Water level simulation in bays by spatial interpolation of tidal constituents, residual water levels, and datums

Abstract

A new method of simulating total water level relative to a datum takes values at the tide gauges and spatially interpolates them throughout the region. The values at the gauges which are spatially interpolated are: (1) each tidal constituent's amplitude and (2) phase value; (3) the residual, or non-tidal, water level; and (4) the offset, which is either the difference between local mean sea level (MSL) and mean lower low water (MLLW), or a tidal datum (either MSL or MLLW) relative to the ellipsoid. The water level at any point is computed by summing the astronomic tide (computed from the interpolated constituents), the interpolated residual, and the interpolated offset. In addition, for a GPS-supported survey, the ellipsoidally referenced MLLW values can be spatially interpolated and used to determine MLLW depth. The spatial interpolation at the core of this method is carried out by the use of a set of weighting functions that quantify the local contribution from each of the shore gauges. The weighting functions are generated numerically by solving Laplace's equation on a grid. The new method of estimating total water levels relative to a datum is called tidal constituent and residual interpolation (TCARI). The TCARI method was tested for accuracy using post-processed kinematic GPS measurements of water level collected by NOS in Galveston Bay, Texas, and San Francisco Bay, California. The root mean square errors were estimated to be 8 cm for the Galveston Bay data and 9.2 cm for the San Francisco Bay data, which is approximately the error in the measurements.