Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Naess (1985) model and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights.Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregressive model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. Thus, the joint distribution of three successive wave heights can be obtained by combining conditional bivariate distributions. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation.Successive wave periods with corresponding wave heights exceeding a certain threshold have also been studied. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights, can be approximated by a multivariate Gaussian distribution.The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea and in the Japan Sea, with laboratory data and numerical simulations.

This study concerns the modelling of complex tidal heterogeneities found in the Lower Jurassic Tilje Formation offshore mid-Norway. The Tilje Formation is characterized by tidal channels, tidal bars (shoals), tidal flats and deltaic deposits. The lithofacies associations have been modelled as large-scale objects with a wide range of shapes (channels, sheets and lobes). In addition small-scale models of the internal bedding structure have been generated in order to calculate effective permeability values at appropriate modelling scales. In order to assess the influence of the static input factors on recovery predictions, several production response variables were recorded for each of the 120 realizations generated. These include: streamline densities, breakthrough time measured in movable pore volume injected, pore volume tracer injected at 50% and 95% tracer fraction in the producer, and recovery factor of movable pore water at 95% tracer fraction in the producer. For this purpose we used a streamline reservoir simulator (Frontsim) with a tracer option (single-phase flow simulations). By using analysis of variance, we identified the following parameters which have the largest influence on single-phase fluid flow: (1) dimension of large-scale bar objects; (2) effective permeabilities of marginal (background) facies; and (3) interaction effects between bar objects and background permeabilities. In addition, the effective permeability values of the marginal facies are highly controlled by certain thresholds in mud content.

This note discusses the approach of specifying a Gaussian Markov random field (GMRF) by the Cholesky triangle of the precision matrix. A such representation can be made extremely sparse using numerical techniques for incomplete sparse Cholesky factorisation, and provide very computational efficient representation for simulating from the GMRF. However, we provide theoretical and empirical justification showing that the sparse Cholesky triangle representation is fragile when conditioning a GMRF on a subset of the variables or observed data, meaning that the computational cost increases.

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Statistics of the nonlinear free surface elevation as well as the nonlinear random wave kinematics in terms of the horizontal velocity component in arbitrary water depth are addressed. Two different methods are considered: a simplified analytical approach based on second-order Stokes wave theory including the sum-frequency effect only, and a second-order random wave model including both sum-frequency and difference-frequency effects. The paper compares results for the statistics of the nonlinear free surface, and the consequences of neglecting the difference-frequency effect in the first method are discussed.