Using interpenetrating subsampling to incorporate interpreter variability into estimation of the total variance of land cover area estimates

Abstract

Reference data obtained by interpreters is a key component of sample-based estimation of area of land cover and land cover change. However, interpreters may disagree when assigning the reference class label for a given sample unit and this inconsistency between interpreters contributes to the overall uncertainty of the estimated area. Interpenetrating subsampling (IPS) offers a practical way to incorporate interpreter variability into an unbiased estimator of the total variance. This method requires partitioning the full sample into g nonoverlapping groups with the sample units in each group then evaluated by a different interpreter and each interpreter determines the reference class data for only one group. The total variance is estimated by the among group variability of the g estimates of area. IPS was applied to estimate the total variance of land cover area estimates for a sample of 300 pixels selected from the Puget Sound region of the Northwest United States. The reference land cover data were obtained by seven interpreters who each labeled all 300 pixels. These data provided a unique opportunity to explore properties of IPS such as variability over different random partitions of the sample into groups and variability over different subsets of interpreters. IPS estimates of total variance were produced for each land cover class for group sizes of g = 2 through g = 6 and all possible combinations of the seven interpreters for each group size. The estimated total variance decreased with increasing number of groups. Incorporating interpreter variance increased the estimated total variance by a factor ranging from 1.08 (agriculture) to 7.06 (grass/shrub) in simple random sampling. The total variance estimates varied substantially over the random partitions of the sample into groups, but this variability decreased as the group size increased. Compared with other total variance estimators, the IPS estimator is simpler to compute and is more cost effective because it does not require repeat interpretations