## 2 Materials and Methods  
### Background  
The estimation of DPT in ambient conditions traditionally relies on empirical equations [18], but there are also theoretical ones. Among the most common approaches for humid air conditions, the rule of thumb suggests a 1 \({}^{\circ}\)C decrease in DPT for every 5% decrease in relative humidity, starting at the dry bulb temperature when RH = 100%, as indicated in Equation (1) [19]. Furthermore, the most relevant empirical equations are the [PERSON]'s equation [31], [PERSON]'s equation [32], and [PERSON] equation [33].  
\[DPT=T-\frac{100-RH}{5} \tag{1}\]  
where:  
* \(T\) refers to the ambient temperature,
* \(RH\) corresponds to the relative humidity of the air. [PERSON]'s equation, described in Equation (2): \[DPT=\frac{273.3\times\left(\ln\left(\frac{17.269}{RH}\right)+\frac{17.269\times T }{237.3+T}\right)}{17.269-\left(\ln\left(\frac{17.269}{RH}\right)+\frac{17.269 \times T}{237.3+T}\right)}\] (2) where:
* \(T\) refers to the ambient temperature,
* \(RH\) corresponds to the relative humidity of the air,
* \(273.3\) and \(17.269\) are non-dimensional coefficients.  
Regarding theoretical equations, the most relevant one is the Clausius-Clapeyron equation [34], described in Equation (3):  
\[DPT=T\left[1-\frac{T\cdot\ln\left(\frac{RH}{100}\right)}{L/R_{w}}\right]^{-1} \tag{3}\]  
where:  
* \(T\) = 273.15 K,
* \(L\) is the enthalpy of vaporization; \(L\) = 2.501 \(\times\) 10\({}^{6}\) \(\frac{\mathrm{I}}{\mathrm{kg}}\) (\(T\) = 273.15K) \(\div\) 2.257 \(\times\) 10\({}^{6}\) \(\frac{\mathrm{I}}{\mathrm{kg}}\) (\(T\) = 373.15K),
* \(R_{w}\) is the gas constant for water vapor; \(R_{w}\) = 461.5 K.  
Equation (3) gives a good approximation to [PERSON] equation (Equation (2)) when \(T\) is close to the value for which \(L\) is chosen, with small but non-negligible errors away from the chosen reference temperature.  
The most commonly used equation to obtain the DPT based on the ambient temperature and relative humidity is the previously defined rule of thumb. Previous works delve into the mathematical basis and accuracy of different relationships between dew point and relative humidity, presenting practical applications like computing the cumulus cloud-base level. However, the exact conversion from relative humidity to DPT is complex. One of the main problems highlighted is the difficulty in achieving highly accurate approximations without sophisticated tools, emphasizing the need for simpler yet reliable methods for practical applications in meteorology and atmospheric science [4]. Based on this, the most common problems associated with existing dew point equations based on temperature and relative humidity include:  
* Complexity: Many existing equations for calculating dew point from temperature and relative humidity are complex and demand a higher computation cost, especially in case of iterative calculations.
* Accuracy: Some equations may lack accuracy, especially in approximating the conversion from relative humidity to DPT, leading to potential errors in moisture content estimations in the air.
* Pressure dependency: The accuracy of dew point calculations can be influenced by variations in pressure, affecting the reliability of the results, especially in scenarios where environmental conditions fluctuate significantly. Additionally, it supposes an additional variable to consider while solving the defined problem.  
Addressing these common issues in dew point equations is essential to improve the accuracy, simplicity, and reliability of calculations related to DPT and relative humidity in atmospheric science and meteorology.