Skip to Main Content
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:
formula
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).

Close Modal

or Create an Account

Close Modal
Close Modal