Improved shallow waters tidal estimates using satellite radar altimetry data and numerical modeling

Abstract

Satellite observations can help in the retrieval of constituents in
shallow waters. Noise contamination, however, makes smaller constituents
irretrievable and large sources of error. Throughout shallow areas, the
constituent’s relevancy changes. For example, near an amphidromic point
where M2 relevance drops, so does the potential of satellite
contribution for improving its accuracy. Moreover, shallow waters are
generally influenced by many constituents (>100). Accurately
retrieving all these constituents with satellite radar altimeter data
alone is not possible. Series length requirements imposed by the
Rayleigh criteria to separate constituents are still unavailable.

Removing unwanted signals from satellite observations improves
least-squares-based harmonic estimates, given an inversion matrix with
the same condition number. This variance reduction is the core of the
remove compute restore approach commonly used. First, residual harmonic
sets are computed with the difference between observations and model
background estimates through conventional or weighted least-squares.
Then, the residual harmonics are added to the background model
estimates.

Here we implemented a method that extends the typical approach by
including model background estimate and error covariance in the
least-squares step. This inclusion helps to weigh between constituents
well represented in the model and those that must be updated.

To test the method, we designed a semi-synthetic experiment. First, we
used tide gauge data to generate a satellite equivalent dataset and
compared estimations between the two methods listed above and the model
estimate. Next, we applied the method to compute tidal estimates along
satellite radar altimeter tracks (T/P Jason) in the 2D Dutch Coastal
Shelf Model (DCSMv6) domain.

Results from the synthetic experiment show that the second method
produces consistently better estimates reducing RSS consistently through
temporal cross-validation. In addition, it provides an effective way of
keeping as many constituents estimates as the model series can resolve,
adding the benefits of satellite observations. Finally, results from
the North Sea implementation show the new estimates increase the
variance reduction of satellite residuals across the whole domain
relative to background tidal estimates. The range of improvements varies
between 0 and 3cm, which is significant given already very accurate
model background estimates. The benefited areas include the English
Channel, the Irish Sea, the English North-Sea Coast, the Bay of Biscay,
the German Bight, and the North Atlantic region close to the upper
boundary of the model domain.