Aggregation of Sampling Units: An Analytical Solution to Predict Variance

Geographical variables generally show spatially structured patterns corresponding to intrinsic characteristics of the environment. The size of the sampling unit has a critical effect on our perception of phenomena and is closely related to the variance and correlation structure of the data. Geostatistical theory uses analytical relationships for change of support (change of sampling unit size), allowing prediction of the variance and autocorrelation structure that would be observed if a survey was conducted using different sampling unit sizes. To check the geostatistical predictions, we use a test case about tree density in the tropical rain forest of the Pasoh Reserve, Malaysia. This data set contains exhaustive information about individual tree locations, so it allows us to simulate and compare various sampling designs. The original data set was reorganized to compute tree densities for 5 times 5-, 10 times 10-, and 20 times 20-meter quadrat sizes. Based upon the 5 times 5-meter data set, the spatial structure is modeled using a nugget effect (white noise) plus an exponential model. The change of support relationships, using within-quadrat variances inferred from the variogram model, predict the spatial autocorrelation structure and new variances corresponding to 10 times 10-meter and 20 times 20-meter quadrats. The theoretical and empirical results agreed closely, whereas neglecting the autocorrelation structure would have led to largely underestimating the variance. As the quadrat size increases, the range of autocorrelation increases, while the variance and the proportion of noise in the data decrease.