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The understanding of methane emission and methane absorption plays a central role both in the atmosphere and on the surface of the Earth. Several important ecological processes, e.g., ebullition of methane and its natural microergodicity request better designs for observations in order to decrease variability in parameter estimation. Thus, a crucial fact, before the measurements are taken, is to give an optimal design of the sites where observations should be collected in order to stabilize the variability of estimators. In this paper we introduce a realistic parametric model of covariance and provide theoretical and numerical results on optimal designs. For parameter estimation D-optimality, while for prediction integrated mean square error and entropy criteria are used. We illustrate applicability of obtained benchmark designs for increasing/measuring the efficiency of the engineering designs for estimation of methane rate in various temperature ranges and under different correlation parameters. We show that in most situations these benchmark designs have higher efficiency. [ABSTRACT FROM AUTHOR]