About xMCA

xMCA, inspired from [EOFs] (https://github.com/ajdawson/eofs), is Maximum Covariance Analysis (sometimes also called SVD) in xarray. API Documentation: http://xmca.readthedocs.io/

How to install

via git

git clone https://github.com/Yefee/xMCA.git
cd xMCA
python setup.py install

Future Plan

In next version, A Monte Carlo method will be added for statistical test.

Example 1

MCA analysis for US surface air temperature and SST over the Pacific. This example is taken from https://atmos.washington.edu/~breth/classes/AS552/matlab/lect/html/MCA_PSSTA_USTA.html

from xMCA import xMCA
import xarray as xr
import matplotlib.pyplot as plt
%matplotlib inline

usta = xr.open_dataarray('xMCA/examples/data/USTA.nc').transpose(*['time', 'lat', 'lon'])
usta.name = 'USTA'
print(usta)

<xarray.DataArray 'USTA' (time: 396, lat: 5, lon: 12)>
array([[[-0.450303, -0.734848, ..., -4.270303, -2.69697 ],
        [ 1.066061,  2.691515, ..., -4.947273, -3.330303],
        ...,
        [      nan, -0.342424, ...,       nan,       nan],
        [      nan,       nan, ...,       nan,       nan]],

       [[ 1.524545,  1.370606, ..., -1.430303,  0.048485],
        [ 1.366364,  2.497273, ..., -0.593939, -0.079697],
        ...,
        [      nan,  0.695455, ...,       nan,       nan],
        [      nan,       nan, ...,       nan,       nan]],

       ...,

       [[ 1.077879,  0.630303, ..., -1.262727, -1.496364],
        [ 1.020606,  0.114848, ..., -0.786667, -0.573939],
        ...,
        [      nan,  1.65    , ...,       nan,       nan],
        [      nan,       nan, ...,       nan,       nan]],

       [[ 1.768182,  2.807879, ...,  0.885758,  0.618182],
        [ 1.555152,  3.435152, ..., -0.416667,  0.185152],
        ...,
        [      nan,  0.012121, ...,       nan,       nan],
        [      nan,       nan, ...,       nan,       nan]]])
Coordinates:
  * lat      (lat) float64 47.5 42.5 37.5 32.5 27.5
  * lon      (lon) float64 -122.5 -117.5 -112.5 -107.5 ... -77.5 -72.5 -67.5
  * time     (time) int64 0 1 2 3 4 5 6 7 8 ... 388 389 390 391 392 393 394 395

sstpc = xr.open_dataarray('xMCA/examples/data/SSTPac.nc').transpose(*['time', 'lat', 'lon'])
sstpc.name = 'SSTPC'
print(sstpc)

<xarray.DataArray 'SSTPC' (time: 396, lat: 30, lon: 84)>
[997920 values with dtype=float64]
Coordinates:
  * lat      (lat) int16 -29 -27 -25 -23 -21 -19 -17 ... 17 19 21 23 25 27 29
  * lon      (lon) uint16 124 126 128 130 132 134 ... 280 282 284 286 288 290
  * time     (time) int64 0 1 2 3 4 5 6 7 8 ... 388 389 390 391 392 393 394 395

Decompsition and retrieve the first and second loadings and expansion coefficeints

'''
decomposition, time should be in the first axis
lp is for SSTPC
rp is for USTA
'''

sst_ts = xMCA(sstpc, usta)
sst_ts.solver()
lp, rp = sst_ts.patterns(n=2)
le, re = sst_ts.expansionCoefs(n=2)
frac = sst_ts.covFracs(n=2)
print(frac)

<xarray.DataArray 'frac' (n: 2)>
array([0.407522, 0.391429])
Coordinates:
  * n        (n) int64 0 1
Attributes:
    long_name:  Fractions explained of the covariance matrix between SSTPC an...

fig, (ax1, ax2) = plt.subplots(2, 2, figsize=(12, 5))
lp[0].plot(ax=ax1[0])
le[0].plot(ax=ax1[1])

rp[0].plot(ax=ax2[0])
re[0].plot(ax=ax2[1])

png

Homogeneous and heterogeneous regression

lh, rh = sst_ts.homogeneousPatterns(n=1)
le, re = sst_ts.heterogeneousPatterns(n=1)

fig, (ax1, ax2) = plt.subplots(2, 2, figsize=(12, 5))
lh[0].plot(ax=ax1[0])
rh[0].plot(ax=ax1[1])

le[0].plot(ax=ax2[0])
re[0].plot(ax=ax2[1])

png

Two-tailed Student-t test

le, re, lphet, rphet = sst_ts.heterogeneousPatterns(n=1, statistical_test=True)

fig, (ax1, ax2) = plt.subplots(2, 2, figsize=(12, 5))
le[0].plot(ax=ax1[0])
re[0].plot(ax=ax1[1])

# Only plot where p<0.01
lphet[0].where(lphet[0]<0.01).plot(ax=ax2[0])
rphet[0].where(rphet[0]<0.01).plot(ax=ax2[1])

png

Example 2

EOF analysis for US surface air temperature and SST over the Pacific This example is taken from https://atmos.washington.edu/~breth/classes/AS552/matlab/lect/html/MCA_PSSTA_USTA.html

from xMCA import xMCA
import xarray as xr
import matplotlib.pyplot as plt
%matplotlib inline

sstpc = xr.open_dataarray('data/SSTPac.nc').transpose(*['time', 'lat', 'lon'])
sstpc.name = 'SSTPC'
print(sstpc)

<xarray.DataArray 'SSTPC' (time: 396, lat: 30, lon: 84)>
[997920 values with dtype=float64]
Coordinates:
  * lat      (lat) int16 -29 -27 -25 -23 -21 -19 -17 ... 17 19 21 23 25 27 29
  * lon      (lon) uint16 124 126 128 130 132 134 ... 280 282 284 286 288 290
  * time     (time) int64 0 1 2 3 4 5 6 7 8 ... 388 389 390 391 392 393 394 395

Decompsition and retrieve the first and second loadings and expansion coefficeints

'''
decomposition, time should be in the first axis
lp is for SSTPC
rp is for USTA
'''

sst_ts = xMCA(sstpc, sstpc.rename('SSTPC_copy'))
sst_ts.solver()
lp, _ = sst_ts.patterns(n=2)
le, _ = sst_ts.expansionCoefs(n=2)
frac = sst_ts.covFracs(n=2)
print(frac)

<xarray.DataArray 'frac' (n: 2)>
array([0.873075, 0.04946 ])
Coordinates:
  * n        (n) int64 0 1
Attributes:
    long_name:  Fractions explained of the covariance matrix between SSTPC an...

fig, ax1 = plt.subplots(1, 2, figsize=(12, 5))
lp[0].plot(ax=ax1[0])
le[0].plot(ax=ax1[1])

png

Regress PC1 to the original SST field

lh, _ = sst_ts.homogeneousPatterns(n=1)

fig, ax1= plt.subplots()
lh[0].plot(ax=ax1)

png

Publications using xMCA

Journal Articles

Hydroclimate footprint of pan-Asian monsoon water isotope during the last deglaciation

Chengfei He, Zhenyu Liu, BL Otto-Bliesner, EC Brady, C Zhu, R Tomas, PU Clark, J Zhu, A Jahn, S Gu, and others

Science Advances, 2021
Abrupt Heinrich Stadial 1 cooling missing in Greenland oxygen isotopes

Chengfei He, Zhengyu Liu, Bette L Otto-Bliesner, Esther C Brady, Chenyu Zhu, Robert Tomas, Christo Buizert, and Jeffrey P Severinghaus

Science Advances, 2021
Deglacial variability of South China hydroclimate heavily contributed by autumn rainfall

Chengfei He, Zhengyu Liu, Bette L Otto-Bliesner, Esther C Brady, Chenyu Zhu, Robert Tomas, Sifan Gu, Jing Han, and Yishuai Jin

Nature communications, 2021