Maximum Covariance Analysis

class for MCA or SVD analysis

Parameter

• data1 and data2 (np.ndarray): shape (time, * space grid number)

Method

• solve: solve the SVD results

• get_pc(npt): get EC of first npt modes

• get_pt(npt): get spatial patterns of first npt modes

• get_eign: get eign values of SVD(MCA) result

• get_varperc: get the proportion of mode variance

• get_heterogeneous_map

• get_homogeneous_map

Example

Load Modules

import sacpy as scp
import xarray as xr
import matplotlib.pyplot as plt
import numpy as np
import sacpy.Map
import cartopy.crs as ccrs

Load Data (10m wind,SST)

sst = scp.load_sst()['sst'].loc["1991":"2021", -20:30, 150:275]
ssta = scp.get_anom(sst)
u = scp.load_10mwind()['u']
v = scp.load_10mwind()['v']

uua = scp.get_anom(u)
vua = scp.get_anom(v)
uv = np.concatenate([np.array(uua)[...,np.newaxis],np.array(vua)[...,np.newaxis]],axis=-1)

MCA analysis

svd = scp.SVD(ssta,uv,complex=False)
svd.solve()

Get the result

ptl, ptr = svd.get_pt(3)
pcl,pcr = svd.get_pc(3)

upt ,vpt = ptr[...,0] , ptr[...,1]
sst_pt = ptl

Plot

import cartopy.crs as ccrs
import sacpy.Map
lon , lat = np.array(ssta.lon) , np.array(ssta.lat)
fig = plt.figure(figsize=[12,9])
ax = fig.add_subplot(221,projection=ccrs.PlateCarree(central_longitude=180))
m1 = ax.scontourf(lon,lat,sst_pt[0],cmap='RdBu_r',levels=np.linspace(-0.1,0.1,11),extend="both")
ax.scontour(m1,colors="black")
ax.squiver(lon,lat,upt[0],vpt[0])
ax.init_map(smally=2.5)
ax.set_title("Mode1")
ax2 = fig.add_subplot(222)
ax2.plot(sst.time,pcl[0],label="left")
ax2.plot(sst.time,pcr[0],label="right")
ax2.legend()
ax2.set_title("EC1")
ax3 = fig.add_subplot(223,projection=ccrs.PlateCarree(central_longitude=180))
m2 = ax3.scontourf(lon,lat,sst_pt[1],cmap='RdBu_r',levels=np.linspace(-0.1,0.1,11),extend="both")
ax3.squiver(lon,lat,upt[1],vpt[1])
ax3.scontour(m2,colors="black")
ax3.init_map(smally=2.5)
ax3.set_title("Mode2")
ax4 = fig.add_subplot(224)
ax4.plot(sst.time,pcl[1],label="left")
ax4.plot(sst.time,pcr[1],label="right")
ax4.legend()
ax4.set_title("EC2")
cb_ax = fig.add_axes([0.1,0.06,0.4,0.02])
fig.colorbar(m1,cax=cb_ax,orientation="horizontal")

<matplotlib.colorbar.Colorbar at 0x158a3e070>

get heterogeneous or homogeneous map

htl,htr = svd.get_heterogeneous_map(npt=2)
# plt.contourf(htl[0,0])
htl.shape,htr.shape

((2, 11, 26), (2, 11, 26, 2))

htl,htr = svd.get_homogeneous_map(npt=2)
# plt.contourf(htl[0,0])
htl.shape,htr.shape

((2, 11, 26), (2, 11, 26, 2))