动态最优多因子组合的华北汛期降水模式误差估计及预报

利用国家气候中心季节预报1983—2009年27年模式预报结果,结合74项环流指数及美国国家海洋局和大气管理局提供的40个气候指数和美国气候预报中心实际降水分析资料,采用资料诊断分析和数值模拟实验相结合的方法,通过多因子的历史相似信息提取预报相似年,获得预报场的误差订正项.在这一订正思路的基础上,考虑前期关键影响因子的选取、多因子组合的优化配置,构建适用于不同预报年的区域动力-统计模式预报误差订正方案.以华北为例,探索多因子最优组合的多元客观相似判据,发展基于多因子动力-统计模式预报误差的动态订正新技术,改善华北夏季降水预报效果,提高预报技巧.通过2005—2009年独立样本回报结果表明,动态最优多因子组合相似订正方法距平相关系数评分相对于系统订正方法有着显著的提高,该订正方案对华北地区的夏季降水预测有着很好的业务前景,具有重要的应用价值,即将投入业务运行. 关键词： 关键因子集 模式误差估计 汛期降水 预测     

汛期降水相似动力预报——模式误差主分量相似预报方法

针对相似动力预报中模式预报误差的估计问题,提出将模式误差的直接相似订正问题转化成模式误差主分量的相似预报问题.客观上将模式误差主分量分成可预报和不可预报两部分, 对于可预报主分量采用最优多因子动态配置方案进行相似预报, 而对于不可预报部分则用系统平均代替.基于国家气候中心季节预报业务模式、 美国气候预报中心组合降雨分析资料及国家气候中心气候系统诊断预报室74项环流指数和美国国家海洋和大气管理局的40个气候指数,对东北区域汛期降水进行了预报试验. 2005—2010年6年独立样本检验预报平均距平相关系数为0.29,较系统误差订正预报的0.04有较大提高, 证实该方案能提高国家气候中心季节预报业务模式汛期降水预报水平.     

长江中下游汛期降水模式预测误差相似性及其可预报度

对数值模式预测误差进行相似预报进而订正模式预报结果,是提高模式预报水平的有效手段之一.本文从数值模式预测误差场存在相似性的角度出发,研究了长江中下游汛期降水逐年模式误差场间的相似性及其可预报性,探讨了数值模式预测误差在历史资料中的相似信息量,发现利用相似误差订正可以明显提高模式预报水平.进一步对历史模式预测误差场进行经验正交函数(EOF)分解,着重研究了误差场前三个特征向量的空间分布及其时间系数演化规律,发现对各分量分别进行相似预报可以简化预报对象,并且针对性更强,可以提高其潜在预报水平.在研究数值模式预测误差场相似性的基础上,定义了数值模式预测误差的相似可预报度,用以衡量逐年模式预测误差的可预测性,发现模式预测误差场前三个分量的相似可预报度明显高于原始模式误差场,揭示出有针对性地分别预报模式预测误差各分量的潜在应用价值.     

基于延伸期可预报性的集合预报方法和数值试验

集合预报是考虑初始条件和模式不确定性的有效途径. 结合延伸期可预报性特征,对具有不同特性的可预报分量和随机分量采用不同的集合预报方案和策略,发展了一种基于延伸期可预报性的集合预报新方法(PBEP).该方法以延伸期数值预报模式为平台,对可预报分量采用多个模式误差订正方案,从考虑模式不确定性的角度进行集合;而对随机分量则利用历史资料从气候概率的角度给出集合概率分布,避免模式误差对随机分量概率分布的影响.试验结果表明,相比于国家气候中心的业务动力延伸集合预报系统,该集合预报方法对全球各区域环流预报技巧均有提高,对不同空间尺度的波也有不同程度的改进,显示出潜在的业务应用前景.     

模式误差弱约束四维变分同化研究

经典四维变分同化(four dimensional variational data assimilation,简称4dvar)中认为模式是完美的, 而实际数值模式中存在的模式误差将对变分同化效果产生直接影响, 弱约束4dvar的提出为4dvar中考虑模式误差的影响提供了一种可行途径. 研究了基于模式误差控制变量的弱约束4dvar基本理论, 并在一维浅水方程组中对其同化效果及估计模式误差的有效性进行相关数值实验研究. 结果表明,在模式误差不可忽略的情况下,模式误差弱约束4dvar在整个区间 (包括同化区间和预报区间)上预报误差均比传统4dvar小, 在模式误差相对较大时改进效果更明显,具有明显优越性; 并且,模式误差弱约束4dvar能有效估计模式误差大小及分布形式.     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.     

旱涝预测的演化建模方法

发展了一种旱涝预测的演化建模方法, 数值试验结果表明, 该方法能够从历史资料中准确地挖掘出气候要素演化的主要动力学特征, 所建立的模型不仅能够较好地模拟要素的历史演变情况, 而且还能够对未来的演变趋势进行准确的预测. 对于演化建模所得到的误差较大的模型, 对其预测误差序列进行二次演化建模可明显提高模型的预测精度.     

一类非线性发展方程的特征中心差分法

给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度u_t及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,u_t对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性.     

优化模式物理参数的扩展四维变分同化方法

数值模拟的一个重要误差来源是模式物理参数,为提高模拟准确率,如何改进模式物理参数是亟需解决的问题.本文对经典四维变分同化技术进行了改进,提出了一种新的利用观测资料来同时优化模式初始场和物理参数的扩展四维变分同化方法,并以Ekman边界层模式和Lorenz模式为例进行了数值试验.结果表明,利用本文提出的新方法,通过对观测资料的变分同化,可以在实现对模式初始场进行优化的同时,纠正了模式物理参数中的误差,从而有效提高了模式的模拟准确率.该方法对于改进数值模式物理参数有着重要的促进意义.     

基于观测器的模型不确定的耦合时空混沌H∞跟踪控制

考虑子系统的时空耦合作用及模型的不确定性,实现模型不确定的耦合时空混沌的 跟踪控制非常困难.然而耦合时空混沌的每个子系统用一系列模糊逻辑模型逼近,同时考虑子 系统状态的不可测性,采用模糊观测器来估计子系统的状态.由于混沌模型的很多参数和动态 特性很难准确地确定即模型具有不确定性,因此在用模糊模型逼近的同时定会产生建模误差. 基于模糊模型及状态观测器,考虑混沌模型的不确定性,提出一种Ｈ∞ 模糊跟踪控制方法,实现模型不确定性的耦合时空混沌的鲁棒跟踪控制.将控制方 案表征为求解线性矩阵不等式问题,并用凸优化方法 关键词： 耦合时空混沌 模糊模型 模糊观测器 Ｈ∞模糊跟踪控 制 线性矩阵不等式     

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction(NWP). Considering the continuous evolution of the atmosphere, the observed data(ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers’ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.     

On optimal solution error covariances in variational data assimilation problems

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection–diffusion model.     

Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function. The data contain errors (observation and background errors), hence there will be errors in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can often be approximated by the inverse Hessian of the cost functional. Here we focus on highly nonlinear dynamics, in which case this approximation may not be valid. The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance. Two new methods for computing this covariance are presented: the fully nonlinear ensemble method with sampling error compensation and the ‘effective inverse Hessian’ method. The second method relies on the efficient computation of the inverse Hessian by the quasi-Newton BFGS method with preconditioning. Numerical examples are presented for the model governed by Burgers equation with a nonlinear viscous term.     

Analogue correction method of errors and its application to numerical weather prediction

In this paper, an analogue correction method of errors (ACE) based on a complicated atmospheric model is further developed and applied to numerical weather prediction (NWP). The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model. Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.     

吸收散射性三维矩形介质内辐射源项的反问题

提出了一种由边界出射辐射强度反演吸收散射性三维矩形介质内辐射源项分布的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对介质辐射特性、光学厚度等参数对反演精度影响的分析,结果表明,即使存在测量误差,本文所提出的方法可较精确地反演辐射源项。     

Inverse radiation problem of temperature distribution in one-dimensional isotropically scattering participating slab with variable refractive index

In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.     

抛物型方程的演化参数识别方法

给出了一种利用演化计算方法求解微分方程中的参数识别类型反问题的方法。该方法把参数识别问题转化为泛函的优化问题用演化算法来求解,指定待定参数的函数类形式,用遗传算法(Genetic Algorithms)来演化待求参数的最优估计值,并将该方法运用于线性扩散方程和拟线性对流扩散反方程反问题的数值模拟中。     

A new inverse approach for the equivalent gray radiative property of a non-gray medium using a modified zonal method and the complex-variable-differentiation method

Non-gray radiative properties of an absorbing, emitting, non-gray participating medium significantly increase the difficulty of solving the radiative transfer equation. This paper presents a new inverse approach for the equivalent gray radiative property of a non-gray medium. In this approach, the unknown equivalent gray radiative properties are treated as the optimization variables, and the errors to be minimized are the differences between the calculated temperatures and the measured ones. The measured data are simulated by solving the direct problem, in which a modified zonal method together with the Edwards exponential wide-band model is employed. In the inverse problem, the sensitivity coefficients are first calculated by the complex-variable-differentiation method, and then the least-square method and the Newton-Raphson iterative method are employed to minimize the target function. The effectiveness and efficiency of the inverse problem are demonstrated in an example, and another case is given to show the accuracy and potential of the proposed algorithm. The effects of the measurement error and the number of measurement points on the accuracy of the inverse analysis are also investigated in detail.     

Geoacoustic inversion based on reflection model of effective density fluid approximation

In order to obtain the physical and geoacoustic properties of marine sediments,an inverse method using reflection loss of different grazing angles is presented.The reflection loss is calculated according to the reflection model of effective density fluid approximation.A two-step hybrid optimization algorithm combining differential evolution and particle swarm optimization along with Bayesian inversion is employed in estimation of porosity,mean grain size,mass density and bulk modulus of grains.Based on the above physical parameters,geoacoustic parameters,including sound speed and attenuation,are further calculated.According to the numerical simulations,we can draw a conclusion that all the parameters can be well estimated with the exception of bulk modulus of grains.In particular,this indirect inverse method for bottom geoacoustic parameters performs high accuracy and strong robustness.The relative errors are 0.092%and 17%,respectively.Finally,measured reflection loss data of sandy sediments at the bottom of a water tank is analyzed,and the estimation value,uncertainty and correlation of each parameter are presented.The availability of this inverse method is verified through comparison between inverse results and part of measured parameters.     

A deep learning method for solving third-order nonlinear evolution equations

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.