  Shallow water equations are extensively considered in the domains of oceans,
atmospheric modelling, and engineering research (Franca et al., 2022), which
play significant roles in floods and tsunami governance. Nonetheless, the
accurate prediction of shallow water behaviours is regarded as an arduous
undertaking, particularly when confronted with multi-dimensional data and
potential errors within the model. To address these challenges and improve the
accuracy of forecasts, this study employs an integrated approach, involving
dimensionality reduction methods, deep learning architectures, and data
assimilation techniques. Indeed, Reduced-order modelling facilitates the
conversions of high-dimensional data, extracting important features and
attenuating the complexity of problems (Zhong et al., 2023). Subsequently,
three different predictive models are utilized to prognosticate shallow water
data in the reduced latent space, followed by comparisons of their prediction
performance. Moreover, Bach and Ghil (2023) propose that through the
amalgamation of model forecasts with observational metrics, the data
assimilation algorithm can rectify their discrepancies, thereby enhancing the
model's predictive prowess. Finally, the experimental results demonstrate that
prediction values are congruent with actual observations, which accentuates the
resilience and effectiveness of this comprehensive methodology. Its potential
to accurately forecast shallow water data holds the applicability and
referential significance in preventing storm swell and other meteorological
events.
