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:
1
where hs and ht 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.
Table 1

Definition of semivariogram models and associated parameters

Modelγ(h)Range of h
1. Spherical model  0ha
h > a
2. Exponential model  h0
3. Gaussian model  h0
4. Power model cha h0; 0 < a2
5. Nugget model h=0
h0
6. Linear model ch h0
7. Linear-with-sill model  0ha
h > a
8. Circular model  0ha
9. Pentaspherical model  0ha
h > a
10. Logarithmic model h=0
h >0
11. Periodic model  h0
Modelγ(h)Range of h
1. Spherical model  0ha
h > a
2. Exponential model  h0
3. Gaussian model  h0
4. Power model cha h0; 0 < a2
5. Nugget model h=0
h0
6. Linear model ch h0
7. Linear-with-sill model  0ha
h > a
8. Circular model  0ha
9. Pentaspherical model  0ha
h > a
10. Logarithmic model h=0
h >0
11. Periodic model  h0

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

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