The GOCE Geoid in Support to Sea Level Analysis

Transcription

1 The GOCE Geoid in Support to Sea Level Analysis The geoid is a very useful quantity for oceanographers Thomas Gruber Astronomical & Physical Geodesy (IAPG) Technische Universität München

2 1. Characteristics of GOCE Geoid Solutions Signal Characteristics Estimated Errors True Errors Outline 2. Oceans and the Geoid Problem Description MDT at Tide Gauges Height System Unification Geodetic MDT s 3. Summary & Conclusions

3 SQRT Signal Degree Variance in Geoid [m] GOCE Geoid - Signal Characteristic Signal Degree Variances (GOCE RL5 vs. earlier Models) EGM2008 Tscherning-Rapp DIR5 TIM1 TIM2 TIM3 TIM4 TIM Full Signal Content up to d/o Goal was d/o Degree

4 GOCE Geoid - Signal Characteristic EGM2008 Data Coverage 12.0% of Land 42.9% of Land 45.1% of Land Map Source: Pavlis, N. K., Holmes, S., Kenyon, S., Factor, J The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research 117

5 GOCE Geoid - Signal Characteristic Gravity Anomalies Signal GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5 TIM 3.14 DIR 1.07

6 GOCE Geoid - Signal Characteristic Gravity Anomalies Signal GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5 TIM DIR

7 GOCE Geoid - Signal Characteristic Gravity Anomalies Signal GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5 TIM DIR

8 GOCE Geoid - Signal Characteristic Gravity Anomalies Signal GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5 TIM DIR

9 GOCE Geoid - Signal Characteristic Gravity Anomalies Signal GOCE vs. EGM2008 Gravity Anomalies [mgal] (up to d/o 200) RMS of Differences in Test Area [mgal] Rel. 1 Rel. 2 Rel. 3 Rel. 4 Rel. 5 TIM DIR

10 GOCE Geoid - Estimated Errors Maps of Geoid Error from VCM Propagation (Full Resolution) Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation) TIM5 Degree/Order & Area 200 Global TIM5 [cm] DIR5 [cm] 200 Germany 220 Global 220 Germany Full Global Full Germany DIR5

11 GOCE Geoid - Estimated Errors Maps of Geoid Error from VCM Propagation (Degree/Order 220) Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation) TIM5 Degree/Order & Area 200 Global TIM5 [cm] DIR5 [cm] 200 Germany 220 Global Germany Full Global Full Germany DIR5

12 GOCE Geoid - Estimated Errors Maps of Geoid Error from VCM Propagation (Degree/Order 200) Geoid Error Comparison (Global from cum. Error Degree Variances, Germany from VCM Propagation) TIM5 Degree/Order & Area TIM5 [cm] DIR5 [cm] 200 Global Germany Global Germany Full Global Full Germany DIR5

13 RMS Geoid Height Difference [m] Germany GOCE Geoid - True Errors RMS of Geoid Differences at GPS-Levelling Points after planar Fit (Omission Error estimated from EGM2008) 0.1 EGM2008 TIM1 TIM2 TIM3 TIM4 TIM5 DIR cm 2.7 cm 0.01 Acknowledgement: GPS levelling data for have been provided for validation purposes by BKG, Frankfurt/Main Degree

14 GOCE Geoid - True Errors Estimated error from GOCE-DIR5 at D/O 200 in Germany (formal): 0.5 cm Estimated error from GOCE-TIM5 at D/O 200 in Germany (calibrated based on gradient residuals): 1.4 cm Differences at GPS/Levelling Stations in Germany for both models at D/O 200 (after planar fit) using EGM2008 for omission error: 2.8 cm GPS/Levelling geoid error is composed by: GPS height error: 1.5 cm Normal height accuracy after planar fit: 1.5 cm Error of EGM2008 used for omission error: 1.0 cm Total after error propagation: 2.4 cm Attempt to derive a realistic error: GOCE geoid error (reverse error propagation) 1.4 to 1.5 cm

15 Oceans & Geoid Problem Description GPS Benchmarks Tide Gauge Benchmark Levelling Network Local Vertical Datum (Equipotential Surface) Local Physical Height Local Geoid Height GOCE Equipotential Surface (long wavelengths) GOCE Physical Height GOCE Geoid Height True Equipotential Surface (short wavelengths) Omission Error C Vertical Datum C B Vertical Datum B A Vertical Datum A

16 Oceans & Geoid MDT at Tide Gauges 1. Geodetic MDT at Tide Gauges from Satellite Altimetry minus GOCE Geoid 2. Geodetic MDT at Tide Gauges from GNSS Levelling: GNSS Height at Tide Gauge minus Tide Gauge Recording minus GOCE Geoid 3. Oceanographic MDT from Ocean Model at Tide Gauges

17 Oceans & Geoid MDT at Tide Gauges (Study performed by Phil Woodworth, NOC) Sea level slope at tide gauges along the east coast of North America from classical geodetic leveling (top: USA in red, Canada in blue), from an ocean circulation model (black) and from GNSS-Levelling based on GOCE DIR5 & EGM2008 (bottom: red & blue)

18 Oceans & Geoid - Height System Unification by GNSS Levelling H ia from spirit levelling referring to height datum A (e.g. tide gauge) h i from GNSS positioning referring to a specific ellipsoid Observed Geoid Height referring to vertical Datum A N h H A i i ia Geoid A N i N A0 GOCE N i res N i N A0 Computed Geoid Height referring to mean Geoid N N N GOCE res i i i Geoid height from GOCE model Residual geoid height (omission) Geoid Height Offset of vertical Datum A wrt. mean Geoid. Observation Equation A GOCE res N N ( N N ) i i i Height System Offset wrt. Geoid NA0 Mean( N)

19 Oceans & Geoid - Height System Unification by GNSS Levelling GOCE TIM5 Model truncated at D/O 200 NA0 Mean( N)

20 Oceans & Geoid - Height System Unification by GNSS Levelling Samoa Guam & Marianas Guam Marianas w/o omission error (signal) with omission error (signal)

21 Oceans & Geoid - Height System Unification by GNSS Levelling GOCE Geoid -72 Japan -101 Australia (Mainland) +4 England -11 Greece Germany Brazil -2 Canada USA (1999) -115 USA (2009) GOCE-TIM5 (0-200) & EGM2008 ( ) GOCE-TIM5 (0-200) GOCE Geoid -67 Japan -97 Australia (Mainland) +4 England -15 Greece Germany Brazil Canada USA (1999) USA (2009) Results from Rapp (1994) (Bulletin Geodesique 69, p.26-31) based on JGM-2 / OSU91A and Geoid Heights on Doppler Stations.

22 Oceans & Geoid - Geodetic MDT s Patterns of MDT solutions applying the geodetic approach based on spherical harmonic expansions by differencing geoid models from a MSS model (GSFC00.2 ). GRACE + altimetric/terrestrial gravity GRACE + GOCE + altimetric/terrestrial gravity GRACE + GOCE + altimetric/terrestrial gravity applying improved combination scheme with complete variance-covariance information up to highest possible degree (from computational point of view).

23 Summary & Conclusions Full signal of GOCE-based satellite-only model up to degree and order Estimated absolute geoid error of rel. 5 models at d/o 200 roughly 1.5 cm or better. GOCE geoid at tide gauges quality depends on size of the omission error. Quantification needs detailed local geoid knowledge Averaging of GNSS Levelling differences can cancel out omission error (depending on geoid roughness and station distribution). Offsets derived by this method are only applicable to single tide gauge stations in case there are no system distortions in levelling networks. Geodetic MDT solutions need consistently modelled geoid information up to highest possible deree.