# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### Federated Learning for Stream Flow Rate Estimation  
In this section, we present a pioneering approach for estimating stream flow rates through the application of federated learning. This innovative framework facilitates the construction of predictive models while concurrently safeguarding the confidentiality of data from individual stream gauging stations. We operationalize this approach within the context of the Besdegirmen (E12A003) station situated within the Porsuk Stream sub  
Figure 7: The structure of extra trees applied to the river flow data. basin of the Sakarya Basin, as well as the Melekbahce (E21A033) station located within the Munzur water sub-basin of the Upper Euphrates basin. These stations gather essential daily metrics, including average flow rates, mean air temperatures, and cumulative daily precipitation data. Referred to as federated learning for stream flow rate estimation (FL-SFRE), this novel method represents a paradigm shift in stream and river flow prediction. It offers a solution to the quandary of predicting such rates while preserving the integrity of data collected across diverse geographical locales. Conventional stream flow rate prediction methodologies rely heavily on centralized data aggregation from an array of stream gauging stations. This practice, however, raises substantial concerns regarding the security and privacy of data. In stark contrast, federated learning engenders a modus operandi that fosters model training by tapping into data distributed across multiple stations, thus circumventing the need for centralizing primary data. The operational trajectory commences with data partitioning into distinct subsets, each corresponding to the data amassed by individual stream gauging stations and retained locally. The foundation rests upon initiating a global machine learning model with shared weights and biases. Employing sophisticated algorithms, such as federated averaging, each station independently imparts training to this global model using its localized dataset. Notably, throughout this training process, stations refrain from transmitting raw data; instead, they only exchange model updates, or gradients, with the central server. This decentralized strategy is pivotal, as it safeguards the confidentiality of sensitive data, fortifying data privacy and security. With each iterative training cycle, the central server adeptly amalgamates the model updates disseminated by each station, culminating in an updated global model. Subsequently, this enhanced model is reciprocated to each station for supplementary localized training. This iterative progression ensues until the model attains convergence and acquires satisfactory performance metrics, validated against each station's local benchmark dataset. The core tenet of the proposed federated learning technique rests upon its capacity to integrate diverse data sources holistically. This convergence adheres to a paramount principle--preserving data privacy--while yielding forecasts of unparalleled accuracy for stream flow rates. The crux of this methodology hinges on the seamless amalgamation of data sources while vigilantly safeguarding the confidentiality of this information. The federated learning framework is architecturally designed to obviate the necessity for central data pooling, thereby ensuring the preservation of data sources, a salient concern, mainly when dealing with sensitive hydrological data. Concurrently, the bedrock principle of federated learning resides in its exceptional ability to harness the collective intelligence inherent within diverse datasets. This entails a meticulous orchestration that seamlessly combines data from each station while retaining the unique nuances intrinsic to each data source. This collaborative and decentralized amalgamation fundamentally augments the predictive potential of the model. A distinguishing factor of this approach is its profound precision in rendering forecasts.