Assimilation of water level data into a coastal hydrodynamic model by an adjoint optimal technique

An adjoint data assimilation system has been developed to assimilate coastal subtidal water level data into a hydrodynamic model. In this system, a linear two-dimensional Princeton Ocean Model with an orthogonal curvilinear grid system is used as the forward model. The wind drag coefficient is used as a convenient control variable (approximately representing errors in the forecasting wind fields that are usually the primary cause of errors in model-produced water levels). The cost function is defined in terms of the water level misfits between the observations and model outputs. The limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method for large-scale optimization is implemented to minimize the cost function. Identical twin experiments with model-generated pseudo-observations are performed and the results show that the true solution of the control variable can be recovered efficiently by assimilating pseudo-observations at limited locations into the model. The results from actual subtidal water level data assimilation experiments show that the simulated subtidal water levels with data assimilation are better than those without data assimilation even if only one control variable is used. The results from the experiment with 16 control variables demonstrate that the correlation coefficients are greater than 0.93 and the RMS errors are less than 5.3 cm at 18 coastal water level gauge stations. The nowcast/forecast experiments demonstrate that the subtidal water level forecasts are improved by water level data assimilation in the first 6 h. The average RMS error of the subtidal water level forecasts over the 18 water level gauge stations is reduced by 3 cm.