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To better understand the physical mechanism of undertow, field observations were conducted during barred and planar beach states on the Hasaki coast in Japan. The two observation periods spanned 21 days from May 13 to June 2 in 2016, and 13 days from May 9 to May 22 in 2017, respectively. A horizontal acoustic Doppler current profiler was used to measure the undertow velocity and water level. The observed data were statistically analyzed to investigate the characteristics of the spatial and wave-energetic distributions of the undertow exceedance probability,  P E. The results reveal that when the wave energy flux level was high, the undertow velocity increased, as did its  P E. By contrast, the undertow  P Eduring a low-wave-energy level decreased with greater water depths. Here, a Weibull distribution was applied to explain  P Eof the undertow. The Weibull parameters: scale and shape were estimated by the combination of normalized values of the wave energy flux, relative surf zone locations, and normalized water depths, and this generalized equation was considered a statistical model for estimating undertow  P E. A comparison of the statistical model against the measurement demonstrates that the model accurately predicted the undertow  P Ewith a small error.

Statistical modeling of undertow on a natural beach