737
1 INTRODUCTION
The determination of the height in the vertical
reference frame in force in Poland is based both on
nationalregulations(CouncilofMinistersRegulation,
2012) and on the resolution adopted by the EUREF
subcommittee(EUREFSymposium,2000).Currently,
thePL‐KRON86‐NHverticalreferenceframeisinuse
in Poland – a normal height system referred to a
quasi‐geoid of the av
erage level of the Baltic Sea
determined by the zero level of the mareograph in
Kronstadt.AccordingtotheRegulation,bytheendof
2019,PolandwilladoptthePL‐EVRF2007‐NHvertical
referenceframe,i.e. anormalheightsystemreferred
totheav
eragelevelofthe North Seadefinedby the
zero level of the mareograph in Amsterdam. The
ellipsoidal height of a point on the sea surface, for
example on a drilling platform, can be determined
using GNSS observations with the use of RTK
networktechnologyimplementedontheASG‐EUPOS
network. The evaluation of the potentia
l use of this
techniqueintheoffshoreareawasthesubjectofprior
research (Rogowski et al., 2015). The cited work
involved a number ofmeasurement experiments
conducted to evaluate the usability of the ASG‐
EUPOSsystemwiththeuseofRTK/
VRStechnology.
DataforcorrectionwasobtainedviatheInternetfrom
Orange mobile network. In the offshore area,
discrepanciesinthehorizontalcomponentreachupto
3cmbecausetheRTK/VRScorrectionisextrapolated.
Since the height component is determined with an
error twice as large, one can esti
mate thatit will be
determined with an error of up to 5 centimetres.
Another problem is the range of mobile network
whichcoversalmostthewholeGulfofGdańskbutin
the coastal zone does not exceed 10 Mm. These are
only estimates because, unfortunately, network
administrators do not want to share any data. The
tra
nsition to the normal height in the Amsterdam
systemrequirestheknowledgeoftheheightanomaly
obtained, as we propose, from the EGM 2008 geoid
model and the correction of the quasi‐geoid to the
averageNorthSea level.Forthispurpose,wesuggest
tousedatafromtheofficialPolishquasi‐geoidmodel
anddatafromanot
hermodeldistributedbyGUGiK.
The next step is to determine the height of a point
abovetheseafloor.Inthiscase,wecanuseanecho
Determination of normal heights in the area of Polish
Economic Zone
J
.B.Rogowski
GdyniaMaritimeUniversity,Gdynia,Poland
M.Kłęk
M
ariaSkłodowska‐CurieWarsawAcademy,Warsaw,Poland
ABSTRACT:ThearticlepresentsamethodofdeterminingtheleveloftheseabedinthePolishreferencesystem.
TheauthorsshowhowtodeterminetheellipsoidalheightoftheseabedusingGNSSmeasurementsandsingle‐
beamechosounders.Theauthorsproposethetransitiontothesystemofnormalheightsreferredtotheav
erage
leveloftheNorthSeaasdefinedbythetide‐gaugeinAmsterdamtobemadeusingtheEGM2008modeland
data from the official Polish quasi‐geoid model as well as data from another model distributed by GUGiK
(HeadOfficeofGeodesyandCartography).Theart
iclepresentsalsopotentialerrorsofthepresentedmethod.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 4
December 2017
DOI:10.12716/1001.11.04.22
738
sounder or employ methods typical for underwater
mining.
2 DESCRIPTIONOFTHEMETHOD
2.1 Geodeticheightsystems
Thefundamentalconceptinheightsystemsappliedis
theso‐calledgeopotentialnumberC.Itisequaltothe
differencebetweenthepotentialofthegeoidW
0and
of the point on the surface of the Earth W
P. The
following relationship can be shown between the
geopotential number C, gravitational acceleration g
andtheheighth.
0
0
P
P
C W W gdh
Depending on the gravitational acceleration used
todeterminetheheightsystem,wemayreceive:
H
ort
–orthometricheightsystem
ort
C
H
g
where:
g – average value of gravitational acceleration
between the geoid and the physical surface ofthe
Earth.
H
nor
–normalheightsystem
nor
C
H
where:
– the average value of normal gravitational
acceleration along the vertical line of the normal
gravityfield.
H
dyn
–dynamicheightsystem
45
0
dyn
C
H
where:
45
0
– the normal gravitational acceleration for
latitude45°.
Thenormalaccelerationofgravityisrelatedtothe
concept of equipotential ellipsoid that meets the
followingconditions:
Thesizeandshapeoftheellipsoidcorrespondto
the assumed ellipsoid that best approximates the
geoid,
Themassofthe ellipsoid
is equal tothemass of
theEarth.
The angular velocity of the ellipsoid spinω
corresponds to the velocity in the rotation of the
Earth.
The surface of an ellipsoid is by definition an
equipotential surface with potential U
0. This
potentialisequaltothepotentialonthegeoidW
0.
Thisconditionisasfollows:
00
UWconst
Normalaccelerationisequalto:
gradU
TheapplicableglobalGRS80referencesystemcan
berepresentedbythefollowingrelationship:
22
9.780327 1 0.0053024 0.0000058 2
s
in sin ms


where:
φ–latitude.
The vertical gradient of gravitational acceleration
canbecalculatedusingtheformula:

2
12
d
f
qfsinB
dh a

where:
a–semi‐majoraxisofellipsoid,
f–flatteningoftheellipsoid,
B–ellipsoidalwidth,
22
ab
q
GM
3 THEPRINCIPLEOFDETERMININGTHE
NORMALHEIGHTOFAPOINTATSEALEVEL
The principle of determining the normal heightof a
point at sea level, e.g. a drilling platform, research
vessel,etc.isshowninFigure1.
Figure1 Determining the normal height of a point at sea
level
AsfollowsfromtheprinciplepresentedinFigure
1, the quasi‐geoid model is required in order
todetermine normal height. We propose to use the
EGM 2008 model. The official Earth Gravitational
Model EGM2008 has been publicly released by the
U.S. National Geospatial‐Intelligence Agency (NGA)
EGMDevelopment Team.This
gravitational consists
ofsphericalharmoniccoefficientscompletetodegree
739
and order 2159, and contains additional coefficients
extending itto degree 2190 and order 2159. For this
model, there are online calculators available on the
following websites: http://earth‐info.nga.mil/GandG/
wgs84/gravitymod/egm2008/, http://icgem.gfz‐
potsdam.de/ICGEM/, http://www.softpedia.com/get/
Science‐CAD/AllTrans‐EGM2008‐Calculator.shtml.
Thesecalculatorsallowyoutodeterminetheheightof
a quasi‐geoid with
arelatively high accuracy (3 – 5
cm)andgridresolution(1ʹx1ʹ).Fortheareaweare
interestedin,wecancreateamapthatcanfurtherbe
used to determine the value corresponding to the
objectposition.AnexampleofsuchamapforGulfof
GdańskisshowninFig.2(Pałczyńska,2017).
The fact that all of the above calculators use the
WGS84ellipsoidproves to be problematic.A slight
differenceintheparametersoftheWGS84andGRS
80ellipsoidscanbefoundinthedataobtainedfrom
the
abovementionedcalculators.
Table1.
_______________________________________________
Parameters WGS84GRS80
_______________________________________________
a63781376378137
1/f298.257223563 298.257222101
_______________________________________________
Figure2MapofEGM2008quasi‐geoidforGulfofGdańsk
(Pałczyńska,2017)
Figure3NormalheightcorrectionreferredtotheEGM2008
quasi‐geoidtotheAmsterdamsystem.
Normal heights for the PL‐EVRF2007‐NHsystem
canbedeterminedusingΔζcorrectionfordatafrom
the EGM 2008 model and data from official models
published athttp://www.gugik.gov.pl/bip/prawo/
modele‐danych. The transition from the normal
heights referred tothe EGM 2008 quasi‐geoid to the
quasi‐geoid passing through the
zero level of the
mareographinAmsterdamisshowninFigure3.
Calculatingtheheightoftheseafloorrequiresthe
knowledge of the height difference between the
positionoftheGNSSantennaandtheseabed.Itcan
be determined with an echo sounder or with other
methodsusedinunderwater
mining.
4 SUMMARYANDCONCLUSIONS
The data necessary for the transition from PL‐
KRON86‐NHhighreferencesystemtoPL‐EVRF2007‐
NH system is available on the website of the Head
OfficeofGeodesy and Cartography at the following
address:http://www.gugik.gov.pl/bip/prawo/modele‐
danych. The data to determine the correction to the
EGM2008 quasi‐geoidinorder to calculateaheight
in the PL‐EVRF2007‐NH system can be obtained
through the comparison of the data from the Polish
official quasi‐geoid model available at
http://www.gugik.gov.pl/__data/assets/text_file/0017/
1844/gugik‐geoid2011.txt and data from the EGM
2008 model. The authors estimate that the error in
the
determination of the seabed height in the PL‐
EVRF2007‐NHframeamountstoabout10cm.
LITERATURE
Czarnecki K., (2010), Geodezja współczesna w zarysie.
Katowice:WydawnictwoGall.
RogowskiJ.,SpechtC.,WeintritA.,LeszczyńskiW.,(2015),
EvaluationofPositioningFunctionalityinASGEUPOS
forHydrographyandOff‐ShoreNavigation,TransNav:
International Journal on Marine Navigation and Safety
ofSeaTransportation,Vol.9No.2
,pp.221‐227.
PałczyńskaI.,(2017),OpracowaniemapygeoidyEGM2008dla
ZatokiGdańskiej.(Master’sthesis),FacultyofNavigation,
GdyniaMaritimeAcademy,Unpublishedmanuscript.
RegulationoftheCouncilofMinistersof15October2012on
thestatespatialreferencesystem,JournalofLawsofthe
Republic of Poland, Warsaw, 14 November 2012,
Item
1247(inPolish).
ResolutionNo.5oftheEUREFSymposiuminTromsø,22–
24 June 2000. Available from: http://www.euref.eu/
symposia/book2000/P_340_341.pdf
http://www.euref.eu/symposia/book2000/P_340_341.pdf
http://earth‐
info.nga.mil/GandG/wgs84/gravitymod/egm2008/
http://icgem.gfz‐potsdam.de/ICGEM/
http://www.softpedia.com/get/Science‐CAD/AllTrans‐
EGM2008‐Calculator.shtml
http://www.gugik.gov.pl/bip/prawo/modele‐danych
http://www.gugik.gov.pl/data/assets/text_file/0017/1844/gu
gik‐geoid2011.txt
http://www.gugik.gov.pl/data/assets/text_file/0016/1843/gu
gik‐evrf2007.txt