# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### Methodology  
The elucidation of our research's procedural methodology is encapsulated within Figure 3. This graphical representation unveils the successive strides we undertook to fathom our research objectives. Our research was fueled by two principal sources of data: the daily river flow rate data accrued from stream gauging stations and the temperature and precipitation data harvested from meteorological measuring stations. The foundational stage of our methodology entailed data preprocessing, a requisite preparatory step akin to refining raw materials before crafting a masterpiece. To ensure uniformity and accuracy, we applied a standard calendar-based preprocessing technique, harmonizing our data for further in-depth scrutiny. This preparatory phase served as the bedrock upon which our subsequent analyses were erected. Our analytical journey then pivoted towards a selection of autonomous machine learning techniques, encompassing LR, SVR, and DT, which were further examined via RF and ETR. These methodologies were meticulously orchestrated to decipher intricate patterns concealed within the dataset. However, a novel and pivotal facet of our methodology was the integration of the WT technique. This technique, analogous to an adept interpreter fluent in both temporal and frequency dialects, is adept at deconstructing time series data into a spectrum of frequency components. This analytical agility empowers us to discern subtle fluctuations that might otherwise evade detection. The architecture of our WT deployment entailed the selection of specific wavelet functions and scales. These wavelet functions operate as analytical lenses, allowing us to focus on distinct temporal scales, from micro-fluctuations to macro-trends. The outcome of this transformative analysis was subsequently amalgamated with the results of our machine learning methodologies. This convergence engenders a symbiotic enhancement that augments the precision of our estimations. The apex of our endeavor resides in the harmonization of outcomes. This involves a juxtaposition of the outcomes attained through our wavelet-augmented model vis-a-vis those emanating from machine learning methodologies. This comparative analysis serves as a crucible of validation, affirming the robustness and veracity of our findings. A meticulous adherence to the sequential stages depicted in our methodological flowchart begets a profundity of insights into the dynamic ebb and flow of river rates. The intricate interplay between meteorological determinants and water resource behaviour is laid bare, illuminating a nuanced comprehension of the dynamics governing this ecological nexus. The marriage of wavelet models and machine learning techniques transfigures data into informed insights, redefining our understanding of hydrological processes and bestowing an enriched contribution to the realm of water resource management and hydrological investigation. As shown in Figure 3, this study analyzed flow data from stream gauging stations and daily climatic data to examine the factors influencing river flow rate comprehensively. In order to estimate the river's flow rate accurately, the stream gauging stations, and precipitation and temperature data were meticulously examined. The initial phase involved pre-processing the data to remedy any errors or omissions. To enhance the model's performance and eliminate outliers, the data were further normalized to fall within the interval [0, 1]. This normalization procedure is intended to maximize the predictive capabilities of the model. The underlying relationships between the dataset variables were revealed using descriptive statistical analysis with metrics such as arithmetic mean, mode, median, quartiles (Q1, Q2, and Q3), and box diagrams. These analyses were essential in comprehend the patterns and trends within the data, thereby contributing to the interpretation  
Figure 3: River flow forecasting process flowchart: integrating machine learning and preprocessing. of the study's findings.