Determination of Wind Stress from Water Level Fluctuations.

An inverse method for determining wind stress from water level fluctuations is tested in several ideal cases and is applied to observations of Lake Erie water levels and over-water wind to compute over-water drag coefficients. The method is based on the linearized, vertically-integrated shallow water equations with rotation and friction terms. It is shown that the free surface fluctuation can be expressed as the convolution integral of time and space dependent wind stress with a response function kernel. An explicit form for the response function in terms of the normal modes of the system is given. If wind stress is taken as the unknown and water level fluctuation as a prescribed quantity, the integral equation relating them does not have a unique solution. However, it is shown that, with some reasonable assumptions about the spatial variability of the wind stress field, a unique solution for wind stress in terms of water level fluctuations can be obtained. The method is applied to hourly observations of Lake Erie water levels from 12 stations around the lake for the period May to October, 1979. The calculated hourly wind stress directions agree with wind directions observed from buoys on the lake for wind speeds greater than 7.5 m s('-1). The agreement improves as wind speed increases. Calculated wind stress magnitudes are used with observed wind speeds to determine over-water drag coefficients as a function of wind speed and atmospheric stability. The average calculated drag coefficients for 2.5 m s('-1) wind speed classes at wind speeds greater than 7.5 m s('-1) increase with wind speed and decrease with atmospheric stability. The average 4 m drag coefficient for neutral conditions and wind speeds greater than 7.5 m s('-1) is 1.81 x 10('-3).PhDPhysical oceanographyUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/158343/1/8116331.pd