Postdoctoral Fellow, Department of Atmospheric Sciences
Department of Atmospheric Sciences
Christopher Bretherton, Departments of Atmospheric Sciences and Applied Mathematics
Nathan Kutz, Department of Applied Mathematics
Ph.D., Atmosphere-Ocean Science and Mathematics, Courant Institute of Mathematical Sciences, New York University, 2017
B.S., Statistics and Mathematics, New York University, 2011
In climate models, the partial differential equations which govern atmospheric and oceanic flows are only approximated to a very coarse resolution of around 100km, which is much larger than much of everyday weather. Sub-grid-scale pheneomena which are smaller than this, such as rain and clouds, are typically approximated using statistical models, which are known as physical paramaterizations.
Historically, physical parameterizations have been formulated using human physical intuition, and any free parameters they contain are tuned by hand to match observations. This approach has been more successful for some problems than others, and in particular there are persistent biases in both the mean-state and variability of rainfall patterns in climate models. Despite this, there has been very few changes in the past two decades in how rain processes are parametrized.
At the same time, powerful techinques have been developed in the field of machine learning which can help break this deadlock. Rain processes are highly intermittent, stochastic, and nonlinear, so making progress will require a physics-aware application of probabilistic modeling and nonlinear regression techinques to the powerful datasets available from observations and high-resolution numerical models.