# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Inversion of three-dimensional tidal currents in marginal seas by assimilating satellite altimetry. (English) Zbl 1225.76300
Summary: The four-dimensional variational data assimilation technology based on the theory of inverse problem is applied to simulate the three-dimensional tidal currents in the marginal seas by assimilating the satellite altimetry. The model is calibrated by the twin experiments where the prescribed open boundary conditions for a three-dimensional barotropic tidal model are successfully inverted. By assimilating the tidal harmonic constants derived from TOPEX/Poseidon altimeter data, the open boundary conditions are optimized and the ${M}_{2}$ tidal currents in the Bohai and Yellow Seas (BYS) are simulated in the practical experiment. During the assimilation, the cost function and the gradients of cost function with respect to the open boundary conditions have been decreased significantly. Although the current observations are not assimilated into the model, the cost function composed of the data misfit between model-produced and observed currents is still decreased from 1.00 to 0.09, which demonstrates the reasonability and feasibility of inverting tidal currents from satellite altimetry or other elevation measurements. The co-tidal charts and the near-surface ${M}_{2}$ tidal current ellipses obtained in the practical experiment are in good agreement with the observed tides and tidal currents in BYS.
##### MSC:
 76U05 Rotating fluids 86A05 Hydrology, hydrography, oceanography 86A22 Inverse problems in geophysics
L-BFGS