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About uptide

uptide is a python package for tidal calculations. It computes tidal free surface heights or velocities from the amplitudes and phases of the tidal constituents. These amplitudes and phases can be read from global tidal solutions such as TPXO or FES2014. They can be read directly from the netCDF files provided by these sources. Some limited functionality for tidal harmonic analysis is also available,


  • python 3 or 2.7 (deprecated)
  • numpy
  • to read from netCDF sources: python netCDF support. The netCDF4 package is recommended. To install:
sudo CC=mpicc pip install netcdf4

or use the python-netcdf4 package on Ubuntu and Debian.

  • for FES2014 support: the FES package. To build from source (note that there is unfortunately no longer a simple pip install):
git clone --recursive
cd fes/
mkdir build
cd build
make install

where <prefix> should be the installation. When using a python virtual environment you can use $VIRTUAL_ENV. When using conda replace the above with a single step: conda install -c fbriol fes (untested).

NOTE: it seems this does not currently work with the Ubuntu/Debian libnetcdf13 package (run make test to test which would segfault). For users in a firedrake environment, it is recommended to use the netcdf build by petsc. This is done by replacing the cmake step with:


The exact paths may change in the future. The last option is to avoid cmake stripping these paths in the install.


Reconstruction from given amplitudes and phases

Given the phase and amplitudes of the harmonic constituents (M2, S2, etc.) reconstruct the tidal signal at an arbitrary date and time (including nodal corrections).

import uptide
import datetime
tide = uptide.Tides(['M2', 'S2'])  # select which constituents to use
tide.set_initial_time(datetime.datetime(2001,1,1,12,0,0))  # set t=0 at 1 Jan 2001, UTC 12:00
amp = [2.0, 1.0]  # amplitudes of M2 and S2
pha = [0., 3.14159]  # phases (in radians!) for M2 and S2

import numpy as np
t = np.arange(0, 30*24*3600, 600)
import matplotlib.pyplot as plt
eta = tide.from_amplitude_phase(amp, pha, t)
plt.plot(t, eta)

If not timezone is provided, the initial datetime is assumed to be in UTC. Otherwise use pytz and do something like:

import pytz
adam = pytz.timezone('Europe/Amsterdam')
tide.set_initial_time(datetime.datetime(2001,1,1,12,0,0, tzinfo=adam))

Note that the nodal corrections (the 18.6 years cycle associated with lunar precession), are only calculated for the date-time set with set_initial_time (t=0). If the time you calculate the signal for deviates significantly from t=0, you can recompute the correction for any later time t:


Reconstruct the tide from global solutions like TPXO, FES04 or FES2014

For TPXO, we can only use those regional solutions (see map here) for which a netcdf version is given:

  • Atlantic Ocean 2011:
  • Bering Sea:
  • European Shelf 2008:
  • Indian Ocean 2011:
  • Mediterranean:
  • Gulf of Mexico:
  • North Australia:
  • Pacific Ocean:

Each solution comes with a grid file, and a amplitude and phase file for the elevations (currents are currently not supported):

grid_file = '<some_path>/'
data_file = '<some_path>/'
tnci = OTPSncTidalInterpolator(tide, grid_file, data_file, ranges=((-4.0, 0.0), (58.0, 61.0)))

The optional ranges argument should give a longitude, lattiude bounding box of the region of interest (smaller means more efficient)

For FES2014, after installing the fes library following the instructions above, you can either use

tnci = uptide.FES2014TidalInterpolator('<path to an ocean_tide.ini file>')

in which case all constituents specified in the specified ocean_tide.ini are used, or

tnci = uptide.FES2014TidalInterpolator(tide, '<path to all the individual constituent files>')

where tide is a Tides object set-up as in the previous section. In the latter case it only uses the constituents specified in the definition of tide and t=0 is also defined based on the tide-object.

For either TPXO or FES2014, we can now obtain the reconstructed signal for time t, using

eta = tnci.get_val(x)

where the tuple x is the longitude,latitude (TPXO) or latitude,longitude (FES2014) coordinates of the point of interest.

From a given time signal compute the harmonic constituents

Given a time signal eta (say surface elevations) at times t (eta and t should be equal-length arrays) we can do a harmonic analysis

amp,pha = uptide.harmonic_analysis(tide, eta, t)

where amp and pha are the amplitudes and phases of each constituent defined in tide.constitunents. So to get the "M2" amplitude and phase:

idx= tide.constituents.index('M2')
print("M2 amplitude and phase:", amp[idx], pha[idx])

Note that the harmonic analysis is a least squares inversion, which means that the result for each individual constituent may depend on what other constituents are specified in tide in particular constituents with a close frequency. You should therefore ensure that the time-period of the signal is long enough to distinguish each pair of constituents. A useful criterion for this is given by the so called Rayleigh criterion. As an example

tide = uptide.Tides(['M2', 'S2'])
print(tide.get_minimum_Rayleigh_period()/86400.)  # 14 days, a spring neap cycle
tide = uptide.Tides(['M2', 'S2', 'N2', 'K2', 'O1', 'P1', 'Q1', 'M4'])
print(tide.get_minimum_Rayleigh_period()/86400.)  # half a year! why is this so long?
ind1, ind2 = tide.get_closest_constituents()  # get the constituents with the closest frequency
print('The two closest constituents are:', tide.constituents[ind1], tide.constituents[ind2])
print('Their periods are {} and {} hours.'.format(2*pi/[ind1]/3600., 2*pi/[ind2]/3600))
tide = uptide.Tides(['M2', 'S2', 'N2', 'O1', 'P1', 'Q1', 'M4'])  # let's remove K2
print(tide.get_minimum_Rayleigh_period()/86400.)  # a month, much better!

You can also automatically select the constituents that can be resolved within a certain period:

constituents  = ['M2', 'S2', 'N2', 'K2', 'O1', 'P1', 'Q1', 'M4']
print(select_constituents(constituents, 15*86400))

Make sure that you provide the constituents in order of importance (most important ones first), as that will determine which constituents will be eliminated first.

For the harmonic analysis of a velocity signal. First do a harmonic analysis of the u and v components separately

au,pu = uptide.harmonic_analysis(tide, u, t)
av,pv = uptide.harmonic_analysis(tide, v, t)

after which you can use

a,b,theta,g = uptide.tidal_ellipse_parameters(au, pu, av, pv)

which returns the amplitudes along the major and minor axes (a and b), the inclination (theta), and the phase.


python package for tidal calculations







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