AbstractDetermining relationships between convective and environmental diagnostics can improve our understanding of mechanisms controlling tropical convection, and consequently, result in better representations of convection in coarsely resolved models. We identify important diagnostic relationships in observations taken during the Dynamics of the Madden‐Julian Oscillation (DYNAMO) campaign and perform weak temperature gradient (WTG) simulations of DYNAMO convection to determine if the observed relationships are reproduced in our model. We find that the WTG approximation models local changes in the diagnostics used in the study—precipitation rate, atmospheric stability, moisture, and gross moist stability (GMS)—and reproduces diagnostic relationships suggested in previous studies; an increase in precipitation rate is correlated with increased atmospheric moisture content, which, in turn, is correlated with greater atmospheric stability. Large‐scale atmospheric stability—changes of which might be related to balanced dynamics, we speculate—seems to be a candidate for a convective controlling mechanism. Observed and modeled interactions of local convection with the large‐scale environment—quantified by the GMS—are in agreement with the theory of Inoue and Back (2015b); the GMS increases from small, positive or negative, values during developing convection and further increases for decaying convection past a critical GMS found at peak precipitation rates, atmospheric stability, and moisture content. Understanding the link between the critical GMS and the diagnostics—still a standing problem—could further our understanding of interactions between local convection and the large‐scale environment.