# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 1 Introduction
This study focuses on the integration of linear regression (LR), SVR, decision tree (DT), RF, and extra trees regression (ETR) methods to enhance their predictive capabilities [20]. The daily average flow, total precipitation, and average air temperature guide the investigation. To enhance the pursuit of accuracy, a hybrid methodology combines wavelet analysis with various algorithms, ultimately using exponential smoothing techniques to address the difficulties arising from incomplete data [21]. The rationale behind developing this hybrid model stems from the foundation of water resource management. With aspirations to mitigate the challenges posed by water shortage and climatic variability, this entity aims to assume a prominent role in promoting a resilient and equitable water future [22]. This study aims to provide a comprehensive framework for harmoniously integrating water resources and human needs via rigorous scientific analysis and mathematical hybridization [23]. The scholarly exposition presents a comprehensive analysis of the complex relationship between environmental changes and water supplies, offering valuable insights and contributions to the field. In the context of widespread worldwide water concerns, this paper serves as a compelling analysis, examining the consequences for Turkey with meticulous attention to detail. This research examines the impact of human interventions, such as the construction of roads and development along riverbanks, on the natural flow patterns of rivers. These interventions introduce unpredictability into the forecasting of river behavior, so complicating the process. The relentless decrease in available surface water resources presents a looming concern, emphasizing the pressing need for effective resource management measures. Focusing on the water landscape of Turkey, this paper examines the seeming contradiction between the country's abundant yearly water potential of 450 billion m\({}^{3}\) and the challenges posed by evaporation, changing river flows, and inter-regional imports. The unequal allocation of this resource has garnered significant attention, prompting a solid demand for fair and just management practices. This research reveals a concerning pattern of decreasing per capita water availability, highlighting the urgency of addressing water stress and emphasizing the importance of adopting sustainable water management practices. In order to tackle these issues, the researchers employ a comprehensive range of analytical methodologies, including time series analysis, wavelet transformation, and a collection of machine learning algorithms such as LR, SVR, DT, RF, and ETR. The symphony reaches its peak with a combination of a hybrid opus, in which wavelet analysis collaborates with each method, effectively improving their ability to make predictions and signaling the emergence of exponential smoothing for handling missing data. The implications of this scientific expedition significantly impact the water resource management field, resulting in valuable discoveries and practical techniques. As an illuminating beacon, it guides in making educated decisions and implementing sustainable planning, serving as a valuable resource in addressing the complex challenges surrounding global water issues. By incorporating sophisticated analytical frameworks and using the potential of hybrid approaches, this research emerges as a remarkable architectural achievement, serving as a fundamental guide for designing water management strategies in an era dominated by the pursuit of balance.