## 4 Results and Discussion
### Deep Learning Model Forecasting Performance  
The Temporal Fusion Transformer (TFT) model, trained using the bias-corrected synthetic discharge as its primary input, exhibited strong predictive performance and interpretability. Table 2 summarizes its point-forecast performance alongside two benchmarks: raw (uncorrected) synthetic discharge inputs and an \"ideal\" model trained directly on observed discharge. For the 24-h horizon, the TFT achieved an NSE of 0.84, KGE of 0.89, and RMSE of 0.301 m\({}^{3}\)/s, substantially outperforming the uncorrected input model (NSE = 0.55, KGE = 0.67, RMSE = 1.084 m\({}^{3}\)/s) and approaching the observed-input case (NSE = 0.90, KGE = 0.92, RMSE = 0.247 m\({}^{3}\)/s) Our model's performance is comparable to our previous work [34], where the TFT was benchmarked against other models (NSE= 0.9234, KGE= 0.9585) as well as against results reported in similar studies, as summarized in Table 1. (e.g., NSE = 0.78-0.99, KGE \(\approx\) 0.70-0.90),  
Figure 8: Comparison of observed discharge, HEC-HMS simulated discharge, and bias-corrected discharge for the period 2018–2024. The plot highlights improvements in alignment between corrected predictions and observed values following error correction. The results clearly indicate that the bias-corrected synthetic discharge enhances predictive performance compared to uncorrected synthetic inputs, closely approaching the ideal scenario using observed discharge data. This indicates that the proposed hybrid approach successfully bridges the gap between purely synthetic and observed data-driven forecasting methods. Table 3 presents the predictive performance of the proposed hybrid model across 24-, 48-, and 72-h forecast horizons. As expected, the model accuracy exhibited a gradual decline with increasing lead time. For the 24-h horizon, the model achieved strong performance, with an NSE of 0.84 and KGE of 0.89, indicating high reliability in short-term forecasting. The root mean square error (RMSE) remained low at 0.301 m\({}^{3}\)/s. At 48 and 72 h, the model retained reasonable skill, with the NSE and KGE remaining above 0.70 at both horizons. This gradual performance degradation is expected in multi-step forecasting tasks. An important advantage of the TFT is its built-in probabilistic forecasting. As shown in Table 4, the mean Continuous Ranked Probability Score (CRPS) improved from 0.155 to 0.074 m\({}^{3}\)/s after bias correction, while the empirical coverage rates for the 60%, 80%, and 98% predictive intervals rose from 52.2%, 71.2%, and 89.4% (raw inputs) to 63.4%, 79.1%, and 96.6% (bias-corrected inputs), respectively. The close alignment between the nominal and empirical coverage confirms that the TFT is capable of producing reliable uncertainty bounds, which is a critical feature for water management. \begin{table}
\begin{tabular}{c c c c} \hline
**Model Input Type** & **Mean CRPS** & **60\% cov.** & **80\% cov.** & **98\% cov.** \\ \hline Raw Synthetic Discharge (uncorrected) & 0.615 & 0.522 & 0.712 & 0.894 \\ \hline Bias-corrected Synthetic Discharge & 0.174 & 0.634 & 0.791 & 0.966 \\ \hline Observed Discharge (ideal case) & 0.151 & 0.621 & 0.806 & 0.974 \\ \hline \end{tabular}
\end{table} 
Table 4: Probabilistic forecast performance using different input types. Metrics include Continuous Ranked Probability Score (CRPS) and empirical coverage percentages for 60%, 80%, and 98% prediction intervals. The bias-corrected inputs yielded improved reliability and uncertainty quantification. \begin{table}
\begin{tabular}{c c c c} \hline
**Model Input Type** & **NSE** & **KGE** & **RMSE** \\ \hline Raw Synthetic Discharge (uncorrected) & 0.55 & 0.67 & 1.084 \\ \hline Bias-corrected Synthetic Discharge & 0.84 & 0.89 & 0.301 \\ \hline Observed Discharge (ideal case) & 0.90 & 0.92 & 0.247 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of streamflow forecast accuracy using different model input types. Performance metrics include Nash-Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency (KGE), and Root Mean Square Error (RMSE).