Incorporating scale into spatio-temporal variability: applications to soil quality and yield data

Some observations are more variable in space and relatively less variable in time or vice versa. Based on the major source of variability, regionalized variable theory is used to construct either spatial or temporal semivariograms. Examples include georeferenced soil data, with primarily spatial variability, and daily weather data, with primarily temporal variability, as input to dynamic simulation models. However, for the proper interpretation of the output variables resulting from these simulations, it is important to describe both their spatial and temporal variabilities. A variance model is presented in which time is treated as a third dimension added to a two dimensional space. This spatio-temporal variance model is used in Case I to construct spatio-temporal variograms of hydrologic model output. The spatio-temporal variograms were used to examine the differences between two calculation schemes involving different hydrologic models. Input data to simulation models are based on a certain support size. For each support size a semivariogram may be constructed to represent the variability. The relationship between the support size of data and the distribution of their values can be described by a power function. Incorporating the relationship between variance and support size yielded a universal variance model relating the variance with lag distance and support size. This variance-support model was applied in Case II to agronomic yield data obtained from a study focusing on the improvement of land use in central Cote d’Ivoire. q 1998 Elsevier Science B.V. All rights reserved. ˆ