predict

• Predict tidal values using harmonic constants

  • At a single time (map) such as for imagery

  • Multiple times and locations (drift) such as for airborne and satellite altimetry

  • Time series at a location (time_series) such as to compare with tide gauges

• Predicts tidal values from minor constituents inferred using major constituents

• Predicts long-period equilibrium ocean tides

• Predicts solid earth tidal values following IERS Conventions

Calling Sequence

import pyTMD.predict
ht = pyTMD.predict.time_series(time, hc, con)

Source code

pyTMD.predict.map(t: float | numpy.ndarray, hc: ndarray, constituents: list | numpy.ndarray, deltat: float | numpy.ndarray = 0.0, corrections: str = 'OTIS')

Predict tides at a single time using harmonic constants [1]

Parameters

t: float or np.ndarray

days relative to 1992-01-01T00:00:00

hc: np.ndarray

harmonic constant vector

constituents: list or np.ndarray

tidal constituent IDs

deltat: float or np.ndarray, default 0.0

time correction for converting to Ephemeris Time (days)

corrections: str, default ‘OTIS’

use nodal corrections from OTIS/ATLAS or GOT/FES models

Returns

ht: np.ndarray

tide values reconstructed using the nodal corrections

References

1

G. D. Egbert and S. Y. Erofeeva, “Efficient Inverse Modeling of Barotropic Ocean Tides,” Journal of Atmospheric and Oceanic Technology, 19(2), 183–204, (2002). doi: 10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2

pyTMD.predict.drift(t: float | numpy.ndarray, hc: ndarray, constituents: list | numpy.ndarray, deltat: float | numpy.ndarray = 0.0, corrections: str = 'OTIS')

Predict tides at multiple times and locations using harmonic constants [1]

Parameters

t: float or np.ndarray

days relative to 1992-01-01T00:00:00

hc: np.ndarray

harmonic constant vector

constituents: list or np.ndarray

tidal constituent IDs

deltat: float or np.ndarray, default 0.0

time correction for converting to Ephemeris Time (days)

corrections: str, default ‘OTIS’

use nodal corrections from OTIS/ATLAS or GOT/FES models

Returns

ht: np.ndarray

tidal time series reconstructed using the nodal corrections

References

1

G. D. Egbert and S. Y. Erofeeva, “Efficient Inverse Modeling of Barotropic Ocean Tides,” Journal of Atmospheric and Oceanic Technology, 19(2), 183–204, (2002). doi: 10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2

pyTMD.predict.time_series(t: float | numpy.ndarray, hc: ndarray, constituents: list | numpy.ndarray, deltat: float | numpy.ndarray = 0.0, corrections: str = 'OTIS')

Predict tidal time series at a single location using harmonic constants [1]

Parameters

t: float or np.ndarray

days relative to 1992-01-01T00:00:00

hc: np.ndarray

harmonic constant vector

constituents: list or np.ndarray

tidal constituent IDs

deltat: float or np.ndarray, default 0.0

time correction for converting to Ephemeris Time (days)

corrections: str, default ‘OTIS’

use nodal corrections from OTIS/ATLAS or GOT/FES models

Returns

ht: np.ndarray

tidal time series reconstructed using the nodal corrections

References

1

G. D. Egbert and S. Y. Erofeeva, “Efficient Inverse Modeling of Barotropic Ocean Tides,” Journal of Atmospheric and Oceanic Technology, 19(2), 183–204, (2002). doi: 10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2

pyTMD.predict.infer_minor(t: float | numpy.ndarray, zmajor: ndarray, constituents: list | numpy.ndarray, **kwargs)

Infer the tidal values for minor constituents using their relation with major constituents [1] [2] [3] [4]

Parameters

t: float or np.ndarray

days relative to 1992-01-01T00:00:00

zmajor: np.ndarray

Complex HC for given constituents/points

constituents: list

tidal constituent IDs

deltat: float or np.ndarray, default 0.0

time correction for converting to Ephemeris Time (days)

corrections: str, default ‘OTIS’

use nodal corrections from OTIS/ATLAS or GOT/FES models

Returns

dh: np.ndarray

tidal time series for minor constituents

References

1

A. T. Doodson and H. D. Warburg, “Admiralty Manual of Tides”, HMSO, London, (1941).

2

P. Schureman, “Manual of Harmonic Analysis and Prediction of Tides,” US Coast and Geodetic Survey, Special Publication, 98, (1958).

3

M. G. G. Foreman and R. F. Henry, “The harmonic analysis of tidal model time series,” Advances in Water Resources, 12(3), 109–120, (1989). doi: 10.1016/0309-1708(89)90017-1

4

G. D. Egbert and S. Y. Erofeeva, “Efficient Inverse Modeling of Barotropic Ocean Tides,” Journal of Atmospheric and Oceanic Technology, 19(2), 183–204, (2002). doi: 10.1175/1520-0426(2002)019<0183:EIMOBO>2.0.CO;2

pyTMD.predict.equilibrium_tide(t: ndarray, lat: ndarray)

Compute the long-period equilibrium tides the summation of fifteen tidal spectral lines from Cartwright-Tayler-Edden tables [1] [2]

Parameters

t: np.ndarray

time (days relative to January 1, 1992)

lat: np.ndarray

latitudes (degrees north)

Returns

lpet: np.ndarray

long-period equilibrium tide in meters

References

1

D. E. Cartwright and R. J. Tayler, “New Computations of the Tide-generating Potential,” Geophysical Journal of the Royal Astronomical Society, 23(1), 45–73. (1971). doi: 10.1111/j.1365-246X.1971.tb01803.x

2

D. E. Cartwright and A. C. Edden, “Corrected Tables of Tidal Harmonics,” Geophysical Journal of the Royal Astronomical Society, 33(3), 253–264, (1973). doi: 10.1111/j.1365-246X.1973.tb03420.x

pyTMD.predict.solid_earth_tide(t: ndarray, XYZ: ndarray, SXYZ: ndarray, LXYZ: ndarray, a_axis: float = 6378136.6, tide_system: str = 'tide_free', **kwargs)

Compute the solid Earth tides due to the gravitational attraction of the moon and sun [1] [2] [3] [4]

Parameters

t: np.ndarray

Time (days relative to January 1, 1992)

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

SXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the sun (meters)

LXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the moon (meters)

a_axis: float, default 6378136.3

Semi-major axis of the Earth (meters)

tide_system: str, default ‘tide_free’

Permanent tide system for the output solid Earth tide

• 'tide_free': no permanent direct and indirect tidal potentials

• 'mean_tide': permanent tidal potentials (direct and indirect)

Returns

dxt: np.ndarray

Solid Earth tide in meters in Cartesian coordinates

References

1

P. M. Mathews, B. A. Buffett, T. A. Herring and I. I Shapiro, “Forced nutations of the Earth: Influence of inner core dynamics: 1. Theory”, Journal of Geophysical Research: Solid Earth, 96(B5), 8219–8242, (1991). doi: 10.1029/90JB01955

2

P. M. Mathews, V. Dehant and J. M. Gipson, “Tidal station displacements”, Journal of Geophysical Research: Solid Earth, 102(B9), 20469–20477, (1997). doi: 10.1029/97JB01515

3

J. C. Ries, R. J. Eanes, C. K. Shum and M. M. Watkins, “Progress in the determination of the gravitational coefficient of the Earth”, Geophysical Research Letters, 19(6), 529–531, (1992). doi: 10.1029/92GL00259

4

J. M. Wahr, “Body tides on an elliptical, rotating, elastic and oceanless Earth”, Geophysical Journal of the Royal Astronomical Society, 64(3), 677–703, (1981). doi: 10.1111/j.1365-246X.1981.tb02690.x

pyTMD.predict._out_of_phase_diurnal(XYZ: ndarray, SXYZ: ndarray, LXYZ: ndarray, F2_solar: ndarray, F2_lunar: ndarray)

Computes the out-of-phase corrections induced by mantle anelasticity in the diurnal band

Parameters

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

SXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the sun (meters)

LXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the moon (meters)

F2_solar: np.ndarray

Factors for the sun

F2_lunar: np.ndarray

Factors for the moon

pyTMD.predict._out_of_phase_semidiurnal(XYZ: ndarray, SXYZ: ndarray, LXYZ: ndarray, F2_solar: ndarray, F2_lunar: ndarray)

Computes the out-of-phase corrections induced by mantle anelasticity in the semi-diurnal band

Parameters

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

SXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the sun (meters)

LXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the moon (meters)

F2_solar: np.ndarray

Factors for the sun

F2_lunar: np.ndarray

Factors for the moon

pyTMD.predict._latitude_dependence(XYZ: ndarray, SXYZ: ndarray, LXYZ: ndarray, F2_solar: ndarray, F2_lunar: ndarray)

Computes the corrections induced by the latitude of the dependence given by L¹

Parameters

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

SXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the sun (meters)

LXYZ: np.ndarray

Earth-centered Earth-fixed coordinates of the moon (meters)

F2_solar: np.ndarray

Factors for the sun

F2_lunar: np.ndarray

Factors for the moon

pyTMD.predict._frequency_dependence_diurnal(XYZ: ndarray, MJD: ndarray)

Computes the in-phase and out-of-phase corrections induced by mantle anelasticity in the diurnal band

Parameters

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

MJD: np.ndarray

Modified Julian Day (MJD)

pyTMD.predict._frequency_dependence_long_period(XYZ: ndarray, MJD: ndarray)

Computes the in-phase and out-of-phase corrections induced by mantle anelasticity in the long-period band

Parameters

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

MJD: np.ndarray

Modified Julian Day (MJD)

pyTMD.predict._free_to_mean(XYZ: ndarray, h2: float | numpy.ndarray, l2: float | numpy.ndarray)

Calculate offsets for converting the permanent tide from a tide-free to a mean-tide state

Parameters

XYZ: np.ndarray

Cartesian coordinates of the station (meters)

h2: float or np.ndarray

Degree-2 Love number of vertical displacement

l2: float or np.ndarray

Degree-2 Love (Shida) number of horizontal displacement