Examination for adjoint boundary conditions in initial water elevation estimation problems

A Numerical Study of Tsunami Generation by Horizontal Displacement of Sloping Seafloor

Journal of Earthquake and Tsunami ◽

10.1142/s1793431120500189 ◽

2020 ◽

Vol 14 (04) ◽

pp. 2050018 ◽

Cited By ~ 1

Author(s):

Chentong Hu ◽

Yifan Wu ◽

Chao An ◽

Hua Liu

Keyword(s):

Numerical Study ◽

Horizontal Displacement ◽

Vertical Displacement ◽

Horizontal Motion ◽

Generation Process ◽

Tsunami Generation ◽

Initial Water ◽

Horizontal Momentum ◽

The Difference ◽

Water Elevation

Tsunamis are generated primarily by the vertical displacement of the seafloor if the seafloor is flat. If the seafloor is slanted, the horizontal motion also contributes to the generation of tsunamis. A previous study proposed that such effects can be estimated by simply calculating the elevation of water due to the horizontal displacement of the slope. Two more studies later argued that the horizontal motion also results in horizontal momentum of the water, which amplifies the tsunami generation. In this study, we numerically simulate the tsunami generation process of flat and sloping seafloor. It is found that, for the flat seafloor, the initial water elevation equals the vertical seafloor displacement. For the sloping seafloor, the initial water elevation deviates from the vertical seafloor displacement, and the difference can be accurately evaluated by the horizontal seafloor displacement. Thus, the initial horizontal momentum of the water is negligible for tsunami generation.

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

Abstract and Applied Analysis ◽

10.1155/2013/282593 ◽

2013 ◽

Vol 2013 ◽

pp. 1-14 ◽

Cited By ~ 3

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.”

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Quasi-online flood forecasting downstream of dams based on rainfall thresholds

Hydrology Research ◽

10.2166/nh.2013.048 ◽

2013 ◽

Vol 45 (4-5) ◽

pp. 519-528 ◽

Cited By ~ 2

Author(s):

Bahram Saghafian ◽

Saeed Golian ◽

Hossein Khodadadi

Keyword(s):

Cross Sections ◽

Flood Control ◽

Flood Forecasting ◽

Rainfall Threshold ◽

Risk Tolerance ◽

Initial Water ◽

Reservoir Routing ◽

Prone Area ◽

Southwestern Iran ◽

Water Elevation

Dams are built to supply water to users and often to protect people and properties against floods in downstream areas. Efficiency of dams for flood control is improved substantially if a flood forecasting system is implemented. Rainfall threshold (RT) depths correspond to the occurrence of critical discharge at given cross-sections for given rainfall durations and initial soil moisture conditions of the upstream watershed. Here, we present an RT-based approach for offline flood forecasting downstream of dams. The proposed methodology incorporates rainfall-runoff and reservoir routing models while the spatial distribution of rainfall is probabilistically modeled based on a Monte Carlo approach. The RT curves are derived as a function of initial water elevation in the reservoir. The algorithm is implemented for a flood-prone area downstream of a dam in southwestern Iran. The results showed a clear rise in the RT values compared to the no-dam case, which is mainly due to the reservoir routing effect. The rate of rise in the RT values decreased with higher initial water elevation in the reservoir. The proposed method also provides the operator with the flexibility of adopting one of the various RT curves subject to different probabilities based on risk tolerance.

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Tsunami waveform inversion by numerical finite-elements Green’s functions

Natural Hazards and Earth System Science ◽

10.5194/nhess-1-187-2001 ◽

2001 ◽

Vol 1 (4) ◽

pp. 187-194 ◽

Cited By ~ 18

Author(s):

A. Piatanesi ◽

S. Tinti ◽

G. Pagnoni

Keyword(s):

Green's Functions ◽

Green’S Functions ◽

Least Square ◽

Inversion Method ◽

Initial State ◽

Initial Water ◽

Common Information ◽

Data Space ◽

Tide Gage ◽

Water Elevation

Abstract. During the last few years, the steady increase in the quantity and quality of the data concerning tsunamis has led to an increasing interest in the inversion problem for tsunami data. This work addresses the usually ill-posed problem of the hydrodynamical inversion of tsunami tide-gage records to infer the initial sea perturbation. We use an inversion method for which the data space consists of a given number of waveforms and the model parameter space is represented by the values of the initial water elevation field at a given number of points. The forward model, i.e. the calculation of the synthetic tide-gage records from an initial water elevation field, is based on the linear shallow water equations and is simply solved by applying the appropriate Green’s functions to the known initial state. The inversion of tide-gage records to determine the initial state results in the least square inversion of a rectangular system of linear equations. When the inversions are unconstrained, we found that in order to attain good results, the dimension of the data space has to be much larger than that of the model space parameter. We also show that a large number of waveforms is not sufficient to ensure a good inversion if the corresponding stations do not have a good azimuthal coverage with respect to source directivity. To improve the inversions we use the available a priori information on the source, generally coming from the inversion of seismological data. In this paper we show how to implement very common information about a tsunamigenic seismic source, i.e. the earthquake source region, as a set of spatial constraints. The results are very satisfactory, since even a rough localisation of the source enables us to invert correctly the initial elevation field.

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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