On Detection of a Wave Age Dependency for the Sea Surface Roughness

Abstract

The wave age dependency of the nondimensional sea surface roughness (also called the Charnock parameter) is investigated with data from the new field measurement program at R?dsand in the Danish Baltic Sea. An increasing Charnock parameter with inverse wave age is found, which can be described by a power-law relation. Friction velocity is a common quantity in both the Charnock parameter and wave age. Thus self-correlation effects are unavoidable in the relation between them. The significance of self-correlation is investigated by employing an artificial ?dataset? with randomized wave parameters. It is found that self-correlation severely influences the relation. For the R?dsand dataset the difference between real and randomized ?data? was found to be within the measurement uncertainty. By using a small subset of the data it was found that the importance of self-correlation increases for a narrower range of wave age values. This supports the conclusion of Johnson et al. that because of the scatter and self-correlation problems the coefficients of the power-law relation can only be obtained from the analysis of an aggregated dataset with a wide wave age range combining measurements from several sites. The dependency between wave age and sea roughness has been discussed extensively in the literature with different and sometimes conflicting results. A wide range of coefficients has been found for the power-law relation between the Charnock parameter and wave age for different datasets. It is shown that self-correlation contributes to such differences, since it depends on the range of wave age values present in the datasets. Also, data are often selected for rough flow conditions with the Reynolds roughness number. It is shown that for datasets with large scatter this can lead to misleading results with regard to the relationship between wave age and Charnock parameter. Two different methods to overcome this problem are presented.