import datetime

print(f"Last updated on {datetime.date.today()}. __falwa__.version: {__import__('falwa').__version__}")

Last updated on 2026-03-15. __falwa__.version: 2.3.3

Using the object-oriented interface (BarotropicField) to compute equivalent latitude and local wave activity (total, cyclonic and anticyclonic)

import os
import xarray as xr
import numpy as np
import matplotlib.pyplot as plt
from falwa.barotropic_field import BarotropicField

pi = np.pi

Example of using the object BarotropicField (2D flow)

# === Load data and coordinates ===
data_folder_path = os.getcwd() + "../../../tests/data/"
readFile = xr.open_dataset(f'{data_folder_path}barotropic_vorticity.nc', engine='netcdf4')
abs_vorticity = readFile.absolute_vorticity.values

xlon = np.linspace(0, 360., 512, endpoint=False)
ylat = np.linspace(-90, 90., 256, endpoint=True)
nlon = xlon.size
nlat = ylat.size
Earth_radius = 6.378e+6
dphi = (ylat[2]-ylat[1])*pi/180.
area = 2.*pi*Earth_radius**2 * (np.cos(ylat[:, np.newaxis]*pi/180.)
                                * dphi)/float(nlon) * np.ones((nlat, nlon))

Create a BarotropicField object

cc1 = BarotropicField(xlon, ylat, pv_field=abs_vorticity)  # area computed in the class assumed uniform grid

Compute equivalent latitude and local wave activity

# Compute Equivalent Latitudes
cc1_eqvlat = cc1.equivalent_latitudes

# Compute Local Wave Activity
cc1_lwa = cc1.lwa

Plot the results

# --- Color axis for plotting LWA --- #
lwa_caxis = np.linspace(0, cc1_lwa.max(), 31, endpoint=True)

# --- Plot the abs. vorticity field, LWA and equivalent-latitude relationship and LWA --- #
fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(14,4))

# Absolute vorticity map
c = ax1.contourf(xlon,ylat,cc1.pv_field,31)
cb = plt.colorbar(c)
cb.formatter.set_powerlimits((0, 0))
cb.ax.yaxis.set_offset_position('right')
cb.update_ticks()
ax1.set_title('Absolute vorticity [1/s]')
ax1.set_xlabel('Longitude (degree)')
ax1.set_ylabel('Latitude (degree)')

# LWA (full domain)
c2 = ax2.contourf(xlon,ylat,cc1_lwa,lwa_caxis)
plt.colorbar(c2)
ax2.set_title('Local Wave Activity [m/s]')
ax2.set_xlabel('Longitude (degree)')
ax2.set_ylabel('Latitude (degree)')

# Equivalent-latitude relationship Q(y)
ax3.plot(cc1_eqvlat, ylat, 'b', label='Equivalent-latitude relationship')
ax3.plot(np.mean(cc1.pv_field,axis=1),ylat,'g',label='zonal mean abs. vorticity')
plt.ticklabel_format(style='sci', axis='x', scilimits=(0,0))
plt.ylim(-90,90)
plt.legend(loc=4,fontsize=10)
plt.title('Equivalent-latitude profile')
plt.ylabel('Latitude (degree)')
plt.xlabel('Q(y) [1/s] | y = latitude')
plt.tight_layout()
plt.show()

Compute local wave activity partitioned into anticyclonic and cyclonic components

This can be done by setting the input parameter return_partitioned_lwa=True

cc2 = BarotropicField(xlon, ylat, pv_field=abs_vorticity, return_partitioned_lwa=True)  # area computed in the class assumed uniform grid
# Compute Equivalent Latitudes
qref = cc2.equivalent_latitudes
# Compute Local Wave Activity
lwa_partitioned = cc2.lwa

fig2, (ax4, ax5, ax6) = plt.subplots(1, 3, figsize=(14,4))
c4 = ax4.contourf(xlon,ylat,lwa_partitioned.sum(axis=0),lwa_caxis)
plt.colorbar(c4)
ax4.set_title('Local Wave Activity [m/s]')
ax4.set_xlabel('Longitude (degree)')
ax4.set_ylabel('Latitude (degree)')

# Anti-cyclonic LWA (full domain)
antycyclonic_lwa = np.concatenate((lwa_partitioned[1, :128, :], lwa_partitioned[0, -128:, :]), axis=0)
c5 = ax5.contourf(xlon,ylat,antycyclonic_lwa,lwa_caxis)
plt.colorbar(c5)
ax5.set_title('Local Wave Activity (anticyclonic) [m/s]')
ax5.set_xlabel('Longitude (degree)')
ax5.set_ylabel('Latitude (degree)')

# Cyclonic LWA (full domain)
cyclonic_lwa = np.concatenate((lwa_partitioned[0, :128, :], lwa_partitioned[1, -128:, :]), axis=0)
c6 = ax6.contourf(xlon,ylat,cyclonic_lwa,lwa_caxis)
plt.colorbar(c6)
ax6.set_title('Local Wave Activity (cyclonic) [m/s]')
ax6.set_xlabel('Longitude (degree)')
ax6.set_ylabel('Latitude (degree)')

plt.tight_layout()
plt.show()