Anastassia Baxevani

Velocities for moving random surfaces

For a stationary two-dimensional random field evolving in time, we derive statistical distributions of appropriately defined velocities. The results are based on a generalization of the Rice formula. We discuss importance of identifying the correct form of the distribution which accounts for the sampling bias. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. Examples include changes of atmospheric pressure, variation of air pollution, or dynamical models of the sea surface elevation. We study the last application in more detail by applying the derived results to Gaussian fields representing irregular sea surfaces. In particular, we study statistical properties of velocities both for the sea surface and for the envelope field based on this surface. The latter is better fitted to study wave group velocities and is of particular interest for engineering applications. For wave and wave group velocities, numerical computations of distributions are presented and illustrated graphically.

A spatiotemporal precipitation generator based on a censored latent Gaussian field

A daily stochastic spatiotemporal precipitation generator that yields precipitation realizations that are quantitatively consistent is described. The methodology relies on a latent Gaussian field that drives both the occurrence and intensity of the precipitation process. For the precipitation intensity, the marginal distributions, which are space and time dependent, are described by a composite model of a gamma distribution for observations below some threshold with a generalized Pareto distribution modeling the excesses above the threshold. Model parameters are estimated from data and extrapolated to locations and times with no direct observations using linear regression of position covariates. One advantage of such a model is that stochastic generator parameters are readily available at any location and time of the year inside the stationarity regions. The methodology is illustrated for a network of 12 locations in Sweden. Performance of the model is judged through its ability to accurately reproduce a series of spatial dependence measures and weather indices.

Note on the Distribution of Extreme Wave Crests

The sea elevation at a fixed point is modeled by means of a second order model, which is a smooth algebraic function of a vector valued Gaussian process. Asymptotic methods, presented first in [1], are used to estimate the mean upcrossing intensity μ(h). The intensity is then used to determine the density of crest height in a second order sea. Numerical examples illustrate the method. The proposed approximation is used to estimate the design crest height for a specified return period.

Very short-term spatio-temporal wind power prediction using a censored Gaussian field

Wind power is a renewable energy resource, that has relatively cheap installation costs and it is highly possible that will become the main energy resource in the near future. Wind power needs to be integrated efficiently into electricity grids, and to optimize the power dispatch, techniques to predict the level of wind power and the associated variability are critical. Ideally, one would like to obtain reliable probability density forecasts for the wind power distributions. We aim at contributing to the literature of wind power prediction by developing and analysing a spatio-temporal methodology for wind power production, that is tested on wind power data from Denmark. We use anisotropic spatio-temporal correlation models to account for the propagation of weather fronts, and a transformed latent Gaussian field model to accommodate the probability masses that occur in wind power distribution due to chains of zeros. We apply the model to generate multi-step ahead probability predictions for wind power generated at both locations where wind farms already exist but also to nearby locations.

Random spectral measure for non Gaussian moving averages

ABSTRACT We study the distribution of phases and amplitudes for the spectral representation of weighted moving averages of a general noise measure. The simple independent structure, known for the Gaussian case, and involving Rayleigh amplitude and uniform phase distributions, is lost for the non Gaussian noise case. We show that the amplitude/phase distributions exhibit a rich and more complex structure depending not just on the covariance of the process but specifically on the form of the kernel and the noise distribution. We present a theoretical tool for studying these distributions that follows from a proof of the spectral theorem that yields an explicit expression for the spectral measure. The main interest is in noise measures based on second-order Lévy motions since such measures are easily available through independent sampling. We approximate the spectral stochastic measure by independent noise increments which allows us to obtain amplitude/phase distributions that is of fundamental interest for analyzing processes in the frequency domain. For the purpose of approximating the moving average process through sums of trigonometric functions, we assess the mean square error of discretization of the spectral representation. For a specified accuracy, the approximation is explicitly given. We illustrate the method for the moving averages driven by the Laplace motion.