A comparison of error budgets for vertical positioning using traditional and RTK GPS approaches USM GPS workshop March 16-18, 2004 R.M. Hare, P.Eng., C.L.S. Canadian Hydrographic Service

Objectives To examine vertical error budgets for traditional and RTK GPS hydrography in estuarine/riverine, coastal, offshore and oceanic areas To examine vertical error budgets for traditional and RTK GPS hydrography in estuarine/riverine, coastal, offshore and oceanic areas To provide some insight into the requirements for RTK GPS through an examination of operational scenarios To provide some insight into the requirements for RTK GPS through an examination of operational scenarios

Vertical positioning Ship and launch sounding Ship and launch sounding –Estuarine/Riverine (very shallow, 5-20 m, EM3000) –Coastal (shallow, m, EM3000) –Offshore (medium, m, EM1002) –Oceanic (deep, 800 m – F.O.D., EM121A) Airborne (lidar) sounding (1-50 m) Airborne (lidar) sounding (1-50 m) Lidar topography Lidar topography Drying heights & elevations Drying heights & elevations Wave heights/tides from buoys Wave heights/tides from buoys Establishment/recovery of vertical datum Establishment/recovery of vertical datum

Traditional sounding reduction D = d + draft – WL d = r cos (θ+R) cos P r = range Θ = beam angle R = Roll angle P = Pitch angle Dynamic draft Charted Depth, D Chart datum Measured Depth, d Tide, WL θ r

Sounding error budgets - traditional Soundings Soundings –Measurement –Refraction –Attitude Heave Heave –Measurement –Induced by R&P Dynamic draft Dynamic draft –Static draft –Squat –Load changes –Buoyancy changes Tides/water levels Tides/water levels –Measurement –Filtering –Spatial prediction –Time synchronization

RTK GPS sounding reduction Dynamic draft Charted Depth, D Chart datum Measured Depth, d Tide, WL θ r Ellipsoid GPS RTK, Z Separation Model, M Antenna Height, A D = d + A – Z – M A = Δx sinP + Δy cosP sinR + Δz cosP cosR

Sounding error budgets – RTK GPS Soundings Soundings –Measurement –Refraction –Attitude RTK GPS elevation RTK GPS elevation Antenna height Antenna height –Lever arm –Roll and Pitch Separation model Separation model –Chart-datum – Ellipsoid

Four West Coast scenarios Scenario Estuarine/ Riverine CoastalOffshoreOceanic Location Fraser River Patricia Bay Nitinat Canyon Osborne Seamount MBESEM3000EM3000EM1002EM121A Depth 15 m 60 m 600 m 2500 m Distance <10 km <40 km > 40 km GPSRTKRTKLRKRTG ConditionsCalmCalmModerateRough Swell 0.2 m 0.4 m 1.5 m 4 m R&P 2 ° 7 ° 10 ° Refraction 2 m/s 1 m/s 0.5 m/s Sep. Model 0.2 m 0.05 m 0.3 m 0.1 m

Operational Scenarios Canada’s West Coast Canada’s West Coast –Osborne Seamount –Nitinat Canyon –Fraser River –Patricia Bay (IOS)

Permanent Water Level Network Victoria Patricia Bay New Westminster Vancouver Pt Atkinson Campbell River Port Hardy Bamfield Tofino Winter Harbour Bella Bella Prince Rupert Queen Charlotte City GPS Benchmarks Datum Separation values 20.34

Assumptions - GPS Coastal and Estuarine or Riverine (0 – 10 km): local RTK GPS Coastal and Estuarine or Riverine (0 – 10 km): local RTK GPS –Vertical accuracy: +/ m (68%) 1 Offshore (10 – 40 km): Long-range kinematic (LRK) Offshore (10 – 40 km): Long-range kinematic (LRK) –Vertical accuracy: +/ m (68%) 2 Oceanic (> 40 km): Global system, e.g. C-Nav (RTG) Oceanic (> 40 km): Global system, e.g. C-Nav (RTG) –Vertical accuracy: +/ m (68%) 3 All values for real-time at highest data rate All values for real-time at highest data rate 1. G. Lachapelle, Personal communication, Thales Navigation Aquarius LRK specifications at 20Hz, 40 km 3. C&C Technologies DGPS-PI Static accuracy of C-Nav RTG V13.1

Other assumptions Offshore and Oceanic surveys Offshore and Oceanic surveys –Done by ship –Larger lever arm –Greater draft uncertainty –More stable sound speed structure –No local tide gauge –Oceanographic phenomena Estuarine and Riverine surveys Estuarine and Riverine surveys –Done by launch –Draft uncertainty from buoyancy changes –Possible salt wedges –Sloping or stepped chart datum

Oceanographic phenomena: El Niño

Sea surface height maps showing the Haida and Sitka Eddies Sea surface elevations measured by TOPEX/Poseidon and ERS-2 satellite altimeters. Red regions denote high sea surface Blue regions denote depressions. Annotations by Ocean Science and Productivity Division, DFO Science

Fraser River scenario ElementValueTraditional RTK GPS Depth 15 m 0.09/0.15 Refraction 2 m/s 0.01/0.18 Roll angle 2°2°2°2°0/0.12 Heave 0.2 m 0.14N/A GPS Z N/A0.04 Lever arm 4.9 m N/A0.03 Tides <3.8 m 0.20N/A Dynamic Draft 0.8 m 0.10N/A Separation model ~ 21 m N/A 0.20 m TPE (95%) 0.23/ /0.30

Patricia Bay scenario ElementValueTraditional RTK GPS Depth 60 m 0.12/0.63 Refraction 1 m/s 0.03/0.46 Roll angle 2°2°2°2°0/0.51 Heave 0.4 m 0.14N/A GPS Z N/A0.04 Lever arm 4.9 m N/A0.03 Tides 3.8 m 0.05N/A Dynamic Draft 0.8 m 0.07N/A Separation model 20.8 m N/A 0.05 m TPE (95%) 0.21/ /0.92

Nitinat Canyon scenario ElementValueTraditional RTK GPS Depth 600 m 1.26/1.49 Refraction 0.5 m/s 0.13/0.55 Roll angle 7°7°7°7°0/2.54 Heave 1.5 m 0.21N/A GPS Z N/A0.12 Lever arm 22 m N/A0.03 Tides 4.1 m 0.3N/A Dynamic Draft 4 m 0.14N/A Separation model ~20 m N/A 0.30 m TPE (95%) 1.6/3.01.5/3.0

Osborne Seamount scenario ElementValueTraditional RTK GPS Depth 2500 m 4.7/8.9 Refraction 0.5 m/s 0.9/2.9 Roll angle 10° 0/6.7 Heave 4 m 0.55N/A GPS Z N/A0.35 Lever arm 28 m N/A0.04 Tides 2 m 0.2N/A Dynamic Draft 6 m 0.18N/A Separation model 10 m? N/A 0.10 m TPE (95%) 5.8/9.25.8/9.2

Comparison

Observations RTK GPS provides greater incremental improvement in shallow-water and for near-nadir beams RTK GPS provides greater incremental improvement in shallow-water and for near-nadir beams Sounder system errors tend to dominate - variable error contribution Sounder system errors tend to dominate - variable error contribution

Conclusions RTK GPS does not appear to provide huge benefits over traditional methods in terms of reducing total sounding error RTK GPS does not appear to provide huge benefits over traditional methods in terms of reducing total sounding error Benefits may come from operational efficiencies Benefits may come from operational efficiencies –No tide gauge installation –No need to measure dynamic draft –Possible heave estimation/reduction from higher data rate RTK elevations

Remaining questions Can we expect significant improvement from post-mission GPS? Can we expect significant improvement from post-mission GPS? Can/will GPS replace VRU for heave compensation? Can/will GPS replace VRU for heave compensation? How can we quantify real separation model errors? How can we quantify real separation model errors?