Spatiotemporal probabilistic wind vector forecasting over Saudi Arabia
type: Item
instance of: scholarly article
title: Spatiotemporal probabilistic wind vector forecasting over Saudi Arabia
zbMATH Open document ID: 1475.62278
DOI: 10.1214/20-AOAS1347
author: Amanda Lenzi
author: Marc G. Genton
published in: The Annals of Applied Statistics
publication date: 2021-08-04T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aoas/1600454870
review text: Motivated by a data set with observations from 28 wind stations in Saudi Arabia, the authors propose statistical models for probabilistic forecasting of wind vectors. In the proposed univariate model the value \(Y(s,t)\) denotes the square-root transformed wind speed at station \(s\) and time \(t\). There is assumed that \(Y(s,t)\) has a normal distribution, \(Y(s,t)\sim N(\mu(s,t),\sigma^2)\), where \(\sigma^2\) is the variance of a Gaussian white noise and \(\mu(s,t)\) is the mean function which includes the fixed and random effects. It is of the form \[ Y(s,t) \mu(s,t) = \beta_0 + \beta_1 \mathrm{Temp}(s,t) + \beta_2 \mathrm{Elev}(s) + \beta_3 \sin\{\theta(s,t)\} + \beta_4 \cos\{\theta(s,t)\} + f (H(t)) + W(s,t), \] where \(\beta_0\) is the intercept, \(\text{Temp}(s,t) \) is the covariance temperature, \(\mathrm{Elev}(s)\) is the elevation that is constant in time, \(\theta(s,t)\) represents the wind direction for each location and time, \(f (H(t))\) is a smooth function known as the ``time-of-day'' effect, \(W(s,t)\) is a spatiotemporal model with first order autoregressive dependence \[ W(s,t) = aW (s,t - 1) + Z(s,t),\, t = 2,\dots,T, \,|a| < 1. \] Here \(Z(s,t)\) is a realization of a Gaussian random field (GRF) with mean zero and the covariance function \[ \mathrm{cov}\{Z(s,t),Z(s',t')\}=\frac{\sigma^2_z}{\Gamma(v)2^{v-1}}(kh)^vK_v(kh)\cdot\delta_{t}^{t'}, h=\|s-s'\|, \] where \(K_v(\cdot)\) is the modified Bessel function of the second kind of order \(v\), \(\delta_{t}^{t'}\) is the Kronecker function. In the developed bivariate model a wind vector is determined by west-east (horizontal), denoted by \(U(s,t)\), and north-south (vertical), denoted by \(U(s,t)\), components wich are assumed to be Gaussian \(U(s,t)\sim N(\mu_u(s,t),\sigma_u^2)\) and \(V(s,t)\sim N(\mu_v(s,t),\sigma_v^2)\), where \(\sigma_u^2\) and \(\sigma_v^2\) are variances of the white noise and \(\mu_u(s,t)\) and \(\mu_v(s,t)\) are means of the random processes of the form \(Y(s,t)\) with …
Mathematics Subject Classification ID: 62P12
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 86A10
zbMATH DE Number: 7378431
zbMATH Keywords: spatio-temporal models
zbMATH Keywords: spatio-temporal point patterns
zbMATH Keywords: Gaussian random field
zbMATH Keywords: Bayesian inference
zbMATH Keywords: coregionalization spatial and spatio-temporal models
zbMATH Keywords: measurement error spatial models
zbMATH Keywords: sampling
zbMATH Keywords: survival analysis
zbMATH Keywords: space-time regression
zbMATH Keywords: penalized complexity
reviewed by: M. P. Moklyachuk
describes a project that uses: Stem
describes a project that uses: R
describes a project that uses: INLA
describes a project that uses: R-INLA
describes a project that uses: raster
describes a project that uses: spBayes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7378431