Some Experiments with Multivariate Objective Analysis Scheme of Heights and Winds Using Optimum Interpolation

A two-dimensional, multitvariate objective analysis scheme for simultaneous analysis of geopotential height and wind fields has been developed over Indian and adjoining region for use in numerical weather prediction. The height-height correlations calculated using daily data of four July months (1976-1979), are used to derive the other autocorrelations and cross-correlations assuming geostropic relationship. A Gaussian function is used to model the autocorrelation function. Since the scheme is multivariate the regression coefficients (weights) are matrix.Near the equator, the geostrophic approximation relating mass and wind is decoupled in a way similar to Bergman (1979). The objective analyses were made over Indian and adjoining region for 850, 700, 500, 300 and 200 hPa levels for the period from 4 July to 8 July 1979, 12 GMT. The analyses obtained using multivariate optimum interpolation scheme depict the synoptic situations satisfactorily. The analyses were also compared with the FGGE analyses (from ECMWF) and also with the station observations by computing the root mean square (RMS) errors and the RMS errors are comparable with those obtained in other similar studies.

An effective method for improving the accuracy of Argo objective analysis

Based on the optimal interpolation objective analysis of the Argo data, improvements are made to the em- pirical formula of a background error covariance matrix widely used in data assimilation and objective anal- ysis systems. Specifically, an estimation of correlation scales that can improve effectively the accuracy of Ar- go objective analysis has been developed. This method can automatically adapt to the gradient change of a variable and is referred to as ＂gradient-dependent correlation scale method＂. Its effect on the Argo objective analysis is verified theoretically with Gaussian pulse and spectrum analysis. The results of one-dimensional simulation experiment show that the gradient-dependent correlation scales can improve the adaptability of the objective analysis system, making it possible for the analysis scheme to fully absorb the shortwave information of observation in areas with larger oceanographic gradients. The new scheme is applied to the Argo data obiective analysis system in the Pacific Ocean. The results are obviously improved.

ELASTIC DYNAMIC ANALYSIS OF MODERATELY THICK PLATE USING MESHLESS LRPIM

A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.

Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity

A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete cavitation solution is obtained, and the convergence of the method is proved. An algorithm combined a gradient type method with a damped quasi-Newton method is applied to solve the discretized nonlinear equilibrium equations. Numerical experiments show that the Fourier-Chebyshev spectral method is efficient and capable of producing accurate numerical cavitation solutions.