$Id: README 6756 2018-01-15 16:06:54Z flaterco $

    harmgen:  Derive harmonic constants from water level observations.
    Copyright (C) 1998  David Flater.

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <>.

This package is available from


The math in was based on an APL file contributed by Charles Read,
a professional mathematician and occasional sailor who made very short work
of the fearsome least squares analysis.  The subsequent extension to handle
multiple years was explained by Björn Brill.  The relevant emails are
included in the distribution for their educational value (files C_J_Read.txt
and Bjoern_Brill.txt).

Software prerequisites

Required:  Congen (libcongen), available from

Required:  Compatible version of Octave, available from

  Some help on installing Octave from source is available at

Optional:  Harmbase2, available from  Harmgen is designed to
integrate with Harmbase2, but you don't need Harmbase2 if all you want is the
harmonic constants.

Hardware requirements

The amount of memory needed for the least squares computation is proportional
to the product of the number of observations with the number of constituents.
A modern desktop PC with multiple gigabytes of RAM can easly handle hundreds
of thousands of observations and over 100 constituents.

Preface / caution

The reliability of both the input and the output of Harmgen has to be
assessed rather than assumed.  A minimum-length time series, even one of high
quality, is unlikely to determine the long-term constituents with much
accuracy.  If the input data quality is low, the quality of results will also
be low.

Data requirements

You will need, at a minimum, a year's worth of water level observations, at
least one per hour.  More years is better, to a point.  19 years is a
complete epoch; beyond that, the risks of using increasingly old data
probably exceed the benefits.  If you are in an area where silting, dredging,
or an earthquake has affected the behavior of the tides, the useful range may
be significantly shorter than 19 years.

Observations should be taken at periodic or random intervals.  It doesn't
matter if there are gaps, if the interval changes halfway through, etc.
However, a time series consisting of only the high and low tides is *not*
good enough.  One observation per hour is a reasonable minimum; ten per hour
is not unreasonable; more than ten per hour is unlikely to improve results.

This time series should be formatted the same as XTide's raw mode output,
with Unix time_t timestamps on the left (these are in seconds since
1970-01-01 00:00 UTC) and observations on the right:

902856260 1.088975
902859860 0.751052
902863460 0.511209

You will also need a Congen input file that defines the constituent set that
you want to use.  The distribution comes with three examples that you can use

 congen_1yr.txt:   140 constituents, usable with at least 1 year of data.
 congen_5yrs.txt:  144 constituents, usable with at least 5 years of data.
 congen_9yrs.txt:  145 constituents, usable with at least 9 years of data.

The install process copies these three files into the pkgdata directory,
which normally is /usr/local/share/harmgen.

Length of time series versus available constituents

Harmgen does a basic check to ensure that the time series covers a long
enough span of time to make it possible to distinguish all of the available
constituents from each other.  This does not mean that the results will be
reliable, only that they might be.  If the time series is definitely not long
enough, Harmgen reports errors similar to the following.

  The time series of length 1.998558 average Gregorian years
  is too short to separate the following constituents from each other:
    3MKS2 (26.8701754 deg/hr) and 2NS2 (26.8794590 deg/hr)
      delta = 0.226053 rotations/year
    NLK2 (27.8860711 deg/hr) and 2N2 (27.8953548 deg/hr)
      delta = 0.226053 rotations/year
    MSL6 (88.5125831 deg/hr) and SNK6 (88.5218668 deg/hr)
      delta = 0.226053 rotations/year
    3ML8 (116.4807916 deg/hr) and 2MNK8 (116.4900752 deg/hr)
      delta = 0.226053 rotations/year

You must either get a longer time series or comment out one (or both) of each
pair of colliding constituents in the Congen input file.  The files
congen_1yr.txt and congen_5yrs.txt that are provided in the distribution were
both produced by commenting out constituents from congen_9yrs.txt to
eliminate collisions.

If a time series shorter than 1 year is used, long-term constituents cannot
reliably be determined through the analysis that Harmgen performs, and you
will get the following error:

  The time series of length 0.834948 average Gregorian years
  is too short to resolve SA (0.0410686 deg/hr, 1.000001 rotations/year)

To have any hope of obtaining acceptable results with a short time series,
the long-term constituents must be replaced with inferred values.  libtcd and
XTide provide a capability to infer some constituents when a station is
loaded, but the effectiveness of this feature when used in conjunction with
Harmgen and time serieses shorter than 1 year has not been tested.

The error checks described above are based solely on the earliest and latest
times appearing in the time series.  They will not save you if the time
series has enormous gaps.

If you want to ignore the errors and proceed anyway, use the --force
command-line option.

Compiling and installing harmgen

bash-3.1$ ./configure
bash-3.1$ make
bash-3.1$ su
bash-3.1# make install

Harmgen is packaged with the popular and portable GNU automake, so all usual
GNU tricks should work.  Help on configuration options can be found in the
INSTALL file or obtained by entering ./configure --help.

The files that get installed are:

In ${exec_prefix}/bin:      harmgen (the actual application that you run)
In ${exec_prefix}/libexec: (script needed by the application)
In $(datadir)/harmgen:      congen_1yr.txt congen_5yrs.txt congen_9yrs.txt

By default, the three directories listed above resolve to /usr/local/bin,
/usr/local/libexec, and /usr/local/share/harmgen respectively.

Running harmgen

You must do 'make install' before running harmgen because the harmgen
application needs to find the script in the libexec directory.

The harmgen program has three mandatory parameters:
  The name of the Congen input file
  The name of the time series input file
  The name of the output file

The --force parameter disables error stops.  The --maxconstituents and
--minamplitude parameters specify policy for discarding constituents, as
described in the next section.  All remaining parameters are for specifying
metadata that are simply passed through into the output.  They are all
optional; however, to get acceptable results, it is highly advisable to
specify at least the station name, units and timezone.

The time zone is specified with a zoneinfo identifier such as
:America/New_York.  There is no really good documentation on zoneinfo, so see
"List of likely choices for timezone" at the end of this README.

Usage: harmgen [--name "Station name"]
               [--original_name "Original station name"]
               [--station_id_context "Organization assigning ID"]
               [--station_id "ID"]
               [--coordinates N.NNNNN N.NNNNN]    -90..90 °N  -180..180 °E
               [--timezone "Zoneinfo time zone spec"]
               [--country "Country"]
               [--units meters|feet|knots]
               [--min_dir N]                       0..359 ° true
               [--max_dir N]                       0..359 ° true
               [--legalese "1-line legal notice"]
               [--notes "Warnings to users"]
               [--comments "Info about this station"]
               [--source "Harmgen using data from XYZ"]
               [--restriction "Public domain"]
               [--xfields "EtCetera:  Et cetera."]
               [--datum "Lowest Astronomical Tide"]
               [--datum_override N.NN]
               [--maxconstituents N]
               [--minamplitude N.NN]

When executed, the harmgen program will do the following:

  (1)  Generate a file called "oct_input" containing the data needed
  by the Octave script.

  (2)  Invoke, which runs the Octave script.  It may run
  for a long time and consume lots of memory with no visible
  progress.  In the end, the file "oct_output" is created.

  (3)  When the script exits, harmgen reads the contents of
  oct_output, makes final adjustments, and writes the output to

The intermediate files "oct_input" and "oct_output" will be left laying
around so that you can inspect or reuse them if troubleshooting is needed.
Otherwise, to avoid confusion, please delete them before running harmgen

Discarding constituents

Two command-line options allow you to set policy on discarding constituents.
They can be used together without conflict.

--maxconstituents N    Sort constituents by descending amplitude and retain
                       at most the top N of them.

--minamplitude N.NN    Discard constituents with amplitude less than the
                       specified number.

Using the new station

If all you wanted was the harmonic constants, you can extract them from the
human-readable output-file.sql using a text editor and take it from there.
However, the output of Harmgen is designed to be used with Harmbase2, a
harmonic constant management package that handles all the details.  Harmbase2
is available from

To create a TCD file containing only the new station, you would load the
empty Harmbase2 schema, load the new station, and export:

bash-3.1$ createdb harmbase2
bash-3.1$ psql harmbase2 < harmbase2.sql
bash-3.1$ psql harmbase2 < output-file.sql 
bash-3.1$ hbexport --optimize test.tcd

XTide is able to use multiple TCD files simultaneously, so you just need to
add the new TCD file to your HFILE_PATH:

export HFILE_PATH=/usr/local/share/xtide/harmonics.tcd:/home/somebody/test.tcd

If you want to go to the trouble of merging your new data into a distributed
TCD file, you just need to substitute that TCD file's database dump for the
empty harmbase2.sql schema:

bash-3.1$ createdb harmbase2
bash-3.1$ psql harmbase2 < harmonics-dwf-20*.sql
bash-3.1$ psql harmbase2 < output-file.sql 
bash-3.1$ hbexport --optimize test.tcd

The most recent database dump is available from


The interface between Harmgen and Harmbase2 depends on canonical naming of
constituents.  If you rename constituents, modify constituent definitions or
create new ones in the input to Harmgen, you must make the same changes in
the constituents table of the Harmbase2 schema.  There is no way for
Harmbase2 to defend against semantic mismatches when all it gets is a name.
You just have to use the same definitions in both places.


1.  Harmgen dies with the following errors:
      sh: /usr/local/libexec/ No such file or directory
      oct_output: No such file or directory

    Cause:  You didn't do 'make install' before running harmgen.

2.  libc aborts with a free() or invalid pointer error, Octave dies
    with "error: memory exhausted" or Octave gets killed after
    thrashing for a while.

    Most likely cause:  You ran out of memory.  There are three ways
    to fix this:

    1.  Reduce the number of constituents in the Congen input file.
    2.  Reduce the number of observations in the time series.
    3.  Add memory.

    Once you determine which constituents aren't going to get any
    amplitude you can delete those and start over with more observations.

3.  Predictions are off by some even multiple of hours.

    Possible cause #1:  Wrong timezone.  In this case, the predictions
    aren't actually *wrong*, they are just expressed in the wrong time
    zone (e.g., 4 PM Central Time is equivalent to 5 PM Eastern Time).

    Possible cause #2:  Wrong conversion of time series.  The
    timestamps in the time series file are expressed in seconds since
    1970-01-01 00:00 UTC.  If you did this conversion from 1970-01-01
    00:00 local time then everything will be wrong.

    Possible cause #3:  You changed the meridian in the SQL output
    from 0:00.  NEVER do that!  You are allowed to change the
    timezone, but DO NOT change the meridian from 0:00.

4.  Predictions are off by an average of 25 minutes.

    The predictions are actually off by 12 hours.  The most significant
    constituent of tides cycles in 12 hours 25 minutes, so in many cases a
    12 hour shift is easy to overlook.  See previous problem.

5.  The results are complete garbage.

    Witnessed with Octave 3.0.0.  Upgrading to Octave 3.0.1 solved the


Manual of Harmonic Analysis and Prediction of Tides.  Special Publication
No. 98, Revised (1940) Edition (reprinted 1958 with corrections; reprinted
again 1994).  United States Government Printing Office, 1994.

Computer Applications to Tides in the National Ocean Survey.  Supplement to
Manual of Harmonic Analysis and Prediction of Tides (Special Publication
No. 98).  National Ocean Service, National Oceanic and Atmospheric
Administration, U.S. Department of Commerce, January 1982.

List of likely choices for timezone

The following list is from an old version of zoneinfo.  For the latest, see
the data distribution available at

Legal values of timezone include, but are not limited to:


-- DWF