Global vertical datum unification based on the combination of the fixed gravimetric and the scalar free geodetic boundary value problems

Transcription

1 Global vertical datum unification based on the combination of the fixed gravimetric and the scalar free geodetic boundary value problems Laura Sánchez contribution to the IAG-IC.: Vertical Reference Frames GGEO 8 Symposium Chania, June 4, 8

2 Motivation World Height System (WHS) (IAG-IC.: Vertical Reference Frames, Ihde et al. 7) Consistent modelling of geometric and physical parameters, i.e. h = H N + ζ ( H + N ) in a global frame with high accuracy (> -9 ) Geometrical Component Coordinates: h (t), dh/dt Definition: ITRS + Level ellipsoid (h = ) a. (a, J, ω, GM) or b. (W, J, ω, GM) Realization:. Related to the ITRS (ITRF). Conventional ellipsoid Conventions: IERS Conventions Ellipsoid constants, W, U values, reference tide system have to be aligned to the physical conventions! hysical Component Coord.: otential differences -ΔW (t) = W (t) W (t); dδw /dt Definition: W = const. (as a convention) Realization:. Selection of a global W value. Determination of the local W, values 3. Connection of W, with W 4. Geometrical representation of W and W, (i.e. geoid comp.) 5. otential differences into physical heights (H or H N ) Zero tide system Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

3 Considerations on W, W, The reference level (W, W, ) for potential differences can arbitrarily be appointed, but it is preferred that this level refers to the mean sea level and it shall be derived from actual observations of the Earth s gravity field and of the sea surface (Gauss/Listing geoid definition); The direct determination of absolute potential values (W, W, ) from observational data is not possible, adequate constraints are required; These constraints (mainly the vanishing of the gravitational potential V at infinity) are only reliable in the frame of the Geodetic Boundary Value roblem (GBV); hence, the determination of suitable W or W,, values is exclusively feasible by solving the GBV; This procedure reduces the arbitrariness of the reference level; the obtained W values will be in agreement with the geodetic observations included for solving the GBV. Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

4 Determination of W and W, Ocean areas Fixed gravimetric GBV Estimation of the potential of the level surface that best approximates the mean sea surface Geometry of the boundary surface (mean sea surface) is known from satellite altimetry This value is appointed as the global reference level W Land areas Scalar-free GBV (Molodensky App) Since the observational data included in the boundary conditions refer to different vertical datums, we obtain as many W, values as existing height systems. GVB shall homogeneously be solved in all datum zones ( = J); i.e, gravity anomalies at ground level, the same GGM, the same reference ellipsoid, etc. Relationships W -W,, W, -W,+ through vertical datum unification strategies Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

5 W (W, ) in the GBV frame Formulation Constraints Solution Ocean areas Land areas T = outside boundary surface ; T = W U T r = δg T T r r δw = W, = g U δw r = W W T = at ; T dσ = k ; T dσ = k ; k + k = T i i T dσ = sea ΔGM T = + R R land = ; B = δg (gravity disturbances) B S ( ψ ) dσ + G S( ψ ) 4π n= 4 σ R π σ n = J ; B dσ = g g = Δg ; g = ΔC ; etc., δw r Results + S ( ψ ) = S' ( ψ ) = ln ( ) sin ψ sin( ψ ) S( ψ ) W W = U W = γ γ h dσ + T γ dσ = sin ( ψ ) ζ ψ 6sin + 5cosψ... T + δw = γ Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

6 Numerical results: W value Solution of the fixed gravimetric GBV taken as input data: Geometry of the mean sea surface: CLS model (Hernandez, Schaeffer ), DGFI annual models derived from T/ Gravity disturbances from GGM: EGM8 model (avlis et al. 8) and EIGEN-GL4S (GRGS/GFZ 6) MSS CLS Latitude range 8 N 78 S W [m s - ] (EGM8, n = 5) ,4 ±,64 W [m s - ] (EIGEN-GL4S, n = 5) ,38 ±,64 67 N 67 S 53,94 ±,6 53,83 ±,63 6 N 6 S 53,8 ±,55 53, ±,56 Other W computations: Best fitting ellipsoid: U = ,85 m s - (GRS8) 856,88 (Rapp, 995) Mean potential value from = + n [ C nm cosmλ... ] W = ,5 (Nesvorny and Sima 994) 856,5 (Ries 995) 856, (Bursa et al. ) 854,7 (Bursa el al. 6) 853,4 (Sánchez 5) W GM r n= m= Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

7 Vertical datum unification Coastal approach Continental approach Oceanic approach Constraint for the empirical determination of the δw terms: γ h ( W W ) T δw = Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

8 Observation equations for Vertical datum unification Oceanic approach (SSTop around tide gauges) Data: Satellite altimetry and satelliteonly GGM, SSTop at coast lines by including also tide gauge records. Coastal approach (reference tide gauges) Data: GS positioning at tide gauges, spirit levelling with gravity corrections, terrestrial gravity data and satellite-only GGM. T T T = δw h γ = δw Continental approach (geometric reference stations) Data: GS positioning at reference stations (including border points), spirit levelling with gravity corrections, terrestrial gravity data and satellite-only GGM. ( W W + T ) h γ = δw ( W W + T ) ( W W + T ) = δw δw Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

9 Numerical results: SIRGAS example Input data: Local quasigeoid models GNSS positioning, mean sea surface heights, Geopotential numbers from levelling H N, h, ζ, SSTop at epoch., zero tide system Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

10 Numerical results: SIRGAS example Sánchez, L.; GGEO 8 Symposium, June 3-7, 8

11 Closing remarks The determination of δw i must be based on regional geoids of high resolution. The GGMs do not provide the required accuracy and resolution. δw i terms shall be estimated at the definition period of the local reference levels, i.e. the sea level rise and the vertical crustal movements must be taken into account, and all heights (h, H N, ζ, SSTop) shall be reduced to a reference epoch. The determination of δw i requires the three proposed approaches: coastal, terrestrial, and oceanic approach. Their isolated evaluation leads to unreliable values. The discussion about introducing orthometric or normal heights should be a question of the realization, not of the definition. However, the global vertical system must support both types of heights. In this way, its reference level should be determined where both surfaces (geoid and quasigeoid) are the same: in oceanic areas. Although the reference level should be defined by a fixed W value (for the computation of geopotential numbers), it must also be realized geometrically by the (quasi)geoid determination (solution of the GBV). The uniqueness, reliability and repeatability of the global reference level W can be guaranteed by introducing specific conventions only, e. g. V =, mean sea surface model, global gravity model, tide system, reference epoch, etc. On the contrary, it will be exist as many height systems as W computations. Sánchez, L.; GGEO 8 Symposium, June 3-7, 8