Adjustment time for road surface temperature during weather changes

Transcription

1 Meteorol. Appl. 8, (2001) Adjustment time for road surface temperature during weather changes U Postgård, Department of Earth Sciences, Physical Geography, Göteborg University, Box 460, SE Göteborg, Sweden The object of this study is to examine the possibility of developing a model that can determine road surface adjustment times to new conditions after weather changes. Situations where the weather changes from clear to overcast conditions are studied in order to produce a worst-case scenario. One hypothesis tested is that the decrease in road surface temperature (RST) differences between shaded and sun-exposed stations on clear days can be used to determine the reduction in RST difference on days with weather changes. A relationship that describes the variation in RST difference as a function of time of day and season is developed. For clear days a fourth-order polynomial can describe the relationship between RST differences and time of day. The coefficient in the polynomial depends on maximal solar elevation. Validation of the model for clear days showed that the deviation between modelled and measured values varied between 0.3 and 0.5 C. It was also possible to use the clear day relationship to predict the decrease in RST differences for situations with weather changes, but during these situations the deviations between modelled and measured values were higher and also tended to show a positive bias. 1. Introduction To assist the safe movement of traffic and to minimise delays and accidents caused by slippery roads more studies on temperature variations on road surfaces are needed. A Road Weather Information System (RWIS), with stations in different environments along roads, has been developed in several countries to record relevant data to aid such studies. In Sweden, 670 stations are included in the RWIS. Different areas along a road have different risks of slipperiness depending on different weather conditions. Consequently, stations are located in areas with different terrain characteristics so that early warning of low temperatures can be given. Measured air temperature, road surface temperature (RST), wind speed, humidity and precipitation are valuable data to be used in determining the level and type of winter road maintenance that may be required. Data from the stations are used in numerical energy balance models in order to forecast the temperature development at the stations (Nysten, 1980; Rayer, 1987; Thornes, 1989; Thornes & Shao, 1992; Bogren & Gustavsson, 1994; Shao & Lister, 1996; Jacobs & Raatz, 1996; Sass, 1997). The real-time data from the stations and the forecasts help the highway authorities to decide when and where maintenance action is needed. This increases the effectiveness of their actions and minimises the costs. Thornes (1989) showed, in a cost-benefit analysis, that salt wastage was reduced by 15% when the UK national ice-prediction system was installed and this resulted in a significant decrease in salt costs. Reducing salt usage can result in some environmental benefits since excessive use of salt may lead to vehicle corrosion and problems with construction work (Field et al., 1974; Jutengren, 1995). There is also a risk of soil and water resources being adversely affected (Field et al., 1974; Scott, 1981; Bäckman & Folkesson, 1996). Although the data from the stations and the forecasts may be useful in road maintenance, they do not give any information about the temperature variations along the road between the stations. Methods to extrapolate the values from the stations are, however, required to detect all areas prone to slipperiness. According to Thornes (1989), mobile measurements during extreme, intermediate and dampened weather situations can be used to make these extrapolations. Bogren et al. (1992) and Gustavsson & Bogren (1993) used another approach and developed a local climate model (LCM) to describe and predict the variations along the roads. Thermal mappings, historical data from the RWIS stations and topographical maps were used, dependent on weather conditions, to divide the roads into different segments (Bogren & Gustavsson, 1991). In the LCM, the weather situations with well-defined temperature variations along the road are classified into three main categories: clear and calm nights clear days cloudy and windy conditions 397

2 U Postgård Data from synoptic stations and RWIS stations are processed in an algorithm to decide which situation prevails at any given time. The temperature at each road segment is then calculated using data from the stations in the RWIS. However, it is not enough to study these main categories in order to make reliable extrapolations along the road. Influences of variation in cloud and wind can be studied by comparing these extreme situations with measured RST differences during other situations. More studies need to be made on the transition between different categories since changes in weather can create the risk of a lag effect at the road surface (Gustavsson & Bogren, 1990; Gustavsson, 1991; Wood & Clark, 1999; Bogren et al., 2000a; Postgård & Lindqvist, 2001). In order to analyse how great this lag effect can be and to consider a worst-case scenario, weather changes from clear to overcast conditions were studied (Postgård & Lindqvist, 2001) since large temperature differences can develop along the road during clear day conditions. It was shown that the changes in RST can be up to 3.5 hours slower than changes in air temperature during the passage of a warm front if the front was preceded by clear weather. At shaded stations the RST changed even more slowly than air temperature. Postgård & Lindqvist (2001) also showed that it took more than six hours for the RST to adjust to the new conditions for their studied case at the beginning of March when the front arrived late during the evening. This effect ought to be greater when the front arrives closer to noon since temperature differences between shaded and sun-exposed stations are larger. A greater effect can probably also develop for situations later during the season when the differences between shaded and sun-exposed stations are more pronounced. The object of this study is to analyse further the transition between different weather situations and to develop a model to determine the time required for a road surface to adjust to new weather conditions. The analyses focus on the most extreme weather, i.e. when there is a change from clear to overcast conditions. Validation of the model is also performed. the preceding weather the temperature difference when the front arrived the timing of the front arrival wind speed and precipitation. The largest adjustment times are obtained when the weather changes from clear to overcast conditions both during the day and at night. This study focuses mainly on finding a way to model change from clear day to overcast situations. When developing the model to determine the time it takes for the road surface to adjust to the new conditions after weather changes, two hypotheses were formulated: The adjustment time will increase as the RST difference between shaded and sun exposed stations increases when the front arrives. The developed RST differences between shaded and sun-exposed stations when the front arrives decrease in the same way as the maximum difference during clear day conditions if the magnitude of the differences is the same. A day in the beginning of March is used to test these hypotheses. On this occasion a maximum difference of 9 C between shaded and sun-exposed stations occurred for clear day conditions (Figure 1). If it is assumed that the front arrives at 14:30 LST, when the maximum RST difference is established, and that the hypotheses are correct, the RST difference diminishes during the day and finally reaches the same level as the overcast conditions (dashed line). If the front s time of arrival is known, a comparison of these two curves can give a value of the adjustment time to the new condition (7.5 h for this example). The magnitude of the RST difference between shaded and sun-exposed stations when the front arrives, T, will determine the adjustment time to the overcast condition, t. The larger the 2. Background As already mentioned the temperature variations along the road in the LCM are classified into three main categories: clear and calm nights clear days cloudy and windy conditions Choosing the correct prevailing temperature category and making reliable extrapolations of the temperatures along the road are both essential to the prevention of road slipperiness. Determining the RST adjustment time after a change in weather increases the possibility of doing this. Postgård & Lindqvist (2001) showed that the adjustment time depended on: 398 Figure 1. The decline of the road surface temperature (RST) difference between shaded station 640 and open station 605 during the clear day on 8 March 1996 (solid line). The magnitude of the RST difference, expressed as T, change during the season. Mean values for 11 overcast days during the season are also presented (dashed line) together with t, which expresses the time it takes for the RST differences between the shaded and sun-exposed station to diminish.

3 Adjustment time for road surface temperature value of T, the larger t will be. If the front arrives later, T will be less. Then a clear day situation with the same T as for the day with weather change has to be found. It can occur at another time of the season where the magnitude of T at 14:00 LST is the same. Before these hypotheses can be tested, it is necessary to develop a function that describes how the maximum RST difference at 14 h between shaded and sunexposed stations decreases with time (Figure 1) and season. Bogren et al. (2000b) found that the variation in maximum temperature difference between shaded and sun-exposed stations at noon, RST diff, depends on the solar elevation, β, according to: RST diff = 0.46β (1) Solar elevation increases throughout the season according to: sin β = sin ϕ sin δ + cos ϕ cos δ cos h (2) where ϕ is the latitude of the site, δ is the solar declination and h is the hour angle. A sine function can be used to describe the declination, δ, as a function of the day of the year, N, according to: δ = 23.4 cos [360(N + 10)/365] (3) Maximum solar elevation at noon, β max, thus varies according to: β max = (90 ϕ) ± δ (4) Bogren et al. (2000b) also found that the established RST difference prevailed several hours after sunset depending on the magnitude of the difference. The decline of RST difference after sunset was described as a fifth-order polynomial dependent on hours after sunset, and the constants were determined by time of the year. Since the studies by Bogren (1991) and Bogren et al. (2000b) showed a close relationship between RST difference and maximum solar elevation during clear day conditions, maximum solar elevation is probably one factor that can be used to develop a relationship that describes a RST difference, which decreases with time of the day and season. This possibility is analysed in this study and the relationship is tested for situations where the weather changed from clear to cloudy conditions. 3. Data and methods 3.1. Meteorological data and RWIS stations Data from the synoptic weather station at Jönköping airport (57 46 N, E) during October to March for the years 1992 to 1997 were used and appropriate weather events were selected. At Jönköping airport cloud cover and wind speed are recorded every three hours. The following selection criteria were used: Clear days had to have cloud cover of less than 2 oktas during the period between 10:00 LST and 04:00 LST the following day. The overcast days had to have cloud cover of 7 to 8 oktas during the same period. The days with a change from clear to overcast conditions had to have cloud cover of less than 2 oktas during at least two consecutive observations and then an increase in cloud cover to 8 oktas during the studied time period. The clear night which experienced a change in the weather had to have cloud cover of 0 to 1 oktas and a wind speed less than 2 m s 1 during the entire previous day and evening and then a change in weather and wind speed by 22:00 LST. The field stations included in the study are located in the south-central part of Sweden, close to Lake Vättern (Figure 2). Five different field stations (605, 607, 614, 629, 640, 1512 and 1513) within the Swedish RWIS are used. For a description of each station see Table 1. Every half an hour the stations calculate mean values of precipitation, humidity, wind speed, air temperature and road surface temperature. The levels of the sensors and instrument specifications are presented in Table Data analysis The temperature differences between shaded station 640 and open station 605 were used to develop the relationship between RST differences, time of the day and season for clear day conditions. A negative difference indicates that the shaded station is colder than station 605. Station 640 was used because it is shaded for almost the entire day during a large part of the winter season and as a consequence gave worst-case scenarios. An independent data set was used to evaluate the developed relationship. The temperature differences between stations 614 and 605 were analysed in order to see if this developed relationship was applicable to other stations as well. The model was also tested for days with weather changes and any deviations from the modelled temperatures were studied. In addition to station 640, stations 607 and 629 were used to test the first hypothesis the greater the RST difference when the front arrives, the greater the RST adjustment time. These stations are shaded and experienced colder temperatures than open station 605 on a clear day. Finally, to investigate whether the same temperature development can also be used to determine the decline of temperature differences between hilltop and valley 399

4 U Postgård Figure 2. Map of the study area and locations of the seven selected RWIS stations and the synoptic weather station at Jönköping airport. stations during clear nights which undergo a weather change, the open stations 1512 and 1513 are used. Station 1512, which is open and situated on a hilltop, is used as a reference station for comparison with the open valley station Note that this analysis differs from the earlier analysis in that neither of these two stations is shaded by forest. A negative value indicates that the valley station is colder than the open hilly station. 4. Model development 4.1. Clear conditions Data from twenty-one clear days during October 1992 to March 1997 were used to develop a relationship between RST difference and time of the day that describes the temperature decrease from 14:00 LST to midnight presented in Figure 1. A fourth-order polynomial can describe the RST difference at different times of the day: RST diff = A t 4 + B t 3 + C t 2 + D t + E (5) where t is half-hour periods after 14:00 LST and A, B, C, D and E are coefficients that do not depend upon t. The calculated RST difference is a negative value that indicates that the shaded station (640) is colder than the sun-exposed station (605). This relationship can be used to calculate the RST difference for a specific halfhour period after 14:00 LST. To obtain a RST difference development over the entire evening, one calculation for every half hour period has to be done. The fourth-order relationship between the RST differences and half-hour periods were calculated for all 21 days and the coefficients of determination, R 2, varied between 0.89 and The magnitude of the RST difference ( T in Figure 1) for the different days depended on solar elevation and the constants (A to E) for the studied days were correlated to maximum solar elevation, β max, calculated according to equations (3) and (4). In Figure 3 the relationships for each coefficient in equation (5) are presented. The coefficients can be calculated with the following equations: A = β max β max (6) R 2 = 0.86 B = β max β max (7) R 2 = 0.87 C = β max β max (8) R 2 = 0.84 D = β max β max 1.76 (9) R 2 = 0.56 E = 0.45 β max (10) R 2 = 0.87 The fifth constant, E, (in C) describes how the RST difference at 14:00 LST varies with maximum solar elevation in the same way as in equation (1) Validation of the model An independent data set was used to validate the established relationship between RST difference and time of the day. The test days were clear during the entire day Table 1. Description of the RWIS stations that are used. Station Altitude (m asl) Description Open and wind-exposed Close to a small lake. Shaded at noon and during the afternoon Shaded by trees from morning to afternoon during the period October to the beginning of March Shaded at noon and afternoon by dense forest Shaded by topography and forest from morning to afternoon during the period October to the middle of February. From mid-february to the end of March it is shaded at noon and during the afternoon Open and hilly site Open site situated in the bottom of a large valley. 400

5 Table 2. Instrument specifications for the measuring equipment at the RWIS stations. Adjustment time for road surface temperature Variable Level Accuracy Sampling Instrument frequency Air temperature 2.0 m ± 0.3 C 30 min Lambrecht Road surface lowered 2 mm in ± 0.3 C (sensor) 30 min Pt100, DIN temperature the asphalt top K1A layer Wind speed 5.0 m <10 m s 1 ± 0.1 m s 1 30 min Vaisala, WAA m s 1 ±2% Wind direction 5.0 m min Vaisala, WAV 15 Precipitation 5.0 m +15% to +30% 30 min Optic Eye FFVGSH-5030 depending on duration Figure 3. The relationships between the maximum solar elevation at 14:00 LST and the five coefficients: (a) A, (b) B, (c) C, (d) D and (e) E for the developed polynomial. For each constant 21 clear days are used in the analysis. 401

6 U Postgård and represent different seasonal periods. Figure 4 shows the results of the test over three separate days: 24 January 1993, 16 February 1997 and 10 March The modelled results (dashed lines) correspond well with the measured values (solid lines). The deviation for each studied period between modelled and measured values for the tested three days was calculated using: Deviation = N ( Xi Yi) 2 i = 1 N where X i = modelled value, Y i = measured value and N = number of observations. For 24 January (Figure 4(a)) the deviation was 0.5 C, for 16 February (Figure 4(b)) it was 0.3 C and for 10 March (Figure 4(c)) it was 0.5 C. Since the model was based on the RST difference between two stations it is important to assess whether the same relationship can be used for other stations with the same degree of shading. The temperature differences between shaded station 614 and station 605 were calculated for 16 February 1997 to test if this was the case. During this period station 614 was as shaded as station 640. In Figure 5 the modelled and measured values are plotted and it is evident that the relationship works well for this station as well. The deviation between the modelled and measured values was 0.5 C for the entire studied period, which is slightly higher (0.2 C) than that received for station Test of the model for days with weather changes In order to study if the relationship developed for clear day conditions can also be used for days with changing weather conditions, the model was tested for days with early front arrivals, days with variation in cloud cover and days with late front arrivals (for the selection of these variables, see Postgård & Lindqvist, 2001). Analysis of the relationship between adjustment time and RST differences between shaded and sun-exposed stations when the fronts arrived were studied for shaded stations 607, 629 and 640 and the open station 605. In Figure 6 the result of this analysis is shown for nine different warm front occurrences. The warm front arrival is defined as the time when the air temperature increases as the result of the front s arrival, while the adjustment is defined as the time it takes for the RST difference to reach the same level as on overcast days (Figure 1). It is evident from Figure 6 that the greater the temperature differences when the warm front arrives, the longer the time required to adjust to the 402 Figure 4. The results of the validation test for an independent data set. The analysed days are selected from (a) the beginning (24 January 1993), (b) the middle (16 February 1996) and (c) the end (10 March 1997) of the studied period. In the figure both modelled (dashed line) and measured values (solid line) are presented. new conditions which means that the first hypothesis (stated earlier) is correct. In order to use the model on days with weather changes, it was necessary to calculate maximum solar elevation corresponding to the measured difference with clouds or when the front arrived. This was done using equation (10) which describes the relationship between maximum solar elevation and clear day RST differences at 14:00 LST. The calculated maximum

7 Adjustment time for road surface temperature solar elevation was then used to calculate the RST difference decline using equations (5) to (10). The modelled RST difference development for each of the studied days was then compared with the measured RST difference development and the deviation for each day was calculated. Results for the studied six days are presented in Table Early front arrivals and variation in cloud cover Figure 5. Modelled results for 16 February 1997 compared with measured RST differences between shaded station 614 and open station 605. The model performed well for shaded station 640 and for those stations with similar levels of shading. On two of the first three days presented in Table 3 the front arrived early (2 March 1996 and 22 March 1993) and the third had variation in cloud cover (22 March 1996). These days showed the largest deviation between modelled and measured values, with a variation between 0.7 C and 1.3 C. The modelled values were in general higher than the measured values. During 2 March 1996 the cloud cover increased from 1 to 7 oktas between 07:00 and 13:00 LST and the wind speed increased from 3 to 7 m s 1 at Jönköping airport. No precipitation fell at the stations studied on this day. When the front arrived at 10:30 LST, shaded station 640 was 2.7 C colder than station 605 (Table 3). This temperature difference corresponds to a maximum solar elevation of 13.5 for a clear day (i.e. a day in late January). The modelled RST differences are similar to the measured values during the first 2.5 hours but then the differences between modelled and measured RST differences increase (Figure 7). The deviation between modelled and measured RST difference during the studied 9 hours is 1.0 C. Figure 6. Adjustment time to the new conditions versus road surface temperature difference when the warm front arrived on nine different warm-front occasions. The RST differences are calculated for three shaded stations (607, 629, 640) and one open station (605). During 22 March 1993 at Jönköping airport it was clear during the morning but between 13:00 and 16:00 LST the wind direction changed, wind speed increased and air pressure decreased. Precipitation started to fall at 20:30 LST at station 605 and at 22:00 LST at station 640. Since it is difficult to determine the exact time of Table 3. Characteristics for the days with weather change. The table shows the dates of the studied days; the maximal solar elevation (β max ) at 14:00 LST (according to equations (3) and (4)); the RST difference when the fronts arrived or at 14:00 LST; the calculated maximum solar elevation from RST difference according to equation (10); and the deviation between the modelled and measured RST differences. Date Real β max Time arrival RST diff during Calculated Deviation during the at 14:00 LST of the front front arrival or β max from studied period (LST) at 14:00 LST RST diff 2 March : C C 22 March :00 16: C (14:00) C 22 March :00 10: C (14:00) C and 22: March : C C 12 March : C C (0.2 C between 00:30 03:30 LST) Dec : C C 403

8 U Postgård Figure 7. Comparison between modelled and measured RST differences on 2 March 1996 when there was a change from clear to overcast weather. Figure 8. Comparison between modelled and measured RST differences on 22 March 1993 when there was a change from clear to overcast conditions. The deviation between the modelled and the measured values is 1.3 C. the front s arrival that day, 14:00 LST is used in order to test the model. At 14:00 LST, station 640 was 5.4 C colder than station 605 (Table 3). This difference corresponds to a maximum solar elevation of 19 when equation (10) is used (i.e. a clear day in the middle of March). In this case the modelled values show a good correspondence with the measured values during the three first hours but after that the differences increase and the modelled values are higher than the measured values (Figure 8). The deviation for the entire period is 1.3 C. Between 04:00 and 10:00 LST on 22 March 1996 the cloud cover was 8 oktas and between 13:00 and 16:00 LST the sky was clear. After that the cloud cover increased again and reached 8 oktas by 22:00 LST. No precipitation fell at the selected stations during this period. Since it is difficult to determine the exact time of the front s arrival, 14:00 LST is used to test the model. At 14:00 LST the RST difference between the two stations was 8.3 C. This corresponds to a maximum solar elevation of 26 when equation (10) is used (i.e. a clear day at the end of March). The modelled results are plotted in Figure 9 together with the measured values during the period. The form of the curve is quite well predicted but for most of the period the modelled values are too high. The deviation for the studied period is 0.70 C Late front arrivals Table 3 shows that fronts during the last three days arrived during the evening or night. The deviations between modelled and measured values were smaller for these three days than during days with early front arrival, varying between 0.3 and 0.6 C. From 27 to 28 March 1996 it was clear during the day at Jönköping airport and the cloud cover did not reach 8 oktas until 19:00 LST. Precipitation fell at the stations between 22:00 and 23:00 LST and between 01:00 and 05:00 LST. When the warm front arrived at 20:00 LST, 404 Figure 9. Comparison between modelled and measured RST differences on 22 March 1996 when there was a change from clear to overcast conditions. The deviation between the modelled and the measured values is 0.7 C. the RST at station 640 was 2.8 C colder than at open station 605 (Table 2). The model predicted the decline well (Figure 10) and the deviation for the entire period was 0.3 C. During 12 March 1993 it was clear between 13:00 and 19:00 LST until the warm front arrived at Jönköping airport. Precipitation fell at station 640 between 03:30 and 06:00 LST while station 605 only had minor precipitation at 03:30 LST. At station 640 the front arrived at 00:30 and this station was 2.5 C colder than station 605. The model performed well until 3:30 LST and after that the differences increased (Figure 11). The deviation for the entire period is 0.6 C, while the deviation between 00:30 and 03:30 LST is 0.2 C. The modelled values are higher than the measured values. The data for 15 December 1994 were analysed to see if the model could also be used to calculate the RST difference decline that develops between open valley and open hilltop stations when the weather changes from a clear and calm night to a cloudy situation. On 15 December 1994 it was clear and calm until 19:00 LST. During the observation at 22:00 LST at Jönköping air-

9 Adjustment time for road surface temperature Figure 10. Comparison between modelled and measured RST differences on 27 to 28 March 1996 where there was a change from clear to overcast conditions. The deviation between the modelled and the measured values is 0.3 C. Figure 12. RST differences predicted with the model for station 640 on 15 to 16 December 1994 compared with the measured RST differences between the open valley station 1513 and the open hilltop station It is evident that the decline in RST differences is also similar to RST differences caused by cold air pooling. The deviation between the modelled and measured values is 0.6 C. stations diminishes when the wind speed increases at the valley station. 6. Discussion and conclusion Figure 11. Comparison between modelled and measured RST differences on 12 March 1993 when there was a change from clear to overcast conditions. The deviation between the modelled and the measured values is 0.2 C for the first three hours and 0.6 C for the entire studied period. Deviation increased after 03:30 LST because it started to snow. port the cloud cover was 7 oktas as the warm front arrived. The wind speed at Jönköping airport reached 3 m s 1 at 01:00 LST and then continued to increase. Precipitation fell at the stations from 06:00 LST. During the evening a cold air pool developed at station 1513 (Table 3) and the decline of the established RST difference between this station and the hilly station 1512 was predicted with the model for station 640 above (equations (5) to (10)). In Figure 12 the results are shown together with the measured values. The model performed less well on this night (the values are generally too high), compared with the other situations where there was a late arrival of a front. The deviation during the studied period was 0.7 C. In this case, however, it is important to note that the studied stations are both open and not open and shaded as in the other cases and when developing the model. The RST difference between open valley and hilltop stations during clear and calm nights can also be affected by the wind speed at the different stations. This is evident in Figure 13 where RST and wind speed is presented for station 1512 and The RST difference between the two For clear days the results of this study show that the change in RST difference from 14:00 LST to midnight during the season can be predicted with a fourth-order polynomial, where the coefficients depend on maximum solar elevation. The reason for choosing a fourthorder polynomial was to receive a high coefficient of determination for all the 21 selected days from January to the end of March. The days in March especially needed the high order polynomial, while the RST differences for days earlier in the season could have been calculated with lower order polynomials. The fifth coefficient, E, (equation (10)), which describes how the RST difference at 14:00 LST varies with maximum solar elevation at 14:00 LST (see Figure 3(e)), is similar to equation (1) (Bogren et al., 2000b). The differences in slope and constants for the linear equations can be explained by differences in orientation and slope of the road where the stations are located. Another explanation could lie in the differences in height and density of the screening objects, which also influence the magnitude of the RST differences (Bogren, 1991). The close similarity between the two equations is positive since it demonstrates that the trend is similar for the different stations. The validation of the fourth-order polynomial with the independent data set showed that the deviation from the measurements varied between 0.3 and 0.5 C. Considering that road surface sensors have an accuracy of ±0.3 C, and the maximum error when two sensors are compared can be ± 0.6 C, the model performed well. It should be pointed out, however, that the poly- 405

10 U Postgård Figure 13. RST (solid lines) and wind speed (dashed lines) at the open valley station 1513 and the open hilltop station 1512 on December nomial was developed for a maximum of 19 half-hour periods (9.5 h) and for periods with solar elevations between 9 and 33. It is preferable that the relationship should only be used for 17 half-hour periods since the negative effects of using a fourth-order polynomial become evident during the last two half-hour periods. Although the polynomial relationship was developed only for two stations it has performed well for other stations. The model performed less well during days with a change in weather and modelled values were in general higher than the measured values. The deviation between the model results and the measurements for each studied day varied between 0.3 and 1.3 C (Table 3). The best model results were obtained for the days with a late front arrival, where the deviation varied between 0.3 and 0.6 C. For the days with early front arrival or clouds before noon, the deviations were larger. On 22 March 1993 and March 1996 the decline in RST differences was slower than during the clear days in the middle of February and the beginning of March that were used in the forecasts. One explanation might be the complex cloud situation during these periods, where the cloud cover at 14:00 LST for these days was less than 7 8 oktas. This could result in heating of the sun-exposed station and a delay in decline of RST differences. Bogren et al. (2000a) also showed that, provided that the solar elevation is high, the effect of shading has a significant influence on the road surface temperature, even with cloud cover of 4 6 oktas. The complex cloud situation also made it difficult to determine the exact time at which the front arrived and this has affected the difference between modelled and measured values and resulted in larger deviations. Differences in cloud cover for the stations in the study might be another explanation. Precipitation also increased the deviation between the modelled and measured values as shown for the situation on 12 March 1993 when the differences increased when it started to snow at 03:30 LST. The reason for the larger deviation for this day compared with the 406 other days with precipitation is that station 605 only had a small amount of precipitation lasting half an hour while station 640 had precipitation over several hours. At station 640 the warming of the road surface stopped when the snow fell, which again resulted in larger differences between the two stations. When the surfaces are wet, variation in wind speed may also account for differing results. Since wind speed is not measured at all sites, it is impossible to study the influence of wind speed on the RST difference between the selected shaded and open stations. Wind speed was, however, measured at the two open stations 1512 and 1513 and it is evident that wind speed affected RST during the clear night of 15 December 1994 (see Figure 13). Both this and other studies (Gustavsson & Bogren, 1990; Clark & Wood, 1996; Wood & Clark, 1999; Bogren et al., 2000b; Postgård & Lindqvist, 2001) show the complexity of situations where weather changes can affect the thermal inertia of the road surface. Three categories, which are dependent on weather situation and based on thermal mapping, are not adequate to interpolate site specific forecasts for the entire road stretch as is suggested by Thornes (1989). The lag effect at the road surface has to be considered in the LCM and a method to decide how long it takes for the road surface to adjust is required in the algorithm that chooses temperature patterns. The developed model can be used for this. By comparing modelled RST differences between sun-exposed and shaded reference stations when the front arrives with temperature differences for the same stations during overcast conditions the adjustment time for the road surface can be calculated. This will increase the performance of the LCM. It is also recommended that the model be used for estimating RST difference decline when the front has arrived (indicated by an increase in air temperature) and when conditions are completely overcast since this is when the deviations are smallest. Acknowledgements The Carl Trygger Foundation, The Royal Swedish Academy of Sciences and the Paul and Marie Berghaus Foundation have financially supported this work. The author is also grateful to the Swedish National Road Administration for providing data. I would like to thank my supervisors Professor S. Lindqvist, Dr J. Bogren and Associate Professor T. Gustavsson for valuable comments and help during the preparation of this paper. Thanks also to Professor D. Chen for ideas, Mrs S. Svensson for drawing the map and Mrs S. Cornell for linguistic revision. References Bäckman, L. & Folkesson, L. (1996). Influence of de-icing salt on vegetation, groundwater and soil along two high-

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