A statistical mechanics model for cloud cover: Case of low clouds over the Gulf of Guinea

Abstract. This study uses satellite (MODIS) and reanalysis (ERA5) data to calibrate a stochastic model for low-cloud cover over the Gulf of Guinea. The model, based on the Ising model of ferro-magnetic materials, tracks cloudy and non-cloudy sites on a rectangular lattice. A Hamiltonian that includes external and internal interaction potentials is adopted. MODIS cloud cover data constrain the first three moments of the cloud area fraction (CAF) frequency distributions while the ERA5 boundary layer temperature (T_b) drives the Ising model. A hybrid optimization method is used to learn the internal and external potentials (J₀ and h₀). MODIS CAF frequency distributions, binned by T_b values, are bimodal, indicating three distinct cloud regimes: low-, intermediate-, and high-CAF. The calibrated Ising model reproduces these regimes through its metastable behaviour, characterized by triple equilibria. MODIS data and model results showed near-identical power-law fits of mean CAF to T_b. As T_b decreased, CAF frequency distribution changed from low to moderate to high CAF regimes in both data sets. Both distributions had similar meandering behaviour, with inflection points marking regime changes and deviations from the power law. An optimal J₀ and h₀ parameterization was derived in terms of T_b. The learning algorithm prefers high J₀ and h₀, leading to stable equilibria and exaggerated modal peaks, reminiscent to the Ising model’s behaviour at low temperature. This shortcoming is perhaps due to the crude learning metric. Information theoretic methods, though costly, could be beneficial.