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Abstract A recent theory proposes that tropical depression (TD)‐type waves grow by flattening the mean meridional moisture gradient, consequently weakening the Hadley Cell through a poleward moisture flux. To evaluate this theory, we investigate the seasonality of TD‐type waves and their relation to the Hadley Cell in ERA5 and Coupled Model Intercomparison Project Phase 6 (CMIP6) models. On the basis of the theory, a Hadley Cell instability metric is defined whose variability is largely determined by the background meridional moisture gradient and the sensitivity of rainfall to moisture fluctuations. Results show that both TD‐type wave column moisture variance and eddy moisture fluxes peak when the Hadley Cell instability metric is a maximum. These conditions typically occur when the mean meridional precipitation gradient is strongest and the Hadley Cell is weak and narrow. CMIP6 models that exhibit higher Hadley Cell instability metric simulate stronger TD‐type wave activity in the Northern Hemisphere. 

Abstract The moist processes of the Madden‐Julian Oscillation (MJO) in the Coupled Model Intercomparison Project Phase 6 models are assessed using moisture mode theory‐based diagnostics over the Indian Ocean (10°S–10°N, 75°E–100°E). Results show that no model can capture all the moisture mode properties relative to the reanalysis. Most models satisfy weak temperature gradient balance but have unrealistically fast MJO propagation and a lower moisture‐precipitation correlation. Models that satisfy the most moisture mode criteria reliably simulate a stronger MJO. The background moist static energy (MSE) and low‐level zonal winds are more realistic in the models that satisfy the most criteria. The MSE budget associated with the MJO is also well‐represented in the good models. Capturing the MJO's moisture mode properties over the Indian Ocean is associated with a more realistic representation of the MJO and thus can be employed to diagnose MJO performance.