A data-driven framework for dimensionality reduction and causal inference in climate fields

Fabrizio Falasca, Pavel Perezhogin, Laure Zanna

Published version: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.044202

(The published verson is behind a paywall. Here a preprint version in case: https://arxiv.org/abs/2306.14433)

We propose a data-driven method to

(a) Coarse-grain spatiotemporal climate fields into a set of regional modes of variability. The dimensionality reduction step is based on community detection. We further contribute to community detection in climate data by proposing a simple heuristics to identify local communities/patterns in longitude-latitude space. The communities are found using the Infomap algorithm based on the Map Equation. See for example: https://www.mapequation.org/publications.html#Rosvall-Axelsson-Bergstrom-2009-Map-equation

(b) Causal inference between time series. Causality is inferred through the fluctuation-dissipation theory as first shown in here: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.043436 We further contribute to the framework by proposing an analytical null model for the fluctuation-dissipation relation (FDR).

Packages needed

Main packages needed here are

"Infomap". See this page for installation: https://www.mapequation.org/infomap/ ; Download Infomap version 2.2.0
NetworkX. See https://networkx.org/ ; Download NetworkX version 2.8
netCDF4. See https://unidata.github.io/netcdf4-python/

Note: In the Synthetic folder you find a notebook with synthetic tests. This allows to understand and test the causal framework adopted here. For this none of the packages listed above are needed.

Folders

Synthetic. (For the causal inference step, this is all you need.)

In the main.ipynb notebook we show how to infer causality between a set of time series using the FDR formalism. In the notebook "explaining.ipynb" we provide step-by-steps examples explaining the formalism.

These codes are general and can be used on other sets of time series. If you already have a set of time series and want to study their causal relationships, the code main.ipynb in this folder is all you need.

Global_SST

All codes to (a) dimensionality reduction and (b) causal inference of global sea surface temperature data. All results of the paper are reported in the notebook "main.ipynb".

Preprocessing

Here we give an example of the main preprocessing. To preprocess the data we use the CDO package https://code.mpimet.mpg.de/projects/cdo The preprocessing file is in bash. To evaluate just type: sh preprocess.sh