def t_getconsts(ctime):
"""
t_getconsts - Gets constituent data structures holding
information for tidal analyses
Variables are loaded from 't_constituents_*.npy'
on init and a copy is made now.
When ctime is specified t_getconsts recomputes the frequencies from
the rates-of-change of astronomical parameters at the matlab TIME given.
:Parameters:
ctime: a datetime, the start time of the data input into t_tide.
Note:
Not sure if a copy has to be made here or if they can be used directly.
For now a copy should be much fast then a load.
"""
const = copy.deepcopy(_const)
sat = copy.deepcopy(_sat)
shallow = copy.deepcopy(_shallow)
if ctime.size != 0:
# If no time, just take the "standard" frequencies, otherwise
# compute them from derivatives of astro parameters. This is
# probably a real overkill - the diffs are in the
# 10th decimal place (9th sig fig).
astro, ader = t_astron(ctime)
ii = np.isfinite(const['ishallow'])
const['freq'][~ii] = np.dot(const['doodson'][~ii, :], ader)/24
for k in np.flatnonzero(ii):
ik = ((const['ishallow'][k]-1 +
np.array(range(0, const['nshallow'][k]))).astype(int))
const['freq'][k] = np.dot(const['freq'][shallow['iname'][ik]-1],
shallow['coef'][ik])
return const, sat, shallow
def t_vuf(ltype, ctime, ju, lat=None):
"""T_VUF Computes nodal modulation corrections.
[V,U,F]=T_VUF(TYPE,DATE,JU,LAT) returns the astronomical phase V, the
nodal phase modulation U, and the nodal amplitude correction F at
a decimal date DATE for the components specified by index JU
at a latitude LAT.
TYPE is either 'full' for the 18.6 year set of constitunets, or 'nodal'
for the 1-year set with satellite modulations.
If LAT is not specified, then the Greenwich phase V is computed with
U=0 and F=1.
Note that V and U are in 'cycles', not degrees or radians (i.e.,
multiply by 360 to get degrees).
If LAT is set to NaN, then the nodal corrections are computed for all
satellites that do *not* have a "latitude-dependent" correction
factor. This is for compatibility with the ways things are done in
the xtide package. (The latitude-dependent corrections were zeroed
out there partly because it was convenient, but this was rationalized
by saying that since the forcing of tides can occur at latitudes
other than where they are observed, the idea that observations have
the equilibrium latitude-dependence is possibly bogus anyway).
R. Pawlowicz 11/8/99
1/5/00 - Changed to allow for no LAT setting.
11/8/00 - Added the LAT=NaN option.
10/02/03 - Suuport for 18-year (full) constituent set.
Version 1.2
Get all the info about constituents.
Calculate astronomical arguments at mid-point of data time series.
"""
astro, ader = t_astron(ctime)
if ltype == 'full':
const = t_get18consts(ctime)
# Phase relative to Greenwich (in units of cycles).
v = rem(np.dot(const.doodson, astro) + const.semi, 1)
v = v[(ju-1)]
u = np.zeros(shape=(v.shape, v.shape), dtype='float64')
f = np.ones(shape=(v.shape, v.shape), dtype='float64')
else:
const, sat, shallow = t_getconsts(ctime)
# Phase relative to Greenwich (in units of cycles).
# (This only returns values when we have doodson#s,
# i.e., not for the shallow water components,
# but these will be computed later.)
v = np.fmod(np.dot(const['doodson'], astro) + const['semi'], 1)
if lat is not None:
# If we have a latitude, get nodal corrections.
# Apparently the second-order terms in the tidal potential
# go to zero at the equator, but the third-order terms
# do not. Hence when trying to infer the third-order terms
# from the second-order terms, the nodal correction factors
# blow up. In order to prevent this, it is assumed that the
# equatorial forcing is due to second-order forcing OFF the
# equator, from about the 5 degree location. Latitudes are
# hence (somewhat arbitrarily) forced to be no closer than
# 5 deg to the equator, as per note in Foreman.
if ((np.isfinite(lat)) & (abs(lat) < 5)):
lat = sign(lat) * 5
slat = np.sin(np.pi * lat / 180)
# Satellite amplitude ratio adjustment for latitude.
rr = sat['amprat']
# no amplitude correction
if np.isfinite(lat):
j = np.flatnonzero(sat['ilatfac'] == 1)
# latitude correction for diurnal constituents
rr[j] = rr[j] * 0.36309 * (1.0 - 5.0 * slat * slat) / slat
j = np.flatnonzero(sat['ilatfac'] == 2)
# latitude correction for semi-diurnal constituents
rr[j] = rr[j] * 2.59808 * slat
else:
rr[sat['ilatfac'] > 0] = 0
# Calculate nodal amplitude and phase corrections.
uu = np.fmod(np.dot(sat['deldood'], astro.T[3:6])+sat['phcorr'], 1)
# uu=uudbl-round(uudbl); <_ I think this was wrong.
# The original
# FORTRAN code is: IUU=UUDBL
# UU=UUDBL-IUU
# which is truncation.
# Sum up all of the satellite factors for all satellites.
nsat = np.max(sat['iconst'].shape)
nfreq = np.max(const['isat'].shape)
fsum = np.array(1+sp.sparse.csr_matrix(
(np.squeeze(rr*np.exp(1j*2*np.pi*uu)),
(np.arange(0, nsat), np.squeeze(sat['iconst']-1))),
shape=(nsat, nfreq)).sum(axis=0)).flatten()
f = np.absolute(fsum)
u = np.angle(fsum)/(2*np.pi)
# Compute amplitude and phase corrections
# for shallow water constituents.
for k in np.flatnonzero(np.isfinite(const['ishallow'])):
ik = ((const['ishallow'][k]-1 +
np.array(range(0, const['nshallow'][k]))).astype(int))
iname = shallow['iname'][ik]-1
coef = shallow['coef'][ik]
f[k] = np.prod(np.power(f[iname], coef))
u[k] = np.dot(u[iname], coef)
v[k] = np.dot(v[iname], coef)
f = f[ju]
u = u[ju]
v = v[ju]
else:
# Astronomical arguments only, no nodal corrections.
# Compute phases for shallow water constituents.
for k in np.flatnonzero(np.isfinite(const['ishallow'])):
ik = ((const['ishallow'][k]-1 +
np.array(range(0, const['nshallow'][k]))).astype(int))
v[k] = np.dot(v[shallow['iname'][ik]-1], shallow['coef'][ik])
v = v[ju]
f = np.ones(len(v))
u = np.zeros(len(v))
return v, u, f