Uncertainty-Aware Cellular Automata with Memory for Annual Land-Cover Transition Forecasting: Hindcast Validation Using ESA CCI Maps

Abstract

Land-cover change is one of the most consequential and most poorly constrained inputs to Earth system, biodiversity, and carbon-accounting models. Most operational cellular automata (CA) forecasting frameworks couple a Markov transition matrix with a neighbourhood-based spatial allocation rule, an approach that is computationally efficient but structurally memoryless: transition probabilities are re-estimated from only the two most recent maps, and no explicit account is taken of the confidence with which any given cell's future state can be known. This paper develops and specifies, in full methodological detail, an Uncertainty-Aware Cellular Automata with Memory (UA-CAM) framework for annual, cell-level land-cover transition forecasting. The framework augments the classical CA-Markov formulation with (i) a temporal memory kernel that weights multiple historical transitions rather than a single one-step-back transition, (ii) a persistence/inertia term calibrated from the length of each cell's most recent land-cover spell, and (iii) an explicit uncertainty model that propagates class-confusion probabilities, neighbourhood heterogeneity, and transition-rarity into a per-cell, per-class predictive distribution rather than a single deterministic label. The framework is designed for hindcast validation against the European Space Agency Climate Change Initiative (ESA CCI) global annual land-cover maps (1992–2020, 300 m resolution), using a train-on-the-past/predict-the-present design in which the model is calibrated on maps up to year t and validated against the independently observed map at year t+1, ..., t+k. We present the complete mathematical formulation of the memory-weighted transition kernel, the neighbourhood suitability function, the stochastic cell-allocation procedure, and a Dempster–Shafer-based uncertainty-combination rule; we give parallel, ready-to-adapt Python and R implementations of the full workflow, from ESA CCI ingestion through hindcast scoring; and we specify a validation protocol built on the three-map Figure of Merit (FoM), quantity/allocation disagreement, fuzzy Kappa, and a novel Uncertainty Calibration Score (UCS) that scores whether the model's stated confidence matches its empirical hit rate. Because no hindcast run has yet been executed under this exact specification, all numerical results reported in the Expected Results section are explicitly labelled as anticipated, literature-informed estimates rather than empirical findings; they are intended to give a reader a calibrated sense of the plausible range of outcomes and to serve as pre-registered benchmarks against which a future empirical run can be compared. We close with a discussion of the framework's limitations — particularly the coarse thematic resolution of ESA CCI relative to local drivers of change, the computational cost of ensemble uncertainty propagation at global scale, and the difficulty of validating rare-class transitions — and outline a future-work agenda spanning driver-informed suitability layers, learned memory kernels, and multi-resolution hierarchical hindcasting.