Physical height systems in South America

Transcription

1 Physcal heght systems n South Amerca Actvtes developed wthn SIRGAS: Sstema de Referenca Geocéntrco para las Amércas Laura Sánchez Deutsches Geodätsches Forschungsnsttut (DGFI) SIRGAS Vce-Presdent STSE-GOCE+Heght System Unfcaton Progress Meetng 2 December 14-15, BKG, Frankfurt am Man, Germany

2 Descrpton of exstng physcal heght systems n South Amerca Defnton/realzaton of a unfed heght system for South Amerca Advances and lmtatons n the unfcaton of the South Amercan heght systems

3 Defnton Realzaton Reference geod mean sea level at surface local tde gauges Staton orthometrc sprt levellng wth postons heghts gravty reductons (by defnton, but not n practce)

4 Mean sea level determned at dfferent tde gauges at dfferent defnton perods (most of them unknown) Omsson of vertcal movements (of the Earth crust and sea level)

5 Dfferent levellng epochs assumng dh/dt = 0 Omsson (n general) of gravty reductons or usage of dfferent (orthometrc) hypotheses Unrelable levellng connectons n the Amazonas jungle and Andean regon (> 6000 m) Vertcal networks ndvdually adjusted Unclear reference tde system

6 Tme seres of the GNSS staton BOGA (Bogotá, Colomba) In practce H and N are assumed nvarant

7

8 Include (local and temporal) dscrepances between local reference levels systematc levellng errors dscrepances between dfferent gravty reductons vertcal movement effects

9 There are as many heght systems as reference tde gauges (and appled orthometrc reductons); Relatonshp between the local reference surfaces and a global geod s unknown; Combnaton of levelled heghts wth GNSS postonng and gravty geod models s unrealstc (at meter-level); Relatve precson s hgh, absolute precson s too unrelable for understandng global change phenomena/effects.

10 To provde a hghly precse physcal reference frame (consstent at sub-cm level beyond natonal borders) equvalent to the geometrcal one,.e. SIRGAS (densfcaton of ITRF); To satsfy h-h-n=0 at the cm-level n a global frame; To support determnaton and combnaton of geometrc and physcal heghts; To establsh a smlar realzaton to ITRF/SIRGAS,.e. a global network wth known vertcal coordnates; regonal and natonal densfcatons,.e. ntegraton (transformaton) of the exstng local heght systems.

11 Geometrcal Component Coordnates: Ellpsodal heghts h (t), dh/dt Defnton: ITRS + Level ellpsod (h 0 = 0) a. (a, J 2, ω, GM) or b. (W 0, J 2, ω, GM) Realzaton: 1. Related to the ITRS (SIRGAS/ITRF) 2. Conventonal ellpsod Conventons: IERS Conventons Ellpsod constants, W 0, U 0 values, reference tde system have to be algned to the physcal conventons. Physcal Component Coordnates: Potental dfferences -ΔW P (t) = W 0 (t) W P (t); dδw 0 /dt Defnton: W 0 = const. (as a conventon) Realzaton: 1. Selecton of a W 0 reference value 2. Determnaton of the local reference levels W 0,j 3. Connecton of W 0,j wth W 0 4. Geometrcal representaton of W 0 and W 0,j (.e. geod comp.) 5. Potental dfferences nto physcal heghts (H or H N ) Zero tde system

12 The reference level (W 0, W 0,j ) for potental dfferences can arbtrarly be apponted, and any W 0 value can be ntroduced as a conventon; The real problem s not the W 0 value per se, but ts realzaton. Therefore, t s necessary to adopt a W 0 value estmated from actual observatons of the Earth s gravty feld and of the Earth s surface (sea and land); More than the estmated W 0 value, one should take care of ts relablty and repeatablty; The drect determnaton of absolute potental values (W 0, W 0,j ) from observatonal data s not possble, adequate constrants are requred.

13 At any tde gauge (TG) 1) W = W 0 ( ) 0 Mean value of many TGs N 1 ( ) 2) W0 = W0 N = 1 Wth a reference ellpsod 3) W = U 0 Mean value over ocean areas S O Gravty Boundary Value Problem (GVBP) 5) W0 = U 0 + δw T 1 γ 1 γ Δg = + T δw h γ h γ h 0 ( W W ) 2 4) 0 ds O = mn It cannot realze a global vertcal reference level Its relablty and repeatablty depend on the tde gauges ncluded If the reference ellpsod changes, the reference level changes, too. An equpotental surface averagng the sea surface (DOT) n a geometrc sense s not determned Requred constrants (manly the vanshng of the gravtatonal potental V at nfnty) are only relable n the frame of the GBVP

14 Formulaton Constrants Soluton Ocean areas Fxed gravmetrc GBVP provdes the global reference level (W 0 ) 2 T = 0 outsde boundary surface ; T r = δg Land areas Scalar-free GBVP provdes the local reference levels (W j ) j T = W U T 2 T = g r r δw = W U 0, j j 0 2 δw j r = W W T = 0 at ; T dσ = k ; T dσ = k ; k + k = 0 T00 j j T dσ = 0 sea ΔGM T = + R R land j = 1 ; B 1 = δg (gravty dsturbances) B S ( ψ ) dσ + G S( ψ ) j 4π n= 1 4 σ R π σ n j = 1 J ; B dσ j = g g 1 = Δg ; g 2 = ΔC ; etc. 0 j 0, j 2 δw r j vertcal datum unfcaton strateges

15 Soluton of the fxed gravmetrc GBVP Boundary surface: mean sea t= derved from T/P data (ϕ = 66 N/S, no shallow waters) Boundary condtons: gravty dsturbances derved from EIGEN-5S, n=150 (Förste et al., 2008) Reference ellpsod: GRS80 W 0 = ,15 m 2 s -2 ± 0,05 m 2 s -2 Other computatons: W 0 = ,0 (Bursa et al. 2002) 854,7 (Bursa et al. 2006) 854,5 (Čunderlík et al. 2006) 853,7 (Dayoub et al. 2009) 853,4 (Sánchez 2005) 852,0 (Dayoub et al. 2009)

16 P Determnaton of: δw, = W 0 W δw j = W j W

17 1. Establshment of a vertcal frame ncludng: reference tde gauges, man levellng ponts (nodes), ITRF (SIRGAS, EPN, ) statons; 2. Connecton of the levellng networks between neghbourng countres (or vertcal datum zones): δw ; j = C C j 3. Evaluaton of δw = hγ T C n three approaches: Oceanc approach (DOT around gauges) h from satellte altmetry combned wth tde gauge regstratons; C = 0; T from satellte-only GGM. It must be the same n all tde gauges. 4. Least squares adjustment of (3) and (4). ( ) Coastal approach (reference tde gauges) h from GPS postonng at tde gauge benchmarks; C = 0; T from satellte-only GGM + terrestral gravty. Terrestral approach (geometrc reference statons) h from GPS postonng at SIRGAS statons and levellng nodes, C geopotental numbers from levellng, T from satellte-only GGM + terrestral gravty.

18 Frst approach nput data reference tde gauges δw δ = γ hsat. Alt+ TG T GGM TG W = γ hsirgas TGGM + Terr. Data SIRGAS reference statons δ SIRGAS statons W = γ hsirgas C TGGM + Terr. Data 3. 8 connectons between neghbourng countres δw j = C j C Unknowns: 15 vertcal datums (14 tde gauges + Paraguay) Observaton equatons: 73 Adjusted values: [ ] [ ] T T δw * = A PA 1 A PδH

19 (very!) Prelmnary results Prelmnary results, partly wth smulated nput data! The accuracy of estmated datum dscrepances s at the dm-level; Paraguay presents the largest uncertanty: no tde gauge, no SIRGAS reference staton.

20 Contnental adjustment (free normal equatons) of the levellng networks n South Amerca. Present related tasks are: Identfcaton of levellng gaps (especally between neghbourng countres) Standardzaton of gravty values for computaton of geopotental numbers GNSS postonng at tde gauges Treatment of tme-dependent components (parameters),.e. a reference epoch and dh/dt, dc/dt, dn/dt; Identfcaton (correcton) of uncertantes n δw j due to systematc errors (n levellng networks, GNSS at tde gauges, etc.); Relable combnaton of satellte-only GGMs and terrestral gravty data.

21 (very!) Prelmnary results

22 (very!) Prelmnary results Dalazoana, R.; S.R.C. de Fretas; J.C. Baez; R.T. Luz (2007). Brazlan vertcal datum montorng Vertcal land movements and sea level varatons. Sprnger; IAG Symposa; Vol. 130: Drewes, H.; ; D. Bltzkow; S. Fretas (2002). Scentfc foundatons of the SIRGAS vertcal reference system. Sprnger; IAG Symposa; Vol. 124: Fretas, S.R.C.; A.S. Medna, S.R.S. de Lma (2002). Assocated problems to lnk South Amercan vertcal networks and possble approaches to face them. Sprnger; IAG Symposa; Vol. 124: Luz, R.T., S.R.C. de Fretas, B. Heck, W. Bosch (2009). Challenges and Frst Results Towards the Realzaton of a Consstent Heght System n Brazl. Sprnger; IAG Symposa; Vol. 134: Luz, R.T., W. Bosch, S.R.C. Fretas, B. Heck, R. Dalazoana (2009). Evaluatng the Brazlan Vertcal Datum Through Improved Coastal Satellte Altmetry Data. Sprnger. IAG Symposa, Vol. 133: Natal, M.; C. Brunn; K. Kanuth; H. Drewes (2002). Montorng tde gauges benchmarks n Argentna by GPS. Sprnger; IAG Symposa; Vol. 124:

23 (very!) Prelmnary results Pacno, M.C.; D. Del Coglano; G. Font; J. Morano; P. Natal; E. Laura; R. Ramos; S. Mranda (2007). Actvtes related to the materalzaton of a new vertcal system for Argentna. Sprnger; IAG Symposa; Vol. 130: Sánchez, L. (2002). A reference surface for a unfed heght system n the northern part of South Amerca. Sprnger; IAG Symposa; Vol. 125: Sánchez, L.; W. Martínez (2002). Approach to the new vertcal reference system for Colomba Sprnger; IAG Symposa; Vol. 124: Sánchez, L. (2007). Defnton and realsaton of the SIRGAS vertcal reference system wthn a globally unfed heght system. Sprnger; IAG Symposa; Vol. 130: Sánchez L.(2008). Approach for the establshment of a global vertcal reference level. Sprnger; IAG Symposa Vol. 132, Sánchez, L. (2009). Strategy to Establsh a Global Vertcal Reference System. Sprnger; IAG Symposa; Vol. 134: Sánchez, L., W. Bosch (2009). The role of the TIGA project n the unfcaton of classcal heght systems. Sprnger, IAG Symposa (134): More nformaton at