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Space-Time Variogram Modeling

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Encyclopedia of GIS

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Synonyms

Space-time semivariogram modeling

Definition

Space-time variogram is a function which gives measure of spatiotemporal correlation of the random field \(\{Z(\mathbf{s},t) : \mathbf{s} \in \mathbb{R}^{d},\ t \in \mathbb{R}\}\). Mathematically, space-time variogram, 2γ(s1, t1; s2, t2) is defined as

$$\displaystyle{ 2\gamma (\mathbf{s}_{1},\ t_{1};\mathbf{s}_{2},\ t_{2}) = var[Z(\mathbf{s}_{1},\ t_{1}) - Z(\mathbf{s}_{2},\ t_{2})] }$$
(1)

Half of the variogram function, γ is called semivariogram. In this chapter semivariogram and variogram are used synonymously. By space-time variogram modeling, we mean finding the form of the function γ(s1, t1; s2, t2) for any two given space-time coordinates (s1, t1) and (s2, t2) from available information. In many applications, such as space-time kriging, observations of a space-time process are called one realization of the random field Z. To use only observations for model variogram, an assumption is made that γ(s1, t1; s2, t2) is only...

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Author information

Authors and Affiliations

  1. Centre for Studies in Resources Engineering, Indian Institute of Technology Bombay, Mumbai, India

    Parvatham Venkatachalam & Manoj Kumar

Authors
  1. Parvatham Venkatachalam
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  2. Manoj Kumar
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Corresponding author

Correspondence to Parvatham Venkatachalam .

Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

  2. Management Science and Information Systems Department, Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ, USA

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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Venkatachalam, P., Kumar, M. (2017). Space-Time Variogram Modeling. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_1643

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