We numerically investigate a diffusion-reaction model of an ombrotrophic peatland implementing a Turing instability relying on nutrient accumulation. We propose a systematic and quantitative sorting of the vegetation patterns, based on the statistical analysis of the numbers and filling factor of clusters of both Sphagnum mosses and vascular plants. In particular, we define the transition from Sphagnum-percolating to vascular plant-percolating patterns as the nutrient availability is increased. Our pattern sorting allows us to characterize the peatland pattern stability under climate stress, including strong drought.