Clouds of steel: The ferromagnetic behaviour of low clouds over the Gulf of Guinea

This study uses MODIS and ERA5 data to calibrate a stochastic model for low-cloud cover over the Gulf of Guinea based on the Ising model of ferro-magnetic materials. The Ising model is based on the Gibbs equilibrium measure, which minimizes a Hamiltonian energy that incorporates external and internal interaction potentials. MODIS cloud cover data are used to constraint the first three moments of the cloud area fraction (CAF) frequency distributions while the bulk atmospheric boundary layer (ABL) temperature ($T_{mean}$) is used to drive the Ising model. The strength of the Hamiltonian's internal and external potentials $J_0$ and $h_0$ are machine learned from these data via a hybrid optimization method. The MODIS mean-CAF values are found to be highly correlated with ERA5 ABL temperatures but less so with respect to specific humidity, which is consistent with earlier studies. The MODIS CAF frequency distributions, binned by mean ABL temperature ($T_{mean}$), exhibit a robust bimodal structure, 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—two stable (clear and cloudy states) and one unstable, which is intermediate. The MODIS data and the model results distinctively exhibited comparable deviations from near-identical power-law fits of the mean CAF on temperature. Moreover, as the ABL temperature decreases the CAF frequency distribution undergoes a regime change from low CAF, to a moderate CAF, and high CAF regimes in both MODIS and simulation data. Notably, both data exhibited a meandering behaviour associated with the regime changes. Furthermore, a parameterization of the optimal $J_0$ and $h_0$ as a function of the ERA5 ABL temperature was derived. The learning algorithm’s preference for high $J_0$ and $h_0$ values causes model simulations to favour CAF values near stable equilibria and exaggerate the distribution peaks near critical points. This aligns with the Ising model’s behaviour at low temperatures. To accurately capture observed deviations from equilibrium, smaller values of $h_0$ and $J_0$ are necessary. This could be attributed to the use of crude learning metrics, and information theoretic methods might improve the model.