The benefit of using a covariate for minimizing the sample size needed to estimate mean value of a target variable at field scale

Two-phase sampling design with a covariate gives an unbiased mean value at field scale.Various second phase sampling strategies are easily implemented using R software.The precision of the estimates are assessed for the different sampling strategies.Accounting for a covariate in the second phase of the sampling improves the precision. The objective of this paper is to determine the mean value of Available Water Capacity (AWC) of a soil at field scale in the context of improving the water use efficiency in agriculture. The reasoning in this work consists in determining the minimum number of locations where AWC has to be measured in a 9ha field, using different two-phase sampling strategies, to obtain a mean AWC with an adequate precision. First, 44 locations spaced on a regular square grid were chosen by a systematic random sampling (first phase of the sampling). AWC and Soil Electric Resistivity (SER) were estimated at each location. The 44 locations were then subsampled using four sampling methods and by considering subsets of various sizes, from 1 to 10 (second phase of the sampling). For each combination involving one sampling method and one subset size, 10,000 subsets were generated independently. Each subset was used to estimate one value of the mean of AWC for the field and thus, the average value for the means of the 10,000 subsets. For each combination, we computed the range L of the interval containing 95% of the 10,000 estimated means. As the more precise, the smaller L was the correct estimation for the corresponding combination. One sampling method for the second phase was the simple random sampling, and the three other used the SER as a covariate. The latter led to more precise estimates of the mean AWC than the simple random sampling. A threshold of 30mm, corresponding to one irrigation period in the study area was chosen as the minimum precision required. This threshold was not exceeded for a subset of 5 locations in the cases of sampling methods accounting for the SER as a covariate whereas 8 locations were required for the sampling method that ignores covariate.