ERTID(1)

NAME
ertid - compute body tides on an elastic Earth, or Munk-Cartwright coefficients

DESCRIPTION

Ertid generates the theoretical earth tides on an elastic Earth (the ``body tides'') or the Munk-Cartwright coefficients which describe the different spherical harmonics of the tidal potential. (For a fuller description of these, see Munk and Cartwright [1966]). The tides are computed directly, by finding the positions of the Moon and Sun at each time and computing the resulting earth-tide at a given location.

After asking for the start time, end time, and sample interval (the times are given [in Greenwich time] as year, day-number, and hour), the program asks whether theoretical tides or Munk-Cartwright coefficients are wanted. In the first case, up to one gravity tide, two tilt tides, and three strain tides may be generated for a particular location. (As a special feature, if the number of gravity tides is -1, the potential height on a rigid Earth is generated instead of the gravity tide). The station coordinates needed for this option are given in degrees and decimals, and should be geographic (they are converted to geocentric internally to provide a partial correction for ellipticity). In the second case, Munk-Cartwright coefficients of order 2 or 3 (or both), and species 0 through 2 (or 3) may be computed and written out, the series for each coefficient to a separate file, with real and imaginary parts alternating. All outputs (except for some diagnostic messages) are to ASCII files. Each data series is written to a separate file, the filenames being read in one to a line. The data are written out to the file with a 5(g13.5) format.

Because the solar and lunar positions are calculated anew for each time, the run time goes as the number of points computed.

UNITS

The units and sign conventions are: for potential height, meters and positive up; for gravity, μgals (10$"" sup -8 $ m s$"" sup -2$) and positive for a decrease in g; for tilt, nanoradians and positive for motion of the plumb bob in the azimuth given (or a downwards ground tilt in that direction); for strain, nanostrain and positive for extension.

THEORY

The computation procedure roughly follows that given by Munk and Cartwright (1966): at each time point the positions of the Sun and Moon are found (more precisely, the latitude and longitude of the sublunar and subsolar points, and the ratio of true to mean distance); from these, the tides at the place of observation can be found directly. Munk and Cartwright give the derivation for the potential only; the extension to gravity, tilt, and strain is contained in Appendix C of Berger (1969). The two main sources of error are the imprecision of the solar and lunar ephemerides, and the neglect of the Earth's ellipticity and rotation. The ephemerides used are those of Harrison (1971) for the Moon, with a simple theory for the Sun. The tides computed by this program have been checked against those gotten from a very complete ephemeris by Cartwright and Taylor (1971) and Cartwright and Edden (1973); the level of disagreement was less than $10 sup -3$, which will be important only for the most precise observations of tidal gravity. The program assumes a spherical Earth, with second and third-degree parts of the potential only being taken into account.

It should be noted that this program computes, not the full Earth tide, but that tide less the amount contributed by the permanent deformation (and potential) contributed by the Sun and Moon. For gravity this quantity is known as the Honkasalo correction. The program, in computing this quantity, assumes that the elastic-Earth Love numbers apply. (These are the degree-two numbers, $h sub 2$ = 0.6114, $k sub 2$ = 0.304 and $l sub 2$ = 0.0832.)

REFERENCES

Berger, J. (1969) A Laser Earth Strain Meter, Ph.D. Thesis, University of California, San Diego

Cartwright, D. E., and R. J. Tayler (1971). New computations of the tide-generating potential, Geophys. J. Roy. Astron. Soc., 23, 45-73.

Cartwright, D. E., and A. C. Edden (1973). Corrected tables of tidal harmonics, Geophys. J. Roy. Astron. Soc., 33, 253-264.

Harrison, J. C. (1971). New computer programs for the calculation of Earth tides, Internal Report, Cooperative Institute for Research in Environmental Sciences, University of Colorado.

Munk, W. H., and D. E. Cartwright (1966), Tidal Spectroscopy and Prediction, Phil. Trans. Roy. Soc., Ser. A., 259, 533-581.

AUTHORS
J. Berger, W. Farrell, J. C. Harrison, J. Levine, D. C. Agnew