Incremental inference of boundary forcing for a three-dimensional tidal model: tides in the Taiwan Strait

Abstract

Tides in the Taiwan Strait are predominantly semidiurnal. The semidiurnal tide propagates southward along the mainland (China) coast but is a standing wave on the Taiwan coast. The tidal amplitude is large, reaching about 2 m in the middle of the strait, but diminishing rapidly towards the deeper portion of the strait. An amphidromic point is located off the southwest coast of Taiwan. Tidal currents are strong near the open ends (especially on the Taiwan side) and diminish towards the middles of the strait. A fine-resolution (3 km×3 km), three-dimensional, coastal ocean model is being developed for the Taiwan Strait. In this study, the focus is on validation of tidal sea levels and currents. The limited-area model is driven by tidal elevations on two open ends, of which amplitudes and phases are optimized through a four-dimensional variational assimilation. Specifically, the model uses an incremental approach in which misfits between model results and coastal tidal observations are reduced incrementally through repeat applications of a linear two-dimensional model and its adjoint. The incremental approach is both effective and efficient. The root-mean-squared (rms) error for the dominant M 2 tide is reduced from about 0.15 to 0.06 m, a five-fold reduction in error variance. Moreover, this is achieved with only 3–4 iterations of the three-dimensional model; for comparison, a typical four-dimensional variational assimilation will require an order of magnitude more computation effort. The predicted tidal current ellipses are also compared with the observations from six bottom-mounted Acoustic Doppler Current Profilers (ADCP). The semi-major axis currents generally agree to within 0.05 m/s. The sensitivity of vertical tidal current structure to bottom friction also is examined.