# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods  
### Study Area  
Figure 1 presents an all-encompassing map of the Middle Euphrates Basin's flow observation station network, meticulously positioned along the majestic course of the Euphrates River and its tributaries. Within this comprehensive network, a total of 13 strategically identified stations stand as sentinels, capturing critical data on water flow patterns that traverse this diverse landscape. Encompassing vast swathe of southeast Turkey and northeast Syria, this map also sheds light on the basin's boundary, demarcating the territory where water plays a crucial role in shaping the environment. Streams that meander through the region, weaving their way with unparalleled grace, are brought to the forefront, showcasing the interconnected web of watercourses that breathe life into the land. As a beacon of knowledge and a testament to meticulous observation, Figure 1 stands poised to empower scientists and researchers in their quest to unravel the intricacies of this vibrant ecosystem. Through this invaluable visual aid, a deeper understanding of the basin's hydrological patterns emerges, illuminating the path towards sustainable water management and conservation efforts. The study harnessed flow data from two prominent stream gauging stations, namely Melekbahce (E21A033) in the Firat Basin and Besdegirmen (E12A003) in the Porsuk Creek sub-basin of the Sakarya Basin. These stations provided critical insights into daily average flow patterns, serving as invaluable sources of information for the research. For the Melekbahce station, the study leveraged daily average flow data recorded between the years 1997 and 2022. Likewise, for the Besdegirmen station, the daily average flow data covering an extensive timeframe from 1980 to 2022 were utilized. In addition to flow data, the research also delved into precipitation and temperature data, which played a pivotal role in the analysis. For the Tunceli station (number 17165), the study considered precipitation and temperature data recorded between 1997 and 2022. Similarly, for the Kutahya station (number 17155), the researchers scrutinized the corresponding data spanning a vast period from 1980 to 2022. By integrating these comprehensive datasets from multiple stations and across various timeframes, the study laid the foundation for a comprehensive analysis of water flow patterns, climate trends, and their impact on the respective basins. The meticulous selection and utilization of these data provided the research with a robust framework to draw meaningful insights and  
Figure 1: Study area location of the Melekbahce stream gauging station. make informed decisions pertaining to water resource management and environmental conservation efforts. The study focused on the analysis of flow data from the Porsuk Stream's Besdegirmen stream gauging station, designated as E12A003, located in the Porsuk Stream sub-basin within the Sakarya Basin. This station is situated approximately 17 km away from Kutahya, along the Kutahya-Eskisehir highway. For the analysis, the study considered the daily average flow data recorded at the E12A003 Besdegirmen stream gauging station over a significant period, spanning from the water years of 1980 to 2022. This comprehensive dataset offered a wealth of information about the flow patterns and dynamics of the Porsuk Stream in the Besdegirmen region. Figure 2 shows that the study also incorporated precipitation and temperature data from the broader Kutahya area. The researchers utilized daily data recorded at station number 17155, covering the same extensive timeframe from 1980 to 27 July 2023. This combination of flow, precipitation, and temperature data provided a holistic understanding of the hydrological and climatic trends in the Porsuk Stream sub-basin.