ORIGINAL PAPER

Analysis of a relative offset between vertical datumsat the North and South Islands of New Zealand

Robert Tenzer & Nadim Dayoub & Ahmed Abdalla

Received: 7 June 2012 /Accepted: 11 February 2013 /Published online: 24 February 2013# Società Italiana di Fotogrammetria e Topografia (SIFET) 2013

Abstract The leveling networks realized by 13 differentlocal vertical datums were jointly readjusted at the Southand North Islands of New Zealand. The relation betweenthese two leveling networks and the Word Height Systemwas then defined using GPS-leveling data and the EGM08global geopotential model. In this study, we investigate therelative offset between these two vertical datum realizations.This is done based on comparison of the geometricgeoid/quasigeoid heights (obtained from GPS and newlyadjusted leveling data) with the regional gravimetricgeoid/quasigeoid solutions. Moreover, oceanographic andgeodetic models of mean dynamic topography (MDT) areused to assess the relative offset between these two verticaldatum realizations through the analysis of regional spatialvariations of mean sea level (MSL). The comparison ofGPS-leveling data with regional gravimetric solutions re-veals large systematic distortions (exceeding several deci-meters across New Zealand) between the geometric andgravimetric geoid/quasigeoid heights attributed mainly tosystematic errors within regional gravimetric solutions.The presence of a significant offset between the verticaldatum realizations at the North and South Islands is notconfirmed. The MSL difference between tide gauges inWellington and Dunedin of ∼24 cm is estimated based onthe analysis of MDT models.

Keywords Geoid/quasigeoid . Leveling . Mean dynamictopography . Offset . Vertical datum

Introduction

The geodetic vertical reference system at the North andSouth Islands of New Zealand was realized by 12 majorlocal vertical datums (LVDs) based on precise leveling from11 different tide gauges. The LVD Dunedin-Bluff 1960 wasdefined by fixing the heights of two leveling benchmarksfrom the LVDs Dunedin 1958 and Bluff 1955 instead ofusing the tide-gauge reference benchmarks as the origin.Moreover, additional LVDs were established for surveyingpurposes throughout the country based on precise levelingfrom tide gauges or connecting to existing leveling net-works. For a more detailed review of local leveling net-works in New Zealand and their realization, we referreaders to Gilliland (1987). The LVDs were defined in thesystem of the (approximate) normal-orthometric heights.The cumulative normal-orthometric correction to leveledheight differences was defined based on the GRS67 normalgravity field parameters. The computation of this correctionwas done approximately using a truncated form of theGRS67 normal-orthometric correction formula (Rapp1961). Since LVDs were referenced to the local mean sealevel (MSL) determined based on the analysis of tide-gaugerecords at a certain time, large discrepancies (up to severaldecimeters) exist between individual LVDs.

The unification of LVDs is done typically by a jointadjustment of local leveling networks. Alternatively, gravitydata are used to determine a geoid/quasigeoid model whichis then adopted as the height reference surface. Amos andFeatherstone (2009) argued that the practical implementa-tion of the unified vertical datum in New Zealand through ajoint leveling network adjustment is problematic due to

R. Tenzer (*) :A. AbdallaNational School of Surveying, University of Otago,310 Castle Street,Dunedin, New Zealande-mail: robert.tenzer@surveying.otago.dc.nz

N. DayoubDepartment of Topography, Faculty of Civil Engineering,Tishreen University, Lattakia, Syria

Appl Geomat (2013) 5:133–145DOI 10.1007/s12518-013-0106-8

several factors such as the realization of leveling networksover several decades and their poor spatial coverage, thedefinition of MSL from short-term tide-gauge records, thetectonic configuration of New Zealand characterized bylarge horizontal and vertical motions and sea level variabil-ity. They proposed and applied the iterative gravimetricapproach to compile the first gravimetric quasigeoid modelfor New Zealand–NZGeoid05. Their approach utilizes aniterative determination of the regional gravimetricquasigeoid model and its comparison with the geometricquasigeoid heights obtained from GPS-leveling data foreach LVD. In more recent study, Claessens et al. (2011)used the same approach to determine the regionalquasigeoid model–NZGeoid2009. NZGeoid2009 is the cur-rently adopted official national quasigeoid model for NewZealand. In the most recent studies, the new experimentalregional geoid and quasigeoid models were compiled forNew Zealand using different computational techniques.Abdalla and Tenzer (2011) compiled a gravimetric geoidmodel using the KTH method. For a more detailed descrip-tion of the KTH method, we refer readers to Sjöberg (1991,2003a, b, c). Numerical aspects of the KTH method areexplained, for instance, by Ågren et al. (2009). Tenzer etal. (2012a) applied the boundary element method (BEM) todetermine a gravimetric quasigeoid model for New Zealand.Theoretical and numerical aspects of this method arediscussed in Čunderlík et al. (2008) and Čunderlík andMikula (2009). The latest experimental regional gravimetricquasigeoid model for New Zealand is OTG12 (Abdalla andTenzer 2012b). OTG12 was compiled based on applying thediscretized integral-equation approach for solving the near-zone contribution (see Tenzer and Novák 2008; Tenzer andKlees 2008; Tenzer et al. 2012b). The far-zone contributionto quasigeoid heights was computed using the far-zonemodified spherical harmonics according to the method de-scribed in Tenzer et al. (2009, 2011a).

Despite the aforementioned deficiencies of levelingdata, the accurate determination of the gravimetricgeoid/quasigeoid model is also restricted due to aninsufficient and irregular spatial coverage of terrestrialgravity data in New Zealand. Therefore, levelingdatasets in combination with GPS and gravity data areessential for the realization of a more reliable verticalreference system. Tenzer et al. (2011b) applied the com-bined method for the unification of leveling networks inNew Zealand. This method utilizes the joint levelingnetwork adjustment and a subsequent application ofthe geopotential-value approach. They used the levelingand normal gravity data for a joint adjustment of level-ing networks at the South and North Islands of NewZealand while fixing the heights of tide-gauge referencebenchmarks in Dunedin and Wellington. Their resultsrevealed a good relative precision of leveling data; the

STD of least-squares residuals for the whole countrywas found to be 2 mm. The comparison of the newlydetermined and original normal-orthometric heights con-firmed the presence of large local vertical datum offsetsas well as (local) systematic leveling errors. The GPS-leveling data and the EGM08 global geopotential model(GGM) were then used to estimate the average offsetsof these two vertical datum realizations with respect tothe World Height System (WHS). WHS was defined bythe adopted geoidal geopotential value of W0 =62,636,856±0.5 m2s−2 (Burša et al. 2007). The estimat-ed offsets for the jointly adjusted leveling networks atthe North and South Islands were found to be 10.6 and27.5 cm, respectively (Tenzer et al. 2011b); it corre-sponds to a relative offset between the vertical datumsat the North and South Islands of 16.9 cm. The finalnormal-orthometric heights were obtained from the ad-justed normal-orthometric heights by applying these es-timated offsets.

Different values of W0 were reported by Sanchez (2007)and Dayoub et al. (2012). Sanchez (2007) determined thevalue of W0 using different MSL models and differentGGMs, showing that the choice of MSL and GGM isunimportant for estimating W0, while the latitude domainof the altimetry-derived MSL models plays a major role.The value of W0 estimated by Sanchez (2007) differs by2.5 m2s−2 from the value estimated by Burša et al. (2007). Ina more recent study, Dayoub et al. (2012) reviewed previousstudies using various methods and datasets. They confirmedthe conclusions of Sanchez (2007) but reported andrecommended the value of W0=62,636,854.2±0.2 m2s−2

which differs from the previous two estimates. They alsoconcluded that the dependency ofW0 on the latitude domainis due to MDT. It is worth mentioning that the choice of W0

is not essential for a definition of WHS as the accuraterealization of WHS depends merely on the accurate globalgeoid/quasigeoid model and reliable GPS and leveling data.

In this study, we investigate the reliability of appliedoffsets to the newly established leveling networks at theNorth and South Islands. This is done based on analysis ofthe differences between the geometric (GPS leveling)geoid/quasigeoid heights and the regional gravimetric solu-tions. The relative offset between vertical datums definedwith respect to MSL, observed at tide gauges in Dunedin(South Island) and Wellington (North Island), is also esti-mated based on the analysis of oceanographic and geodetic(altimetry–gravimetric) MDT models.

Input data acquisition

Comparison of the geometric geoid/quasigeoid heights withthe regional gravimetric geoid/quasigeoid solutions requires

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conversion of the newly adjusted normal-orthometricheights (and corrected for the average offsets relative toW0) into the systems of (Molodensky’s) normal and(Helmert’s) orthometric heights. The conversion of thenormal-orthometric to normal heights was done based onapplying the cumulative normal to normal-orthometricheight correction computed from the leveling and gravityanomaly data according to the formula given in Tenzer et al.(2011b). In the absence of the observed gravity data, thegravity anomalies along the leveling lines were generatedfrom the EGM08 coefficients (Pavlis et al. 2008) completeto spherical harmonic degree 2160 (referred in the tide-freesystem). The computed values of the normal to normal-orthometric height correction at the North Island’s levelingbenchmarks are between −4.9 and 10.7 cm. The correspond-ing values of this correction at the South Island’s levelingbenchmarks are between −2.6 and 5.7 cm (cf. Tenzer et al.2011b). The calculated normal heights were then convertedto the orthometric heights by applying the geoid-to-quasigeoid correction. This correction term was computedapproximately as a function of the topographic height andthe simple planar Bouguer gravity anomaly at the levelingbenchmarks (cf. Santos et al. 2006, and reference herein).The values of gravity anomalies at leveling benchmarkswere again generated from the EGM08 coefficients. Thecomputed values of the geoid-to-quasigeoid correction atthe North Island’s leveling benchmarks are between −1.5and 9.0 cm and between −2.5 and 6.5 cm at the SouthIsland’s leveling benchmarks (cf. Tenzer et al. 2011b). Thecorresponding differences between the orthometric andnormal-orthometric heights at leveling benchmarks varybetween −3.2 and 13.0 cm (at the North Island) and between−2.9 to 7.9 cm (at the South Island).

The testing network in New Zealand consists of 1452GPS-leveling benchmarks (772 at the North Island and 680at the South Island). The configuration of GPS-levelingpoints is shown in Fig. 1. The geodetic (ellipsoidal) heightsabove the reference ellipsoid GRS80 are defined in the NewZealand Geodetic Datum 2000 (NZGD2000). NZGD2000 isaligned to the International Terrestrial Reference Frame atthe reference epoch of January 1, 2000 (Blick et al. 2005).

The official quasigeoid model NZGeoid2009 is suppliedto users on a 1×1 arc-deg geographical grid by the LandInformation New Zealand. The experimental geoid andquasigeoid models KTH, BEM and OTG12 were compiledon a 2×2 arc-deg geographical grid. The values of thegeoid/quasigeoid heights at the locations of GPS-levelingtesting points were determined from grid values by applyinga surface fitting technique using a linear weighted function.

We used five different MDT solutions offshore NewZealand to investigate the MSL differences between thetide gauges in Dunedin and Wellington. These MDTmodels include the oceanographic models CSIRO Atlas

of Regional Seas 2009 (CARS2009; Ridgway et al.2002) and the Estimating the Circulation and Climateof the Ocean, Phase II (ECCO2; Menemenlis et al.2008). In addition, we used the geodetic DanishTechnical University MDT model (DTU10; Andersen2010) and the second DOT model DOT.DNSC08MSS-EGM08 from GRACE/JPL. We also employed ageodetic MDT solution derived from the CNES CLS11global mean sea surface (Scharroo 2011; Schaeffer et al.2011) after subtracting the EGM08 marine geoidheights. CLS11 and EGM2008 were made consistentin terms of the reference ellipsoid and tide system(i.e., mean tide). The MDT solutions CARS2009,ECCO2, DTU10, DOT.DNSC08–EGM08, and CLS11–EGM08 at New Zealand’s offshore study area (boundedby the parallels of 30 and 50 arc-deg southern latitudesand the meridians of 165 and 180 arc-deg eastern lon-gitudes) are shown in Fig. 2; the corresponding statisticsare summarized in Table 1.

As seen in Fig. 2, the oceanographic MDT modelsCARS2009, ECCO2, and DOT.DNSC08–EGM08 have alow resolution and spatial coverage. CARS2009 andECCO2 have also a significantly smaller range of valueswithin the study area than the geodetic MDT models; therange of CARS2009 is 81 cm, while it is 71 cm for ECCO2.The MDT range of DTU10 and CLS11–EGM08 is 100 cm.The DOT.DNSC08–EGM08 has the largest MDT variations

Fig. 1 GPS-leveling testing network in New Zealand

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within the study area at the range of 110 cm. All theinvestigated MDT solutions show a similar pattern withprevailing zonal trend of increasing MDT towards tropicalseas due to latitudinal thermal gradient. Regional anomalouspattern associated with the configuration of ocean currents

(dominated by the influence of Tasman and Sub-AntarcticFronts) can also be recognized; for more details, we referreaders to Tenzer et al. (2012a). For our analysis, the mostsignificant regional feature is a slightly higher MSL inWellington compared to Dunedin’s coastal sea.

Fig. 2 Oceanographic andgeodetic MDT solutions: aCARS2009, b ECCO2, cDTU10, d DOT.DNSC08–EGM08, and e CLS11–EGM08

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Numerical analysis

The newly determined orthometric/normal heights at theGPS-leveling testing network were compared with fourregional geoid/quasigeoid models. The geometric geoidheights were calculated from the NZGD2000 geodetic

heights by subtracting the orthometric heights. The geomet-ric quasigeoid heights (i.e., height anomalies) were obtainedfrom the NZGD2000 geodetic heights by subtracting thenormal heights. The differences between the geometric andgravimetric geoid heights were computed for the KTH geoidmodel. The corresponding differences between the geomet-ric and gravimetric quasigeoid heights were computed forthe NZGeoid2009, BEM, and OTG12 quasigeoid models.The same analysis was done using also the original levelingdata defined in 13 LVDs. The differences between the geo-metric and gravimetric geoid/quasigeoid heights for the newlyadjusted and original leveling data are plotted in Figs. 3 and 4,respectively.

The averaged values of differences between the geo-metric and gravimetric geoid/quasigeoid heights at GPS-leveling points were used to estimate the relative offsetbetween the vertical datum realizations at the North andSouth Islands. This was done for the newly adjusted

Fig. 3 Differences between the geometric and gravimetric geoid/quasigeoid heights along meridional (left panels) and parallel (rightpanels) profiles computed using: a KTH, b NZGeoid2009, c BEM, andd OTG12. The geometric geoid/quasigeoid heights were computed

based on the jointly adjusted leveling data at the South and NorthIslands (and corrected for the average offsets relative toW0). The linearregression analysis was applied to fit the differences by a linear trendfunction for each island

Table 1 Statistics of the MDT models: CARS2009, ECCO2, DTU10,DOT.DNSC08–EGM08, and CLS11–EGM08 within the study areashown in Fig. 2

MDT Min(cm)

Max(cm)

Mean(cm)

STD(cm)

CARS2009 164 245 216 17

ECCO2 −24 47 11 20

DTU10 −7 93 58 19

DOT.DNSC08–EGM08 −49 61 27 19

CLS11–EGM08 −31 69 29 18

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leveling data. Moreover, we repeated these computationsusing also the original leveling data attributed to 13LVDs. The results are summarized in Tables 2 and 3.

The estimation of a relative offset between verticaldatum realizations at the North and South Islands couldbe biased by the presence of systematic trend which isseen in plotted differences between the geometric andgravimetric geoid/quasigeoid heights (cf. Fig. 3).Therefore, we estimated the relative offset between theNorth and South Island’s newly established verticaldatums from these differences but taken only at GPS-leveling points in the vicinity of tide gauges inWellington and Dunedin. The results are summarizedin Table 4.

We further investigated the character of systematicdistortions within the leveling networks and regionalgravimetric solutions based on their comparison withthe EGM08 quasigeoid model (computed using thespherical harmonic coefficients complete to degree/orderof 2160). The differences between the GPS-leveling andEGM08 quasigeoid heights for the original and newly

adjusted leveling data are plotted in Fig. 5; statistics ofthese differences are given in Table 5. The differencesbetween the regional gravimetric solutions and EGM08are plotted in Fig. 6; statistics of these differences aregiven in Table 6. The geoid-to-quasigeoid correctionwas applied to the KTH geoid heights for the compar-ison with EGM08.

Finally, we estimated the values of the MSL offset betweentide gauges in Wellington and Dunedin using the MDT solu-tions CARS2009, ECCO2, DTU10, DOT.DNSC08–EGM08,and CLS11–EGM08. The MSL values were calculated byextrapolating the MDT grid values in the vicinity of thesetwo tide gauges. The results are summarized in Table 7.

Discussion

The comparison of the regional gravimetric solutions withthe newly adjusted leveling data (corrected for the averageoffsets relative to W0) shown in Fig. 3 revealed large dis-crepancies. For KTH and NZGeoid2009, the differences

Fig. 3 (continued)

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between the geometric and gravimetric geoid/quasigeoidheights are mainly positive with the largest values at thelower South Island and the corresponding smallest differ-ences at the upper North Island. The significant bias be-tween the BEM gravimetric solution and leveling data isabsent. The largest absolute differences (exceeding ∼50 cm)are seen at the lower South Island and at the upper NorthIsland. The differences between GPS-leveling data andOTG12 reach maxima (of ∼1 m) in the central SouthIsland, while the largest negative differences (of ∼−40 cm)are found at the upper North Island. Elsewhere in the NorthIsland, these differences are typically within ±20 cm.

As seen from these results, the KTH and NZGeoid2009gravimetric solutions are biased with respect to the GPS-leveling results. In addition, the presence of a large systematictrend across New Zealand is seen in all four gravimetricsolutions. The BEM and OTG12 gravimetric solutions have

the largest systematic discrepancies (reaching up to ∼1 m).The misfits of the KTH and NZGeoid2009 gravimetric solu-tions with respect to GPS-leveling data are more similar; therange of the geoid/quasigeoid heights differences is ∼40 cm(for KTH) and ∼50 cm (for NZGeoid2009). These largediscrepancies can be explained by systematic errors withineither gravimetric solutions or leveling data. On the other hand,the presence of a relative offset between the vertical datumrealizations at two islands is less obvious. The geoid/quasigeoidheight differences at GPS-leveling points at the upper SouthIsland and the lower North Island (plotted in Fig. 3) have arelatively smooth character without any significant (inter-islands) discontinuity. Similarly, the linear regression fits ofthe differences between the geometric and gravimetricgeoid/quasigeoid heights computed separately for each islanddo not show significant misfit. This is evident especially for theKTH and NZGeoid2009 solutions. The misfit of the linear

Fig. 4 Differences between the geometric and gravimetric geoid/quasigeoid heights along meridional (left panels) and parallel (rightpanels) profiles computed using: a KTH, b NZGeoid2009, c BEM, andd OTG12. The geometric geoid/quasigeoid heights were computed

using the original leveling data attributed to 13 LVDs. The linearregression analysis was applied to fit the differences by a linear trendfunction for each island

Appl Geomat (2013) 5:133–145 139

regression trends between both islands is less than 10 cm, whilethe corresponding misfit for BEM and OTG12 is ∼20 cm.

In order to better understand the large discrepancies whichwere found between the regional gravimetric solutions and

GPS-leveling data, we further computed the correspondingdifferences while using original leveling data. As seen inFig. 4, the systematic trend and bias in the computed differ-ences between GPS-leveling and gravimetric results is now

Fig. 4 (continued)

Table 2 Values of the relative offset between vertical datum realizations at the North and South Islands computed for the newly adjusted levelingdata using four regional gravimetric solutions (KTH, NZGeoid2009, BEM, and OTG12)

Model KTH NZGeoid2009 BEM OTG12

North Island Min (cm) −70 0 −75 −46

Max (cm) 118 91 70 85

STD (cm) 13 12 16 14

Mean (cm) 40 42 −17 5

South Island Min (cm) −49 17 −84 −44

Max (cm) 100 99 86 121

STD (cm) 14 13 23 18

Mean (cm) 65 63 23 61

Relative offset (cm) −25 −21 −40 −56

Statistics of the differences between the geometric and gravimetric geoid/quasigeoid heights computed individually at the North and South Islands(Table 2)

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much less pronounced. The regional gravimetric solutionsthus better agree with the original leveling data defined in 13LVDs. The KTH and NZGeoid2009 models are systematical-ly biased (of ∼50 cm) from GPS-leveling results. The BEMquasigeoid model is more consistent with GPS-leveling re-sults. The systematic discrepancies are, in this case, seenparticularly at the South Island, where the range of differencesis ∼40 cm. The OTG12 quasigeoid model has, on the otherhand, significantly different fit with GPS-leveling data at theSouth and North Islands.

As seen from the results summarized in Tables 2 and 4,the relative offsets computed when taking into consider-ation only the GPS-leveling points close to tide gauges inWellington and Dunedin are similar to that found whenusing all GPS-leveling points. The estimated relative off-sets are 17 cm (for KTH) and 26 cm (for NZGeoid2009).The relative offsets for BEM and OTG12 are about twotimes larger, namely 52 cm (for BEM) and 44 cm (forOTG12).

The comparison of GPS-leveling data with EGM08(shown in Fig. 5) revealed slightly better agreement of thenewly adjusted leveling data in terms of the mean of differ-ences. The mean of differences is 1 and −3 cm for the Northand South Islands, respectively. The corresponding mean

values of differences obtained when using the original level-ing data are −5 cm (for the North Island) and 5 cm (for theSouth Island). The STD of differences computed using thenewly adjusted leveling data is 11 cm for both islands. TheSTD of differences of 8 cm was found for the originalleveling data at the South Island, while the STD of differ-ences at the North Island is 14 cm.

As seen in Fig. 6, all four regional gravimetric solutions aresystematically displaced from EGM08. The discrepanciesbetween EGM08 and the KTH and NZGeoid2009 regionalgravimetric solutions are similar with the range of differencesapproximately within −80 to−30 cm. A much larger range ofdifferences (approximately within −80 to 40 cm) was foundbetween the EGM08 and BEM quasigeoid heights. Thequasigeoid height differences between the EGM08 andOTG12 models are mainly within −80 and 20 cm.

The analysis of MSL in the vicinity of tide gauges inWellington and Dunedin based on five MDT models showedthat the MSL offsets between these two tide gauges arebetween 18 and 25 cm when taking into consideration onlythe results of the geodetic models DTU10, DOT.DNSC08–EGM08, and CLS11–EGM08 (cf. Table 7). The MSL offsetof 29 cm was found for the oceanographic model CARS2009,while it was only 1 cm for ECCO2. The representative MSL

Table 3 Values of the relative offset between vertical datum realizations at the North and South Islands computed for the original leveling data(defined in 13 LVDs) using four regional gravimetric solutions (KTH, NZGeoid2009, BEM and OTG12)

Model KTH NZGeoid2009 BEM OTG12

North Island Min (cm) −45 −36 −109 −80

Max (cm) 118 140 131 85

STD (cm) 15 15 15 14

Mean (cm) 46 48 −11 11

South Island Min (cm) −56 −55 −90 −51

Max (cm) 93 94 81 126

STD (cm) 12 11 22 16

Mean (cm) 57 55 23 53

Relative offset (cm) −11 −7 −34 −42

Statistics of the differences between the geometric and gravimetric geoid/quasigeoid heights computed individually at the North and South Islands

Table 4 Values of the relative offset between vertical datum realizations at the North and South Islands computed for the newly adjusted levelingdata using four regional gravimetric solutions (KTH, NZGeoid2009, BEM, and OTG12)

Gravimetric model KTH NZGeoid2009 BEM OTG12

North Island Mean (cm) 56 54 10 31

STD (cm) 2 3 2 3

South Island Mean (cm) 73 80 62 75

STD (cm) 6 5 6 4

Relative offset (cm) −17 −26 −52 −44

The differences between the geometric and gravimetric geoid/quasigeoid heights were averaged from the values taken at GPS-leveling points in thevicinity of tide gauges in Wellington and Dunedin

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offset obtained by averaging these results is ∼19 cm. Whendisregarding ECCO2 model (which is more likely unrealisti-cally small), the average MSL offset increases to ∼24 cm.

Summary and concluding remarks

We investigated the relative offset between the verticaldatums at the North and South Islands of New Zealandrealized based on the joint leveling network adjustmentand a subsequent application of the geopotential valueapproach for finding their relative offsets with respect toWHS (defined by the adopted value of the geoidalgeopotential value W0). A possible presence of suchrelative offset could be due to various reasons whichare attributed to the EGM08 commission and omissionerrors as well as systematic errors within GPS and

leveling data. Moreover, additional aspects can affectthe results such as an inconsistent use of permanent tidalsystems and geodetic reference frames and definitions.Not less significant contributions could be caused byvertical tectonic motions, mean sea level variations, andother temporal changes associated with the definitionsand realizations of geodetic vertical datums.

We applied two principally different methods to estimatethe relative offset between the vertical datum realizations atthe North and South Islands. First, we compared GPS-leveling data with regional gravimetric solutions. The re-gional gravimetric solutions were also compared with theglobal model EGM08. Abdalla and Tenzer (2012a)conducted a comparative analysis of the most recentsatellite-only GRACE and GOCE models with EGM08(using spherical harmonics up to degree 250). They haveshown that EGM08 has the best regional agreement with

Fig. 5 Differences between the geometric and EGM2008 (gravimetric) quasigeoid heights computed using: a the original leveling data attributedto 13 LVDs and b the newly adjusted leveling data (and corrected for the average offsets relative to W0)

Table 5 Statistics of the differences between the GPS-leveling and EGM08 quasigeoid heights computed using the original and newly adjustedleveling data shown in Fig. 5

North Island South Island

Original leveling data Newly adjusted leveling data Original leveling data Newly adjusted leveling data

Min (cm) −68 −46 −33 −40

Max (cm) 51 44 40 32

Mean (cm) −5 1 5 −3

STD (cm) 14 11 8 11

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GPS-leveling data in terms of the STD of residuals. Wefurther used various oceanographic and geodetic MDT so-lutions to estimate the MSL offset between the tide gaugesin Wellington and Dunedin. In the comparison between thegeometric and gravimetric geoid/quasigeoid solutions, themajor contribution to the overall error budget is mainly dueto possibly existing systematic errors within leveling net-works and regional gravimetric solutions. On the otherhand, the accuracy estimation of the MSL offset betweentwo (or more) tide gauges (which were used as the origins

for a realization of vertical datums) is restricted mainly by alow accuracy of altimetry data in coastal seas as well as theinaccuracies of a regional marine geoid model.

The analysis of MDT models (CARS2009, DTU10,DOT.DNSC08–EGM08, and CLS11–EGM08 whiledisregarding ECCO2) revealed that the average MSLoffset between tide gauges in Wellington and Dunedinis ∼24 cm. This value is approximately ∼7 cm largerthan the estimated relative offset (16.9 cm) between thejointly adjusted leveling networks at the North and South

Fig. 6 Differences between the EGM08 and regional gravimetric geoid/quasigeoid models: a KTH, b NZGeoid2009, c BEM, and d OTG12

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Islands obtained from their comparison with WHS (cf.Tenzer et al. 2011b).

Since all the regional gravimetric solutions were com-piled from the terrestrial gravity disturbances/anomalies de-fined with respect to the original heights in LVDs, thecomparison of the newly adjusted leveling data with thesegravimetric solutions should reveal the offset between theSouth and North Islands. This assumption was to someextent confirmed by the results obtained from comparingthe KTH and NZGeoid2009 gravimetric solutions withGPS-leveling data. The values of relative offset betweenthe vertical datum realizations and regional gravimetric so-lutions are 25 cm (for KTH) and 21 cm (for NZGeiod2009).The corresponding relative offsets of 17 cm (for KTH) and26 cm (for NZGeiod2009) were obtained when averagingthe geoid/quasigeoid height differences only at GPS-leveling points in close proximity of tide gauges (in orderto avoid a possible effect of systematic errors within level-ing networks and/or regional gravimetric solutions). Allthese estimates of relative offsets are about two timessmaller than the corresponding values obtained from thecomparison of the BEM and OTG12 regional gravimet-ric solutions with GPS-leveling data. The estimates forBEM and OTG12 are more likely unrealistically large.Our results showed that these two gravimetric solutions

have the largest misfits compared to all other solutionsused for the analysis in this study.

The numerical results further showed that the relativeoffset between the vertical datum realizations at theNorth and South Islands was to a large extent eliminat-ed by correcting the heights of leveling benchmarks forthe offset with respect to WHS (after applying thegeopotential-value approach). This is evident from theplotted values of differences between the GPS-levelingdata and regional gravimetric solutions in Fig. 3. Asseen, these differences do not show significant (inter-islands) discontinuity. This finding was also confirmedfrom the comparison of the newly adjusted leveling datawith EGM08 (cf. Fig. 5a). These differences have acontinuous character between both islands.

The comparison of the regional gravimetric solutions withGPS-leveling data revealed the presence of large systematicdiscrepancies. A significant portion of these discrepancies ismore likely to be attributed to the systematic errors withinregional gravimetric solutions. Another source of errors es-pecially at the South Island is due to a low coverage orabsence of gravity measurements throughout the SouthernAlps. Since reliable information about the accuracy of usedgravity, leveling and GPS data are not available, the erroranalysis was not conducted in this study.

Table 7 Values of the MSL offset between the tide gauges (TG) in Wellington and Dunedin computed using the MDT solutions: CARS2009,ECCO2, DTU10, DOT.DNSC08–EGM08, and CLS11–EGM08

Model CARS2009 ECCO2 DTU10 DOT.DNSC08–EGM08 CLS11–EGM2008

TG Wellington (North Island) Min (cm) 201 −3 50 19 12

Max (cm) 216 −2.6 63 31 37

STD (cm) 1 0 3 3 6

Mean (cm) 206 −2 55 23 20

TG Dunedin (South Island) Min (cm) 176 −8 29 −5 −5

Max (cm) 177 −2 42 6 13

STD (cm) 1 1 2 2 3

Mean (cm) 177 −3 31 −2 2

Relative offset (cm) 29 1 24 25 18

Table 6 Statistics of the differences between the EGM08 quasigeoid model and the regional gravimetric solutions (KTH, NZGeoid2009, BEM,and OTG12) shown in Fig. 6

KTH NZGeoid09 BEM OTG12

North Island South Island North Island South Island North Island South Island North Island South Island

Min (cm) −62 −114 −51 −108 −12 −94 −26 −141

Max (cm) −27 −36 −25 −43 41 21 10 −17

Mean (cm) −42 −65 −44 −59 16 −28 −6 −58

STD (cm) 6 11 3 9 10 20 7 17

144 Appl Geomat (2013) 5:133–145

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