Research on Dynamic Trend Prediction Method for Flow Discharge Through Harbor Gates in Tidal Reaches

Abstract

The outflow via the weir gate in coastal estuaries is affected by factors, including channel shape, upstream inputs, sluice gate operations, and tidal variations, leading to nonlinear and transitory correlations between the water stage and discharge. The most common technique utilized to calculate discharge is the weir gate overflow equation. Nonetheless, the significant dynamic fluctuations in upstream and downstream water level differentials during the opening or closing of the gate render the exclusive use of static water level differences inadequate for formulating a connection equation that satisfies accuracy standards. This research proposes a dynamic trend prediction approach that utilizes time-series data of water levels and discharge, accounting for temporal trend variations, as input for simulation with a three-layer backpropagation neural network. In the tidal portions of the Lixia River basin, the correlation coefficients for the discharge of four harbor gates surpassed 0.8, and the mean error diminished to 3.00%. It significantly boosts the fitting accuracy of the results and improves data precision during the transition between gate opening and closure. The novel approach employs intelligent algorithm theory to analyze harbor gate flow, offering a more scientific and accurate representation of the gate’s overflow capacity.

1. Introduction

Coastal estuaries, where riverine and tidal forces converge, exhibit dynamic hydraulic conditions that challenge conventional discharge estimation methods [1,2]. The discharge behavior at tidal sluices in these regions is influenced by factors, such as channel geometry, upstream inflows, sluice gate operations, and tidal fluctuations, which result in nonlinear and transient relationships between the water stage and discharge. Traditional weir flow formulas, which are based on steady-state conditions, often fail to provide accurate discharge estimations under tidal submergence due to difficulties in parameter calibration and minimal head differences during gate operations [3,4]. This limitation has spurred global advancements in hydraulic modeling, machine learning, and hybrid methodologies aimed at improving the accuracy of harbor gate discharge predictions.

In recent years, many scholars have conducted in-depth research on flow calculation methods under complex hydrological conditions. Salmasi and Abraham [5] studied the discharge coefficients of sluice gates equipped with different geometric sills through experiments and proposed an improved multivariate nonlinear regression model. Sadan et al. [6] developed a discharge prediction model for differential weir gate structures, significantly improving calculation accuracy. Scarlatos et al. [3] specifically studied flow estimation methods for spillways under submerged tidal conditions, providing new insights for gate flow calculation in tidal river sections. These studies indicate that traditional weir flow formulas need appropriate modifications and parameter adjustments when applied to tidal river sections. Yousif et al. [7] explored prediction methods for sluice gate scouring parameters, confirming the significant impact of water level differences on gate flow characteristics. However, most of these studies based on traditional hydraulic theory are limited to steady or quasi-steady flow conditions and struggle to accurately describe the complex flow patterns of harbor gates in tidal river sections during flood periods.

Faced with the limitations of traditional methods, intelligent algorithms have gradually become important tools for hydrological simulation. Maxwell et al. [8] pointed out that simulation-based inference can help us learn about hydrologic processes, providing new approaches for flow calculation under complex hydrological conditions. BP neural networks, with their excellent nonlinear mapping capabilities and adaptive learning characteristics, show broad application prospects in hydrological simulation. Yan et al. [9] applied BP neural networks to hydrodynamic flood forecasting in tidal river sections with good results. Zhang et al. [10] successfully corrected non-stationary tidal prediction errors in tidal estuaries using deep learning neural network models. Wang et al. [11] demonstrated the effectiveness of conditional Generative Adversarial Networks in extracting tidal signals from Sea Surface Height data, providing a novel deep learning approach for analyzing complex tidal patterns even in turbulent flow conditions. Gu and Li [4] constructed a tidal sluice discharge calculation model based on artificial neural networks, demonstrating the advantages of this method in handling complex tidal conditions. These studies show that data-driven methods can effectively capture nonlinear relationships between hydrological parameters without requiring a detailed understanding of physical mechanisms. Additionally, Zhang et al. [12] applied hybrid machine learning methods to daily streamflow forecasting using networks of real-time monitoring stations, improving calculation accuracy and prediction capability.

Recently, the integration of hydrological models with other advanced technologies has further expanded new approaches to flow calculation. Li et al. [13] proposed a hybrid approach enhancing process-based hydrological models with embedded neural networks, improving model generalization capability and stability. Wang et al. [14] developed time-guided convolutional neural networks for spatiotemporal urban flood modeling, successfully capturing the spatiotemporal characteristics of hydrodynamic processes. Feinstein et al. [15] used data-driven methods to predict downstream one-dimensional river flow, overcoming challenges in hydrologic river modeling. These studies provide new technical support for harbor gate flow calculation in tidal river sections. Majchrzak et al. [16] reviewed the application of machine learning in turbulent flow simulations, providing theoretical foundations for flow calculation under unsteady conditions. Mei and Smith [17] compared in-sample and out-of-sample model selection approaches for artificial neural network daily streamflow simulation, offering guidance for neural network model optimization.

Despite significant progress in existing research, the following urgent problems remain in harbor gate flow calculation for tidal river sections. According to Yang et al. [18], the structural characteristics and urbanization responses of tidal river systems have unique features, further complicating flow calculations. Furthermore, Liang et al. [19] pointed out that assessing urban flooding requires the consideration of multiphysics coupling, combining rainstorms and tidal effects. Su et al. [20] demonstrated that optimizing reservoir flood control operations considering spillway gate scheduling is crucial for improving discharge precision. Martínez et al. [21] integrated GIS and Tabu search algorithms to optimize tidal monitoring networks, highlighting the critical role of spatial analytics in improving hydraulic model inputs. These studies all suggest the inadequacy of traditional methods in calculating harbor gate flow in tidal river sections.

Based on the above background, this study compares and analyzes the applicability of weir flow formulas and BP neural network-based dynamic trend prediction methods for harbor gates in tidal river sections during flood periods. It innovatively introduces dynamic factors such as the rate of change of upstream and downstream water levels over time as input conditions for neural networks, establishing a new flow calculation method that considers temporal trend changes. This method, through a three-layer BP neural network structure, uses water level data and their temporal trend changes as inputs for simulation, significantly improving the fitting accuracy of calculation results, especially enhancing data precision at adjacent moments during gate opening or closing. The research outcomes propose novel methodologies for precise tidal gate discharge calculations in estuarine environments, while establishing a scientific foundation for hydrological simulations and flood mitigation strategies. These developments tackle the complex issues encountered by coastal areas, especially in situations with compounded threats from external flooding, tidal surges, and localized inundation.

2. Study Area

The Lixia River region has historically faced considerable hydrological hazards, such as external inundations, tidal surges, and regional flooding occurrences, rendering it a vital area for water resource planning and management in Jiangsu Province, China (Figure 1a) [22]. The Lixia River area is a relatively independent and closed hydrological system. That is because the southern portion of the area is closed along the Tongyang Highway, which blocks the entry of water from the highlands in the Tongnan area. The east dike of the Li Canal, the north and south dikes of the Northern Jiangsu Irrigation Canal, and the sea dike serve as peripheral barriers against flooding of the Huai River and tidal waves (Figure 1b). Local precipitation is the main source of runoff in the Lixia River area. Due to the topographic characteristics of the dish-shaped depressions, rainfall initially accumulates in low-lying areas, a process often described as “four water converging into a pond”. This leads to a rapid rise in water levels, followed by a gradual discharge through the harbor channels downstream.

The Lixia River hinterland currently features a self-sustaining drainage system primarily governed by the four harbors, Sheyang River, Huangsha Harbor, Xinyang Harbor, and Doulong Harbor, which discharge directly into the sea, as depicted in Figure 1b. The coastal reclamation zone serves as a conduit for the discharge of floodwaters from the Lixia River hinterland into the ocean. According to the ground level elevation, it also establishes a self-contained drainage region that flows into the sea. The drainage analysis of the coastal harbor channel in representative years indicates that the drainage volume from the four ports accounts for over 60% of the total drainage volume in the Lixia River basin during both yearly and flood seasons. During the year of flooding, the drainage volume from the four harbors in the flood season was about 70% of the total drainage volume for the area. This study primarily examines the flow through the gate at the tidal boundaries of four harbors, Sheyang River, Huangsha Harbor, Xinyang Harbor, and Doulong Harbor, located in the coastal region of the Lixia River.

3. Methods and Principles

3.1. Traditional Weir Gate Flow Formulas

In water conservancy projects, overflow dams and sluice gates are often built to control and regulate the flow, in order to achieve the comprehensive requirements of flood control, irrigation and power generation. In hydraulics, a weir is a structure designed to allow water to flow over its crest. When water passes over the weir without being controlled by gates, this is termed “weir flow”. Weir flow is characterized by a continuous, smooth drop in the water surface as it moves across the overflow structure. Examples of weir flow include the flow over an overflow dam crest, through bridge openings, and at the inlet of a non-pressurized tunnel.

Figure 2 illustrates a generalized schematic diagram of the weir gate. Z₀ denotes the elevation of the base of the weir gate. Z_u represents the water depth upstream of the weir gate. Z_d represents the water depth downstream of the weir gate. H₀ equals the upstream water level Z_u minus Z₀. H_S is the downstream water level Z_d subtracted by Z₀. Q represents the flow of water discharged from upstream to downstream of the gate.

In plain areas, the overflow state of the weir gate is generally characterized by submerged discharge. In practical applications, considering the difficulty of data observation, submerged discharge is typically calculated using the weir flow formula, as follows:

$$\mathrm{Q}=\mathsf{\phi }\mathrm{B}{\mathrm{H}}_s\sqrt{2\mathrm{g}({\mathrm{Z}}_u-{\mathrm{Z}}_d)}$$

(1)

where φ is the submerged discharge coefficient; B is the total width of the gate opening in m; H_S is the water depth above the downstream sill in m; Z_u is the upstream water level of the weir gate in m; Z_d is the downstream water level of the weir gate in m.

The weir flow formula employs fixed parameters and is theoretically optimized for steady-flow conditions. However, in practical field applications, flow regimes are predominantly unsteady, and the use of fixed parameters in such dynamic conditions leads to significant deviations between calculated and observed discharge values.

This study compiles, organizes, and analyzes observed discharge and water level data for four harbor gates—Sheyang River, Huangsha Harbor, Doulong Harbor, and Xinyang Harbor—in the Lixia River area of Jiangsu Province. The primary data sources include observed discharge through the gates and corresponding upstream and downstream water levels during 2003 and 2006.

During large-flow events at coastal harbor gates in Jiangsu, discharge is typically calibrated using the steady water level difference method, and daily average discharge is estimated using the single-tide flow-push method. When applying the steady water level difference method, the water level variation during gate opening is divided into a falling stage and a rising stage. In the falling stage, the difference between the pre-opening steady high water level and the instantaneous measurement level (ΔZ) is used as the correlation factor. In the rising stage, the difference between the steady low water level during gate opening and the instantaneous measurement level (ΔZ′) serves as the correlation factor. Each is then used to establish a water level–discharge relationship corresponding to its own stage.

According to reports relevant to the study area, the coefficient φ is typically a fixed constant less than 1.18. However, as shown in

Table 1. Summary of submerged discharge coefficients and observed discharge.

The Doulong Harbor		The Xinyang Harbor
Submerged Discharge Coefficients	Observed Discharge /(m3/s)	Submerged Discharge Coefficients	Observed Discharge /(m3/s)
0.64	100	0.69	350
0.7	150	0.75	400
0.76	200	0.81	450
0.82	250	0.87	500
0.88	300	0.93	550
0.94	350	0.99	600
1	400	1.05	650
1.06	450	1.11	700
1.12	500	1.17	750
1.18	550	1.23	800
1.24	600	1.29	850
1.3	650	1.35	900
1.36	700	1.41	950
1.42	750	1.47	1000
1.48	800	1.53	1050

, the range of the submerged discharge coefficient remains relatively wide. To assess the impact of this uncertainty, a sensitivity analysis of the data is been introduced.

Therefore, in this study, a clear distinction is made between the observed discharge and the actual discharge. To improve the accuracy of expression, it consistently uses the term observed discharge, which represents the effective equivalent of the true discharge value.

3.2. Dynamic Trends Calculation of Flow Discharge Through Weir Gate Structures

Firstly, obtain hourly or finer data about the weir gate, including the upstream water level of the weir gate Z_u, the downstream water level of the weir gate Z_d, and the discharge through the weir gate Q. Taking the Doulong Harbor among the four harbor gates as an example, it is also necessary to obtain the total width of the gate opening B = 80 m, the elevation of the gate bottom Z₀ = −3 m, and g = 9.8 m/s², using Formula (1) to calculate the time series of the submergence discharge coefficient ${\mathsf{\phi }}_0$, based on the time series of Z_u, Z_d, and Q. A portion of data is presented in

Table 2. Collection of data and calculation of submerged discharge coefficients.

Time	Q (m3/s)	Zu(m)	Zd(m)	φ0
2003/6/11 11:41	114	0.8	0.79	0.8493
2003/6/11 12:41	239	0.67	0.65	1.3073
2003/6/11 13:41	266	0.58	0.55	1.2214
2003/6/12 12:45	140	0.89	0.85	0.5134
2003/6/12 13:31	227	0.75	0.7	0.7747
2003/6/12 14:31	245	0.65	0.6	0.8593
2003/6/12 15:31	277	0.58	0.53	0.9908
2003/6/12 16:40	247	0.53	0.49	0.9991
2003/6/12 17:31	256	0.51	0.47	1.0415

.

Secondly, based on the time series of the Z_u, Z_d, and Q, the trend change at each time step can be calculated, including the rate of change of the upstream water level of the weir gate over time ${\displaystyle \frac{\partial {\mathrm{Z}}_u}{\partial \mathrm{t}}}$, the rate of change of the downstream water level of the weir gate over time ${\displaystyle \frac{\partial {\mathrm{Z}}_d}{\partial \mathrm{t}}}$, the rate of change of the difference between the upstream and downstream water level of the weir gate over time ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_u-\mathrm{Z}}_d\right)}{\partial \mathrm{t}}}$, with the rate of change of the discharge of the weir gate over time ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$, and the excerpts of the data are shown in

Table 3. Summary of input variables for the trend change at each time step.

Time	Zu/m	Zd/m	$\frac{\partial {\mathbf{Z}}_{\mathit{u}}}{\partial \mathbf{t}}$/(m/s)	$\frac{\partial {\mathbf{Z}}_{\mathit{d}}}{\partial \mathbf{t}}$/(m/s)	$\frac{\partial \left({{\mathbf{Z}}_{\mathit{u}}-\mathbf{Z}}_{\mathit{d}}\right)}{\partial \mathbf{t}}$/(m/s)	$\frac{\partial \mathbf{Q}}{\partial \mathbf{t}}$/(m3/s2)
2003/6/11 12:41	0.67	0.65	−3.12	−3.36	0.72	3000.00
2003/6/11 13:41	0.58	0.55	−2.16	−2.40	1.20	648.00
2003/6/12 12:45	0.89	0.85	0.32	0.31	0.07	−131.10
2003/6/12 13:31	0.75	0.7	−4.38	−4.70	2.82	2723.48
2003/6/12 14:31	0.65	0.6	−2.40	−2.40	2.40	432.00
2003/6/12 15:31	0.58	0.53	−1.68	−1.68	2.40	768.00
2003/6/12 16:40	0.53	0.49	−1.04	−0.83	1.88	−626.09
2003/6/12 17:31	0.51	0.47	−0.56	−0.56	2.26	254.12

.

Furthermore, to integrate Z_u, Z_d, ${\displaystyle \frac{\partial {\mathrm{Z}}_u}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial {\mathrm{Z}}_d}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_u-\mathrm{Z}}_d\right)}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$, and the corresponding submergence discharge coefficient of the next time step ${{\mathsf{\phi }}^{\prime }}_0$ as a database set, and to obtain the prediction model of the submergence coefficient, in which Z_u, Z_d, ${\displaystyle \frac{\partial {\mathrm{Z}}_u}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial {\mathrm{Z}}_d}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_u-\mathrm{Z}}_d\right)}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$ can be used to obtain the relationship with ${{\mathsf{\phi }}^{\prime }}_0$.

Finally, various machine learning models, such as the BP neural network model or the RNN neural network model, can be utilized for dynamic trend prediction, employing time-series data as input. Any alternative machine learning model capable of data learning may be utilized in place of the aforementioned neural network model. This study employs the BP neural network model. The BP network is a multi-layer feedforward neural network capable of learning and storing numerous input–output pattern mapping relationships, with its primary advantage being the lack of necessity to disclose the mathematical equations governing these mappings beforehand [23]. The fundamental concept of the BP neural network method comprises two processes: forward propagation of information and backward propagation of mistakes. When the network output deviates from the desired output or fails to satisfy the established accuracy criteria, the output error will be conveyed back to the input layer through a reversal process from the implicit layer. The error signal will thereafter be disseminated to all neurons in each layer, which will utilize it to rectify the network, hence enhancing the accuracy of the outputs [24]. The input layer consists of six neurons, including the upstream water level of the weir gate Z_u, the downstream water level of the weir gate Z_d, the rate of change of the upstream water level of the weir gate over time ${\displaystyle \frac{\partial {\mathrm{Z}}_u}{\partial \mathrm{t}}}$, the rate of change of the downstream water level of the weir gate over time ${\displaystyle \frac{\partial {\mathrm{Z}}_d}{\partial \mathrm{t}}}$, the rate of change of the difference between the upstream and downstream water level of the weir gate over time ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_u-\mathrm{Z}}_d\right)}{\partial \mathrm{t}}}$, with the rate of change of the discharge of the weir gate over time ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$. These inputs introduce temporal variation features. The output layer has one neuron representing the predicted submerged discharge coefficient ${{\mathsf{\phi }}^{\prime }}_0$. The hidden layer contains five neurons, and the tanh (hyperbolic tangent) activation function is used for both the hidden and output layers to effectively capture nonlinear hydrodynamic relationships. The detailed parameter settings of the BP neural network model are summarized in

Table 4. The detailed parameter settings of the BP neural network model.

Parameter	Value
Input/Output Layer Activation Function	Double Sigmoid Cutoff Function
Training Method	High-Precision Processing Method
Hidden Layer Neuron Count	5
Network Connection Rate	1.0
Learning Rate	0.7
Training Coefficient Precision	0.001
Maximum Training Iterations	10,000
Momentum Factor	0.5

.

We also employed 5-fold cross-validation to evaluate the generalization ability of the BP model. Each site’s dataset was divided into five subsets, with four used for training and one for testing in each fold. The results indicate that the model performs robustly across all stations. The average and standard deviation of relative errors are presented in

Table 5. The average and standard deviation of relative errors.

Harbor	Average	Standard Deviation (m3/s)
Doulong Harbor	5.96%	0.052
Huangsha Harbor	6.43%	0.074
Sheyang River	13.95%	0.146
Xinyang Harbor	9.57%	0.089

.

At Doulong Harbor, Huangsha Harbor, and Xinyang Harbor, the mean relative errors were 5.96%, 6.43%, and 9.57%, respectively, with relatively small standard deviations, indicating good output stability of the model. Although the error at Sheyang River was slightly higher (13.9%), it remained within an acceptable range. Overall, the BP neural network model demonstrated strong predictive performance across a variety of operating conditions.

4. Results

4.1. Traditional Static Weir Flow Formula Method

The submerged discharge coefficients were evaluated utilizing the recorded upstream and downstream water levels and discharge data from the four principal port gates in 2003 and 2006. Table 1 presents the correlation between the submerged discharge coefficients and the discharge along the fitted relationship line, using Doulong Harbor and Xinyang Harbor as examples. In the meanwhile, Figure 3 illustrates the correlation between observed discharge and submerged discharge coefficients.

According to the correlation between the observed discharge and the submerged discharge coefficient of the harbor gate (Figure 3), the submerged discharge coefficient under different discharges is obtained. The discharge through the weir gate is then computed using the weir flow Formula (1). Comparative analysis of the discharge through the weir gate calculated by the weir flow formula and the observed discharge in the Doulong Harbor and the Xinyang Harbor is shown in Figure 4 and Figure 5.

The submerged discharge coefficients of the four coastal harbor gates in 2003 and 2006, analyzed using the observed data, were calculated to obtain the discharge through the weir gate. From the relative error of the maximum discharge, that of the Sheyang River gate and the Doulong harbor gate ranged between 37% and 50%, while the Huangsha harbor gate and the Xinyang harbor gate exhibited larger deviations, ranging from 70% to 75%. From the relative error of the average discharge, the Doulong harbor gate exhibited a slightly larger value of 16%, whereas the other three gates remained below 10%.

The point line diagram of calculated and observed discharge reveals that the calculated discharge is centrally clustered among the observed discharge points, suggesting that the weir flow formula offers moderate accuracy in estimating gate discharge. The standard deviation of the discharge error indicates the precision of the observed data aligned with the overflow curve.

Table 6. Statistics on the error in calculating the discharge through the gate by the weir flow equation.

Statistical Results	The Sheyang River Gate	The Huangsha Harbor Gate	The Doulong Harbor Gate	The Xinyang Harbor Gate
Observed Average Discharge/(m3/s)	971	379	372	662
Standard Deviation of Discharge/(m3/s)	235	101	71	178
the Relative Error of the Maximum Discharge	47%	75%	37%	70%
the Relative Error of the Average Discharge	9%	5%	16%	8%

illustrates that the standard deviation of discharge for the four tidal gates varies from 71 m³/s to 235 m³/s, with relative values between 20% and 26%, suggesting moderate fitting performance. The four harbors exhibit significant errors in discharge calculations using the weir flow formula, primarily because they function as tidal gates. This characteristic complicates the discharge fitting process compared to a normal weir gate.

4.2. BP Neural Network-Based Dynamic Trend Prediction Method (DTPM)

This research is based on the use of the three-layer BP neural network method, using the data of the four major harbors in the period of June to September of 2003 and 2006, respectively, using Z_u, Z_d, ${\displaystyle \frac{\partial {\mathrm{Z}}_u}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial {\mathrm{Z}}_d}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_u-\mathrm{Z}}_d\right)}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$ as the input conditions and calculating the four harbors’ discharge through the weir gate. Figure 6 and Figure 7 illustrate the correlation between the calculated and observed discharge via the weir gate in 2006. The findings indicate that the mean correlation coefficient between the input conditions and the observed discharge through weir gates is 0.82, with a relative error ranging from 0.51% to 2.43%. This suggests that the simulated discharge through the weir gate, derived from this dynamic trend prediction method, attains remarkable accuracy and outstanding performance. The graphic indicates that the data acquired by the conventional static weir flow formula method demonstrate considerable variability. For inadequately fitted locations like the Sheyang River Gate and the Huangsha Harbor Gate, R² values are below 0.1 for the weir flow formula method; nevertheless, subsequent application of the DTPM results in data points clustering closely around the trendline with a consistent distribution above and below it, leading to a substantial rise in R² values.

The computed discharge with the DTPM accurately correlates with the observed discharge at each location, rather than serving as a trendline that intersects the midpoint of the cluster of observed discharge points. In comparison to the weir flow formula method (Figure 4 and Figure 5), the DTPM process (Figure 8 and Figure 9) exhibits no significant abrupt changes (for instance, the calculated discharge of 1703 m³/s on 5 July 2006, at 17:10, which has a relative error of 176.88% compared to the observed discharge), nor does it present abnormal outliers (such as the overall deviation of approximately 60% between the calculated discharges on 16 July 2003, at 20:58 and 23 July 2003, at 14:25). In the years 2003 and 2006, the DTPM attains robust fitting devoid of notable outliers.

The detailed discharge correlation coefficients and relative errors are shown in

Table 7. Error analysis of the two methods to calculate the discharge of the four harbors.

Station Name	2003				2006
	Correlation Coefficient		Relative Error		Correlation Coefficient		Relative Error
	(a)	(b)	(a)	(b)	(a)	(b)	(a)	(b)
The Sheyang River Gate	0.48	0.83	9.71%	2.61%	0.06	0.91	19.77%	2.43%
The Huangsha Harbor Gate	−0.05	0.77	11.82%	1.70%	0.11	0.56	6.53%	1.03%
The Xinyang Harbor Gate	−0.26	0.75	36.00%	5.69%	0.44	0.87	9.24%	1.33%
The Doulong Harbor Gate	0.72	0.90	8.15%	2.02%	0.79	0.94	3.39%	0.51%
Average	0.22	0.81	16.42%	3.00%	0.35	0.82	9.73%	1.32%

Notes: (a) represents the weir flow formula method (b) represents the dynamic trend prediction method.

. The experimental results indicate that DTPM significantly outperforms the weir flow formula method across all stations and time periods. The correlation coefficient of DTPM improved substantially, increasing from 0.22 to 0.81 in 2003 and from 0.35 to 0.82 in 2006, with particularly notable enhancements at stations where the weir flow formula method exhibited low or even negative correlation (e.g., the Huangsha Harbor Gate and the Xinyang Harbor Gate). Meanwhile, the relative error of DTPM decreased significantly, dropping from 16.42% to 3.00% in 2003 and from 9.73% to 1.32% in 2006, reducing the error by over 80%. These results demonstrate that DTPM exhibits higher accuracy and stability across different stations, making it more suitable for complex hydrological conditions and a promising approach for further application.

4.3. Calculation Results of Gate Opening and Closing Moments

The analysis of discharge via the weir gate requires a concurrent assessment of overall simulation fidelity and the precision of observed vs. predicted data at designated intervals. To assess the suitability of the DTPM for discharge via the weir gate at harbor gates, we extracted the observed and calculated discharges at the moments of gate opening and closing and performed a comparison analysis. In the current scenario, particularly at the point of gate opening, which marks the commencement of the time series, there is an absence of prior data for reference. It is crucial to swiftly and precisely identify the black-box relationship to model the ensuing time series. Figure 10 is derived from the discharge data of Doulong Harbor and Xinyang Harbor at a certain moment in 2006.

Table 8. Error statistics for specific opening and closing moments.

Station Name	Juncture	Gate Operation	Observed Discharge /(m3/s)	Weir Flow Formula Method		Dynamic Trend Prediction Method
				Calculated Discharge /(m3/s)	Relative Error	Calculated Discharge /(m3/s)	Relative Error
The Doulong Harbor	2006/7/6 12:35	close	477	399	−16.43%	440	−7.80%
	2006/7/6 14:07	open	464	429	−7.45%	453	−2.38%
	2006/7/6 19:35	close	394	299	−24.06%	408	3.53%
	2006/7/6 21:34	open	274	318	16.18%	265	−3.11%
	2006/7/7 14:00	close	485	387	−20.19%	455	−6.09%
	2006/7/7 15:02	open	478	381	−20.40%	456	−4.59%
The Xinyang Harbor	2006/7/5 00:40	close	811	811	−0.05%	799	−1.51%
	2006/7/5 02:00	open	911	792	−13.04%	825	−9.45%
	2006/7/5 02:10	close	615	1703	176.88%	529	−14.06%
	2006/7/6 05:40	open	559	697	24.63%	717	28.28%
	2006/7/6 22:30	close	721	694	−3.74%	692	−4.04%
	2006/7/6 23:14	open	716	681	−4.92%	722	0.87%

presents the specific discharge values and associated relative error statistics at the instances of gate closure and opening.

In the gate status section of the figure, a value of −1 indicates gate closure, a value of 1 signifies gate reopening, and a value of 0 denotes that the gate remains open until its subsequent closure, at which point the value reverts to −1. The weir flow formula approach and the DTPM provide error bars post-discounting, with the width indicating the magnitude of the relative error. The weir flow formula approach clearly indicates that a calculated discharge value is there regardless of whether the gate is large or small at the point of closure. The peak relative error in the moment of gate opening at Xinyang Harbor was 176.88%; however, when accounting for the time series of the DTPM, the relative error for Xinyang Harbor at the same instant was merely 14.06%. In comparison to the weir flow formula approach, the maximum relative error values of the discharge computed by the DTPM at Doulong Harbor and Xinyang Harbor are 7.80% and 28.28%, respectively. The precision of the fitting scenario is superior during the moments of gate opening and closing.

4.4. Comparative Analysis of Computational Results Under Defined Operational Scenarios

In addition to examining prediction accuracy at the initial gate opening moment, we further evaluated the applicability and performance differences between the weir flow formula method and the DTPM under four additional scenarios: high water level, low water level, rapid gate opening, and slow gate opening. Using Doulong Harbor and Xinyang Harbor in 2006 as examples, under high-water-level conditions, the DTPM at Doulong Harbor achieved a mean relative error of 8.98% with a standard deviation of 0.04 m, compared to the traditional method’s 15.27% mean error and 0.09 m standard deviation. A similar trend was observed at Xinyang Harbor. Under low-water-level conditions, the advantage of DTPM over the traditional approach became even more pronounced. At Xinyang Harbor, the traditional method exhibited a high relative error of 27.95%, whereas DTPM reduced the error to just 4.86%. These results indicate that DTPM maintains high prediction accuracy under both high and low water levels, primarily due to its superior capability to capture nonlinear flow dynamics. During rapid gate openings, DTPM yielded relative errors of 5.66% and 6.64% at Doulong and Xinyang Harbors, respectively—both significantly lower than the 11.95% and 8.42% errors produced by the traditional method. In the case of slow gate openings, the advantage of DTPM at Doulong Harbor became even more pronounced, with a relative error of 2.68% compared to 12.49% using the traditional approach. Although DTPM also outperformed the traditional method at Xinyang Harbor under this condition (11.50% vs. 28.89%), its error was relatively higher compared to other scenarios, suggesting that model performance under slow-opening conditions may require further enhancement. Error analysis under four scenarios is provided in

Table 9. Error analysis under four scenarios (referring to deviation assessment in low water level, rapid/slow gate opening, and other operational conditions).

Scenario	Doulong Harbor				Xinyang Harbor
	DTPM		Weir Flow Formula Method		DTPM		Weir Flow Formula Method
	Mean Relative Error	Standard Deviation/m	Mean Relative Error	Standard Deviation/m	Mean Relative Error	Standard Deviation/m	Mean Relative Error	Standard Deviation/m
High Water Level	8.98%	0.04	15.27%	0.09	4.80%	0.03	13.18%	0.09
Low Water Level	6.03%	0.04	17.90%	0.08	4.86%	0.05	27.95%	0.26
Rapid Gate Opening	5.66%	0.03	11.95%	0.11	6.64%	0.02	8.42%	0.09
Slow Gate Opening	2.68%	0.01	12.49%	0.08	11.50%	0.10	28.89%	0.15

.

In summary, across all evaluated scenarios, the DTPM method consistently outperformed the traditional weir flow formula at both Doulong and Xinyang Harbors, achieving a reduction in mean relative error of more than 6% and a reduction in standard deviation of over 0.04 m. This performance advantage stems primarily from DTPM’s ability to represent complex physical processes. Traditional weir flow formulas typically assume a simple power-law relationship between water level difference and discharge. In contrast, DTPM leverages a data-driven approach to learn the coupled relationships among time-series water levels, gate openings, and other influencing factors. This allows it to effectively adapt to complex tidal gate operation conditions, such as high/low water levels and rapid/slow gate movements.

5. Discussion

The volume of simulated data for both the Doulong Harbor Gate and the Xinyang Harbor Gate is comparable, with both employing the DTPM that takes into account the time series. The overall data accuracy indicates that the relative error for both locations is below 1.5% in 2006. However, the correlation coefficient for Doulong Harbor stands at 0.94, whereas Xinyang Harbor has a lower coefficient of 0.87. The simulation results indicate that the relative error for the moment of opening and closing of the gates at Doulong Harbor is below 8%, whereas Xinyang Harbor exhibits a relative error of 28.28%.

These differences are the result of a combination of hydrological, geographical, and engineering factors. From a hydrological perspective, Xinyang Harbor controls a watershed area of 2478 km², while Doulong Harbor controls a significantly larger area of 4428 km². Despite its nearly twofold watershed size, Doulong Harbor exhibits relatively stable hydrological processes. Hydrological data analysis reveals that Xinyang Harbor shows much greater discharge variability under similar rainfall conditions, which increases the complexity of accurate prediction.

Historical river regulation projects have also played a significant role in affecting prediction accuracy. Since 1950, Xinyang Harbor has undergone multiple major channel modifications, including those in 1950, 1957, 1958, 1971, 1975–1978, and from 1991 to the present. These projects involved meander cutoffs, channel dredging, and structural reconstructions. Such extensive human interventions have dramatically altered the natural morphology of the river, resulting in more complex and dynamic flow conditions at Xinyang Harbor compared to Doulong Harbor.

Differences in gate structure and operation management also serve as key contributing factors. A comparison of structural and operational parameters between the sluices at Xinyang and Doulong Harbors is presented in

Table 10. Comparison of the parameters of the two harbor gates.

Station Name	Z0/(m)	B/(m)	Number of Gate Openings	Average of Zu/(m)
The Doulong Harbor Gate	3	80	8	1.71
The Xinyang Harbor Gate	3.5	170	17	1.60

. The structural differences lead to varying levels of discharge calculation complexity, particularly at Xinyang Harbor, where the simultaneous operation of multiple gate openings introduces pronounced interference effects.

Moreover, disparities in design parameters further influence prediction accuracy. Xinyang Harbor is designed for an average daily discharge of 485 m³/s, with a maximum capacity of up to 1540 m³/s. In contrast, Doulong Harbor is designed for a lower average of 200 m³/s and a maximum of 1260 m³/s. These differences in design discharge capacities directly affect the difficulty of accurate flow observation and modeling at the respective sites.

To quantify prediction uncertainty, we calculated the 95% confidence intervals for both sites in the years 2003 and 2006 (

Table 11. The 95% confidence intervals for calculated discharge at Doulong Harbor and Xinyang Harbor.

Station Name	2003		2006
	DTPM	Weir Flow Formula Method	DTPM	Weir Flow Formula Method
The Doulong Harbor Gate	[0.495, 0.525]%	[3.353, 3.427]%	[2.000, 2.040]%	[8.101, 8.199]%
The Xinyang Harbor Gate	[1.305, 1.355]%	[9.174, 9.306]%	[5.645, 5.735]%	[35.904, 36.096]%

). The results show that, regardless of whether the DTPM or the traditional method is used, the confidence intervals at Xinyang Harbor are consistently wider than those at Doulong Harbor. This further confirms the objectively greater difficulty in achieving accurate predictions at Xinyang. Notably, in 2006, the confidence interval for Xinyang Harbor using the traditional method reached [35.904%, 36.096%], which is substantially broader than the corresponding interval for Doulong Harbor [8.101%, 8.199%].

On the other hand, P. D. Scarlatos [3] showed that gates behave very similarly when fully opened as compared to partially opened as long as the upstream water level and the backwater conditions are approximately the same. However, GE Jiankun [25] used the Shapley additive explanations (SHAP) method on the determination to show that the upstream water level of the gates at the irrigation catchment spillway gates is a factor that has the greatest influence on the prediction results of the spillway gate dispatch flow. The proposed method may successfully address the issue of asynchronous water level change trends in both upstream and downstream areas.

In addition, the data simulation in this study was conducted using four harbor sites located in the Lixia River region. These sites are representative of tidal-influenced river reaches in flat plain areas. However, this study did not explore the applicability of the DTPM to other types of tidal sections or sluice structures. Future research will focus on validating the model across a broader range of scenarios and hydraulic conditions to further enhance the generalizability and applicability of the proposed method.

6. Conclusions

Two approaches, specifically the weir flow formula method and the data-driven DTPM, were utilized to compute the discharge of four tidal gates. This study calibrated formula parameters and computed tidal gate discharge utilizing field data from four principal harbor gates in the Lixia River region during a typical flood year. The dataset included Z_u, Z_d, ${\displaystyle \frac{\partial {\mathrm{Z}}_{\mathrm{u}}}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial {\mathrm{Z}}_{\mathrm{d}}}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_{\mathrm{u}}-\mathrm{Z}}_{\mathrm{d}}\right)}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$. The accuracy of different formulas was systematically analyzed, and the conclusion was drawn as follows:

(1) The discharge calculated using the weir flow formula demonstrates a significant discrepancy when juxtaposed with the actual data, suggesting that the conventional method inadequately represents the flow during the inundation of the coastal harbor gate. This arises from the relevance of the weir flow formula under constant flow circumstances. In the river network of the plains affected by backwater levels, tides, and other variables, flood movement often demonstrates non-uniform flow, making the direct use of the formula imprudent.

(2) In calculating the discharge of the harbor gate with the BP neural network-based DTPM, using Z_u, Z_d, ${\displaystyle \frac{\partial {\mathrm{Z}}_{\mathrm{u}}}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial {\mathrm{Z}}_{\mathrm{d}}}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \left({{\mathrm{Z}}_{\mathrm{u}}-\mathrm{Z}}_{\mathrm{d}}\right)}{\partial \mathrm{t}}}$, ${\displaystyle \frac{\partial \mathrm{Q}}{\partial \mathrm{t}}}$ as the input conditions, all the correlation coefficients for discharge exceeded to 0.8. The DTPM attained significant enhancements in correlation coefficients with equivalent datasets while decreasing relative errors to under 3.00%. The Doulong Harbor Gate demonstrated remarkable accuracy, with an inaccuracy of only 0.51%. The results indicate that the DTPM exhibits higher simulation accuracy than the weir flow formula approach.

(3) The suggested DTPM offers substantial benefits in computing instantaneous discharge during gate operations for standard coastal tidal gates, showcasing enhanced proficiency in precisely simulating flow dynamics, particularly during crucial opening and closing stages. This methodology offers a novel framework for investigating the correlation between the outflow and discharge of coastal harbors and tidal levels in areas concurrently subjected to external flood hazards, tidal surges, and localized waterlogging, facilitating accurate simulation and quantitative assessment of tidal gate discharge and drainage efficacy.