LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions oftravelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibriumpoint of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves arealso found.The computational results show that if their amplitudes are equal at the initial time,the amplitudeincrements of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for makingthe amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h fornonlinear instability,the latter is in agreement with the observations in the real atmosphere.     

线性和非线性正压不稳定

本文从无摩擦的、无辐散的非线性正压涡度方程出发,利用行波解,在相平面上对方程的平衡点分别导得线性和非线性正压不稳定判据,与传统的不稳定判据作了比较分析。还求得了线性和非线性不稳定波的解析解,计算结果表明,若初始时刻两者波幅相等,则以后非线性不稳定波幅的增长值总小于线性不稳定波幅的增长值。非线性效应有使线性不稳定指数型增长减缓的作用。不稳定使得振幅比初始时刻增大一倍所需要的时间,对于线性不稳定大约是6h,对于非线性不稳定大约是18h,后者与实际大气中的观测事实是一致的。     

Nonlinear oscillations of semigeostrophic Eady waves in the presence of diffusivity

Analyses are performed to examine the physical processes involved in nonlinear oscillations of Eady baxoclinic waves obtained from viscous semigeostrophic models with two types of boundary conditions (free-slip and non-slip). By comparing with previous studies for the case of the free-slip boundary condition, it is shown that the nonlinear oscillations are produced mainly by the interaction between the baroclinic wave and zonal-mean state (total zonal-mean flow velocity and buoyancy stratification) but the timescale of the nonlinear oscillations is largely controlled by the diffusivity. When the boundary condition is non-slip, the nonlinear oscillations are further damped and slowed by the diffusive process. Since the free-slip (non-slip) boundary condition is the zero drag (infinite drag) limit of the more realistic drag boundary condition,the nonlinear oscillations obtained with the two types of boundary conditions are two extremes for more realistic nonlinear oscillations.     

输入非线性方程误差自回归系统的多新息辨识方法

典型块结构非线性系统包括基本的输入非线性系统、输出非线性系统、输入输出非线性系统、反馈非线性系统等.输入非线性系统包括输入非线性方程误差类系统和输入非线性输出误差类系统.以输入非线性方程误差自回归系统,即输入非线性受控自回归自回归(IN-CARAR)系统为例,分别基于过参数化模型,基于关键项分离原理,基于数据滤波技术以及基于辨识模型分解技术,研究和提出了IN-CARAR系统的随机梯度辨识方法、多新息随机梯度辨识方法、递推最小二乘辨识方法、多新息最小二乘辨识方法.这些方法可以推广到其他输入非线性方程误差系统、输入非线性输出误差类系统、输出非线性方程误差类系统、输出非线性输出类系统、反馈非线性系统等.同时,给出了几个典型辨识算法的计算步骤、流程图和计算量.     

Sensitivity of Nonlinearity on the ENSO Cycle in a Simple Air-sea Coupled Model

In this paper,the influence of the El NioSouthern Oscillation (ENSO) cycle on the sensitivity of nonlinear factors in the numerical simulation is investigated by conducting numerical experiments in a simple air-sea coupled model for ENSO prediction.Two sets of experiments are conducted in which zonal nonlinear factors,meridional nonlinear factors,or both are incorporated into the governing equations for the atmosphere or ocean.The results suggest that the ENSO cycle is very sensitive to the nonlinear factor of the governing equation for the atmosphere or ocean.Thus,incorporating nonlinearity into air-sea coupled models is of exclusive importance for improving ENSO simulation.     

辅助模型辨识方法(3):输入非线性输出误差自回归系统

输入非线性系统包括输入非线性方程误差类系统和输入非线性输出误差类系统.针对输入非线性输出误差自回归系统,分别基于过参数化模型,基于关键项分离原理,基于数据滤波技术,研究了相应的基于过参数化模型的辅助模型递推辨识方法、基于关键项分离的辅助模型递推辨识方法、基于数据滤波的辅助模型递推辨识方法.这些方法可以推广到其他输入非线性输出误差系统、输出非线性输出误差系统、反馈非线性系统等.并给出了几个典型辨识算法的计算步骤、流程图和计算量.     

A Nonlinear Representation of Model Uncertainty in a Convective-Scale Ensemble Prediction System

How to accurately address model uncertainties with consideration of the rapid nonlinear error growth characteristics in a convection-allowing system is a crucial issue for performing convection-scale ensemble forecasts. In this study, a new nonlinear model perturbation technique for convective-scale ensemble forecasts is developed to consider a nonlinear representation of model errors in the Global and Regional Assimilation and Prediction Enhanced System (GRAPES) Convection-Allowing Ensemble Prediction System (CAEPS). The nonlinear forcing singular vector (NFSV) approach, that is, conditional nonlinear optimal perturbation-forcing (CNOP-F), is applied in this study, to construct a nonlinear model perturbation method for GRAPES-CAEPS. Three experiments are performed: One of them is the CTL experiment, without adding any model perturbation; the other two are NFSV-perturbed experiments, which are perturbed by NFSV with two different groups of constraint radii to test the sensitivity of the perturbation magnitude constraint. Verification results show that the NFSV-perturbed experiments achieve an overall improvement and produce more skillful forecasts compared to the CTL experiment, which indicates that the nonlinear NFSV-perturbed method can be used as an effective model perturbation method for convection-scale ensemble forecasts. Additionally, the NFSV-L experiment with large perturbation constraints generally performs better than the NFSV-S experiment with small perturbation constraints in the verification for upper-air and surface weather variables. But for precipitation verification, the NFSV-S experiment performs better in forecasts for light precipitation, and the NFSV-L experiment performs better in forecasts for heavier precipitation, indicating that for different precipitation events, the perturbation magnitude constraint must be carefully selected. All the findings above lay a foundation for the design of nonlinear model perturbation methods for future CAEPSs.     

地-气耦合动力系统的研究

研究了一类地-气耦合系统的非线性模型,目的是创建一个地-气振子模型的非线性方程的渐近求解方法,利用变分迭代方法,构造了对应问题解的近似展开式。即首先引入一组泛函和计算出它们的变分,并算出Lagrange乘子,其次,决定变分迭代,最后得到原地-气振子模型非线性问题解的一致收敛的近似展开式。     

中国冬季气温对ENSO的非线性响应特征

运用一双排套装的非线性神经网络统计模型,讨论了中国冬季气温对ENSO事件的非线性响应特征。结果表明,响应具有较明显的非线性特征,且这种非线性主要表现在振荡强度的差异上,即气温对El Nino事件的响应程度强于对La Nina事件的响应。El Nino位相下,气温的正距平中心主要出现在东北、江淮、福建以及新疆南部;La Nina位相下,上述地区气温出现负距平中心,但振荡强度较弱。气温对ENSO的响应可分为线性响应部分和非线性响应部分,其中非线性响应解释的方差约占线性响应的2/5,因此非线性响应的作用不可忽视。     

Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model

The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For com-parison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear in-stability are discussed by use of the growth rate curves.The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenom-enon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form.