## 3 Materials and Methods
### Framework Overview  
Accurately forecasting streamflow remains a significant challenge in hydrology, particularly due to complexities introduced by human interventions such as irrigation, which are often inadequately represented in conventional physical models. The objective of this study is to investigate a hybrid modeling framework that integrates physically based hydrological simulations with deep learning techniques to enhance streamflow prediction accuracy and reliability, particularly addressing biases arising from human irrigation practices.  
Figure 7 demonstrates the processes of the hybrid framework. Initially, the Hydrologic Engineering Center's Hydrologic Modeling System (HEC-HMS) was utilized to generate synthetic streamflow data. This model integrated meteorological data and watershed characteristics derived from a Digital Elevation Model (DEM), generating physically consistent discharge simulations across the catchment.  
Recognizing that the synthetic discharge generated by HEC-HMS does not inherently account for irrigation-induced streamflow alterations, a dedicated bias correction model was employed. This model learns systematic discrepancies between the physically simulated and observed discharge data attributable to irrigation withdrawals or returns. By correcting these biases, the resulting synthetic discharge data more closely mirror observed flow patterns that reflect actual human management practices within the watershed.  
Finally, the bias-corrected synthetic discharge serves as input into a deep learning model--specifically, a Temporal Fusion Transformer (TFT)--alongside additional meteorological data and temporal variables to predict real observed streamflow. By combining physically informed bias-corrected synthetic data with data-driven predictive capabil  
Figure 6: Standard deviation of streamflow values at different temporal resolutions: (**left**) daily, (**center**) weekly, and (**right**) monthly.  
Figure 7: Overview of the hybrid streamflow forecasting framework. The process integrates digital elevation and meteorological data into the HEC-HMS model to generate synthetic discharge, which is then corrected using an error correction model. The corrected discharge is used as input to a deep learning model for discharge forecasting.  
ities, this stage effectively leverages the strengths of both physical and deep learning modeling approaches.  
For both the bias correction and deep learning stages, the available discharge time series was partitioned using a temporal split, with 80% allocated for training and 20% held out for validation. The validation period spanned from 1 September 2023 to 1 September 2024, covering a full hydrological year and capturing seasonal variability, including both irrigation and non-irrigation periods. This split ensured a realistic evaluation of model generalization under diverse flow conditions while maintaining chronological integrity to avoid data leakage.  
To assess the robustness of our training setup, we compared two sampling strategies: (i) non-overlapping windows, where input-output sequences were spaced apart to avoid redundancy, and (ii) overlapping windows, where the sliding window advanced one timestep at a time. Both approaches produced consistent performance, confirming the stability of the model. These components are described in detail in Sections 3.2.1-3.2.3.