  Accurate and computationally-viable representations of clouds and turbulence
are a long-standing challenge for climate model development. Traditional
parameterizations that crudely but efficiently approximate these processes are
a leading source of uncertainty in long-term projected warming and
precipitation patterns. Machine Learning (ML)-based parameterizations have long
been hailed as a promising alternative with the potential to yield higher
accuracy at a fraction of the cost of more explicit simulations. However, these
ML variants are often unpredictably unstable and inaccurate in \textit{coupled}
testing (i.e. in a downstream hybrid simulation task where they are dynamically
interacting with the large-scale climate model). These issues are exacerbated
in out-of-distribution climates. Certain design decisions such as
``climate-invariant" feature transformation for moisture inputs, input vector
expansion, and temporal history incorporation have been shown to improve
coupled performance, but they may be insufficient for coupled
out-of-distribution generalization. If feature selection and transformations
can inoculate hybrid physics-ML climate models from non-physical,
out-of-distribution extrapolation in a changing climate, there is far greater
potential in extrapolating from observational data. Otherwise, training on
multiple simulated climates becomes an inevitable necessity. While our results
show generalization benefits from these design decisions, the obtained
improvment does not sufficiently preclude the necessity of using multi-climate
simulated training data.

Atmospheric and Oceanic Physics