## 2 Materials and Methods
### The Implemented Algorithm for LST Simulations  
The algorithm developed by MEC aims to predict the Land Surface Temperature (afterwards also called T-skin): it consists of a training algorithm which uses the main quantities connected with ice formation (i.e., air temperature, relative humidity, cloud cover, solar radiation, and wind speed). The algorithm can be divided into two blocks: the first has the forecasted (or observed) air temperature (\({}^{\circ}\)C), solar radiation (W/m\({}^{2}\)), wind speed (m/s), and cloud cover (%) as input, and the estimated LST value (\({}^{\circ}\)C) as output; the second receives the output of the first block (forecasted LST) as input, and, combined with the forecasted value of air relative humidity, is able to provide an alert code for ice formation: 0 (no ice), 1 (low risk), 2 (medium risk), or 3 (high risk). Various steps are necessary, because the output of the meteorological model needs to be trained to best represent the diurnal temperature curve and to best consider nocturnal radiative cooling. According to the algorithm, the evaluation of the ice alert code is performed in four steps, three of which are necessary for the estimation of LST (Equations (2), (3), and (4)), and the last one is used for the computation of the ice alert code. Both the LST values and the ice alert codes are calculated on an hourly basis. Corrections of the hourly air temperature values, in order to improve the matching and the correlation with the real daily temperature profile. The use of an ensemble model has the consequence of smoothing this daily air temperature profile, an aspect that, especially during the night hours, is crucial to the correct forecast of ice. This correction is operated by a simple algebraic formula, with the correction coefficients obtained from a regression model. An example set of the coefficients are reported in Table 1. The temperature correction is also dependent on cloud cover in Table 2 (the clearer the sky, the greater is the temperature variation between night and day) where there is a set of coefficients related to the cloud cover correction. \[T_{2m,bis}(t)=T_{2m}(t)-[\text{(coeff1($t$)}\cdot\text{subpar3($t$)}] \tag{2}\]  
where:  
* \(T_{2m,bis}(t)\), is the air temperature corrected by the algorithm;
* \(T_{2m}(t)\), is the air temperature at time \(t\)_obtained from the mode_; and
* coeff1(t) and subpar3(t) are two coefficients obtained from the regression model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Time (UTC)** & **Coefft1 (-)** \\ \hline
00 & 0.66 \\
01 & 0.72 \\
02 & 0.78 \\
03 & 0.85 \\
04 & 0.98 \\
05 & 1.10 \\
06 & 1.10 \\
07 & 0.90 \\
08 & 0.75 \\
09 & 0.35 \\
10 & \(-\)0.02 \\
11 & \(-\)0.25 \\
12 & \(-\)0.50 \\
13 & \(-\)0.75 \\
14 & \(-\)0.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Coefft1, as a function of the time of the day. Calculation of an intermediate version of surface temperature that takes into account the incoming short-wave solar radiation. The main driver of surface temperature, apart from the air temperature, is radiation forcing: incoming short-wave radiation increases surface temperature during the day, and outgoing long wave radiation decreases surface temperature during the night. To take into account this effect, again a simple algebraic formula has been considered, with the use of a set of parameters, obtained through a regression model. The training of the algorithm with the use of real in-situ observation permits to obtain T-skin values which are more realistic and representative of micro-scale climatological effects than the T-skin values obtained directly from the NWP model. \[Tsk(t)=T_{2m,bis}(t)=(\frac{SW_{down}(t)-\alpha}{\beta}) \tag{3}\]  
where:  
Tsk (t) is the output T-skin, T2m,bis(t) is the air temperature obtained at the previous step, SWdown is the incoming short-wave radiation, \(\alpha\) and \(\beta\) are coefficients obtained from the regression model.