scholarly journals Parameter Estimation for a 2D Tidal Model with POD 4D VAR Data Assimilation

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Shouguo Qian ◽  
Xianqing Lv ◽  
Yanhua Cao ◽  
Fenjing Shao
Keyword(s):  
Data Assimilation ◽  
Altimeter Data ◽  
Open Boundary ◽  
Phase Lag ◽  
Open Boundary Conditions ◽  
Control Variables ◽  
Tidal Model ◽  
Reduced Order ◽  
Spatially Varying ◽  
Proper Orthogonal

Combining the proper orthogonal decomposition (POD) reduced order method and 4D VAR (four-dimensional Variational) data assimilation method with a two-dimensional (2D) tidal model, a model is constructed to simulate theM2tide in the Bohai, Yellow, and East China Seas (BYECS). This model consists of two submodels: the POD reduced order forward model is used to simulate the tides, while its adjoint model is used to optimize the control variables. Numerical experiment is carried out to assimilate the harmonic constants, which are derived from TOPEX/Poseidon (T/P) altimeter data, into the 2D tidal model through optimizing the initial values and the temporally and spatially varying open boundary conditions (OBCs). The absolute mean difference between the model results and observations is 3.2 cm and 2.9∘for amplitude and phase-lag, respectively, better than the results of Lu and Zhang (2006), suggesting that the construction of the POD reduced order model and the inversion of control variables are successful.

scholarly journals Estimation of Open Boundary Conditions Based on an Isopycnic-Coordinate Internal Tidal Model with Adjoint Assimilation Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanqiu Gao ◽  
Guangzhen Jin ◽  
Haibo Chen ◽  
Xianqing Lv
Keyword(s):  
Boundary Conditions ◽  
Internal Tide ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Tidal Model ◽  
Good Ability ◽  
Order Of Magnitude ◽  
Adjoint Assimilation ◽  
Spatially Varying ◽  
Group 1

The isopycnic-coordinate internal tidal model with adjoint assimilation method is developed into a three-layer version. Two groups of ideal experiments are carried out in order to investigate the estimation of spatially varying open boundary conditions (OBCs). In group 1, different independent point schemes (IPSs) are used to invert 6 kinds of prescribed distributions of OBCs. Results show that, after assimilation, the cost functions and their gradient norms are reduced by about 2 orders of magnitude and by about 1 order of magnitude, respectively; the mean absolute errors (MAEs) in OBCs and the vector differences of horizontal current are reduced by 1 order of magnitude and by more than 23.53% compared with the values before assimilation, respectively. The results demonstrate that the three-layered model has a good ability in estimating the spatially varying OBCs; the use of IPSs can effectively improve the estimation precision; fewer independent points are feasible when the distribution is simpler, and appropriately more independent points are required when the distribution is more complex. In group 2, by using the optimal IPSs in group 1, the model is also able to successfully invert the OBCs on a real topography in the Luzon Strait area. The results are important to the study of the internal tide in the South China Sea.

scholarly journals Estimating Smoothly Varying Open Boundary Conditions for a 3D Internal Tidal Model with an Improved Independent Point Scheme

2018 ◽  
Vol 35 (6) ◽  
pp. 1299-1311 ◽  
Author(s):  
Dong Jiang ◽  
Haibo Chen ◽  
Guangzhen Jin ◽  
Xianqing Lv
Keyword(s):  
Boundary Conditions ◽  
Adjoint Method ◽  
Spline Interpolation ◽  
Northern South China Sea ◽  
Altimeter Data ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Independent Point ◽  
Tidal Model ◽  
Point Scheme

AbstractAn improved independent point (IP) scheme was proposed to estimate the open boundary conditions (OBCs) for a 3D internal tidal model through assimilating the TOPEX/Poseidon (T/P) altimeter data. Under the assumption that the OBCs were spatially and smoothly varying, values at a set of independent points along the open boundary were inverted using the adjoint method and values at other points were interpolated by the spline method. The scheme was calibrated through idealized experiments where the M2 tidal constituent in the northern South China Sea was simulated. The OBCs can be successfully inverted with the improved scheme and were better in spatial smoothness than the results obtained with the Cressman interpolation when embedded in the IP scheme. Simulations in realistic domains showed that the errors between simulations and observations were smaller when the spline interpolation was employed instead of the Cressman interpolation. Three boundary conditions of spline interpolation were used in simulations in realistic domains, and the result of the periodic boundary condition had the smallest error compared with the first and second boundary conditions.

scholarly journals Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow Seas

2017 ◽  
Vol 34 (8) ◽  
pp. 1661-1672 ◽  
Author(s):  
Haidong Pan ◽  
Zheng Guo ◽  
Xianqing Lv
Keyword(s):  
Boundary Conditions ◽  
Adjoint Method ◽  
Spline Interpolation ◽  
Altimeter Data ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Tidal Constituent ◽  
Spatially Varying

AbstractOpen boundary conditions (OBCs) of the M2 tidal constituent in the Bohai and Yellow Seas (BYS) were inverted successfully through assimilation of TOPEX/Poseidon (T/P) altimeter data. An improved independent points (IPs) scheme was employed in the inversion. Under the assumption that the OBC was spatially varying, values at a set of IPs along the open boundary were inverted using the adjoint method and those at other points were calculated by the spline interpolation. The OBC inverted with the improved scheme was closer to reality in terms of smoothness than that inverted with the Cressman interpolation. The scheme was calibrated in twin experiments. Practical experiments showed that the misfits between simulated results and observations were smaller when the spline interpolation was used.

scholarly journals Semi-Idealized Study on Estimation of Partly and Fully Space Varying Open Boundary Conditions for Tidal Models

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Jicai Zhang ◽  
Haibo Chen
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Adjoint Method ◽  
Open Boundary ◽  
Feature Points ◽  
Open Boundary Conditions ◽  
Negative Effects ◽  
Control Variables ◽  
Estimation Problems ◽  
Minimum Number

Two strategies for estimating open boundary conditions (OBCs) with adjoint method are compared by carrying out semi-idealized numerical experiments. In the first strategy, the OBC is assumed to be partly space varying and generated by linearly interpolating the values at selected feature points. The advantage is that the values at feature points are taken as control variables so that the variations of the curves can be reproduced by the minimum number of points. In the second strategy, the OBC is assumed to be fully space varying and the values at every open boundary points are taken as control variables. A series of semi-idealized experiments are carried out to compare the effectiveness of two inversion strategies. The results demonstrate that the inversion effect is in inverse proportion to the number of feature points which characterize the spatial complexity of open boundary forcing. The effect of ill-posedness of inverse problem will be amplified if the observations contain noises. The parameter estimation problems with more control variables will be much more sensitive to data noises, and the negative effects of noises can be restricted by reducing the number of control variables. This work provides a concrete evidence that ill-posedness of inverse problem can generate wrong parameter inversion results and produce an unreal “good data fitting.”

scholarly journals Domain Decomposition Method for the Variational Assimilation of the Sea Level in a Model of Open Water Areas Hydrodynamics

2019 ◽  
Vol 7 (6) ◽  
pp. 195 ◽  
Author(s):  
Valery Agoshkov ◽  
Natalia Lezina ◽  
Tatiana Sheloput
Keyword(s):  
Data Assimilation ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Open Water ◽  
Coastal Ocean ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Open Boundary ◽  
Open Boundary Conditions

One of the modern fields in mathematical modelling of water areas is developing hybrid coastal ocean models based on domain decomposition. In coastal ocean modelling a problem to be solved is setting open boundary conditions. One of the methods dealing with open boundaries is variational data assimilation. The purpose of this work is to apply the domain decomposition method to the variational data assimilation problem. The method to solve the problem of restoring boundary functions at the liquid boundaries for a system of linearized shallow water equations is studied. The problem of determining additional unknowns is considered as an inverse problem and solved using well-known approaches. The methodology based on the theory of optimal control and adjoint equations is used. In the paper the theoretical study of the problem is carried out, unique and dense solvability of the problem is proved, an iterative algorithm is proposed and its convergence is studied. The results of the numerical experiments are presented and discussed.

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