  Global climate models represent small-scale processes such as clouds and
convection using quasi-empirical models known as parameterizations, and these
parameterizations are a leading cause of uncertainty in climate projections. A
promising alternative approach is to use machine learning to build new
parameterizations directly from high-resolution model output. However,
parameterizations learned from three-dimensional model output have not yet been
successfully used for simulations of climate. Here we use a random forest to
learn a parameterization of subgrid processes from output of a
three-dimensional high-resolution atmospheric model. Integrating this
parameterization into the atmospheric model leads to stable simulations at
coarse resolution that replicate the climate of the high-resolution simulation.
The parameterization obeys physical constraints and captures important
statistics such as precipitation extremes. The ability to learn from a fully
three-dimensional simulation presents an opportunity for learning
parameterizations from the wide range of global high-resolution simulations
that are now emerging.
