Modelling of road surface temperature from a geographical parameter database. Part 1: Statistical

Transcription

1 Meteorol. Appl. 8, (2001) Modelling of road surface temperature from a geographical parameter database. Part 1: Statistical 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 The variation of road surface temperature across a road network is influenced regionally by meteorological parameters and locally by geographical parameters. A fast and reliable technique is described which allows the continuous collection of high resolution, geographical data including the sky-view factor which is suitable for use in road climate modelling studies. Then, by use of regression analysis, the relative importance of five geographical parameters (altitude, topography, sky-view factor, landuse and road construction) is assessed with respect to road surface temperature and atmospheric stability. Results show that sky-view factors dominate surface temperatures at high atmospheric stability whereas altitude becomes increasingly important as stability decreases. Finally, a statistical road surface temperature model is discussed with the ability to explain up to 75% of the variation of residual road surface temperatures in the study area entirely by the interaction of geographical parameters. 1. Introduction 1.1. Road weather information systems Road surface temperature (RST) is influenced by numerous interacting parameters, which can produce a range of temperature in excess of 10 C at any one time across a road network (Shao et al., 1996). The result is that on marginal nights, while some stretches of road fall below freezing, the majority of the road network may remain above (Shao et al., 1997). Each road network is subject to a regional climate in addition to a large number of microclimates created as a direct consequence of the parameters outlined in Table 1. It is the purpose of a road weather information system to assimilate data from these parameters in order to develop a picture of how RST will vary across a road network in order to predict when and where freezing conditions will occur. Meteorological parameters are monitored by means of strategically based automatic weather stations on the highway network. However, as there are currently only 375 forecast sites for 55,000 km of principal roads in the UK, it is necessary for highway authorities to interpolate the impact of geographical parameters between sites before deciding whether the roads need to be treated or not. The existing technique used for interpolation is thermal mapping. Pioneered during the late 1970s, thermal mapping quantifies the spatial variations of nocturnal RST along a road network (Thornes, 1991). Data are displayed graphically as thermal fingerprints which represent the pattern of residual temperature variations along a set route on a given night (Shao et al., 1996). The amplitude of the thermal fingerprint is dependent upon weather conditions encountered the day preceding and during the survey and is greatest during times of high atmospheric stability. Fingerprint amplitude then gradually decreases in line with stability and is quantified by Pasquill-Gifford stability classes, which consider average wind speeds and cloud cover over the 12-hour period preceding the mapping survey (Table 2). With the exception of extreme nights where cold air advection is evident, general temperature trends remain similar, with the same locations being relatively colder due to systematic variation in geographical parameters. It is anticipated that successful modelling of the relationship between RST and basic geographical parameters per stability class could lead to the replacement of thermal mapping projections with geographical parameter surveys Geographical parameters Thornes & Shao (1991b) tested the sensitivity of individual meteorological parameters in a road weather information system by using a range of input values while the other parameters were held constant. Although prediction errors were mostly attributed to incorrect forecasts of cloud cover, air temperature was the most influential parameter controlling RST and is to be expected as air and surface temperature are closely related (Thornes, 1991; Bogren & Gustavsson, 1991; Lindqvist, 1992). Hence, any variations in air temperature across the mesoscale landscape caused as a 409

2 L Chapman, J E Thornes and A V Bradley Table 1. Parameters that control road surface temperature (adapted from Thornes & Shao, 1991a). Meteorological Geographical Road Construction Solar radiation Latitude Depth of construction Terrestrial radiation Altitude Thermal conductivity Air temperature Topography Thermal diffusivity Cloud cover and type Screening Emissivity Wind speed Sky-view factor Albedo Humidity / dew-point landuse Traffic Precipitation Topographic exposure Table 2. Classification of fingerprints with respect to Pasquill Gifford Stability classes and Thornes (1991) classification (adapted from Pasquill & Smith, 1983). Surface wind speed Thinly overcast or 4/8 oktas of < 4/8 oktas cloud (m s 1 ) low cloud Pasquill Gifford Thornes Pasquill Gifford Thornes stability classes classification stability classes classification <2 G extreme G extreme 2 3 E intermediate F intermediate 3 5 D damped E intermediate 5> D damped D damped consequence of the interaction of geographical parameters will also be evident at the road surface. (a) Latitude Latitude is an important constraint on climate and RST. For example, Scotland has more snow and ice than other parts of the UK (Cornford & Thornes, 1996). Countries at higher latitudes have longer winter seasons, but countries as far south as Greece and Spain still have ice problems (Thornes, 1991). In summary, the main impact of latitude is its influence on the laws of radiation geography with respect to quantities of incoming solar radiation. (b) Altitude RST decreases with altitude as a result of the environmental lapse rate: up to a maximum of 9.8 ºC per 1000 m but more typically 6.5 ºC per 1000 m (Tabony, 1985a). Shao et al. (1997) studied the impact of altitude on RST in Nevada, USA. They showed that altitude had a considerable effect on RST, but the relationship between the variables was often non-linear. As a parameter, the effects of altitude on RST should typically be most apparent during times of low atmospheric stability; however, as stability increases, the increased role of topography should lessen this relationship. (c) Topography Often considered to be the major factor causing differences in RST during extreme nights (Bogren & Gustavsson, 1991), small differences in topography can produce large variations in air temperature and RST 410 across the mesoscale landscape. Several theories have been proposed to explain this phenomenon; for example, Thompson (1986) considers the earlier cessation of turbulent heat transfer in sheltered locations as critical in producing lower temperatures, while Tabony (1985b) discusses the production of horizontal isotherms in small-scale sheltered terrain. Such theories may explain the impact of micro-topography on temperature distribution, but when dealing with larger scale topography, the more commonly accepted cause of temperature variation is the katabatic theory. During stable conditions, a layer of dense cold air forms at the surface and causes a temperature inversion. If the topography is undulating, the layer of cold air becomes mobile and gravitates down slope as a katabatic flow, following lines of drainage until a topographic or thermal barrier is reached. At the top of the temperature inversion, lapse rates return to normal and temperatures are at their warmest. This feature is called the thermal belt (Keen, 1968) and is a dynamic feature whose height varies with the strength of the katabatic flow and the relative size of surrounding topography. In reality, few nights actually have sufficiently low regional wind-speeds for katabatic drainage. Hence, at more moderate velocities the topographic exposure of the valley becomes an important parameter (Gustavsson, 1990). Topographic features dominate airflow at a local level, with wind-speeds increasing with elevation and at exposed sections (Chapman, 2000). The result is that sheltered locations will have decreased RST as a consequence of reduced windspeeds and turbulent heat transfer (Thompson, 1986). Overall, variations in temperature induced by topography often cause the lowest air temperatures on a road

3 Statistical modelling of road surface temperature from a geographical parameter database network to be recorded at valley bottoms. Any variation in air temperature is linearly related to RST (Gustavsson, 1990), but there is a tendency for RST to be slightly higher than air temperature due to the thermal inertia of the road construction (Bogren & Gustavsson, 1991). (d) Screening Screening affects the surface radiation budget by obstructing the incoming daytime short-wave radiation. Topographically screened environments will produce lower RST as a result of less direct short-wave radiation reaching surfaces in shadow (Bogren, 1991). Screening is generally systematic (with the exception of deciduous trees) and is a cause of large deficits in daytime RST at screened locations (Gustavsson & Bogren, 1993). Bogren et al. (2000) statistically modelled the magnitude of such temperature deficits with respect to solar elevation. Deficits were shown to decrease over the afternoon but have the potential to create a lag effect after sunset, particularly at low levels of cloud cover and during early and late winter when solar input is increased. A final consequence of screening is that buildings and forests will afford a degree of wind shelter which will lower RST (Gustavsson, 1995). This theory has been validated at coniferous sites in Sweden where nocturnal RST differences of up to 3 ºC have been found between locations in sheltered forests and exposed areas (Gustavsson et al., 1998; Karlsson, 2000). (e) Sky-view factors Often used as a surrogate for screening in RST studies, the sky-view factor (ψ s ) is a dimensionless parameterisation of the quantity of visible sky at a location. Represented as a value 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). ψ s has a particularly important role in the nocturnal radiation budget, where surface geometry prevents the loss of long-wave radiation from the ground by the replacement of a section of the cold sky hemisphere with a warmer surface (Oke et al., 1991). This results in increased nocturnal air and surface temperatures at locations with low ψ s. For example, Postgård & Nunez (2000) found that ψ s accounted for up to 61% of the variation in RST in a study in southeast Sweden. The dominance of ψ s as a controlling parameter for RST has also been found in many other studies (e.g. Bärring et al., 1985; Elliasson, 1996; Upmanis, 1999). The impact of ψ s will be most noticeable during times of high atmospheric stability, when potential radiation losses are at their greatest. (f) Landuse The impact of landuse on temperature can be clearly seen from urban/rural temperature transects (Johnson, 1985; Graham, 1993). During stable conditions, builtup areas are generally several degrees warmer than surrounding rural areas: a phenomenon known as the urban heat island. Changes in building density and vegetation create microclimatic changes due to variations in surface geometry (e.g. screening, ψ s and reduced turbulent heat transfer due to shelter). Bärring et al. (1985) compared ψ s with surface temperatures along a series of measuring points and found a strong relationship between ψ s and surface temperature. The relationship is strongest in the city centre, but the impact of ψ s can still be significantly detected in suburban areas. Urban climates are further influenced by the thermal properties of construction materials and anthropogenic heat from buildings and traffic (Oke, 1992). For example, Elliasson (1996) discovered the existence of a 4 C horizontal air temperature difference between Gothenburg city centre and a large park to the south-west of the centre during stable conditions. A final factor conducive to increasing urban temperatures is rapid surface runoff which will decrease the latent heat flux in urban areas. The opposite is true at sites in proximity to large water masses where increased humidity diminishes temperature differences. (g) Road construction profiles and traffic densities Subtle variations in RST will be recorded within a road network purely due to variations in the thermal properties of the materials used in road construction. The term thermal memory is used to describe the length of time that a surface stores heat from daytime solar radiation (Thornes, 1991). Roads with deeper construction such as motorways and A-roads have a large thermal memory and are often the warmest sections of a road network. However, if a road crosses a bridge, its construction and thermal memory is reduced. These effects are particularly noticeable during early and late winter when the input of solar radiation is greater. The impact of traffic can also significantly modify RST. In addition to increasing quantities of anthropogenic heat, vehicles cause mixing of hot and cold air layers and also shadow long-wave radiation loss from the road surface (Thornes, 1991). The impact of vehicles can be quantified on multi-laned roads, where the increased volume of slower moving vehicles on nearside lanes can produce increased RST of up to 2 C (Parmenter & Thornes, 1986). The effects of traffic on RST are noticeable on most nights, although larger values are likely to be recorded in stable conditions due to increased potential radiative losses. 2. Methodology 2.1. Study area The study area is shown in Figure 1 and is a circular survey route around south-west Birmingham (52.44 N, 1.92 W), UK. Birmingham was chosen 411

4 L Chapman, J E Thornes and A V Bradley because it has a dense network of automatic road weather stations and a well-developed urban heat island during extreme conditions (Unwin, 1980). The route covers a variety of landuses varying from the high rise (low ψ s ) urban canyons of the city centre to the tree-lined lanes of the Clent Hills in rural Worcestershire. The overall result is that several distinct variations of landuse and road types are encountered on route, from high density terraced housing to woodland, motorways to urban streets. Two surveying techniques were used on the survey route. First, thermal mapping was used to acquire nocturnal RST validation data, and secondly, View Factor Mapping (VFM) was used to survey systematically variations in geographical parameters. Both surveys produce comprehensive datasets, which are combined in this study, to determine the impact of geographical parameters on RST at different levels of atmospheric stability Thermal mapping Over the winter season 1999/2000 the study route was thermally mapped a total of 20 times. Surveys were conducted simply by using a vehicle-mounted infrared camera, which measures the energy flux from the road at 20 m intervals. This was then converted to RST by using the Stefan Boltzmann equation. A constant value for emissivity (0.95) needed to be assumed due to an absence of accurate measurement techniques. Although 0.95 is the commercially accepted value for a road surface, in reality this will vary around a road network with respect to different road surface materials (i.e. asphalt/concrete) and weather conditions (i.e. wet/dry). This can prove to be a considerable source of error because calculated RST is extremely sensitive to even the smallest change in emissivity (Thornes, 1991; Gustavsson, 1999). In addition to the infrared camera, the thermal mapping vehicle was also equipped with an on-board global positioning system (GPS). The advantage of this is that every temperature measurement can be geo-referenced with a latitude/longitude position allowing for easy data plotting in a geographical information system and simple co-referencing with other datasets. To ensure full coverage of the stability classes outlined in Table 2, surveys were carried out over a variety of different times and weather conditions. The time of the survey is crucial as sufficient time needs to be allowed for cooling so that patterns of RST variation around the route are well developed (e.g. canyon cooling and cold air accumulation (Gustavsson, 1999)). Hence, throughout this study, all surveys were carried out between 0100 and 0500 UTC when the cooling rates are at a minimum. Finally, for each route, the standard deviation of RST was calculated for use as a proxy for atmospheric stability. 412 Figure 1. The study route, starting and finishing at the University of Birmingham and traversing anticlockwise through the city centre, before passing through the south-west Birmingham suburbs and north Worcestershire countryside. Major changes in landuse and road type are also shown on the map View factor mapping A total of five daytime VFM surveys were carried out over the winter season 1999/2000 (i.e. leaves off trees). VFM surveys are essentially thermal mapping surveys modified to allow for the continuous surveying of ψ s. Continuous mobile measurements of ψ s have proved difficult, though good estimates have been achieved by Postgård & Nunez (2000) by using a highly polished steel hemisphere to sense radiative temperature differences in the sky. VFM differs from this technique in that it uses actual values of ψ s calculated from fish-eye imagery (Figure 2). This was acquired from a sunroofmounted digital camera equipped with a fish-eye lens. Surveys were carried out in the daytime to allow for suitable light levels to acquire fish-eye imagery, one of which was frame grabbed every second via the cameras video link. Homogeneous cloudy skylines were found to produce the most accurate results, although surveys at dusk also generate good imagery. Finally, during the survey, the surveyor was required to mark any transitions in road type and landuse. An ordinal classification was used for these parameters (Table 3), and was implemented simply by pressing appropriate keys labelled on the standard thermal mapping manual keypad. Overall, the data collected from a VFM survey can be split into two components: an album of fish-eye images and a GPS datafile. This information then acts as the building blocks for the development of a geographical parameter database.

5 Statistical modelling of road surface temperature from a geographical parameter database Table 4. Parameters measured during a VFM survey. Direct measurement Inferred via post processing Latitude Longitude Altitude RST (validation data) Time and date of measurement Sky-view factor (SVF) Road type Landuse Cold air advection (CAPI) Figure 2. Example fish-eye photograph of a typical inner city canyon. The fish-eye lens has a 360 o field of view of the sky hemisphere which enables the intrusion of buildings and trees to be quantified. Table 3. Ordinal classification of landuse and road type used in VFM surveys (road type as used in the standard British road classification system). Classification landuse Road type 1 City centre Motorway 2 Urban A-road 3 Suburban B-road 4 Rural C-road 2.4. Development of the geographical parameter database The variables measured during a VFM survey are summarised in Table 4 and can be split into two groups: those directly measured and those calculated during post processing. Directly measured variables were simply derived at a 20 m spatial resolution from the GPS datafile and form the basis of the geographical parameter database, into which values for ψ s and topography were appended after post processing. (a) Sky-view factors After the completion of a VFM survey, each of the thousands of frame grabbed images need to be processed into a value for ψ s. Using existing techniques, this is potentially a time-consuming task and instead a rapid computerised solution was developed. This approach builds on the work of Steyn et al. (1986) and is explained in more detail in Chapman et al. (2001). Similar techniques have also been developed by Blennow (1995) and Holmer et al. (2000). Initially, the image is converted into an array of greyscale digital numbers between 0 and 255. Then, to reduce processing time, the size of the image is reduced before a contrast improvement algorithm is applied. This enables the rapid delineation of sky pixels in the image by using a fixed threshold value. The resulting binary image of zeros (non-sky pixels) and ones (sky pixels) is then analysed by means of an annular template to calculate ψ s values accurate to within ±0.02. Once calculated, ψ s is appended into the database by matching the time the image was taken with the nearest time recorded in the original GPS datafile. (b) Topography Realistically, if katabatic theory is to be modelled satisfactorily, four dimensions need to be considered. Indeed, substantial research has been undertaken to model the structure (e.g. Papadopoulos et al., 1997), the nature (e.g. Gudiksen et al., 1992) and the dynamics (e.g. Whiteman & McKee, 1982) of katabatic drainage. However, such studies are too complicated to be used to predict the influence of topography during a mobile VFM survey. Instead, the use of empirical formulae was considered to be the most straightforward approach. As part of ongoing work to develop a local climatological model for south-east Sweden, Bogren & Gustavsson (1991) investigated the relationship between RST and the topographical parameters of 140 valleys across Sweden. Though many parameters influence the magnitude of cold air pooling, the use of a multiple regression model identified valley depth and valley width as the most influential parameters during stable conditions: If W 0.01 and D 1 then S = W D (1) where S is the reduction in surface temperature, W is valley width in kilometres and D is valley depth in metres. Bogren & Gustavsson (1991) found that 55% of the variation in RST in valleys could be explained by this simple two-dimensional valley geometry. Hence, by assumption that equation (1) is applicable in the UK as well as Sweden, a simple cold-air pooling index (CAPI) was developed, based around relative variations in altitude. GPS altitude data was differentiated with respect to horizontal distance, thus determining the location of valley bottoms and hilltops. This information was then 413

6 L Chapman, J E Thornes and A V Bradley used to infer the relative height and width of each valley in the survey (Figure 3). Then, if a survey point is defined as in a valley and below the thermal belt (for simplicity, assumed to be 0.15D), the data was run through equation (1) to obtain a prediction of RST reduction at that particular site. A disadvantage of approximating topography with this method is that roads are assumed to follow the maximum dimensions of valleys and that valleys are traversed in such a way their true geometry will show up in altitude variations (i.e. perpendicular); a road running parallel to the valley sides would not be detected as being in a valley location. Upon completion of post processing, ψ s and CAPI are simply appended to the original GPS datafile to produce a geographical parameter database with the fields: Latitude, Longitude, Altitude, CAPI, ψ s, Road type and Landuse. The database is then suitable for use in modelling studies, or alternatively for plotting in a geographical information system to investigate the spatial distribution of individual parameters. 3. Results and discussion 3.1. Repeatability of VFM Surveying The repeatability of VFM surveying was tested by geomatching values of latitude and longitude data across the five surveys. This produced a single database in which latitude, altitude, ψ s and CAPI were analysed using a one-way analysis of variance (ANOVA) and mean correlation coefficients. A statistical analysis was not performed on the ordinal landuse and road type data as it was assumed that human interaction would ensure consistency across surveys. The data distributions of each geographical parameter per survey, accompanied by summary statistics are shown in Figure 4. The results of the ANOVA confirm that the collection of latitude and altitude data is highly repeatable from survey to survey. The maximum correlation of unity for the latitude data indicates the quality of two-dimensional GPS coverage, whereas a slightly lower correlation for altitude data is a consequence of diminished three-dimensional GPS coverage in urban canyons. Unfortunately, such confidence cannot be expressed for the repeatability of the other geographical parameters as the ANOVA shows significant differences in the ψ s and CAPI data distributions. Differences between individual ψ s distributions are possibly due to problems co-registering temporal ψ s data with spatial GPS measurements. As images are frame grabbed at a rate of one per second, the exact position at which an image is taken is a function of the speed of the vehicle. Consequently, when an image time is co-registered to a time recorded in the GPS 414 Figure 3. Relative height and width of valleys along a survey run. W1 and H1 are the width and height parameters for valley one and W2 and H2 are the width and height parameters for valley two. datafile, temporal rounding errors reduce the probability of achieving an exact positional match. A further source of error is the intrusion of high-sided vehicles into the image causing an underestimation of ψ s (Figure 2). This is reduced by mounting the camera on top of the vehicle at 1.9 m, but does lead to a systematic overestimation of road surface ψ s. However, despite these errors affecting the absolute values of ψ s as indicated by the ANOVA, relative values of ψ s remain consistent across surveys (correlation coefficient r = 0.84). With respect to the variations in the CAPI data distribution across surveys, both the correlation coefficient and ANOVA indicate little repeatability. This is intriguing as CAPI is a direct derivative of the altitude data already shown to be consistently repeatable. However, as CAPI uses differentiated altitude data, successful calculation depends upon the relative variation of altitude from point to point. Consistency is found across surveys at a large scale, but at a finer resolution minor altitude variation will affect CAPI. Hence, although the statistics used indicate unrepeatability, the distributions indicate that each survey is in fact very similar Individual parameter analysis By geo-matching latitude and longitude values, geographical parameter data were appended to each of the 20 thermal mapping surveys, producing a 20 m resolution dataset of residual RST and geographical parameters. Appending accuracy was improved by setting a maximum co-registration threshold of ±10 m, above which data was omitted from further analysis. Due to the nature of the geographical data collected, it was anticipated that each variable might not be entirely independent of other geographical parameters. Existence of such co-linearity was tested by consulting correlation matrices developed using two appended thermal mapping surveys that were considered representative of the damped (standard deviation = 0.57) and extreme (standard deviation = 1.28) stability classes shown in Table 2. Minor relationships were found between many of the variables, but these were mostly

7 Statistical modelling of road surface temperature from a geographical parameter database Figure 4. Box plots and ANOVA statistics showing the distribution of values for four continuous geographical parameters collected across five different VFM surveys. Where F = ANOVA F-value, p = ANOVA p-value and r = mean correlation coefficient for the five surveys. insignificant being of the order of r <0.15. However, stronger relationships are evident between other parameters. For example, landuse, latitude, altitude and ψ s were found to be co-linear, largely because of the location of Birmingham city centre on the lowest and most northerly point of the route. This problem could be resolved by the inclusion of a high altitude urban area to the south of the route, though this would be unlikely to remove the inherent relationship between ψ s and landuse (r damped = 0.55; r extreme = 0.6). The relationship between each geographical parameter and residual RST was analysed for continuous levels of atmospheric stability. This was achieved by plotting individual correlation coefficients against the standard deviation of RST for each of the 20 thermal mapping surveys. Figure 5 shows that during stable conditions (i.e. increasing standard deviation), landuse and ψ s are the dominant parameters for the prediction of RST. However, as atmospheric stability decreases, so does the importance of landuse and ψ s, with altitude becoming more influential. As expected, the influence of CAPI is strongest on extreme nights but overall relationships are weak ( r <0.2), indicating a shortcoming of the use of the index in explaining the four-dimensional influence of topography. It is anticipated that this relationship could be improved with better approximations of valley form and katabatic processes derived from digital terrain models. However, even with more sophisticated techniques, correlations are expected to remain low as topography will only strongly affect less than 10% of sites on the study route. Inspection of the influence of road type indicates little trend with respect to atmospheric stability. Initially this was thought to be due to the over-simplistic classification procedure, but a subsequent ANOVA confirmed that varying the road type does have a considerable effect on RST in excess of the 99% significance level. Instead, it appears that the impact of road type on RST is so small that it will be overshadowed by more dominant parameters at all levels of stability. This could be investigated by further research with detailed 415

8 L Chapman, J E Thornes and A V Bradley Figure 5. The influence of five geographical parameters for RST prediction at different levels of atmospheric stability. (Standard deviation of each thermal mapping survey is used as a proxy for atmospheric stability.) 416

9 Statistical modelling of road surface temperature from a geographical parameter database road construction data derived from road coring, although this would prove expensive and difficult Multiple Parameter Analysis A multiple regression analysis was used to determine how much of the variation in residual RST could be explained by the combination of all five geographical parameters. This was achieved by plotting multiple regression correlation coefficients against the standard deviation of RST for each of the 20 thermal mapping surveys (Figure 6). Additionally, data from the same two representative thermal mapping surveys used in section 3.2 were used to fit example regression equations for the damped and extreme stability classes (Table 5). The equations were then used to generate damped and extreme thermal fingerprints for comparison with fingerprints from other representative thermal mapping surveys (Figure 7). The predictive ability of the multiple regression model follows a quadratic trend rising from a minimum 59.1% explanation (r = 0.769) in damped conditions to a maximum 75.3% explanation (r = 0.868) in intermediate conditions. Model accuracy then decreases at higher levels of atmospheric stability due to the problems of accurately incorporating the impact of topography into the model. It is hypothesised that the inclusion of other parameters such as anthropogenic heat, roughness length and traffic density would improve model accuracy, particularly at low levels of atmospheric stability. However, these parameters are difficult to measure and quantify, hence their approximation in this survey as the subjective landuse parameter. The need for continuous measurement of such parameters, or at least an expanded Table 5. Results of a multiple regression analysis to explain variations in residual RST using five geographical parameters. Parameter Regression Coefficients Damped Extreme Constant Landuse Road type Altitude CAPI SVF Explained variance 60% 70% ordinal classification is demonstrated in Figure 7 by abrupt transitions in the modelled extreme fingerprint. Overall, the shortfalls in explanation of RST variation using this five-parameter statistical model shows that other geographical parameters and modelling approaches need to be considered. The statistical model presented cannot be universally applied to a road network as it fails to take into account variations in synoptic conditions. This could possibly be overcome by the inclusion of a coefficient of atmospheric stability on each geographical parameter in the model. However, it is proposed that numerical modelling would offer a more robust solution by enabling accurate modelling of the synoptic situation with respect to both air and surface temperature. The application of numerical modelling would also enable the inclusion of other parameters, such as screening, which cannot be easily parameterised for inclusion in statistical models. Figure 6. Predictive ability of a statistical model incorporating the combined influence of five geographical parameters at different levels of atmospheric stability. 417

10 L Chapman, J E Thornes and A V Bradley Figure 7. Actual and predicted thermal fingerprints for two stability classes. (A = Birmingham city centre, B = Cape Hill and Bearwood urban centres, C = M5 motorway, D = Rural Worcestershire and E = Northfield and Selly Oak urban centres). N.B. The generation of fingerprints between these two classes can be achieved as a function of cloud and wind speed as per Table Conclusions 418 As atmospheric stability increases, RST variations are increasingly influenced by ψ s and topography at the expense of altitude. Multiple regression analysis shows that the use of five simple geographical parameters can explain up to 75% of variations in residual RST data collected by thermal mapping. It is proposed that numerical modelling using the same parameters would yield similarly successful results, particularly with the inclusion of other variables such as traffic, screening and air temperature. The use of a numerical model driven by daily forecast data would provide a dynamic solution capable of producing individual road weather forecasts at a 20 m spatial resolution around the road network. Such an application would signal the end of site interpolation by thermal mapping and thus revolutionise road weather information systems in their current guise. References Bärring, L., Mattson, J. O. & Lindqvist, S. (1985). Canyon geometry, street temperatures and urban heat island in Malmö, Sweden. J. Climatol., 5: Blennow, K. (1995). Sky view factors from high resolution scanned fish-eye lens photographic negatives. J. Atmos. Oceanic Technol., 12: Bogren, J. (1991). Screening effects on road surface temperature and road slipperiness. J. Theoretical Appl. Climatol., 43: Bogren, J. & Gustavsson, T. (1991). Nocturnal air and road surface temperature variations in complex terrain. Int.J. of Climatol., 11:

11 Statistical modelling of road surface temperature from a geographical parameter database Bogren, J., Gustavsson, T., Karlsson, M. & Postgård, U. (2000). The impact of screening on road surface temperature. Meteorol. Appl., 7: Chapman, L. (2000). Assessing topographic exposure. Meteorol. Appl., 7: Chapman, L., Thornes, J. E. & Bradley, A. V. (2001). Rapid determination of canyon geometry parameters for use in surface radiation budgets. Theoretical Appl. Climatol., 69: Cornford, D. & Thornes, J. E. (1996). A comparison between spatial winter indices and expenditure on winter road maintenance in Scotland. Int. J. Climatol., 16: Eliasson, I. (1996). Urban nocturnal temperatures, street geometry and landuse. Atmos. Environ., 30: Graham, E. (1993). The urban heat island of Dublin city during the summer months. Irish Geography, 26: Gudiksen, P. H., Leone Jr, J. M., King, C. W., Ruffieux, D. & Neff, W. D. (1992). Measurements and modelling of the effects of ambient meteorology on nocturnal drainage flows. J. Appl. Meteorol., 31: Gustavsson, T. (1990). Variation in road surface temperature due to topography and wind. Theoretical Appl. Climatol., 41: Gustavsson, T. (1995). A study of air and road-surface temperature variations during clear windy nights. Int. J. Climatol., 15: Gustavsson, T. (1999). Thermal mapping a technique for road climatological studies. Meteorol. Appl., 6: Gustavsson, T. & Bogren, J. (1993). Evaluation of a local climatological model test carried out in the county of Halland, Sweden. Meteorol. Mag., 122: Gustavsson, T., Karlsson, M., Bogren, J. & Lindqvist, S. (1998). Development of temperature patterns during clear nights. J. Appl. Meteorol., 37: Holmer, B, Postgård, U. & Eriksson, M. (2000). Sky view factors in canopies calculated with IDRISI. In unpublished PhD thesis, Road Climate Variations Related to Weather and Topography by U. Postgård, University of Gothenburg, Sweden. Johnson, D. B. (1985). Urban modification of diurnal temperature cycles in Birmingham, UK. J. Climatol., 5: Karlsson, M. (2000). Nocturnal temperature variations between forest and open areas. J. Appl. Meteorol., 39: Keen, K. (1968). The development of a nocturnal warm air layer within a shallow valley. S. African Geog. J., 57: Lindqvist, S. (1992). Local climatological modelling for road stretches and urban areas. Geografiska Annaler, 74: Oke, T. R. (1992). Boundary Layer Climates. Routledge, 435 pp. Oke, T. R., Johnson, G. T., Steyn, D. G., & Watson, I. D. (1991). Simulation of surface urban heat islands under ideal conditions at night. Part 2: Diagnosis of causation. Boundary Layer Meteorol., 56: Papadopoulos, K. H., Helmis, C. G., Soilemes, A. T., Kalogiros, J., Papageorgas, P. G. & Asimakopoulos, D. N. (1997). The structure of katabatic flows down a simple slope. Q. J. R. Meteorol. Soc., 123: Parmenter, B. S. & Thornes, J. E. (1986). The use of a computer model to predict the formation of ice on road surfaces. Transport and Road Research Laboratory Research Report, 1: Pasquill, F. & Smith, F. B. (1983). Atmospheric Diffusion. 3rd edn, Ellis Horwood, 336 pp. Postgård U. & Nunez, N. (2000). Continuous measurements of sky-view factors along roads and their relationship to air and road surface temperature. In unpublished PhD thesis, Road Climate Variations Related to Weather and Topography by U. Postgård, University of Gothenburg, Sweden. Shao, J., Lister, P. J., Hart, G. D. & Pearson, H. B. (1996). Thermal mapping reliability and repeatability. Proceedings of the 6th International Road Weather Conference, Birmingham, April SIRWEC, pp. Shao, J., Swanson, J. C., Patterson, R., Lister, P. J. & McDonald, A. N. (1997). Variation of winter road surface temperature due to topography and application of thermal mapping. Meteorol. Appl., 4: Steyn, D. G., Hay, J. D., Watson, I. D. and Johnson, G. T. (1986). The determination of sky-view factors in urban environments using video imagery. J. Atmos. Oceanic Technol., 3: Tabony, R. C. (1985a). The variation of surface temperature with altitude. Meteorol. Mag., 114: Tabony, R. C. (1985b). Relations between minimum temperature and topography in Great Britain. J. Climatol., 5: Thompson, B. W. (1986). Small-scale katabatics and cold hollows. Weather, 41: Thornes, J. E. (1991). Thermal mapping and road-weather information systems for highway engineers. In A. H. Perry & L. J. Symons (eds.), Highway Meteorology, E & FN Spon, London, pp Thornes, J. E. & Shao, J. (1991a). A comparison of UK ice prediction models. Meteorol. Mag., 120: Thornes, J. E. & Shao, J. (1991b). Spectral analysis and sensitivity tests for a numerical road surface temperature prediction model. Meteorol. Mag., 120: Unwin, D. J. (1980). The synoptic climatology of Birmingham s urban heat island. Weather, 35: Upmanis, H. (1999). The influence of sky-view factor and land-use on city temperatures. Personal communication, University of Gothenburg, Sweden. Whiteman C. D. & McKee, T. B. (1982). Break-up of temperature inversions in deep mountain valleys: Part II. Thermodynamic model. J. Appl. Meteorol., 26: