基于Lorenz模型的集合预报与单一预报的比较研究

根据非线性局部Lyapunov向量方法和增长模繁殖方法,选取Lorenz63模型和Lorenz96模型的不同状态为例,对集合预报与单一预报的预报技巧开展了对比研究.结果表明:与单一预报比较,集合预报的均方根误差和型异常相关有明显改善,随预报时间推移,改善效果越显著,且集合平均优于单一预报的实验个例数逐渐增多.就概率分布(f)而言,单一预报状态的f与真实状态基本一致,不随时间变化;而集合平均预报状态的f则随时间呈现出值域变窄、峰值变大的特点.表明随预报时间的延长,单一预报状态为混沌吸引子上的随机状态,而集合平均预报状态为吸引子子集上的随机状态,这可能是集合平均误差小于单一预报的原因.     

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.     

Impact of nonlinearities and model error on pseudo-inverse calculations

Pseudo-inverse calculations have been made within the operational and research meteorological communities to identify components of the error in the initial state that are responsible for a significant portion of the forecast error. These calculations are based on the assumptions of a perfect model and linear perturbation growth, conditions not realizable in operational forecasting. In this study, the impact of nonlinearities and model error on pseudo-inverse calculations is investigated within an idealized framework using a simple atmospheric model. Forecasts are run within the perfect and imperfect model frameworks, with initial errors of varying sizes. Model error is introduced by changing the model dissipation terms. It is found that for pseudo-inverses composed of a small subset of the leading singular vectors (SVs), the nonlinear forecast correction is often better than the expected theoretical correction, indicating the suppression of error growth both inside and outside the linear pseudo-inverse subspace. As the size of the pseudo-inverse is increased, the nonlinear forecast correction starts to degrade. This forecast degradation coincides with a degradation in the analysis correction. It is possible to improve the forecast by degrading the analysis in the presence of model error, especially when the initial error is very small. However, for initial errors of reasonable magnitude, this is unlikely to happen in instances when the nonlinear forecast correction is better than the theoretical correction. Just as improving the initial state may suppress errors outside of the linear SV subspace, degrading it may likewise increase errors outside the SV subspace. This suggests that the size of the nonlinear correction relative to the expected theoretical correction may be useful in determining when pseudo-inverse perturbations are likely to have improved the analyses.     

Forecasting with imperfect models, dynamically constrained inverse problems, and gradient descent algorithms

This paper is part of a larger study investigating the meaning of, and appropriate procedures for, forecasting with imperfect models. (In the author’s opinion there is currently no satisfactory general theory and practice for doing so with complex nonlinear systems.) The focus of this paper is on initialisation of the forecast. At the heart of every forecasting scheme there is an inverse problem that translates observations of reality into an initial state, or ensemble of states, of the model. Inverse problems are divided into two classes depending on whether the underlying model of reality is that of a stochastic process or a (deterministic) dynamical process. The two classes have quite different formulations of their inverse problems and consequent solutions methods. This paper considers dynamical process models and their inverse problems, which will be referred to as the dynamically constrained inverse problem (DCIP) line. The interpretation and solutions of the DCIP line are investigated and new algorithms for solving them are presented. The new algorithms are modifications of classical gradient descent algorithms. The new algorithms are applied to a low-dimensional chaotic system and a high-dimensional operational weather forecasting model. Our examination of DCIP shows that gradient descent algorithms are an effective way of solving the inverse problem for complex nonlinear system given an imperfect dynamical model.     

Data assimilation and numerical forecasting with imperfect models: The mapping paradigm

Errors in numerical forecasts arise due to errors in the initial conditions and the discrepancies between the model and nature (and may amplify due to chaos). In a quest to reduce forecast errors, initial conditions for forecast integrations are traditionally chosen to be as close to nature as possible. When such an initial condition (analysis) is used to initialize an imperfect model that is systematically different from nature, the model will drift from a state on or near the attractor of nature to a state near the model’s attractor. Such a drift will induce forecast errors.

To reduce drift-induced errors, a mapping paradigm is proposed where a link (i.e., mapping vector) is established between states of nature and corresponding states on (or near) the model attractor. Observations from near the attractor of nature are moved with the mapping vector to the vicinity of the model attractor. Data assimilation is performed with the mapped observations and the mapped initial conditions are then used to initialize model forecasts to be used in the next assimilation cycle. For practical applications, the mapped initial conditions as well as the forecasts are “remapped” back to be close to nature using the mapping vector with an opposite sign.

The mapping paradigm is demonstrated in a setting where a simple Lorenz model is used to generate “nature” and a modified version is used as an imperfect model. The mapping vector is first estimated as the difference between the climate mean of nature and the model. Model related errors in the Lorenz system with the mapping algorithm are reduced by 67%, leading to improvements in the quality of both the numerical forecasts made with the imperfect model and the analyses produced with the forecasts. Considering that the mapping vector may be a function of phase space location or no long-term climatology for nature or the model may be available, an adaptive approach that can be used with a relatively small amount of data was also introduced and successfully tested.     

Electricity,Heat, and Gas Load Forecasting Based on Deep Multitask Learning in Industrial-Park Integrated Energy System

Different energy systems are closely connected with each other in industrial-park integrated energy system (IES). The energy demand forecasting has important impact on IES dispatching and planning. This paper proposes an approach of short-term energy forecasting for electricity, heat, and gas by employing deep multitask learning whose structure is constructed by deep belief network (DBN) and multitask regression layer. The DBN can extract abstract and effective characteristics in an unsupervised fashion, and the multitask regression layer above the DBN is used for supervised prediction. Then, subject to condition of practical demand and model integrity, the whole energy forecasting model is introduced, including preprocessing, normalization, input properties, training stage, and evaluating indicator. Finally, the validity of the algorithm and the accuracy of the energy forecasts for an industrial-park IES system are verified through the simulations using actual operating data from load system. The positive results turn out that the deep multitask learning has great prospects for load forecast.     

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.     

Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, we describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “ensemble Kalman filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. We discuss both the mathematical basis of this approach and its implementation; our primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. We include some numerical results demonstrating the efficiency and accuracy of our implementation for assimilating real atmospheric data with the global forecast model used by the US National Weather Service.     

A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation

We study the Gaussian semiclassical soliton ensemble, a collection of multisoliton solutions of the focusing nonlinear Schrödinger equation. The ensemble is generated by adding a particular asymptotically vanishing sequence of perturbations to Gaussian initial data. Recent results (Lee et al., 2012) [21] suggest that, remarkably, these perturbations — interlaced as they are with the integrable structure of the equation — do not excite the acute modulational instabilities known to be present in the semiclassical regime. Our results here highlight the exceptional nature of these perturbations and provide new insight into the sensitivity properties of the related semiclassical limit problem.     

混沌系统可预报期限随初始误差变化规律研究

利用非线性误差增长理论计算了Logistic映射和Lorenz系统可预报期限随初始误差的变化,发现Logistic映射等简单混沌系统的可预报期限与初始误差的对数存在线性关系.在非线性误差增长理论的框架下,理论分析表明,平均误差增长达到一定值时,误差增长进入明显的非线性增长阶段,最终达到饱和;对于一个确定的混沌系统,在控制参数固定的情况下误差增长的饱和值也是固定的,因此可预报期限只依赖于初始误差. 在可预报期限与初始误差对数存在的线性函数关系式中,线性系数与最大Lyapunov指数有关,在已知混沌系统的最大 关键词： 非线性局部Lyapunov指数 可预报期限 初始误差 混沌系统     

Elementary sequential spectral line and statistical properties of the thermal reservoir of free polyatomic molecules

The formation of vibronic spectra of free polyatomic molecules is studied by taking the concept of sequences as constituent elements of vibronic bands. Statistical properties of the thermal reservoir of oscillators, which randomly perturbs optically active transitions in a polyatomic molecule, are considered. The spectral shape, position, and width of the elementary sequential lines (ESL) are determined. It is shown that the ESLs have a Lorentzian shape if the perturbations are short-term and the pulse shape is symmetric about its origin. The position of the ESLs depends on the total vibrational energy of the thermal reservoir of oscillators in the initial electronic state of a molecule. The analysis of the statistical properties of the thermal reservoir of polyatomic molecules shows that one should distinguish between the ESL linewidth of individual molecules and the ESL linewidth averaged over the entire thermal ensemble. It is shown that individual molecules of the thermal ensemble that have different total vibrational energies are characterized by different widths of the ESLs. Consequently, the exchange and redistribution dynamics of the vibrational energy stored in the initial electronic state should manifest itself in the difference between the single-molecule ESL widths measured at different instants in time.     

基于多个参考态更新的动力相似预报方法及应用

为了更有效地利用历史资料中的相似性信息提高数值模式预报水平,提出了一种新的动力相似预报方法——多参考态更新(MRSU) 法.该方法基于“更新”观点,通过引入相似更新周期(PAU)的概念,将整个预报时段按PAU分成若干小的子时段,在预报进行到PAU时重新选取多个参考态,并采用超平面近似法将相似-动力模式产生的多个预报估计成最佳预报向量,这样就形成了“选取-估计”的循环,不断重复这一过程直到完成整个时段的预报.进一步将简化的MRSU方法应用于T63全球谱模式.月预报试验结果表明,与控制试验相比,MRSU法对逐 关键词： 相似-动力模式 参考态 相似更新周期 月预报     

Nigel calder: ‘The key to the universe’

Recent advances in the use of physico-mathematical models to forecast the weather over the Northern Hemisphere for up to six days ahead are described. A higher-resolution model is used to predict the evolution of smaller-scale weather systems such as fronts and their associated rainfall over western Europe up to 36 h ahead. An example of a five-day numerical forecast and its verification are presented.

The concepts of precision, accuracy, assessment and evaluation of forecasts are discussed together with the factors that ultimately limit their accuracy and range. The improvement in both surface and upper-air forecasts since the introduction of computer models is demonstrated by both objective tests and more subjective judgements.     

Ordinal Time Series Forecasting of the Air Quality Index

This research models and forecasts daily AQI (air quality index) levels in 16 cities/counties of Taiwan, examines their AQI level forecast performance via a rolling window approach over a one-year validation period, including multi-level forecast classification, and measures the forecast accuracy rates. We employ statistical modeling and machine learning with three weather covariates of daily accumulated precipitation, temperature, and wind direction and also include seasonal dummy variables. The study utilizes four models to forecast air quality levels: (1) an autoregressive model with exogenous variables and GARCH (generalized autoregressive conditional heteroskedasticity) errors; (2) an autoregressive multinomial logistic regression; (3) multi-class classification by support vector machine (SVM); (4) neural network autoregression with exogenous variable (NNARX). These models relate to lag-1 AQI values and the previous day’s weather covariates (precipitation and temperature), while wind direction serves as an hour-lag effect based on the idea of nowcasting. The results demonstrate that autoregressive multinomial logistic regression and the SVM method are the best choices for AQI-level predictions regarding the high average and low variation accuracy rates.     

Capturing uncertainties of the underwater acoustic environment based on an ocean-acoustic coupled model

Considering the uncertain effects of temporal and spatial changes in the marine environment on the underwater acoustic environment,we established an ocean-acoustic coupled numerical model and performed a parallel calculation.This model incorporated acoustic calculations into the dynamic ocean,thereby achieving a dynamic forecasting and assessment of the acoustic environment.Furthermore,we adopted the ensemble prediction method to predict the vertical structure of temperature in a classic cross-section,the sound speed of the cross-section of the investigated sea area,and transmission losses.We gave the prediction errors of the sound speed profile as well as the 90%probability interval of transmission losses and the uncertainty histograms of the sound speeds,transmission losses,and sonar ranges at different depths and frequencies.The results reflected the influence of marine temporal and spacial variations on the uncertainties of the underwater acoustic environment,and the results also quantified the uncertainties of the underwater acoustic environment parameters.The experimental results indicate that the method used in this study is able to delineate and quantify the uncertainties of the underwater acoustic environment caused by marine dynamic changes.     

海洋-声学耦合模式捕捉水声环境不确定性

考虑到海洋环境的时空变化对水声环境不确定性的影响,建立了海洋-声学耦合数值模式,实现了并行计算。该模式将声学计算纳入到运动的海洋中,从而实现了对水声环境的动态预报和估计。同时,采用集合预报方法对典型断面的温度垂直结构、实验海区声速剖面和传播损失进行预报,并给出了声速剖面的预报误差、不同深度与频率下,传播损失90%的概率区间以及声速、传播损失、声呐作用距离的不确定性直方图。结果反映了海洋时空变化对水声环境不确定性的影响,量化了水声环境中不确定性的大小。实验结果表明该方法可以刻画海洋动态变化引起的水声环境不确定性,并对其进行了量化和描述。      

Forecasting in the presence of expectations

Physical processes routinely influence economic outcomes, and actions by economic agents can, in turn, influence physical processes. This feedback creates challenges for forecasting and inference, creating the potential for complementarity between models from different academic disciplines. Using the example of prediction of water availability during a drought, we illustrate the potential biases in forecasts that only take part of a coupled system into account. In particular, we show that forecasts can alter the feedbacks between supply and demand, leading to inaccurate prediction about future states of the system. Although the example is specific to drought, the problem of feedback between expectations and forecast quality is not isolated to the particular model–it is relevant to areas as diverse as population assessments for conservation, balancing the electrical grid, and setting macroeconomic policy.     

Application of the nonlinear time series prediction method of genetic algorithm for forecasting surface wind of point station in the South China Sea with scatterometer observations

The present work reports the development of nonlinear time series prediction method of genetic algorithm(GA) with singular spectrum analysis(SSA) for forecasting the surface wind of a point station in the South China Sea(SCS) with scatterometer observations.Before the nonlinear technique GA is used for forecasting the time series of surface wind,the SSA is applied to reduce the noise.The surface wind speed and surface wind components from scatterometer observations at three locations in the SCS have been used to develop and test the technique.The predictions have been compared with persistence forecasts in terms of root mean square error.The predicted surface wind with GA and SSA made up to four days(longer for some point station) in advance have been found to be significantly superior to those made by persistence model.This method can serve as a cost-effective alternate prediction technique for forecasting surface wind of a point station in the SCS basin.     

Accuracy of long-term forecasting geosynchronous satellite motion

The accuracy of forecasting geosynchronous satellite motion for 242-year term of forecast using a numerical model of artificial satellite motion taking into account the main perturbing factors including nonsphericity of the Earth’s gravitational field, attraction by the Moon and the Sun, tides inside the Earth, direct light pressure with allowance for the Earth’s shadow effect, and the Pointing–Robertson effect is considered. It is demonstrated that in this case, perturbations of the Earth’s gravitational field harmonics up to the 27th order must be considered. For regular motions, the maximum error in forecasting the geosynchronous satellite position ranges from 0.14 to 2400 km, the error in forecasting the long semiaxis ranges from 0.013 to 1100 m, and the error in forecasting the subsatellite point longitude ranges from 0.069″ to 3.4° depending on the libration amplitude. The accuracy of forecasting depends on the libration amplitude: the less the libration amplitude, the higher the accuracy of forecasting. For quasi-random trajectories, the integration period for which the errors in forecasting do not exceed values obtained for libration motion is determined by the frequency and proximity of the trajectory to unstable stationary points. For the examples considered, this period is about 200 years. The estimated MEGNO factor confirms the efficiency of the numerical model of artificial satellite motion used to investigate the stochastic properties of geosynchronous satellite motion.