# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 2 Related Work  
In the realm of environmental research, the intricate relationship between environmental conditions and water resources has garnered immense scientific interest [24; 25]. Human activities and waste discharge along river routes have contributed to unpredictable and irregular river flows, particularly noticeable in countries witnessing high sector diversity, where industrialization and urbanization, driven by population growth, disrupt the hydrological balance of local basins [26; 27; 28; 29]. Climate change and the escalating global population density have exacerbated the issue of dwindling water resources, resulting in a widespread water crisis [30]. Although our planet boasts a vast water reserve of approximately 1384.12 million km\({}^{3}\), encompassing oceans, groundwater, glaciers, and atmospheric water vapor, the accessible surface water accounts for a mere 0.0225 million km\({}^{3}\), underscoring the urgent need for efficient water management [31]. Turkey, blessed with a water potential of 450 billion m\({}^{3}\) annually, faces water usage challenges due to various factors like evaporation, river flow, and neighboring inflows [32; 33]. The actual efficient usage of water stands at 95 billion m\({}^{3}\) out of the available 112 billion m\({}^{3}\), revealing disparities across 25 watersheds in Turkey, with different issues and dynamics in each region. For instance, pollution poses a significant threat to basins like Ergene and Large Menderes [34; 35; 36]. The average amount of annual water per person in Turkey has witnessed a decline, from 1652 m\({}^{3}\) in 2000 to 1346 m\({}^{3}\) in 2020, indicating a nation grappling with water stress [37; 38]. To overcome these challenges, conducting studies that maximize the utilization of existing water resources becomes imperative. By analyzing water and atmospheric data, including groundwater and surface runoff, researchers can obtain meaningful results to enhance water resource management [39; 40]. Time series analysis, which involves examining numerical values over a specific timeframe, plays a pivotal role in understanding water movements and estimating future water potential [41; 42]. In the domain of river flow forecasting, regression models and machine learning algorithms have emerged as valuable tools. Regression analysis has been applied to estimate flow data in basins like the Euphrates, yielding promising outcomes [43]. Furthermore, machine learning models such as SVR, DT, and RF have demonstrated high prediction performance [44; 45; 46; 47]. The WT technique, which analyzes time series in both frequency and time domains, has further enhanced river flow analysis estimates [48; 49]. The present study centers on the Tunceli Munzur sub-basin of the Upper Euphrates basin and the Besdegrimen rivers in the Kuitahya Porsuk Stream Basin. Employing LR, SVR, DT, RF, and ETR algorithms, researchers compare their prediction performances using daily average flow, total daily precipitation, and daily average air temperature as input parameters [50]. To optimize estimation performance, a hybrid method using wavelet analysis has been devised for each algorithm, alongside incorporating exponential smoothing for handling missing data [50]. After analyzing the above studies, the intricate realm of water resource understanding and management has emerged as a pressing global concern, driven by climate change and population growth. The integration of advanced analytical techniques and machine learning algorithms serves as a beacon of hope, aiming to optimize water resource management and tackle challenges related to river flow prediction, water usage efficiency, and environmental sustainability. By delving deeper into these methodologies, we can foster effective water management practices, ensuring water availability for the well-being of future generations [37].