Statistical sampling theory offers several sampling designs that are well-suited to geophysical research. Simple random sampling is the most commonly used formal methodology, in which the probability that any unit is sampled is known. Generally, units to be sampled are selected using a random number generator so that each unit has an equal chance of selection. In stratified sampling, the sampling frame is partitioned so that similar observed variable measurements are in each stratum. Systematic sampling attempts to capture the full variability within an area by obtaining samples at some predetermined interval. Adaptive cluster sampling is a relatively new methodology that allows additional units to be sampled, based on preceding sampling observations. The systematic adaptive sampling method applies adaptive cluster sampling to a systematic design. Selecting an appropriate design requires an understanding of the variability in the parameter of interest as well as the spatial covariance structure. This paper addresses such critical issues as sampling density, number of samples to collect, and assessment of the dimensions of a subregion to be sampled. While many researchers use the sampling designs presented herein, it is possible that inappropriate estimating equations were used. Formulas required to calculate unbiased, precise estimators for each of the designs are presented. The collection of CO2 flux degassing measurements from the Mud Volcano area, Yellowstone during the 1997 field season is used as a case study to outline the logical steps in selecting a sampling design. Although the case study used a stratified adaptive cluster sampling design, simpler designs can be developed based on the theory presented herein. ¿ 2000 American Geophysical Union