••;;. Scientltk ••:. Research
11 The 2nd China Satell ite Navigation Confere nce
Detecting the Lagoon Level Surface with GPS/RTK-Measurements Vag uer G. Ferreira' , Silvio R. C. de Freitas 2, Bernhard Heck) I
Department of Geomatics Science & En gineering. Hohai University. Nanj ing. China -' (;('o matics Department. Federal University ofParana, Curitiba, Brazil "Geodetic Institute of Karlsruhe. Karlsruh e University, Karlsru he. Germany Email: vagnel.gf@gma il.com.
[email protected]. hed V!J;:ik uni-karlsruhe.de
bst ract : The approach here presented is based in the use of a water surface as a reference for studying ysical aspects related to the gravity field. The purpose is to usc the mean sur face o f the lagoon system as an proximation of an equipotential sur face close to geoid. Instantaneous water levels were also observed in veral places with Glo bal Positioning System (GPS) where a single reference station provides the real-tim e corrections, in this case, the Real Time Kinematic (RTK) is a technique used. In addition, three tide gauges t registered the heights o f the water level in the lagoons were also used. It was possible to determine an proximatcd equipotentia l surface from the mean lagoon level (MLL) with accuracy better than 0.09 Jl1 and link it with the vertical datum . How to eliminate the instantaneous water level deviation from an equipotial surface during the campaign was the main hurdle to negotiate. 'cywords: heights; geoid; water level
tracting effects, meteo rological distur bances. local basin resonances a.n d un-rnodeled tidal driving forces w ith seasonal effects. Similar studies by using GPS on buoy are being conducted in Argentina with the aim of determining a local geoid model in the Tierra del Fuego, southern Argentine, from the dynamics of Lake Fagnano 121. In Baltic Sea, PI compared the gravimetric geoid 0 11 the sea areas with an independent method, like Gf'Svleveling on the mainland. They take into account the tilt o f water level at the moment of measurement and then was possible observed the relative change of the geoid , which serves as a comparison to the gravimetric geoid solution. The study is conducted in Brazi lian Vertical Datum Reg ion (BVD), southern Brazil in order to improve the geodetic control in this region. In this context, it was analyzed the behavior of three linked lagoons. the so called Imarui Lagoon System, under the influence of ocean dynamics in the contiguous region of the BVD. Finally, the connection of the local equipotential surface related to the Imarui Lagoon System with the BVD was realized from several points to the Datum. The lagoon system has a mean height close to orthomctric-zcro with respect to BV\) . The details of the approach arc provided in the next sections.
oduct ion many remote areas our knowledge about the geoid s not reach the increasing demands related with of the Global Positioning System (GPS) for all al survey purpo ses. The geoid determination has been traded in connection with the Geodetic ry Value Problem (GBVP) by using gravity ies referred to local height systems. A different h consists on using a natural water surface as a mdicator for an equipotential surface of the gravity GPS surveying methods, either kinematic GPS I Time Kinematic (RTK), GPSIRTK, the measts of water level and observations at tide gauge stations it is possible to establish an equipotential c. By analyzing of the hourly water level high it is le to determine an equipotential surface from the lagoons level (MLL) in the form: MLL = equipotential surface + e
( I)
the term s refers to the influence of several disg processes on the lagoon system. undistu rbed surface of the lagoons has not a regupe and cannot be express in a single mathematical I. If there were no tidal forcing, no differences in density, no currents and no atmospheric forcing, a surface would take the form of an equipotential , ce Ill . The same can be inferred for the lagoon sys10 a first approximation. The most impo rtant of poseffects over the lagoons are near offshore ocean s, density heterogeneities, surro und ing mass at-
2 Method From the measurements of the lagoon water levels it is possible to investigate jf the MLL can be considered a suitable reference for materializing an equipotential surface, TIle geometry of the proposed study is shown in the Figure I . .
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978- 1-935068 -73-0 '0 20 11 Scilccs.
·.;:. Scientific ••:. Research
S9: Basic Technologies and Scientific A pplication of Satellite Navig
I n ~ ti lll ta IWO~ l;lgf h l l1 l~\ ~ l
A very str aightforw ard interpol at ion is a linea r bination of the distance 'i = r(xu"\) between the and X o as defi ne in [hJ, in th is way we can get:
11',111, 1.
It
1;.l\i\,'~
](xo)= i > J (x,) ,. 1
J.)
w here Lag.n on bot tom
}!(r (x o' x ))
a, =
'
n
Lg(r(x o' x,) )
Figure I. Geometry for stu dying the M L L
I
in (5), the dista nce 'i
C onside ring F igure I it is possible to no te that the eq uipotential surface, W 1/U ' o f the Earth grav ity field
IXa -
de term ined from the MLL has no constant ellips oidal height h . The relationsh ip betw een elli pso ida l heigh ts ob tained from G PS measurement s and heights es tab lished spirit leveling and gravity data is given by (4]:
Xi
I
=r (-,o, x,)
is often c hose n to
I, the abs o lute val ue of the differenc e o f
X o ,with
Xi
g( r) being a function of the di sta nce.
According Figure 3, w ith the ob serva tion s of the w lev el (A, ) and homologou s points on land around lagoon sys te m ( Hi ) by G PSfRT K. it is possible irn
N=h- H
(2)
m ent a local lev eling network Vi E I. 2, 3. " ', n. J; the points AI a co rrec tion for the instantaneous de"
Where h is the el lipsoi dal hei gh t. H is the ortho metric height and N is the geo ida l height. The effect of the plumb line c urva ture ha s been neglected in the relation (2); a disc ussion fo r this prob lem ca n be fo und in, e.g.,
tion fo r each site shou ld be appl ied. In this process co ns idered the phase delays estim ated from the rela positi on betw ee n the two nea rest tide gauge sta tions.
[5)
The separation be tween the insta nta neo us lagoon level and M LL shown in Figure 2.
d
A
I
OJ
;,
----------------1-.1L1:
I
"-~- /
I!
3 1J "30'
3 1 J 00'
Figure 4. Posit ion of the tidal gauge stations related to Imar ui lagoon system and the BV D
(7) possible to see a very similar form of the resid ual tide Set ) series at each TG station (Figures 5. 6 and 7). T he
Z'J(1) is the mean sea level whi ch cha nges ly with time, T (I) is the tidal part of variation and
residua ls at each TG stat ion have shown a long period trend of dec reas ing level of abou t 50 em. Th e correlation analysis of the residua l time series from the TG stations, consider ing the phase lag between them is shown in Tab le 1. As shown, there is a strong correlation betw een the remaining signa ls at the TG stations .
is the meteorological surge com ponent. rn the harmonic tidal anal ysis it is also possible to secu lar tren ds but it is limited by the da ta w indow. spectral analysis can be con side red as an impo rtant because it can put in evidence red noise in the reI ride.
suits, Analysis and Discussion Tid al analysis
::
e water levels were continuously and simul tane. measured at three TG stati ons (TG-OI , TG-02 and 3 ) in the three lagoo ns. The distri bution of the staIS shown in Figure 4. In the present wo rk the time at each tide gauge wa s onl y 107 days lon g. For th is the analysis of secular trends is not reasonable. measuring the water level, an accur acy of around m for ind ividual tide gauges mean level det erminaafter harmon ic components discrimination and res determ inat ion, was possible. water level was measured with the 20 min utes infor sam pling . The pha se lag of the AI2 wave (the
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