# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### Methodology
The subsequent step involved employing five distinct machine learning algorithms. These algorithms facilitated the development of predictive methods and models based on historical data, a valuable asset for forecasting future river flow rates. As the narrative pivots to Figure 3, the focus intensifies on the comprehensive analysis of flow data sourced from stream gauging stations, alongside the integration of daily climatic data. The meticulous dissection of influential factors that impinge upon river flow rates becomes the primary motif. This analytical quest delves deep into the details encapsulated within the stream gauging stations, coupled with meticulous scrutiny of precipitation and temperature data. It is a meticulous excavation of relevant data points, akin to an archaeological expedition, meticulously unveiling the hidden relics of information. The subsequent phase transpires in the realm of data preprocessing. This critical phase shares a semblance with refining raw ore to unearth precious metals, as it strives to ameliorate errors or inconsistencies within the data. Notably, the data undergo a normalization process, akin to sculpting a masterpiece, refining the data's integrity and enhancing their compatibility. The data are molded into a normalized scale spanning [0, 1], thereby amplifying the predictive prowess of ensuing models. Descriptive statistical analyses stand as our navigational compass, navigating through the intricate patterns imprinted within the data tapestry. Analogous to deciphering hieroglyphs etched on ancient monuments, we glean insights through metrics like arithmetic mean, mode, median, quartiles, and box diagrams. These analyses bestow a panoramic view of the underlying data landscape, facilitating a more comprehensive interpretation of our study's findings. Machine learning algorithms subsequently take center stage. They function as virtuoso musicians orchestrating a symphony of historical data, composing predictive methods that illuminate the trajectory of future river flow rates. It is akin to extrapolating the forthcoming note in a musical sequence based on the symphony's preceding movements. A hybrid method incorporating the potent WT technique was developed to further enhance the forecasts' efficacy. The study aimed to improve the accuracy and precision of the forecasted river flow rates by re-analyzing the data using this hybrid technique. Finally, the performance of the various forecasting methods was compared, and the results of the future river flow rate forecast were presented, providing valuable insights into the dynamic nature of water resources and their prospective consequences. As a subset of artificial intelligence, machine learning played a crucial role throughout this study, facilitating the development of computational methods, information extraction, continuous learning, and predictive conclusions from processed data. Utilizing the power of machine learning algorithms, the study sought to identify meaningful patterns and trends within the data, thereby contributing to the advancement of hydrological research and predictive modeling [53, 54, 55, 56]. Feature engineering and selection: the pivotal role of feature engineering and selection in our analysis is underscored by their profound influence on the accuracy of our predictive models. Delving into the intricacies of these aspects, we elucidate the rationale behind our chosen features and their relevance in estimating future water potential. Our selection of features was meticulously guided by their inherent significance in delineating the hydrological processes under scrutiny. The triad of daily river flow rate, temperature, and precipitation data was chosen due to their well-established correlation with river behavior. The daily river flow rate encapsulates the essence of water movement, while temperature and precipitation serve as proxies for climatic influences that significantly impact flow dynamics.