The Madden-Julian Oscillation (MJO) is a planetary-scale envelope of tropical convective cloud clusters coupled with large-scale circulation, which propagates eastward with an intraseasonal time scale (30-60 days). The MJO interacts with many weather and climate phenomena in the Earth system, including extreme events, thereby providing a key source of predictability in the intraseasonal time scale. Unfortunately, however, many global climate models (GCMs) continue to struggle with a poor representation of the MJO, with only incremental improvement across model generations. The unsatisfactory model performance and slow progress call for a new type of diagnostics that can provide insights into the root cause of model biases.

The MJO research community has developed a set of process-oriented diagnostics for MJO simulation, which has then been applied to a wide variety of model simulations. Many MJO process-oriented diagnostics focus on the moist thermodynamics in the tropical atmosphere, whose representation in GCMs is directly affected by the parameterizations of moist processes, such as cumulus convection and cloud microphysics. We will present an overview of the development of several MJO process-oriented diagnostics and showcase their applications to GCM simulations, including those that participated in the 5^th and 6^th Coupled Model Intercomparison Project. The results of applying MJO process-oriented diagnostics to GCMs collectively underscore an accurate representation of the interactions among moisture, convection, cloud, and radiation, and the horizontal and vertical gradient of mean moisture as critical aspects for GCM to simulate a realistic MJO.