AI-Empowered Latent Four-dimensional Variational Data Assimilation for River Discharge Forecasting

Flood forecasting and warning, as a proactive strategy to mitigate potential adverse consequences, has attracted significant attention. However, river discharge forecasting, a crucial component of flood forecasting, presents challenges due to the high dimensionality of its parameters, often suffering from issues like low forecasting accuracy and high computational costs. Four-dimensional variational data assimilation (4D-Var), as a technique that integrates information from various sources to improve forecasting accuracy, has the advantage of incorporating the time dimension, which enables it to provide more precise predictions, making it well suited for river discharge forecasting. However, traditional hydrological forecasting models and 4D-Var methods are highly time-consuming, and 4D-Var requires access to tangent linear and adjoint models in order to evaluate the cost function, which limits their practical application in river discharge forecasting. Therefore, this paper proposes an AI-empowered latent 4D-Var methodology to address these two issues: eliminating the reliance on the tangent linear model and adjoint model, and lowering the computational cost associated with traditional methods. The method first uses a convolutional autoencoder (CAE) to compress the state field into a latent space, then employs a long short-term memory (LSTM) network as the surrogate model for the forward model in this latent space, and finally minimizes the cost function of 4D-Var directly in the latent space without the need for the tangent linear or adjoint models. We test the proposed AI-empowered latent 4D-Var on real datasets, utilizing data from the European Flood Awareness System (EFAS) as the state field and LamaH-CE as the observational data. Our method outperforms the EFAS historical simulation and the two baseline models, Voronoi-based LSTM and latent three-dimensional variational data assimilation (latent 3D-Var), across five evaluation metrics. Furthermore, the proposed method completes 500 iterations for the predictions of the next day river discharge in just 100 seconds, demonstrating significant computational efficiency. In practice, we tested our method on a flood event occurred in June 2013, where it provided more accurate and timely forecasting compared to other methods, particularly the EFAS historical simulation. Moreover, this method is not only applicable to flood forecasting, but also holds significant potential in various other fields. <list list-type="simple" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <list-item> 4D-Var, latent data assimilation, neural network, river discharge, flood forecasting. </list-item> </list>