Estimating the Variance of the Proportion of Contaminated Soil by Petroleum Spills Using Two-Dimensional Systematic Sampling under Different Approaches

In leading petroleum-producing countries like Kuwait, Brazil, Iran, Iraq and Mexico oil spills frequently occur on land, causing serious damage to crop fields. Soil remediation requires constant monitoring of the polluted area. One common monitoring method involves two-dimensional systematic sampling, which can be used to estimate the proportion of the contaminated soil and study the oil spills’ geographic distribution. A well-known issue using this sampling design involves the analytical derivation of variance of the sample mean (proportion), which requires at least two independent samples. To address the problem, this research proposed a variance estimator based on regression and a corrected estimator using the autocorrelation Geary Index under the model-assisted approach. The construction of the estimators was assisted by geo-statistical models by simulating an auxiliary variable. Similar populations to those in real oil spills were recreated, and the accuracy of proposed estimators was evaluated by comparing their performance with other well-known estimators. The factors considered in this simulation study were: a) the model for simulating the populations (exponential and wave), b) the mean and the variance of the process, c) the level of autocorrelation among units. Given the statistical and computing burdens (bias, ratio between estimated and real variance, convergence and computer time), under the exponential model, the regression estimator showed the best performance; and for the wave model, the corrected version performed even better.