A hybrid data assimilation and machine learning approach for improving forecast skill in models strongly driven by boundary conditions

Data assimilation (DA) has shown to be a powerful method to improve hydronumeric models by integration of observations. However, in systems which are strongly governed by boundary conditions, the benefits of DA are typically limited to improvements of hindcast and quickly fade in forecasts where no observations are available. Where sufficient historical observations are available, machine learning (ML) models can be an attractive alternative for providing accurate forecasts of hydrodynamic conditions.

With the goal to improve the forecast, we propose a hybrid approach combining a physics-based numerical model with a machine learning approach via data assimilation. The ML model delivers accurate forecasts in a few points where historical observations are available. These results are then treated as synthetic observations by data assimilation which transfers the improvements to surrounding positions and other model variables.

This approach is illustrated with a case-study from the Elbe Estuary. Here, an operational two-dimensional hydronumeric model, strongly driven by boundary conditions, is used to compute the hydraulic conditions in the estuary with the main purpose of ensuring safe nautical navigation. The existing model is extended with an Ensemble Kalman Filter data assimilation approach where an ensemble is created by stochastic perturbation of model forcings.

During hindcast, data from two stations of the estuary are assimilated to improve numerical model results and initial conditions for the forecast. To maximize forecasting skill, a Long-short-term-memory machine learning approach is used to provide synthetic observations at assimilation stations during the forecast.

Results from the hybrid model compared to a baseline model, without assimilation, at independent validation stations show that the hybrid model can reduce forecast errors by 40% for water levels and prolongs the positive influence of data assimilation significantly.