Piecewise Polynomial Expression of Beach Profiles

This paper advances a piecewise polynomial-based concept of beach profile geometric representation, the Piecewise Weighted Polynomial Interpolation Function (PWPIF) expression. Conventional monotonic power function or exponential function expressions of beach profile do not correlate well with actual field conditions. An alternative approach, the cubic spline interpolation function, has problems with overfluctuation. The PWPIF expression is both a conceptual and practical beach profile geometric model with a higher degree of approximation to reality in that (i) it correctly expresses the undulated morphology (e.g., bar-trough); (ii) it copes well with the overfluctuation that the cubic spline interpolation curve sustains; (iii) it gives a more realistic representation of beach profiles without missing important morphological information contained in seemingly irregular variation appearances, as it makes full use of all the gathered topographical information in establishing its coefficients; and (iv) it represents a flexible and all-inclusive approach towards expressing multiple beach profile types. The PWPIF expression has been tested against 667 sets of beach profile data measured from actual field as well as laboratory conditions. As a spatial model, it can act as a more-realistic geometric framework in beach analysis, helping to characterise beach morphological elements (beach position, slope, and volume). Temporal analysis of profile changes also benefits from this geometric model.