Tidal gravity factors for known

Tidal gravity factors for selected stations around the world.

Three main tidal gravity prediction programs are available through the ICET WEB site:

PREDICT from ETERNA 3.4,

MT80w,

T-soft.

The characteristics of these programs are discussed in Ducarme B., 2006

Comparison of some tidal prediction programs and accuracy assessment of tidal gravity predictions.

Bull. Inf. Marées Terrestres, 141, 11175-11184

The input format of the three programs is really different, so that we must provide here 3 different sets of input parameters.

The TAM1200 (Tamura, 1987) tidal potential is used as default option.

Tidal gravity prediction on the real Earth

The main problem for tidal gravity prediction is that the Earth tides are strongly perturbed by the influence of the oceanic tides which modify the tidal parameters distribution at the surface of the Earth. The oceanic tides produce a direct attraction due to the moving water masses, a flexure of the crust and an additional change of the potential due to the mass redistribution. The effect can reach up to 10% of the Earth body tides, but is generally at the level of a few percent. The uncertainties and contradictions between different ocean tides models are such that the dispersion of the corresponding modeled tidal parameters d_m, a_m is generally at the level of a few tenths of a per cent. In coastal areas it can easily exceed 1%.

We use hereafter the general definition of the amplitude factor δ as the ratio A/A_th of the tidal amplitude with respect to the astronomical tidal amplitude A_th (Melchior, 1978).

For the main tidal waves, we build the modeled tidal factors based on the body tide amplitude R(A_th.d_model ,0), where d_model is the amplitude factor computed using a model of the response of the Earth to the tidal force, and the ocean load vector L(L,l), computed from different ocean tides models. The modelled vector A_m(A_m,a_m) is given as

A_m=R+L

(1)

The modelled amplitude factor d_m is simply given by the ratio A_m/A_th.

The R vector depends on the choice of the body tides model describing the response of the Earth to the tidal forces. Dehant et al., 1999 proposed two different models the elastic one and the non-hydrostatic/anelastic one. The discrepancy between the elastic and anelastic models is at the level of 0.15%. On the grounds of previous comparisons between the two models (Baker and Bos, 2003, Ducarme et al., 2006), based on the superconducting gravimeter array (Global Geodynamics Project, Crossley et al., 1999), we decided to use the DDW99 non-hydrostatic/anelastic model (DDW99/NH) as a standard.

In such a way the modeled tidal factors are defined as

A_m(d_m.A_th, a_m) = R(d_DDW99NHlA_th.,0) + L(L,l)

(2)

We computed modeled tidal factors using 9 different ocean tides models (ORI96, CSR3, CSR4, FES95, FES02, FES04, NAO99, GOT00 and TPX06). The tidal loading vector L was evaluated by performing a convolution integral between the ocean tide models and the load Green's function computed by Farrell (1972). The Green’s functions are tabulated according to the angular distance between the station and the load. The water mass is condensed at the centre of each cell and the Green’s function is interpolated according to the angular distance. This computation is rather delicate for coastal stations and models computed on a coarse grid, as the station can be located very close to the centre of the cell. The numerical effect can be largely overestimated. To avoid this problem our tidal loading computation checks the position of the station with respect to the centre of the grid. If the station is located inside the cell, this cell is eliminated from the integration and the result is considered as not reliable (Melchior et al., 1980). We can consider two groups of models, the older models until 1996 (ORI96, CSR3, FES95) on one hand, and the new generation of models (CSR4, FES02, FES04, GOTOO, NA099 and TPX06) on the other. For the first generation of models, the effect of the imperfect mass conservation is corrected on the basis of the code developed by Moens (Melchior et al., 1980). Following Zahran’s (2000) suggestion, we computed mean tidal loadings for different combinations of models.

As most of the ocean tide models do not provide the smaller tidal constituents J1, OO1, M3, M4 we provide only the theoretical amplitude factors of the corresponding groups. For the long period constituents we use always the mean of the 3 recent models NAO99, TPX06 and FES04 to compute the loading for Mf. For the annual and semi-annual solar waves Sa and Ssa the tidal loading is not the main perturbation. The contributions from meteorological and hydrological sources are preponderant. Tidal gravity analyses Superconducting Gravimeters data determined observed tidal factor larger than 2 for Sa (Ducarme et al, 2006), while global models are required for effective pressure corrections (Neumeyer et al., 2004). Continental water storage fluctuations induce strong seasonal effects (Peter et al, 1995; Neumeyer et al, 2006). As these very long period tidal waves are only important for absolute gravity measurements and deserve a special treatment we use also the body tides model values for tidal predictions. The constant tidal effect called M0S0 should be treated with a special care in order to follow the resolutions of the International Association of Geodesy (IAG). In gravimetry one should follow the “zero tide” correction principle i.e. one should remove only the astronomical part of the M0S0 tide and not the constant deformation. Clearly speaking the amplitude factor of M0S0 should be put equal to one.

2. Organization of the tables

The tidal stations are distributed between different regions presented on the top. By clicking on a region you get the list of the stations actually present in this region.

You can choice between 6 possible links, with 2 options for each format (PREDICT, MT80w and T-soft). The options correspond to the mean of the 9 ocean tide models or the mean of the 6 recent ones only.

Clicking on one link will connect you to the first station of the corresponding region. Then you can search for the required station by its name or its station number.

The available parameters will depend on the selected format.

For predict you can directly use the data as *.ini file. To run a prediction you have only to fill:

SAMPLERATE= #data sampling in seconds(integer)

INITIALEPO= xxxx xx xx #initial epoch in year, month, day

PREDICSPAN= #time span in hours(integer)

according to ETERNA manual.

For MT80w the data can be used directly as STATION file.

Station coordinates in first line

col.1-2: component (gravity=0)

col.3-12 : longitude (East positive)

col.13-22: latitude (North positive)

col.23-32: altitude in km

col.33-42: gravity in gal

col.53-62: scale factor (standard=1.)

Comments until 99

Station number

Tidal parameters of the different wave groups

col.1-4: beginning of group in TAM1200 potential

col.6-9: end of group

col.12-14: wave name

col.33-40: amplitude factor

col.49-57: phase difference with respect to local tide, lag negative

col.59-67: standard deviation of the set of models (amplitude factor)

col.68-76: standard deviation of the set of models (phase difference)

For T-soft the data should be inserted in the LOCAT.TSD data base, following T-soft manual. .

BIBLIOGRAPHY

Baker T.F., Bos M.S. (2003) Validating Earth and ocean models using tidal gravity

measurements. Geophys. J. Int., 152, 468-485.

Crossley, D., Hinderer, J., Casula, G., Francis, O., Hsu, H. T., Imanishi, Y., Jentzsch, G., Kääriaïnen, J., Merriam, J., Meurers, B., Neumeyer, J., Richter, B., Shibuya, K., Sato, T., Van Dam, T. (1999). Network of superconducting gravimeters benefits a number of disciplines. EOS, 80, 11, 121/125-126.

Dehant, V., P. Defraigne, and J. Wahr (1999): Tides for a convective Earth. Journal Geophys. Res., 104, B1, 1035-1058.

Ducarme B., Vandercoilden L., Venedikov A.P., 2006. The analysis of LP waves and polar

motion effects by ETERNA and VAV methods. Bulletin Inf. Marées Terrestres, 141, 11201-

11210.

Ducarme B., Sun H. P., Xu J. Q., 2006. Determination of the free core nutation period from tidal

gravity observations of the GGP superconducting gravimeter network. Journal of Geodesy, 81,

179-187, DOI: 10.1007/s00190-006-0098-9.

Farrell, W.E. (1972): Deformation of the Earth by surface load. Rev. Geophys., 10, 761-779.

Melchior, P., M. Moens and B. Ducarme (1980): Computations of tidal gravity loading and attraction effects. Royal Observatory of Belgium, Bull. Obs. Marées Terrestres, 4, 5, 95-133.

Neumeyer J., Hagedorn J., Leitloff J., Schmidt T. (2004) Gravity reduction with three-

dimensional atmospheric pressure data for precise ground gravity measurements.

Journal of Geodynamics, 38, 437-450

Neumeyer J., Barthelmes F., Dierks O., Flechtner F., Harnisch M., Harnisch G., Hinderer J.,

Imanishi Y., Kroner C., Meurers B., Petrovic S., Reigber Ch., Schmidt R., Schwintzer P., Sun

H.-P., Virtanen H. (2006) Combination of temporal gravity variations resulting from

Superconducting Gravimeter recordings, GRACE satellite observations and global hydrology

models. Journal of Geodesy, doi: 10.1007/S00190-005-0014-8.

Peter G., Klopping F.J., Berstis K.J., (1995) Observing and modeling gravity changes caused by

soil moisture and groudwater table variations with superconducting gravimeters in Richmond,

Florida, U.S.A.. Cahiers du Centre Européen de Géodynamique et de Séismologie, 11, 147-158

Tamura, Y. (1987): A harmonic development of the tide generating potential. Bull. Inf. Marées Terrestres, 99,6813-6855.

Zahran, K.H. (2000): Accuracy assessment of Ocean Tide loading computations for precise geodetic observations. PhD thesis, Universität Hannover.