Machine Learning for estimating Cross Domain Covariance (& Correlation) relationships in coupled atmosphere-ocean DA systems

Proof of Concept

As a proof of concept, we use a feedforward neural network to predict the surface atmosphere-ocean temperature correlation structure. The main idea is to use the neural network to extend the statistical significance of a small ensemble. The truth is derived from an 80 member ensemble run, and as a first step we have removed coastal points and regions covered by sea ice. At a given location, the neural network makes a prediction based on the following features (which we can definitely optimize further!):

• Atmosphere: 2 meter humidity, 2 meter temperature, sensible heat flux due to rainfall, total precip, surface horizontal wind speed
• Ocean: SST, surface height, horizontal surface speed, barotropic current speed, mixed layer depth, mean eddy kinetic energy

Each "feature" is taken as a small-ensemble average, which, for now, is derived from 5 member subsets. For details on the neural network architecture, see notebooks/surface_feedforward_regression.ipynb.

The map shows the true and predicted surface temperature correlation field. The plot on the right indicates prediction skill, showing a bivariate histogram between the predicted and true data (brighter colors indicate higher data density). The histogram contains 99.9% of the data, and the final 0.01% is represented by the scatter plot. The faint gray line indicates the 1:1 line where prediction = truth.

These specific results are generated by a KFold approach, see notebooks/surface_feedforward_regression_kfold.ipynb for details.

Using this package

Create environment with

conda env create -f environment.yaml

And add to path with

import sys
sys.path.append("/path/to/mlcdc")

Eventually, we'll move this to pip/conda-forge.