Vertical Reference Frames Simple Geometry or Measurement Sciences or a complex combination of both?

Transcription

1 Vertical Reference Frames Simple Geometry or Measurement Sciences or a complex combination of both? By David Philip The views expressed in this presentation are based on my own web-based research to date and are given in good faith as being factually and historically accurate. All Sources of material are duly acknowledged. The answers to a number of s sent to a number of busy experts were also very much appreciated 1

2 How well do today s vertical Datums, measurement technologies, and models match the practical realities nearshore and offshore the UK? 2

3 OUTLINE Introduction and brief history Land levelling systematic errors Vertical Datums Tidal regime around UK Sea Level Observations Altimetry Tidal Models and Tidal Data Geoids Accuracy 3

4 A brief review of the third Dimension Five basic questions to be answered How? What? When? Why? Who? 4

5 The main influences» Military» Scientific» Political» Commercial It should be appreciated that in the last 40 years there has been a revolution in measurement technology. Has our knowledge and appreciation of the vertical references kept pace with these changes or is it lagging further and further behind? Does our approach to the vertical dimension need to change? What is accuracy? Closeness to the truth. Is the Truth of 1918 the same as the Truth of 2009? 5

6 MILITARY INFLUENCE Military recognition that warship navigational safety relied on reliable charts. Charts show accurate least depths to a defined Chart Datum. Measured depths need to be tidally reduced. UK Hydrographic Office was established in 1795 and first Hydrographer appointed. An organisation of military officers and civilian scientists are the Hydrographic technical experts. Shared charting information benefits trade. Admiralty Charts made available for Merchant Marine 1819 Hydrography had a traditional international approach to the rights of passage over the high seas and the sharing of data. Is this gradually changing? Are organisations and nations becoming more and more territorial and is data sharing is reducing in some areas? 6

7 HISTORICAL CONTEXT First Hydrographic Chart completed and published 1801 First Admiralty Tide Tables published 1830 (4 Ports) First North Sea co-tidal chart estimated (Rev. W.Whewell) 1836 First Hydrographic Tides Officer appointed 1912 J. Proudman and A. T. Doodson compute first True Co-tidal Constituent Chart for North Sea 1924 A. T. Doodson and R.H. Cochran first True Co-tidal Constituent Chart for English and Irish Channels 1932 British Isles Co-tidal and Co-range chart 5058 published 1971 Included contributions from Belgium, Denmark, France, Germany, Netherlands, and Norway 5 th Edition published 29 th March 1996 Included offshore tidal data provided by Oil Companies. 7

8 Why is a consistent Vertical Reference Frame needed? On mainland UK all mapping heights are referred to Newlyn Datum. A few Islands have their own local Datum. Eg Shetland, Orkney, Isle of Man etc Charts use Chart Datum. This varies from place to place as it is dictated by the range of tide. It is usually close to LAT but potentially in excess of 30 different types of Tidal Datums exist worldwide. In the UK coastal zone there is data overlap with different conventions used by different agencies. (Hydrographic Office, Ordnance Survey, British Geological Survey) Integrating data in the coastal zone requires some careful work by a professional surveyor. UK Tidal data has never been adjusted to provide a homogeneous spatial vertical reference. 8

9 UK land heighting history The original level Datum of Liverpool used for the First Levelling of UK was discarded in 1921 but used 47 tidal stations around the English, Welsh, and Scottish coasts. 2 nd Geodetic Levelling completed in 1921 using 3 Tidal stations but had 0.8 feet misclose Newlyn Dunbar. All UK mainland heights based only on Newlyn Tide Gauge observations (Epoch 1918). 3 rd Geodetic levelling the systematic error was found to be even greater at 1.2 feet. A choice of two heighting systems could now be used but both are based only on Newlyn. UK scientific heighting on Newlyn Datum was based on the 2 nd Adjustment of 3 rd Geodetic levelling but has a systematic slope error of about 0.5 metres from south to north of the UK. The scientific levelling slope has been proved scientifically three times by different methods by UK Oceanographers It has also been proved scientifically from a number of geoid derivations using gravity data namely EDIN89, EDIN91, OX92, OSGM02, EDIN04. There is currently one exception in OSGM05 which indicates a much reduced slope but in comparison with 2 nd Geodetic levelling Warping one data set to another eg OSGM02 merely perpetuates a known error. It does not make it right. What is the 4 parameter shift required to fit OSGM02 to Ellipsoid heights on ETRF89? Can scientific reality be redefined by assertion? Does a lack of clarity cause confusion? 9

10 29 UK Ports MSL nd Adjustment 3 rd Geodetic Levelling EGM Warped OSGM02 Levelling, MSL, and the EGM2008 Geoid 29 East and West Coast Ports (Epoch 1967) Height Difference - metres East Coast West Coast East Coast EGM2008 West Coast EGM2008 Linear (East Coast) Linear (West Coast) Linear (West Coast EGM2008) Linear (East Coast EGM2008) -0.2 Northing - metres 10

11 Levelling and MSL North South UK Level Slopes y = 5E-07x R 2 = Height Difference from MSL y = 3E-07x R 2 = y = 2E-07x R 2 = Adj 3 GL Epoch Adj 2 GL Epoch 1918 EGM Warped OSGM02 1 Adj 2 GL Epoch 2000 Linear (2Adj 3 GL Epoch 1967) Linear (1 Adj 2 GL Epoch 1918) Linear (EGM Warped OSGM02) Linear (1 Adj 2 GL Epoch 2000) -0.2 Northing - metres 11

12 TIDAL REGIMES DEEP OCEANS In the DEEP oceans the tidal influence of sun and moon are dominant with a small tidal range of 1 metre major tidal constituents dominate. SHALLOW SHELF SEAS The effects of friction caused by water depth, seabed gradients, and seabed material create non-linear Shallow water tides with extreme tidal ranges in enclosed basins. This generates compound and overtides with many constituents. Estuaries and rivers create further distortions. 12

13 BATHYMETRY UKCS BERR Atlas of UK Marine Renewable Energy Resources. A Strategic Environmental Assessment Report March 2008 Crown Copyright Produced By: ABPmer, The Met Office, Proudman Oceanographic Laboratory 13

14 PEAK FLOWS - SPRING and NEAP TIDES courtesy BERR Atlas of UK Marine Renewable Energy Resources 14

15 MEAN SPRING and NEAP TIDAL RANGE courtesy BERR Atlas of UK Marine Renewable Energy Resources 15

16 Fig 3.28 UKSeaMap Seabed Landscapes in UK Crown copyright 16

17 SEA LEVEL MEASUREMENTS It should be appreciated that sea level observations are highly variable and very noisy. Two principal elements:- 1. Predictable Forces 18.6 year cycle Astronomical Location Deep Ocean Shallow shelf sea 2. Un-predictable annual seasonal cycle Meteorological (Pressure, Wind) Temperature and salinity (El Nino) 17

18 Sea Levels at Newlyn : Analysis of Trends for Future Flooding Risks Courtesy Isabel B. Araujo and David T. Pugh The 18.6 year Astronomical Cycle 18

19 Maximum and Minimum Trends Courtesy Isabel B. Araujo and David T. Pugh 19

20 Newlyn Annual mean sea level (mm) Courtesy Isabel B. Araujo and David T. Pugh Rising Sea Level Sea level rise metres 20

21 Unpredictability Dangers of short term trends -Management of change Courtesy Isabel B. Araujo and David T. Pugh Gauge change 21

22 ALTIMETRY STATUS SUMMARY Courtesy Andersen O.B. and Knudsen P. (2009) DNSC08 mean sea surface and mean dynamic topography models 8 different altimetry satellites have been used to collect data. They have a range of accuracies, observation periods, repeat tracks, ground track spacing, and coverage limits but have been used in a combined solution Accuracy a priori estimates 0.6 to 11 centimetres Observation periods 0.6 to 12 years Repeat tracks 0 to 445 Ground Track spacing 6 to 340 kilometres North/South coverage limits +/- 65 to +/- 82 Degrees ICESat coverage Arctic coverage +72 to

23 LATEST DEVELOPMENTS in DNSC08 global mss and mdt Latest result determined by the Danish National Space Center has a number of key attributes and limitations 1. First Global MSS without a polar gap. 2. First with a 10 year temporal period. 3. First to extend coverage to the poles. 4. No significant voids or data gaps. 5. MDT surface linked with EGM2008 Geoid 6. Incomplete temporal averaging eg El Nino 7. Longterm coverage limited in N/S Extent 8. Geoid model assistance only needed to complete polar coverage 23

24 SATELLITE ALTIMETRY Processing Focus Wet Tropospheric Correction Dry tropospheric Correction Ionospheric Correction Air pressure Correction Wind Correction Tidal Correction Items highlighted in RED are the most significant 24

25 COASTAL ZONE is key area for altimetry improvements Loss of the radiometer correction information within 10 s of Kilometres of the coast degrades altimetry results. Improvements reported in 2007 using ECMWF Modelling to within10 Kilometres (Madsen, Hoyer, Tscherning) This is the key connection area between higher accuracy altimetry mean sea surface and port tide gauges This also coincides with weakest area for gravity data and also results in geoidal uncertainty Result Dynamic Topograghy remains of very limited accuracy in the nearshore area 25

26 IMPROVEMENTS IN SATELLITE ALTIMETRY Deep Oceans and Shallow Seas a comparison Courtesy R.D. Ray Thoughts on Shallow Water Tides and Altimetry 26

27 OFFSHORE VALIDATION LOCATIONS around UK Offshore Pressure gauges and Dutch Platforms Courtesy R. D. Ray Thoughts on shallow water tides and altimetry? UK Platforms? More Pressure Gauge data? 27

28 Correlation between Tide Gauge Port ABERDEEN and satellite altimetry Courtesy K.S.Madsen MSc Disertation 28

29 CORRELATION A correlation greater than 0.8 would be described as STRONG A correlation less than 0.5 would be described as WEAK What would be a sensible correlation distance limit between an onshore tide gauge and an offshore location? 29

30 Correlation between Tide Gauge Port CROMER and satellite altimetry Courtesy K.S.Madsen MSc Disertation 30

31 TIDE MODELS Accuracy and developments Two Basic Types Empirical deduced model (Altimetry analysis) Finite element hydrodynamic model (bathymetric nodes) Global Accuracy in open deep ocean Typical RMS 0.01m Worst case 0.03 metres Significant errors shallow waters - non-linear tides polar regions sea ice, limited or lack of altimetry coverage RMS metres Global Models GOT00.2, FES2004, TPX0.7 New modesls EOT08a (Savcenko & Bosch) and GOT4.7 (Ray 2008) Notably the determination of shallow water tides Regional Models of note NW Mediterrranean MOG2D, NW Europe POL 2nm, West of Portugal Mohid The more modern the model the more attention paid to the problem areas. Still scope for significant further improvement 31

32 Figure 1 : Variance differences of SSH at crossovers with EOT08a vs FES04 for Jason-1 and EnviSat missions over Blue and red colours indicate improvement and deterioration respectively with EOT08a. JASON 1 Courtesy - Performance estimation of recent tide models using altimetry and Tide gauge measurements L. Carrere, J-F Legeais, E. Bronner 32

33 Figure 1 : Variance differences of SSH at crossovers with EOT08a vs FES04 for Jason-1 and EnviSat missions over Blue and red colours indicate improvement and deterioration respectively with EOT08a. ENVISAT Courtesy - Performance estimation of recent tide models using altimetry and Tide gauge measurements L. Carrere, J-F Legeais, E. Bronner 33

34 Sources of UK TIDAL DATA and MSL 2 Primary sources of tidal data identified by Iliffe et al (2007) for VORF. 75 P Stations Source PSMSL Monthly Average (1807-to date) 22 P Stations Source PSMSL Monthly Average 20 years of modern data (1960 onwards) 385 Admiralty Tide Tables months or less data (majority only one month) 25 3 months to 1 year 107 more than 1 year 51 in rivers and more than 2 kilometres from open sea A further 10 identified as anomalous A note of caution. These observations have been collectively labelled as gauges. For many Ports this may be valid but for a significant number it has been tide poles and human recorders that collected the data. Integrated Coastal Zone Report identified that although ATT had Tidal Information for 800 ports around UK only 339 have all the constituent data. No UK offshore pressure gauge (POL and others) data has been used. No offshore UK Platform data has been used 34

35 DEFINING The GEOID Choice of a normal gravitational potential field (encompassing the reference ellipsoid) Choice of which specific level surface is "the" geoid. It approximates to mean sea level over the oceans Knowledge of what permanent tide system the geopotential model refers to (a choice of three) Knowledge of how the potential field acts inside topographic masses 35

36 GEOIDS Astrogeodetic Geoid Gravimetric Geoid Quasi-geoid Local Regional Global 36

37 Tidal Types of Geoid Tide-free (or nontidal) This geoid would exist for a tide-free Earth with all (direct and indirect) tidal effects of the Sun and Moon removed. Positioning (e.g.,from GPS) is given in the Tide Free system on WGS84 Ellipsoid. This requires that GPS/Leveling applications use a Tide Free geoid for Surveyors. Mean Tide This geoid exists in the presence of the Sun and the Moon A mean tide value includes both direct and indirect permanent tidal distortions. Mean Tide system is given with respect to the IDEAL mean Earth ellipsoid. Its mainly for users working in oceanographic applications. Zero Tide This geoid would exist if the permanent direct effects of the Sun and Moon are removed, but the indirect effect component related to the elastic deformation of the Earth is retained. (Very theoretical) Geodesists are supposed (as per an IAG resolution) to work in Zero Tide but generally they don t apart from Finland and Sweden. 37

38 GEOID TYPE DIFFERENCES Difference - centim etres Geoid semi-major axis flatenning TIDE FREE / ZERO TIDE / MEAN TIDE / Mean Tide - Zero Tide Zero Tide - Tide Free Mean Tide - Tide Free Geodetic Latitude 38

39 EGM96 Courtesy Chapter 11, of the EGM96 report (NASA/TP ), Best Estimates WGS84 Values GM = e14 m3s 2 GM_o = e14 m3s 2 W_o = m2s 2 U_o = m2s 2 a_ideal_tidefree = m a = m 1/f_Ideal_TideFree = (**) 1/f = By computation Zeta_o = cm By computation Zeta_o = cm (**) Love number k_2=0.3 used. Value adopted the rounded value: Zeta_o = -53 cm. WGS84 ellipsoid, whose origin is at the center of mass of Earth, as defined by WGS84 (G873)/ITRF94, and whose axes are aligned with the indicated reference frames. 39

40 EGM2008 Courtesy N.Pavlis Current Best Estimates WGS84 Values GM = e14 m3s 2 GM_o = e14 m3s 2 W_o = m2s 2 U_o = m2s 2 a_ideal_tidefree = m a = m 1/f_Ideal_TideFree = (**) 1/f = By computation Zeta_o = cm By computation Zeta_o = cm (**) Love number k_2=0.3 used. Value adopted the rounded value: Zeta_o = -41 cm. Compare EGM96 Value : Zeta_o = -53 cm Difference : -12 cm 40

41 Critical calibration of altimetry measurements Courtesy N. Pavlis The primary reason for the change in the numerical value of Zeta_o from the EGM96 model (-53 cm) to the current best estimate (-41 cm), was the discovery by Ouan-Zan Zanife (CLS, France) of an error in the Oscillator Drift correction applied to TOPEX altimetry data (see page 34 in Sciences-International/d p/ ). The erroneous correction was producing TOPEX Sea Surface Heights, biased by about cm. Unfortunately, this error was discovered after the estimated Zeta_o and had created/released for the EGM96_WGS84 geoid grid back in the EGM96 days. This error was also the reason why Rapp's (1995) best estimate of the equatorial radius ( m in the Mean Tide system) is off by 12 cm from Bursa's (1999) estimate ( m in the same Mean Tide system). 41

42 Height Anomaly or Geoid undulation Comparing Apples with Apples HEIGHT ANOMALIES (with respect to an IDEAL reference ellipsoid,in the Mean-Tide Permanent Tide system). The difference between a HEIGHT ANOMALY and a GEOID UNDULATION is proportional to the Bouguer anomaly times the elevation (see Heiskanen and Moritz, 1967, Section 8-13). Over ocean areas, height anomalies and geoid undulations are identical, provided of course that both have been computed with respect to the same ellipsoid, and both refer to the same Permanent Tide system. Over land these differences become more significant. Ben Nevis about 0.11 metres, Mount Everest 4.4 metres 42

43 Equatorial radius for scaling Ellipsoid semi-major axis There is "a" used as a SCALING parameter of the potential coefficients assigned for every geopotential model m value used for EGM2008 and EGM96 There is an "a" associated with the ellipsoid to which a set of geoid undulations refer. Changing the scaling parameter "a" associated with a model by a few decimeters has negligible effect on the geoid undulations computed from this model. Changing the "a" associated with the ellipsoid to which a set of geoid undulations refer, amounts to introducing a zero-degree geoid undulation term. In this case, delta a = - delta_n. According to Bursa et al. (1999), using the value of 0.3 for the second-degree Love number a 1/f Tide-Free : m Zero-Tide: m Mean-Tide: m

44 GEOID DIFFERENCES EGG08 and EGM96 Courtesy T. Gruber Evaluation of the EGM Gravity Field by means of GPS Levelling and Sea Surface Topography solutions 44

45 GEOID DIFFERENCES EGG08 and EGM2008 Courtesy T. Gruber Evaluation of the EGM Gravity Field by means of GPS Levelling and Sea Surface Topography solutions 45

46 GEOID DIFFERENCES EGG08 and EIGEN-5C Courtesy T. Gruber Evaluation of the EGM Gravity Field by means of GPS Levelling and Sea Surface Topography solutions 46

47 UK FBM Distribution H1 s and H2 s UK 188 FBM Distribution DUNCANSBY HEAD DUNBAR EAST Northing H1 FBM's H2 FBM's LISKEARD Easting 47

48 FBM's used in 2ND and 3RD GEODETIC LEVELLING Northing - m etres H1 England Wales H2 England Wales H1 Scotland H2 Scotland H1 and H2 Not common to 2GL and 3GL Easting - metres 48

49 1.000 Levelling Slopes v EGM2008 Common H1 and H2 FBM's Heig ht Difference rd GL England and Wales 3rd GL Scotland 2nd GL England and Wales 2nd GL Scotland Latitude 53 Degrees North Linear (3rd GL England and Wales) Linear (3rd GL Scotland) Linear (2nd GL England and Wales) Linear (2nd GL Scotland) Northing - metres 49

50 Geoid Height Differences Global and Local Mean Difference EGM OSGM / metres Mean Difference EGM EGM / metres Mean Difference EGM OSU91A / metres 50

51 GEOID MODEL COMPARISONS North - South GEOID Height Differences EGM2008, OSGM02, EGM96, OSU91A 82 UK H1 FBM's 106 UK H2 FBM's Height Difference - metres H1 EGM OSGM02 H1 EGM EGM96 H1 EGM OSU91A H2 EGM OSGM02 H2 EGM EGM96 H2 EGM OSU91A Poly. (H1 EGM EGM96) Poly. (H2 EGM OSGM02) Poly. (H1 EGM OSGM02) Poly. (H2 EGM EGM96) Poly. (H1 EGM OSU91A) Poly. (H2 EGM OSU91A) Northing 51

52 GEOID MODEL COMPARISONS West - East GEOID Height Differences EGM2008, OSGM02, EGM96, OSU91A 82 UK H1 FBM's, and 106 UK H2 FBM's Height Difference - metres H1 EGM OSGM02 H1 EGM EGM96 H1 EGM OSU91A H2 EGM OSGM02 H2 EGM EGM96 H2 EGM OSU91A Linear (H1 EGM OSGM02) Linear (H1 EGM EGM96) Linear (H1 EGM OSU91A) Linear (H2 EGM OSGM02) Linear (H2 EGM EGM96) Linear (H2 EGM OSU91A) Easting 52

53 SEA SURFACE TOPOGRAPHY DYNAMIC OCEAN TOPOGRAPHY The mean dynamic ocean topography (DOT) is the difference between the timeaveraged sea surface and the geoid. All geoid slopes are 'horizontal equipotential surfaces with respect to gravity. Any tilt of the the ocean sea surface relative to the horizontal measures the strength of surface 'geostrophic' currents or wind driven currents. The DOT is a measures of the long-term-averaged strength of ocean currents, the 'steady-state' circulation. Eg. The Gulf Stream, The DOT can be deduced by geodeticaly differencing an accurate altimetric mean sea surface and an accurate geoid. The DOT can also be constructed by combining in-situ oceanoraphic data (temperature and salinity of seawater, direct measurements of current velocity, etc). A third way is by combining the geodetic estimate (altimetry and geoid) with the traditional oceanographic estimate. This most significant deepwater dynamic ocean topography features are of the order of to -1.8 metre at maximum. On the shallow continental shelf seas these features are much less significant and one or two orders of magnitude less.ie 0.02 metres to 0.2 metres 53

54 SEA SURFACE TOPOGRAPHY UK and IRELAND or DYNAMIC OCEAN TOPOGRAPHY 320 GPS measured Tide Gauges Around Britain TG DNSC08MSS Mean = 1.24 cm, Std = 6.8 cm Comparison by Marek Ziebart, UCL London, Courtesy Andersen et al. The DNSC08 global Mean sea surface and Bathymetry. Presented EGU-2008, Vienna, Austria, April,

55 ACCURACY A quote from FIG Guide on the Development of a Vertical Reference Surface for Hydrography. No.37 September 2006 Section 3.3 Sub para Accuracy The accuracy of the model will depend on many factors and the total error budget should be kept in mind at all times. All data contains errors and hence all models have an error associated with them. The key factor is knowing the errors. The greatest danger is to use data without knowing how accurate it is. Poor data is not useless data, but it should be treated according to its accuracy. 55

56 ACCURACY SUMMARY Typical Range Worst Altimetry oceans to Altimetry Shelf Seas to Altimetry nearshore not available??? Tides oceans to Tides Shelf Seas to Tides Nearshore to Geoid Oceans to Geoid Shelf Seas to Geoid - Nearshore no gravity data??? 56

57 The Accuracy of UK Co-tidal Charts FIG Publication No.37 Page 16 Quote For example, the UK co-tidal model has a quoted accuracy of +/- 0.5 m in the vertical for the ranges and therefore any separation model developed using these can be no more accurate than this. This figure is actually the 2 sigma figure although unstated. It is based purely on an estimate and has no statistical basis. As a North Sea user of the co-tidal chart for 35 years the figure does not match my practical experience. Observed offshore tides match predictions very well in calm and settled conditions. My estimate with statistical evidence is better than +/- 0.1 metres (one sigma) in the North Sea and West of Shetland The unpredictable part is the daily and seasonal meteorological surge effects induced by wind and pressure systems and even the variations in temperature and salinity. 57

58 CONCLUSION With today s enhanced GPS we at last have a 3-D measurement system capable of providing high accuracy, quickly and cost effectively. Our improving knowledge of the geoid means we are now approaching the true figure of the earth both locally and globally There are still key areas where gravity and altimetry data is missing or of poor quality. The perpetuation of historical heighting errors is confusing, inefficient, ineffective, and extremely wasteful. A broader, more measured, and balanced solution is required There are very real dangers in jumping to the wrong conclusions too quickly. New technologies take time to fully develop and mature. 58

59 RECOMENDATION There is a pressing need to maintain and perpetuate the Hydrographic tradition of a collective approach to real quality and genuine accuracy compatible with the most modern measurement technology. Well considered collective solutions are more cost effective to implement and maintain and reduce the need for future change. At a time of dramatic technological developments the need to consult broadly and look outward rather than inward is key. 59

60 FINAL QUESTIONS? Do scientists make good surveyors? or Do surveyors make good scientists? or What is Hydrography? Mathematics and Measurement Sciences 60