Whilst the Euclidean distance is widely used to quantify difference between two multidimensional vectors, it is not well-suited to discrete distributions such as the GRID because of insensitivity to redistribution between bins. To illustrate this, the distribution X = [0,1,0,0,0] (with X representing the first five bins of an RDF) will have the same Euclidean distance to Y = [1,0,0,0,0] and Z = [0,0,0,0,1], although X and Y are closer if viewed as a binned distribution. A more appropriate measure of distance for such distributions is the earth mover's distance (EMD). This metric (also known as the Wasserstein distance) can be considered as the minimum amount of 'work' needed to transform one distribution into another, analogous to moving piles of earth (identical distributions have EMD = 0). Such a metric has recently been suggested as a way to quantify compositional similarity in inorganic materials. In this work, we have used EMD to compare between GRID distributions by computing the 1D pairwise (ith -ith) distances, before finally computing the mean EMD across all GRID groups. Note, however, that a different weighting within the mean could be applied to favour short-or longrange similarity, or alternatively a 2D EMD could compare across all GRID groups at once, at the expense of computational time.