Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

1 IntroductionThe El Ni’o atmospheric physics oscillation is anabnormal phenomenon involved in the tropical Pacificocean- atmosphere interactions. Studies on the El Ni(ophenomenon are very attractive (Lin et al., 2000; Linet al., 2001, 2002; Wang, 2001; Feng et al., 2001;Feng et al., 2002; Liu et al., 2002; Wei and Chen,2003; Xie et al., 2002; Zhu et al., 2002; Pu et al.,2003; Gu et al., 2004; Yu and Liu, 2004). Lin and Mo(2004), Mo and Lin (2004) and Mo et al. (2004) alsostudied a s…     

Monitoring the Kuroshio Extension with Dynamically Constrained Synthesis of the Acoustic Tomography, Satellite Altimeter and in situ Data

A finite-difference quasigeostrophic (QG) model of an open ocean region has been employed to produce a dynamically constrained synthesis of acoustic tomography and satellite altimetry data with in situ observations. The assimilation algorithm is based upon the 4D variational data interpolation scheme controlled by the model's initial and boundary conditions. The data sets analyzed include direct and differential travel times measured at the array of five acoustic transceivers deployed by JAMSTEC in the region of the Kuroshio Extension in 1997, Topex/Poseidon altimetry, CTD soundings, and ADCP velocity profiles. The region monitored is located within the area 27.5°–36.5°N, 143°–155°. The results of assimilation show that mesoscale variability can be effectively reconstructed by five transceivers measuring direct and reciprocal travel times supported by relatively sparse in situ measurements. The misfits between model and data lie within the observational error bars for all the data types used in assimilation. We have compared the results of assimilation with the statistical inversion of travel time data and analyzed energy balances of the optimized model solution. Energy exchange between the depth-averaged and shear components of the observed currents reveals a weak decay of the barotropic mode at the rate of 0.2 ± 0.7⋅10⁻⁵ cm²/s³ due to topographic interaction. Mean currents in the region are unstable with an estimate of the available potential energy flux from the mean current to the eddies of 4.7 ± 2.3⋅10⁻⁵ cm²/s³. Kinetic energy transition has the same sign and is estimated as 2.8 ± 2.5⋅10⁻⁵ cm²/s³. Potential enstrophy is transferred to the mesoscale at a rate of 5.5 ± 2.7⋅10⁻¹⁸ s⁻³. These figures provide observational evidence of the properties of free geostrophic turbulence which were predicted by theory and observed in numerical experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Unified Variational Principle of Fluid Mechanics and Application on Solitary Subdomain or Point

-According to basic equations of fluid mechanics, this paper presents a unified variational principle of fluid mechanics (UVPFM) by using the optimization method of weighted residuals (OMWR). The advantages are as follows, the establishment of the functional and the variational principle is easy, it can change various problems of fluid mechanics derived by basic equations into a unified optimization problem, and the solution is the optimum one in some sense. According to the OMWR for the solitary subdomain, this paper uses UVPFM onto any solitary subdomain and gives the solution of the hydrodynamics equation which is suitable only for that solitary subdomain. According to the OMWR for solitary point, this paper uses UVPFM to any solitary point and gives the solution of the hydrodynamics equation (point solution) which is suitable only for that solitary point. As the solution for the solitary subdomain or solitary point is developed independently, the compatibility with other subdomain or other points, do     

A Reconstruction of Observed Profiles in the Sea East of Japan Using Vertical Coupled Temperature-Salinity EOF Modes

It is important to estimate hard-to-observe parameters in the ocean interior from easy-to-observe parameters. This study therefore demostrates a reconstruction of observed temperature and salinity profiles of the sea east of Japan (30°≈40°N, 140°≈150°E). The reconstruction was done by estimating suboptimal state from several values of the observed profiles and/or sea surface dynamic height (SDH) calculated from the profiles. The estimation used a variational method with vertical coupled temperature-salinity empirical orthogonal function (EOF) modes. Profiles of temperature and salinity in the subtropical region are effectively reconstructed from in situ temperature profile data, or sea surface temperature (SST) and SDH. For example, the analyzed temperature field from SST and SDH has an accuracy to within 1°C in the subtropical region. Salinity in the sea north of Kuroshio, however, is difficult to estimate because of its complex variability which is less correlated with temperature than in the subtropical region. Sea surface salinity is useful to estimate the subsurface structure. We also show the possibility that the estimation is improved by considering nonlinearity in the equation calculating SDH from temperature and salinity analysis values in order to examine the misfit between analysis and observation. Analysis using TOPEX/POSEIDON altimetry data instead of SDH was also performed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar)

I present the derivation of the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar), which is developed for adopting a non-diagonal background error covariance matrix in nonlinear variational analyses (i.e., analyses employing a non-quadratic cost function). POpULar is based on the idea of a linear preconditioned conjugate gradient method widely adopted in ocean data assimilation systems. POpULar uses the background error covariance matrix as a preconditioner without any decomposition of the matrix. This preconditioning accelerates the convergence. Moreover, the inverse of the matrix is not required. POpULar therefore allows us easily to handle the correlations among deviations of control variables (i.e., the variables which will be analyzed) from their background in nonlinear problems. In order to demonstrate the usefulness of POpULar, we illustrate two effects which are often neglected in studies of ocean data assimilation before. One is the effect of correlations among the deviations of control variables in an adjoint analysis. The other is the nonlinear effect of sea surface dynamic height calculation required when sea surface height observation is employed in a three-dimensional ocean analysis. As the results, these effects are not so small to neglect.     

变分同化方法在Lorenz系统中的简单应用研究

利用Lorenz模式作变分同化数值试验，通过对一个简单系统的讨论，介绍四维变分同化方法。对初值敏感性和观测点的个数及观测值作了对比试验，发现随着模式对初值敏感性的增加，同化效果会越来越差；观测点越少，观测值误差越大，这些都会影响同化效果，甚至导致同化失败。     

求解变分不等式的Newton迭代的半局部收敛性分析

分析了求解变分不等式Newton方法的半局部收敛性，建立了类似于Kantorovich定理的收敛性结果。该结果不仅为判断Newton方法的收敛性提供了可计算的充分条件，也给出了Newton方法的收敛域以及问题解的存在区域。同时，文章也得到了Newton方法的若干收敛性质，包含收敛阶以及可计算的误差估计式等。     

变参考慢度Born近似傅氏偏移

针对常规Born近似傅氏偏移方法对于剧烈横向变速介质不能精确成像的状况而提出了变参考慢度Born近似傅氏偏移，理论上解决了任意速度变化地质模型的偏移成像问题。此外，为进一步提高复杂地层的成像精度和波场延拓算子的稳定性，对散射波场的计算公式作了改进。将改进的方法运用于盐丘模型的正演和偏移试验，并与常规Born近似偏移方法相比较，可明显看出变参考慢度Born近似傅氏偏移方法在效果上要优于后者，其处理速度横向变化的能力大大增强。     

GPS折射角资料的变分同化试验

越来越多的新型观测资料为数值天气预报水平的进一步提高提供了许多新的机会。在各种新型的观测资料中,GPS(全球定位卫星系统)折射角资料无疑是非常重要的。GPS折射角资料具有分辨率高、全天候探测、覆盖全球等优点,实现对GPS折射角资料的变分同化,将具有非常重要的意义。文中介绍了如何获得及同化GPS折射角资料的原理。对GPS折射角资料的变分同化可以分为两种:间接同化和直接同化,文中对这两种方法都作了具体介绍。在变分同化的最小化过程中,计算效率无疑是最重要的,而优化步长的计算又直接关系到算法效率的成败。根据最小化算法的特点,通过数学推导,得出一种适合于各种最小化算法的计算优化步长的自适应方法。最后,还利用1995年10月11日的GPS折射角资料进行了数值试验,结果表明了变分同化方法和计算优化步长方法的有效性。