A Coupled Model to Simulate Snow Behavior on Roads

Transcription

1 500 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 A Coupled Model to Simulate Snow Behavior on Roads LUDOVIC BOUILLOUD Météo-France/Centre National de Recherches Météorologiques/Centre d Etudes de la Neige, Saint-Martin d Hères, France ERIC MARTIN Météo-France/Centre National de Recherches Météorologiques/Groupe de Météorologie de Moyenne Echelle, Toulouse, France (Manuscript received 8 March 2005, in final form 26 August 2005) ABSTRACT To develop a decision-making tool for road management in winter, a numerical model resulting from the coupling of a soil model and a snow model was developed and validated using experimental results from a comprehensive experimental field campaign during three winters (1997/98, 1998/99, and 1999/2000). The coupling of the models has been done through an implicit calculation of the conduction flux between snow and road. An equivalent thermal resistance has been used to take into account the different road snow interface configurations. For this purpose, a parameterization of water-saturated snow was introduced. This model permits the simulation of the snow behavior on a road, and it takes into account different interfacial configurations according to snow and road types and the snowpack evolution (freezing, melting, grain type). Comparisons of experimental and simulated results for typical snowfall events or over the entire winter showed that the model was able to simulate road surface temperature, snow occurrence on the road, and snow-layer evolution with good accuracy. 1. Introduction During winter, many roads located in cold or temperate regions (e.g., North America, Europe) are subject to severe climatic conditions associated with snow and ice. These conditions have serious consequences on driving conditions, reducing the traffic flow dramatically. In this context, a road weather forecasting system can help to organize the maintenance services, reduce the accident risk, and maintain, as practicable as possible, the road network. The prediction of the road conditions requires the production of accurate forecasts of the thermal and hydrological states of the road surface: temperature, water content, and snow occurrence or height. Since the 1980s, several numerical models were developed to predict road surface conditions (Thornes 1984; Rayer 1987; Shao 1990; Sass 1992; Crevier and Delage 2001). They focused mainly on road surface temperature and ice. Corresponding author address: Ludovic Bouilloud, Centre d Etudes de la Neige, Centre National de Recherches Météorologiques, Météo-France, 1441 rue de la Piscine, Saint-Martin d Hères Cedex, France. ludovic.bouilloud@meteo.fr The ice was usually treated as a bucket-type reservoir on road. More detailed representations of ice are difficult to simulate because of the complexity of the phenomena involved (rainwater freezing, hoarfrost, freezing surface water, freezing fog). Most of the iceforecasting models were expert systems that integrate atmospheric conditions and local meteorological effects (Norrman 2000; Karlson 2001; Knollhoff et al. 2003). Concerning snow, the expert systems were based on snow precipitation forecasts. They did not account for the highly variable thermal fluxes during snow deposition and the snow road interface properties. A research project has been conducted in France since 1995, which joins the expertise of the Center d Etudes de la Neige (CEN; Météo-France), the Center d Etudes Techniques de l Equipement (CETE) in Lyon and Nancy, the Laboratoire Central des Ponts et Chaussées (LCPC), and the Direction Départementale de l Equipement de l Isère (DDE 38). This project had two main goals. The first was to increase the knowledge of snow behavior on pavement, notably processes related to road snow interface physics, deicing effects, and snow compacting by traffic (Borel and Brzoska 2000; Muzet et al. 2000). The second goal was to develop a model with the ability to account for these phe American Meteorological Society

2 MARCH 2006 B O U I L L O U D A N D M A R T I N 501 nomena, in order to build a comprehensive decisionmaking tool for winter-road exploitation. This paper describes the first step of the development of this model. At this stage, the goals of the model are to simulate the road surface temperature, the moment at which the snow begins to accumulate on the road surface, the characteristics of the interface between the snow and the road, the road liquid water, and the ice content on the road surface. This study only focuses on the natural deposition of snow on roads, and the model does not take into account traffic or deicing effects at this stage. The present paper describes the model and its validation. First, the physical and numerical principles of the model are described. Then, the model validation is carried out by comparison with the results to observational data from a test site in the French Alps. 2. Model description The model is constituted by the coupling of two onedimensional models: the land surface Interactions between Soil, Biosphere, and Atmosphere (ISBA) model (Noilhan and Planton 1989), adapted to road conditions, and the snow model CROCUS (Brun et al. 1989, 1992). The name of the model ( GELCRO ) is such because of a preliminary coupling between the GEL1D road model (Frémond 1979) and the CROCUS model. However, the GEL1D model was not able to account for hydrological processes, turbulent fluxes, or porous pavement at the level needed by the project, which is why it was replaced by ISBA. a. ISBA The ISBA land surface scheme simulates the interaction between the soil, the biosphere, and the atmosphere in mesoscale, regional, and climate atmospheric models. ISBA is a simple, physically based scheme that solves the water and energy budgets. ISBA has been validated in numerous experiments at different spatial and temporal scales (Noilhan and Mahfouf 1996). The ISBA version used here is the diffusion version (ISBA- DF) (Boone et al. 2000): a multilayer resolution scheme of the heat and mass transfer equation in a porous medium. Several changes were introduced into the model for the winter-road surface-forecasting problem. All of the processes associated with vegetation (evapotranspiration, root water extraction, vegetation thermal inertia, water interception) were removed. Only hydrological and thermal transfer interactions between the soil and atmosphere were taken into account. Dry thermal conductivity and density were defined at each node according to the road constitution as opposed to being derived from the natural soil properties as in the original model version (i.e., as a function of the sand clay loam proportions). Another modification was necessary concerning the water content of each layer. Roads are impermeable, except in a thin surface layer (depending on the material); the hydrological transfers were removed below this zone in the model. The road simulated in the model was a thick structure typical for highways in France. The surface was constituted of semigrainy bituminous concrete. The hydrological transfers remained possible over a depth of m (corresponding to one calculation node), with a porosity corresponding to a maximal volumetric water content of 6.35%. Outside of this surface layer, the total water (ice liquid) content remained constant. The physical properties of the road are described in Table 1. In the model, the soil (the road and the natural soil below) had a depth of approximately 9 m, so that a nil flux lower boundary condition for temperature is reasonable. The depth and properties of the physical layers are shown in Table 1, as is the numerical discretization of the model. The number of nodes by physical layer is determined in order to precisely describe the phenomena near the surface while preserving sufficient nodes in the deep layer for a good representation of the annual temperature cycle, and in order to limit calculation costs. Two snow scheme options are available in ISBA (Douville et al. 1995; Boone and Etchevers 2001), but they cannot simulate the highly variable thermal fluxes, the snow grain types, and the capillary rise at the road snow interface. This is the reason why these schemes are not used in this study. TABLE 1. Physical and calculation properties of soil layers, where z is the thickness, is the density, k dry is the dry thermal conductivity, and W sat is the porosity. Material z (m) (kg m 3 ) k dry (W m 1 K 1 ) W sat (%) Nodes Semigrainy bituminous concrete Semigrainy bituminous concrete Sand gravel cement mix Subgrade Natural soil

3 502 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 b. CROCUS CROCUS (Brun et al. 1989, 1992) is a detailed snow model used for avalanche forecasting by Météo-France (Durand et al. 1999). It simulates the energy, mass, and stratigraphy evolution of snow cover as a function of meteorological conditions. It computes the evolution of temperature, density, liquid water content, and layering of the snowpack. The number of layers varies from 1 to 50, depending on the snow depth. The originality of this model is its ability to simulate snow metamorphism, which is crucial for an accurate simulation of the properties of the snow road interface (see further sections 2d and 2e). A parameterization of the water-saturated snow layer at the base of the snow cover was introduced in the model. This type of snow plays a major role in some road problems, because this water-saturated layer can freeze, thereby causing dangerous traffic conditions. This modification will be detailed in section 2d. The last major modification introduced was the time repartition of snowfall events. In the original code, for the case of a low hourly snowfall (lower than 0.01 m of new snow depth), the snowfall was added to the snowpack once an hour. For the needs of this study, the hourly snowfall was spread out over each time step (5 min) in order to reproduce, as accurately as possible, a continuous snowfall (with a minimum value of m snow depth to prevent numerical problems). In the original version of CROCUS, the number and depth of layers were determined by the model itself according to the total snow depth and the layering of the snowpack. This provoked some numerical instability in the highly variable snow road thermal flux. It was therefore decided to hold the thickness of the first snow layer above the road at a constant value of m by partial aggregation with the layer above (except if the simulated snow depth is too low). c. Coupling principle In the following, the term layer is used to describe a numerical layer after discretization. Hence, each physical layer of the road is represented by several nodes. Each snow layer had its own physical properties, so numerical layers were equivalent to physical layers. It should be mentioned that the ISBA and CROCUS equations were solved using finite-difference schemes, so that each layer was represented by one node located at the middle of the layer. The time step of the coupled model was 5 min. The road surface temperature evolution is governed by the following equation: T s c T 1 p t t R N H LE p t F cond F adv F sol G, 1 where c T was the heat capacity of the road surface layer, T s was the temperature of the road surface layer, p t represented the time proportion of snow presence during the time step, R N was the net radiation at the surface, H and LE were the sensible and latent heat fluxes from the atmosphere, F cond was the conduction flux between snow and road, F adv was the advection flux from snow cover runoff, F sol was the solar flux at the bottom of the snow cover, and G is the soil heat flux [all fluxes are positive when directed to the road surface layer in Eq. (1)]. In its original version, the ISBA model used a p N coefficient representing the spatial snow coverage on the surface. For road applications, it has been considered that the surface was flat and vegetation free, so this coefficient was removed and replaced by the p t coefficient defined above. For the snow-free case (p t 0), or for snowmelt during the time step (0 p t 1), the atmospheric fluxes R N, H, and LE from the road were calculated by the ISBA model. Over the snow, the fluxes were calculated similarly by CROCUS using different albedo, emissivity, and roughness length values. The advection flux F adv was calculated by the ISBA model, with the water runoff given by CROCUS. The solar flux at the bottom of the snow cover F sol was determined by CROCUS. To prevent numerical instability, the calculation of the conduction flux F cond was implicit. The method used to calculate the fluxes as well as the temporal integration of the two models depended on the road snow interface characteristics. d. Parameterization of capillary rise and water-saturated snow height Capillary forces are responsible for liquid water retention in the snow, and they depend primarily on the grain type. The maximum holding capacity of snow varies from 5% to 10% of the total mass. The excess water percolates down into the snow cover. Water saturation associated with capillary rise is possible above the road snow interface over a depth of several centimeters, depending on snow grain type and road characteristics. This layer modifies the thermal exchanges as well as the mechanical properties at the interface. Capillary rise usually occurs in the case of rain, melting of the snowpack, or a positive road surface temperature. 1) CONDITION FOR CAPILLARY RISE The presence of snow within the road surface roughness elements allows capillary rise of water from the

4 MARCH 2006 B O U I L L O U D A N D M A R T I N 503 road snow interface to the snow. The finescale rugosity geometry depends on material type and road construction. It is highly variable, even within pavement. One of the consequences of this variability is that it is impossible to separate a road layer from a bottom snow layer (Borel 2000). Therefore, a very simple parameterization for the retention volume at the road surface was used. The retention volume V ret was defined by V ret C ret V pore s V ice s, where V pore s was the pore volume of the road surface layer, V ice s was the volume of ice inside the road surface layer pore, and C ret was the nondimensional coefficient characterizing the retention. If the liquid water volume on the road surface layer V ws was greater than the retention volume V ret, capillary rise from the road surface was possible (until the maximum retention value was reached). It was not possible to obtain values of C ret from literature or field measurements. Following the sensitivity tests done with C ret varying from 0.01 to 1, which showed a low sensitivity of the results to this parameter, it was decided set this value to ) WATER-SATURATED SNOW HEIGHT Coléou and Lesaffre (1998) and Coléou et al. (1999) studied water saturation in snow and found a relation between grain type (mean convex radius of snow grains) and water-saturated snow height. The formulation proposed by Borel (2000), who completed the aforementioned work by adding a dependence on road surface type, was used herein. The maximum saturation height h max (m) was defined by 1 P i 1 h max C P i r m i, where P(i) was the porosity of the considered layer, r m (i) was the mean convex grain radius (m) of the considered layer, and C was a coefficient depending on the surface road material ( m 2 for a porous pavement, m 2 for an impermeable pavement, and 10 5 m 2 in the particular case of ice presence on the road surface). In the model, capillary rise and water-saturated snow 2 3 height were taken into account partly at the beginning of the time step and partly at the end of the time step in order to limit numerical instabilities and errors in the determination of the type of the snow road interface. The principle is that if water in the road surface exceeded the retention value, the air is replaced in each snow layer by water from the bottom to the top, until the maximum saturation height is reached or until the road water bucket has returned to its retention value. At the beginning of the time step, water from rain and the road surface reservoir was used. At the end of the time step, water from the percolation of snow was used. If the maximum saturation height was reached, water exceeding saturation ran off the road surface. e. Thermal resistance at the interface To define an equivalent thermal resistance R th between the road upper node and the snow lower node, we used the interface classification established during the GELCRO field experiment (Table 2). Here R th was a function of R s (the thermal resistance of the road surface layer, between the node and the surface, assuming that the node is in the middle of the layer), R N1 (the thermal resistance of the first snow layer between the node and the surface), and R int (the interfacial thermal resistance), which depended on the interface configuration. Wet snow in Table 2 means that the bottom snow layer contains liquid water and wet road means that the road surface layer water content is greater than its retention value. The presence of water in the lower snow layer leads to perfect capillary contact between snow and the road, so there is no interfacial resistance, and the snow layer is at 0 C (isothermal), so that thermal conductivity is infinite inside the snow layer. In contrast, for the case of dry snow on a dry road, the presence of air inside the road surface porosity generates an interfacial resistance, depending on the road surface material. Two particular situations needed special treatment. The first one was the case of partial freezing of the bottom snow layer resulting from a cold road. Even if there was liquid water in the layer and the node temperature was equal to 0 C, the conductivity inside the TABLE 2. Equivalent thermal resistance R th at the snow road interface in the GELCRO model; R s represents the thermal resistance of the road surface layer (between the node and the surface), R N1 is the thermal resistance of the first snow layer (between the node and the surface), and R int is the interfacial thermal resistance. Snow state Dry Wet Dry (previously wet, totally frozen) Wet (bottom frozen) Road state Dry R s R N1 R int R s R s R N1 R s R N1 Wet (Impossible) R s R s R N1 R s R N1

5 504 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 snow layer was not infinite. In the CROCUS model, in order to distinguish between cases of wet snow and wet snow frozen at the snowpack base, a historical interface variable was introduced. The second one applied to the case of a dry snow resulting from the total freezing of the water: the presence of refrozen water removed the interfacial thermal resistance. The case (not described above; dry snow on a wet road) was impossible, in practice, because of capillary rise. The interface is the layer where snow and road cannot be distinguished. We used the interface definition of Borel (2000). The interface had two different parts, each with its own thermal properties. The snow interface was independent of the road surface material; it was defined with a depth ( z N int ) of m and a conductivity (k N int ) of W m 1 K 1. The road interface was road surface material dependant. For a porous pavement, it was defined as having a depth ( z S int) of m and a conductivity (k S int ) of 0.4 W m 1 K 1, and for an impermeable asphalt it was defined using a depth ( z S int ) of m and a conductivity (k S int )of0.7wm 1 K 1. The interface thermal resistance was given by R int z N int k N int z S int k S int R S eq R N eq, where R S eq and R N eq were snow and road thermal resistances corresponding to the interface depth (because they were already taken into account in the equivalent thermal resistance, R th ). f. Numerical solution 4 The very different snow and road thermal properties, the phase changes, and the rapidly changing interface properties complicated the numerical calculations of the temperature profile. For the time integration, it was necessary to distinguish many cases depending on the initial temperature and water content of the bottom snow layer and the possible phase change in this layer during the time step. For instance, if the bottom snow layer was initially dry (temperature below 0 C), a new temperature profile was calculated for the snow and the road. If the new temperature of the bottom snow layer remained below 0 C, there was no interface change, and the new snow temperature profile was saved in CROCUS. ISBA was then run with the upper flux condition F cond deduced from the previous calculation. If the new temperature of the bottom snow layer was equal to or above 0 C, a new calculation was done for the road and the lower snow layer (assuming that its new temperature was equal to 0 C) with a wet snow wet road interface. The new CROCUS and ISBA profiles were then recalculated using F cond deduced from the second calculation. In the case of initial wet snow above the road, several calculations were done in order to determine, prior to CROCUS and ISBA temporal integration, the temperature of the lower snow layer and the interface characteristics. In some cases, it was necessary to introduce a numerical flux (F fr ) to account for the cold flux necessary to freeze the liquid water in the bottom layer to avoid numerical instability. The complete algorithm is summarized in Fig. 1. The original 5-min time step of the coupled model was reduced to 30 s in the case of a snowfall on a warm, snow-free road (equivalent to a thermal shock). The hydrological transfer between snow and road was managed in CROCUS at the end of the time step, after the evolution of snow cover temperature; the runoff at the base of the snow cover (melting, excess after snowwater saturation, and rain amount that reaches the snow cover bottom) was added to ISBA for hydrological transfer in the road. Capillary rise in the snow cover was taken into account partly at the beginning of the time step and partly at the end. 3. Model validation The model validation was done through a comparison between simulated and observed variables in a field experiment. In this section, sensitivity results of the model are shown after a description of the experimental field site. The results for three typical snowfall events are discussed. Last, the results of long-term runs during the three winters of the experiment are presented. In all of the runs, the initial temperature profile of the model was derived from temperature measurements in the road, or (for the natural soil deep temperatures from 1 to 9 m) from a 10-yr spinup simulation with the measured atmospheric data at Col de Porte. a. Field experiment 1) DESCRIPTION OF THE FIELD SITE The field site was built within the Météo-France experimental station located at the Col de Porte (1320 m, French Alps). Despite a relatively low elevation, frequent snowfalls occur at this site, leading to a prolonged snow cover presence (from October to May, on average). This site, described in Fig. 2, is equipped with all of the classical meteorological sensors (for measuring air temperature, humidity, wind speed, and liquid and solid precipitation, and with shortwave and longwave radiation sensors). For the needs of this project, six experimental pavements (2 m 3 m) were constructed.

6 MARCH 2006 B O U I L L O U D A N D M A R T I N 505 FIG. 1. Flowchart of the different cases for the numerical resolution of the conduction flux between the road and the snow for coupling: T t N1 and W t N1 are, respectively, the temperature and the liquid water content of the first snow layer at the beginning of the time step; R t th and R t t/2 th are the equivalent thermal resistance between the road surface layer and the first snow-layer nodes, respectively, at the beginning of the time step, and they are implicitly calculated to take into account interface modification during the time step; F fr is a source flux corresponding to the opposite of the cold flux necessary to totally freeze the liquid water in the first snow layer.

7 506 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 The pavements covered the diversity of the structures used in France, from thin pavements (usually used for low-traffic-density roads) to pavements typically used in highways, with either a sand gravel bituminous mix or a sand gravel cement mix. Different surface layers were used: semigrainy bituminous concrete, very thin bituminous concrete, drainage bituminous concrete, or gravel. These pavements were equipped with numerous sensors, including snow depth sensors, temperature probes (from the surface to a depth ranging from 0.29 to 0.6 m, according to the different pavements built), and video cameras. The cameras made it possible to observe the pavement becoming snow covered and to characterize the snow evolution for different weather conditions. The type of road used in the model (described in Table 1) was a thick structure, composed of m of semigrainy bituminous concrete in the surface layer, m of sand gravel cement mix, and m of subgrade. An experimental study was done by the LCPC to determine thermal properties of each pavement. Automatic measurements were supplemented by manual measurements. They consisted of measurement of the snow height on each pavement, measurement of the snow density, description of the stratigraphy, and specifically the snow pavement interface, measurement of the water-saturated snow height (if it exists), and measurement of the snow temperature with a vertical resolution of m in order to obtain a detailed thermal profile. In the absence of a natural snowmelt event, snow was removed from pavements after a few days, in order to obtain a snow-free road for the following snowfall. The experiment was performed during three winters: 1997/ 98, 1998/99, and 1999/2000. Thanks to a significant mobilization of the laboratory, a 60-event database (20 for 1997/98, 28 for 1998/99, and 12 for 1999/2000) was obtained. FIG. 2. The experimental field site at Col de Porte (1320 m, French Alps). 2) RESULTS The events were classified according to the air and road surface temperature at the beginning of the snowfall. Concerning snowfall, two states were defined: moist or dry snowfall. Snow was classified as moist if the air temperature was near 0 C and dry if the air temperature was lower than 1.5 C. Between 1.5 and 0.5 C the snowfall classification was determined according to the observed grain type. Road state was defined very carefully by its thermal and hydrological state. Therefore, the road was defined as cold if, at the beginning of the snowfall, the surface temperature was negative, and warm if the surface temperature was positive. The road was defined as being wet (or frozen in the case of a cold road) if the water content exceeded the water retention in the surface layer, and was dry otherwise. The distribution of the different types of events are shown in Table 3. Some types of events were never observed during the campaign, such as a snowfall on a frozen road, or a moist snowfall on a cold road. The latter case was unlikely to occur at the Col de Porte, where moist snowfalls are usually preceded by rain. Several treatments were made to the meteorological data in order to obtain the best possible forcing for the model. A correction of solar fluxes has been applied for each pavement to account for the difference in the solar mask between the sensor and each pavement. The horizon (trees, building, mountains), which is highly variable in the experimental field, was measured for the solar radiation sensor and each pavement. Using a simple theoretical model, the direct and diffuse solar radiation were then estimated for each pavement. Corrections were applied to snowfall precipitation according to the wind speed. Last, a manual determination of the precipitation type (rain or snow) was necessary for cases of rain followed by snow or a rain and snow mixture. TABLE 3. Classification of snowfall events during the three winter experiments. Road surface state Warm: T s 0 C Cold: T s 0 C Dry Wet Dry Frozen Snow state Dry snow 10 cases 2 cases 15 cases 0 case Moist snow 4 cases 29 cases 0 case 0 case

8 MARCH 2006 B O U I L L O U D A N D M A R T I N 507 b. Sensitivity experiments A sensitivity study was done in order to determine some model parameters not obtained from direct measurements. It was done for two snow-free periods: a relatively cold period (mean road surface temperature: 1.06 C) from 1 to 22 February 1998 (period 1), and a relatively warm period (mean road surface temperature: 4.73 C) from 9 to 25 March 2000 (period 2). Sensitivity tests were done on the following parameters: albedo, emissivity, roughness length, road material dry thermal conductivity, natural soil dry thermal conductivity, and dry specific heat capacity. The heat capacity of road materials is, in most cases, not measured. In literature, mean values were proposed for asphalt roads (800 J kg 1 K 1 ) by Alexanderson et al. (1990) and for natural soil (736 J kg 1 K 1 ) by Peters-Lidard et al. (1998). Frémond (1979) used a value of 836 J kg 1 K 1 in the French model GEL1D. It is important to note that the model calculates a thermal conductivity depending on the water and ice contents of the layer. So, for the road materials (where the water content is very low) thermal conductivity was approximately equal to dry thermal conductivity. In the natural soil (where liquid water content can reach higher values), the soil thermal conductivity might be significantly different from the dry value (in the considered case, with a water-saturated porosity used in the model of 42.5%, the effective conductivity is equal approximately to 1.5 W m 1 K 1, while the dry conductivity is equal to3wm 1 K 1 ). The road thermal conductivity was set equal to 2 Wm 1 K 1, based on the measurements. According to the LCPC data (J. Livet 2003, personal communication), the albedo of the semigrainy bituminous concrete varied from 0.04 to Emissivity mainly depends on aggregate type, material, and age, and varies from 0.96 to 1. Thermal conductivities (which take into account water content) were around 1.9Wm 1 K 1 for the road and around 1.5 W m 1 K 1 for the natural soil. Several runs were made, with variations for a single parameter within a reasonable physical range and fixed initial values for the other parameters. Initial values of road properties were an albedo of 0.1, an emissivity of 1, a roughness length of m, a road dry thermal conductivity of 2Wm 1 K 1,a natural soil dry thermal conductivity of 3Wm 1 K 1, and a dry specific heat capacity of 836 J kg 1 K 1. Results of sensitivity tests of these parameters on the road surface temperature (T s ) and 0.6-m-deep temperature (T 0.6m ) are given in Table 4, and they are expressed using mean error (ME) and root-mean-square error (rmse). The best scores were different for the two events, and improvement of road surface temperature scores were sometime associated with a decrease of deep temperature scores. However, our aim was not to determine the best set of parameters to fit the observations, but to verify that the values proposed were reasonable. The value of albedo and roughness length used in the model runs were 0.07 and m, respectively. They were chosen in order to maximize the road surface temperature scores in both runs. The emissivity used was It is the lower physical limit of emissivity, even if the best scores were obtained with a lower emissivity for period 1. The tests showed also that the model sensitivity to the dry specific heat capacity was low, and that the LCPC value of 836 J kg 1 K 1 was appropriate. c. Model results for three selected events Results from three typical snowfall events are given in this section in order to show the model performance under three different situations: a winter episode where rain transformed into snow, a winter cold snowfall episode, and a spring situation. The first, from 16 to 26 February 1998, was an event where rain transformed into snow. This event integrated a manual snow removal on 24 February Model results are compared with measurements in Fig. 3. The model was able to simulate the temperature fluctuations for a case of a snow-free road, and the temperature drop during the snowfall with good accuracy. The differences seen around 1200 UTC (corresponding to the solar radiation maximum) were because of uncertainties in the determination of the solar masks. Concerning the snow depth, the model was able to simulate the occurrence of snow accurately, but there were significant differences in snow depth. Several causes were possible for this discrepancy. The first one was relative to the event type (rain transforming into moist snow). Indeed, it was quite difficult to precisely know the snow rain proportion in a rain snow mixture event. An overestimation of the liquid precipitation proportion was possible (and correspondingly an underestimation of the solid precipitation proportion), causing the simulated snow depth to be lower than the measured snowfall. Another possible cause could be a difference between the simulated and real snow densities. The model simulated a good interface configuration, with the formation of a water-saturated snow layer. The measured height at 1100 UTC 22 February 1998 was approximately 0.01 m, while the simulated height was only m (the difference might be because of the above-mentioned uncertainties in the precipitation phase or because of an initial presence of liquid water on the road). The simulated road snow

9 508 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 TABLE 4. Results of sensitivity tests of thermal properties of road in terms of the road surface and 0.6-m-deep temperatures for period 1 (1 22 Feb 1998) and period 2 (9 25 Mar 2000). Event 1 Event 2 T s T 0.6m T s T 0.6m Thermal property ME Rmse ME Rmse ME Rmse ME Rmse Albedo Emissivity Rugosity length (m) Road thermal conductivity (W m 1 K 1 ) Soil thermal conductivity (W m 1 K 1 ) Dry specific heat capacity (J kg 1 K 1 ) conduction flux reached approximately 100 W m 2 at the beginning of the snowfall, and decreased rapidly with road cooling (Fig. 4). Note that this flux could reach very high values: almost 100 W m 2 in this case, but it can be as high as 500 W m 2 if the road surface was very warm (e.g., 10 C). The second event, from 12 to 23 December 1998, consisted of a dry snowfall on a cold road, with snow removal on 22 December Results are shown in Fig. 5. The surface temperature simulation was good (despite the differences resulting from solar masks), but the snow-depth simulation showed some differences. The beginning of the snowfall (until 0000 UTC 21 December 1998) was simulated with a good accuracy, but afterward the measured snow depth suddenly increased by approximately 0.25 m, while simulated snow depth remained constant. This difference was because of snow transport by wind, a phenomenon that was not

10 MARCH 2006 B O U I L L O U D A N D M A R T I N 509 FIG. 3. Event-1 comparison of (top) the simulated (solid line) and measured (dashed line) snow depth, with simulation of the water-saturated snow depth (thick line) and with a snow removal (SR). (bottom) Simulated (solid line) and measured (dashed line) road surface temperatures. simulated by the model. During the night from 21 to 22 December 1998, the wind speed was very high (it reached approximately 10 m s 1 ) and was responsible for snowdrift formation, which was verified by the video records. In most cases, the snow-depth simulation error resulting from snow transport by the wind in the experimental field was on the order of a few centimeters. This case (here approximately 0.3 m) was unique in the database. Contrary to the first event, there was no water-saturated snow layer simulated. In the absence of manual measurements, this result was verified owing to the negative road surface temperature. The third selected event, from 7 to 20 April 2000, consisted in a succession of three snowfalls: a moist FIG. 4. Simulated conduction flux between the road and the snow during event 1.

11 510 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 FIG. 5. Same as Fig. 3, but for event 2. snowfall on a warm road, and two events with rainfall transforming into snow. Contrary to the previous events, there was no manual snow removal. The results for road surface temperature and the snow depth are shown in Fig. 6. The occurrence of snow on the road was simulated with accuracy, but the snow melting was simulated later than observed. This problem was because of the snow precipitation amount. This event happened during April with spring meteorological conditions. As explained in the event classification presentation, snowfalls were generally preceded by rainfalls, which led to an uncertainty because it was quite difficult to precisely determine the transition time between rain and snow or the proportion between rain and snow in a snow rainfall mixture. Another possible explanation for this difference may come from inhomogeneous snow on the pavement. It has been observed that, in some cases, parts of the pavement remained snow free for several days while other parts were still covered by snow. This situation induced lateral heat fluxes that accelerated the melting, even if these fluxes could not be quantified in our experiment. This phenomenon happened for the majority of the natural snowmelt events. Despite some discrepancies, the GELCRO model has proved that it was able to accurately simulate the occurrence of snow on the road in the three episodes. The following section is devoted to tests over longer periods without reinitialization. d. Model results for a long-term simulation The 1998/99 winter (from 1 November 1998 to 30 April 1999) contained the highest number of snowfall events (28) among the three observed winters. Figures 7 and 8 show the model performance for the road surface temperature and the snow cover during December 1998, which was representative of winter situations, and March 1999, which had warmer conditions. A detailed examination of video records allowed the validation of the simulated snow depth during the snow-depth sensor breakdown, or when snow depth was lower than the sensor detection capacity. This was the case for 9 days during the winter. An example can be seen in Fig. 7 (days 36 and 37), where the pavements were covered by snow despite the snow-depth sensor indications. The problem of snowdrift formation on 21 December 1998 (simulated day 50) was detailed in section 3c, and this phenomenon was responsible for the snow-depth difference the next day too. At the end of

12 MARCH 2006 B O U I L L O U D A N D M A R T I N 511 FIG. 6. Same as Fig. 3, but for event 3. the winter, as in Fig. 8, the relatively warm conditions allowed natural melting in most cases. However, as explained in section 3c, natural melting was spatially inhomogeneous, causing differences between natural and simulated one-dimensional melting. Significant differences in total snow height were seen in six events (e.g., day 40 in Fig. 7). These events were characterized by rain and snow mixtures (uncertainties in the phase determination). Despite these punctual discrepancies, the complete winter run without any reinitialization (except the reproduction of the manual snow removal) showed that the model performances were satisfactory when looking at surface temperature and snow occurrence reproduction on the road. In some cases, the simulation of snow depth was not very precise, but this problem is not very important concerning the GELCRO application. Indeed, this model aims to be a decision-making tool for winter-road exploitation, so the main point is to predict the moment at which the snow begins to accumulate on the road, not the snow depth, because there are frequent snow removals on the roads. Manual measurements of the water-saturated snowlayer height were made 12 times during the 1998/99 winter. Table 5 compares the simulated and measured water-saturated snow-layer height. There was a good agreement between the simulated and the measured water-saturated snow depth, except in a few cases. A snow rain event occurred on 14 November 1998 (with an uncertainty in the proportion of liquid amount). Measurements from 16 November 1998 were done at the beginning of the event, which happened immediately after the snow removal following a previous event: the presence of a water-saturated snow layer at this time was probably because of water remaining after snow removal. On 22 and 23 March 1999, two measurements were performed that allowed the observation of the evolution of the saturated snow layer. On 22 March, the observed water-saturated snow layer was greater than the simulated one, probably because of a higher measured road snow temperature at the beginning of the snowfall, leading to a higher conduction flux, and therefore more melting than in the simulation. For the second measurement, the measured water-saturated layer had decreased and was lower than that which was simulated. Differences were probably caused by differences between the snow grain type in the simulation and in the observations. However, it is important to notice that in most of the cases, the model accurately simulated the absence or the presence of a water-

13 512 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 FIG. 7. December 1998 comparison of (top) the simulated (solid line) and the measured (dashed line) snow depth, along with the simulated water-saturated snow depth (thick line) and snow removals ( ). (bottom) The simulated (solid line) and the measured (dashed line) road surface temperature. saturated snow layer. These relatively good results on punctual measurements were reinforced by the comparison of simulated and measured road surface temperatures: a road surface temperature equal to 0 C indicates, in most cases, that there is a water-saturated layer present. The quality of the results for the two other winters were very similar. Table 6 shows some road temperature and snow-depth statistical parameters. However, it was observed that for the 1997/98 winter, the rmse was higher than for the two other simulated winters. This difference is because of the experimental conditions at the end of the winter, when the model did not reproduce the rapid snowmelt on the experimental pavement that occurred from 10 to 30 April 1998 (a period with three snowfall events, without any manual snow removal). During some days in this period, the model simulated a road surface temperature equal to 0 C, while the road was snow free and its observed surface temperature reached 45 C. If we exclude this period, we can consider that the results were very stable from one winter to another, with an rmse of about 3 C for the road surface temperature, and 1 C for the temperature at a 0.6-m depth. Statistics concerning snow depth were not very representative of real simulation results because of errors in the measured snow depth during some periods. To verify the ability of the model to run in an operational environment, it was important to check if there were any long-term biases. Figure 9 shows the comparison between the simulated and measured 0.6-m-deep temperatures for the 1998/99 winter simulation. The overall shape of the temperature evolution was well reproduced. The larger differences occurred at the beginning of the period (November) and during spring. To explain the difference between measurements and simulations, some other tests were done. The 0.35-mdeep simulated temperature was compared with measurements, with different boundary conditions than were found in the long-term run (called the initial run) presented above. In the first sensitivity run, conditions were the same as in the initial run, except that the surface and 0.6-m-deep temperatures were prescribed at the lower and upper boundaries. In the second sen-

14 MARCH 2006 B O U I L L O U D A N D M A R T I N 513 FIG. 8. Same as Fig. 7, but for March sitivity run, conditions were the same as in the initial run, except that the 0.6-m-deep temperature was prescribed at the lower boundary. In the third sensitivity run, conditions were the same as in the initial run (as before), except that the road surface temperature was prescribed at the upper boundary. All of the runs had the same initial conditions. Results are shown in Figs. 10a d. Simulation results with both the top- and bottommeasured road temperatures as boundary conditions (Fig. 10b) led to the conclusion that the poor 0.35-mdeep temperature simulation was not because of road thermal properties. However, some differences could be seen when the temperature reached 0 C (e.g., at days 75 or 120 of the simulation). This was probably because of phase change. In the model, the road water content was constant and accounted for typical values for this type of material. But, as observed at the site, the experimental pavements were not totally impermeable: some water flows were observed and the road water content probably varied with time. The results of the runs with either the observed road bottom or the road surface temperatures as boundary conditions, showed that the 0.35-m-deep temperature deviation was because of the combination of the surface temperature and natural soil temperature deviations. The deep soil properties (thermal conductivity, density, liquid water content, porosity) and temperature were not measured at this site (these measurements are in- TABLE 5. Comparison of simulated and observed water-saturated snow depths during manual measurements, for the 1998/99 winter. Date 27 Oct Nov Nov Nov Nov Dec 1998 Simulated water-saturated snow depth (m) Measured water-saturated snow depth (m) Date 4 Jan Feb Mar Mar Mar Mar 1999 Simulated water-saturated snow depth (m) Measured water-saturated snow depth (m) Wet interface

15 514 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 45 TABLE 6. Statistical results (rmse and mean error) from the comparison between measured and simulated road surface and 0.6-m-deep temperatures, and snow depth, for the winters of 1997/98, 1998/99, and 1999/2000. Road surface temperature 0.6-m-deep temperature Snow depth Rmse ( C) Mean error ( C) Rmse ( C) Mean error ( C) Rmse (m) Mean error (m) Winter 1997/ Winter 1998/ Winter 1999/ deed extremely rare for this type of surface), which was why we used a preliminary 10-yr run to reach an equilibrium for the deep soil. However, there was probably a small interannual variability, which is not taken into account in this study (however, the tests in sections 2b showed that the influence of deep soil temperature on surface temperature is very low). A sensitivity test was done concerning the road type. It was observed that, even if different roads had different hydrological and thermal properties, differences of the occurrence of snow on the road were negligible in both the model and the observations. The time range between the first and the last appearance was low, generally from 10 to 30 min in the field experiment, so it was impossible to reproduce these differences with hourly time-step forcing data for the model. Some differences were observed in the term of natural melting, but they remained negligible (several hours) in comparison with uncertainties explained previously in the cases of natural melting. 4. Conclusions A model adapted to the simulation of snow occurrence on the road was developed using the snow model CROCUS and the ISBA land surface model. The coupling of these two models required special attention because of the very different thermal and hydrological properties of the snow and the road, and the different configurations of the interface between them. This model was validated using results from a comprehensive field campaign held at the Col de Porte laboratory in France. The results demonstrated that the model was able to accurately simulate the road surface temperature evolution and the presence of snow on the road. Problems concerning the snow depth simulation were encountered, but they were not critical because the main interest of this model was to determine the moment at which the snow begins to accumulate on the road surface. Further model validation is planned with data from other sites in France. In a second step, the use of the ISBA CROCUS coupled model as an operational forecasting system is envisaged. Before this, two research directions will be explored. The first one is the improvement of the model, in order to simulate conditions closer to the real conditions (snow compaction, partial integration of deicers, and traffic effects) according to research results in these domains. Traffic effects are numerous. Some of these are partially known, such as the thermal contribution of vehicles (Ishikawa et al. 1999; Prusa 2002), but some are difficult to quantify, such as the effect of contaminant on the snow albedo. The second research theme pertains to the development of a preoperational chain for snow prediction on a road using predicted meteorological conditions. FIG. 9. Winter 1998/99 comparison of the simulated (solid line) and the measured (dashed line) 0.6-m-deep road temperature.