## 2 Materials and Methods
### Equation Finding  
#### 2.3.1 Preliminary Considerations  
The computational cost of an equation refers to the amount of computational resources required to solve it. This cost is typically measured in terms of: (1) time complexity, i.e., the number of elementary operations needed to solve the equation as a function of the input size (number of variables, terms); and (2) space complexity, i.e., the memory required to store the intermediate results during the solving process [35]. For most applications, like water harvesting, weather forecasting, or optimization processes, where the DPT estimation involves iterative calculations, complexity can be significant beyond just the number of operations. Complex equations with many variables or nested operations may require more calculations and memory to store intermediate results, increasing both time and space complexity. However, reducing the number of variables can simplify implementation and improve accessibility without substantially affecting computational efficiency. The primary advantage lies in making the model easier to understand and apply, rather than in dramatically lowering computational requirements. Therefore, the objective is to find a model that, despite considering fewer parameters, yields results with minimal error and maintains practical usability. Figure 1: Workflow diagram of the modeling, optimization, and testing process. Given the aforementioned premises, certain considerations must be taken into account. Determining the dew point for given ambient temperature and relative humidity involves a minimum of two variables. Although psychrometric charts are typically used to obtain the dew point, the process based on these two variables is manual. Reducing computational cost impels simplifying the complexity of the mathematical operations used. Therefore, the use of polynomial equations is justified as an optimal method for approximation and reduction of computational cost, considering the inherent complexity of the equations relevant in this context. Based on this, the subsequent variables are adopted:  
* _X_: Ambient temperature,
* _Y_: Relative humidity,
* _Z_: Dew point temperature. Defining the background to consider, it is also necessary to include the relevant boundary conditions. Understanding the relationship between temperature and relative humidity in atmospheric conditions is crucial for explaining water condensation. The psychrometric chart is a key tool in this regard, providing important insights. Specifically, the horizontal line at 0 \({}^{\circ}\)C on the chart, shown in Figure 2, marks the acceptable range where temperature and relative humidity intersect within feasible limits. To ensure scientific accuracy, it is important to note that points below this line on the chart can be disregarded, as they do not significantly contribute to the analysis. This helps to minimize irrelevant factors and unnecessary complexity, resulting in a more precise dataset needed to develop a new equation. The delineation of the horizontal line at 0 \({}^{\circ}\)C on the psychometric chart corresponds to a specific relationship between temperature and relative humidity. This line, which marks the boundary of permissible atmospheric conditions for water condensation, can be defined as \(RH_{Min}\) using the equation:  
\[RH_{Min}\geq 130.31\cdot e^{(-0.061\cdot T)} \tag{4}\]  
where:  
* _RH_ represents relative humidity,
* \(T\) denotes temperature in degrees Celsius,
* \(e\) is Euler's number. This equation encapsulates the empirical relationship between temperature and relative humidity along the 0 \({}^{\circ}\)C line, defining that RH should not be less than \(RH_{Min}\). By plotting this equation, it is possible to visually represent the range of temperature and relative humidity values where condensation of water vapor occurs under atmospheric conditions, as shown in Figure 3.  
Figure 2: Psychometric chart [36].