A new best estimate for the conventional value W 0

Transcription

1 - Final Report of the G on Vertical Datum tandardization - L. ánchez Deutsches Geodätisches Forschungsinstitut, Technische Universität München DGFI-TUM, Germany R. Čunderlí, K. Miula, Z. Minarechová Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, lova University of Technology in Bratislava, lovaia N. Dayoub Department of Topography, Faculty of Civil Engineering, Tishreen University, yria Z. Šíma Astronomical Institute, Academy of ciences, Prague, Czech Republic V. Vatrt Faculty of Civil Engineering, Brno University of Technology, Czech Republic M. Vojtíšová Geographic ervice of the Czech Armed Forces, Czech Republic

2 Introduction is understood as the potential value of the geoid; ince there are an infinite number of equipotential surfaces, the geoid is to be defined arbitrarily by convention; Usual convention: the geoid is the equipotential surface of the Earth s gravity field that best fits (in a least square sense) the undisturbed mean sea level; ince to satisfy this condition is not possible and since the sea level changes, a convention about mean sea level (time span and area) is also needed: mean value at a local tide gauge = 1 n ( i) mean value a several tide gauges = n i= 1 potential value of a best fitting ellipsoid in ocean areas ( i) = U mean value over ocean areas sampled globally ( ) d min =

3 and the IER Conventions In 1991, the International Astronomical Union introduced timescales for the relativistic definition of the celestial space-time reference frame; The relationship between Geocentric Coordinate Time (TCG), and Terrestrial Time (TT) depends on the constant L G = c For this reason, the IER Conventions included a value and updated this value regularly according to new best-estimates: Year L G ± 3 m s ± (Chovitz 1988) (IAU 1991, Recommendation IV, note 6) ± 3 m s ± (Burša et al. 199) (Fuushima 1995) ± 1 m s ± (Burša 1995a) (McCarthy 1996, Tab. 4.1) ±.5 m s (as defining constant) (Burša et al. 1998, Groten 1999) (IAU, Resolution B1.9) In, L G is declared as defining constant, i.e. it should not change with new estimations of. The corresponding value is the bestestimate available in

4 Concept underlying the 1998 value ( ±.5 m s - ) atellite altimetry provides the coordinates ϕ, λ, h of points M describing the sea surface. If the sea surface topography h T is reduced, points (M ) on the geoid are obtained; Using the coordinates (ϕ, λ, h-h T ) and a global gravity model (GGM), the potential value at any point M on the geoid (i.e. ) can be computed; ince points on the geoid cannot be materialised in practice, is estimated by satisfying the condition (cf. Burša et al. 1998, Eq. [5]): h T d = min Approximation applied for the estimation of the 1998 value (adapted from Burša et al. 1997, Fig. 4, and Burša et al. 1998, Fig. 1). Models applied by Burša et al. 1998: Burša s own mean sea surface model from T/P (1993 to 1996) h T PCM4b (tammer et al. 1996) GGM EGM96 (Lemoine et al. 1998)

5 Recent computations (since 5) based on newer models of the sea surface and the Earth s gravity field Recent estimations 1998 value

6 oring Group on Vertical Datum tandardisation Common initiative of GG Theme 1: Global Height ystem Main objective: to provide a recommendation of the value to be appointed as the reference level of the international height reference system; Term: 11 15; International Gravity Field ervice (IGF) IAG Commission : Gravity Field IAG Commission 1: Reference Frames Members: J. Ågren (weden), R. Čunderlí (lovaia), N. Dayoub (yria), J. Huang (Canada), R. Klees (The Netherlands), J. Mäinen (Finland), K. Miula (lovaia), Z. Minarechová (lovaia), P. Moore (United Kingdom), D. Roman (UA), Z. Šima (Czech Republic), C. Tocho (Argentina), V. Vatrt (Czech Republic), M. Vojtisova (Czech Republic), Y. ang (UA).

7 oring Group on Vertical Datum tandardisation Aspects analysed within the G-VD: Different estimation methodologies but the same input models (for redundancy); ensitivity of the estimation on the Earth's gravity field model Dependence of on the omission error of the global gravity model Influence of the time-dependent Earth's gravity field changes on ensitivity of the estimation on the mean sea surface model Influence of time-dependent sea surface changes on Effects of the sea surface topography on the estimation of Dependence of the empirical estimation on the tide system Rigorous error propagation analysis to estimate the influence of the input data uncertainties on the estimation.

8 Basic approach for the empirical estimation of ( ) min = d As proposed by acerdote and ansò (1): γ Ξ = d d σ γ σ γ 1 Condition: ea surface topography: olution: δλ δϕ ϕ δ δ γ δ γ γ cos = + = h T U for error propagation analysis If the sea surface topography Ξ is reduced from the see surface heights h (as Burša et al proposed): ( ) [ ] Ξ + = h T U 1 1 δ δ γ

9 Input data for the empirical estimation of h from a mean sea surface model: CL11 (chaeffer et al. 1), DTU1 (Andersen 1) own computed yearly models (199-13) cross calibrated data from the DGFI-penADB (chwate et al. 1) with covariance matrixes (Bosch et al. 14), 9 missions. T from a global gravity model: EGM96 (Lemoine et al. 1998), EGM8 (Pavlis et al. 1), EIGEN- 6C and 6EIGEN-6C3stat (Förste et al. 1), GC3 (Mayer-Gürr et al. 1), DIR-R4 (Bruinsma et al. 13), TIM-R4 (Pail et al. 11), GGM5 (Tapley et al. 13), monthly models from GRACE GFZ Release 5. Ξ from the (oceanographic) Model ECC- (Menemenlis et al. 8) U, γ from GR8 penadb: pen Altimeter Database,

10 Dependence of the estimate on the choice of the gravity model Computations in zero tide system with the M-CNE-CL11 sea surface model. 1) estimations based on models including GRACE, GCE and atellite Laser Ranging (Lageos) data are practically identical. Max. differences.1 m s -. ) The use of a satellite-only gravity model is suitable. After n = the largest differences are.1 m s -.

11 Dependence of the estimate on the choice of the gravity model Changes in the estimates after applying the monthly GRACE-based models GFZ Release 5 and the time-dependent harmonics of the model EIGEN-6C. The linear trend of using the GFZ Release 5 is x1-4 m s - a -1, while the linear trend using EIGEN-6C is -.647x1-4 m s - a -1. 3) easonal variations of the Earth s gravity model can be neglected (max. variation.3 m s - ).

12 Dependence of the estimate on the mean sea surface model Potential differences (divided by the normal gravity) between the estimations derived from the models M-CNE-CL11 and DTU1 (computations in zero tide system with the GGM EIGEN-6C3). By using the models CL11 and DTU1 there is a difference of.31 m s -, which reflects the mean discrepancy of ~ 3 cm between both models. Possible causes: Different strategies to process the altimetry data; Different reductions taen into account in each model; Different periods (interannual ocean variability).

13 Dependence of the estimate on the mean sea surface model Alternative: use of yearly mean sea surface models The estimates reflect (with opposite sign) the sea level rise measured by satellite altimetry; Max. difference.46 m s - ; These variations shall not be understood as a change in, but in the sea level; i.e. the geoid is not growing/decreasing with the mean sea level! This only means that the mean sea level coincides with a different equipotential surface depending on the period utilized for the average of the sea surface heights.

14 Reliability of the estimate Until now, all the computations assumed error free input data (M and GGM). By rigorous error propagation analysis (as jöberg 11 proposed), the value estimate decreases by about.3 m s -. tandard deviation (σ h ) of the mean sea surface heights for the year 5. tandard deviation (σ T ) of the anomalous potential derived from the model EIGEN-6C3 (n = ). tandard deviation ( σ = σ T + γ σ h ) of the gravity potential values computed at the sea heights (h) for the year 5 with the model EIGEN-6C3 (n = ). estimates assuming error free input data (blue series) and applying a proper error propagation computation (red series).

15 Dependence of the estimate on the tide system In theory: 1) the value depends only on - the volume enclosed by the surface = - the geocentric gravity constant GM - angular velocity of the Earth s rotation ω ) Direct and indirect effects of the tidal potential on are compensated by the deformation of the corresponding level surface, but the volume enclosed by this surface does not change; i.e. the potential value does not change. Empirically: determination in the three tide systems: [ ] TF ZT - =.78 m s [ ] - MT TF =.665 m s [ ] MT ZT - =.943 m s

16 Conclusions 1) Computations carried out within the G-VD demonstrate that the 1998 value ( ±.5 m s - ) is not in agreement (and consequently it is not reproducible) with the newest geodetic models describing geometry and physics of the Earth. ) The 1998 value is not suitable as a conventional reference value and a better estimate for has to be adopted by the IAG for the definition and realization of the IHR. 3) As reference level, the conventional value has to be fixed (without time variations); but it has to have a clear relationship with the sea surface (as convention for the realization of the geoid).

17 Conclusions 4) e propose to adopt the potential value obtained for the year 1 after fitting the yearly estimations by means of a lineal regression: = m s - rounded to = m s - 5) The formal error of this value is ±. m s -. However, as convention the adopted is understood free of error. 6) The introduction of a reference value is not accepted by the whole geodetic community. There are a variety of approaches to avoid a value. 7) Results provided by the G-VD are for those approaches requesting a reliable value.