Estimating the necessary sampling size of surface soil moisture at different scales using a random combination method

To develop a sampling strategy of surface soil moisture, a random combination method (RCM) was proposed and used to estimate the necessary sampling size (NSS) of soil moisture at different sampling areas. The RCM was developed based on the bootstrap sampling procedure and consideration of all possible sub-sampling combinations of available data. To examine the method, field experiments were conducted in sampling domains of 10×10, 20×20, 40×40, 55×55, 80×80, and 160×160m2. Comparisons of the RCM with other commonly used sampling methods, including the statistical, geostatistical, stratified sampling, and bootstrap methods, indicated that the RCM provided rational and efficient sampling strategies. Under the same accuracy, estimated NSS values using the RCM were much smaller than those by the statistical and bootstrap methods. In addition, the RCM has the advantage of requiring less input information, whereas the statistical and stratified sampling methods require independent data with the normal distribution, the stratified sampling method requires stratified allocation information, and the geostatistical method requires the semivariogram model. The RCM was applied to estimate the NSS of soil moisture at different scales (i.e. squares with sides of 10, 20, 40, 80, and 160m). Estimated values of the NSS under confidence levels of 90% and 95% with relative errors of 5% and 10% were linearly related to the coefficients of variation calculated from the experimental data. To enhance calculation efficiency of the RCM, the procedure was simplified using a small sub-sample size, which dramatically reduced the computation time for the NSS estimation.