Defining Higher-Order Turbulent Moment Closures with Random Forests

Unresolved turbulent advection must be parameterized in atmospheric models. Modern higher-order closure schemes depend on analytic moment closure assumptions that diagnose higher-order moments in terms of lower-order ones. These are then tested against Large-Eddy Simulation (LES) higher-order moment relations. However, these relations may not be neatly analytic in nature. Rather than rely on an analytic higher-order moment closure, can we use machine learning on LES data itself to define a higher-order moment closure?

A random forest is an ensemble of decision trees which are each constructed using a random subset of the training data. The computation time of an output is short, and scales with the logarithm of the number of training samples. Using the Python package scikit-learn, the quantitative performance of a random forest trained on LES data in relating second-order moments involving of vertical velocity, potential temperature, and total water mixing ratio to third-order moments of the same is investigated.

Results will be presented from a random forest trained to perform second-order moment closure on the “fast” and “slow” stratocumulus to cumulus composite cases in Sandu and Stevens (2011), and tested against the “reference” case. Preliminary results show all third-order moments are predicted with r values greater than 0.90, and with negligible bias.

Results will be presented for random forests trained and tested on different samples of LES runs from the MAGIC field campaign, which took place in the stratocumulus to cumulus transition region between Los Angeles, CA and Honolulu, HI over the course of a year. This will establish whether these LES runs sample the relationships between second and third-order moments well enough to define them for this region.

The ability of the random forest to function across scales is investigated by training random forests on varying analysis grid resolutions and testing them at different resolutions of a BOMEX non-precipitating shallow cumulus LES run, with resolutions ranging from 800m to 25.6km. While this work focuses on second-order closure, random forests performing first-order and third-order moment closure will also be assessed using the BOMEX case.

This work will help establish the feasibility of using a random forest to define a higher-order moment closure, and provide insight into the range of LES cases required to train a useful forest for such a purpose. Future work will involve the development of a higher-order turbulence closure parameterization using such a random forest as its higher-order moment closure.