MLLW and the NAD83 Ellipsoid: An Investigation of Local Offsets and Trends Using PPK and Gauge Derived Water Surfaces. Abstract: Authors Doug Lockhart, Fugro Pelagos, Inc. Andy Orthmann, Fugro Pelagos, Inc. During the 2004 field season, Fugro Pelagos, Inc. (FPI) collected hydrographic data for NOAA on the Alaska Peninsula near Shumigan and in South East Alaska near Sitka. This data was reduced to MLLW using tide gauges and traditional tide zoning methods for delivery to NOAA. FPI also collected inertially corrected, kinematic GPS data during all phases of hydrographic data acquisition. Kinematic positions and elevations, referenced to the NAD83 ellipsoid, were calculated for the survey vessels at 50Hz update rates. The kinematic positions were substituted for the real time DGPS positions and included in the delivery to NOAA. If the relationship between MLLW and the ellipsoid is known, it is possible to use KGPS elevations in place of tidal data, heave compensation and squat/settlement. However, it is also possible, with this data set, to examine the relationship between the tide zone model and the NAD83 datum over the entire survey area. In this work, NAD83 is compared to the tide zone model over the survey areas in Shumigan and Sitka. The hydrographic surfaces, for both reduction methods, are examined for cohesiveness. The results are used to draw conclusions about the tide zone model and the applicability of KGPS altitude as a tide gauge substitute. Introduction: Fugro Pelagos, Inc collected hydrographic data for NOAA on the Alaska Peninsula near Sand Point and the Shumigan Islands and near Sitka in South East Alaska during the summer of 2004. A single tide gauge and zoning scheme was used to reduce soundings to MLLW during operations and for delivery to NOAA. At both sites, FPI installed kinematic GPS base stations. Applanix PosMV s configured with dual frequency Novatel GPS cards were used for vessel position and orientation. Full bandwidth (200 Hz) IMU data was logged along with raw GPS pseudo ranges during multibeam acquisition. During post processing, the logged PosMV data was reprocessed in PosPac. This process calculated 50 Hz inertially constrained kinematic positions and altitudes along with vessel orientation parameters: heading, pitch and roll. In a simplified model, a hydrographic sounding from a multibeam survey can be considered to be the combination of 6 components: a raw depth from the multibeam, an offset from the sounder to a reference point (RP), static draft at the RP, dynamic draft containing both squat and settlement components, heave, and a tide correction. This calculation results in the tide corrected soundings, referenced to MLLW, that were delivered to NOAA to meet the charting requirement. It is also possible, using the post processed kinematic altitudes, to calculate soundings based on an ellipsoidal datum, in this case, NAD83. These calculations have been carried out on the Sitka and Shumigan data sets. The resulting data products give insight into the relationship
between MLLW and the ellipsoid across the entire survey area. It also appears that local hydraulic and meteorological effects that are not measured by the tide gauge can be observed. Calculations: Tide corrected soundings are calculated using the components shown in Figure 1. The relationship between the ellipsoid and the tidal datum is irrelevant in this calculation and, in many cases, is not known. A slope or undulation in the tidal datum is of no consequence as long as it is a static feature. Standard (Tidal) Model : Depth from MLLW = (Raw Depth) + (Sonar to RP) + (Draft) + (D-draft) (Heave) (Correction to MLLW) Figure 1: Tide Corrected Sounding Referenced to MLLW Soundings can be referenced to an ellipsoid by using the relationship shown in Figure 2. In this case the relationship between the ellipsoid and tidal datum is also irrelevant for the calculation of the sounding. However, by subtracting the ellipsoidal sounding from the tidal sounding we will obtain the separation between MLLW and the ellipsoid. Alternatively, the separation could be analyzed by creating a tide curve from the vessel altitude, comparing this to the tide gauge data. This allows for an easy comparison in time, but a poor comparison spatially. It also loses the resolution of the altitude data.
Ellipsoidal Model: Depth from Ellipsoid = (Raw Depth) + (Sonar to RP) + (Draft) (Correction to Ellipsoid) (Correction to Ellipsoid) = (Altitude) (Draft) Figure 2: Sounding referenced to ellipsoidal datum This work used the former procedure comparing ellipsoidal soundings to tidal soundings for the following reasons: 1) Subtracting MLLW soundings from ellipsoidal soundings results in a continuous surface of MLLW/ellipsoid separation at the resolution of the multibeam survey. While it is true that every sounding on a given ping will have the same separation, the data presented in this manner is easier to visualize. 2) Since soundings are used as an intermediate calculation in the procedure, it is possible to compare sounding positions from both methods. Starting with the same kinematic position at the common reference point in both cases, the soundings should have the same position on the seafloor if refracted through the same water column. This technique also verifies that the sound velocity profile has been entered at the same point in each instance and that it has not, inadvertently, moved one calculation up or down in the water column with respect to the other. This aids in checking for gross errors in dynamic draft or altitude. This procedure is essentially measuring from the seafloor to the ellipsoid and from the seafloor to MLLW and then calculating the difference between the two datums everywhere in the survey area. In real time, the PosMV uses the top center of the top hat, the casing around the IMU, as its reference point. PosPac, the processing software, uses the center of mass of the IMU itself as the reference point. This relationship is shown in Figure 3. PosPac software will report an offset between the user-entered primary GPS offset and its own calculated GPS offset if this change in reference point is neglected. The final calculated elevation appears very robust and
does not change significantly with a 10 cm vertical error in the primary antenna offset. However, the draft needs to be modified to reflect the new reference point. Figure 3: Relative locations of the PosMV and PosPac reference points After processing in PosPac, position and altitude data are inserted in the Caris HIPS file structure. All data were calculated at 50 Hz. Positions are substituted in using the generic data parser. The correction to the ellipsoid, altitude minus draft, is used in place of the tide file. The Caris vessel configuration file is modified to ignore heave since the heave component is contained in the altitude. The general processing method was as follows: 1. KGPS/Attitude data post-processed resulting in PPK positions, altitude and attitude. 2. A duplicate copy of the original tidal data set is created. 3. Vessel configuration files are modified to account for offsets changes and to remove heave. 4. Lines without PPK altitude data are identified and removed from both sets. 5. Altitude data loaded in to Caris as a tide for each line, corrected for waterline offset. 6. Dynamic draft corrections are removed from the PPK GPS data set. 7. The PPK GPS data set is SVP corrected to remove heave corrections from original processing. 8. Tidal data set is SVP corrected to ensure same profiles are used in both data sets. 9. All lines are re-merged.
10. Grids are created and exported in XYZ format. 11. PPK data set is corrected for the known MLLW / ellipsoid separation in Sand Point or Sitka. This value was determined at the tide gauge by John Oswald & Associates, LLC. 12. Both data sets are rendered and analyzed in Fledermaus. Difference surface and contours are created. Results - Shumigan Data coverage for the Shumigan survey is shown in Figure 4. The areas where a complete PPK solution was calculated are shown. Holes in the data are almost all from logging issues associated with the 200 Hz IMU data in the PosMV. Data were collected using two vessels: Quicksilver and Surveyor 1. Quicksilver used a Reson 8101, Surveyor 1 was fitted with an 8111. Both had identical PosMV and acquisition suite configurations using Pelagos Precise Timing. Corrected depths (MLLW) at Shumigan ranged from 0 to 200m and the tide range was generally 2 to 3 meters during the survey. Figure 4: Shumigan survey area. Only data areas with both ellipsoid and tide reduced soundings are shown.
The general relationship between NAD83, MLLW and NAVD88 (Geoid99) is shown in Figure 5. The NAD83 to MLLW separation for Shumigan, as measured by the technique described here, is shown in Figure 6. This surface is corrected for the NAD83 to MLLW separation at the Sand Point tide gauge, 945-9450. Oswald & Associates reported the Sand Point Separation as 16.318m. Figure 5: Geoid99 and MLLW separations at Sand Point Gauge 945-9450 (From Oswald & Associates) A number of features are immediately apparent in Figure 6. There is a regional Northwest to Southeast dip in the surface. On closer inspection it looks like the separation mimics the general bathymetry. The geoid separation (Geoid99) in this area also follows the general bathymetry, as shown in Figure 7. There is general agreement between the difference surface shown in Figure 6 and the geoid separation shown in Figure 7. This result demonstrates that tidal datum tracks NAVD88 (Geoid99). However, taken from another perspective, it may be possible to use the NAD83 to MLLW separation to better model the geoid height. There are clearly a number of localized features in Figure 6 that don t appear in Figure 7. These local features can be placed into 4 categories: 1- Local meteorological variations that affect the survey vessel differently than the tide gauge, 2- Transient hydraulic effects such as a tidal bore or Maelstrom like features or any other event that occurs between the bandwidth of the tide gauge and heave sensor, 3- Geoid undulations below the resolution of the Geiod99 model and finally, 4- Noise from any of a number of sources not limited to: a. PPK processing accuracy limitations, b. error in vessel squat settlement estimation in rough weather or while maneuvering and c. error in static draft measurement.
Figure 6: Shumigan NAD83 to MLLW separation from PPK bathy MLLW bathy. Data is corrected for NAD83 to MLLW separation at the Sand Point gauge Static draft, for the survey vessels used, varied by a few centimeters from day to day. Figure 8 shows the daily waterline measurements from one of the survey vessels, M/V Quicksilver. The large changes in draft are typically associated with vessel refueling. During survey operations, draft changes of about 1-2 cm are common. This waterline change should be relatively linear during a survey day and should not result in an abrupt discontinuity in the PPK altitude calculation.
Figure 7: Geiod99, 50 m grid, using the same color lookup table shown in Figure 6 Quicksilver Waterlines - JD125 to JD206-0.35-0.37 Static Draft -0.39-0.41-0.43-0.45-0.47 125 129 133 136 140 144 147 149 153 161 Julian Day Figure 8: Survey Vessel (Quicksilver) draft variation 165 170 175 179 183 188 192 200 204
Results - Sitka Bathymetry for the Sitka survey area is shown in Figure 9. As noted with the Shumigan data set, only areas where both ellipsoid and tide reduced soundings were calculated are shown. Shoals-1000T LIDAR data was also collected in Sitka along the shoreline on the eastern side of the sheet. It is possible to extract water surface elevation data from the Shoals-1000T. The process is, of course, very different from the technique described earlier in this paper. Figure 9: Sitka Bathymetry. Only data areas with both ellipsoid and tide reduced soundings are shown The NAD83 to MLLW separation at Sitka is shown in Figure 10 and the Geiod99 separation in Figure 11. The same look up table is used in both figures. The two surfaces have the same general trend but the slopes differ. Near the Sitka tide gauge in the Northeast corner of the survey area, the PPK calculated separation has less slope than the Geiod99 separation. In order for the surfaces to converge at the tide gauge, the PPK calculated separation in the uncharted area between the northeast corner of the survey area and the tide gauge will need to have a greater slope than the Geoid99 model. This feature was also noticed during LIDAR operations.
Like the Shumigan data, the Sitka MLLW to ellipsoid separation data exhibits a number of artifacts that are not seen in either the tide reduced bathymetry or the Geiod99 model. Some of these are particularly compelling and appear to be the result of sea surface undulations that are not captured by either the tide gauge or the heave sensor. John Hughes Clark has previously suggested the possibility of such motion. An example is shown in Figure 12. The profile is taken along the western edge of the survey area. An artifact that has the look of an uncorrected long period swell is clearly visible in the data. The original tide reduced data was processed using TrueHeave, which uses a sample window of about 100 seconds for its filter. The longest event that this filter will see is about 50 seconds or 0.02 Hz. The tide gauge, on the other hand, is sampling on six minutes intervals. The shortest events that it will measure, in both phase and amplitude, are on the order of 24 minutes or 0.0007 Hz. Everything in between these two frequencies goes unmeasured in tide and heave reduced data. However, it is captured using inertially aided PPK processing Figure 10: Sitka NAD83 to MLLW separation from PPK bathy MLLW bathy. Data is corrected for NAD83 to MLLW separation at the Sitka gauge
Figure 11: Geiod99, 50 m grid, using the same color lookup table shown in 10 Figure 12: Sitka MLLW ellipsoid separation, short term variance
Conclusions: Knowledge of the ellipsoid to MLLW separation at a tide gauge is not sufficient to correct a KGPS hydrographic survey to MLLW. The separation must be known over the entire survey area. Geoid99 model in these areas appears to be a good estimate for the shape of the ellipsoid to MLLW separation. Using the technique described, it is possible to estimate, and/or refine, the geoid model from hydrographic data by using PPK altitude and tide gauge separation values. Undulations in the water surface that fall in between the bandwidth of the tide gauge and the heave sensor can be identified and corrected. These deviations from the tidal datum cannot be measured by tide gauge and heave reduced data. Further investigations should include explicit confirmation of the latest geoid model as a pattern for ellipsoid to MLLW separation. The effect of short-term variations in sea surface elevation on the hydrographic error budget should be analyzed. Acknowledgments: The Authors and Fugro Pelagos, Inc would like to thank NOAA, National Ocean Service Office of Coast Survey for funding the data collection and processing for this work. We also received valuable assistance from John Oswald & Associates, Applanix, and Optech, Inc. References: John Oswald & Associates, LLC, Determination of the Separation between the ellipsoid and MLLW in the Shumigan Islands, Alaska, Prepared for LCMF and Fugro Pelagos, Inc., Delivered to NOAA National Ocean Service Office of Coast Survey. John E. Hughes Clarke, Swath Sonar Surveying: A multi-sensor integration nightmare, presented at the Applanix Users Group Conference, 2004, Toronto, Ontario.