Estimation methods of local scour depths under complex marine environment have not been well understood for bridge design and constructions. This study focuses on estimating the maximum local scour depth at multiple piles of sea/bay-crossing bridges by developing a new formula using compiled 58 laboratory data and 21 field data. Scale model experiments of three practical bridges in China (Jiashao Bridge, Hangzhou Bay Bridge, and Jintang Bridge) were first conducted, and the results were used to calibrate the proposed universal formula. This formula was developed by using dimensional analysis and considering pile dimension, pile format and type, incoming wave flow condition, wave flow characteristics (acceleration of gravity, density, and dynamic viscosity), and sediment grain size. After the parameters were calibrated, two sets of field measurement data and two independent sets of laboratory testing data of maximum local scour depth were utilized to verify the formula. The results show a relatively good match between the calculated values from the formula and the measured data from the experiment and the field. The new formula is promising to be used to predict the maximum local scour depth at piles for the design of practical sea/bay-crossing bridges in the marine environment.

Water level simulation for complex water river networks is complex, and existing forecasting models are mainly used for single-channel rivers. In this paper, we present a new data assimilation model based on the ensemble Kalman filter (EnKF) for accurate water level simulation in complex river networks. The EnKF-based data model was tested on simulated water level data from a river network hydrodynamic model and optimized through parameter analysis. It was then applied to a real mountainous single-channel river and plain river network and compared with a data assimilation model based on the extended Kalman filter (EKF). The results showed that the EnKF-based model, with a medium ensemble sample size of 100–150, normal observation noise of 0.0001–0.01 m, and a high standard deviation of 0.01–0.1 m, outperformed the EKF-based model, with a 49% reduction in simulation errors, a 45% reduction in calculation cost, and a 43% reduction in filtering time. Furthermore, the EnKF-based data assimilation model predicted the water level in the plain river network better than the mountainous single-channel river. Around 5 to 8 h were required for data assimilation; afterwards, the model could make accurate predictions covering 20 to 30 h. The EnKF-based data assimilation model offers a potential solution for water level predictions in river networks.

The accuracy and reliability of hydrodynamic models are sensitive to both hydraulic state variables and model parameters, particularly the bed roughness, while their simultaneous real-time corrections and corresponding effects still need to be well-established and understood. This paper presents a real-time data assimilation model that corrects channel-bed roughness and water level in a river network hydrodynamic model, ensuring its accuracy and reliability. Experiments and parameter analysis evaluated the effect of initial roughness and observation noise level on model performance. Correcting both roughness and water level improved filtering time and forecasting accuracy by up to 63% and 80%, respectively, compared to methods only correcting water level. The filtering time was reduced by 44–63%, and the water level forecasting RMSE decreased by up to 80%. Both models experienced increased filtering time and forecasting error as observation noise increased, but the proposed model had a lower increase. With accurate hydraulic state measurement (e.g., 0.005 m error), the model achieved negligible water level forecasting error after 7 h of data assimilation. The model's accuracy depended on the initial channel-bed roughness, and the algorithm enables real-time roughness correction, making it useful for flood forecasting.

The accurate and efficient estimation of bed roughness using limited historical observational data is well-established. This paper presents a new parameter-inversion model for estimating bed roughness in hydrodynamic models that constrains the roughness distribution between river sections. The impact of various factors on the accuracy of inversed roughness was analyzed through a numerical experiment with the number of measurement stations, observed data amount, initial bed roughness, observational noise, and the weight of the regularization term. The results indicate that increasing the number of measurement stations and the amount of observed data significantly improves the robustness of the model, with an optimal parameter setting of 3 stations and 30 observed data. The initial roughness had little impact on the model, and the model showed good noise resistance capacity, with the error significantly reduced by controlling the smoothness level of inversed roughness using a small weight of the regularization term (i.e., 100). An experiment conducted on a real river using the calibrated model parameters shows a forecasted water level RMSE of 0.041 m, 31% less than that from the Federal Emergency Management Agency. The proposed model provides a new approach to estimating bed roughness parameters in hydrodynamic models and can help in improving the accuracy of water-level forecasting.

This study proposes an adaptive local time stepping (LTS) method based on a two-dimensional shallow water model for simulating multi-scale storm surge inundation in coastal regions. By dynamically monitoring the variation in the proportion of dry/wet cells during the simulation, the method adaptively adjusts the maximum local time step level, improving computational efficiency and minimizing human intervention in traditional LTS schemes. Through a series of idealized cases, this paper derives an empirical criterion for selecting the maximum LTS level and performs detailed analysis for two typical scenarios: in the absence of dry cells, the optimal LTS level is based on the maximum local time step under quiescent conditions; in complex hydrodynamic models with dry cells, the adaptive adjustment strategy based on the dry cell proportion is required to handle the increased computational complexity. The results show that when the proportion of dry cells was between 40% and 70%, the maximum LTS level increased by one level, and when it exceeded 70%, the maximum LTS level increased by two levels, with a recommended maximum limit of 7 levels. In ideal cases, the adaptive LTS method improves efficiency, with speedups of up to 5.83 times compared to traditional methods. Furthermore, the adaptive LTS method is successfully applied to storm surge and seawater inundation simulations, with validation through comparison with observational data. In particular, the simulation of the seawater backflow event in Erjiegou demonstrated the method’s ability to capture both the occurrence time and extent of seawater backflow, confirming its efficiency and reliability in complex hydrodynamic processes. The proposed method holds significant promise for applications in storm surge forecasting, disaster assessment, and emergency management.