Доклади на Българската академия на науките Comptes rendus de l’Acad´ emie bulgare des Sciences Tome 60, No 10, 2007 PHYSIQUE GEOGRAPHIQUE Oc´ eanologie AUTOREGRESSIVE (AR) BISPECTRA OF WIND WAVES IN THE COASTAL ZONE Nataliya Andreeva, Zhivelina Cherneva (Submitted by Academician T. Nikolov on June 25, 2007 ) Abstract The paper examines the second-order non-linearity of the wind waves by bis- pectral analysis based on non-parametric (conventional) and parametric approaches. The parametric technique is presented by model that is in the class of autoregressive (AR) processes. The wave measurements are taken at depth 1.6 m in the coastal zone of the Bulgarian part of the Black Sea. The bispectral estimates are evaluated by aforementioned approaches and subsequently are compared in order to establish whether AR modelling is applicable to analysis of the nonlinear wind waves propa- gating in the coastal zone. The results show good agreement between conventional and parametric estimates. Key words: wind waves, nonlinear interactions, cumulants, non-parametric and parametric bispectra Introduction. Bispectra and higher-order spectra have been recognized as useful technique for investigation of nonlinear properties of random waves. The higher-order spectral theory was developed by [ 1–3 ], but it has gained its strongets advance in signal processing and system theory [ 4, 5 ]. The bispectrum and higher-order spectra estimation techniques may be separated into two classes: conventional and parametric. Conventional methods may be classi- fied into direct and indirect techniques [ 1 ], while parametric uses autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) models [ 4 ], as only autoregressive model is applied in the present paper. Conventional bispectra estimation was used to study some aspects of nonlinear dynamics of shoaling waves in [ 6–9 ], etc. AR models for bispectral estimation were applied in signal processing by [ 10, 11 ], etc. The present paper aims to introduce parametric bispectra estimation into the field of oceanology, in order to verify whether AR modelling is applicable for description of second-order nonlinear interactions between shoaling wind waves. The study has been developed within the project “Probabilistic models of wind waves as a non- linear and nonstationary process”, contract No 1408/04 financed by the National Science Fund of the Bulgarian Ministry of Eduction and Science. 1093