Joint spatio-temporal analysis of a linear and a directional variable: space-time modeling of wave heights and wave directions in the Adriatic Sea

It is valuable to have a better understanding of factors that influence sea motion and to provide more accurate forecasts. In particular, we are motivated by data on wave heights and outgoing wave directions over a region in the Adriatic sea during the time of a storm, with the overarching goal of understanding the association between wave directions and wave heights to enable improved prediction of wave behavior. Our contribution is to develop a fully model-based approach to capture joint structured spatial and temporal dependence between a linear and an angular variable. Model fitting is carried out using a suitable data augmented Markov chain Monte Carlo (MCMC) algorithm. We illustrate with data outputs from a deterministic wave model for a region in the Adriatic Sea. The proposed joint model framework enables both spatial interpolation and temporal forecasting.

[1]  Gould Al.  A Regression Technique for Angular Variates , 1969 .

[2]  A. Gould.  A regression technique for angular variates. , 1969, Biometrics.

[3]  Kanti V. Mardia,et al.  Statistics of Directional Data , 1972 .

[4]  P. J. Laycock,et al.  Optimal design: Regression models for directions , 1975 .

[5]  K. V. Mardia,et al.  Linear-Circular Correlation Coefficients and Rhythmometry , 1976 .

[6]  R. Johnson,et al.  Measures and models for angular correlation and angular-linear correlation. [correlation of random variables] , 1976 .

[7]  Richard A. Johnson,et al.  Some Angular-Linear Distributions and Related Regression Models , 1978 .

[8]  Kanti V. Mardia,et al.  A Model for Cylindrical Variables with Applications , 1978 .

[9]  Alan J. Lee,et al.  Regression Models for an Angular Response , 1992 .

[10]  C. Small.  The statistical theory of shape , 1996 .

[11]  Ming-Hui Chen,et al.  Monte Carlo Estimation of Bayesian Credible and HPD Intervals , 1999 .

[12]  S. R. Jammalamadaka,et al.  Topics in Circular Statistics , 2001 .

[13]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[14]  M. Stein.  Space–Time Covariance Functions , 2005 .

[15]  Christopher K. Wikle,et al.  Atmospheric Modeling, Data Assimilation, and Predictability , 2005, Technometrics.

[16]  Daniel S. Wilks,et al.  Comparison of ensemble‐MOS methods in the Lorenz '96 setting , 2006 .

[17]  Pier Luigi Conti,et al.  Statistical contributions to the analysis of environmental risks along the coastline , 2007 .

[18]  Igor Rychlik,et al.  Spatio-temporal statistical modelling of significant wave height , 2009 .

[19]  S. R. Jammalamadaka,et al.  Directional Statistics, I , 2011 .

[20]  Anne Cuzol,et al.  Preprint 2009 : 39 Space-time models for moving fields with an application to significant wave height fields , 2009 .

[21]  Giovanna Jona-Lasinio,et al.  Spatial analysis of wave direction data using wrapped Gaussian processes , 2012, 1301.1446.

[22]  A. Maruotti,et al.  A Multivariate Hidden Markov Model for the Identification of Sea Regimes from Incomplete Skewed and Circular Time Series , 2012 .

[23]  Danny Modlin,et al.  Circular conditional autoregressive modeling of vector fields , 2012, Environmetrics.

[24]  A. Gelfand,et al.  Directional data analysis under the general projected normal distribution. , 2013, Statistical methodology.

[25]  F. Lagona,et al.  Maximum likelihood estimation of bivariate circular hidden Markov models from incomplete data , 2013 .

[26]  A. Gelfand,et al.  Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes , 2014 .