## 3 Results
Figure 4: Surface representation of the defined equations (blue) and dataset (red). (a) 1 st degree equation; (b) 2 nd degree equation. The obtained first-degree equation produces a parabolic distribution of the errors, with maximum values up to 6 \({}^{\circ}\)C over the observed values, while underestimations reach 3 \({}^{\circ}\)C under observed values. The 3D surface plot in Figure 5a shows significant variances with pronounced peaks and troughs, highlighting extensive underestimations under high temperature and mid to low humidity, and overestimations under cooler, highly humid conditions. The 2D heatmap, Figure 5b, clearly illustrates the errors with vertical gradients that show increasing error magnitudes with rising temperatures across nearly all humidity levels, confirming the tendency of the equation to overestimate dew point in warmer conditions. The obtained second-degree equation produces a non-homogeneous distribution of the errors, with maximum values up to 1.2 \({}^{\circ}\)C over the observed values, while underestimations reach a difference of 3 \({}^{\circ}\)C under observed values. Figure 5c shows that underestimation errors are more pronounced in conditions of high temperature and low humidity, which is evident in the deeper areas of the graph. Conversely, the equation demonstrates greater precision under conditions of high relative humidity, as indicated by lower elevations on the \(Z\)-axis. Additionally, slight overestimations are noted in conditions of intermediate temperature and high humidity. It is important to highlight that the values in the lower left corner, which show a value of zero, are excluded from the analysis due to being outside the established boundary conditions. This exclusion is relevant, as these values do not contribute to the analysis. Figure 5d displays a flat representation of the surface shown in Figure 5c as a heat map for a more generalized view. The performance across a broad range of environmental conditions is robust. Specifically, in conditions of high relative humidity, close to 100%, and across all temperature ranges, the equation exhibits remarkable precision, reflected by the more neutral colors in the visualization. Figure 5: Error rate of the 1 st and 2 nd Degree Eqs. vs. Observed data. (**a**) 1 st D.E. 3D representation. (**b**) 1 st D.E. Planar representation. (**c**) 2 nd D.E. 3D representation. (**d**) 2 nd D.E. Planar representation. Figure 6 shows the graphical representations of the error rate obtained using the Thumb equation as a representative example of a commonly used equation for estimating DPT from ambient temperature and relative humidity. The results highlight substantial errors. Specifically, the 3D surface plot from Figure 6 displays a significant underestimation of dew point at lower temperatures, increasing together with the relative humidity. Conversely, at higher temperatures, it produces homogeneous accurate results independently from the relative humidity. In the case of the 2D heatmap in Figure 6, it provides a detailed visualization of these discrepancies across the temperature and humidity spectrum. The error magnitude increases markedly with temperature, peaking particularly in the higher temperature ranges, where errors escalate to over 12 units. This gradient shift from cool to warm hues in the heatmap clearly illustrates how the error magnitude is exacerbated by increasing temperatures, regardless of humidity levels. This analysis reveals that the traditionally used model has limited efficacy under varying climatic conditions, particularly failing to provide reliable predictions at higher temperatures. Following the graphical presentations, an analysis of statistical parameters is conducted. This analysis, which results are shown in Table 2, includes R-squared (R\({}^{2}\)), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), Mean Absolute Error (MAE), and Standard Deviation.