How different are parameterisation packages really and how can we interpret stochastic perturbations?

In the Model Uncertainty-Model Intercomparison Project (MUMIP) we compare parameterisation packages from different modelling centres using their single-column modelling (SCM) frameworks. We will showcase the dataset from an Indian Ocean experiment at a 0.2 degrees grid covering one month, with about 10 million simulations of each model. These parametrised models are compared against a convection-permitting benchmark from DYAMOND under common dynamical constraints. We will show differences and similarities in precipitation patterns and physics tendencies among four models and show how these differences can be generalised. Following earlier works, we find that at coarse grids that do not resolve convection, parameterisation packages tend to produce overconfident tendencies compared to the convection-permitting benchmark. Furthermore, we test several hypotheses on the MUMIP dataset to explain the differences. We use the data to explore the foundations of stochastic physical parametrisations. Would stochastic physics effectively overcome the overconfidence for good reasons? May the stochastic perturbations actually have a physically meaningful quantitative interpretation? Can stochastic physics be used to partially overcome truncation and grid spacing limitations?