The spatiotemporal semivariogram model is widely applied to deal with the spatially and temporally correlated variable (Gneiting *et al.* 2005). The spatiotemporal semivariogram is expressed as:where *h*_{s} and *h*_{t} represent the distance and time lag, respectively, and *Z*(*x,t*) denotes the spatiotemporal variable at time *t* and position *x*. Table 1 shows some well-known theoretical semivariogram models. These spatiotemporal semivariogram models have been published to describe the behavior of spatial and temporal semivariograms, such as the product of semivariograms (Rodriguez-Iturbe & Mejia 1974), the integrated product of semivariograms (Dimitrakopoulos & Luo 1993), and the product-sum model (De Cesare *et al.* 2001, 2002). Among the above spatiotemporal semivariogram models, the product-sum model can provide a large class of flexible models and require less constraint symmetry between the spatial and temporal correlation components without an arbitrary space-time metric (Gneiting *et al.* 2005). This study therefore adopts the product-sum method to calculate the spatio-temporal semivariogram of *Z*(*x,t*). The concept of the spatiotemporal semivariogram model is briefly described below.

1

Table 1

Model . | γ(h)
. | Range of h
. |
---|---|---|

1. Spherical model | 0 ≦ h ≦ a | |

c | h > a | |

2. Exponential model | h ≧ 0 | |

3. Gaussian model | h ≧ 0 | |

4. Power model | ch^{a} | h ≧ 0; 0 < a ≦ 2 |

5. Nugget model | 0 | h=0 |

c | h ≧ 0 | |

6. Linear model | ch | h ≧ 0 |

7. Linear-with-sill model | 0 ≦ h ≦ a | |

c | h > a | |

8. Circular model | 0 ≦ h ≦ a | |

9. Pentaspherical model | 0 ≦ h ≦ a | |

c | h > a | |

10. Logarithmic model | 0 | h=0 |

h >0 | ||

11. Periodic model | h ≧ 0 |

Model . | γ(h)
. | Range of h
. |
---|---|---|

1. Spherical model | 0 ≦ h ≦ a | |

c | h > a | |

2. Exponential model | h ≧ 0 | |

3. Gaussian model | h ≧ 0 | |

4. Power model | ch^{a} | h ≧ 0; 0 < a ≦ 2 |

5. Nugget model | 0 | h=0 |

c | h ≧ 0 | |

6. Linear model | ch | h ≧ 0 |

7. Linear-with-sill model | 0 ≦ h ≦ a | |

c | h > a | |

8. Circular model | 0 ≦ h ≦ a | |

9. Pentaspherical model | 0 ≦ h ≦ a | |

c | h > a | |

10. Logarithmic model | 0 | h=0 |

h >0 | ||

11. Periodic model | h ≧ 0 |

Note: *c* and *a* denote the sill and influence ranges and *h* denotes distance (Davis 1973).

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