 2001a). Unfortunately, good quality road construction data is realistically only available from highway core samples. These are expensive, site specific and ultimately impractical sources of data, and thus numerous assumptions have to be made in models. The ordinal classification used in the GPD is basic but objective and numerical modelling enables this simple classification to be developed further. The model assumes a flexible pavement with a constant damping depth of 72 cm split into five calculation zones. However, variations in construction of this 72 cm profile with respect to materials and thermal properties are parameterised in the model with respect to the ordinal road classification. The general assumption here is that the higher a road s classification the greater the proportion of its profile that will be represented by asphalt and concrete at the expense of the soil sub-base (Table 4). Approximations of road construction per class are difficult as no standard design procedure exists. However, consultation of the British road procedure illustrates that the assumptions made are appropriate (O Flaherty, 1988) Table 4. Variations in the materials and thermal properties of the ordinal classified road construction profiles used in the model (adapted from Thornes (1984) and O Flaherty (1988)). Depth (cm) Motorway (1) A-Road (2) B-Road (3) C-Road (4) Materials Asphalt Asphalt Asphalt Asphalt Asphalt Asphalt Asphalt Concrete 9 18 Asphalt Asphalt Concrete Concrete Concrete Concrete Concrete Concrete Concrete 80% Concrete 50% Concrete Subgrade/Soil 20% Subgrade/Soil 50% Subgrade/Soil Over 72cm Subgrade/Soil Subgrade/Soil Subgrade/Soil Subgrade/Soil Average thermal conductivity cal cm 1 sec 1 C cal cm 1 sec 1 C cal cm 1 sec -1 C cal cm 1 sec -1 C Note: The thermal diffusivity of asphalt, concrete and soil is cm 2 sec 1, cm 2 sec 1 and cm 2 sec 1 respectively. 427

8 L Chapman, J E Thornes and A V Bradley Depending on the road classification, the model is thus run with different values for thermal conductivity and for diffusivity encountered within the profile to calculate the temperature for each zone. Values for thermal conductivity and diffusivity are the same as used by Thornes (1984) and are also shown in Table 4. Thermal properties for soil are more difficult to parameterise as values will vary with soil type and wetness. For simplicity, the soil beneath a road was assumed to consist of dry organic matter. The information is then entered into a heat conduction equation in the original model, thus allowing the temperature to be forecast at the five depths. (g) Impact of Traffic Theoretical simulation of the influence of traffic on RST is difficult (Shao, 1990). However, as traffic has been shown to account for up to a 2 C difference between slow and fast lanes on a motorway (Parmenter & Thornes, 1986), its inclusion as a parameter is essential. A general traffic algorithm is used in the model which considers atmospheric stability along with both ordinal road and landuse classifications. The three key effects of traffic outlined by Thornes (1991) are treated in the model as follows: 1. The increased input of anthropogenic heat causes differential heating of the road. This is accounted for in the model by introducing a slight bias a (Table 5) depending on landuse and road classifications. City centres and motorways are assumed to be the most heavily used sections of road. There is then a logarithmic decrease in bias through urban areas, suburbia and finally rural areas. 2. Cars also shadow long-wave radiation loss from the road surface, and this has been incorporated into the radiation budget as a coefficient on outgoing radiation similar to the ψ s. This is parameterised in the model as a shadow co-efficient b (Table 5), which is incorporated into equation Finally, cars also cause increased turbulence. This is dealt with simply by increasing wind speed by 2 ms -1 in the energy balance. It is accepted that the treatment of traffic in the model is simplistic and could be improved by considering traffic densities and RST. However, accurate traffic density data are not freely available, and determining the impact of traffic on RST is difficult. On the plus side, the impact of this algorithm produces local RST differences of around 2 C on stable nights comparable to the results of traffic impact found by Parmenter & Thornes (1986) and Shao (1990). (h) Landuse One example of the impact of landuse has been demonstrated by the parameterisation of traffic densities. This enables a measure of anthropogenic heat into the model. Oke (1992) identifies several other parameters which cause rural/urban temperature differences. Canyon geometry was isolated as the main cause of the urban heat island and is adequately covered in the model by means of the ψ s and screening. However, Oke (1981) identifies a further feature of canyon geometry which contributes to the urban heat island phenomena the impact on wind. Turbulent heat transfer can be reduced in sheltered areas and this effect needs to be incorporated into the model. This is achieved by varying roughness length with respect to the ordinal landuse classification. Roughness length (Z 0 ) is a measure of aerodynamic roughness which controls the height which the logarithmic wind profile extrapolates to zero (Oke, 1992). Z 0 is a function of shape, density and height of surface elements, and values can vary considerably from location to location. It is not unusual to find Z 0 approaching 8 m in the centre of large cities compared to just 0.5 m for suburbia (Barry & Chorley, 1992). Owing to the often complicated interaction of surface elements, Z 0 is notoriously difficult to calculate, causing large variations in estimates in the literature. Values were based on the landuse classification and taken from a table of Z 0 values assimilated from the scientific literature (e.g. Barry & Chorley, 1992; Linacre, 1992; Weiranga, 1993; Theurer et al., 1993). The values per landuse class are summarised in Table 5 and have been rounded up to follow an exponential decay curve. One exception to this rule are the rural motorways which have been placed at a value of 50 cm instead of the original 15 cm value proposed by Thornes (1984). This is because the original value was considered too small to represent a heavily used road Table 5. Values of parameters used in the model in relation to the ordinal classification of landuse and roadtype. (a = traffic bias (ºC), b = traffic coefficient, Z 0 = roughness length (m)) 428 Motorway (1) A-Road (2) B-Road (3) C-Road (4) a b Z 0 a b Z 0 a b Z 0 a b Z 0 City centre (1) Urban (2) Suburban(3) Rural (4)

9 which passes trees, pylons and cuttings. It is accepted that the use of such values is a major oversimplification as they do not take into account variations in static building elements within classes, wind direction, or dynamic variations of traffic elements. 3. Sensitivity analyses 3.1. Model sensitivity to individual geographical parameters The same methodology as Thornes & Shao (1991b) was used to determine the impact of meteorological parameters on road weather forecast curves so that the impact of varying geographical parameters could be tested in the numerical model. A series of sensitivity analyses were conducted assuming stable conditions where individually all but one of the eight geographical parameters was held constant. The impact of varying the solar input was also tested by running the sensitivity tests twice: first, on the shortest day (21 December 1999), and second on a day in late winter/early spring (21 March 2000) (Figure 4). Consideration of these sensitivity tests enables the effect of geographical parameters to be categorised into three distinct groups: (a) Latitude and screening These parameters control the amount of incoming solar radiation and create a lag/lead effect which can be detected well into the night. This subsequently controls the time at which RST falls below freezing. As would be expected, latitude and screening cause the largest variation of RST during the day, but have little control on the overall minimum nocturnal temperature as radiative cooling processes begin to dominate after sunset. The strength of the lag/lead effect is dependent on Julian day with respect to quantities of incoming solar and gradually reduces throughout the night, in accord with the studies of Bogren et al. (2000a). Numerical modelling of RST from a geographical parameter database (c) Landuse and road type These are the most complicated of the parameters under study as they affect RST differently during the day than at night. This has implications regarding the impact of the parameters for different Julian days as well as consequences for individual lag/lead effects. Canyon geometry results in urban areas tending to remain cooler in the day but retaining their heat more throughout the night (although these differences are sensitive to the amount of incoming solar radiation). Different classifications of road remain at similar temperatures throughout the day, but cool at different rates after sunset when subtle differences in their construction become apparent. The impact of traffic further ensures that major roads retain their heat more, whereas variations in thermal properties mean that minor roads will cool quicker (Thornes & Shao, 1991b) Model sensitivity due to geographical parameters and atmospheric stability A GPD (with added screening data) was created for the survey route shown in Figure 2, and was also surveyed by thermal mapping 20 times over the winter season 1999/2000. RST data from each thermal mapping survey were appended into the GPD by means of co-registering latitude and longitude values and used as validation data. Appending accuracy was improved by setting a maximum co-registration threshold of ±10 m, above which data were omitted from further analysis. Finally, the standard deviation of RST was calculated for each thermal mapping survey for use as a proxy for atmospheric stability. The relationship between the eight geographical parameters and residual RST was analysed for continuous levels of atmospheric stability. This was achieved by plotting individual Pearson correlation coefficients against the standard deviation of RST for each of the 20 thermal mapping surveys (Figure 5). (b) Altitude and sky-view factor The impact of these geographical parameters remains constant throughout the day creating consistent differences in temperature throughout the 24-hour period. The model is particularly sensitive to changes in ψ s, with differences of 5 C between ψ s of 1.0 and 0.6 in late winter/early spring. Sensitivity increases owing to larger potential surface temperature differences on account of the increased levels of incoming short-wave radiation. The magnitude of the model sensitivity is comparable with other ψ s studies (e.g. Bärring et al., 1985; Eliasson, 1996). The impact of altitude is constant across both days as it is controlled by stability and not incoming radiation. With increasing atmospheric stability, ψ s and roughness length (landuse) are the dominant parameters for the prediction of RST. The influence of ψ s on RST has long been accepted as the major cause of nocturnal RST variation due to the dominance of radiative transfer processes after sunset. However, care must be taken when making inferences about the importance of Z 0 as a parameter. As values for Z 0 are assigned to ordinal landuse categories, these categories will also be representative of any variation in canyon geometry and the thermal properties of materials associated with urbanisation. Hence, it is unlikely that roughness length in itself can account for the variation in RST as suggested in Figure 4. However, the importance of including Z 0 in the model is shown by the two distinct relationships evident within the Z 0 analysis. A negative correlation between roughness and RST indicates high wind speeds, which results in an urban cold island effect. 429

10 L Chapman, J E Thornes and A V Bradley Figure 4. Sensitivity tests showing the model outputs to changes in geographical parameters. 1 = City Centre, 2 = Urban, 3 = Suburban, 4 = Rural. This causes Birmingham city centre to have the lowest RST on the study route. In reality, this is not the case and hence the negative relationship on windy nights. The impact of screening and road construction are also dominant at higher levels of atmospheric stability, the effects of which could not be fully determined by statistical modelling in Chapman et al. (2001a). The correlation between screening and RST is negative owing to 430 screened areas in the day also being likely to have a low ψ s. This means that cooling rates are less defined at these locations making them warmer at night. Conversely, exposed areas receive more direct radiation in the day but will cool quickly after sunset. The effects of topography are small due to the few locations affected, but the impact does increase with stability as would be expected due to the increased occur-

11 Numerical modelling of RST from a geographical parameter database Figure 5. The influence of eight geographical parameters for RST prediction at different levels of atmospheric stability. (The standard deviation of each thermal mapping run is used as a proxy for stability.) rence of temperature inversions under clear and calm conditions. Similarly, the impact of traffic increases in stable conditions as a result of cars shading radiation loss from the road surface in heavily used areas. At lower levels of atmospheric stability, when radiative cooling processes are less influential, altitude becomes the dominant parameter in controlling RST at the expense of other parameters. Finally, the impacts of latitude are minor, as would be expected at this scale. These results are largely in agreement with the statistical relationships derived in the companion paper (Chapman et al., 2001a). However, due to the problems of multi-colinearity in the statistical model, these results are considered more representative owing to a greater confidence in the independent nature of these relationships. 431

12 L Chapman, J E Thornes and A V Bradley 4. Model performance 4.1 Meteorological data Road weather forecasts were obtained for the Sedgley outstation (10 km west of the survey route),which also provided the initial daytime measurement of RST in addition to retrospective measurements of air temperature, dew-point, precipitation and cloud. However, retrospective wind speed, cloud cover and cloud height measurements are not reliable/available from UK RWIS outstations and have had to be taken from Coleshill automatic weather station run by the UK Met. Office (15 km east of the survey route). Wind speed data required conversion from knots and was logarithmically corrected to a height of 20 m before input into the model. Finally, a simple cloud classification procedure (HMSO, 1982) was used to allocate cloud height to one of the three classes: (under 60 m = low(1); m = medium(2); over 200 m = high(3)). Ideally, the weather data should be acquired from a site located on the study route. This was not possible in this study and the sites were chosen for analysis on account of their close proximity. The Sedgley outstation was chosen for analysis as it was the only forecast site which could provide a full forecast archive for the winter season Actual versus predicted RST The model was run twice using forecast and retrospective meteorological data for each of the 20 thermal mapping surveys conducted around the study route, with the predictive ability of the model being tested with RST validation data acquired from each thermal mapping survey. The time and position of each thermal mapping datapoint were compared with the model output for the same time and location, achieved by matching GPS values of latitude and longitude between the thermal mapping survey and the GPD (see section 3.2). Summary statistics were then calculated relating to the model performance and are summarised in Table 6. A large range in model explanation can be seen; r forecast = 0.69 to 0.84 (average 61% explanation) and r retrospective = 0.69 to 0.85 (average 64% explanation). The performance of the model in predicting trends in RST around the route is considered to be good, and indeed the other statistics achieved are equally promising. Average bias around the route is just 0.19 ºC, standard deviation of bias is 0.70 ºC and r.m.s is 1.00 ºC which is comparable to the level of performance achieved by ICEBREAK in the study by Thornes & Shao (1991a) shown in Table 1. This study was based on model performance at the actual forecast site, and it is very encouraging to obtain results similar to those of a numerical model which projects RSTs away from the forecast site. The possibility that the predictive ability of the model will vary at different levels of atmospheric stability was tested by plotting the standard deviation of the thermal mapping survey against the retrospective summary statistics shown in Table 6. The results are shown in Figure 6 and indicate some shortcomings in model performance at different levels of stability. Overall, the predictive ability of the model was greatest at interme- Table 6. Summary table of the predictive ability of the numerical model for 20 nights forecast and retrospective data (bias, SD and r.m.s in ºC) 432 Forecast results Retrospective results Date n SD r R 2 bias SD r.m.s r R 2 bias SD r.m.s Dec Dec Dec Dec Dec Dec Dec Jan Jan Feb Feb Feb Feb Feb Feb Feb Mar Mar Mar Mar Averaged Values

13 Numerical modelling of RST from a geographical parameter database Figure 6. Model performance quantified in correlation coefficients, bias, standard deviation of bias and r.m.s at different levels of atmospheric stability. diate levels. A fall in model accuracy at high levels of atmospheric stability could be attributed to the oversimplification of topography as an index whereas a decrease in model accuracy in unstable conditions could be a result of the parameterisation of variables into rigid deterministic stability classes. Overall, it is anticipated that improved consideration of topography and altitude is the key step in increasing model explanation. It is hoped that a digital terrain model will eventually improve this situation. Although good results have been achieved using thermal mapping data for validation, it is important to realise that this method of validation is not ideal. The repeatability of thermal mapping is often brought into question due to the technique itself being subject to a number of systematic and random errors, e.g. problems with varying vehicle radiation, the changing of lanes due to slow moving traffic (shown by variations in n in Table 6), varying location of temperature reading and atmospheric absorption and attenuation (Thornes, 1991; Gustavsson, 1999). In fact, correlations of the 20 thermal mapping runs in similar stability classes around the study route yield typical linear correlations, r, of between 0.80 and 0.90 (a value which in theory acts as an upper level for model performance). Such relatively low correlations between surveys could also be a consequence of errors caused by the difficulties in achieving an exact co-registration between the GPD and thermal mapping datapoints; it is highly unlikely that the exact same point source will be sampled during two mobile surveys. Unfortunately, RST is highly variable over even a small scale and a slight misalignment by a couple of metres could prove to be a source of considerable error. Further problems are caused by the model requiring testing at a continuous range of atmospheric stability and not just in predefined deterministic stability classes (Shao, 2000). Surveys were sometimes conducted at times when a thermal mapping survey would not normally be carried out, e.g. during light precipitation or changeable weather conditions. The latter is particularly problematic as lag effects exist between the change in weather condition and road surface condition (Wood & Clark, 1999; Shao, 2000; Postgård & Lindqvist, 2001). In these situations, the accuracy of the model is particularly dependent upon the quality of the forecast. The magnitude of the calculated values for bias, r.m.s and standard deviation of bias all increase in line with atmospheric stability (Figure 5). This appears to indicate that although the model is less accurate at low levels of stability, the predictions are more precise. The greater potential variation in RST at higher levels of stability also provides more margin for error, which accounts for the increase in values in line with standard deviation of surveys. Indeed, minor forecast errors will significantly affect the precision of the model. If a forecast is too warm (i.e. skies clear later than expected) this will be reflected in the bias and r.m.s values (e.g. survey 8). The opposite is true if the forecast is too cold (e.g. 433

14 L Chapman, J E Thornes and A V Bradley survey 9). Interestingly, the model demonstrates a slight negative bias at low levels of atmospheric stability and a slight positive bias in more stable conditions. This is thought to be a consequence of advection not being incorporated into the model. In reality, variations in RST between neighbouring locations will not be as distinct as those predicted as heat transfer processes will to some extent, smooth and dampen minor differences. Wind and cloud are notoriously variable, both spatially and temporally, making them hard to forecast and are a major source of error in all RWIS. As these two meteorological parameters form the main criteria for defining atmospheric stability, they are ultimately the most important variables in the model (Thornes & Shao, 1991b); an incorrect forecast of cloud cover will severely affect the quality of thermal projections and ultimately the models predictive ability. This is a common problem in any road ice prediction model and is why models are further tested using retrospective forecast data. However, even then meteorological data are taken from a single site which may not be representative of the survey route as a whole. Hence, research needs to be conducted in improving forecast accuracy. It is anticipated that this could be achieved by forecasting for the entire route using a mesoscale model such as RAMS (Regional Atmospheric Modelling System). 5. Conclusions A new ice prediction strategy has been outlined which models RST by the systematic surveying and numerical modelling of geographical parameters along a selected route. Although the numerical model presented is considered basic due to its largely zero-dimensional operation, it has shown that up to 72% of the variation in RST around a survey route can be achieved by the numerical modelling of geographical parameters (subject to atmospheric stability). Although this result is marginally lower than the 75% explanation achieved from statistical modelling by Chapman et al. (2001a), the method is far more dynamic and potentially suitable for forecast purposes. It is anticipated that greater explanation in RST variation could be achieved by the use of a mesoscale model such as RAMS to provide a dynamic forecast solution. Surveying improvements could also lead to improved data quality in the GPD, for example the use of a continuous spectrum of landuse, road construction and traffic density statistics. In particular, a digital terrain model, which can accurately survey topography in more dimensions, would be advantageous, as would be the inclusion of other parameters such as distance from water sources and the location of bridges. The testing of other survey routes is also required. The differences in RST encountered on the survey route are very 434 marked (with a range of up to 12 C per survey), and so testing on the scale of smaller local authority salting routes is required. Despite these criticisms, the outlined technique does allow for a rapid and dynamic appraisal of variations in RST around a selected route. These can then be used in a geographical information system to create a fast, costeffective, user-friendly road weather forecast. It is hoped that with further research the dynamic nature of this approach will eventually eliminate the need for forecast thermal maps: RST will be successfully modelled for any time of the night at a wider range of atmospheric stability than current thermal mapping techniques. References Astbury, A. (1996) Use of a high resolution mesoscale model to prepare site specific road temperature. Proceedings of the 6th International Road Weather Conference, Birmingham, April 1996, SIRWEC. pp Bärring, L., Mattsson, J. O. & Lindqvist, S. (1985) Canyon geometry, street temperatures and urban heat islands in Malmö, Sweden. J. Climatol. 5: Barry, R. G. & Chorley, R. J. (1992) Atmosphere, Weather & Climate. Routledge. 6th edition. Best, M. J. (1998) A model to predict surface temperatures. Boundary Layer Meteorol. 88: Blomqvist, G. (1998) Impact of de-icing salt on roadside vegetation a literature review. Swedish National Road and Transport Research Institute, 427A. Bogren, J. (1991) Screening effects on road surface temperature and road slipperiness. Theoretical Appl. Climatol. 43: Bogren, J. & Gustavsson, T. (1989) Modelling of local climate for prediction of road slipperiness. Phys. Geog. 10: Bogren, J. & Gustavsson, T. (1991) Nocturnal air and road surface temperature variations in complex terrain. Int. J. Climatol. 11: Bogren, J., Gustavsson, T., & Lindqvist, S. (1992) A description of a local climatological model used to predict temperature variations along stretches of road. Meteorol. Mag. 121: Bogren, J., Gustavsson, T., Karlsson, M. & Postgård, U. (2000a) The impact of screening on road surface temperature. Meteorol. Applic. 7: Bogren, J., Gustavsson, T. & Postgård, U. (2000b) Temperature differences in relation to weather parameters. Int. J. Climatol. 20: Boselly, S. E., Doore, G. S., Thornes, J. E., Ulbery, C. & Einst, D. D. (1993) Road Weather Information Systems. Volume 1: Research report. Washington DC, USA. Bradley, A. V., Thornes, J. E. & Chapman, L. (2001a) Variation and prediction of urban canyon geometry from sky-view factor transects. Atmos. Science Letters pp 1 11 doi: /asle Bradley, A. V., Thornes, J. E., Chapman, L., Unwin, D. & Roy, M. (2001b) Modelling spatial and temporal road thermal climatology in rural and urban areas using a GIS. Climate Research (in press). Chapman, L., Thornes, J. E., Bradley, A. V. (2001a) Statistical