Abstract
This paper presents an incremental variational method to assimilate the observed tidal harmonic constants using a frequency domain linearized shallow water equation. A cost function was constructed with tidal boundary conditions and tidal forcing as its control (independent) variables. To minimize the cost function, optimal boundary conditions and tidal forcing were derived using a conventional dual 4-Dimensional Variational (4D-Var) Physical-space Statistical Analysis System. The tangent linear and adjoint model were solved by using a finite element method. By adapting the incremental form, the variational method streamlines the workflow to provide the incremental correction to the boundary conditions and tidal forcing of a hydrodynamic forward model. The method was tested for semi-diurnal M2 tides in a regional sea with a complex tidal system. The results demonstrate a 65–72% reduction of tidal harmonic constant vector error by assimilating the observed M2 tidal harmonic constants. In addition to improving the tides of a hydrodynamic model by optimizing boundary conditions and tidal forcing, the method computes a spatially varying uncertainty of individual tidal constituents in the model. The method provides a versatile tool for mapping the spatially continuous tides and currents in coastal and estuarine waters by assimilating the harmonic constants of individual tidal constituents of observed tides and currents.
Highlights
Tidal data assimilation is essential to improve accuracy in a number of important modeling applications in the National Ocean Service (NOS), National Oceanic and Atmospheric Administration (NOAA)
The incremental form of the variational scheme enables the data assimilation to be used for adjustment of boundary conditions and model corrections for linear or non-linear hydrodynamic models in general
This paper presents a generalized framework of an incremental variational data assimilation method to assimilate the tidal harmonic constants into a hydrodynamic model using a frequency domain linearized shallow water equation
Summary
Tidal data assimilation is essential to improve accuracy in a number of important modeling applications in the National Ocean Service (NOS), National Oceanic and Atmospheric Administration (NOAA). Tang et al [3] have shown that the improvement in tide model accuracy can reduce the uncertainty in the tidal datum products. Up to this point, the offshore boundary inputs to the tide model [3] used for VDatum were taken directly from tidal databases without assimilation of tides. A tide assimilation scheme is needed to optimize and improve the offshore tidal boundary conditions and the resulting simulation accuracy of the ADCIRC [4] tide modeling for VDatum applications
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