Rank-Based Copula-Adjusted Mann–Kendall (R-CaMK)—A Copula–Vine Framework for Trend Detection and Sensor Selection in Spatially Dependent Environmental Networks

A Rank-Based Copula-Adjusted Mann–Kendall (R-CaMK) is proposed, with an end-to-end mathematical and computational framework that integrates rank-based multivariate dependence modelling (regular vines where data permit, Gaussian copula fallback otherwise), parametric spatial bootstrap for calibrated Mann–Kendall inference, and integer programming for budgeted sensor selection. At each site, the deterministic trend is removed, AR(1) margins are fitted, and residuals are transformed to ranks; the joint rank structure is modelled via R-vines or a Gaussian copula. Spatially coherent null series are simulated from the fitted model to estimate VarS for the Mann–Kendall S-statistic and to compute empirical p-values. A detection score wj is defined and an integer linear programme (ILP) is solved to select sensors under cost/budget constraints. Simulation experiments show improved Type-I control and realistic power estimation relative to standard corrections; an application to seven long annual maximum flow sites in New South Wales demonstrates calibrated inference and operational selection decisions.