共查询到18条相似文献，搜索用时 218 毫秒
1.
从一般的谱展开方程出发，详细推导了误差增长方程。结果表明误差增长率主要由准确解的切线性方程所决定，扰动非线性平流作用不产生方差意义下的误差增长，而只起分配误差的作用。轨线不稳定是产生误差增长的根本原因。文中提出了计算轨线不稳定增长率的方法。这一方法也适合于时间演变状态不稳定问题的讨论，对Ｌｏｒｅｎｚ系统的轨线不稳定计算表明了理论分析的正确及其意义。 相似文献
2.
误差非线性的增长理论及可预报性研究 总被引：2，自引：9，他引：2
对非线性系统的误差发展方程不作线性化近似，直接用原始的误差发展方程来研究初始误差的发展，提出了误差非线性的增长理论。首先，在相空间中定义一个非线性误差传播算子，初始误差在这个算子的作用下，可以非线性发展成任意时刻的误差；然后，在此基础上，引入了非线性局部Lyapunov指数的概念。由平均非线性局部Lyapunov指数可以得到误差平均相对增长随时间的演变情况；对于一个混沌系统，误差平均相对增长被证明将趋于一个饱和值，利用这个饱和值，混沌系统的可预报期限可以被定量地确定。误差非线性的增长理论可以应用于有限尺度大小初始扰动的可预报性研究，较误差的线性增长理论有明显的优越性。 相似文献
3.
目前国际上采用的奇异向量集合预报初值扰动法对于初值不确定性的描述存在一定的不足,为了更有效地反映初始误差的时空多尺度特性,基于GRAPES全球奇异向量计算技术,计算了不同空间分辨率及不同最优时间间隔的多个尺度的奇异向量,并采用基于高斯分布的线性组合法来构造多尺度奇异向量的扰动初值,以代表在相空间中增长最快的多尺度初值误差模态。通过2019年1月19日的初值扰动集合预报试验,对比分析了单一尺度奇异向量初值扰动法与多尺度初值扰动法的扰动特征及集合预报效果。结果表明,多尺度奇异向量初值扰动法为区域集合预报提供的初始扰动场是合理的,扰动的大小随时间增长,且在空间分布上较好地反映了当前大气的斜压不稳定特征。此外,多尺度奇异向量扰动可以描述一定的大尺度以及中小尺度运动误差特征,较单一尺度奇异向量扰动能反映出更多初始场的不确定性信息。检验分析表明,GRAPES多尺度奇异向量集合预报在集合一致性、连续等级概率评分、离群值等方面有一定的优势,相比于单一尺度奇异向量法有较好的预报技巧。因此,基于GRAPES的多尺度奇异向量初值扰动法对于集合预报的预报效果有一定的提高,能为构建一套完善的GRAPES区域奇异向量集合预报系统提供一定的科学依据和应用基础。 相似文献
4.
基于Lorenz系统提取数值模式可预报分量的初步试验 总被引：1，自引：0，他引：1
针对数值预报模式中存在的非线性混沌特性, 从提取可预报分量的思路出发, 阐述了在数值模式中提取可预报分量的方法, 并利用Lorenz系统进行了相关数值试验。研究发现, Lorenz系统初始误差在相空间中的增长速度是不同的, 某些方向的误差增长速度较慢, 即存在对初值扰动不敏感、相对稳定的可预报分量。根据数值模式切线性误差算子的特征值演化规律, 提取出数值模式的可预报分量, 并将模式变量在其基底上进行投影变换, 建立了可预报分量数值模式。在此基础上, 研究了Lorenz系统的混沌状态、模式参数误差及外部随机噪声对提取可预报分量的影响, 发现基于可预报分量的数值模式, 具有更好的预报技巧。 相似文献
5.
集合预报开创了业务数值天气预报的新纪元 总被引：5，自引：0，他引：5
近年来世界上随着几个气象中心的集合预报投入业务,标志着业务数值天气预报进行了一个新的纪元,在任何进修大气的起初状态是不知道的,只有近似地描述大气,所以确切地说,天气预报问题应该提为大气的相空间中合适的概率密度函数随时间的演变。在误差的增长超出线性动力学范畴之外,集合预报是预报大气概率密度函数演变唯一可行的方法。可用扰动的产生是集合预报的主要问题之一。沿着预报系统的相空间中最不稳定的方向来扰动初始条 相似文献
6.
提出用自然正交函数分解的方法来开拓相空间，从而研究有限区域上大气系统的混沌性质。与利用时间滞后作漂移来开拓相空间方法相比较，前者充分保证了相空间各基矢量的正交性，弥补了后者只能对单点资料进行计算的不足。文中利用欧洲中期数值天气预报中心1980－1986年北半球亚洲地区的500hPa位势高度场逐日格点资料进行了EOF分解并计算得到了该地区大气系统的分维数为D＝6．2，从而表明，为支撑该地区大气系统的混沌吸引子至少应取7维系统或以7个变量才能作出描述。 相似文献
7.
8.
利用时间滞后延拓相空间的方法，将南京地区一维月降水量资料序列拓展成高维相空间，计算得到降水系统的分维数为３．６，表明该系统是一混沌系统，其自由度最小取４。在具有二次非线性项的假设下求解设定的动力系统程数，建立降水预报方程。预报检验结果表明，利用该方法作局地降水气候预报具有一定的准确度。 相似文献
9.
基于相空间重构的西太平洋副高指数的动力随机性与复杂性 总被引：1，自引：0，他引：1
基于NCEP/NCAR再分析资料,计算了西太平洋副热带高压脊线指数的逐候时间序列,对该时间序列进行了相空间重构,对相空间重构中最佳嵌入维数和延迟时间的选择进行了分析,画出了相应的伪相图,同时还对副高脊线指数吸引子的关联维数进行了计算,得到副高脊线指数关联维数为3.10±0.05.通过动力参数的计算和重构后相空间递归图的分析,讨论了副高活动的动力随机性和复杂性.分析结果对副高系统复杂性和可预报性的认识以及副高动力模型反演有参考意义. 相似文献
10.
利用33模Lorenz系统得到的"理想"混沌时空序列,作为时空混沌序列"发生器".通过状态空间重构,建立"场时间序列"局域近似预测模型,对资料空间分辨率,资料的长度、噪音,以及模型的参数选取等因素进行敏感性试验分析,了解时空混沌序列预测中误差产生和增长的一些影响因素.得到以下初步结论:对于理想混沌时空序列(33模Lorenz系统)而言,与系统相适应的资料空间分辨率和较长的资料长度都将会提高预测精度;可预报时效与资料长度之间近似服从指数关系.另外,在建立预测模型时,适当的邻近点数目,以及采用二阶映射关系和迭代法都可以有效地改善预测精度.对于加入噪音的混沌时间序列,通过"场时间序列"的局域近似方法和4阶自回归方法的预测试验的对比表明,前者显示了更强的抗"干扰"能力.以上结论可以有分析地应用于短期气候预测中. 相似文献
11.
The localized features on chaotic attractor in phase space and predictability are investigated in thepresent study.It will be suggested that the localized features in phase space have to be considered indetermining the predictability.The notions of the local instability including the finite-time and local-time instabilities which determine the growth rate of error are introduced,and the calculation methodsare discussed in detail.The results from the calculation of the 3-component Lorenz model show thatsuch instability,correspondingly the growth rate of error,varies dramatically as the trajectoriesevolve on the chaotic attractor.The region in which the growth rate of error is small is localizedconsiderably,and is separable from the region in which the growth rate is large.The localpredictability is of important interest.It is also suggested that such localized features may be the maincause for a great deal of case-to-case variability of the predictive skill in the operational forecasts. 相似文献
12.
The purpose of this paper is to study the dynamical mechanism of error growth in the numerical weather prediction.The error is defined in the sense of generalized energy,simply called energy error.From the spectral form of the primitive equations,we have derived the evolution equations of error in detail.The analyses of these equations have shown that the error growth rate is determined by the tangent linear equations.The nonlinear advection caused by the error perturbation itself contributes nothing to the error growth rate,and only redistributes the error.Furthermore,an approach to calculation of the error growth rate has been developed,which can also be used to study the local instability of time-independent basic state as well as time-dependence basic state.This approach is applied to well-known Lorenz's system,and the results are indicative of the correctness and significance of the theoretical analyses. 相似文献
13.
Sensitivity simulations are conducted in AREM (Advanced Regional Eta-Coordinate numerical heavy-rain prediction Model) for a torrential precipitation in June 2008 along South China to investigate the effect of initial uncertainty on precipitation predictability. It is found that the strong initial-condition sensitivity for precipitation prediction can be attributed to the upscale evolution of error growth. However, different modality of error growth can be observed in lower and upper layers. Compared with lower-level, significant error growth in the upper-layer appears over both convective area and high jet stream. It thus indicates that the error growth depends on both moist convection due to convective instability and the wind shear associated with dynamic instability. As heavy rainfall process can be described as a series of energy conversion, it reveals that the advection-term and latent heating serve as significant energy sources. Moreover, the dominant source terms of error-energy growth are nonlinearity advection (ADVT) and difference in latent heating (DLHT), with the latter being largely responsible for the rapid error growth in the initial stage. In this sense, the occurrence of precipitation and error-growth share the energy source, which implies the inherent predictability of heavy rainfall. In addition, a decomposition of ADVT further indicates that the flow-dependent error growth is closely related to the atmospheric instability. Thus the system growing from unstable flow regime has its intrinsic predictability. 相似文献
14.
Christina Karamperidou Mark A. Cane Upmanu Lall Andrew T. Wittenberg 《Climate Dynamics》2014,42(1-2):253-270
The presence of rich ENSO variability in the long unforced simulation of GFDL’s CM2.1 motivates the use of tools from dynamical systems theory to study variability in ENSO predictability, and its connections to ENSO magnitude, frequency, and physical evolution. Local Lyapunov exponents (LLEs) estimated from the monthly NINO3 SSTa model output are used to characterize periods of increased or decreased predictability. The LLEs describe the growth of infinitesimal perturbations due to internal variability, and are a measure of the immediate predictive uncertainty at any given point in the system phase-space. The LLE-derived predictability estimates are compared with those obtained from the error growth in a set of re-forecast experiments with CM2.1. It is shown that the LLEs underestimate the error growth for short forecast lead times (less than 8 months), while they overestimate it for longer lead times. The departure of LLE-derived error growth rates from the re-forecast rates is a linear function of forecast lead time, and is also sensitive to the length of the time series used for the LLE calculation. The LLE-derived error growth rate is closer to that estimated from the re-forecasts for a lead time of 4 months. In the 2,000-year long simulation, the LLE-derived predictability at the 4-month lead time varies (multi)decadally only by 9–18 %. Active ENSO periods are more predictable than inactive ones, while epochs with regular periodicity and moderate magnitude are classified as the most predictable by the LLEs. Events with a deeper thermocline in the west Pacific up to five years prior to their peak, along with an earlier deepening of the thermocline in the east Pacific in the months preceding the peak, are classified as more predictable. Also, the GCM is found to be less predictable than nature under this measure of predictability. 相似文献
15.
根据非线性局部Lyapunov指数的方法, 以Logistic映射和Lorenz系统的试验数据序列为例, 研究了在初始误差存在的情况下, 随机误差对混沌系统可预报性的影响。结果表明: 初始误差和随机误差对可预报期限影响所起的作用大小主要取决于两者的相对大小。当初始误差远大于随机误差时, 系统的可预报期限主要由初始误差决定, 可以不考虑随机误差对预报模式可预报性的影响; 反之, 当随机误差远大于初始误差时, 系统的可预报期限主要由随机误差决定; 当初始误差和随机误差量级相当时, 两者都对系统的可预报期限起重要作用。在后两种情况下, 在考虑初始误差对可预报性影响的同时还必须考虑随机误差的作用。此外, 我们在已知系统精确的控制方程和误差演化方程的条件下, 研究了随机误差对可预报性的影响, 理论所得结果与试验数据所得结果相似。这表明在随机误差较小的情况下, 对系统可预报期限的估计相对准确, 但在随机误差较大的情况下, 可预报期限的估计误差也较大。本文利用三种不同的滤波方法对序列进行了试验, 结果表明, Lanczos高通滤波得到的高频序列与原始加入的噪声序列无论是在强度上还是在演变趋势上都表现得相当一致, 其能有效地去除高频噪音继而提高对系统的可预报期限的估计, 这对实际气象观测资料如何有效地去除噪音具有一定的启发意义。 相似文献
16.
A Case Study of the Error Growth and Predictability of a Meiyu Frontal Heavy Precipitation Event 
下载免费PDF全文
下载免费PDF全文 The Advanced Regional Eta-coordinate Model (AREM) is used to explore the predictability of a heavy rainfall event along the Meiyu front in China during 3-4 July 2003.Based on the sensitivity of precipitation prediction to initial data sources and initial uncertainties in different variables,the evolution of error growth and the associated mechanism are described and discussed in detail in this paper.The results indicate that the smaller-amplitude initial error presents a faster growth rate and its growth is characterized by a transition from localized growth to widespread expansion error.Such modality of the error growth is closely related to the evolvement of the precipitation episode,and consequcntly remarkable forecast divergence is found near the rainband,indicating that the rainfall area is a sensitive region for error growth.The initial error in the rainband contributes significantly to the forecast divergence,and its amplification and propagation are largely determined by the initial moisture distribution.The moisture condition also affects the error growth on smaller scales and the subsequent upscale error cascade.In addition,the error growth defined by an energy norm reveals that large error energy collocates well with the strong latent heating,implying that the occurrence of precipitation and error growth share the same energy source-the latent heat.This may impose an intrinsic predictability limit on the prediction of heavy precipitation. 相似文献
17.
A case study of the error growth and predictability of a Meiyu frontal heavy precipitation event 下载免费PDF全文
下载免费PDF全文 The Advanced Regional Eta-coordinate Model (AREM) is used to explore the predictability of a heavy rainfall event along the Meiyu front in China during 3-4 July 2003. Based on the sensitivity of precipitation prediction to initial data sources and initial uncertainties in different variables, the evolution of error growth and the associated mechanism are described and discussed in detail in this paper. The results indicate that the smaller-amplitude initial error presents a faster growth rate and its growth... 相似文献
18.
Chen Yingyi 《大气科学进展》1993,10(4):497-503
The dimensions of attractors and predictability are estimated from phase space trajectories of observed 500 hPa height over the Northern Hemisphere. As a first estimate the dimensions of attractors are about 11.5 and the doubling time of the initial error is 6 to 7 days for original data. But the former is shorter and the latter is longer for low frequency data set.To verify if the predictability estimated by this method and by general circulation model is identical, the doubling time of the initial error of a model data set by both methods is estimated. It is shown that the predictability obtained from phase space trajectories is overestimated to sufficient small initial error. But it is underestimated to the time being equal to the climatological RMS error. 相似文献