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Semiparametric Semivariogram Modeling with a Scaling Criterion for Node Spacing: A Case Study of Solar Radiation Distribution in Thailand

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  • Sompop Moonchai

    (Advanced Research Center for Computational Simulation (ARCCoS), Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand)

  • Nawinda Chutsagulprom

    (Advanced Research Center for Computational Simulation (ARCCoS), Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand)

Abstract

Geostatistical interpolation methods, sometimes referred to as kriging, have been proven effective and efficient for the estimation of target quantity at ungauged sites. The merit of the kriging approach relies heavily on the semivariograms in which the parametric functions are prevalently used. In this work, we explore the semiparametric semivariogram where no close-form semivariogram is required. By additionally enforcing the monotonicity condition in order to suppress the presence of spurious oscillation, a scaling of the nodes of the semiparametric kriging is proposed. To this end, the solar radiation estimates across extensive but unmeasured regions in Thailand using three different semivariogram models are undertaken. A cross validation analysis is carried out in order to justify the performance of each approach. The best results are achieved by the semiparametric model with an improvement of around 7–13% compared to those obtained from the parametric semivariograms.

Suggested Citation

  • Sompop Moonchai & Nawinda Chutsagulprom, 2020. "Semiparametric Semivariogram Modeling with a Scaling Criterion for Node Spacing: A Case Study of Solar Radiation Distribution in Thailand," Mathematics, MDPI, vol. 8(12), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2173-:d:457341
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    References listed on IDEAS

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    1. Shapiro, A. & Botha, J. D., 1991. "Variogram fitting with a general class of conditionally nonnegative definite functions," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 87-96, January.
    2. Wu, Wei & Tang, Xiao-Ping & Yang, Chao & Guo, Nai-Jia & Liu, Hong-Bin, 2013. "Spatial estimation of monthly mean daily sunshine hours and solar radiation across mainland China," Renewable Energy, Elsevier, vol. 57(C), pages 546-553.
    3. Carmack, Patrick S. & Spence, Jeffrey S. & Schucany, William R. & Gunst, Richard F. & Lin, Qihua & Haley, Robert W., 2012. "A new class of semiparametric semivariogram and nugget estimators," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1737-1747.
    4. Genton, Marc G. & Gorsich, David J., 2002. "Nonparametric variogram and covariogram estimation with Fourier-Bessel matrices," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 47-57, November.
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