Mathematical Geosciences

, Volume 47, Issue 2, pp 149–171 | Cite as

Wavelet-Based Semiparametric Estimation of Ocean Surface Temperature

  • M. D. Ruiz-Medina
  • M. P. Frías


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 



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.

Supplementary material

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Supplementary material 1 (pdf 39 KB)
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Supplementary material 2 (pdf 39 KB)
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Supplementary material 3 (pdf 31 KB)
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Supplementary material 4 (pdf 31 KB)


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Copyright information

© International Association for Mathematical Geosciences 2014

Authors and Affiliations

  1. 1.Department of Statistics and O.R, Faculty of SciencesUniversity of GranadaGranadaSpain
  2. 2.Department of Statistics and O.RUniversity of JaénJaénSpain

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