Rainbows and climate change: A tutorial on climate model diagnostics and parameterization

Earth system models (ESMs) must represent processes below the grid scale of a model using representations (parameterizations) of physical and chemical processes. As a tutorial exercise to understand diagnostics and parameterization, this work presents a representation of rainbows for an ESM: the Community Earth System Model version 2 (CESM2). Using the "state" of the model, basic physical laws, and some assumptions, we generate a representation of this unique optical phenomenon as a diagnostic output. Rainbow occurrence and its possible changes are related to cloud occurrence and rain formation, which are critical uncertainties for climate change prediction. The work highlights issues which are typical of many diagnostic parameterizations such as assumptions, uncertain parameters, and the difficulty of evaluation against uncertain observations. Results agree qualitatively with limited available global "observations" of rainbows. Rainbows are seen in expected locations in the subtropics over the ocean where broken clouds and frequent precipitation occur. The diurnal peak is in the morning over ocean and in the evening over land. The representation of rainbows is found to be quantitatively sensitive to the assumed amount of cloudiness and the amount of stratiform rain. Rainbows are projected to have decreased, mostly in the Northern Hemisphere, due to aerosol pollution effects increasing cloud coverage since 1850. In the future, continued climate change is projected to decrease cloud cover, associated with a positive cloud feedback. As a result the rainbow diagnostic projects that rainbows will increase in the future, with the largest changes at midlatitudes. The diagnostic may be useful for assessing cloud parameterizations and is an exercise in how to build and test parameterizations of atmospheric phenomena.