15-17 NOVEMBER 2012 Global Height System Unification by ... · PDF fileGlobal Height System...

Global Height System Unification

by means of the GOCE Geoid

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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

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Source: J. Ihde, BKG

International Jubilee Conference UACEG2012: Science & Practice 15-17 November 2012, Sofia

Motivation


Proliferation of vertical datums >100 height systems and chart datums, inconsistently realized

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Motivation



Promise of gravity missions GOCE: 1-2 cm geoid globally at 100 km resolution

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Motivation



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

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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

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Credit: Hofmann-Wellenhof & Moritz, 2006


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

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Source: IAPG


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


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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

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Credit: R. Pail, IPAG


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


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


∑++=−−−=

J

i

iPo

ijoPP

jPP fNNNNNHh

resGOCE 1δδ


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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)



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?


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

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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


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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)


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


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


-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

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15

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-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

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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)

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credit: C. Gerlach International Jubilee Conference UACEG2012: Science & Practice


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


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


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)


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


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

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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



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