Prediction of significant wave height using spatial function

Determining the contribution of variables from stations surrounding a pivot station to variables at the pivot station is very important for many purposes. In this regard, a Regional Dependency Function (RDF) among the variables needs to be obtained. RDF can be used to estimate missing data, determine the location and optimum number of measurement stations (station network design), estimate the potential of a variable under consideration and calculate radius of influence. However, conventional geostatistical methods cannot be employed to achieve the above mentioned uses as they have a number of limitations. As a result, a new method called Slope Point Cumulative Semi-Variogram (SPCSV), was developed to obtain RDF and to address all the limitations of the conventional geostatistical methods. SPCSV was developed by using data from 22 wave measurement stations located off the west coast of the United States. The objective of the study was to predict the significant wave height and determining the influence of radius of the pivot station using this method. Also, the SPCSV method was compared with two other geostatistical methods known as Point Cumulative Semi-Variogram (PCSV) and Trigonometric Point Cumulative Semi-Variogram (TPCSV) using the same data set by taking the mean relative error (MRE) as a performance evaluation criterion. The MRE of the SPCSV method was found to be 6%, which is acceptable in engineering applications. The superiority of the SPCSV method in predicting the significant wave height over the PCSV and TPCSV methods is presented both numerically and graphically.