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Global Height System Unification
by means of the GOCE Geoid
1
Michael G. Sideris and Elena V. Rangelova Department of Geomatics Engineering, University of Calgary
International Jubilee Conference UACEG2012: Science & Practice
UNIVERSITY OF ARCHITECTURE, CIVIL ENGINEERING AND GEODESY 15-17 NOVEMBER 2012
Motivation
Essential for global change monitoring SL change; ocean circulation; coastal hazards
2
Source: J. Ihde, BKG
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Motivation
Essential for global change monitoring SL change; ocean circulation; coastal hazards
Proliferation of vertical datums >100 height systems and chart datums, inconsistently realized
3
Source: J. Ihde, BKG
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Motivation
Essential for global change monitoring SL change; ocean circulation; coastal hazards
Proliferation of vertical datums >100 height systems and chart datums, inconsistently realized
Promise of gravity missions GOCE: 1-2 cm geoid globally at 100 km resolution
4
Source: J. Ihde, BKG
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Motivation
Essential for global change monitoring SL change; ocean circulation; coastal hazards
Proliferation of vertical datums >100 height systems and chart datums, inconsistently realized
Promise of gravity missions GOCE: 1-2 cm geoid globally at 100 km resolution
International initiatives towards height system unification EUVN-DA: Densification Action of the European Unified Vertical Network EVRF2007: European Vertical Reference Frame 2007 NA Height Modernization: Establishment of a geoid-based NA vertical datum IAG ICP1.2: Vertical Reference Frames GGOS Theme 1: Global Unified Height System ESA STSE GOCE+ Theme 1: Height System Unification with GOCE
5
Source: J. Ihde, BKG
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Vertical Reference Frame (1)
Definition The realization of a system for elevations that supports physical and geometric heights globally with ppb relative accuracy
Recall that h = H + N = H* + ζ and dH = -dW/g Geometrical (ellipsoid, h) and physical (geoid, H or C) components must be specified Po, W(Po) = Wo
Vertical Datum A level, zero-height surface with a conventional value Wo A Wo value does not imply knowledge of the level surface itself
Realization and Unification Data: GNSS/SLR, geodetic & ocean leveling, TGs, altimetry, gravity, GGMs Zero-tide system (BVP solution requirement) Convert C to H or H*, or vice versa Select/determine global Wo value Determine local Wo
j values and connect Woj to Wo
6
Credit: Hofmann-Wellenhof & Moritz, 2006
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Vertical Reference Frame (2) Wo can be obtained from, e.g., ellipsoidal parameters (Wo = Uo), or computed/assigned to a tide gauge
or from a GGM and/or altimetry and/or MSL fit
or from the solution of a (generalized) geodetic BVP
WP can be obtained either from the BVP solution for TP
WP = UP + TP or from levelling plus gravity (given Wo)
or from GNSS/SLR and
geodetic/ocean levelling
TP = γNP = γ (hP – HP)
Consistent use of standards, theory and data is essential
7
Source: IAPG
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Determination of Wo (1)
Classical (physical) approach to Wo The geoid: a level surface having a conventional Wo value
Select Wo = Uo (potential of reference ellipsoid)
Problems with the geoid surface: Surface is unknown
Surface not optimally approximating the mean sea level (MSL)
The geodetic/oceanographic approach to Wo The (Gauss-Listing) geoid: level surface around which the average permanent
SST, HS, is near zero when averaged globally over all oceanic regions Ss
WP computed from gravity data
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
8
Determination of Wo (2)
Open problems Spatial coverage/integration area and Choice of models ~14 cm from 80°/80° to 60°/60° ocean coverage
Choice of reference epoch and long-term variations of MSL (and PGR) All data sets must be referenced to reference epoch (by international convention)
Choice of tide system Zero-tide geoid & zero/mean-tide crust, plus transformations to other tide systems
Maximum degree, nmax, of (satellite-only?) GGM nmax of 140 to 200 seems to be sufficient (Bursa et al., 2007)
GOCE-derived models are prime candidates!
International Jubilee Conference UACEG2012: Science & Practice
15-17 November 2012, Sofia 9
GOCE's Contribution (1)
GOCE: Gravity field and steady-state Ocean Circulation Explorer Measures 1st derivatives of g
Relevant applications Geodesy: geoid, gravity, height systems Oceanography: improved MSL/ocean
circulation
COCE contributes the long to medium wavelengths of the geoid-based vertical datum
10 International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
GOCE's Contribution (2)
Mission specifications Geoid & geoid accuracy: 1-2 cm & 1 mGal Resolution: 100 km (half-wavelength) or nmax = 200
Current/future performance status Accuracy estimates for GOCE stand-alone solutions
11
Credit: R. Pail, IPAG
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
source: Sanchez (modified)
Vertical Datum Unification (1)
Principle
In a global datum (no superscript), as well as in a local datum (superscript j),
h = H*+ ζ, or h = H + N, should be satisfied for all points P
Simplified vertical datum unification Application of the above equations on land, at tide gauges and in oceans in
iterative (due to various inconsistencies) least-squares solution schemes 12 International Jubilee Conference UACEG2012: Science & Practice
15-17 November 2012, Sofia
Vertical Datum Unification (2)
Rigorous BVP Approach to Datum Unification with GOCE The global datum: Po, W(Po) = Wo, ∆Wo = Wo - Uo
Problem input and output:
The local datum: Poj, W(Po
j) = Woj, δWo
j = Wo - Wo
j
Problem input and output:
The datum potential offset, δWoj, causes both a direct effect on N, δNj, and an
indirect effect δTj/γ through the gravity anomalies
13 International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
∑++=−−−=
J
i
iPo
ijoPP
jPP fNNNNNHh
resGOCE 1δδ
Vertical Datum Unification (3)
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The height system (vertical datum) offsets are computed by means of the least-squares solution of the system of observation equations:
offset of datum j indirect bias term
0=− eGMGM Residual or omission part (e.g., from EGM2008 in band d/o 251-2190)
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Vertical Datum Unification (4)
Important questions to be answered (for NA) are:
What Wo value should be used?
What is the best GOCE-based GGM to provide the long wavelengths of the geoid and to what maximum degree and order should be used?
What are the offsets between existing vertical datums?
How large would then be the residual geoid from gravity/topography and is it allowable to omit it?
How large is the indirect effect and is it allowable to omit it?
What are the requirements in terms of standards/consistency of data?
How important are the temporal changes?
15 International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
The North American Case
Continental-size, outdated levelling-based vertical datums CGVD28 (Canada), NAVD88 (USA and Mexico) Unofficial datums: NAVD88 and Nov07 (Canada)
Large systematic errors Error accumulation and tilts of NAVD88 and Nov07 Local and regional distortions in CGVD28
Rapid accuracy degradation GIA, earthquakes, subsidence, frost heave, local instabilities of benchmarks
The North American initiative for a geoid-based vertical datum Canada (2013), USA (2022), NAVRS (2022) One geoid model realized for the continent
accuracy:1-2 cm in the coastal and flat areas, 3-5 cm in the mountainous regions Defined by Wo = 62636856 m2/s2 determined at tide gauges in North America A time-variable component will also be specified
16 International Jubilee Conference UACEG2012: Science & Practice
15-17 November 2012, Sofia
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Height systems
CGVD28 Official height system Normal-orthometric heights
NAVD88 International datum Helmert-orthometric heights
Nov07 Unofficial datum Helmert-orthometric heights
• over-constrained • piece-wise densification • large distortions • outdated (based on a 84-year
old adjustment)
The Canadian Height Datums
• a minimum constraint adjustment
• a large east-west tilt • large differences with the USA NAVD88 heights
• a minimum constraint adjustment
• care taken of systematic errors • used for geoid model validation
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
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Data Sets
Canada: 308 BMs + 95 TGs Heights in CGVD28, NAVD88 and
Nov07
USA: 18399 points NAVD88 height datum
All GNSS points transformed to ITRF2005(2006.0)
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
The North American Wo value
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Wo computed with 22 Canadian tide gauges with 19 years of water level data No tide gauge record gaps
Pacific region: 12 stations; Atlantic region: 10 stations
Consistent epoch (2008.0) of the mean water level and the GNSS ellipsoidal heights
Corrections for vertical crustal motion and sea level change
Gravity Field Model Wo (m2/s2) δN, cm
go_cons_gcf_2_tim_r3 (d/o 180) 62636855.47 5
go_cons_gcf_2_tim_r3 (d/o 250) 62636856.20 2
go_cons_gcf_2_tim_r3+EGM2008 (d/o 181 to 2190) 62636856.75 8
go_cons_gcf_2_tim_r3+ EGM2008 (d/o 251 to 2190) 62636856.38 4
CGG2010 62636856.74 7
Wo value close to 62636856 m2/s2
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
The GGMs performance in different spectral bands Significant improvement from GOCE R1 to R2 and from R2 to R3 observed GRACE-based models lose signal at lower degrees
itg_grace2010s ~ d/o 160 in Canada and USA; eigen_5s ~ d/o 110 in Canada and 140 in USA
In the spectral band d/o 100 to 150, TIM2, TIM3 and GOCO03S perform slightly better than EGM2008 but after ~ d/o 180 their performance deteriorates rapidly
Validation of GOCE GGMs
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Canada USA
GNSS benchmarks sample the unknown, large regional distortions
GNSS tide gauges are therefore more appropriate for offset computation CGVD28 was constrained by the Atlantic and Pacific mean sea level - No coast-to-coast tilt
Effect of the omission term is Significant
larger when tide gauges are used
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The CGVD28 Offset
-8
-13
-9
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
-32 cm is a representative value of the CGVD28 offset
Offset is affected by the large EW tilt of 1.5 m in Canada
EW and NS tilts in the USA compensate each other
Effect of the GGM omission term is significant on Canada (too few benchmarks)
is small in the USA (averages out due to much denser and regular data point coverage )
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The NAVD88 Offset
8
15
9
2
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
-48 cm is a representative value of the NAVD88 offset
Offset less affected by the datum EW tilt The adjustment procedure limits the propagation of errors from the Atlantic to the Pacific coast
Similar to the USA NAVD88 offset Same definition as NAVD88
Origin at Rimoiski, Québec
Effect of the omission term is still significant
smaller when tide gauges are used
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The Nov07 Offset
8 15
10
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Mean offsets are computed with respect to the Wo = 62636856 m2/s2 equipotential surface
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Effect of the Indirect Bias Term ,jN cmδ ,jN cmδ ( ),jd N cmδ
Country Datum Offset, cm
Canada CGVD28 -30
USA NAVD88 -50
Mexico NAVD88 -50
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Indirect Bias Term ,jN cmδ ,jN cmδ ( ),jd N cmδ
Stokes
Consistency Requirements (1)
Consistency requirements Standards geodetic constants atmosphere, permanent tides linear model in spherical, ellipsoidal, higher(?) order approximation Stokes versus Molodensky solution, etc.
Same spectral band in all data sets
Comparable precision of h, H and N or ζ, and proper stochastic error models E.g.: full vs sparse error CV matrix of SHCs (EGM96 to n = 70 example below)
26
credit: C. Gerlach International Jubilee Conference UACEG2012: Science & Practice
15-17 November 2012, Sofia
Consistency Requirements (2) Same gravimetric and geometric coordinate system scale (n = 0), origin (n = 1), and orientation
If GOCE is not geo-localized in a geocentric reference frame, the N1 term must be added to the previous equations:
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x-offset only y-offset only z-offset only
offset in x,y,z
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Credit ESA STSE GOCE+ Theme 1
HSU with GOCE
Consistency Requirements (3) Consistent models, processing, data epochs & datums, and data reductions Example: MSL - What definition and ocean model?
MIT model constrained by 50 years of Met Office hydrographic data
blue: TG data
black: model
Example: GOCE + terrestrial data: Can the geoid be better than EGM08's? Only in Alaska and NW part of Canada
can some improvement be seen over EGM08
Differences between the GOCE combined model
(TW01 up to degree 210 and terrestrial data) and
EGM2008 up to degree 2190
Example: GGMs - GOCE vs GOCE+GRACE vs GOCE+GRACE+LAGEOS? Under investigation
28 International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Temporal variations atmospheric and ocean loading
GIA, crustal motion, subsidence… GIA effects at tide gauges – Northern Europe example
separate sea level change from land uplift/subsidence
GIA effects at benchmarks – North America example
Temporal Changes (1)
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source: G. Woppelmann (2010) source: Rangelova and Sideris (2012)
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
Temporal Changes (2) Required corrections for geoid and benchmarks
Main contributors to temporal changes (by order of magnitude)
» Hydrology > GIA & Ice sheets > geoid change
» separation of signals is crucial Required height updates for cm-level accuracy (in Canada)
» geoid datum: every decade
» benchmarks: every 2 years (in areas of high GIA)
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Credit: E. Rangelova
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
What have we learned so far?
Selection of Wo is not critical but offsets are Wo can be computed in a convenient way (e.g., fit to tide gauges)
Datum offsets are very important and should be precisely computed Currently, GOCE models are accurate only up to degree 180 Must be supplemented by local data or other models like EGM2008
Omission effect should be carefully computed Can average out only for well-distributed benchmarks over large areas
Indirect effect is negligible Data consistency important though difficult to achieve Temporal changes should not be neglected on datum (geoid) are important on decadal scale on benchmarks (avrual elevations) are important on biannual scale
31 International Jubilee Conference UACEG2012: Science & Practice
15-17 November 2012, Sofia
Towards a World Height System
Theory is well-developed, but there are challenges w.r.t.: The realization of the World Vertical Reference Frame/Datum Consistent conventions, standards and parameters, including Wo value Precise computation of the static geoid surface corresponding to Wo
The connection of the global datum to the local ones Systematic errors in the data; Inconsistent height systems and BVP solutions Reliable error models and global distribution of "observation" stations
The temporal effects and a common reference epoch for all data/models Zero-epoch selection, best static datum and models for the time changes
The alignment of the WHS (actually the IVRF) with the ITRF The IVRF should eventually be provided together with the ITRF
Gravity satellite mission data are critical GOCE: contributions to better global static geoid, Wo value GRACE (and follow-on's): temporal changes of the global geoid
32 International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia
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THANK YOU