The most intuitive method for estimating wave parameters is to evaluate the time series of sea surface displacement measured at a single point. A time series is a sequence of repeated measurements taken over a specified period of time. Analyzing such a record of the surface displacement provides statistical information about the waves, offering insights into their characteristics and behavior. The analysis includes tracing the surface displacement above and below the mean water level. Individual waves are then identified by the points where the trace crosses the mean level, which define the start and end of each wave and can be used to determine individual wave heights (H) and periods (L) (Figure 1). This approach is commonly referred to as the zero-crossing method.
The individual waves in the record can be characterized by period (defined by where it crosses the mean water level) and height (defined by the distance from trough to crest between crossings). The result of this exercise is a wave record composed of many waves with a variety of heights and periods.
When waves are ranked by their height and/or period, the resulting order can be used to calculate common statistical estimates. Two of the most widely applied are the Significant Wave Height (Hs) and the Mean Period (Tz). The significant wave height, sometimes denoted as H3, is defined as the mean height of the highest one-third of all waves in the record. This parameter was introduced by oceanographer Walter Munk during World War II as an estimate of the wave heights typically observed from a fixed point at sea. Because wave height is directly related to wave energy, larger waves are generally considered more “significant” than smaller ones. It is important to note, however, that the significant wave height is a statistical measure representing the sampling period as a whole, and not any individual wave. In practice, some waves will be higher and others lower than the calculated significant wave height.
The mean period is defined as the average of all wave periods in the record. Additional parameters that can be derived from the same record by the ranking mentioned above include the maximum wave height (Hmax), which is simply the largest wave measured, and the mean height of the largest 10% of waves (H10). Both Hmax and H10 are commonly applied in coastal design and assessment, but they can only be obtained when direct measurements of surface displacement are available. Such direct measurements are possible with all Nortek instruments equipped with a vertical beam that functions as an altimeter, including all generations of AWACs as well as the Signature 1000, 500, and 250. By contrast, indirect measurements of waves, such as those based on pressure or velocity, cannot provide these parameters and instead require the use of spectral analysis. The most comprehensive approach is therefore to combine both time-series and spectral analyses.
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