APPLICATION OF THE LOG-HYPERBOLIC DISTRIBUTION TO HAWAIIAN BEACH SANDS

Statistical parameters of the log-normal distribution have been widely used in the textural analysis of particle size data. Graphical or mom ent measures have traditionally been used to discriminate between envi ronments and for paleoenvironmental reconstruction. However, recent wo rk has indicated that the log-hyperbolic probability density function may be more appropriate for quantifying observed mass frequency data o f sediments. The objective of this study is to assess the applicabilit y of the log-hyperbolic distribution for characterizing Hawai'ian carb onate beach sands, and to test whether this model can discriminate bet ween beach subenvironments. A grid-based design was used to sample the upper sedimentation unit at 126 locations on Waimanalo Beach, Oahu, H awai'i. The log-hyperbolic distribution fit 70% of the sand samples. E xploratory data analysis indicated that the beach had a complex textur al pattern. Therefore, the beach was divided into a backshore zone, an d the foreshore was divided into three separate zones, the lower, midd le, and upper foreshore. Size and sorting parameters of the log-hyperb olic distribution indicated little significant difference between the upper foreshore and backshore sediments. Typical gain size (nu) was co arsest in the lower foreshore (0.43 mm) and finest in the mid-foreshor e (0.23 mm). Upper foreshore and backshore sediments were the best sor ted (i.e., the highest values of delta, zeta, and kappa), while the lo wer and middle foreshore zones were the most poorly sorted. The distri bution shape (asymmetry) parameter pi indicated that all four subenvir onments were significantly different, with a median value of -0.45 for the lower foreshore, and a negative skewness (chi) of -0.13. These va lues indicate a dominant coarse population and a subordinate fine popu lation. A hydrodynamic hypothesis is presented to explain the complex spatial pattern of beach sediments. This involves energy dissipation a nd traction load deposition in the lower foreshore, and subsequent sho reward transport of finer particles in the less competent swash. Infil tration into the beach sediments produces a shoreward fining sequence that is subsequently modified by selective aeolian transport.