Ocean Tide Loading in the British Isles

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Ocean Tide Loading in the British Isles

• Craig Allinson
• c.r.allinson_at_ncl.ac.uk

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Introduction

• Aim Measure Ocean Tide Loading (OTL) in the
  British Isles directly from GPS measurements.
• Data from BIGF archive, OSI, OSNI, CIL
• Difficult to estimate accurately current models
  show discrepancies in areas throughout the
  British Isles.
• OTL is Complicated in the British Isles
  (coastline and the propagation of tides)

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OTL in the British Isles
Animation provided by Dr Matt King, Newcastle
University
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Model Results

• RMS complex-valued amplitude difference (mm) for
  the vertical M2 OTL component from the following
  OTL models
• FES99, GOT00.2, FES95.2, TPXO.2 and CSR3
• Which are the most accurate?

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Measuring OTL from GPS

• Aim Estimate the amplitude and phase of each
  constituent, at each station in the network.
• Estimate the Vertical, East and North components
  of each OTL constituent
• Signals are strongly correlated difficult to
  separate
• OTL signals range 11.97-12.66 hours
  (semi-diurnal) and 23.97-25.83 hours (diurnal)
• Estimation Strategy
• Process 1000-day span of GPS data at each
  location (or as much data as possible)
• Use the PPP approach in the GIPSY/OASIS II
  software
• Each location processed independently
• Each RINEX file (24-hour data span) processed
  independently
• Estimate the 8 harmonic constituents along with
  Wet Z troposphere and site coordinates
• Minimize/model inaccuracies in GPS measurement
• Troposphere modeled as a random walk parameter
• JPL final precise orbits used

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Estimation Strategy

• Retain the following information for further
  post-processing
• parameter estimates
• Variance/covariance information
• Least Squares solution
• Kalman filter approach
• Adjust parameter estimates using covariance
  information
• Apply correct scaling to the weight matrices
  (iterative solution)
• Then apply astronomical argument correction and
  nodal corrections
• Results in an averaged estimate of each
  constituent.
• Accuracy improves as more data is added to the
  solution
• Current progress - 12 GPS sites have been
  processed so far.

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Location map of GPS stations

• The 12 GPS stations used in the study to date.
• Chosen to cover a range of locations with
  differing OTL magnitudes.
• Distributed throughout the British Isles, in
  coastal and inland locations.
• Contours show the predicted M2 amplitude from
  FES99 OTL model (mm).

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LEED Results

• 1000-day final results for the vertical OTL
  component, with 95 confidence error ellipses
  (scale in mm) .
• Model data provided from the FES99, FES95.2,
  GOT00.2, CSR3, TPXO.2, TPXO.6 and NAO.99b models
• Model agreement
• Generally good for amplitude component
• Best agreement with FES99 misfit of just 7,
  compared to TPXO.2 22.
• gt2000-days required to resolve K2, K1, P1 and Q1

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Current Work Data span study

• Aim to establish the necessary quantity of data
  to sufficiently resolve the OTL estimates
• Estimates from the Kalman filter method improve
  as more data is added into the solution
• N-days of GPS data in the solution.
• Where N 1,2,3.25,30,35..100,125,150..200
• Each N-day result compared to true 1000-day
  result.
• Can establish the level of accuracy achievable
  with N-days of data
• Useful for establishment of temporary stations

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LEED Results Case study

• Case study LEED, chosen as it is a good
  representation of results from other locations.
• Convergence graph M2 complex-valued amplitude
  from all stations (vertical component)

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Results - Vertical Component
Diurnal
K1
Q1
O1
Semi-diurnal
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Results North/East Components

• North/East components are half the magnitude of
  the vertical component.
• Convergence appears to be better in North/East
  signal
• Not true, Just smaller in magnitude
• Actually follow same trend

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Conclusion

• Kalman filter estimation method requires a
  minimum of 90-days for sufficient resolution of
  diurnal and semi-diurnal components
• Useful for temporary stations
• The 1000-day results have shown good resolution
  for M2, S2 and O1
• For a similar resolution, at least 2000-days are
  required for the K2, K1, P1 and Q1 constituents
• N2 constituent has unexpected large misfit??
• Future Work
• Process data and produce combined results for all
  semi-diurnal and diurnal constituents
• Define specific method to estimate longer-period
  signals and generate estimates

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Questions?