Sampling with probability proportional to prediction (3P sampling) using covariates derived from spherical images

Abstract

Using a two-phase sampling approach with systematic selection of large samples of covariates followed by a sampling with probability proportional to prediction (3P sampling) process to subsample field measures of the parameters of interest can be an efficient design to sample larger forest areas. To assist in obtaining predictions for each sample plot consistently and rapidly, we propose using a 360° spherical camera. In this study, three covariates derived from spherical images were evaluated: (i) basal area (P[BA]); (ii) sum of squared heights per hectare (P[SHT]); and (iii) stem fraction (P[SF]). These covariates were used to estimate volume. Sample simulations showed no biases in volume estimates for any of the three covariates. Overall, P[SF] had the lowest standard error percentages across different simulated sample sizes (10% for five subsamples to 2.5% for 50 subsamples), even though it had the lowest correlations with field volume (correlation = 0.30–0.31). This may be a result of the relatively consistent stand conditions within the study site. Based on our results, standard errors of 5% were obtainable with measurement fractions of about 25% of the number of image-based predictions when using P[SF] or P[BA] and 75% when using P[SHT].