J. Catalão (1) and M.J. Sevilla (2)

(1)

1

J. Catalão

(1)

_{, M.}

J. Sevilla

(2)

(1) Univ. Lisboa, IDL, LATTEX, Lisboa , Portugal (2) Instituto de Astronomía y Geodesia (CSIC-UCM), Universidade Complutense de Madrid

J. Catalão

(2)

2

¾

Determination of a centimetre geoid surface

¾

Determination of vertical data differences in ICA area (about 20

height data)

¾

Determination of a tailored geoid for GPS survey applications

.

ICAUHS

project

(

Iberian

-

Canaries

-

Azores Unified Height System

).

Join project between

Join project between InstitutoInstitutoD. Luis, LATTEX (Univ. D. Luis, LATTEX (Univ. LisboaLisboa), ), InstitutoInstitutoGeogrGeográáficofico Português

Português and and UniversidadeUniversidadeComplutenseComplutensede Madrid aimed at the determination of de Madrid aimed at the determination of the geoid height and the vertical data unification in ICA region

the geoid height and the vertical data unification in ICA region..

Main Objective:

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3

Height datum connection

P A 0 P P P P c W W T U W − = + = γ − − = T (W U ) N P 0 0

∑

₌

∫∫

σ         σ ψ π γ + γ + γ ∆ − = − − n 1 j j 0 ,i 0 ,i 0 i P i P P j d ). ( S 4 1 C 2 C W N H h

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4

Previous Studies

Catalão, J. and M.J.Sevilla (1998). “Geoid Studies in the North-East Atlantic (Azores-Portugal).” Geodesy on the Move, IAG symposia: Symposium n. 119. Eds. R. Forsberg, M.Feissel, R.Dietrich. Springer-Verlag, pp. 269-274.

Catalão, J. and M.J.Sevilla (1999). “The effect of high precision bathymetric model on geoid computation.” IGS Bulletin, N. 10, pp 91-99.

Catalão, J. and M.J. Sevilla, (1999) “Comparison between EGM96 and FCUL96B tailored geopotential model for the north-east Atlantic.” Bollettino di Geofisica ed Teorica applicatta, Vol. 40, n.3-4, pp. 255-260.

Catalão, J. and M.J. Sevilla (2004), “Inner and minimum constraint adjustment of marine gravity data”. Computers and Geosciences, Vol. 30, Issues 9-10 pp. 949-957, DOI: 10.1016/j.cageo.2004.06.004

Catalão, J., (2006) “Iberia-Azores Gravity Model (IAGRM) using multi-source gravity data”. Earth, Planets, Space, 58, 277–286, 2006.

Catalão,J., M. Bos, C. Antunes (2007). A new high precision gravity and geoid model for the Azores archipelago. IN: Geophysical Research Abstracts Vol. 9, 04831, 2007, ISSN: 1029-7006, SRef-ID: 1607-7962/gra/EGU2007-A-04831. European

Geosciences Union – General Assembly 2007 VIENNA, AUSTRIA, 15 – 20 april 2007.

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Reposição do

EGM96

(EIGEN-C03) e

dos efeitos RTM

Methodology

(

GM c

)

ind GM

S

(

)

g

t

d

N

4 R

N

ψ

∆

−

∆

+

σ

+

πγ

+

=

∫∫

tc

)

H

(

G

2 g

g

_RTM

=

∆

_FA

−

∆

_GGM

−

π

ρ

_P

−

_ref

+

∆

Gravity data editing, merging and gridding

Geoid height computation

Vertical datum differences

∑

_∫∫

= _σ

















σ

ψ

π

γ

+

γ

+

γ

∆

−

=

−

n 1 j j 0 ,i 0 ,i 0 i P i P P j

d

).

(

S

4

1 C

2 C

W

N

H

h

i io W W C U W W₀ = ₀− ₀ ; = ₀− ₀ ∆

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6

Catalão, J. and M.J. Sevilla “Inner and minimum constraint adjustment of marine gravity data”.

Computers and Geosciences, Vol. 30, Issues 9-10 pp. 949-957, DOI: 10.1016/j.cageo.2004.06.004

Marine and land gravity

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2,403,171 data points, grid of 1,2´ x 1.5´ (1921 x 1251)

Gravity anomaly model

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8

Resolution: 500 m

Digital Terrain Model

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9

Digital Terrain Model

DTM (100 m resolution)

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10

Geoid Height

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11

Cycle 1 to 364

EMQ before tilt/bias removal = 0.11 m EMQ after tilt/bias removal = 0.08 m

Mean Sea Surface

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12

(m)

Validation on the Atlantic

TOPEX

KMSS04

mean Std min max

N - SSH(TOPEX) - MDT (Rio & Hernandez) -0.97 0.110 -1.502 0.100

N - MSSH(KMSS04) - MDT (Rio & Hernandez) 0.183 0.192 -1.244 1.946

After Tilt/Bias removal

N -SSH(TOPEX)-MDT (Rio & Hernandez) 0.0 0.084 -0.500 1.048

N - MSSH(KMSS04)- MDT (Rio & Hernandez) 0.0 0.156 -1.069 1.771

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N vertices mean std min max Portugal Mainland 134 -0.86 0.103 -1.087 -0.391 0.00 0.088 -0.248 0.499 Spain Mainland 313 -1.019 0.117 -1.325 -0.398 0.0 0.104 -0.231 0.515 S. Miguel (Azores) 77 0.440 0.258 0.102 1.057 0.000 0.125 -0.208 0.276 Faial (Azores) 33 -0.60 0.065 -0.720 -0.502 0.0 0.022 -0.041 0.043 Pico (Azores) 55 -0.645 0.196 -1.058 -0.297 0.0 0.125 -0.340 0.258 Terceira (Azores) 61 -0.566 0.111 -0.837 -0.211 0.00 0.090 -0.202 0.320 Lanzarote (Canary) 33 -0.048 0.081 -0.197 0.099 0.0 0.06 -0.123 0.123 Madeira (Madeira) 36 -0.198 0.146 -0.44 0.091 0.0 0.133 -0.251 0.281 (m)

Validation on Land

{

i

}

0 0 N i Z sin i Y sin cos i X cos cos p N i P H P h ) i 0 N ,i Z ,i Y ,i X ( f ∆ ∆ ∆ = − − − φ λ∆ + φ λ∆ + φ∆ + = -9.5 -9 -8.5 -8 -7.5 -7 -6.5 37 37.5 38 38.5 39 39.5 40 40.5 41 41.5 42

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Tailored to Portugal Geodesy

Correction surface

Determined from:

136 levelling marks

128 First order vertices

835 Second Order vertices

Tailored geoid precision

1 cm on levelling marks

3.2 cm on RGN pilars

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Height datum differences to WHS

U₀=62636860.850 m2_s-2 _; W₀=62636856.0 m2_s-2 _{(Bursa et al.,)} dW0 Lanz ar ote Ma deira Faial Pico S. Migue l Te rc ei ra Po rtugal Spain -0.4 -0.2 0.0 0.2 0.4 Relat ion bet ween vert ical dat a (m) Relative to ICAGM07 Relative to WHS

∑

=

_∫∫

_σ         σ ψ π γ + γ + γ ∆ − ∆ ∆ ∆ = − − n 1 j j 0 ,i 0 ,i 0 0 i i i i P i P P j d ). ( S 4 1 C 2 C W ) N , Z , Y , X ( f N H h 1 clk i io W W C U W W₀ = ₀− ₀ ; = ₀− ₀ ∆ Datum W0 (m2s-2) dH (cm) ICAGM07 62636855.395 6.2 Lanzarote 62636851.369 47.3 Madeira 62636852.730 33.4 Faial 62636856.438 -4.5 Pico 62636856.807 -8.2 S. Miguel 62636855.500 5.1 Terceira 62636856.094 -1.0 Portugal 62636858.840 -29.0 Spain 62636860.222 -43.1

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16

¾

Demonstrou-

Demonstrou

-

se que

é

possí

poss

ível, com os dados actuais,

vel, com os dados actuais,

determinar a ondula

ção do ge

ç

ão do geó

ó

ide com uma precisão melhor que

5 cm.

¾

Verificou-

Verificou

-se que

se que

é

possí

poss

ível estabelecer a liga

vel estabelecer a ligaç

ção entre os

ão entre os

data

verticais dos A

çores e do continente com um erro

ç

ores e do continente com um erro infeiro

infeiro

a 5 cm.

¾

Definiç

Defini

ç

ão de um ú

ão de um

único referencial geod

nico referencial geodé

ésico (

sico (planim

planimé

é

trico

e

altim

altimé

é

trico)

¾

Adopç

Adop

ção deste sistema na Infra

ão deste sistema na Infra-

-estrutura Nacional de

estrutura Nacional de

Informa

ç

ão Geográ

ão Geogr

áfica.

fica.

Recomenda

ç

ões

Conclusions

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17

Rio, M.-H. & Hernandez, F., 2004. A mean dynamic topography computed over the World Ocean from altimetry in situ measurements and a geóide model. J. Geophysical Research, 109, C12032,