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Tides and the Moon

Background
Time varying spatially uniform gravitational force fields are undetectable because each atom is accelerated in the same direction with the same magnitude. Only spatial variations of a gravitational field are important. Also recall that the gravitational force field outside a spherically symmetric mass distribution acts as though the total mass were located at the center of the distribution.

In the present Atmosphere-Ocean Model, the Earth is assumed to be spherical (except for topography) and gravity is assumed to be due to the Earth's mass, to have uniform magnitude, and to be directed toward the center. Without correcting the spherical Earth assumption, future versions of the Atmosphere-Ocean Model will add realistic tides due to the Moon and Sun. Each body will be located precisely in time and space, and its gravitational force on the Earth's center will be subtracted from that on the Earth's surface.

Eastward and northward components of these tidal accelerations will be applied directly to the ocean currents (and atmospheric winds?) during their dynamic integrations. The vertical component of tidal accelerations could be added to the Earth's gravity and that would affect the currents via the pressure gradient force, but this effect on the horizontal currents would be about four orders of magnitude smaller than the direct horizontal tidal accelerations. Bottom friction and vertical mixing in the ocean may be adjusted to optimize comparisons between the Model's generated tidal elevations with observations.

Note that the horizontal components of tidal accelerations are maximized on the Earth's surface about one eighth of the circumfrence from the point on the surface where the Moon (or Sun) is directly overhead or on the opposite side of the Earth, and it is these horizontal components that accelerate the currents that move the ocean water toward where the Moon (or Sun) is directly overhead or on the opposite side of the Earth.


Produce a vector color plot of the gravitational perturbations on the Earth's surface due to the Moon and Sun using local topographic coordinates (east, north and upward). Horizontal tidal acceleration is depicted as arrows; the magnitude of the horizontal vector is proportional to the area of the arrow. Vertical tidal acceleration is depicted via the color scale; positive values reduce the strength of the Earth's gravity. Greenwich Mean Time is used, not local time.

Enter year (A.D.), month (1-12), date (1-31), hour (0-23), and minute (0-59):

Tidal accelerations due to: Moon Sun Both

Produce a table of moonset, moonrise and fullness as a function of latitude, longitude, year and month.


Fortran programs related to tides and the Moon
MOON.SUB Fortran subroutine that returns positioning of the Moon from an input time
ORBIT.SUB Fortran subroutine that returns positioning of the Sun from an input time
TIDES.FOR Fortran program writes a DataFile with three records, one for each topocentric coordinate, of the gravitainonal perturbations of tides
VECCPSIJ.FOR Fortran program writes a PostScript file that displays three components of a field using vectors superimposed over a color plot.

Page Links to 4x3 Atmophere-Ocean Model
COLOR PLOTS STATISTICS MODEL DOC MODEL DATA SUNLIGHT PUBLICA
LINE PLOTS GEN INFO MODEL CODE OBSERVE DATA TIDES and MOON PEOPLE
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Curator: Gary L. Russell . . . . . 2005/06/10/11:52:48