# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### The Environment: Software Tools and Hardware
Through DWT, we extract valuable frequency components from these indicators, enabling the identification of temporal patterns and anomalies across different scales. This application forms the foundation for accurate stream flow rate estimation by incorporating comprehensive insights from diverse water quality metrics. The core novelty of our approach emerges through the strategic integration of wavelet transform with federated learning for stream flow rate estimation (FL-SFRE). This novel fusion tackles the conundrum of predictive modelingwhile preserving data privacy across geographical locales. Conventionally, stream flow rate predictions rely on centralized data aggregation, risking data security. In contrast, our method introduces a decentralized approach by harnessing data from multiple stream gauging stations while ensuring the confidentiality of raw data. The FL-SFRE approach is architecturally designed to circumvent central data pooling, preserving the integrity of sensitive hydrological data. The synergy between WT and FL materializes through the operational trajectory of FL-SFRE. We partition data into subsets corresponding to individual stations, which retain essential daily metrics locally. A global machine learning model is initiated, and each station trains this model using localized datasets via sophisticated algorithms like federated averaging. Notably, the exchange of model updates with the central server eliminates the need for raw data transmission, ensuring data privacy. This iterative process culminates in an updated global model, eventually leading to enhanced predictive accuracy. The novelty of our approach lies in the seamless amalgamation of WT's frequency-based insights and FL's decentralized, privacy-preserving framework. This convergence empowers the model to predict stream flow rates accurately across diverse scenarios while preserving the sanctity of data privacy. Furthermore, this pioneering concept of combining diverse data sources with FL transcends the hydrology domain, offering insights for various industries grappling with data privacy and prediction accuracy concerns. In the healthcare, finance, and energy management sectors, our approach's potential is transformative. To conclude, our novelty stems from the synergy between wavelet transform and federated learning, redefining predictive modeling by harmonizing data-driven insights with stringent data privacy requirements. This fusion of diverse data sources, coupled with decentralized training, holds the promise of accurate predictions across multifaceted scenarios while safeguarding sensitive information, marking a significant advancement in the realm of predictive modeling. In summary, FL revolutionizes stream flow rate estimation by decentralizing data collaboration, while DWT fortifies our hybrid approach to water quality prediction by deciphering intricate temporal patterns. Both methodologies empower the field of hydrology with unprecedented accuracy, versatility, and data privacy, shaping a new trajectory for predictive modeling and resource management. Meanwhile, the essence of DWT in our hybrid methodology lies in its potential to dissect water quality parameters into distinct frequency components. This approach empowers us to recognize patterns and anomalies across various temporal scales. Integrating DWT into our analysis, we couple ML algorithms to predict future water quality trends. Using extracted wavelet coefficients as features and historical water quality data as labels, we leverage techniques like LR, SVR, DT, RF, and ETR to enhance predictive capabilities. Our implementation involves a three-level wavelet tree for velocity data, with Daubechies filters steering our h(n) and g(n) filters. This integration amplifies our methodology's efficacy in achieving precise predictions amidst dynamic environmental conditions.