A unified methodology for the analysis, completion and simulation of nonstationary time series with missing values, with application to wave data

A new methodology for the analysis, missing-value completion and simulation of an incomplete nonstationary time series of wave data is presented and v alidated. The method is based on the nonstationary modelling of long-term t ime series developed by the authors [J. Geophys. Res. 100 (1995) 16,149]. T he missing-value completion is performed at the level of the series of the uncorrelated residuals, obtained after having removed both any systematic t rend (e.g. monotone and periodic components) and the correlation structure of the remaining stationary part. The incomplete time series of uncorrelate d residuals is then completed by means of simulated data from a population with the same probability law. Combining then all estimated components, a n ew nonstationary time series without missing values is constructed. Any num ber of time series with the same statistical structure can be obtained by u sing different populations of uncorrelated residuals. The missing-value com pletion procedure is applied to an incomplete time series of significant wa ve height, and validated using two synthetic time series having the typical structure of many-year long time series of significant wave height. The mi ssing-value patterns used for validation have been obtained from existing ( measured) wave datasets with 16.5 and 33% missing values, respectively. (C) 2001 Elsevier Science Ltd. All rights reserved.