def partition(self,
wsp_darr,
wdir_darr,
dep_darr,
agefac=1.7,
wscut=0.3333,
hs_min=0.001,
nearest=False,
max_swells=5):
"""Partition wave spectra using WW3 watershed algorithm.
Args:
- wsp_darr (DataArray): wind speed (m/s).
- wdir_darr (DataArray): Wind direction (degree).
- dep_darr (DataArray): Water depth (m).
- agefac (float): Age factor.
- wscut (float): Wind speed cutoff.
- hs_min (float): minimum Hs for assigning swell partition.
- nearest (bool): if True, wsp, wdir and dep are allowed to be taken from the.
nearest point if not matching positions in SpecArray (slower).
- max_swells: maximum number of swells to extract
Returns:
- part_spec (SpecArray): partitioned spectra with one extra dimension
representig partition number.
Note:
- All input DataArray objects must have same non-spectral
dimensions as SpecArray.
References:
- Hanson, Jeffrey L., et al. "Pacific hindcast performance of three numerical
wave models." Journal of Atmospheric and Oceanic Technology 26.8 (2009): 1614-1633.
TODO:
- We currently loop through each spectrum to calculate the partitions which
is slow. Ideally we should handle the problem in a multi-dimensional way.
"""
# Assert spectral dims are present in spectra and non-spectral dims are present in winds and depths
assert attrs.FREQNAME in self._obj.dims and attrs.DIRNAME in self._obj.dims, (
'partition requires E(freq,dir) but freq|dir '
'dimensions not in SpecArray dimensions (%s)' % (self._obj.dims))
for darr in (wsp_darr, wdir_darr, dep_darr):
# Conditional below aims at allowing wsp, wdir, dep to be DataArrays within the SpecArray. not working yet
if isinstance(darr, str):
darr = getattr(self, darr)
assert set(darr.dims) == self._non_spec_dims, (
'%s dimensions (%s) need matching non-spectral dimensions '
'in SpecArray (%s) for consistent slicing' %
(darr.name, set(darr.dims), self._non_spec_dims))
from wavespectra.specpart import specpart
# Initialise output - one SpecArray for each partition
all_parts = [0 * self._obj]
# Predefine these for speed
dirs = self.dir.values
freqs = self.freq.values
ndir = len(dirs)
nfreq = len(freqs)
# Slice each possible 2D, freq-dir array out of the full data array
slice_ids = {
dim: range(self._obj[dim].size)
for dim in self._non_spec_dims
}
for slice_dict in self._product(slice_ids):
specarr = self._obj[slice_dict]
if nearest:
slice_dict_nearest = {
key: self._obj[key][val].values
for key, val in slice_dict.items()
}
wsp = float(
wsp_darr.sel(method='nearest', **slice_dict_nearest))
wdir = float(
wdir_darr.sel(method='nearest', **slice_dict_nearest))
dep = float(
dep_darr.sel(method='nearest', **slice_dict_nearest))
else:
wsp = float(wsp_darr[slice_dict])
wdir = float(wdir_darr[slice_dict])
dep = float(dep_darr[slice_dict])
Up = agefac * wsp * np.cos(D2R * (dirs - wdir))
windbool = np.tile(Up, (nfreq, 1)) > np.tile(
self.celerity(dep, freqs)[:, _], (1, ndir))
spectrum = specarr.values
part_array = specpart.partition(spectrum)
part_array_max = part_array.max()
#TODO: join the two loops in a while loop
# Assign new partition if multiple valleys and satisfying some conditions
for part in range(1, part_array_max + 1):
part_spec = np.where(part_array == part, spectrum,
0.) # Current partition
imax, imin = self._inflection(part_spec, dfres=0.01, fmin=0.05)
if len(imin) > 0:
part_spec[imin[0].squeeze():, :] = 0
newpart = part_spec > 0
if newpart.sum() > 20:
part_array_max += 1
part_array[newpart] = part_array_max
# Group sea partitions and sort swells by hs
swell_hs_parts = np.zeros(part_array_max + 1) # +1 because of sea
for part in range(1, part_array_max + 1):
part_spec = np.where(part_array == part, spectrum,
0.) # Current partition
W = part_spec[windbool].sum() / part_spec.sum()
if W > wscut:
part_array[part_array == part] = 0
swell_hs_parts[part] = 0 # not really needed
else:
swell_hs_parts[part] = hs(part_spec, freqs, dirs)
sortedparts = np.flipud(swell_hs_parts[1:].argsort() + 1)
num_swells = min(max_swells, sum(swell_hs_parts[1:] > hs_min))
parts = np.concatenate(([0], sortedparts[:num_swells]))
# Extend partitions list if any extra one has been detected
for dummy in range(1 + num_swells - len(all_parts)):
all_parts.append(0 * self._obj)
for ind, part in enumerate(parts):
all_parts[ind][slice_dict] = np.where(part_array == part,
spectrum, 0.)
# Concatenate partitions along new axis
part_coord = xr.DataArray(data=range(len(all_parts)),
coords={'part': range(len(all_parts))},
dims=('part', ),
name='part',
attrs=OrderedDict(
(('standard_name',
'spectral_partition_number'), ('units',
''))))
return xr.concat(all_parts, dim=part_coord)
def nppart(spectrum,
freq,
dir,
wspd,
wdir,
dpt,
swells=3,
agefac=1.7,
wscut=0.3333):
"""Watershed partition on a numpy array.
Args:
- spectrum (2darray): Wave spectrum array with shape (nf, nd).
- freq (1darray): Wave frequency array with shape (nf).
- dir (1darray): Wave direction array with shape (nd).
- wspd (float): Wind speed.
- wdir (float): Wind direction.
- dpt (float): Water depth.
- swells (int): Number of swell partitions to compute.
- agefac (float): Age factor.
- wscut (float): Wind speed cutoff.
Returns:
- specpart (3darray): Wave spectrum partitions with shape (np, nf, nd).
"""
part_array = specpart.partition(spectrum)
Up = agefac * wspd * np.cos(D2R * (dir - wdir))
windbool = np.tile(Up, (freq.size, 1)) > np.tile(
celerity(freq, dpt)[:, np.newaxis], (1, dir.size))
ipeak = 1 # values from specpart.partition start at 1
part_array_max = part_array.max()
# partitions_hs_swell = np.zeros(part_array_max + 1) # zero is used for sea
partitions_hs_swell = np.zeros(part_array_max + 1) # zero is used for sea
while ipeak <= part_array_max:
part_spec = np.where(part_array == ipeak, spectrum, 0.0)
# Assign new partition if multiple valleys and satisfying conditions
__, imin = inflection(part_spec, freq, dfres=0.01, fmin=0.05)
if len(imin) > 0:
part_spec_new = part_spec.copy()
part_spec_new[imin[0].squeeze():, :] = 0
newpart = part_spec_new > 0
if newpart.sum() > 20:
part_spec[newpart] = 0
part_array_max += 1
part_array[newpart] = part_array_max
partitions_hs_swell = np.append(partitions_hs_swell, 0)
# Assign sea partition
W = part_spec[windbool].sum() / part_spec.sum()
if W > wscut:
part_array[part_array == ipeak] = 0
else:
partitions_hs_swell[ipeak] = hs(part_spec, freq, dir)
ipeak += 1
sorted_swells = np.flipud(partitions_hs_swell[1:].argsort() + 1)
parts = np.concatenate(([0], sorted_swells[:swells]))
all_parts = []
for part in parts:
all_parts.append(np.where(part_array == part, spectrum, 0.0))
# Extend partitions list if it is less than swells
if len(all_parts) < swells + 1:
nullspec = 0 * spectrum
nmiss = (swells + 1) - len(all_parts)
for i in range(nmiss):
all_parts.append(nullspec)
return np.array(all_parts)
def partition(
self,
wsp_darr=None,
wdir_darr=None,
dep_darr=None,
agefac=1.7,
wscut=0.3333,
hs_min=0.001,
nearest=False,
max_swells=5,
fortran_code=True,
):
"""Partition wave spectra using WW3 watershed algorithm.
Args:
- wsp_darr (DataArray): wind speed (m/s).
- wdir_darr (DataArray): Wind direction (degree).
- dep_darr (DataArray): Water depth (m).
- agefac (float): Age factor.
- wscut (float): Wind speed cutoff.
- hs_min (float): minimum Hs for assigning swell partition.
- nearest (bool): if True, wsp, wdir and dep are allowed to be taken from the.
nearest point if not matching positions in SpecArray (slower).
- max_swells (int): maximum number of swells to extract
- fortran_code (bool): use fortran partition code or (~30x slower) pure python
Returns:
- part_spec (SpecArray): partitioned spectra with one extra dimension
representig partition number.
Note:
- All input DataArray objects must have same non-spectral
dimensions as SpecArray.
References:
- Hanson, Jeffrey L., et al. "Pacific hindcast performance of three numerical
wave models." Journal of Atmospheric and Oceanic Technology 26.8 (2009): 1614-1633.
TODO:
- We currently loop through each spectrum to calculate the partitions which
is slow. Ideally we should handle the problem in a multi-dimensional way.
"""
# Assert spectral dims are present in spectra and non-spectral dims are present in winds and depths
assert attrs.FREQNAME in self._obj.dims and attrs.DIRNAME in self._obj.dims, (
"partition requires E(freq,dir) but freq|dir "
"dimensions not in SpecArray dimensions (%s)" % (self._obj.dims))
for darr in (wsp_darr, wdir_darr, dep_darr):
# Conditional below aims at allowing wsp, wdir, dep to be DataArrays within the SpecArray. not working yet
if isinstance(darr, str):
darr = getattr(self, darr)
assert set(darr.dims) == self._non_spec_dims, (
"%s dimensions (%s) need matching non-spectral dimensions "
"in SpecArray (%s) for consistent slicing" %
(darr.name, set(darr.dims), self._non_spec_dims))
if fortran_code:
from wavespectra.specpart import specpart
else:
from wavespectra.core import specpartpy as specpart
# Initialise output - one SpecArray for each partition
all_parts = [0 * self._obj.load() for i in range(1 + max_swells)]
# Predefine these for speed
dirs = self.dir.values
freqs = self.freq.values
dfarr = self.dfarr.values
ndir = len(dirs)
nfreq = len(freqs)
wsp_darr.load()
wdir_darr.load()
dep_darr.load()
# Slice each possible 2D, freq-dir array out of the full data array
slice_ids = {
dim: range(self._obj[dim].size)
for dim in self._non_spec_dims
}
for slice_dict in self._product(slice_ids):
spectrum = self._obj[slice_dict].values
if nearest:
slice_dict_nearest = {
key: self._obj[key][val].values
for key, val in slice_dict.items()
}
wsp = float(
wsp_darr.sel(method="nearest", **slice_dict_nearest))
wdir = float(
wdir_darr.sel(method="nearest", **slice_dict_nearest))
dep = float(
dep_darr.sel(method="nearest", **slice_dict_nearest))
else:
wsp = float(wsp_darr[slice_dict])
wdir = float(wdir_darr[slice_dict])
dep = float(dep_darr[slice_dict])
Up = agefac * wsp * np.cos(D2R * (dirs - wdir))
windbool = np.tile(Up, (nfreq, 1)) > np.tile(
self.celerity(dep, freqs)[:, _], (1, ndir))
part_array = specpart.partition(spectrum)
ipeak = 1 # values from specpart.partition start at 1
part_array_max = part_array.max()
partitions_hs_swell = np.zeros(
part_array_max +
1) # +1 because zeroth index is used for windseas
while ipeak <= part_array_max:
part_spec = np.where(part_array == ipeak, spectrum,
0.0) # Current partition
# Assign new partition if multiple valleys and satisfying some conditions
imax, imin = self._inflection(part_spec, dfres=0.01, fmin=0.05)
if len(imin) > 0:
# TODO: swap part_spec and part_spec_new and deal with more than one imin value ?
part_spec_new = part_spec.copy()
part_spec_new[imin[0].squeeze():, :] = 0
newpart = part_spec_new > 0
if newpart.sum() > 20:
part_spec[newpart] = 0
part_array_max += 1
part_array[newpart] = part_array_max
partitions_hs_swell = np.append(partitions_hs_swell, 0)
# Group sea partitions and sort swells by hs
W = np.dot((part_spec * windbool).sum(1), dfarr) / np.dot(
part_spec.sum(1), dfarr)
if W > wscut:
part_array[part_array == ipeak] = 0 # mark as windsea
else:
partitions_hs_swell[ipeak] = hs(part_spec, freqs, dirs)
ipeak += 1
num_swells = min(max_swells, sum(partitions_hs_swell > hs_min))
sorted_swells = np.flipud(partitions_hs_swell[1:].argsort() + 1)
parts = np.concatenate(([0], sorted_swells[:num_swells]))
for ind, part in enumerate(parts):
all_parts[ind][slice_dict] = np.where(part_array == part,
spectrum, 0.0)
# Concatenate partitions along new axis
part_coord = xr.DataArray(
data=range(len(all_parts)),
coords={"part": range(len(all_parts))},
dims=("part", ),
name="part",
attrs=OrderedDict((("standard_name", "spectral_partition_number"),
("units", ""))),
)
return xr.concat(all_parts, dim=part_coord)
def partition(self,
wsp_darr,
wdir_darr,
dep_darr,
agefac=1.7,
wscut=0.3333,
hs_min=0.001,
nearest=False):
"""Partition wave spectra using WW3 watershed algorithm.
Args:
- wsp_darr (DataArray): wind speed (m/s).
- wdir_darr (DataArray): Wind direction (degree).
- dep_darr (DataArray): Water depth (m).
- agefac (float): Age factor.
- wscut (float): Wind speed cutoff.
- hs_min (float): minimum Hs for assigning swell partition.
- nearest (bool): if True, wsp, wdir and dep are allowed to be taken from the.
nearest point if not matching positions in SpecArray (slower).
Returns:
- part_spec (SpecArray): partitioned spectra with one extra dimension
representig partition number.
Note:
- All input DataArray objects must have same non-spectral
dimensions as SpecArray.
TODO:
- We currently loop through each spectrum to calculate the partitions which
is slow. Ideally we should handle the problem in a multi-dimensional way.
"""
# Assert spectral dims are present in spectra and non-spectral dims are present in winds and depths
assert attrs.FREQNAME in self._obj.dims and attrs.DIRNAME in self._obj.dims, (
'partition requires E(freq,dir) but freq|dir '
'dimensions not in SpecArray dimensions (%s)' % (self._obj.dims))
for darr in (wsp_darr, wdir_darr, dep_darr):
# Conditional below aims at allowing wsp, wdir, dep to be DataArrays within the SpecArray. not working yet
if isinstance(darr, str):
darr = getattr(self, darr)
assert set(darr.dims) == self._non_spec_dims, (
'%s dimensions (%s) need matching non-spectral dimensions '
'in SpecArray (%s) for consistent slicing' %
(darr.name, set(darr.dims), self._non_spec_dims))
from wavespectra.specpart import specpart
# Initialise output - one SpecArray for each partition
all_parts = [0 * self._obj]
# Predefine these for speed
dirs = self.dir.values
freqs = self.freq.values
ndir = len(dirs)
nfreq = len(freqs)
# Slice each possible 2D, freq-dir array out of the full data array
slice_ids = {
dim: range(self._obj[dim].size)
for dim in self._non_spec_dims
}
for slice_dict in self._product(slice_ids):
specarr = self._obj[slice_dict]
if nearest:
slice_dict_nearest = {
key: self._obj[key][val].values
for key, val in slice_dict.items()
}
wsp = float(
wsp_darr.sel(method='nearest', **slice_dict_nearest))
wdir = float(
wdir_darr.sel(method='nearest', **slice_dict_nearest))
dep = float(
dep_darr.sel(method='nearest', **slice_dict_nearest))
else:
wsp = float(wsp_darr[slice_dict])
wdir = float(wdir_darr[slice_dict])
dep = float(dep_darr[slice_dict])
spectrum = specarr.values
part_array = specpart.partition(spectrum)
nparts = part_array.max()
# Assign new partition if multiple valleys and satisfying some conditions
for part in range(1, nparts + 1):
part_spec = np.where(part_array == part, spectrum,
0.) # Current partition only
imax, imin = self._inflection(part_spec, dfres=0.01, fmin=0.05)
if len(imin) > 0:
part_spec[imin[0].squeeze():, :] = 0
newpart = part_spec > 0
if newpart.sum() > 20:
nparts += 1
part_array[newpart] = nparts
# Extend partitions list if any extra one has been detected (+1 because of sea)
if len(all_parts) < nparts + 1:
for new_part_number in set(range(nparts + 1)).difference(
range(len(all_parts))):
all_parts.append(0 * self._obj)
# Assign sea and swells partitions based on wind and wave properties
sea = 0 * spectrum
swells = list()
hs_swell = list()
Up = agefac * wsp * np.cos(D2R * (dirs - wdir))
for part in range(1, nparts + 1):
part_spec = np.where(part_array == part, spectrum,
0.) # Current partition only
W = part_spec[np.tile(Up, (nfreq, 1)) > \
np.tile(self.celerity(dep, freqs)[:,_], (1, ndir))].sum() / part_spec.sum()
if W > wscut:
sea += part_spec
else:
_hs = hs(part_spec, freqs, dirs)
if _hs > hs_min:
swells.append(part_spec)
hs_swell.append(_hs)
hs_swell = [
h + np.random.rand() * 1e-10 for h in hs_swell
] # If two or more partitions with same Hs
if len(swells) > 1:
swells = [
x for (y, x) in sorted(zip(hs_swell, swells), reverse=True)
]
# Updating partition SpecArrays for current slice
all_parts[0][slice_dict] = sea
for ind, swell in enumerate(swells):
all_parts[ind + 1][slice_dict] = swell
# Concatenate partitions along new axis
part_coord = xr.DataArray(data=range(len(all_parts)),
coords={'part': range(len(all_parts))},
dims=('part', ),
name='part',
attrs=OrderedDict(
(('standard_name',
'spectral_partition_number'), ('units',
''))))
return xr.concat(all_parts, dim=part_coord)
