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This paper introduces a new test design technique and numerical property of implicit time integration techniques, described as "aliasing" of the external load that must be considered during the algorithm design process. If the bound is sufficiently small, A theorem determines whether a representative solution with aliasing can be bounded up to a set point by external force values and therefore treated as acceptable. This is not an issue for the U0 family of algorithms within the GSSSS-II framework, which contains many common and closely related techniques. However, the numerically dissatisfivable GSSSS II V0 family of methods is shown to have bounded aliasing that is not suitable for practical dynamic computations, while the "structically dissipative" Chang Family Method is shown to have unbounded aliasing that is not suitable for practical dynamic computations.
Source link: https://onlinelibrary.wiley.com/doi/10.1002/nme.6956
We show that daily Gravity Recovery And Climate Experiment results can be used to refine the non-tidal Dynamic Atmospheric Correction used to de-alias Jason altimetry and reduce high frequency errors. We first develop empirical function maps based on the ocean'model component of the DAC, then fit the GRACE and Jason results to those maps in order to achieve this. GRACE can show more of the 10-20-day altimetry signal in the combined Indian/Atlantic/Pacific region than the original dealiasing model can. We find that GRACE can demonstrate more of the first six modes in the North Pacific, 19 modes in the Southern Ocean, and three modes in the combined Indian/Atlantic/Pacific region than the original decoding model can. During times when GRACE data is available, we recombined these first GRACE modes with the remaining ocean-only DAC results to produce updated 10–20-day model. With less aliased signals incorrectly propagated to longer stretches, increased Jason altimetry results with improved Jason altimetry results with less aliased signals, which will result in higher Jason altimetry data with less aliased signals incorrectly propagated to longer stretches.
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