def lon_lat_to_cartesian(lon, lat, radius=1):
"""
calculates lon, lat coordinates of a point on a sphere with
radius radius
"""
# Unpack xarray object into plane arrays
if hasattr(lon, 'data'):
lon = lon.data
if hasattr(lat, 'data'):
lat = lat.data
if lon.ndim != lat.ndim:
raise ValueError('coordinate must share the same number of dimensions')
if lon.ndim == 1:
lon, lat = np.meshgrid(lon, lat)
lon_r = xu.radians(lon)
lat_r = xu.radians(lat)
x = radius * xu.cos(lat_r) * xu.cos(lon_r)
y = radius * xu.cos(lat_r) * xu.sin(lon_r)
z = radius * xu.sin(lat_r)
return x.flatten(), y.flatten(), z.flatten()
def distance_to_point(self, lat, lon):
"""
Use Haversine formula to estimate distances from all
gridpoints to a given location (lat, lon)
"""
R = 6371. # Radius of earth in km
lat = np.radians(lat)
lon = np.radians(lon)
dlat = lat - xu.radians(self['lat'].values)
dlon = lon - xu.radians(self['lon'].values)
a = xu.sin(dlat/2)**2 + xu.cos(lat) * xu.cos(xu.radians(self['lat'].values)) * \
xu.sin(dlon/2)**2
c = 2 * xu.arctan2(xu.sqrt(a), xu.sqrt(1.0-a))
return R*c
def distance_to_point(self, lat, lon):
"""
Use Haversine formula to estimate distances from all
gridpoints to a given location (lat, lon)
"""
R = 6371. # Radius of earth in km
lat = np.radians(lat)
lon = np.radians(lon)
dlat = lat - xu.radians(self['lat'].values)
dlon = lon - xu.radians(self['lon'].values)
a = xu.sin(dlat/2)**2 + xu.cos(lat) * xu.cos(xu.radians(self['lat'].values)) * \
xu.sin(dlon/2)**2
c = 2 * xu.arctan2(xu.sqrt(a), xu.sqrt(1.0 - a))
return R * c
def nearest_points(self, lat, lon, npt=1):
"""
Use the lat-lon arrays to return a list of indices
of the nearest npt points to the given lat-lon
"""
# Use sin of lat lon to handle periodic
# and not worry about if we are in negative
# degrees
dist = xu.hypot(xu.sin(xu.radians(self['lat'].values)) -
xu.sin(xu.radians(lat)),\
xu.cos(xu.radians(self['lon'].values)) -
xu.cos(xu.radians(lon)))
# Get indices of the flattened array
nearest_raw = dist.argsort(axis=None)[:npt]
# Convert back to 2-d coords
nearest = np.unravel_index(nearest_raw, self['lat'].shape)
return nearest
def nearest_points(self, lat, lon, npt=1):
"""
Use the lat-lon arrays to return a list of indices
of the nearest npt points to the given lat-lon
"""
# Use sin of lat lon to handle periodic
# and not worry about if we are in negative
# degrees
dist = xu.hypot(xu.sin(xu.radians(self['lat'].values)) -
xu.sin(xu.radians(lat)),\
xu.cos(xu.radians(self['lon'].values)) -
xu.cos(xu.radians(lon)))
# Get indices of the flattened array
nearest_raw = dist.argsort(axis=None)[:npt]
# Convert back to 2-d coords
nearest = np.unravel_index(nearest_raw, self['lat'].shape)
return nearest
def atmospheric_path_length_correction(data, cos_zen, limit=88.):
"""Perform Sun zenith angle correction.
This function uses the correction method proposed by
Li and Shibata (2006): https://doi.org/10.1175/JAS3682.1
The correction is limited to *limit* degrees (default: 88.0 degrees). For
larger zenith angles, the correction is the same as at the *limit*. Both
*data* and *cos_zen* are given as 2-dimensional Numpy arrays or Numpy
MaskedArrays, and they should have equal shapes.
"""
# Convert the zenith angle limit to cosine of zenith angle
limit = xu.cos(xu.radians(limit))
# Cosine correction
corr = _get_sunz_corr_li_and_shibata(cos_zen)
# Use constant value (the limit) for larger zenith
# angles
corr_lim = _get_sunz_corr_li_and_shibata(limit)
corr = corr.where(cos_zen > limit).fillna(corr_lim)
return data * corr
def atmospheric_path_length_correction(data, cos_zen, limit=88.):
"""Perform Sun zenith angle correction.
This function uses the correction method proposed by
Li and Shibata (2006): https://doi.org/10.1175/JAS3682.1
The correction is limited to *limit* degrees (default: 88.0 degrees). For
larger zenith angles, the correction is the same as at the *limit*. Both
*data* and *cos_zen* are given as 2-dimensional Numpy arrays or Numpy
MaskedArrays, and they should have equal shapes.
"""
# Convert the zenith angle limit to cosine of zenith angle
limit = xu.cos(xu.radians(limit))
# Cosine correction
corr = _get_sunz_corr_li_and_shibata(cos_zen)
# Use constant value (the limit) for larger zenith
# angles
corr_lim = _get_sunz_corr_li_and_shibata(limit)
corr = corr.where(cos_zen > limit).fillna(corr_lim)
return data * corr