Statistical modelling of wintertime road surface friction


I. Juga, Finnish Meteorological Institute, Meteorological Research Dept., P.O. Box 503, FI-00101 Helsinki, Finland. E-mail:


Prevailing road surface conditions, the grip between tyres and the road surface, strongly correlate with traffic accident rate. Surface friction is reduced especially during snowfall or icing. Friction observations derived from Vaisala's optical DSC111 sensors, operated during two winter seasons (2007/2008, 2008/2009) at several Finnish roadside stations have been used. The devices measure the depth of water, snow and ice on the road surface and also produce an estimate of prevailing friction. The observations have been used to develop statistical equations to model road surface friction. The model has been evaluated against an independent dataset from winter 2009/2010. The goal thereafter was to integrate the scheme into the road weather service of the Finnish Meteorological Institute by combining background information from a road weather model with the derived statistical equations.

1. Introduction

The risk of traffic accidents depends on various factors, but, undoubtedly, adverse weather conditions increase accident rates. This is especially valid during winter conditions (Andreescu and Frost, 1998; Norrman et al., 2000; Salli et al., 2008). Andersson (2010) investigated the connection between winter road conditions and traffic accidents. During a mild winter in Sweden, plenty of accidents occurred due to slipperiness caused by hoar frost formation or icing. During a cold winter, snow proved to be the main cause for accidents. Snowfall and ice formation on the road surface result in decreased grip (friction) and thus substantially lengthen the braking distances (Wallman and Åström, 2001; Haavasoja and Pilli-Sihvola, 2010). Poor visibility combined with reduced friction will cause dangerous driving conditions under dense snowfall, especially if the worsening of weather is sudden. This can result in severe car pile-ups with dramatic consequences along the highways (Juga et al., 2010).

Real-time weather warning services for drivers and for road maintenance authorities are needed to mitigate the effects of adverse weather conditions. This calls for a sufficient observation network and skilful models to predict road conditions. Operational road weather models exist in many countries and a good example is the Model of the Environment and Temperature of Roads (METRo) developed by Environment Canada to predict road condition and temperature (Crevier and Delage, 2001; Linden and Drobot, 2010). METRo solves the energy balance at the pavement surface, calculates the heat conduction in the road material, and estimates the accumulation of water, snow and ice on the road based on precipitation, evaporation and runoff. The model uses past road weather observations for road temperature profile initialization and takes the meteorological forecasts from an operational Numerical Weather Prediction (NWP) model. These input data for METRo can be modified by the duty meteorologist if needed. Also the Danish Meteorological Institute (DMI) has developed a road condition model with external forcing by their operational limited area NWP model (Sass, 1997; Mahura et al., 2008). The model produces road weather forecasts for pre-defined sites, which are equipped with observing devices. These observations are used for the road weather model initialization. The number of calculation points has been increased substantially to cover the entire road network in Denmark (Mahura et al., 2008). In the Netherlands, MeteoConsult has made progress in producing road condition and temperature forecasts for the road network by using the output from an energy balance road model, high resolution weather forecasts and data concerning sky and sun view factors on the routes (Van den Berg, 2009).

At the Finnish Meteorological Institute (FMI), a tailor-made road weather model was developed and introduced into operations in 1999–2000. This one-dimensional energy balance model calculates the vertical heat transfer in the ground and at the ground–atmosphere interface. The special conditions prevailing at the road surface and underneath are taken into account, and the effect of traffic is also included in the model (Kangas et al., 2006). The model is forced at its upper boundary with output from a NWP model (either raw model data or data modified by the duty meteorologist). This large-scale input provides a horizontal coupling between individual computation points. At the lower boundary, the climatological ground temperature is used as a boundary condition. The most important output of the road weather model is road surface temperature, but also several other parameters are calculated: the thickness of water, snow and ice cover on the surface, the state of the road surface and the road condition index giving an estimate of prevailing driving conditions (categorized as normal, bad, very bad). The output from the road weather model is used by the duty forecasters when issuing road weather warnings. Some end-customers use the model output directly in their own applications.

The spatial and temporal variation of road weather variables (and especially temperature) is typically large. In the UK, Chapman et al. (2001a) investigated factors having an influence on road surface temperature (TR), which is an important parameter related to slipperiness. They found out that the variation in TR is influenced regionally by other meteorological variables and locally by geographical parameters. The sky-view factor had most influence on TR especially when the atmospheric stability was high. It appeared that up to 75% of the variance of TR could be explained by a statistical regression model of five geographical parameters. Also, TR prediction based on the numerical modelling of surveyed geographical parameters was investigated, giving results comparable to existing UK road weather models (Chapman et al., 2001b).

The great spatial variability of TR puts challenge on maintenance personnel especially during marginal conditions, when temperature hovers around 0 °C. Road Weather Information Systems (RWIS), where all the relevant road weather observations and forecasts are gathered, are used for helping maintenance personnel to plan their maintenance actions. RWIS have been in use for many years and have proved to be a very useful tool for maintenance. However, maintenance personnel can find their work stressful and they may be afraid of taking a wrong decision (Gustavsson et al., 2008). Consequently, RWIS have been developed in such a way that the decision making is transferred away from the highway engineer towards the forecaster (Chapman and Thornes, 2011). Then, a RWIS becomes a Maintenance Decision Support System (MDSS), giving for example the following advice: When to perform activity, where to perform activity and the type of activity (Gustavsson et al., 2008). In the USA, MDSSs have been piloted and implemented with promising results (Petty and Mahoney, 2008; Mewes et al., 2010), bringing substantial savings in salt usage and overwork compensation. The US MDSS uses the METRo for pavement condition forecasting (Linden and Drobot, 2010). Taking full use of an MDSS requires a spatial forecast component with good resolution (route-based forecast). To ensure that the maintenance personnel will have full confidence in the quality of the forecast, the resolution needs to be of the same order as that presently used in decision making, i.e. ca 50 m (Chapman and Thornes, 2011).

The FMI and the Finnish Transport Agency (FTA) have provided jointly a road weather warning service since 1997. This service employs a three-level categorization: normal, bad and very bad driving conditions. The warnings cover a 24 h period and are based on real-time road weather observations, road condition observations made by the maintenance personnel and the output from the FMI road weather model. Road surface friction is an important parameter in the guidelines for the warning thresholds. The friction coefficient (Cf) has a scale from 0 to 1. Good grip between the tyres and road surface means Cf values typically around 0.80 ± 0.10, and for the most slippery cases around 0.20 or even below (Haavasoja and Pilli-Sihvola, 2010). The braking distance at a speed of 100 km h−1 can increase from 50 to 200 m when bare road conditions change to icy conditions. General guidelines in Finland concerning friction are defined as follows: normal conditions, Cf above 0.3; bad conditions, Cf between 0.15 and 0.3; very bad road conditions, Cf below 0.15.

Friction can be measured with various devices and instruments, including mechanical and optical ones (see Section '2. Road surface friction and how to measure it'). The FTA uses friction criteria when supervising winter maintenance activities and actions, and when managing variable speed limits and warnings along the roads. Low friction is also associated with high accident rates. With Cf below 0.15, the accident rate can be four times higher than under conditions with Cf around 0.35–0.44 (Wallman and Åström, 2001).

All these facts have given motivation for the development of forecasting tools for road surface friction. A major practical challenge for operational slipperiness forecasting is the consideration of how to take into account the road maintenance operations like salting or snow ploughing.

2. Road surface friction and how to measure it

Friction, by definition, is the force that resists the relative motion of materials which are in contact with each other. Dry friction is considered if the materials in contact are solid. If the materials have no relative motion, static friction is concerned, and we are dealing with kinetic friction if the materials are in relative motion. The frictional contact between moving materials converts kinetic energy into heat. When an object slides over ice, a very thin water film is formed due to the released energy (if the temperature is not very low) resulting in more slippery ice than in pure dry contact (Makkonen, 1994, 2003). If the temperature is near 0 °C, the water film may have a scale of millimetres resulting in wet (lubricated) friction.

2.1. Friction coefficient

The coefficient of friction (Cf) between two surfaces is the ratio of the force required to move one over the other to the total force pressing the two together (Weast, 1971). Friction is a statistical concept, since the friction force represents the sum of a very large number of interactions between the molecules of the materials in contact (Alonso and Finn, 1973). These interactions have to be determined in a collective way by some experimental method and approximated by the coefficient of friction. The Cf has different values depending whether for example a slider on ice is at rest (static friction) or moving (kinetic friction). According to Alonso and Finn (1973), it has been found experimentally that the static Cf is larger than kinetic Cf for all tested materials. In the specific case of a road surface, Cf can be considered as a measure of the grip between the car tyres and the road surface. The friction between rubber tyres and a wet or icy pavement surface is a complex physical mechanism. A theoretical friction model was investigated by Makkonen (2003) in the ARTTU project (Arctic friction research study), where model results were compared to friction field measurements in northern Finland. A relatively good consistency between theory and observations was reported.

Road surface friction can be studied in a simplified way. When a vehicle (with a mass, m) moves in a horizontal direction and its speed is decreased by braking, the two principal affecting forces are: the horizontal friction force, Ff = ma, caused by the braking (deceleration a of the vehicle) and the vertical (normal) force, Fn = mg, caused by the load (or gravity, g = 9.81 ms−2). For most practical purposes, the sliding friction force Ff may be considered as proportional to the normal force Fn:Ff = CfFn (Alonso and Finn, 1973). The coefficient of (kinetic) friction can then be written as (Hall et al., 2009; Haavasoja and Pilli-Sihvola, 2010):

equation image(1)

The possible tilting of the road surface and the wind drag have been neglected. Equation (1) shows that Cf is not dependent on the mass of the object and that friction can be calculated directly by measuring the acceleration while braking or speeding up. In reality, the load has some effect on friction due to the deformation of rubber tyre contact asperities: the rubber friction on ice decreases with increasing load according to measurements (Makkonen, 2003). The percentage of slipping (or the slip rate) has also a small effect on Cf, the maximum values of Cf typically occurring at slip rates of 7–20%. The slip rate, Δv/v, is the ratio of the relative speed Δv between a moving vehicle and the braking tyre to the apparent speed v of the vehicle (so, the slip rate is 100% for lock braking). The acceleration (deceleration) is somewhat different for different loads or different slip rates on ice. As mentioned earlier, Cf has a scale from 0 to 1.

When a vehicle is driving at speed, v, it has a kinetic energy, Ek = mv2/2. In a lock braking situation, the kinetic energy equals to the work done by the friction force. The formula for Ek hence becomes, Ek = FfL = maL, where L is the braking distance required to stop the vehicle completely. Introducing a = Cfg from Equation (1) gives:

equation image(2)

It follows from Equation (2) that the friction coefficient can be calculated by measuring the stopping distance as well as the driving speed just before lock braking. Equations (1) and (2) enable the use of two practical methods for friction estimation, although the latter is not possible in dense traffic. On the other hand, with Equation (2) the required braking distances for certain speeds as function of different friction coefficient values can be calculated.

2.2. Measuring road surface friction

Wet pavement friction (or ‘skid resistance’) measurements are carried out to assess and monitor pavement quality in many countries. Wintertime friction measurements are performed especially in northern Europe to monitor slipperiness due to snow and ice and to supervise the work of maintenance contractors. Measuring techniques include various mechanical devices trailed by a car (Wallman and Åström, 2001), whereby a tyre is braked from free rolling as the friction force experienced by the wheel hub is dependent on the slip. As mentioned earlier in Section '2.1. Friction coefficient', maximum friction is typically observed at slip rates of 7–20% and it can be clearly higher than for the locked wheel friction (100% slip). Traction Watcher One (TWO) is an example of mechanical friction measuring instruments. It has two tandem wheels and a fixed slip of 15% with one wheel rolling 15% more slowly than the other. The friction coefficient is obtained based on the measured force that resists the rolling of the slower wheel (Pilli-Sihvola, 2008). The TWO instrument has been used for example by the FTA and its maintenance contractors in Finland. Reviews of different friction measurement methods and devices have been compiled e.g. by Wallman and Åström (2001), COST (2008) and Hall et al. (2009).

Friction can be calculated (using Equation (1)) if the acceleration during braking (or speeding up) is measured as mentioned in Section '2.1. Friction coefficient' Modern cell phones with built-in acceleration sensors can be used to measure friction (Haavasoja and Pilli-Sihvola, 2010). Hence, friction can even be estimated by simply installing an application program to a mobile phone. The acceleration sensor is calibrated by the acceleration of gravity. Measuring friction with the cell phone application software requires only a short instant braking to obtain a friction estimate.

Friction can be estimated by combining different in-vehicle and environmental information from various ‘intelligent’ sensors. This was investigated in the EU project FRICTI@N, where an on-board system for measuring and estimating tyre-road friction was created (Koskinen and Peussa, 2009).

2.3. The Vaisala DSC111 sensor

The Vaisala Remote Road Surface State Sensor, DSC111, is a relatively new device to monitor road conditions. The instrument measures the state of the road surface optically, producing a value of the water content of the amount of snow, ice and water on the road surface (with a resolution of 0.01 mm) as well as an estimate of friction (Vaisala, 2010). In addition, road surface temperature is measured by a collateral DST111 instrument. The instruments can be installed either in a stationary location above the road surface or on a moving vehicle. The instrument's measuring area has a diameter of ca 20 cm at a 10 m height from the road surface. Accurate measurements can be made also during intense traffic. The DSC111 is based on active transmission of infrared light on the road surface and detection of the back-scattered signal at selected wavelengths (Bridge, 2008). The presence of water and ice can be detected independent of each other. Because white ice, i.e. snow or hoar frost, reflects light better than black ice, these main types of ice can be differentiated from each other. The observed absorption signal is transformed and interpreted as amounts of water, snow and ice in millimetres of water equivalent. The state of the road surface (dry, moist, wet, icy, snowy/frosty, slushy) can be determined with this information and, consequently, friction can be estimated based on a pre-modelled formula. The DSC111 friction measurements are reported to have relatively good correspondence with friction measured by other devices (Bridge, 2008; Pilli-Sihvola, 2008). However, latest validations show that friction measurements from a moving vehicle with DSC111 are not necessarily of good quality (Yrjö Pilli-Sihvola, personal communication; Malmivuo, 2011).

Data produced by the DSC111/DST111 instruments were ideal for the study presented in this paper, because road surface temperature, layer thickness of water, snow and ice as well as friction are obtained at the same time at the same location. The relationship between friction and other variables can be modelled applying statistical regression analysis. This statistical association can be formulated by adapting as regression variables output of the meteorological parameters produced by the FMI operational road weather model. This ‘Perfect Prog’ method takes the NWP forecasts for future meteorological variables at face value, assuming them to be perfect (Wilks, 1995). One of the uncertainties concerning the dependent data in this study is that even the ‘observed’ friction from the optical device is also based on a modelled formula. Therefore, there has to be reliance on a good agreement of such friction estimates with those friction values measured simultaneously with other devices when carrying out field test measurements.

3. Data and methods

The Finnish Transport Agency operates more than 100 road weather stations with optical DSC111 (and DST111) instruments installed. Data from ca 20 stations were used in this study and four representative stations were selected for model building. The research was performed under the EU FP7 project ROADIDEA and is described in ROADIDEA public documents (ROADIDEA, 2009) and as conference proceedings by Hippi et al. (2009, 2010) and Nurmi et al. (2010).

The statistical friction equations based on linear regression were calculated using a dependent data set covering two winters, 2007/2008 and 2008/2009 (November to March) at four road weather stations: Utti, Anjala, Orivesi and Kuopio (Figure 1). The equations were validated against an independent data set from winter 2009/2010. The dependent data from the two winters and four stations covered a total of 207 943 observations, of which 19.5% were associated with snow and ice covered roads, 31% with water covered roads, and 49.5% with a dry road surface. The relatively small proportion of cases with snow and ice covered road conditions was somewhat surprising. One cause may have been that the major roads in Finland are well maintained during winter, but another important factor was that winter 2007/2008 was very mild.

Figure 1.

Locations of Utti, Anjala, Orivesi and Kuopio road weather stations. This figure is available in colour online at

The following weather-related parameters were used as independent predictors (symbols given in brackets) for each individual observation time: road surface temperature (TR) in° C, relative humidity (RH) in %, precipitation intensity (PI) in mm of water equivalent per hour, and height (thickness) of snow, ice and water layers (HS, HI, HW) in mm of water equivalent. In addition, the sum of snow and ice thickness (HS + HI) and the difference between road surface and dew point temperature (TR − TD) were used. The latter provides an indication of potential formation of hoar frost, with TR < TD (Karlsson, 2001). The derived dependent variable, friction coefficient (Cf), has a scale from 0.1 to 0.82.

Table 1 displays the Pearson correlation coefficients (or simply, correlation, R) between observed friction coefficient (Cf) and the independent parameters in different temperature and road condition categories. Relatively high correspondence was found between Cf and parameters HS, HI, HS + HI and HW (in the latter case the road being wet). The parameter TR − TD indicated some correlation with friction, but the highest correlation was found under conditions with TR > 0 °C (condensation without ice formation). The parameter TR had a minor correlation with Cf in cases when the road was snow and ice covered. However, it has a distinct role in the statistical equations as shown later. It can be seen from Table 1 that HS + HI had a somewhat higher correlation with friction in cases with TR ≤ 0 °C than under conditions with HS + HI > 0 mm. The higher correlations are probably explained by the high number of cases with a dry road surface and a high friction value (then, HS = 0 and HI = 0, increasing the total correlation of snow and ice). We are here mostly interested in cases when the road is covered with snow, ice or water and the associated decrease in friction.

Table 1. Correlation coefficients between different physical parameters and friction based on dependent data from winters 2007/2008 and 2008/2009. (a) Under all conditions, (b) with TR > 0 °C, (c) with HW > 0, HS + HI = 0, (d) with TR ≤ 0 °C and (e) with HS + HI > 0
  1. The observations were made with the DSC111/DST111 device.

(a) All data0.19− 0.19− 0.2− 0.59− 0.55− 0.680.17− 0.02
(b) TR > 0 °C0.04− 0.41− 0.350.38− 0.87
(c) HW > 0, HS + HI = 00.00− 0.16− 0.230.23− 0.87
(d) TR ≤ 0 °C0.07− 0.22− 0.23− 0.59− 0.54− 0.670.22− 0.01
(e) HS + HI > 00.17− 0.14− 0.10− 0.50− 0.29− 0.560.100.28

Individual models for snow and ice covered roads and wet roads (covered only by water) were developed. Scatter plots of observed friction against the thickness of snow and/or ice as well as against the water layer thickness are shown in Figure 2. The distributions are quite wide and nonlinear and, hence, an appropriate mathematical operator was adapted, after which linear regression could be applied. The function between friction and road parameters can be, e.g. a square-root function or a logarithmic function. Investigations with the square root law are given first here, while the influence of logarithmic dependency is discussed in Section '4.3. Applying a logarithmic function to snow and ice thickness'

Figure 2.

Scatter plots of friction coefficient (Cf) against (a) HS + HI (water content in mm), Pearson correlation R = − 0.56; (b) HS (water content in mm), R = − 0.50; (c) HI (mm), R = − 0.29; (d) HW (mm), R = − 0.87. Data are based on DSC111 measurements during winters 2007/2008 and 2008/2009 in Utti, Anjala, Orivesi and Kuopio (source: Finnish Transport Agency). Plots (a) to (c) are associated with cases with at least some snow and/or ice on the road (HS + HI > 0). Plot (d) is for cases when the road surface was wet (covered only by water (HW > 0))

The square root law proved to be a quite useful method. Applying a square root function on the thickness of water, ice and snow layers improved the correlations in the dependent data set (Figure 3). For example, the correlation between snow and friction increased from − 0.50 to − 0.71. Also, the correlation between water layer thickness and friction improved substantially after applying the square root function and the distribution became more linear. However, the distribution between ice and friction remained quite random and wide with R improving only marginally. This random relation between friction and ice was found a bit surprising. It might be associated with the frequent use of salt on the main roads affecting the structure of the ice. This issue is discussed in more detail in Section '4. Results'. On the other hand, ice on the road surface is quite often covered with a snow, slush or water layer giving an indication that the optical instrument may experience difficulties in measuring ice thickness (and structure) under such circumstances. It should be noted that hazardous situations may occur when an icy surface is covered with loose material: snow on ice may change the rubber-ice friction to ice–ice friction, reducing the friction coefficient further (Makkonen, 2003).

Figure 3.

Scatter plots of friction coefficient (Cf) against the square root of the thickness of (a) snow and ice layer (HS + HI), correlation R = − 0.74; (b) snow layer (HS), R = − 0.71; (c) ice layer (HI), R = − 0.36; (d) water layer (HW), R = − 0.97. Original data are same as in Figure 2

The ‘general’ regression equations were calculated using the whole dependent data set of winters 2007/2008 and 2008/2009. For comparison, individual local equations were calculated for the four sites, Utti, Anjala, Orivesi and Kuopio. Both the ‘general’ and local equations were then tested with the independent data set of winter 2009/2010 at these four locations. The role of the road surface temperature was investigated more thoroughly to see whether the skill of the regression could be further improved by introducing a nonlinear temperature dependency factor into the equation (see Section '4.2. Modelling challenges: road surface temperature and the use of salt'). The influence of road salt and super cooled water (existing simultaneously with snow and ice) on the average friction will also be discussed in this connection.

4. Results

4.1. Statistical friction equations and their validation

Separate distinct models were developed for snow and/or ice covered roads and wet roads based on the correlation analysis of Table 1. A special situation appears when all these three forms exist simultaneously. The statistical regression equations for friction are:

Friction coefficient CFsi for snow and ice covered road surface:

equation image(3)

Friction coefficient CFw for water covered road surface:

equation image(4)

Friction coefficient CFsiw, with existing snow, ice and water on road surface:

equation image(5)

The regression coefficients A1, B1 etc. were calculated for the ‘general model’ using the whole dependent data and for the local point models using the data from that specific location only. The correlations for the ‘general model’ and local models are shown in Table 2. The ‘general model’ for formula CFsi yielded a correlation of R = 0.84 with the dependent data meaning that the model explains 70% of the total variance of observed friction. Road surface temperature (TR) proved to be an important parameter in CFsi. Omitting it would decrease R2 to 0.63. The role of TR is discussed further in Section '4.2. Modelling challenges: road surface temperature and the use of salt' In contrast, adding parameters TR − TD or RH into the regression analysis did not improve R2 considerably.

Table 2. Correlation coefficients for formulas CFsi, CFsiw and CFw based on dependent data from winters 2007/2008 and 2008/2009
 General modelLocal model, UttiLocal model, AnjalaLocal model, OrivesiLocal model, Kuopio
  1. Correlation (R) and R squared for the ‘general model’ and the local models for Utti, Anjala, Orivesi and Kuopio. Conditions for CFsi and CFsiw: HS + HI > 0; for CFw: HW > 0, HS + HI = 0.


The simultaneous presence of snow, ice and water (formula CFsiw) is due to the road surface temperature being close to 0 °C or following salting actions. If salt is used under sub-zero temperatures the melting of snow and ice will result in a super cooled water layer. The effect of salting is not included in the present version of FMI road weather model and, consequently, super cooled water cannot exist in the model. This means that the operational use of CFsiw is not applicable and CFsi is used instead. Anyway, CFsiw reached somewhat higher R values than CFsi (Table 2). The local models for Utti and Anjala resulted in higher R values than the ‘general model’ (for both CFsi and CFsiw, see Table 2), but the results were the opposite for the Orivesi local model. The model for wet roads (CFw) had very high correlation values both for the general and local models and the results could not be improved much by adding extra regression parameters.

In the second phase, Equations (3)(5) were validated against independent data from winter 2009/2010 at the four observation stations. The observed thicknesses of snow, ice and water were used to calculate the modelled friction CFsi, CFsiw and CFw, and they were then validated against observed friction (Table 3). The results show that the correlation for CFw (water covered roads) was very high at all four locations indicating a straightforward, simple relationship between water layer thickness and friction. However, over wet road surfaces friction depends also on the speed of the vehicle, decreasing with increasing speed (Makkonen, 2003; COST, 2008), and the morphology of the tyre surface is very important to ensure a good grip. Thus, the simple formula CFw gives just an estimation of the average grip on a wet road.

Table 3. Correlation coefficients for the modelled ‘general’ friction of formulas CFsi, CFsiw, CFw tested with independent friction observations from winter 2009/2010 at the four locations: Utti, Anjala, Orivesi and Kuopio (three top rows)
  1. The correlations for the local friction models are shown on the three lowest rows. Conditions for CFsi and CFsiw: HS + HI > 0; for CFw: HW > 0, HS + HI = 0.

CFsi, local model0.850.870.820.53
CFsiw, local model0.860.880.850.62
CFw, local model0.980.980.970.96

Formulae CFsi and CFsiw for snow and ice covered roads yield lower correlations. The results for Utti and Anjala (in south-eastern Finland) are relatively good (see also Figure 4), but the values for Kuopio are much weaker. This might result from winter 2009/2010 having had, on average, much smaller ice thicknesses than the two previous winters in Kuopio (in eastern Finland). However, winter 2009/2010 was cold especially in eastern and northern parts of Finland with probably more days with dry cold winter weather and loose/drifting snow on the roads than ice. The local models for CFsi and CFsiw had somewhat higher correlations than the ‘general model’ except for Utti, where the ‘general model’ had slightly higher correlations than the local single point model. Comparing the correlations of CFsi and CFsiw shows that the inclusion of water in the equation for snow and ice covered roads (i.e. shifting from CFsi to CFsiw) improves the correlations indicating that slushy conditions are better modelled with CFsiw. Concerning wet snow, an additional frictional mechanism, capillary suction, would increase friction (Makkonen, 2003).

Figure 4.

(a) Scatter plot of observed friction coefficient (Cf) and modelled friction coefficient (formula CFsi from Equation (3)) in cases of snowy and icy road surfaces (R = 0.86). (b) The same for wet roads (formula CFw from Equation (4), R = 0.98). Based on the independent data from Utti during winter 2009/2010

The validity of the friction formulas are visualized by the scatter plots of Figures 4 and 5. First, Figure 4 shows that although the distribution of modelled versus observed friction is quite wide and curved, the result is relatively satisfactory overall. The majority of data points are close to the diagonal, except for the upper end, where the model shows systematic under prediction. Further improvements are therefore needed. On the other hand, the results look very good for wet roads (CFw; Figure 4(b)) as was expected from the high correlations shown in Table 3.

Figure 5.

(a) Modelled friction (formula CFsi from Equation (3)) and (b) observed friction Cf as function of observed thickness of snow and ice (HS + HI, water content in mm). Based on independent observations at Utti station during winter 2009/2010

Figures 5(a) and (b) show the relationship between modelled and observed friction on the observed thickness of snow and ice, respectively. We can see that the modelled friction distribution reproduces the observed one quite well. Although the absolute values of modelled friction are under predicted at the lower end (too many of them remaining at the low 0.1 level), the accuracy might be sufficient since practical applications use a categorization with pre-defined thresholds (e.g., 0.6/0.3/0.15).

4.2. Modelling challenges: road surface temperature and the use of salt

It appears from observations that friction depends on road surface temperature when the road is covered with snow and ice, although the correlation is quite low (see Table 1). The variability of observed friction (Cf) is high, especially in the temperature range between − 5 to 0 °C, covering almost the entire measuring range of the DSC111 instrument (0.1–0.82). The use of salt and the simultaneous presence of water with snow and ice could explain this feature.

The cases with at least a thin, uniform layer of snow and ice on the road were investigated in detail, i.e. all cases when the water content is at least 0.1 mm (a total of 22 327 observations in the dependent data set, Figure 6). This corresponds to a layer thickness of 0.1 mm or more of pure ice or 1 mm or more of pure snow. By using this threshold and neglecting the ‘noise’ due to cases with a very thin, possibly non-uniform snow and ice layer it was possible to focus on cases when the road was actually covered by a substantial snow and ice layer.

Figure 6.

Dependence of observed friction (Cf) on road surface temperature (TR,° C) only for the cases exceeding the threshold HS + HI (water content) ≥ 0.1 mm. (a) All such cases (22 327 observations, friction mean = 0.27, standard deviation STD = 0.15), (b) as in (a) but only cases when there is also water simultaneously with the snow and/or ice layer (4185 observations, friction mean = 0.48, STD = 0.14), (c) as in (a) but when there is only snow and/or ice without water (18 142 observations, friction mean = 0.22, STD = 0.10), and (d) dependence of Cf on water layer thickness (HW, in mm, when existing simultaneously with snow and/or ice (HS + HI ≥ 0.1 mm), 4185 observations). Based on the dependent data from winters 2007/2008 and 2008/2009

Figure 6(a) shows that at low temperatures (below − 10 °C) the scale of observed friction on snowy and icy roads is quite narrow and Cf remains mostly below 0.3. This is probably a consequence of salting normally not being done in Finland at such low temperatures. Comparing Figures 6(a)–(c) indicates that much of the variability of Cf is related to the presence of water (in most cases super-cooled) simultaneously with snow and ice. The average friction in those cases (Figure 6(b)) was 0.48 compared to 0.22 in cases with dry snow and ice (Figure 6(c)). The lowest temperature for observed super-cooled water within the snow and ice layer was ca − 9 °C (Figure 6(b)). Figure 6(d) shows that friction increases rapidly with increasing water amount within the snow and ice layer. This might partly explain the wide distribution between friction and ice, as already discussed in Section '3. Data and methods'. Ice that contains salt becomes softer with higher friction value and eventually melts. Haavasoja and Pilli-Sihvola (2010) point out that a solution of water and de-icing chemicals may freeze and the newly formed ice is mechanically softer than clean ice resulting in higher Cf.

The average observed Cf and the standard deviation (STD) of Cf was calculated in bins of 1 °C (0….− 1, − 1…. − 2 etc., Figure 7) in order to get a more comprehensive picture of the relation between road surface temperature and friction for conditions with snow and ice on the road. It appeared that the average friction for the two winters' dependent data had the highest value 0.45 in the 0….− 1 °C category (Figure 7(a)), and decreasing with decreasing temperature. Without frequent use of salt at observation sites on these main roads, the average friction would probably be lower at temperatures just below zero.

Figure 7.

(a) Mean observed friction coefficient (Cf) as function of road surface temperature (TR), presented in 1 °C bins, (b) standard deviation (STD) of Cf versus TR in the 1 C bins, (c) number of cases (Nobs) in each 1 °C road surface temperature bin. Distributions are based on cases exceeding the threshold HS + HI (water content) ≥ 0.1 mm). Based on the dependent data from winters 2007/2008 and 2008/2009

The STD of friction was largest when the road temperature was close below zero and decreasing with colder temperatures (Figure 7(b)). It must be pointed out that if cases having HS + HI between 0.01 and 0.09 mm were to be included, the STD would be much higher and the average Cf somewhat higher in cold temperatures. It appears from Figure 7(c) that the majority of cases with snow and ice covered road surfaces fall into the temperature interval − 7 to − 0 °C and the maximum being around − 3 °C. This is the range where salting is most effective.

The results presented in Figures 6 and 7 are related to wintry conditions on Finnish major roads. On secondary roads with less maintenance the conditions might often be more slippery when the temperature is around 0 °C. It is generally known from experiments that Cf of pure ice decreases with increasing temperature (Weast, 1971; Makkonen, 1994, 2003). According to Moore (1975), ice is most slippery at 0 °C. However, the frequent use of de-icing chemicals on main roads at temperatures around 0 C or slightly below causes an inverse behaviour (i.e. increase) of the average Cf, thus improving traffic safety. The results found in this study are also in line with the findings of Andersson and Chapman (2011) concerning slipperiness. Although the most dangerous road surface temperature has been shown to be around 0 °C, the study in Sweden indicated that accidents actually were more common at temperatures below − 3 °C.

The low average friction (Cf) at the cold end (−20…− 15 °C) of Figure 7(a) is questionable due to the fact that Cf of ice increases towards colder temperatures. According to Makkonen (2003), Cf of rubber on ice has a value of 0.1, or even lower, at temperatures just below 0 °C. Cf then increases to ca 0.4 when the ice temperature decreases to − 15 °C. Our data covered relatively few cold cases and in many of them snow and ice were observed simultaneously. As presented in Section '3. Data and methods', snow on ice can further reduce friction.

Since the current version of the FMI road weather model does not include the effect of salting operations and the possibility for super-cooled water, the formula for CFsi should be used in friction prediction applications. Because road surface temperature is included in the equation, the average behaviour of friction as a function of temperature (mostly due to salting) was taken into account in a statistical way. The large variability in friction cannot be predicted properly by the statistical model equation and the average dependence is not linear (Figure 7(a). This means that the model probably predicts too low friction values at extreme cold temperatures (−20…− 10 °C). Therefore, a nonlinear parameter was introduced:

equation image(6)

It was tested in the formula of CFsi replacing the road surface temperature (TR). The new parameter was adjusted to have a value of zero at 0 °C temperature (Figure 8). It has moderate correlation with friction in the dependent data set (R = 0.50, R2 = 0.25) under conditions when HS + HI ≥ 0.1 mm. The correlation decreases to 0.23, when all cases with snow and ice on the road (HS + HI > 0) are taken into account. Anyway, the introduction of TRlog improved R slightly, from 0.84 to 0.86, in the dependent data. Even a greater rise in the correlation was found when using the independent data from Orivesi and Kuopio stations.

Figure 8.

(a) Logarithmically modulated road surface temperature parameter for calculating formula CFsi (Equation (3)), TRlog = − log(−(TR − 1)), as a function of standard TR (° C). (b) Scatter plot of observed friction coefficient (Cf) and parameter TRlog in cases when HS + HI ≥ 0.1 mm (correlation R = 0.50, R2 = 0.25). Based on the dependent data from winters 2007/2008 and 2008/2009

4.3. Applying a logarithmic function to snow and ice thickness

Applying the square-root function on parameters HS, HI and HW improved the correlations with observed friction in the dependent data set. Another technique which could be applied on the wide, curved distributions (see Figure 2) would be to use a logarithmic function. A new version formula CFsi (Equation (3)) was derived using log(HS), log(HI) and TRlog (from Equation (6)) as independent variables:

equation image(7)

The logarithmic function cannot, however, be applied on the whole domain if a parameter produces a zero value. This was quite often the case in these data when either snow or ice alone was observed on the road surface. Therefore, the assumption was made that in cases when HS > 0 and HI = 0 and when HI > 0 and HS = 0, the zero value was replaced by a thickness of 0.005 mm. This value is about half of the accuracy of the optical measuring instrument, advertised as 0.01 mm by the manufacturer. The regression technique was applied with these assumptions on the dependent data. The resulting ‘general equation’ had substantially higher correlations than the previous square-root versions of the formula for CFsi, R = 0.90 compared to R = 0.84 (and to R = 0.86 when using TRlog instead of TR in Equation (3)).

When testing the new equation with independent data from winter 2009/2010 at the Utti station, the correlation was high at R = 0.89 (compared to 0.86 of the square-root version). It was even higher for the Anjala station, R = 0.93 (see also Figure 9). The contingency tables for friction thresholds of 0.3 or 0.15 (Table 4) also show good results for the modelled friction formula CFsi, b using Anjala station data (which showed clearly the best results among the four stations). Thus, a higher amount of friction variability can be explained by the model by applying a logarithmic function than by using the square-root dependency. The disadvantage is that the assumption of replacing 0 by a small artificial value like 0.005 as described above had to be made. Alternatively, independent equations for snow and for ice could be used in cases when there is either snow or ice alone on the road.

Figure 9.

Scatter plot of observed friction coefficient (Cf) and modelled friction coefficient (formula CFsi, b, Equation (7)) in case of snowy and/or icy road surface (HS + HI > 0). Correlation R = 0.93 (R2 = 0.86). Based on the independent data at Anjala station during winter 2009/2010

Table 4. Contingency tables for modelled friction from formula CFsi, b with the logarithmic dependency (general model, Equation (7)) and observed friction Cf: (a) using 0.3 as the friction threshold, and (b) using 0.15 as the friction threshold. The Heidke Skill Score (HSS) for (a) is 0.80 and for (b) HSS = 0.65. Based on the independent data from Anjala during winter 2009/2010
 Cf≤0.3Cf > 0.3SUM
CFsi, b≤0.32541832624
CFsi, b > 0.340019192319
 Cf≤0.15Cf > 0.15SUM
CFsi, b≤0.1547785562
CFsi, b > 0.1532640554381

4.4. Accuracy of the background information for the friction model

It has been shown that road surface friction can be modelled with statistical equations, explaining over 70% of the total variance of the observed friction. The optical device used for friction observations has demonstrated quite good consistency with other friction measuring devices. The equations can be applied, after fine-tuning, in a forecasting mode based on input from the FMI road weather model, the input parameters being road surface temperature and thickness of snow, ice and water layers.

One fundamental issue in using these equations is whether the quality of input information is good enough (the ‘Perfect Prog’ approach). Accurate prediction of the amounts of snow, ice and water on the road surface is a challenging task. It requires high-quality forecasts of the general meteorological situation (by a numerical weather prediction model) and, in addition, specific forecasts of the road conditions by a road weather model which tackles various complex processes such as the vertical energy transfer at the road surface and the effects of traffic flow. Inaccuracies in the predicted thicknesses of snow and ice can cause large errors in the eventual friction forecast output.

A practical friction prediction pilot experiment was organized within the EU project ROADIDEA during winter 2008/2009 in collaboration between project partners, the FMI, Destia (Finland) and Demis (The Netherlands). Real-time road condition and friction forecasts for Finland were issued on the project website ( The skill of the product was evaluated on a daily basis and it turned out that the predicted friction was systematically too low in many cases. The main reason proved to be too large thickness values of snow and ice in the input information (coming from the FMI road weather model). The equations in the road weather model responsible for the wearing of snow and ice from the road surface were fine-tuned accordingly in order to reduce this bias.

5. Discussion and concluding remarks

Modelling road surface friction is a new way to analyse and predict slipperiness. As described in Section '2.3. The Vaisala DSC111 sensor', this work was based on observations made with the optical Vaisala DSC111 instrument, while the statistical model was developed to simulate the measuring instrument itself in a simple way. The results look promising although the verification results indicate that there is room for further investigation and improvements. The statistical model could be improved with more extensive data coverage of different kinds of weather situations. The mathematical and statistical methods used in the equations could also be further improved and fine-tuned. For example, the use of logistic regression (Wilks, 1995) instead of linear regression could be examined. The road weather model is responsible for producing the meteorological input into the friction model. Hence, it is very important to validate and improve this model, too.

A major shortcoming challenging improvements in the road weather model is the unavailability of road maintenance actions (e.g., salting, ploughing) to be entered into the model. With this in mind, the friction forecasts should rather be regarded as risk forecasts giving an indication of the worst road conditions that might exist. An alternative approach to deterministic forecasting could be to produce probabilistic friction forecasts by using ensemble prediction data from NWP models as background information. This would entail several parallel model runs to produce probability distributions of road weather parameters and friction. Either deterministic or probabilistic friction forecasts could be adapted to various warning services and customer products.


We thank Esa Tarkiainen, Finnish Transport Agency, for providing the road weather observation data. We acknowledge Professor Sylvain Joffre, FMI, for his review and valuable comments to improve this paper. This work was partly funded by the EU/FP7 Project ROADIDEA, where the main objective was to develop new and innovative ideas and products for the traffic and transport sectors.