Rainfall Assimilation Using a New Four-Dimensional Variational Method:A Single-Point Observation Experiment

Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.

Weighted variation after projection method for low-lying nonyrast states

We propose a simple algorithm to further improve the previous variation after projection(VAP)wave functions for low-lying nonyrast states.We attach a weight factor to each calculated energy;then,the sum of these weighted energies is minimized.It turns out that a low-lying nonyrast VAP wave function can be further optimized when the weight factor for the corresponding energy is far larger than the other ones.Based on the improved WVAP wave functions,the energy-variance extrapolation method is applied to estimate the exact shell model energies.The calculated results for nuclei in the sd and pf model spaces clearly show that the extrapolated energies for all the calculated states are very close to the exact shell model ones within 10 keV.

Finding optimal basis states for variation after projection nuclear wave functions

The variation after projection(VAP)method is expected to be an efficient way of obtaining the optimized nuclear wave functions,which can be as close as possible to the exact shell model ones.However,we found that there are two additional problems that may seriously affect the convergence of the VAP iteration.The first problem is the existence of irrelevant projected basis states.At a VAP iteration,the Hill-Wheeler(HW)equation is composed of all updated projected basis states.If one of these projected basis states does not mix with a calculated wave function of interest,which is obtained by solving this HW equation,it is likely that this basis state will never mix with this wave function even after the VAP iteration converges.The other problem is the poor orthonormality among the projected basis states,which seriously affects the accuracy of the calculated VAP wave function.In the present work,solutions for these two problems are proposed,and examples are presented to test the validity.With the present solutions,the most important projected basis states can be reliably obtained,and the fully optimized VAP wave functions can be accurately and efficiently calculated.

Extending the VDPC+BCS formalism by including three-body forces

Recently,Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian.The present study extends this formalism by including three-body forces.The result is the same as the so-called variation after particle-number projection in the BCS case,but now,the particle number is always conserved,and the time-consuming projection is avoided.Specifically,analytical formulas of the average energy are derived along with its gradient for a three-body Hamiltonian in terms of the coherent-pair structure.Gradient vanishment is required to obtain analytical expressions for the pair structure at the energy minimum.The new algorithm iterates on these pair-structure expressions to minimize energy for a three-body Hamiltonian.The new code is numerically demonstrated when applied to realistic two-body forces and random three-body forces in large model spaces.The average energy can be minimized to practically any arbitrary precision.

The Connection Between the Metric and Generalized Projection Operators in Banach Spaces

In this paper we study the connection between the metric projection operator PK ： B →K, where B is a reflexive Banach space with dual space B^＊ and K is a non-empty closed convex subset of B, and the generalized projection operators ∏K ： B → K and πK ： B^＊ → K. We also present some results in non-reflexive Banach spaces.

CT local reconstruction of solid rocket motor based on PI-POCS-TVM

In order to test the defects of solid rocket motor(SRM)accurately and efficiently,the computed tomography(CT)inspection scheme for SRM's defects was investigated and a CT local reconstruction algorithm called prior information-projection onto convex sets-total variation minimization(PI-POCS-TVM)was developed.The SRM was first inspected by industrial CT(ICT)to generate a low-resolution SRM image used as the prior information,then high-resolution local inspection was carried out for SRM's defects.To validate the effectiveness of the CT inspection scheme for SRM's defects,one SRM was inspected by a narrow fan beam ICT system.Filtered back projection(FBP)algorithm,POCS,POCS-TVM and PI-POCS-TVM algorithms were applied to reconstruct CT images.The performance of these algorithms was also compared.Results demonstrated the effectiveness of the CT inspection scheme for SRM's defects.Moreover,the PI-POCS-TVM algorithm has better local reconstruction image quality than the other three algorithms,showing great significance for accurate measurement of SRM's defects.