7. Advanced Calculation and Statistical Methods

7. Advanced Calculation and Statistical Methods#

Calculate Relative Vorticity and Divergence#

Simple statistics can be done with xarray’s methods. When it comes to meteorological variables, we can use the MetPy library. MetPy supports xarray, which means that we can apply DataArray to MetPy functions. Below is an example to calculate relative vorticity using metpy.calc.vorticity.

Example 5: Calculate relative vorticity at the 850-hPa level in December 2017.

Step 1: Read data and select the spatial and temporal ranges.

latn = 30 
lats = -20

uds = xr.open_dataset('data/ncep_r2_uv850/u850.2017.nc')
vds = xr.open_dataset('data/ncep_r2_uv850/v850.2017.nc')
u = uds.sel(time=slice('2017-12-01','2017-12-31'), 
            level=850,
            lat=slice(latn,lats),
            lon=slice(lon1,lon2)).uwnd
v = vds.sel(time=slice('2017-12-01','2017-12-31'), 
            level=850,
            lat=slice(latn,lats),
            lon=slice(lon1,lon2)).vwnd

Step 2: Calculate relative vorticity. Ensure that the vorticity function requires units for the wind field. Import metpy.units and attach it to the wind variables.

import metpy.calc as mpcalc
from metpy.units import units
vor = mpcalc.vorticity(u*units('m/s'), v*units('m/s'))
vorm = vor.mean(axis=0)
vorm

<xarray.DataArray (lat: 21, lon: 33)> Size: 6kB
<Quantity([[ 2.27227035e-06 -6.35822645e-06 -1.46749070e-05 -2.08053115e-05
  -2.30204190e-05 -2.14179636e-05 -1.73882539e-05 -1.29046760e-05
  -9.84929500e-06 -9.54206099e-06 -1.12507049e-05 -1.23807539e-05
  -1.01248504e-05 -4.97617877e-06 -9.28601335e-07 -2.13257232e-06
  -8.04519296e-06 -1.36745794e-05 -1.37081362e-05 -8.49913312e-06
  -2.77764758e-06 -1.18851542e-06 -3.59719131e-06 -6.00788240e-06
  -5.68558831e-06 -3.57765352e-06 -2.98596786e-06 -5.61280440e-06
  -9.78352706e-06 -1.28709753e-05 -1.36409031e-05 -1.30405734e-05
  -1.21284570e-05]
 [ 1.59641488e-06  1.27951490e-07 -2.96147587e-06 -6.09627077e-06
  -7.14075885e-06 -6.30349598e-06 -5.16875042e-06 -4.56615673e-06
  -4.01070010e-06 -3.29133037e-06 -3.14996178e-06 -4.03313727e-06
  -5.06772766e-06 -5.30085544e-06 -5.33611754e-06 -7.06711890e-06
  -1.08910896e-05 -1.43131536e-05 -1.42338578e-05 -1.03047389e-05
  -5.71612173e-06 -3.96175474e-06 -5.53658936e-06 -7.88921794e-06
  -8.64479278e-06 -8.03751306e-06 -8.04710263e-06 -9.82336098e-06
  -1.24495122e-05 -1.41660453e-05 -1.44190610e-05 -1.42504704e-05
  -1.44654921e-05]
 [-2.25853323e-06  1.13172266e-06  2.50715062e-06  3.24109081e-06
   4.54796451e-06  5.22032636e-06  3.42384104e-06  8.61968466e-08
...
  -8.52059086e-06 -1.10716107e-05 -1.19881288e-05 -1.13950856e-05
  -9.98141214e-06]
 [ 3.40814844e-07 -1.87193747e-06 -2.55199434e-06 -1.83217317e-06
  -7.07930811e-07 -2.45485863e-07 -7.17219789e-07 -1.21135839e-06
  -6.77305687e-07  1.98063110e-07 -8.42058040e-07 -4.36596747e-06
  -7.21982209e-06 -6.11138032e-06 -2.24744337e-06  6.50249030e-08
  -5.85517420e-07 -8.93727851e-07  1.92617077e-06  5.34523983e-06
   4.91827661e-06  6.98802749e-07 -2.36916696e-06 -8.49899076e-07
   3.18171194e-06  5.20927594e-06  3.40469449e-06 -5.15668196e-07
  -4.15454945e-06 -6.51466556e-06 -7.57468620e-06 -7.70031620e-06
  -7.32678885e-06]
 [ 3.86059996e-06  4.83366406e-07 -1.67842807e-06 -2.14714011e-06
  -1.31075583e-06 -6.41593796e-07 -9.82999754e-07 -1.46979384e-06
  -7.01365099e-07  5.12796672e-07 -4.05116393e-07 -4.63963087e-06
  -8.87224706e-06 -8.92474419e-06 -4.83957896e-06 -1.08197146e-06
  -7.43141058e-07 -2.15767543e-06 -1.95926642e-06 -1.83126193e-07
  -9.75771821e-09 -3.08505634e-06 -6.80966442e-06 -7.53604087e-06
  -4.54671714e-06 -6.88500940e-08  3.41230334e-06  4.97175514e-06
   4.77222735e-06  3.07068630e-06  7.25767405e-07 -1.38476001e-06
  -2.89335635e-06]], '1 / second')>
Coordinates:
  * lon      (lon) float32 132B 80.0 82.5 85.0 87.5 ... 152.5 155.0 157.5 160.0
  * lat      (lat) float32 84B 30.0 27.5 25.0 22.5 ... -12.5 -15.0 -17.5 -20.0
    level    float32 4B 850.0

In the preview of the variable vorm above, it includes information such as “Magnitude” and “Units”. A DataArray with unit information is referred to as a unit-aware array type. When applying this DataArray to follow-up calculations, the unit information will be preserved. However, some libraries and functions other than MetPy may not recognize unit-aware array types, leading to errors. In such cases, we can use .dequantify() to convert it to an ordinary DataArray, which is called a unit-naive array type.

The unit will be converted to an ordinary text attribute.

This example highlights the advantages of using xarray.DataArray over numpy.array. With numpy.array, you would need to specify the number of latitude and longitude axes, as well as provide the longitude and latitude arrays. However, since the latitude and longitude labels and dimension names are already stored in the DataArray, you only need to provide the wind DataArrays. This makes the code significantly simpler.

Step 3: Plotting.

import cmaps

proj = ccrs.PlateCarree()  
fig, ax = plt.subplots(1,1,subplot_kw={'projection':proj}) 

vorm = vorm * 10e5
vorPlot = (vorm.plot.contourf("lon", "lat",  
                              ax=ax,       
                              levels=np.arange(-20,24,4), 
                              cmap=cmaps.CBR_coldhot,  
                              add_colorbar=True, 
                              extend='both', 
                              cbar_kwargs={'orientation': 'horizontal', 'aspect': 30, 'label': r'[$10^{-5}$ s$^{-1}$]'}) #設定color bar
                              )
ax.set_extent([lon1,lon2,lats,latn],crs=proj)
ax.set_xticks(np.arange(80,180,20), crs=proj)
ax.set_yticks(np.arange(-20,40,10), crs=proj)
lon_formatter = LONGITUDE_FORMATTER
lat_formatter = LATITUDE_FORMATTER   
ax.xaxis.set_major_formatter(lon_formatter)
ax.yaxis.set_major_formatter(lat_formatter) 
ax.coastlines()
                         
ax.set_title(' ')
ax.set_title('850-hPa Vorticity, December 2017', loc='left')
ax.set_ylabel(' ')             # 設定坐標軸名稱。
ax.set_xlabel(' ')
plt.show()

_images/0119c49de221b1889889a116c7f7600309e072e5ffaa99947736609a6bb84257.png

Exercise

Similar to Example 5, but for divergence (metpy.calc.divergence).

Empirical Orthogonal Functions (EOF)#

Can use eofs or xeofs libraries. For eofs, see instructions on their website.

from eofs.xarray import Eof

Set

solver = Eof(data_array)

solver includes several methods:

solver.eofs(): Calculates EOF modes. The neofs option specifies the number of modes to compute.
solver.pcs(): Computes the time series of principal components.
solver.varianceFraction(): Computes the ratio of variance explained by each EOF mode, indicating how much percentage of the original data variance each mode can explain.
solver.reconstructedField(): Reconstructs the variable using EOF modes and their principal components.
solver.projectField(): Projects the variable onto the EOF modes.

xeof library has more extensive EOF methods, such as multivariate EOF and rotate EOF. See instructions on their website.

7. Advanced Calculation and Statistical Methods

Contents

7. Advanced Calculation and Statistical Methods#

Regridding#

Coarsen Grid Resolution#

Running Mean#

Correlation Map#

Conditional Control with `where`#

Calculate Relative Vorticity and Divergence#

Empirical Orthogonal Functions (EOF)#

7. Advanced Calculation and Statistical Methods

Contents

7. Advanced Calculation and Statistical Methods#

Regridding#

Coarsen Grid Resolution#

Running Mean#

Correlation Map#

Conditional Control with where#

Calculate Relative Vorticity and Divergence#

Empirical Orthogonal Functions (EOF)#

Conditional Control with `where`#