Generic differentiation routines on the sphere. These make no assumptions about the grid type (e.g. Arakawa C, etc.) or advection scheme used. Instead these are basic second-order differences, assuming grid coordinates are at the grid cell centers, but on the sphere. It is assumed the boundaries in latitude and longitude are periodic, i.e. that things are on a global domain. Therefore, centered differences are possible everywhere.
xdiff supports taking the derivative of both scalar (e.g. when computing a
gradient) and vector components (e.g. when computing a divergence). Be sure to
use the appropriate option when taking a meridional derivative, see Del in
cylindrical and spherical
coordinates. In
the zonal direction, there is no distinction.
xdiff supports taking zonal and meridional derivatives on global data; data
must be global, because at the moment, periodicity in both dimensions is
assumed.
import numpy as np
import xarray as xr
import xdiff
DLON = 1.
lon = np.arange(0. + DLON / 2., 360., DLON)
lon = xr.DataArray(lon, [('lon', lon)])
DLAT = 1.
lat = np.arange(-90. + DLAT / 2., 90., DLAT)
lat = xr.DataArray(lat, [('lat', lat)])
rad_lon = np.deg2rad(lon)
rad_lat = np.deg2rad(lat)
f = xdiff.EARTH_RADIUS * np.cos(rad_lat) * np.sin(6 * rad_lon)
df_dlon = xdiff.d_dlon(f)
df_dlat = xdiff.d_dlat(f)Note that if the names for longitude and latitude were not the default ('lon'
and 'lat'), we could specify those dimension names into the call to d_dlon or
d_dlat:
df_dlon = xdiff.d_dlon(f, lon_dim='longitude', lat_dim='latitude')
df_dlat = xdiff.d_dlat(f, lon_dim='longitude', lat_dim='latitude')If you found yourself doing this a lot, you could reset the global default options:
xdiff.set_options(lon_dim='longitude', lat_dim='latitude')
df_dlon = d_dlon(f)
df_dlat = d_dlat(f)Currently the only option for installing xdiff is from source:
$ git clone https://github.com/spencerkclark/xdiff.git
$ cd xdiff
$ pip install -e .
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Seager, R., & Henderson, N. (2013). Diagnostic Computation of Moisture Budgets in the ERA-Interim Reanalysis with Reference to Analysis of CMIP-Archived Atmospheric Model Data. Journal of Climate, 26(20), 7876–7901. https://doi.org/10.1175/JCLI-D-13-00018.1