Convection-wave coupling is a central topic in tropical atmospheric dynamics. To understand how clouds respond to wave-like large-scale vertical motion with varying periods, we build a microscopic cloud ensemble model with multiple independent cloud members. The lifecycle of each cloud member is simulated as a dual-threshold process of boundary layer equivalent potential temperature, which evolves alternatively between the shallow and deep convective stages. The stage alternation is characterized by the elimination of convective inhibition energy (CIN) and the exhaustion of convective available potential energy (CAPE). The cloud response exhibits two regimes. When the wave period is close to the convective lifecycle timescale, the cloud ensemble exhibits a resonant response, with individual clouds being synchronized to the wave. The rainfall rate lags the low-level large-scale vertical velocity. When the wave period is much longer than the convective lifecycle timescale, the cloud ensemble exhibits a quasi-equilibrium response. The rainfall rate does not significantly lag the low-level large-scale vertical velocity, and synchronization is weak. The cloud synchronization is caused by the phase and frequency adjustment of individual clouds, which is conducted by the modulation of CIN by temperature in the lower troposphere and the modulation of CAPE by moisture convergence in the boundary layer. Based on the microscopic cloud ensemble model, an analytical theory of the rainfall response amplitude and response phase is derived, which generally agrees with cloud-permitting simulations.

Dr. Hao Fu is currently a faculty member at Nanjing University, studying the fluid dynamics of tropical cyclones, waves, and clouds. He earned his Ph.D. from Stanford University, under the supervision of Prof. Morgan O’Neill, and received Stanford Earth System Science Award for Scholarly/Research Achievement. He was a fellow of the WHOI GFD Program (2023) and a T. C. Chamberlin postdoctoral fellow (2023-2025) at the University of Chicago, working with Prof. Da Yang. He enjoys applying a combination of theoretical models, numerical simulations, and laboratory experiments to understand weather and climate.