Extracting the interference components of normal modes in shallow water waveguide using singular value decomposition method

The normal mode interference characteristic in shallow water waveguide is a valu- able topic in the fields of underwater acoustic. A method for extracting the interference components of normal modes from broadband acoustic propagation data recorded by a single hy- drophone without any prior information is present in this paper. First, a Hermitian matrix is formed by the power spectral density. Second, a singular value decomposition （SVD） is performed on the Hermitian matrix to obtain the orthonormal eigenvectors, which are proportional to the interference components of normal modes. The fundamental equations of the new extracting method are derived based on normal mode and waveguide invariant theory. And the validity of the present method is verified by the numerical simulation and experimental results. In addition, the extracted results of normal-mode interference components are intended to be used for passive ranging of broadband sources.

Scattering of Surface Water Waves Involving Semi-infinite Floating Elastic Plates on Water of Finite Depth

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Mobility and equilibrium stability analysis of pin-jointed mechanisms with equilibrium matrix SVD

Under certain load pattern, the geometrically indeterminate pin-jointed mechanisms will present certain shapes to keep static equalization. This paper proposes a matrix-based method to determine the mobility and equilibrium stability of mechanisms according to the effects of the external loads. The first and second variations of the potential energy function of mechanisms under conservative force field are analyzed. Based on the singular value decomposition (SVD) method, a new crite- rion for the mobility and equilibrium stability of mechanisms can be concluded by analyzing the equilibrium matrix. The mobility and stability of mechanisms can be classified by unified matrix formulae. A number of examples are given to demonstrate the proposed criterion. In the end, criteria are summarized in a table.

Doppler Radar Data Assimilation with a Local SVD-En3DVar Method

An observation localization scheme is introduced into an ensemble-based three-dimensional variational （3DVar） assimilation method based on the singular value decomposition technique （SVD-En3DVar） to im- prove assimilation skill. A point-by-point analysis technique is adopted in which the weight of each obser- vation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting （WRF） model, is designed to test the scheme. The results are compared with those ob- tained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from i0 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.

Quasi-3-yr Cycle of Rainy Season Precipitation in Tibet Related to Different Types of ENSO during 1981–2015

The rainy season precipitation in Tibet（RSPT） is a direct cause for local floods/droughts. It also indirectly affects the thermal conditions of the Tibetan Plateau, which can result in anomalous patterns of atmospheric circulation over East Asia. The interannual variability of the RSPT is often linked with the El Ni？o–Southern Oscillation（ENSO）, but the relevant mechanisms are far from being understood, particularly for different types of ENSO events. We investigated the interannual variation of the RSPT in association with different types of ENSO. A quasi-3-yr period of the RSPT（less–more–more precipitation） was significant at the 95% confidence level. A joint multi-taper method with singular value decomposition analysis of the coupled field between the RSPT and the sea surface temperature（SST）revealed that the developing eastern Pacific type El Ni？o was accompanied by a decrease in the RSPT. The shift from the central Pacific type El Ni？o to the eastern Pacific La Ni？a was accompanied by an increase in the RSPT. Weakening of the central Pacific La Ni？a was accompanied by an increase in the RSPT. Analysis of the mechanism of this coupling, using the same analysis method but other climatic factors, indicated that the gradually strengthening eastern Pacific El Ni？o can inhibit the Walker circulation, weakening the South Asian summer monsoon, and resulting in transport of less water vapor from the Bay of Bengal to Tibet. The change from the central Pacific El Ni？o to the eastern Pacific La Ni？a led to continued strengthening of the Walker circulation with westward movement of the ascending area. This enhanced the South Asian summer monsoon over the Arabian Sea and transported more water vapor to Tibet. The decreasing central Pacific La Ni？a accompanied by persistent cooling of SSTs in the equatorial Pacific led to a strong eastern North Pacific summer monsoon, causing an anomaly in the easterly transport of water vapor from the Sea of Japan to Tibet and increased RSPT.