Fra momentan vannstand til lokal geoideinformasjon From instantaneous sea level to local geoid information

Transcription

1 Fra momentan vannstand til lokal geoideinformasjon From instantaneous sea level to local geoid information Geometric geoid determination by using vessel borne GNSS/INS, tide gauges and air borne laserscanning. S. Roemer, L. K. Nesheim, Kartverket sjødivisjonen, Norwegian Hydrographic Service Geodesi- og hydrografidagene 217, Nov

2 Contents Introduction Instantaneous Sea Level (ISL) Combination of vessel-borne GNSS/INS & tide gauge(s) Generell information Principle Precondition and data processing Challenge Results Air-borne laserscanning Generell information Data analysis Results From relative shape to absolute heights MSL, geoid Conclusions and outlook References Questions? 2/27

3 Introduction Instantaneous Sea Level (ISL) The SL and its variations are affected by different phenomenons, e.g. atmosphere... wind & pressure gravity, gravitation... earth, moon & sun (tides) density... temperature, salinity currents... different causes and effects It is often and rightly especially on global and regional scales considered as a complex surface providing a fundament for a variety of scientific researches on different fields. The maybe most common quantities to discribe the SL are the mean sea level (MSL 1 ) and the mean dynamic topography (MDT 1 ) in combination with the geoid 2. MSL geoid = MDT (1) 1 often used at larger time scales like e.g years 2 Here, we are using geoid as equivalent to quasi geoid assuming that the difference at sea is in practice insignificant. 3/27

4 Introduction Instantaneous Sea Level (ISL) At shorter time scales information on the total dynamic topography (TDT) is necessary to discribe the ISL with respect to the geoid. ISL(t) geoid = TDT(t) (2) TDT includes e.g. tides, atmosphere, seiches, height effects from density variations & currents. Local scale 3 : The topography is approximately one hundredth of the geoid undulations. This means that the shape of the sea surface is dominated by local variations of gravity. 4 Objective 1. How and how precisely (relatively) can this relative gravity signal be extracted from geometric ISL-observations? Vessel borne GNSS/INS measurements, tide gauge(s) Air borne laserscanning 2. What kind of height reference is most suitable and accurate (absolute) to transform the (relative) shape to absolute heights? 3 often many km 2 4 Introduction To Physical Oceanography. Robert H. Stewart, Department of Oceanograpy 4/27

5 Combination of vessel-borne GNSS/INS & tide gauge(s) Generell information 2 Project felles referanseramme ( common reference frame ) 62 6'" 62 4'48" 62 3'36" '" 5 26'24" 5 28'48" 1 Test area Vanylvsfjorden, Søre Sunmøre, between Måløy and Ålesund 5 31'12" Kartverket geodesidivisjon gravimety (air, sea, land) levelling static GNSS Kartverket sjødivisjon a tide gauges vessel-borne GNSS/INS, speed through water, water density profiles, air pressure a Norwegian Hydrographic Service 5/27

6 Combination of vessel-borne GNSS/INS & tide gauge(s) Principle The ellipsoidal height of the ISL H p,t ISL is observed at vessel position p and at time t. The ellipsoidal height of the geoid H p geoid is. The signal of TDT s p,t TDT is unknown. Replacing the signal s p,t TDT at p by sq,t TDT leads to a systematic signal deviation s p,t TDT H p geoid = Hp,t ISL sp,t TDT (3) at tide-gauge position q ) at p. ( sp,t TDT H p geoid + sp,t TDT = Hp,t ISL sq,t TDT (4) Using SL-differenes reduces the effect of TDT (tides, atmosphere, density, currents) to much smaller local variations of these effects. They are not necessarily insignificant & has to be handled properly. 6/27

7 Combination of vessel-borne GNSS/INS & tide gauge(s) Precondition and data processing 1. Vessel coordinate system, sensor alignment 2. Attitude calibration 3. Squat calibration (vessel speed dynamic draft) 4. GNSS/INS-data processing using by Tightly coupled GNSS (PPP, DGNSS) and INS Attitude correction (roll, pitch, heading) Squat correction HIV-correction H p,t ISL 5. Using tide gauge observations to correct SL-variations s q,t TDT 6. Maybe other data discribing currents, water density, air pressure 7. Analysis H p geoid + sp,t TDT 5 5 including uncorrected residual effects connected to tides, seiches, atmosphere, density variations, currents,... 7/27

8 Combination of vessel-borne GNSS/INS & tide gauge(s) Challenge Variations (moving vessel) gravity H p geoid TDT: s p,t TDT residual errors TDT-variations s p,t TDT (at one location) min a ± some cm (calm conditions) idealization precision a Physical? Seiches? Sea gravimeter? 8/27

9 Combination of vessel-borne GNSS/INS & tide gauge(s) Challenge How to handle TDT-variations? Single observations: The only way to correct single ISL-observations for TDT is modelling. The principle is discussed by Slobbe (213). But is it possible to reach cm-accuracy at local scales? Redundant observations: TDT minimises by combining redundant information in space and time. Is it expensive? Data from our own bathymetric surveys would be perfect suited & are free of charge! Let s se how it works... 9/27

10 Combination of vessel-borne GNSS/INS & tide gauge(s) What kind of signal can we expect? The geoid should reflect the steeply sloping fjord topography. The plumb lines are bended and the potential surfaces are curved. The resolution of existing geoid models is limited. In combination with rough topography it can be expected that the models are smoother than the real potential surface. HES(t ) ISL(t i ) h r b HES(t ) i Fjord cross section W fjord topography W... geoid model ISL around an imaginary hydrostatic equilibrium surface (HES) at observation time t i HES at reference time t h... height of HES(t i ) relative to HES(t ) Bias b minimizes residuals [r] between HES(t ) & the used reference model W 1/27

11 Combination of vessel-borne GNSS/INS & tide gauge(s) Results m relative height relative height 2 m '" 62 6'" '48" 62 4'48" '36" '36" 5 24'" 5 26'24" 5 28'48" 5 31'12" Quasi geoid model HREF216a NN2 EUREF '" 5 26'24" 5 28'48" 5 31'12" SL-based surface obtained by GNSS/INS (vessel: Anda) & local tide gauge data. quite smooth as expected equivalent large scale gradient represents mainly large scale more details at local scale features ( 1cm gradient N-S) correlating with local topography both above and below sea level 11 / 27

12 Combination of vessel-borne GNSS/INS & tide gauge(s) Results m Lomvi relative height 2.18 Anda 62 6'" '" '48" '48" '36" 5 24'" 62 3'36" 5 26'24" 5 31'12" '48" Hydrograf Anda + Lomvi2 + Hydrograf '" '" '48" '48" '36" '36" 12 / 27

13 Combination of vessel-borne GNSS/INS & tide gauge(s) Results: Standard deviation < ±1cm m relative height Anda - HREF 62 6'" Lomvi - HREF '" '48". 62 4'48" '36" 62 3'36" 5 24'" 5 26'24" 5 28'48" 5 31'12" relative height 2 1 Hydrograf - HREF '" (A + L + H) - HREF 62 6'" '48" '48" '36" 62 3'36" 13 / 27

14 Combination of vessel-borne GNSS/INS & tide gauge(s) Interpretation relative height m relative height m A + L + H 2 (A + L + H) - HREF '" '" '48" 62 4'48" '36" HES(t ) 5 24'" 5 26'24" 5 28'48" ISL(t i ) h r b HES(t ) i W 5 31'12" fjord topography 62 3'36" 5 24'" 5 26'24" 5 28'48" 5 31'12" Expected pattern (signal [-2cm, +2cm]) MDT some noise, residual errors mainly spectral inconsistency: SHIP: 1km 2 resolution versus HREF: a couple of km 2 resolution 14/27

15 Combination of vessel-borne GNSS/INS & tide gauge(s) Results: Laser scanning test area (bathymetry and water surface) < ±2cm relative height m relative height m 62 2'24" 62 2'24" '12" 62 19'12" '" 62 18'" 5 38'24" 5 4'48" 5 43'12" 5 '36" 5 48'" 5 5'24" 5 38'24" 5 4'48" 5 43'12" 5 '36" 5 48'" 5 5'24" HREF216b (bathymetry area) Anda- HREF '24" 62 2'24" '12" 62 19'12" '" 62 18'" 5 38'24" 5 4'48" 5 43'12" 5 '36" 5 48'" 5 5'24" 5 38'24" 5 4'48" '12" 5 '36" 5 48'" 5 5'24" HREF216b (laser area) Anda- HREF /27

16 Air-borne laserscanning Project felles referanseramme ( common reference frame ) Air-borne laserscanning of the sea surface in the Søre Sunmøre area (SW from Ålesund). 3 frequencies (2 x red, 1 x green) 2 strips (NW-SE) 5 strips (NE-SW) overflight time approximately at low water (avoiding/minimizing currents & related height effects on SL) few minutes per strip (minimizing SL changes in time) GNSS/INS-processing: by 16/27

17 Air-borne laserscanning Data analysis 1. Processing of GNSS/INS & laser data (done by terratec) 2. Water surface data: strip- & block-wise 6 analysis/statistics Point density (data selection & elimination) Mean/median (wave elimination) standard deviation Outlier detection/elimination 3. Identification of overlapping blocks (between different strips) 4. Cross-over-point analysis Least squares estimation 25 unknown parameters (1 bias per strip) absorbing/eliminating water level changes in time e.g. by tides,... possible systematical height positioning errors 568 blocks (35km 2 ) 332 overlapping blocks (2km 2, 58%) residuals: ±1.8cm (1-sigma) 5. Bias correction: 1 per strip & 1 ( b ) for the whole data set 6. GMT (blockmean, visualization) 6 (25m x 25m) 17/27

18 Air-borne laserscanning Results TDT variations vertical residual errors σ = ±1.8cm Generall coverage (superimposed) & residuals between crossover points (blocks, 25m) between bias corrected strips 18/27

19 Air-borne laserscanning Results Residuals between bias-corrected blocks ( cross-over points, σ = ±1.8cm) 19/27

20 Air-borne laserscanning Results Residuals between bias-corrected SL from laser data & HREF216b. σ = ±18mm reflecting noise, residual errors & spectral inconsistency. 2/27

21 Air-borne laserscanning Results 25m x 25m ±18mm noise/residual errors TDT (signal) spectral inconsistency 1km x 1km 1km x 1km ±12mm (block) ±15mm (overall) 25m x 25m noise/residual errors TDT Residuals between bias corrected SL & HREF216b at different spatial resolutions. spectral inconsistency 21/27

22 From relative shape to absolute heights MSL, geoid To relate the obtained relative height information shape (both from vessel- and air borne measurements) to e.g. other datasets or models it has to be connected to a suitable absolute height system. MSL 7 computed by NHS includes atmospheric effects the geoid 8 not. MSL 7 is therefore less stable, predictable, accurate than the geoid. Annual mean SL and its teoretical standard deviation (TSD, error bars). The statistical standard deviation (±4cm/year, ±1cm/18.6years) is much larger than TSD. One of the main reasons is the non normal distribution of atmospheric effects. 7 under average meteorological conditions 8 and e.g. other MSL-models based on radar altimetry 22/27

23 From relative shape to absolute heights MSL, geoid Classical hydrographic leveling... used to transfer MSL between two tide gauges based of non valid assumptions on e.g. identical average meteorological conditions gives (due to variable weather conditions) results depending on observation time/length... is not suitable for precise applications. In practice the observation span is too short to discribe MSL under average meteorological conditions valid for a 18,6 years period. Using the geoid as reference for MSL (and other related water levels like LAT 9 ) in connection with modelling is a possible way out (Slobbe, 213). 9 lowest astronomical tide 23/27

24 Conclusions and outlook Vessel borne GNSS/INS tide gauge & air borne laser scanning The obtained geometrical shape contains much more information from local gravity variations than from MSL. ±1cm to ±2cm relative precision was reached without utilization of sophisticated calculations, all possible corrections, modelling and for this reason the potential of these data. Main challenges Handling of spectral inconsistency (high- versus low-frequent information) Using the geoid as height reference Handling of atmosphere to achieve consistency between tide gauges, altimetry and gravimetry Air borne laserscanning Combination with tide gauges possible (absolute level, control purposes) More data from other areas Main challenges Overlap is neccesary; less overlap than scheduled anyway ±2cm Collocation in place of gmt blockmean 24/27

25 Conclusions and outlook Vessel borne GNSS/INS tide gauge DGNSS in place of PPP Bunkering correction Using speed through water for squat calibration and data correction Using density data Comparison with vessel borne gravimetry Atmospheric corrections Main challenges Interpolation between several tide gauges (correct level, level estimation) Collocation in place of blockmean Cross over point analyses 25/27

26 References Tightly coupled precise point positioning and inertial navigation systems Narve S. Kjørsvik et al., 21 Roadmap to a mutually consistent set of offshore vertical reference frames, D.C. Slobbe, 213 Extraction of geoid heights from shipborne GNSS measurements along the Weser River in northern Germany, Lavrov, D. and Even-Tzur, G. and Reinking, 213 Sjødivisjonens nye målebåter innmåling, GNSS/INS-basert dypgåendekalibrering, vannstands- og geoidemåling, S. Roemer, L.K. Nesheim, Geodesi & Hydrografidagene, 214 GNSS/INS-basert dypgåendekalibrering og vannstandsmåling, S. Roemer, L.K. Nesheim, Geodesi & Hydrografidagene, 215 Introduction To Physical Oceanography, Robert H. Stewart, Department of Oceanograpy 26/27

27 Questions? Thank you! You are welcome to ask questions if you first answer my following question :-) How would you call the kind of surface which is in principle geometric and not a gravitric in priciple not a potential surface of the earth s gravity field in principle not MSL e.g. due to the non representative atmosperic conditions related to a surface which is definitively not a potential surface on global scale in practice and under certain conditions (or by using suitable corrections) realising a potential surface on a local scale acceptable by any disciplines? 27/27