http://www-gik.bau-verm.uni-karlsruhe.de/~iagetc/eterna33.htm, Last update: 1997 August 27
An earlier version of this paper has been published in Bulletin d'Informations Marees Terrestres, vol. 124, 9425-9439, Bruxelles 1996.
by Hans-Georg Wenzel,
Black Forest Observatory Schiltach,
Heubach 206, D-77709 WOLFACH.
The new version 3.30 of the earth tide data processing package ETERNA is available since October 1st, 1996. The earth tide processing package ETERNA version 3.30 allows the recording, preprocessing and analysis of earth tide observations under operating system MS-DOS on an IBM-AT compatible personal computer 80386/387 upwards. The new standard format for the storage and exchange of high rate or high resolution earth tide data (Wenzel 1995) is used in all parts of the ETERNA 3.30 package. Compared to previous versions, we have included into the earth tide analysis package ETERNA (Wenzel 1994b,c) the most accurate tidal potential catalogue by Hartmannn and Wenzel (1995a,b). In all programs, the DUT1 correction due to the Earth's variable rotation has been implemented using DUT1 values provided by the International Earth Rotation Service (IERS). Together with the Hartmann and Wenzel (1995a,b) tidal potential catalogue, this upgrade enables the preprocessing and analysis of earth tide observations and the prediction of earth tide signals with a model accuracy better than 1 ngal (1 ngal = 0.01 nm/s²).
Several parts of the ETERNA earth tide analysis package have been rewritten and several other pieces have been added. For the computation of tidal signals, we have implemented recursion formulas which reduce the total computation time for some data sets down to 35% compared to previous versions without loss of accuracy. The computation of gravity variation due to polar motion and due to length of day variation from IERS data are implemented in the programs. The ETERNA package has benn given a new and better structure, and several programs have been renamed (e.g. the former program ETERNA has been renamed to ANALYZE, the former program ETGTAB has been renamed to PREDICT, the former program PRETERNA has been splitted into programs DETIDE, DESPIKE and DECIMATE). The program LOAD89 (provided by O. Francis) has been included, which enables the computation of ocean loading effects from different ocean tide models (Schwiderski 1980, CSR3.20, FES952). An on-line manual with search and export functions is provided to assist the user by his operations. We believe that a substantial improvement with respect to accuracy, flexibility and operational comfort has been achieved compared to previous versions of the package. ETERNA 3.30 is currently the only earth tide data processing package beeing able to process earth tide observations with a model accuracy better than 1 ngal.
The ETERNA 3.30 package is installed by an automatic installation procedure within several directories (Table 1, Fig. 1). It contains 21 programs (with 38 515 program records in total) and covers together with the necessary data files 180 MByte. Thus, the ETERNA 3.30 package is provided to the user on CD-rom.
|01||ANALYZE.FOR||Analysis or earth tide observations|
|02||BENCHMAR.FOR||Comparison of model tides with benchmark series|
|03||DECIMATE.FOR||Decimation of earth tide observations|
|04||DESPIKE.FOR||Despiking of earth tide observations|
|05||DETIDE.FOR||Calibration and detiding of earth tide observations|
|06||ETSTEP.FOR||Eavluation of recorded step response|
|07||IERS.FOR||Transformation of earth rotation and polar motion data|
|08||INSTALCD.FOR||Installation of the ETERNA 3.30 package from CD-rom|
|09||HELPME33.FOR||On-line manual of the ETERNA 3.30 package|
|10||LOAD89.FOR||Ocean tide loading computation|
|11||PREDICT.FOR||Computation of synthetic model tides|
|12||PREGRED.CPP||Graphical editing of earth tide observations|
|13||PREPLOT.BAS||Visualization of earth tide observations|
|14||PRINTGL.EXE||hard copy for HPGL-files|
|15||PLOTDATA.FOR||Plot of earth tide observations|
|16||PLOTFIL.FOR||Plot of numerical filter gain|
|17||PLOTSPEC.FOR||Plot of spectra of earth tide residuals|
|18||PLOTHIST.FOR||Plot of histograms of earth tide residuals|
|19||RECTIDE.BAS||Digital recording of earth tide signals|
|20||TRANS.FOR||Transformation from International Format into PRETERNA Format|
|21||WPAREX.FOR||Interpolation of synthetic gravity tide parameters from global grid|
Fig. 1: Directories of earth tide data processing package ETERNA version 3.30
Digitital earth tide data acquisition can be carried out with program RECTIDE (in MS-QuickBasic), which allows the sampling of data from different sensors at 1 s or 5 s interval. After on-line subtraction of on-line computed model tides from the data, the residuals are displayed on the colour screen of the PC. The sampled data are numerically filtered using a symmetrical FIR lowpass filter with zero phase shift; the filtered data are decimated to 1 min interval and the decimated data are stored on hard disk.
The preprocessing of high rate earth tide data and meteorological data can be carried out with programs DECIMATE, DETIDE, DESPIKE (in Fortran 77/90) and PREGRED (in Visual C++). The data preprocessing is carried out using a remove-restore technique: At first all well-known signals (e.g. computed model tides and computed air pressure influence) are removed with program DETIDE. The graphical editor PREGRED (Vetter and Wenzel 1995) is a very comfortable tool to delete corrupted parts of the data, to correct steps and to interpolate gaps under graphical control of the operator. With program DESPIKE, the residual signal (the earth tide sensors drift) is automatically cleaned (destepped, despiked, and degapped) and the known signals are added back to the cleaned residual signal. The corrected samples at high rate are finally numerically filtered and decimated using program DECIMATE. For the data preprocessing may be used
The analysis of earth tide observations can be carried out with program ANALYZE (in Fortran 77/90), using the least squares adjustment procedure with multi channel input to derive tidal parameters, pole tide parameters and meteorological regression parameters. The spectrum of the residuals is used to derive standard deviations of the adjusted parameters. The mathematical model of of the ANALYZE earth tide analysis program has been developed by Chojnicki (1973) and modified and completed by Schüller (1976, 1977a, 1977b, 1978, 1986) and Wenzel (1976a, 1976b, 1977, 1994a, 1994b). With ANALYZE version 3.30 may be used
The prediction of earth tide signals can be carried out with program PREDICT (in Fortran 77/90), using the same parameter model as in program ANALYZE. With PREDICT version 3.30 may be used
The computation of ocean tide loading effects can be carried out with program LOAD89 (in Fortran 77/90), using different ocean tide models (Schwiderski 1980, CSR3.0, FES952) and Green's functions for the PREM earth model.
Within 1995, a new tidal potential catalogue (Hartmann and Wenzel 1995a, 1995b) became available, which allows the computation of earth tide signals with an accuracy better than 1 ngal, as has been verified by comparison with different benchmark gravity tide series (Wenzel 1996). Therefore, the Hartmann and Wenzel (1995) tidal potential catalogue using in total 12935 tidal waves has been implemented into the ETERNA package version 3.30. This tidal potential catalogue includes the potential due to the Moon up to degree 6, to the Sun up to degree 3, to the planets Mercury, Venus, Mars, Jupiter and Saturn to degree 2, and the potential due to the Earth's flattening by the Moon and by the Sun. The errors of gravity tides computed from the Hartmann and Wenzel (1995) tidal potential catalogue are 1.4 pm/s² rms and 10.4 pm/s² at maximum (1 pm/s² = 0.001 nm/s² = 0.1 ngal), as has been verified by comparison with several different benchmark gravity tide series (Wenzel 1996).
Because the computation of tides using the full 12935 tidal waves of the Hartmann and Wenzel (1995) tidal potential catalogue is rather time comsuming and may often be unnecessary compared to the accuracy of the data, a truncation parameter may be used to truncate the tidal potential catalog at some amplitude threshold, which degrades the accuracy of the computed tides but saves computation time. Due to the truncation option, there is in principle no need to use other tidal potential catalogues, even if very rough tidal computations shall be carried out. Nevertheless, we have made available with ETERNA 3.30 seven different tidal potential catalogues for comparison purpose. Because the Hartmann and Wenzel (1995) tidal potential catalogue uses a straightforward and simple normalization beeing different from the complicated Doodson (1921) normalization, the tidal potential catalogues of Doodson (1921), Cartwright et al. (1971, 1973), Büllesfeld (1985), Tamura (1987), Xi (1989) and Roosbeek (1996) have been transformed into the Hartmann and Wenzel (1995) normalization. Resulting from intensive accuracy tests, the astronomical arguments given by Tamura (1987) are used for the tidal potential catalogues of Doodson (1921), Cartwright et al. (1971,1973), Büllesfeld (1985), Tamura (1987) and Xi (1989). For Roosbeek (1996) and Hartmann and Wenzel (1995), the astronomical arguments given by Hartmann and Wenzel (1995) are used.
Because the astronomical arguments are computed by polynomials of up to degree 4, it is necessary to recompute the phases of the tidal waves from the astronomical arguments at monthly interval in order to achieve the desired accuracy for the computation of the tidal signals. For the computation of the tidal signals we have implemented recursion formulas which reduce the total computation time of programs ANALYZE, DETIDE and PREDICT for some data sets down to 35% compared to previous versions without loss of accuracy.
Within ETERNA 3.30, the time scale of the observations (or predicted signals) is assumed to be UTC (Universal Time Coordinated), which is distributed by radio transmitters and by GPS (Global Positioning System). For the accurate computation of tides, the time scales UT1 (Universal Time no. 1, describes the rotation of the Earth) and TDB (Dynamical Barycentric Time, used to describe the positions of the celestial bodies) have to be made available. Within ETERNA 3.30 we have implemented for the first time for tidal computations the correction DUT1 = UT1 - UTC, which is interpolated from daily tabulated values of DUT1 provided by the International Earth Rotation Service IERS. The difference DDT = TDT - UTC, which is constant for several months or years, is also taken from a table. The difference TDB - TDT (a few msec only) is computed from a closed formula. The neglection of the DUT1 correction can reach 0.1 nm/s² at maximum for gravity tides (see Fig. 6, 7).
The accuracy of the tidal potential catalogue by Hartmann and Wenzel (1995) has been estimated by comparison with several gravity tide benchmark series (Wenzel 1996). We have used here a gravity tide benchmark series called BFDE403F (which is supplied with the ETERNA 3.30 package) computed from the most recent and most accurate DE403/LE403 ephemerides (Standish et al. 1995) to verify the accuracy of the model tide computation within ETERNA 3.30. The series BFDE403F consists of hourly gravity tides for a rigid model Earth computed directly from the ephemerides of the Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn at station BFO Schiltach (48.3306 deg N latitude, 8.3300 deg E longitude, 589 m elevation) between January 1st 1987 and December 31st 1994. This benchmark series has been computed for the UTC time scale and has included the corrections DUT1 and DDT. The accuracy of the BFDE403F benchmark gravity tide series itself is estimated to be better than 1 pm/s² = 0.001 nm/s². In Fig. 2 and 4 are given residuals of the earth tide analysis from program ANALYZE for the benchmark gravity tide series when using the tidal potential catalogues of Tamura (1987) and Hartmann and Wenzel (1995); in Fig. 3 and 5 are given the corresponding Fourier amplitude spectra. One has to have in mind that the residuals of the least squares adjustment always underestimate the errors because the parameters determined by least squares adjustment absorb to a certain extend the errors. We can see maximum errors of 0.5 nm/s² and 0.012 nm/s² resp. in time domain and 0.015 nm/s² and 0.0005 nm/s² resp. in frequency domain for the tidal potential catalogues of Tamura (1987) and Hartmann and Wenzel (1995) resp. In Tab. 2 is given the last page from program ANALYZE for the benchmark gravity tide series when using the full Hartmann and Wenzel (1995) tidal potential catalogue. The maximum error of the adjusted tidal parameters is 0.00012 and 0.0174 degree for the very small wave M4. In Fig. 6 and 7 are given the residuals and their Fourier amplitude spectrum for the benchmark gravity tide series BFDE403F when using the Hartmann and Wenzel (1995) tidal potential catalogue but neglecting the DUT1 correction within program ANALYZE. We can see that the DUT1 correction can amount up to 0.1 nm/s² in time domain and up to 0.005 nm/s² in frequency domain.
Fig. 2: Residuals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Tamura (1987) tidal potential catalogue; DUT1 corrected.
Fig. 3: Amplitude spectrum of rssiduals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Tamura (1987) tidal potential catalogue; DUT1 corrected.
Fig. 4: Residuals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Hartmann and Wenzel (1995) tidal potential catalogue; DUT1 corrected.
Fig. 5: Amplitude spectrum of residuals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Hartmann and Wenzel (1995) tidal potential catalogue; DUT1 corrected.
Fig. 6: Residuals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Hartmann and Wenzel (1995) tidal potential catalogue; DUT1 not corrected.
Fig. 7: Amplitude spectrum of residuals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Hartmann and Wenzel (1995) tidal potential catalogue; DUT1 not corrected.
Program ANALYZE, version 3.30 960908 File: bfde403f #################################################################### # Gravimetric Earth tide station BFO Schiltach Germany. # # Black Forest Observatory, Geodetic and Geophysical Institutes, # # Universities Karlsruhe and Stuttgart, Germany. # # 48.3306N 8.3300E H589M gravity, # # Hourly gravity tides due to the Moon, the Sun, the Mercury, # # the Venus, the Mars, the Jupiter and the Saturn for a rigid # # Earth model computed from DE403 ephemerides using program # # DE403T.FOR for station BFO Schiltach, including earth flattening # # effects. All waves with amplitude factor 1.000, phase lead 0.00 # # deg. Time corrections UT1-UTC and TDB-UTC applied. # #################################################################### Latitude: 48.3306 deg, longitude: 8.3300 deg, azimuth: 0.000 deg. Summary of observation data : 19870101 0...19941231230000 Number of recorded days in total : 2922.00 Hartmann+Wenzel (1995) tidal potential used with threshold 0.10E-10 Rigid Earth model used. Inertial correction not applied UNITY window used for least squares adjustment. Numerical filter is no filter with 1 coefficients. Spectral condition number of normal equations: 153.754 Estimation of noise by FOURIER-spectrum of residuals 0.1 cpd band 0.0000 nm/s**2 1.0 cpd band 0.0000 nm/s**2 2.0 cpd band 0.0000 nm/s**2 3.0 cpd band 0.0000 nm/s**2 4.0 cpd band 0.0000 nm/s**2 white noise 0.0000 nm/s**2 adjusted tidal parameters : from to wave ampl. ampl.fac. stdv. ph. lead stdv. [cpd] [cpd] [nm/s**2 ] [deg] [deg] 0.000133 0.004107 SA 18.0753 1.00001 0.00139 0.0004 0.0850 0.004108 0.020884 SSA 20.0570 1.00000 0.00001 0.0000 0.0004 0.020885 0.054747 MM 22.7684 1.00000 0.00000 -0.0001 0.0001 0.054748 0.091348 MF 43.1106 1.00000 0.00000 0.0000 0.0000 0.091349 0.501369 MTM 8.2543 1.00000 0.00000 -0.0001 0.0000 0.501370 0.911390 Q1 59.1071 1.00000 0.00000 0.0001 0.0000 0.911391 0.947991 O1 308.7114 1.00000 0.00000 0.0000 0.0000 0.947992 0.981854 M1 24.2657 0.99999 0.00000 0.0000 0.0001 0.981855 0.998631 P1 143.6185 1.00000 0.00000 0.0000 0.0000 0.998632 1.001369 S1 3.3961 1.00002 0.00001 -0.0021 0.0008 1.001370 1.004107 K1 433.9797 1.00000 0.00000 0.0000 0.0000 1.004108 1.006845 PSI1 3.3977 1.00001 0.00001 0.0002 0.0005 1.006846 1.023622 PHI1 6.1807 1.00000 0.00001 0.0000 0.0003 1.023623 1.057485 J1 24.2748 1.00000 0.00000 -0.0003 0.0001 1.057486 1.470243 OO1 13.2799 1.00000 0.00000 -0.0006 0.0001 1.470244 1.880264 2N2 10.1612 0.99999 0.00000 0.0006 0.0001 1.880265 1.914128 N2 63.6222 1.00000 0.00000 0.0000 0.0000 1.914129 1.950419 M2 332.2900 1.00000 0.00000 0.0000 0.0000 1.950420 1.984282 L2 9.3932 1.00000 0.00000 0.0000 0.0001 1.984283 2.002736 S2 154.5844 1.00000 0.00000 0.0000 0.0000 2.002737 2.451943 K2 42.0094 1.00000 0.00000 -0.0001 0.0000 2.451944 3.381478 M3 4.3445 1.00000 0.00000 -0.0001 0.0000 3.381379 4.347615 M4 0.0527 0.99988 0.00001 -0.0174 0.0006 4.347616 7.000000 M5M6 0.0006 0.99990 0.00090 0.0076 0.0517 Adjusted TSCHEBYSCHEFF polynomial bias parameters : block degree bias stdv. 1 0 203.610176 nm/s**2 0.000024 nm/s**2 1 1 0.002443 nm/s**2 0.000043 nm/s**2 1 2 0.000009 nm/s**2 0.000018 nm/s**2 Standard deviation of weight unit: 0.001 Degree of freedom: 70077 Max. correlation: 0.866 bias 1 1 with Y-wave-SA Standard deviation: 0.001 nm/s**2 Routine GEOEXT. Execution time= 2531.410 sec
The earth tide data processing package ETERNA 3.30 is available to anybody; the package should however not be copied and given to third parties by any user. In order to cover the expenses for copying and distributing the ETERNA 3.30 package, a fee of US $ 300,- has to be charged to university and research institutes. The program files, data files and result files are distributed on one CD-rom together with a manual. All programs can be executed on an IBM-AT compatible personal computer 80386/387 upwards under MS-DOS operating system. Requests for the ETERNA 3.30 package should be submitted to:
Please use the order form given below for your conveniance.
| Order form for the ETERNA 3.30 package
I hereby order the ETERNA 3.30 package for scientific use only
in my university or research
____ I have added an international bank cheque of US
$ 300,- payable to Baden-Württembergische
____ I have transferred US $ 300,- to Baden-Württembergische
Bank Karlsruhe, account no.
Please send this form back to:
Prof.Dr.-Ing. H.-G. Wenzel,
The implemenatation of the Hartmann and Wenzel (1995) tidal potential catalogue into the ETERNA 3.30 package was the final stroke under a four years project to improve the accuracy of the available tidal potential catalogues. We have now in our hands several tools to process earth tide data with very low model tide errors below 1 ngal. We believe that a substantial improvement with respect to accuracy, flexibility and operational comfort has been achieved compared to previous versions of the ETERNA package. ETERNA 3.30 is currently the only earth tide data processing package with a model tide accuracy better than 1 ngal.
Data and programs used in the ETERNA 3.30 package have been supplied by O. Francis and F. Roosbeek (Observatoire Royal de Belgique, Bruxelles), T. Hartmann (Institut für Theoretische Astrophysik, Universität Tübingen/Germany), International Earth Rotation Service, Paris/France, B. Richter (Institut für Angewandte Geodäsie, Frankfurt a.M./Germany), E.M. Standish (Jet Propulsion Laboratory, Pasadena/USA), Q. Xi (Center for Analysis and Prediction, State Seismological Bureau, Beijing/China), and Y. Tamura (National Astronomical Observatory, Mizusawa/Japan). This is gratefully acknowledged.
This page has been established in HTML 3.2 in August 1997 by Hans-Georg Wenzel and is still in progress.