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 Optimization of Open Boundary Conditions in a 3D Internal Tidal Model with the Adjoint Method around Hawaii

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Anzhou Cao ◽  
Haibo Chen ◽  
Jicai Zhang ◽  
Xianqing Lv
Keyword(s):  
Boundary Conditions ◽  
Adjoint Method ◽  
Internal Tide ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Tidal Model ◽  
Open Boundaries ◽  
Surface Manifestation

Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs) in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients ofM2internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs). In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP) strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, theM2internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.

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 Estimation of Open Boundary Conditions for an Internal Tidal Model with Adjoint Method: A Comparative Study on Optimization Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Haibo Chen ◽  
Chunbao Miao ◽  
Xianqing Lv
Keyword(s):  
Boundary Conditions ◽  
Line Search ◽  
Adjoint Method ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Open Boundary ◽  
Unknown Boundary ◽  
Bfgs Method ◽  
Open Boundary Conditions ◽  
Tidal Model

Based on an internal tidal model, the practical performances of the limited-memory BFGS (L-BFGS) method and two gradient descent (GD) methods (the normal one with Wolfe’s line search and the simplified one) are investigated computationally through a series of ideal experiments in which the open boundary conditions (OBCs) are inverted by assimilating the interior observations with the adjoint method. In the case that the observations closer to the unknown boundary are included for assimilation, the L-BFGS method performs the best. As compared with the simplified GD method, the normal one really uses less iteration to reach a satisfactory solution, but its advantage over the simplified one is much smaller than expected. In the case that only the observations that are further from the unknown boundary are assimilated, the simplified GD method performs the best instead, whereas the performances of the other two methods are not satisfactory. The advanced L-BFGS algorithm and Wolfe’s line search still need to be improved when applied to the practical cases. The simplified GD method, which is controllable and easy to implement, should be regarded seriously as a choice, especially when the classical advanced optimization techniques fail or perform poorly.

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 Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

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