# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 5 Conclusions  
In the course of this research endeavor, we embarked on a rigorous investigation into the estimation of stream flow rates, drawing from the wealth of data procured from two prominent stream gauging stations in Turkey: Melekbahce (E21A033), situated within the Munzur water sub-basin of the Upper Euphrates basin, and Besdegirmen (E12A003), \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Stations** & **Method Inputs** & **Best Method** & \begin{tabular}{c} **MSE** \\ **(mm\({}^{2}\))** \\ \end{tabular} & **R\({}^{2}\) (\%)** \\ \hline LR-SVR-DT-RF-ETR & \begin{tabular}{c} Besdegirmen \\ Melekbahce \\ \end{tabular} & \begin{tabular}{c} Favg. Psum, Tavg \\ Favg, Psum, Tavg \\ Favg, Psum, Tavg \\ \end{tabular} & ETR & 220.7 & 88 \\ \hline W-LR-SVR-DT-RF-ETR & \
\begin{tabular}{c} Besdegirmen \\ Melekbahce \\ \end{tabular} &
\begin{tabular}{c} Wavelet-Favg, Psum, Tavg \\ Wavelet-Favg, Psum, Tavg \\ Wavelet-Favg, Psum, Tavg \\ \end{tabular} & WT-ETR & 96.3 & 97.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of method results data. nesteded in the Porsuk Stream sub-basin of the Sakarya Basin. Our methodology was underpinned by the judicious integration of daily average flow, daily average air temperature, and daily total precipitation data, culminating in a robust stream flow rate estimation model. Amid the pantheon of machine learning algorithms explored, the RF and ET models emerged as paragons of performance. The pioneering inclusion of WT into our machine learning framework heralded a paradigm shift, ushering in pronounced ameliorations in our outcomes, as meticulously depicted in Figures 11 and 12. This novel synergy of WT and machine learning engendered an approximate 10% surge in efficacy, a testament to its far-reaching influence on the precision and elucidation of trends within temporally intricate and sporadic datasets. The ramifications of our study radiate expansively, resonating with the Ministry of Agriculture and Forestry and other pertinent authorities. These prognostications of flow rates are poised to be salient linchpins in the orchestration of essential undertakings, encompassing the conservation of soil and water resources, augmentation of rural water supply, and judicious management of wastewater. Moreover, the culmination of our findings casts a spotlight on the prodigious potential harbored by machine learning algorithms, synergistically entwined with the prowess of WT. This amalgamation not only enriches our comprehension of water resources but also empowers researchers and policymakers to chart informed trajectories, yielding positive ramifications for water-centric initiatives and the calculus of agricultural strategy. As we pivot towards the horizons of prospective research, a plethora of exciting possibilities beckon. The uncharted terrain of groundwater level prediction and flood forecasting beckons us, where the marriage of these methodologies promises to chart new territories of insight. In tandem, the integration of colossal datasets and cloud technology poses an enticing avenue to invigorate our water management paradigms further. Furthermore, the intricate interplay between water utilization and economic dynamics tantalizes as a realm for exploration. Delving into this intersection could potentially yield transformative revelations, furnishing strategic contours for water resource management in consonance with broader economic imperatives. Our trajectory of inquiry thus extends beyond the confines of the current study, propelling us towards an enlightened domain of holistic water management strategies that coalesce scientific rigor and pragmatic utility. As these avenues unfurl, our collective efforts converge in the pursuit of a sustainable and resilient water management ethos, forging a dynamic nexus between scientific exploration and tangible impact. Methodology, M.A.C. and Z.A. ; Software, U.A., M.A.C. and Z.A. ; Data curation, U.A., M.A.C. and Z.A. ; Writing - original draft, U.A.