Weibull Random Fields for Spatially Dependent Positive Data: An Application to Mining Haul Roads

Summary Positive spatial data in remote sensing and infrastructure monitoring are often strictly positive, skewed and spatially dependent. Motivated by LiDAR intensity returns from mining haul roads, we propose a geostatistical framework based on Weibull random fields for modelling spatial degradation patterns within a condition‐monitoring setting. Three constructions are studied: a Weibull field obtained from a transformation of Gaussian random fields, a Gaussian‐copula Weibull field and a new Clayton‐copula Weibull field with a parameter controlling departures from reflection symmetry. For the Clayton–Weibull construction, we establish stationarity, mean‐square continuity and mean‐square differentiability under conditions inherited from the latent Gaussian correlation model. For all three models, closed‐form bivariate densities enable scalable inference through nearest‐neighbour weighted pairwise composite likelihood. An expanded simulation study evaluates parameter recovery, model discrimination and standard‐error calibration across sample sizes, spatial dependence levels, marginal skewness and Clayton asymmetry. The method is applied to LiDAR intensity data from an open‐pit copper mine in Chile (), where information criteria favour a Clayton‐based specification with moderate asymmetry and improved agreement with empirical spatial dependence. The methods are implemented in the GeoModels R package.