Generation of Hudson River Tidal Datums Using a Hybrid Data Assimilation Method

Abstract

A hybrid data assimilation (H-DA) method is introduced and applied to the calculation of tidal datums for the tidal Hudson River. The hybrid method is a combination of Newtonian Relaxation (nudging), integrated into the physics of a numerical hydrodynamic code, and error interpolation. It takes better advantage of available observed water level data along the Hudson River compared to previous methods that have been applied to the area.

Observed water level data at 4 observation stations along the Hudson River were used for data assimilation. Errors at the observation stations were interpolated to synthetic stations at multiple intermediate locations without observed water level data in order to more effectively nudge a high-resolution barotropic two-dimensional hydrodynamic model. Multiple configurations were tested and compared with free model results (without H-DA) to quantify improvements in the simulated water level time series after H-DA against independent observation records.

The H-DA model results were then used to calculate tidal datum maps over the entire tidal Hudson River. The new datums were verified against tidal datums calculated using historical water level data at 12 observation stations. Compared to the free model, the model with data assimilation greatly improved the tidal datum result. RMS Error for MSL, MHHW, MHW, MLW and MLLW decreased by 65-75%, while RMSE for DTL and MTL decreased by 28% and 50%, respectively.

Compared to preexisting and spatially more limited Hudson River datums (NOAA VDatum), H-DA resulted in improved RMSE for MSL, MHHW, MHW, DTL and MTL over VDatum’s domain. RMSE for MLW and MLLW did not improve but where within 1cm of the corresponding VDatum. Finally, compared to our previous study in which a three-dimensional diagnostic rendition of the same numerical model was applied to the Hudson River to improve VDatum results, the faster two-dimensional model with H-DA improved all calculated tidal datums except for MLLW, for which RMSE was greater by 0.7cm.