Influence of discrete step size on wind setup component of storm surge

Open coast storm surge water levels consist of wind setup due to wind shear at the water surface; a wave setup component caused by wind induced waves transferring momentum to the water column; an atmospheric pressure head component due to the atmospheric pressure deficit over the spatial extent of the storm system; a Coriolis forced setup or setdown component due to the effects of the rotation of the earth acting on the wind driven alongshore current at the coast; a possible seiche component due to resonance effects initiated by moving wind system, and, if astronomical tides are present, an astronomical tide component (although the tide is typically considered to be a forced astronomical event and not really a direct part of the external wind-driven meteorological component of storm surge). Typically the most important component of a storm surge is the wind setup component, especially on the U.S. East Coast and the Gulf of Mexico shorelines. In many approaches to storm surge modeling, a constant depth approximation is invoked over a limited step size in the computational domain. The use of a constant depth approximation has received little attention in the literature although can be very important to the resulting magnitude of the computed storm surge. The importance of discrete step size to the wind setup storm surge component is considered herein with a simple case computation of the wind setup component on a linear slope offshore profile. The present study findings show that the constant depth approximation to wind setup storm surge estimation is biased on the low side (except in extremely shallow water depths) and can provide large errors if discrete step size is not sufficiently resolved. Guidance has been provided on the error that one might encounter for various step sizes on different slopes.