## 1 Introduction  
The presence of ice on roads has always been a key factor during the cold season: first, it is one of the main causes of road accidents [1; 2; 3], then, it has huge environmental and economic impacts due to counteract measures adopted in order to reduce its hazard [4]. Generally, ice is considered more serious than snow on a road, since ice is not often visible, and it does not induce drivers to pay closer attention to road conditions and to moderate their speed. To face and reduce these risks on roads, the main precautionary measure is salt spreading, which is harmful not only for the environment [5], but it also constitutes one of the highest expenses for public administrations both for the cost of chemical solvents and for its highly corrosive properties which, subsequently, require road restorations and interventions. De-icing operations necessitate strategies that take into account the probability of triggering the phenomenon, considering different modalities how it can occur and including other variables such as the presence of traffic, sun exposure, and meteorological conditions in the area. Last, but not least, it is important to know the different types of solvents and their mode of action [6], as well as the possible negative effects of their use on soil and water quality [7]. Many types of salt are highly corrosive, and they can both contribute to the deterioration of concrete, steel structures and tires, due to the formation of holes and grains. Dissolution of salt sediments on the roadside may poison the micro fauna and soil in the nearby terrains, which become a hostile environment for plant growth. Its dissolution in water courses may produce changes in the ecosystems and it can be toxic to fishes; in fact, nitrogen and soluble phosphate favor the algae bloom and weed aquatic vegetation. Nevertheless, salt is commonly used in Italy, where this study is focused on, due to its main action of lowering the freezing point of the water. The presence of salt diminishes the vapor pressure of the solution, which remains in equilibrium with ice at a lower temperature. In particular, as described by the [PERSON]'s law, the freezing-point depression is defined as the difference between the freezing temperature of solvent and the solution (Equation (1))  
\[\Delta T_{F}=K_{F}\cdot b\cdot i \tag{1}\]  
where:  
\(\Delta T_{F}\) is the freezing-point depression, defined as TF (pure solvent) \(-\) TF (solution). \(K_{F}\) is the cryoscopic constant, which is dependent on the properties of the solvent, not the solute; for water, \(K_{F}\) is equal to 1.853 \({}^{\circ}\)C\(\cdot\)kg/mol. \(b\) is the molality (moles solute per kilogram of solvent), in particular 1 mole of NaCl is equal to 58.44 g melt in 1 kg of water. \(i\) is the van't Hoff factor (number of ion particles per individual molecule of solute, e.g., \(i\) = 2 for NaCl and 3 for BaCl\({}_{2}\)). For instance, to lower the freezing point of water by 2 \({}^{\circ}\)C, 2/(1.853 \(\cdot\) 2) = 0.54 moles are necessary for each liter of water which equals to 31.45 g of sodium chloride. Let\({}^{\prime}\)s do a practical example: if we have 10 cm of snow at a temperature of 0 \({}^{\circ}\)C which correspond to about 10 mm over a square meter or 10 L/m\({}^{2}\), 314.5 g of sodium chloride would occur to lower the freezing temperature by 2 \({}^{\circ}\)C. Hence, considering an average cost of 0.07 \(\epsilon\)/kg for NaCl, the result is a cost of 0.02 \(\epsilon\) per square meter of surface. This means that for a 6-m width roadway, about \(\epsilon\) 120 are required for each kilometer. For a city like Milan, where there are about 2000 km of roads, each intervention on the entire network would have a cost of about 240,000 \(\epsilon\) only for purchasing salt. Hence, a good forecast system of road surface temperature has a noteworthy economic impact and it becomes an important aspect for traffic safety and winter paving maintenance.