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Basic Information

Name of Program



6.x / September 2009


September 2009


analysis of numerically calculated results (2D/3D and profile-data, extra points) and measurements (single timeseries)
tidal harmonic analysis
static (alternative) bathymetry
universal direct access format for 2D/3D-data
universal direct access format for profile-data
single timeseries, extra points
constituent ellipse

Short Description of Functionality

The program FRQWF is a postprocessor for different numerical models (e.g. TRIM-2D, TRIM-3D, TELEMAC-2D, UNTRIM2007, etc.) and field measurments. FRQWF automatically computes so called harmonic constants for different (selected) tidal harmonic constituents. Various main as well as shallow water constituents (compound tides and overtides) can be analysed. The data must be given as time-series (in universal direct access data format or results at extra points or single time series). The results of FRQWF analyses may be visualised/displayed with the graphical postprocessors HVIEW2D (for 2D/3D-data) or LQ2PRO (for profile-data).

For default, within the period of data analysis the following tidal harmonic constituents can be calculated by means of a Tidal Harmonic Analysis (some numbers are optionally calculated):

  • semiannual: Ssa
  • monthly: Mm
  • fortnightly: Mf
  • daily: Q1, O1, P1, K1, MP1 and SO1
  • semidiurnal: N2, M2, L2, S2, K2, MNS2, 2MS2, MSN2 and 2SM2
  • terdiurnal: MO3 and MK3
  • quarterdiurnal: MN4, M4, MS4, MK 4and S4
  • sixth diurnal: M6 and 2MS6
  • eighth diurnal: M8

A different set of constituents can be used when a modified file .tidkenn.dat is present in the working directory! This file must contain the constituents Mf, M2, M4, M6 und M8 as a minimum set!

analysis of time series of scalars:

The followig physical parameters can be analysed:

  1. water level (direct access files, single stations, extra points)
  2. salinity
  3. temperature
  4. suspended load concentration

For each tidal harmonic constituent the following values are being calculated for the period of data analysis:

  1. amplitude of the constituent
  2. local phase of the constituent adjusted to 01.01.yyyy 00:00 UTC.

The following relationships can be evaluated for the M2-tide and her corresponding overtides (e.g. M4, M6 and M8):

  1. amplitude ratio (M4:M2) and phase difference 2*phase(M2)-phase(M4)
  2. amplitude ratio (M6:M2) and phase difference 3*phase(M2)-phase(M6)
  3. amplitude ratio (M8:M2) and phase difference 4*phase(M2)-phase(M8)

FRQWF gives additional information about single stations:

  • The amplitude ratio (Ai : A(M2)) of each partial tide i and the M2-tide can be evaluated as well as the phase difference between tide i and the M2-tide.
  • The errors of the analysis are evaluated and stored to the ASCII-version of frqsingle.dat/tex. They give information about the quality of the analysis.

In addition also the highest and lowest water levels are determined for the period of data analysis. Minimum bathyemtry is also computed in case input data were generated for an alternative bathymetry. Analysis of single stations includes calculation of the form factor F = (amplitude(K1) + amplitude(O1)) : (amplitude(M2) + amplitude(S2)). This value is stored to the printer file. The form factor F indicates the form of the tidal signal:

  • F < 0.25: semidiurnal form
  • 0.25 < f < 1.5: mixed, mainly semidiurnal form
  • 1.5 < f < 3.0: mixed, mainly diurnal form
  • F > 3.0: diurnal form

analysis of time series of vectors:

A single station analysis can also be done on two-dimensional, vertically averaged vectors. For each tidal harmonic constituent the following values are being calculated for the period of data analysis:

  1. amplitudes of the constituent (component by component)
  2. local phases of the constituent (component by component) adjusted to 01.01.yyyy 00:00 UTC.

A transformation to the constituent ellipse parameters is done for better understanding of the characteristics of the constituents.

Inside the LaTeX-tables and the automatically generated PDF-document (see below) the analysis is transformed to constituent ellipse parameters:

  1. length of the major semiaxis (= maximum vector strength)
  2. length of the minor semiaxis (absolute value = minimum vector strength, positive sign = vector rotates counterclockwise)
  3. common local phase of the constituent adjusted to 01.01.yyyy 00:00 UTC
  4. inclination of the major axis against North (positiv means inclination to the east).

During the analysis of model data (BAW direct access data format) the following parameters are calculated:

  1. vector of the major semiaxis (= maximum vector)
  2. common local phase of the constituent adjusted to 01.01.yyyy 00:00 UTC
  3. ratio of the length of the minor to the length of the major semiaxis.
  4. phase shift of the constituent ellipse to the local phase of the waterlevel of the contituent.


  1. general input data (filetype frqwf.dat)
  2. (optional) list of keys .tidkenn.dat (files of type kennungen.dat)
  3. computed time series data which shall be analysed (files of type dirz.bin.r, dirz.bin.i, and dirz.bin).
    The waterlevel series must always be present in addition to the physical timeseries. The latter can be provided by a separate file. The same is true for time dependent bathymatry in case input data were generated above alternative bathymetry.
  4. or single timeseries (files of type boewrt.dat)
  5. or results at extra points (files of type knoerg.bin)
  6. or list of files of one of the types boewrt.dat, knoerg.bin . (file of type dateiliste.dat)
  7. grid file and/or specific locations (in dependence on the computed data to be analysed):


  1. (if not provided on startup) list of keys .tidkenn.dat (files of type kennungen.dat)
  2. results of tidal harmonic analysis (files of type dirz.bin.r, dirz.bin.i, and dirz.bin)
  3. file containing results of single stations (type geopos.dat)
  4. file containing a table with results of a single station (type frqsingle.dat/tex)
  5. a LaTeX-file "Partialtiden.???.tex' containing a table of content and a reference to the file(s) of type frqsingle.dat/tex)
  6. a Postscript file "Partialtiden.???.ps" (example) containing a table of content and the results of single stations
  7. a PDF file "Partialtiden.???.pdf" Partialtiden_001.pdf containing a table of content and the results of single stations
  8. general input data for the program FRQCOMBI
  9. informative printer file (filetype Frqwf.sdr). Results of single stations are also reported there.
  10. (optional) trace of program execution (filetype Frqwf.trc)


Amplitude and phase of the selected tidal harmonic constituents are determined by means of a least square approximation.

The following rules should (must) be respected by the user of the program:

  • the period of data analysis should be as long as possible;
  • the period of data analysis must exceed the longest period of the tidal harmonic constituent for which amplitude and phase shall be calculated;
  • the phase difference between the various tidal harmonic constituents which are analysed must total at least one full period (360 degrees). For example the signals for the M2 and the S2 tide can be properly separated only when the analysis period is larger than a spring-neap cycle.
  • when analysing files of type knoerg.bin a wrong reference date leads to wrong results in the phases!!!

Tidal harmonic analysis is only performed for areas which are permanently covered by water.


The actual version uses single precision LAPACK procedures to solve the linear algebra problem. If you want to analyse a lot of single time series of the same filetype at once you should put it into a list of files via "ls -1 *.dat > dateiliste.dat". This is possible for files of type boewrt.dat and knoerg.bin. You choose the analysis type BOEWRTLST or KNOERGLST and give the filename of the file list inside the input control file! The correct reference date for files of type knoerg.bin is the reference date of the model run which created them! If you are not sure about the reference date, please convert them with the program EXKNO to files of type boewrt.dat. Stations, which contain the time in other timezone than "MET", must have the timezone in header information (only supported by boewrt.dat). Allowed timezones are for example MET, EET, UTC, +iH, -iH. The i of the last two expressions represents an INTEGER number between 0 and 12.

Several features have been added to the processing of single stations. They are set in the optional datablock SINGLE which is located in a file of type frqwf.dat. The names of the concerned output-files are automatically generated. The time zone can be set in that file, too. A PDF file can be created by copying the corresponding Postscript file to a watched Adobe Acrobat Distiller directory. Frqwf waits for the PDF for a certain time. If the PDF is not finished then, the program execution will end regularly and the user will have to move the PDF back into the working directory on his own.

LaTeX has to be installed in order to run the UNIX-script generating Postscript successfully. Because on SGI systems LaTeX is not available, the UNIX-Script remains in the working directory and the user can start the process on another machine.

Program(s) to run before this Program


Program(s) to run after this Program


Additional Information



Additional software

LAPACK, LaTeX, Adobe Acrobat Distiller

Original Version

R. Fritzsch, G. Lang


G. Seiß, P. Schade, G. Lang, S. Spohr


Dietrich G., Kalle K. , Krauss W., Siedler G. - Allgemeine Meereskunde, Kapitel 9 Gezeitenerscheinungen. Gebrüder Borntraeger Berlin, Stuttgart, 1975.
Foreman M.G.G. - Manual for Tidal Currents Analysis and Prediction Institute of Ocean Sciences, Patricia Bay Sidney, British Columbia, 1979-1996.

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