Spatial autoregressive functional plug-in prediction of ocean surface temperature

Abstract

This paper addresses the problem of spatial functional extrapolation in the framework of spatial autoregressive Hilbertian processes of order one (SARH(1) processes) introduced in Ruiz-Medina (J Muitivar Anal 102:292-305, 2011a). Moment-based estimators of the operators involved in the state equation of these processes are computed by projection into a suitable orthogonal basis. Specifically, the eigenfunction basis diagonalizing the autocovariance operator is considered. An estimation algorithm is designed for the implementation of the resulting SARH(1)-plug-in projection extrapolator from temporal curves irregularly distributed in space. Its performance is illustrated with a real-data example, where the problem of spatial functional extrapolation of ocean surface temperature profiles is addressed. This problem is crucial in the assessment of climate change anomalies. The data are collected from the public oceanographic biooptical database: The World-wide Ocean Optics Database. Cross Validation (C.V.) procedures are applied for the evaluation of the estimation results derived.

Spatial functional prediction from spatial autoregressive Hilbertian processes

“…The data set studied consists of mean annual daily ocean surface temperature profiles with data size ( Because weather stations are irregularly spaced (see Figure 5 below), mean annual daily temperature profiles are converted into areal data by computation of average block functional values corresponding to the boxes of a 6 25 computational grid, limited to the surrounding area of the weather stations at each region. Grid spacing is locally fitted to the spatial density of weather stations, in order to obtain a homogeneous aggregation level of temperature profiles per block (see Ruiz-Medina and Espejo, 2011a). Interpolation, according to the empirical spatiotemporal dependence structure of the data, is performed over the empty boxes.…”

“…The discrete compactly support wavelet transform is suitable to process strongly correlated data and to eliminate border effects (see Ruiz-Medina and Espejo, 2011b). The projection based on the auto-covariance eigenfunction system leads to an important dimension reduction and to a sparse version of equation system (13), in terms of diagonal matrices in its block-matrix diagonal, reducing computational cost (see Ruiz-Medina and Espejo, 2011a).…”

“…The present paper proposes a projection estimation methodology in the SARH(1) context, based on the spectral diagonalization of SARH(1) parameters. Recently, in Ruiz‐Medina and Espejo (), two alternative projection methodologies, respectively, based on the spectral decomposition of the auto‐covariance operator and on the discrete compactly supported wavelet transform, were considered. The auto‐covariance eigenfunction system leads to an important dimension reduction of the problem, while the discrete interval wavelet transform allows to removing border effects and redundancy in the data.…”

Gegenbauer random fields

“…A functional spatial extrapolator is obtained in Ruiz-Medina [27], based on the method of moments, by projection into the biorthogonal eigenfunction system that provides the spectral decomposition of the in nite-dimensional parameters involved in the state equation. Alternative projection methodologies are investigated in Ruiz-Medina and Espejo [28,29], respectively based on the autocovariance eigenfunction system and the discrete interval wavelet transform. In the spatial time series context, weak-dependence is usually assumed, but this condition is not always satis ed.…”

Modelling collocation uncertainty of 3D atmospheric profiles

“…Applications of functional data analysis can be found in various scientific areas, including climatological and environmental ones (see e.g. [24], [6], [2], [13]). However, to our knowledge, little reference is made to heteroskedasticity in the functional data literature.…”