Tide gravitational correction based on I.M. Longman's Formulas for Computing the Tidal Accelerations Due to the Moon and the Sun
tidegravity is a Python library which implements Ivor Longman’s scheme for computing the tidal accelerations due to the moon and sun, as published by I.M. Longman in the Journal of Geophysical Research, Vol 64, no. 12, 1959 This can be useful for correcting gravimetric survey data, as the gravitational forces due to the tidal effects of the Sun and Moon can be on the order of several hundred microGals, depending on the surveyors location and the relative positions of the Sun and Moon to each other, and the surveyor.
The numpy and pandas libraries are required for processing tide corrections, and importing trajectory data for correction
The matplotlib library is an optional requirement and is currently only used in the examples to plot a visual representation of the data.
The following API functions are provided (subject to change in future releases):
solve_longman_tide(lat, lon, alt, time)
Solve for total gravity correction due to Sun/Moon from numpy array inputs
solve_longman_tide_scalar(lat, lon, alt, time)
Wrapper around solve_longman_tide, accepts single scalar values for lat/lon/alt and a single DateTime object
solve_point_corr(lat, lon, alt, t0, n=3600, increment=’S’)
Return tidal correction over a time span defined by t0 with n points at given increment for static (scalar) position parameters
solve_tide_df(df, lat=’lat’, lon=’lon’, alt=’alt’)
Wrapper accepting a pandas DataFrame (df) object as the input, df should have a DatetimeIndex, and lat/lon/alt columns. Alternate column names can be provided via parameters, which will then be used to extract components from the input DataFrame.
- I.M. Longman “Forumlas for Computing the Tidal Accelerations Due to the Moon and the Sun” Journal of Geophysical Research, vol. 64, no. 12, 1959, pp. 2351-2355
- P. Schureman “Manual of harmonic analysis and prediction of tides” U.S. Coast and Geodetic Survey, 1958
This library is based on the work of John Leeman’s LongmanTide Python implementation. LongmanTide
There are several example scripts in the examples directory illustrating how to use the longmantide solving functions.
Here is a simple demonstration of calculating a correction series for a static latitude/longitude/altitude over a specified time period, with intervals of 1 second.
from datetime import datetime from tidegravity import solve_point_corr # Example static data for Denver, January 1, 2018 lat = 39.7392 lon = -104.9903 # Note: West should be entered as a negative longitude value alt = 1609.3 t0 = datetime(2018, 1, 1, 12, 0, 0) # Calculate corrections for one day (60*60*24 points), with 1 second resolution result_df = solve_point_corr(lat, lon, alt, t0, n=60*60*24, increment='S') # Result is a pandas DataFrame, with a DatetimeIndex, and correction # values in the 'total_corr' column i.e. corrections = result_df['total_corr'].values # Plot the corrections using matplotlib from matplotlib import pyplot as plt plt.plot(corrections) plt.ylabel('Tidal Correction [mGals]') plt.show()
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