Robust Quantile-Structure Inversion for Cloud Model Parameter Identification

Cloud-model hyper-entropy can be overestimated when a scale-inflated subpopulation broadens the tails. We develop a quantile-based estimator that removes location and common scale before recovering cloud shape. Influence normalization balances the selected contrasts, and a prespecified correction addresses centered scale inflation. The theory proves global injectivity of the shape-contrast map for every positive shape ratio, establishes local stability under data and numerical-score perturbations, derives a mixed-rate limit for the singular cloud center, and gives boundary-projected and fixed-positive finite-step limits for the contamination correction. Independently checked numerical integration supports the reference calculations. Simulations and real-data-calibrated semi-synthetic experiments show a clean-sample efficiency cost and improved recovery under moderate scale inflation. A controlled loss ablation attributes the observed gains to the structural construction and weighting rather than active Huber clipping. Benchmark applications illustrate how the estimator can be integrated into a cloud-clustering workflow.