Fractional-order pseudodifferential equations are considered to represent ocean climate variability when anomalous diffusion processes affect heat transfer in ocean surface. The driven process of these equations is assumed to be a regular spatiotemporal Gaussian random field representing normal conditions in the ocean. Linear regression in the log-wavelet domain is applied for the estimation of the parameters characterizing the pseudodifferential equation defining the anomalous diffusion process. The non-parametric framework is adopted in the estimation of the probability distribution of the driven spatiotemporal random field. Finally, ocean surface temperature values are approximated by plug-in least-square estimation from the computed parameter estimates, the estimated distribution of the driven process, and the integral version of the fractional-order pseudodifferential equation. The ability of the approach presented to process strong spatial-correlated ocean surface temperature curve data is illustrated with a real-data example, where sample information from weather stations in Hawaii ocean is analyzed.
Fractional-order pseudodifferential equations Global warming Log-wavelet regression Ocean surface temperature anomalies Spatial functional statistical estimation
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This work has been supported in part by project MTM2012-32674 (co-funded FEDER) of the DGI, MEC, and P09-FQM-5052 of the Andalousian CICE, Spain.
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