Graphical and Statistical Analysis of Nonlinear Internal Wave Dynamics Using Spatio-Temporal Array Observations: Preliminary Results

Tidally driven internal wave packets are an important dynamical process influencing mixing of nutrients, salinity, and temperature in coastal waters over daily, weekly, monthly, and seasonal time scales.Past parameterization of nonlinear internal wave dynamics off the northwest coast of Australia included time dependent empirical orthogonal function analysis which successfully quantified temperature fluctuations in the water column over a semidiurnal time scale.Seasonal time scale internal wave analysis has been carried out using an array of pressure measurements distributed over the same continental shelf area and using a variety of statistical algorithms.Over a 4-month time span Bayesian belief networks, quantifying covariance between mooring-based observation posts, demonstrate an indirect wave signal propagation pathway between posts suggesting the influence of the bottom boundary layer on spatial internal wave coherence.The use of Wiener filtering, least mean square filtering, and hidden Markov modeling between observation posts separated in space suggests anisotropic wave signal propagation consistent with the M2 barotropic propagation of energy from west to east along the continental shelf.High energy pressure event statistical estimation using Morlet wavelet analysis, a parameterization of steep internal wave groups, shows strong local maxima at distinct local time scales of 1-2 days and 15 days at different nodes.Further analysis of maximum wave pressure events reveals a strong fit to the generalized extreme value distribution consistent with the shape parameter varying with each observation post.Bayesian belief networks for maximum pressure energy values show a nodal-edge structure different from the Bayesian belief network previously calculated parameterizing both low and high energy pressure waves.Strong edge connections exist primarily for adjacent observation posts suggesting possible steep wave attenuation.In addition, the Bayesian belief network has arrows pointing in the direction opposite to the general M2 barotropic energy flux.All extreme value statistical results are consistent with the impact of hurricanes Iggy and Lua causing disruption of the general flow of wave energy.