Precipitation equations and their applications to the analysis of diurnal variation of tropical oceanic rainfall

<jats:p>The cloud, water, and heat budgets lay down a foundation for studying relations between precipitation, clouds, and environmental water vapor and thermal conditions. The water vapor constrained precipitation equation is derived by combining cloud budget with water vapor budget, whereas the thermally constrained precipitation equation is derived by combining cloud budget with heat budget. The precipitation equations are applied to analyze the diurnal variations of tropical oceanic rainfall using the 21 day two‐dimensional cloud‐resolving model simulation during Tropical Ocean–Global Atmosphere Coupled Ocean‐Atmosphere Response Experiment and two additional sensitivity experiments. One sensitivity experiment excludes the diurnal variation of large‐scale forcing, and the other experiment excludes the diurnal variation of solar zenith angle. The analysis shows that the diurnal variations of water vapor convergence and heat divergence associated with diurnally varying imposed large‐scale upward motions play a primary role in the development of rainfall peaks in both afternoon and nighttime, whereas the diurnal variation of radiation is secondary in the formation of nocturnal rainfall peak. The diurnal variation of radiation associated with diurnally varying solar zenith angle determines the diurnal variations of tropical oceanic rainfall when the diurnal variation of large‐scale circulation is absent. The diurnal variations of rainfall can be concisely described by simplified diurnally perturbed surface rainfall equations.</jats:p>