## 3 Results and Discussion  
### Saturated Water Vapour Pressure  
The saturated water vapour pressure values obtained with the formulations in Table 1 are plotted as a function of temperature in Figure 1 for a temperature range between 0 and 150 \({}^{\circ}\)C.  
Figure 1 shows that all the formulations inspected obtain similar values of the saturated water vapour pressure for the lower temperatures. However, the formulations diverge increasingly with temperature, with notable differences at 150 \({}^{\circ}\)C. To illustrate the drift of each formulation, their relative error \(RE_{\rm pv0}\), Equation (9), with respect to the reference of Equation (1) [4] is plotted in Figure 2.  
Figure 1: Saturated water vapour pressure as a function of temperature in the temperature range 0–150 \({}^{\circ}\)C for the different formulations analysed, Equations (1)–(8) [4; 5; 6; 7; 8; 9; 10; 11; 12]. Note that the results of Equations (2) and (3) practically overlap with the reference values of Equation (1).  
Analysing Figure 2, [PERSON]'s [6] equation, Equation (3), is the saturated water vapour pressure formulation with the least error in the temperature range analysed, 0-150 \({}^{\circ}\)C, and also in the more limited temperature range, 0-100 \({}^{\circ}\)C. The relative error of Equation (3) is kept within \(\pm\)0.2% in the temperature range 0-150 \({}^{\circ}\)C, and is up to \(\pm\)0.006% in the range 0-100 \({}^{\circ}\)C. Among the other formulations, only [PERSON]'s [5] equation, Equation (2), limits its relative error under \(\pm\)1.0% in the temperature range 0-150 \({}^{\circ}\)C. On the side of the lower accuracy, Equation (7), [PERSON] et al. [10] and [PERSON] et al. [11], and Equation (8), [PERSON] and [PERSON] [12], both show relative errors higher than 10% for temperatures higher than 90 \({}^{\circ}\)C.  
Equation (3) is able to reproduce the reference saturated water pressure values with a notably lower error than Equations (2) and (4)-(8). This result should not be surprising, since Equation (3) is the one containing the highest number of parameters from the equations in Table 1 after the reference of [PERSON] and [PERSON] [4], Equation (1), (5 compared to 2-4 parameters). Then, it should be analysed if the increase in number of parameters is justified or if, on the contrary, Equation (3) is overfitted. To this end, the AIC and the BIC were applied to the models, and the values of Akaike weights \(Aw\) from the AIC, Equation (11), and posterior model probabilities \(Bp\) from the BIC, Equation (13), were computed for all of them. For a number of observations equidistant between 0.01 and 150 \({}^{\circ}\)C of \(n=3\), \(Aw\) and \(Bp\) are plotted for Equations (2)\(-\)(8) in Figure 3. In the computations, the number of parameters \(k\) of Equations (2)\(-\)(8) are (4, 5, 3, 2, 2, 2, 2) (Table 1). The residual \(\varepsilon\) has been computed as the difference between the pressure obtained with each formulation and that of Equation (1). For any \(n\), both information criteria for model selection yield the same result: the selected model for the data is Equation (3), the formulation by [PERSON] [6]. It obtains \(Aw>0.977\) and \(Bp>0.985\) for any \(n\geq 3\), and \(Aw>0.999\) and \(Bp>0.999\) for any \(n\geq 5\). The rest of models, Equations (2) and (4)-(8), obtain \(Aw<0.023\) and \(Bp<0.015\) for any \(n\geq 3\), and tend to 0 with increasing \(n\). Then, the increase in number of parameters for  
Figure 2: Relative error in the saturated water vapour pressure, \(RE_{\text{pv0}}\), with respect to the reference, Equation (1) [4], as a function of temperature for the different formulations analysed. Equations (2)-(8) [5; 6; 7; 8; 9; 10; 11; 12].  
Equation (3) with respect to the rest of equations is justified with the increase in accuracy (information) they provide.