Eof tutorial

Using COAsT to compute the Empirical Orthogonal Functions (EOFs) of your data

Relevant imports and filepath configuration

# Begin by importing coast and other packages
import coast
import xarray as xr
import matplotlib.pyplot as plt

# Define some file paths
root = "./"
dn_files = root + "./example_files/"

fn_nemo_dat_t = dn_files + "nemo_data_T_grid.nc"
fn_nemo_dom   = dn_files + "coast_example_nemo_domain.nc"
fn_nemo_config = root + "./config/example_nemo_grid_t.json"

/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pydap/lib.py:5: DeprecationWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2871: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2871: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap.responses')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2350: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2871: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap.handlers')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2350: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2871: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap.tests')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2350: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('pydap')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages
/usr/share/miniconda/envs/coast/lib/python3.10/site-packages/pkg_resources/__init__.py:2871: DeprecationWarning: Deprecated call to `pkg_resources.declare_namespace('sphinxcontrib')`.
Implementing implicit namespace packages (as specified in PEP 420) is preferred to `pkg_resources.declare_namespace`. See https://setuptools.pypa.io/en/latest/references/keywords.html#keyword-namespace-packages

Loading data

# Load data variables that are on the NEMO t-grid

nemo_t = coast.Gridded( fn_data = fn_nemo_dat_t, fn_domain = fn_nemo_dom, config = fn_nemo_config )

Compute EOF

For a variable (or subset of a variable) with two spatial dimensions and one temporal dimension, i.e. (x,y,t), the EOFs, temporal projections and variance explained can be computed by calling the ‘eofs’ method, and passing in the ssh DataArray as an argument. For example, for the sea surface height field, we can do

eof_data = coast.compute_eofs( nemo_t.dataset.ssh )

The method returns an xarray dataset that contains the EOFs, temporal projections and variance as DataArrays

#eof_data  # uncomment to print data object summary

Inspect EOFs

The variance explained of the first four modes is

# eof_data.variance.sel(mode=[1,2,3,4])  ## uncomment

Plotting

And the EOFs and temporal projections can be quick plotted:

eof_data.EOF.sel(mode=[1,2,3,4]).plot.pcolormesh(col='mode',col_wrap=2,x='longitude',y='latitude')

<xarray.plot.facetgrid.FacetGrid at 0x7f0104539b40>

eof_data.temporal_proj.sel(mode=[1,2,3,4]).plot(col='mode',col_wrap=2,x='time')

<xarray.plot.facetgrid.FacetGrid at 0x7f00ebff6290>

Complex EOFs

The more exotic hilbert complex EOFs can also be computed to investigate the propagation of variability, for example:

heof_data = coast.compute_hilbert_eofs( nemo_t.dataset.ssh )
#heof_data # uncomment to print data object summary

now with the modes expressed by their amplitude and phase, the spatial propagation of the variability can be examined through the EOF_phase.