## 3 Methods
### Model Performance Evaluation  
The reliability of the model simulation results was verified using the process simulation verification rate, peak simulation error, peak present time error, root mean square error (RMSE), and Nash-Sutcliffe coefficient (NSE), as shown in Table 2.  
(1) Process Simulation Verification Rate  
When the error of a simulation is less than the permissible error, it is considered a qualified simulation. The percentage of accurate simulations out of the total number of simulated occurrences is referred to as the verification rate, which indicates the overall level of accuracy of many simulations. The process simulation verification rate is calculated as follows:  
\[QR=\frac{n}{m}\times 100\% \tag{10}\]  
where \(QR\) is the verification rate (%); \(n\) is the number of qualified simulations; and \(m\) is the total number of simulations. The verification rates were greater than 85% for grade A accuracy, 70-85% for grade B accuracy, and 60-70% for grade C accuracy.  
(2) Peak Simulation Error  
The peak water level simulation error was taken as 20% of the measured variability during the foresight period when the permissible error of the water level was less than 0.1 m, and this value was used as the permissible error, which was calculated as follows [22]:  
\[E_{Z}=|\hat{y}_{i,m}-y_{i,m}| \tag{11}\]  
where \(E_{Z}\) represents the peak simulation error, with a smaller value indicating a better performance of the model; \(\hat{y}_{i,m}\) represents the simulated peak water level; and \(y_{i,m}\) represents the observed peak water level.  
(3) Peak Present Time Error  
The peak present time permit error is 30% of the time distance between the simulation-based time and the measured flood peak occurrence time. When the permit error is less than 3 h or one calculation time period length, then 3 h or one calculation time period length is used as the permit error. The peak present time error was calculated as follows [22]:  
\[E_{T}=\left|T_{\hat{y}_{i,m}}-T_{y_{i,m}}\right| \tag{12}\]  
where \(E_{T}\) represents the peak present time error, with a smaller value indicating a better fit of the model; \(T_{\hat{y}_{i,m}}\) represents the simulated peak present time; and \(T_{y_{i,m}}\) represents the observed peak present time.  
(4) Root Mean Square Error (RMSE)  
The \(RMSE\) represents the residual value between the simulated and observed values and is used to evaluate the average error of the model. Therefore, a smaller \(RMSE\) value indicates a better fit between the observed and simulated values. The formula for this is shown in (13):  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}{(y_{i}-\hat{y}_{i})^{2}}} \tag{13}\]  
where \(n\) is the number of samples, \(y_{i}\) is the observed water level, \(\hat{y}_{i}\) is the simulated water level, and n is the time-series length.  
(5) Nash-Sutcliffe Coefficient (NSE)  
\begin{table}
\begin{tabular}{c c} \hline
**Indicator** & **Value Fluctuation Range** \\ \hline Process Forecast Verification Rate (QR) & A: \(>\)85\%; B: 70–85\%; C: 60–70\% \\ Peak Forecast Error (E\({}_{Z}\)) & 0–0.1 \\ Peak Forecast Error (E\({}_{T}\)) & 0–0.1 \\ Peak Prsent Time Error (E\({}_{T}\)) & [0, 0.3 \(\times\) (T\({}_{P}-\) T\({}_{0}\))] \\ Root Mean Square Error (RMSE) & [0, +\(\infty\)] \\ Nash–Sutcliffe Coefficient (NSE) & [\(-\infty\), 1] \\ \hline \end{tabular}
\end{table}
Table 2: List of assessment indicators.  
The \(NSE\) indicates the degree of fit between the simulated and observed values and serves as an indicator of the model's efficiency. The range of values for \(NSE\) is as follows: when \(NSE\) > 0.75, the simulation quality is excellent; when \(0.36<NSE<0.75\), the simulation quality is satisfactory; when \(NSE\) < 0.36, the simulation quality is unsatisfactory [23]. The formula is as follows (14):  
\[NSE=1-\frac{\sum\limits_{i=1}^{n}{{{(y_{i}-\hat{y}_{i})}^{2}}}}{\sum\limits_{i =1}^{n}{{{(y_{i}-\overline{y})}^{2}}}} \tag{14}\]  
where \(\overline{y}\) is the average of the observed water level, and the others are as above.