def test_trapezoid(self):
data = np.arange(0.0, 30.1, 0.1)
correct = np.arange(0.0, 1.0, 0.01)
correct = np.concatenate((correct, np.ones(101), correct[::-1]))
result = util.trapezoid(data, 0.0, 10.0, 20.0, 30.0)
np.testing.assert_array_almost_equal(result, correct, decimal=9)
def classify_echo_fuzzy(dat, weights=None, trpz=None, thresh=0.5):
"""Fuzzy echo classification and clutter identification based on \
polarimetric moments.
The implementation is based on :cite:`Vulpiani2012`. At the
moment, it only distinguishes between meteorological and non-meteorological
echos.
.. versionchanged:: 1.4.0
The implementation was extended using depolarization ratio (dr)
and clutter phase alignment (cpa).
For Clutter Phase Alignment (CPA) see :cite:`Hubbert2009a` and
:cite:`Hubbert2009b`
For each decision variable and radar bin, the algorithm uses trapezoidal
functions in order to define the membership to the non-meteorological
echo class.
Based on pre-defined weights, a linear combination of the different degrees
of membership is computed. The echo is assumed to be non-meteorological
in case the linear combination exceeds a threshold.
At the moment, the following decision variables are considered:
- Texture of differential reflectivity (zdr) (mandatory)
- Texture of correlation coefficient (rho) (mandatory)
- Texture of differential propagation phase (phidp) (mandatory)
- Doppler velocity (dop) (mandatory)
- Static clutter map (map) (mandatory)
- Correlation coefficient (rho2) (additional)
- Depolarization Ratio (dr), computed from
correlation coefficient & differential reflectivity (additional)
- clutter phase alignment (cpa) (additional)
Parameters
----------
dat : dict
dictionary of arrays.
Contains the data of the decision variables. The shapes of the arrays
should be (..., number of beams, number of gates) and the shapes need
to be identical or be broadcastable.
weights : dict
dictionary of floats.
Defines the weights of the decision variables.
trpz : dict
dictionary of lists of floats.
Contains the arguments of the trapezoidal membership functions for each
decision variable
thresh : float
Threshold below which membership in non-meteorological membership class
is assumed.
Returns
-------
output : tuple
a tuple of two boolean arrays of same shape as the input arrays
The first array boolean array indicates non-meteorological echos based
on the fuzzy classification.
The second boolean array indicates where all the polarimetric moments
had missing values which could be used as an additional information
criterion.
See Also
--------
:func:`~wradlib.dp.texture` - texture
:func:`~wradlib.dp.depolarization` - depolarization ratio
"""
# Check the inputs
# mandatory data keys
dkeys = ["zdr", "rho", "phi", "dop", "map"]
# usable wkeys
wkeys = ["zdr", "rho", "phi", "dop", "map", "rho2", "dr", "cpa"]
# usable tkeys
tkeys = ["zdr", "rho", "phi", "dop", "map", "rho2", "dr", "cpa"]
# default weights
weights_default = {"zdr": 0.4, "rho": 0.4, "phi": 0.1,
"dop": 0.1, "map": 0.5,
"rho2": 0.4, "dr": 0.4, "cpa": 0.4}
if weights is None:
weights = weights_default
else:
weights = dict(list(weights_default.items()) + list(weights.items()))
# default trapezoidal membership functions
trpz_default = {"zdr": [0.7, 1.0, 9999, 9999],
"rho": [0.1, 0.15, 9999, 9999],
"phi": [15, 20, 10000, 10000],
"dop": [-0.2, -0.1, 0.1, 0.2],
"map": [1, 1, 9999, 9999],
"rho2": [-9999, -9999, 0.95, 0.98],
"dr": [-20, -12, 9999, 9999],
"cpa": [0.6, 0.9, 9999, 9999]}
if trpz is None:
trpz = trpz_default
else:
trpz = dict(list(trpz_default.items()) + list(trpz.items()))
# check data conformity
assert np.all(np.in1d(dkeys, list(dat.keys()))), \
"Argument dat of classify_echo_fuzzy must be a dictionary " \
"with mandatory keywords %r." % (dkeys,)
assert np.all(np.in1d(wkeys, list(weights.keys()))), \
"Argument weights of classify_echo_fuzzy must be a dictionary " \
"with keywords %r." % (wkeys,)
assert np.all(np.in1d(tkeys, list(trpz.keys()))), \
"Argument trpz of classify_echo_fuzzy must be a dictionary " \
"with keywords %r." % (tkeys,)
# copy rho to rho2
dat['rho2'] = dat['rho'].copy()
shape = None
for key in dkeys:
if not dat[key] is None:
if shape is None:
shape = dat[key].shape
else:
assert dat[key].shape[-2:] == shape[-2:], \
"Arrays of the decision variables have inconsistent " \
"shapes: %r vs. %r" % (dat[key].shape, shape)
else:
print("WARNING: Missing decision variable: %s" % key)
# If all dual-pol moments are NaN, can we assume that and echo is
# non-meteorological?
# Successively identify those bins where all moments are NaN
nmom = ['rho', 'zdr', 'phi', 'dr', 'cpa'] # 'dop'
nan_mask = np.isnan(dat['rho'])
for mom in nmom[1:]:
try:
nan_mask &= np.isnan(dat[mom])
except KeyError:
pass
# Replace missing data by NaN
dummy = np.zeros(shape) * np.nan
for key in dat.keys():
if dat[key] is None:
dat[key] = dummy
# membership in meteorological class for each variable
qres = dict()
for key in dat.keys():
if key not in tkeys:
continue
if key in ['zdr', 'rho', 'phi']:
d = dp.texture(dat[key])
else:
d = dat[key]
qres[key] = 1. - util.trapezoid(d,
trpz[key][0],
trpz[key][1],
trpz[key][2],
trpz[key][3])
# create weight arrays which are zero where the data is NaN
# This way, each pixel "adapts" to the local data availability
wres = dict()
for key in dat.keys():
if key not in wkeys:
continue
wres[key] = _weight_array(qres[key], weights[key])
# Membership in meteorological class after combining all variables
qsum = []
wsum = []
for key in dat.keys():
if key not in wkeys:
continue
# weighted sum, also removing NaN from data
qsum.append(np.nan_to_num(qres[key]) * wres[key])
wsum.append(wres[key])
q = np.array(qsum).sum(axis=0) / np.array(wsum).sum(axis=0)
# flag low quality
return np.where(q < thresh, True, False), nan_mask
def test_trapezoid(self):
data = np.arange(0., 30.1, 0.1)
correct = np.arange(0., 1., 0.01)
correct = np.concatenate((correct, np.ones(101), correct[::-1]))
result = util.trapezoid(data, 0., 10., 20., 30.)
np.testing.assert_array_almost_equal(result, correct, decimal=9)