Numerical methods for integrating particle-size frequency distributions

This article presents a suite of numerical methods contained within a Matlab toolbox for constructing complete particle-size distributions from diverse particle-size data. These centre around the application of a constrained cubic-spline interpolation to logit-transformed cumulative percentage frequency data. This approach allows for the robust prediction of frequency values for a set of common particle-size categories. The scheme also calculates realistic, smoothly tapering tails for open-ended distributions using a non-linear extrapolation algorithm. An inversion of established graphic measures to calculate graphic cumulative percentiles is also presented. The robustness of the interpolation–extrapolation model is assessed using particle-size data from 4885 sediment samples from The Netherlands. The influence of the number, size and position of particle-size categories on the accuracy of modeled particle-size distributions was investigated by running a series of simulations using the empirical data set. Goodness-of-fit statistics between modeled distributions and input data are calculated by measuring the Euclidean distance between log-ratio transformed particle-size distributions. Technique accuracy, estimated as the mean goodness-of-fit between repeat sample measurements, was used to identify optimum model parameters. Simulations demonstrate that the data can be accurately characterized by 22 equal-width particle-size categories and 63 equiprobable particle-size categories. Optimal interpolation parameters are highly dependent on the density and position of particle-size categories in the original data set and on the overall level of technique accuracy.