## 4 Discussion  
This study evaluated two models designed to estimate DPT from ambient temperature and relative humidity. The performance of each model was analyzed through statistical parameters and error distribution. Considering the statistical parameters, the R-squared (R\({}^{2}\)) values range over 0.95 in all cases, with the proposed second-degree equation achieving a perfect score of 1.00, indicating that it captures all the variance in the dependent variable from the predictors. The RMSE and MSE both highlight the second-degree equation as the most accurate, showing the smallest errors among the three compared equations, while the Thumb equation exhibits the highest errors, suggesting it is the least precise. The MAE confirms this pattern, with the second-degree equation again showing the lowest error, indicative of predictions that are closest to the observations. Lastly, the STD of the errors also confirms this trend, with the second-degree equation showing the least variability in its predictions. Overall, the second-degree equation outperforms the other two across all considered metrics, making it the most reliable and accurate for practical applications,  
Figure 8: Execution Time and Memory usage vs. Iteration. (**a**) Execution time for results stored one by one; (**b**) memory usage for results stored one by one; (**c**) execution time for results stored in sets of 100 iterations; (**d**) memory usage for results stored in sets of 100 iterations. while the Thumb equation, despite having a decent R-squared value, proves less reliable due to its higher error rates and greater estimation variability. The error distributions highlight the relative performance of the equations across varied environmental conditions. It is possible to observe that while the second-degree equation maintained a consistent accuracy across a wide range of temperatures and humidities, the first-degree equation struggled, particularly under extreme conditions. The same problem was observed in the Thumb equation under low temperature conditions. This variance in performance underscores the importance of choosing a model that robustly handles the complex interactions between multiple atmospheric variables. Furthermore, these findings suggest that models relying on a linear structure, like the Thumb and first-degree equations, may not fully account for the non-linear interactions between temperature and relative humidity under extreme conditions. By contrast, the second-degree equation, with its quadratic components, is inherently better equipped to capture such complexities, enhancing its reliability for applications where fluctuations in environmental conditions are prevalent. This study's results highlighted several factors influencing model accuracy, including the complexity of the model, the quality and range of the dataset, and the mathematical robustness of the modeling process. The iterative approach adopted in this study, involving repeated refinement and validation of the models, helped simplify the final equations, providing shorter and more user-friendly coefficients. This process was crucial in ensuring that the models remained adaptable and accurate over diverse testing scenarios. The analysis of the results of computational cost reveals important insights into the efficiency of the equations under different input sizes. Focusing on execution time, the rule of thumb and 1 st degree equation exhibit the fastest computation times across all tested sizes. Their simplicity in terms of arithmetic operations contributes to their efficiency. The 2 nd degree equation shows a moderate increase in execution time, particularly for larger input sizes. This can be attributed to the quadratic terms, which require more computational resources, while the Magnus-Teten equation is the slowest among all the tested equations, with a significant increase in execution time for larger inputs. This is expected due to the logarithmic and multiple division operations involved.