# An application study on adjoint-based variational wave assimilation scheme in German Bight with low spatial observation coverage

## Abstract

A variational assimilation scheme was modified for practical application of wave simulation in German Bight. Sensitivity analysis showed that responses of sparsely distributed observing sites to the errors of boundary conditions on wave boundaries crucially depend on observing locations and wave conditions. Therefore, a scheme designed for low spatial observation coverage is proposed. The scheme assumes that control variables can be expressed by a set of spatially uniform variables (referred to as basic control variable) adding varying perturbations. The basic control variables are assumed containing all the errors, so assimilation can proceed through adjusting them only. Twin experiments with pseudo-observations were conducted to assess the feasibility of the scheme with basic control variables. The proposed scheme using a single observational location shows a comparable assimilation effect to the original scheme without the basic control variable assumption using 25 observational locations, reducing the spectrum root mean square errors by approximately 50% throughout the whole computation domain. The practical experiment was performed over 1 day, considering both wave boundary conditions and wind fields as control variables. The spectrum root mean square errors at the validation buoy decreased by more than 60% via the proposed assimilation scheme with observations from a single in situ buoy. Overall, although the basic variable assumption will overestimate the spatial correlation of the errors and consequently adjust the control variables improperly in some areas, the scheme remains a good option for nearshore wave simulation where sea states are strongly correlated when observations are spatially limited.

## Keywords

Adjoint-based variational assimilation Wave modelling Sensitivity Observation coverage## Notes

### Acknowledgements

We gratefully acknowledge financial support from the China Scholarship Council. In addition, we are grateful to BSH, who kindly provided the in situ spectral data from buoys in the study area.

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