| Summary: | Approved for public release; distribution is unlimited. === A wave height transformation model is developed using surface roller theory. Roller energy production is included in the energy flux balance equation to predict rms wave height for randomly varying, irregular waves over arbitrary bathymetry. The dissipation function is defined using wave roller theory, where the area of the roller is defined from a simple bore analogy. The Rayleigh distribution is used to statistically describe wave heights as waves shoal, break, and dissipate. Model predictions are compared with data acquired on both barred and near planar beaches. The surface roller wave height transformation model predicts rms wave heights with an average rms error of 6.5% for a barred beach over three days, 3.0% for two planar beaches over four days, and 4.5% average error for all locations over seven days. The model has two free parameters, alpha representing the type of breaker and gamma a measure of breaking wave saturation, also a function of beach slope. Optimal values of both parameters are chosen by model fitting. The model is sensitive to gamma, but not sigma. The surface roller model improves the bore dissipation model Thornton and Guza, 1983 by decreasing the average rms error by 40% while decreasing model sensitivity to input parameters.
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