# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### Data Pre-Processing Details  
In our quest for accurate and dependable results, we took great care to ensure that the data we used underwent thorough pre-processing. This step was crucial to make sure that our analysis would be reliable, free from errors, and truly reflective of the natural patterns we sought to uncover in the daily average flow, total daily precipitation, and daily  
Figure 2: Study area (E12A003) location of Porsuk Creek Besdegirmen stream gauging station.  
average air temperature values. Let us delve into the details of how we handled missing data, outliers, and potential issues.  
Addressing missing data: we know that missing data can throw a wrench in the works, distorting our insights. So, we tackled this challenge head-on. Whenever we found gaps in our flow, precipitation, or temperature data, we employed some clever techniques to fill in those gaps. We used methods like linear interpolation, mean imputation, and backward filling, depending on what suited the situation best. The idea was to be consistent and strategic in our approach to maintain the data's integrity.  
Taming outliers: outliers are like the rebels of the dataset, capable of causing quite a stir. To keep things under control, we enlisted the help of some trusty outlier detection techniques. We scanned the data for those oddball values using tools like the Z-score, Tukey's fences, and interquartile range (IQR) analysis. When we found outliers, we decided whether to whip them into shape through transformations or, if necessary, show them the door. It was all about finding a balance between maintaining the data's true essence and eliminating any undue influences.  
Nipping data errors in the bud: data errors are like those sneaky typos that can sneak in and spoil the party. We were not going to let that happen. We carefully scrutinized the data, cross-checking them with other reliable sources and our own understanding of the subject matter. Whenever we spotted any inconsistencies or oddities, we took swift action to correct them. This ensured that our data remained trustworthy and dependable. By meticulously attending to these data preprocessing steps, we set the stage for a solid and dependable foundation. These steps were carried out consistently across all stations and variables, ensuring that the data we used were clean, reliable, and ready to reveal the hidden insights about water flow patterns, climate dynamics, and their interconnectedness in our study area.  
The upcoming sections will delve into the intricacies of the WT technique and how it was seamlessly woven into our hybrid model. We will discuss the specific choices we made, like which wavelet functions and scales we opted for, and how we made sure that this transformation worked in harmony with the other methods. Additionally, we will go into detail about the features we considered, the parameters that guided our models, our validation strategy, and a deep dive into the strengths and weaknesses of individual methods. These efforts are all geared towards presenting a clear and comprehensive picture of our methodology, ensuring that others can follow our footsteps and achieve similar results.