## 2 Related Work
### Hybrid Approaches and Post-Processing  
Hybrid techniques combining conventional physically based models with data-driven techniques are becoming more frequent in the literature. A prominent approach is utilizing outputs from a physical model (like simulated streamflow) as additional inputs to a data-driven model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Study (Author and Year)** & **Methodology** & **Forecast Horizon and Data** & **Performance Metrics** & **Gap Addressed by This Study** \\ \hline [PERSON] et al. (2023) [21] & LSTM, CNN, ConvLSTM & 1–6 h ahead streamflow & NSE up to 0.995 & No attention; no hybrid integration \\ \hline [PERSON] et al. (2021) [23] & DIFF-FFNN-LSTM hybrid & 1 h ahead (lagged flows and rainfall) & NSE = 0.99; RMSE = 9.31 m\({}^{3}\)/s & Single horizon; no attention \\ \hline [PERSON] et al. (2024) [26] & Temporal Fusion Transformer & 60 min ahead sewer overflow & VE = 36.9 L; PE = 77.4 L/s & Urban focus; no physical model integration \\ \hline [PERSON] and [PERSON] (2024) [27] & Temporal Fusion Transformer & 1 day ahead across multiple basins & KGE = 0.704 & Daily only; no physical model integration \\ \hline [PERSON] et al. (2025) [28] & XGBost-based PP-ML framework & Daily NWM v2.1 flows & Median KGE = 0.69; Phjas = 6.21 & No multi-horizon forecasting \\ \hline [PERSON] et al. (2022) [29] & VMD-CNN and SVR post-processing & Daily WRF-Hydro streamflow & CNN: NSE = 0.72; CC = 0.87; RMSE = 34.8 m\({}^{3}\)/s & Post-processing only; no multi-horizon forecasting \\ \hline This study & Hybrid: HEC-HMS + TFT & 24, 48, 72 h & NSE = 0.84–0.71; KGE = 0.89–0.78 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of key related studies in hydrological forecasting, comparing methodology, forecast horizon and data, performance metrics, and gaps addressed by the present hybrid TFT framework. A clear example is a hybrid rainfall-runoff model in India that combined the WEAP physical model with a neural network, using both simulated flow and meteorological inputs as features. This stacked approach significantly improved performance, achieving NSE values of 0.96 (calibration) and 0.92 (validation) compared to \(\sim\)0.85 for each model individually [35]. In semi-arid environments, the MODWT-GPR3 sym4 hybrid model outperformed standalone ML models with near-perfect validation metrics (R = 0.99, NSE = 0.98) [36]. Similar hybrid approaches combining remote sensing, deep learning-based land cover mapping, and SWAT modeling have been used to enhance predictions of water related variables [37]  
These case studies reveal several consistent advantages of hybrid approaches. Key takeaways from recent studies on hybrid modeling include the following:  
1. Hybrid methods usually outperform either model alone, often yielding improved accuracy in catchments where purely physical or purely ML approaches fall short. 2. Incorporating physical knowledge tends to make ML models more robust in data-scarce and non-stationary contexts, providing an important benefit for ungauged basins and changing climates. 3. From an operational perspective, hybrid models are pragmatic and feasible. Agencies can integrate ML modules into existing forecasting workflows with minimal disruption [19]. In addition, post-processing techniques have been demonstrated to be effective in reducing the bias of physically based models. One of the simplest strategies is using a data-driven model to correct systematic errors. A recent study [28] developed a post-processing ML framework to bias-correct U.S. National Water Model (NWM) streamflow simulations. The NWM, a physics-based nationwide hydrology model, struggled in regulated basins (e.g., with reservoirs) because it did not explicitly model reservoir operations. Comparisons have shown that machine learning can outperform classical bias correction: For instance, one study found that support vector regression (SVR) and convolutional neural network (CNN) models used as post-processors outperformed quantile mapping in correcting daily streamflow simulations [29].