Spatial estimation of unidirectional wave evolution based on ensemble data assimilation (Q6572759)

The manuscript addresses the challenge of accurately predicting the spatial evolution of surface gravity waves. The primary scientific problem explored in this study pertains to the limitations of existing nonlinear wave models, particularly their sensitivity to initial conditions, which complicates the accurate prediction of wave evolution over extended spatial domains. This sensitivity often leads to the accumulation of errors, especially when initial conditions are derived from noisy or imperfect measurements, such as those obtained from buoys or laboratory wave probes. The study proposes to overcome these limitations by integrating data assimilation techniques, specifically the Ensemble Kalman Filter (EnKF), with the viscous modified Nonlinear Schrödinger (MNLS) equation. This integration aims to improve the robustness and accuracy of the wave model, allowing for better prediction of wave evolution by combining model forecasts with observational data.\N\NTo develop their approach, the authors constructed a coupled framework that utilises the EnKF to assimilate data into the MNLS wave model. The framework is designed to integrate noisy observational data with the underlying physical wave model, thereby generating a more reliable estimation of wave dynamics. The MNLS equation, which extends the classical Nonlinear Schrödinger (NLS) equation by incorporating viscosity effects, serves as the basis for simulating wave propagation. The EnKF, functioning within a Bayesian framework, optimises predictions by iteratively adjusting model outputs to better match observational data. This method is particularly advantageous for addressing the phase shifts and nonlinearities inherent in wave systems, which traditional models often struggle to handle effectively. Key techniques, such as adaptive inflation and localisation, were employed to enhance the performance of the data assimilation process, minimising sampling errors and spurious correlations that could otherwise degrade model accuracy.\N\NThe methodology was validated through a series of experiments, including both synthetic and laboratory-based scenarios. In the synthetic tests, the researchers generated data by superimposing Gaussian noise on clean MNLS simulations to create a set of perturbed observations. These were then used to evaluate how well the EnKF-MNLS framework could reconstruct the true wave patterns compared to standard, non-assimilative models. The experiments demonstrated that the framework successfully reduced the errors associated with initial condition uncertainties, maintaining closer alignment with the true wave dynamics over longer distances. Additionally, laboratory experiments were conducted in a towing tank to observe real wave behaviours under controlled conditions, further verifying the framework's efficacy. These experiments confirmed that the EnKF-MNLS model could significantly outperform traditional MNLS simulations by minimising deviations caused by initial measurement inaccuracies.\N\NThe main findings of the study reveal that the EnKF-MNLS coupled framework can substantially enhance the prediction of wave spatial evolution, particularly in scenarios where standard models are prone to phase drift and error accumulation. By effectively combining physical modelling with statistical data assimilation, the proposed method can filter out noise and correct for deviations that arise from imperfect initial conditions. The research also highlights the importance of including viscosity in the MNLS equation, as it provides a more realistic representation of wave dissipation effects, which are crucial for accurate long-range predictions.\N\NThe significance of this work lies in its potential applications to a wide range of oceanographic and maritime engineering problems. Accurate wave forecasts are essential for the safety and efficiency of offshore operations, including tidal and wave energy extraction, navigation, and coastal protection. By advancing the integration of data assimilation with nonlinear wave models, the study offers a robust framework that could lead to improved predictive capabilities in both research and operational contexts. The proposed EnKF-MNLS framework not only enhances the understanding of wave dynamics but also provides a practical tool for real-world applications where high-fidelity predictions are critical. Future work may explore further improvements, including the incorporation of additional external factors like wind, as well as the use of machine learning techniques to complement the data assimilation process, potentially leading to even more accurate and reliable wave forecasts.