Find in Library

The breaking wave height is a crucial parameter for coastal studies but direct measurements constitute a difficult task due to logistical and technical constraints. This paper presents two new practical methods for estimating the breaking wave height from digital images collected by shore-based video monitoring systems. Both methods use time-exposure (Timex) images and exploit the cross-shore length (<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>H</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula>) of the typical time-averaged signature of breaking wave foam. The first method (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <msub> <mi>s</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula>) combines <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>H</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> and a series of video-derived parameters with the beach profile elevation to obtain the breaking wave height through an empirical formulation. The second method (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <msub> <mi>s</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>v</mi> <mn>24</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula>) is based on the empirical finding that <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>H</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> can be associated with the local water depth at breaking, thus it can be used to estimate the breaking wave height without the requirement of local bathymetry. Both methods were applied and verified against field data collected at the Portuguese Atlantic coast over two days using video acquired by an online-streaming surfcam. Furthermore, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <msub> <mi>s</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>v</mi> <mn>24</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> was applied on coastal images acquired at four additional field sites during distinct hydrodynamic conditions, and the results were compared to a series of different wave sources. Achievements suggest that <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <msub> <mi>s</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> method represents a good alternative to numerical hydrodynamic modeling when local bathymetry is available. In fact, the differences against modeled breaking wave height, ranging from 1 to 3 m at the case study, returned a root-mean-square-error of 0.2 m. The <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <msub> <mi>s</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>v</mi> <mn>24</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> method, when applied on video data collected at five sites, assessed a normalized root-mean-square-error of 18% on average, for dataset of about 900 records and breaking wave height ranging between 0.1 and 3.8 m. These differences demonstrate the potential of <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <msub> <mi>s</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>v</mi> <mn>24</mn> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> in estimating breaking wave height merely using Timex images, with the main advantage of not requiring the beach profile. Both methods can be easily implemented as cost-effective tools for hydrodynamic applications in the operational coastal video systems worldwide. In addition, the methods have the potential to be coupled to the numerous other Timex applications for morphodynamic studies.