constituents

• Calculates constituent parameters and nodal arguments

Note

Originally based on Richard Ray’s ARGUMENTS fortran subroutine

Source code

pyTMD.constituents.arguments(MJD: ndarray, constituents: list | ndarray, **kwargs)

Calculates the nodal corrections for tidal constituents [18, 22, 58, 66]

Parameters:

MJD: np.ndarray

Modified Julian day of input date

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, FES or GOT models

climate_solar_perigee: bool, default False

Compute climatologically affected terms without \(P_s\)

M1: str, default ‘perth5’

Coefficients to use for M1 tides

• 'Doodson'

• 'Ray'

• 'Schureman'

• 'perth5'

Returns:

pu: np.ndarray

Nodal correction angle (radians)

pf: np.ndarray

Nodal modulation factor

G: np.ndarray

Phase correction (degrees)

pyTMD.constituents.minor_arguments(MJD: ndarray, **kwargs)

Calculates the nodal corrections for minor tidal constituents in order to infer their values [18, 20, 22, 66]

Parameters:

MJD: np.ndarray

Modified Julian day of input date

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, FES or GOT models

Returns:

pu: np.ndarray

Nodal correction angle (radians)

pf: np.ndarray

Nodal modulation factor

G: np.ndarray

Phase correction (degrees)

pyTMD.constituents.coefficients_table(constituents: list | tuple | ndarray | str, **kwargs)

Doodson table coefficients for tidal constituents [17, 18, 58]

Parameters:

constituents: list, tuple, np.ndarray or str

Tidal constituent IDs

corrections: str, default ‘OTIS’

Use coefficients from OTIS, FES or GOT models

climate_solar_perigee: bool, default False

Compute climatologically affected terms without \(P_s\)

file: str or pathlib.Path, default `coefficients.json`

JSON file of Doodson coefficients

Returns:

coef: np.ndarray

Doodson coefficients (Cartwright numbers) for each constituent

pyTMD.constituents.doodson_number(constituents: str | list | ndarray, **kwargs)

Calculates the Doodson or Cartwright number for tidal constituents [17]

Parameters:

constituents: str, list or np.ndarray

Tidal constituent ID(s)

corrections: str, default ‘OTIS’

Use arguments from OTIS, FES or GOT models

formalism: str, default ‘Doodson’

Constituent identifier formalism

• 'Cartwright'

• 'Doodson'

• 'Extended'

raise_error: bool, default True

Raise ValueError if constituent is unsupported

Returns:

numbers: float, np.ndarray or dict

Doodson or Cartwright number for each constituent

pyTMD.constituents.nodal_modulation(n: ndarray, p: ndarray, constituents: list | tuple | ndarray | str, **kwargs)

Calculates the nodal corrections for tidal constituents [18, 22, 59, 66]

Calculates factors for compound tides using recursion

Parameters:

n: np.ndarray

Mean longitude of ascending lunar node (degrees)

p: np.ndarray

Mean longitude of lunar perigee (degrees)

constituents: list, tuple, np.ndarray or str

Tidal constituent IDs

corrections: str, default ‘OTIS’

Use nodal corrections from OTIS, FES or GOT models

M1: str, default ‘perth5’

Coefficients to use for M1 tides

• 'Doodson'

• 'Ray'

• 'Schureman'

• 'perth5'

Returns:

u: np.ndarray

Nodal correction angle (radians)

f: np.ndarray

Nodal modulation factor

pyTMD.constituents.group_modulation(h: ndarray, n: ndarray, p: ndarray, ps: ndarray, constituents: list | tuple | ndarray | str, **kwargs)

Calculates the generalized modulations for tidal groups [59, 62]

Uses the default nodal modulations for unsupported tidal groups

Parameters:

h: np.ndarray

Mean longitude of sun (degrees)

n: np.ndarray

Mean longitude of ascending lunar node (degrees)

p: np.ndarray

Mean longitude of lunar perigee (degrees)

ps: np.ndarray

Mean longitude of solar perigee (degrees)

constituents: list, tuple, np.ndarray or str

Tidal constituent IDs

Returns:

f: np.ndarray

Modulation factor

u: np.ndarray

Angle correction (radians)

pyTMD.constituents.frequency(constituents: list | ndarray, **kwargs)

Wrapper function for calculating the angular frequency for tidal constituents [59]

Parameters:

constituents: list

Tidal constituent IDs

corrections: str, default ‘OTIS’

Use nodal corrections from OTIS, FES or GOT models

M1: str, default ‘perth5’

Coefficients to use for M1 tides

• 'Doodson'

• 'Ray'

• 'Schureman'

• 'perth5'

Returns:

omega: np.ndarray

Angular frequency (radians per second)

pyTMD.constituents.aliasing_period(constituents: list | ndarray, sampling: float | ndarray, **kwargs)

Calculates the tidal aliasing for a repeat period

Parameters:

constituents: list

Tidal constituent IDs

sampling: float

Sampling repeat period (seconds)

corrections: str, default ‘OTIS’

Use nodal corrections from OTIS, FES or GOT models

M1: str, default ‘perth5’

Coefficients to use for M1 tides

• 'Doodson'

• 'Ray'

• 'Schureman'

• 'perth5'

Returns:

period: np.ndarray

Tidal aliasing period (seconds)

pyTMD.constituents._constituent_parameters(c: str | list, **kwargs)

Loads parameters for a given tidal constituent [20]

Parameters:

c: str or list

Tidal constituent ID(s)

raise_error: bool, default False

Raise ValueError if constituent is unsupported

Returns:

amplitude: float or np.ndarray

Amplitude of equilibrium tide for tidal constituent(s) (meters)

phase: float or np.ndarray

Phase of tidal constituent(s) (radians)

omega: float or np.ndarray

Angular frequency of constituent(s) (radians)

alpha: float or np.ndarray

Load Love number of tidal constituent(s)

species: int or np.ndarray

Spherical harmonic dependence of tidal constituent(s)

pyTMD.constituents._parse_tide_potential_table(table: str | Path, skiprows: int = 1, columns: int = 1, include_degree: bool = True, include_planets: bool = False)

Parse tables of tide-generating potential

Parameters:

table: str or pathlib.Path

Table of tide-generating potentials

skiprows: int, default 1

Number of header rows to skip in the table

columns: int, default 1

Number of amplitude columns in the table

include_degree: bool, default True

Table includes spherical harmonic degree

include_planets: bool, default False

Table includes coefficients for mean longitudes of planets

Returns:

CTE: np.ndarray

Cartwright-Tayler-Edden table values

pyTMD.constituents._parse_rotation_rate_table()

Parse table of tidal constituent rotation rates from Ray and Erofeeva [63]

Returns:

ZROT: np.ndarray

Rotation rate table values

pyTMD.constituents._parse_name(constituent: str) → str

Parses for tidal constituents using regular expressions and remapping of known cases

Parameters:

constituent: str

Text containing the name of a tidal constituent

pyTMD.constituents._to_constituent_id(coef: list | ndarray, **kwargs)

Converts Cartwright numbers into a tidal constituent ID

Parameters:

coef: list or np.ndarray

Doodson coefficients (Cartwright numbers) for constituent

corrections: str, default ‘GOT’

Use coefficients from OTIS, FES or GOT models

climate_solar_perigee: bool, default False

Use climatologically affected terms without \(P_s\)

arguments: int, default 7

Number of astronomical arguments to use

file: str or pathlib.Path, default `coefficients.json`

JSON file of Doodson coefficients

raise_error: bool, default True

Raise ValueError if constituent is unsupported

Returns:

c: str

Tidal constituent ID

pyTMD.constituents._to_doodson_number(coef: list | ndarray, **kwargs)

Converts Cartwright numbers into a Doodson number

Parameters:

coef: list or np.ndarray

Doodson coefficients (Cartwright numbers) for constituent

astype: type, default float

Output data type for default case

raise_error: bool, default True

Raise ValueError if constituent is unsupported

Returns:

DO: float or string

Doodson number for constituent

pyTMD.constituents._to_extended_doodson(coef: list | ndarray, **kwargs)

Converts Cartwright numbers into an UKHO Extended Doodson number

Parameters:

coef: list or np.ndarray

Doodson coefficients (Cartwright numbers) for constituent

Returns:

XDO: string

Extended Doodson number for constituent

pyTMD.constituents._from_doodson_number(DO: str | float | ndarray, **kwargs)

Converts Doodson numbers into Cartwright numbers

Parameters:

DO: str, float or np.ndarray

Doodson number for constituent

Returns:

coef: np.ndarray

Doodson coefficients (Cartwright numbers) for constituent

pyTMD.constituents._from_extended_doodson(XDO: str | str_, **kwargs)

Converts UKHO Extended Doodson number into Cartwright numbers

Parameters:

XDO: string

Extended Doodson number for constituent

Returns:

coef: np.ndarray

Doodson coefficients (Cartwright numbers) for constituent