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1.
In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase. 相似文献
2.
The backward nonlinear local Lyapunov exponent method(BNLLE) is applied to quantify the predictability of warm and cold events in the Lorenz model. Results show that the maximum prediction lead times of warm and cold events present obvious layered structures in phase space. The maximum prediction lead times of each warm(cold) event on individual circles concentric with the distribution of warm(cold) regime events are roughly the same, whereas the maximum prediction lead time of events on other circles are different. Statistical results show that warm events are more predictable than cold events. 相似文献
3.
In this study, the relationship between the limit of predictability and initial error was investigated using two simple chaotic systems:the Lorenz model, which possesses a single characteristic time scale, and the coupled Lorenz model, which possesses two different characteristic time scales. The limit of predictability is defined here as the time at which the error reaches 95% of its saturation level; nonlinear behaviors of the error growth are therefore involved in the definition of the limit of predictability. Our results show that the logarithmic function performs well in describing the relationship between the limit of predictability and initial error in both models, although the coefficients in the logarithmic function were not constant across the examined range of initial errors. Compared with the Lorenz model, in the coupled Lorenz model-in which the slow dynamics and the fast dynamics interact with each other-there is a more complex relationship between the limit of predictability and initial error. The limit of predictability of the Lorenz model is unbounded as the initial error becomes infinitesimally small; therefore, the limit of predictability of the Lorenz model may be extended by reducing the amplitude of the initial error. In contrast, if there exists a fixed initial error in the fast dynamics of the coupled Lorenz model, the slow dynamics has an intrinsic finite limit of predictability that cannot be extended by reducing the amplitude of the initial error in the slow dynamics, and vice versa. The findings reported here reveal the possible existence of an intrinsic finite limit of predictability in a coupled system that possesses many scales of time or motion. 相似文献
4.
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
5.
With the Zebiak-Cane (ZC) model, the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation (CNOP). The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model. By analyzing the behavior of CNOP- type errors, we find that for the normal states and the relatively weak EI Nino events in the ZC model, the predictions tend to yield false alarms due to the uncertainties caused by CNOP. For the relatively strong EI Nino events, the ZC model largely underestimates their intensities. Also, our results suggest that the error growth of EI Nino in the ZC model depends on the phases of both the annual cycle and ENSO. The condition during northern spring and summer is most favorable for the error growth. The ENSO prediction bestriding these two seasons may be the most difficult. A linear singular vector (LSV) approach is also used to estimate the error growth of ENSO, but it underestimates the prediction uncertainties of ENSO in the ZC model. This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes. CNOP yields the severest prediction uncertainty. That is to say, the prediction skill of ENSO is closely related to the types of initial error. This finding illustrates a theoretical basis of data assimilation. It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill. 相似文献
6.
With the Zebiak-Cane （ZC） model, the initial error that has the largest effect on ENSO prediction is explored by conditional nonlinear optimal perturbation （CNOP）. The results demonstrate that CNOP-type errors cause the largest prediction error of ENSO in the ZC model. By analyzing the behavior of CNOPtype errors, we find that for the normal states and the relatively weak E1 Nifio events in the ZC model, the predictions tend to yield false alarms due to the uncertainties caused by CNOP. For the relatively strong E1 Nino events, the ZC model largely underestimates their intensities. Also, our results suggest that the error growth of E1 Nifio in the ZC model depends on the phases of both the annual cycle and ENSO. The condition during northern spring and summer is most favorable for the error growth. The ENSO prediction bestriding these two seasons may be the most difficult. A linear singular vector （LSV） approach is also used to estimate the error growth of ENSO, but it underestimates the prediction uncertainties of ENSO in the ZC model. This result indicates that the different initial errors cause different amplitudes of prediction errors though they have same magnitudes. CNOP yields the severest prediction uncertainty. That is to say, the prediction skill of ENSO is closely related to the types of initial error. This finding illustrates a theoretical basis of data assimilation. It is expected that a data assimilation method can filter the initial errors related to CNOP and improve the ENSO forecast skill. 相似文献
7.
数值模式预报时效对计算精度和时间步长的依赖关系 总被引：6，自引：0，他引：6
通过数值计算研究Lorenz非线性动力系统,探讨了非线性动力系统中初值问题的解对时间步长和计算精度的依赖关系,从新的角度研究动力系统的预报时效问题,讨论了评价舍入误差对预报时效影响程度的方法。实验结果表明:动力系统的预报时效不仅与初值误差有关,而且在一定条件下敏感地依赖于计算采用的时间步长和计算精度。 相似文献
8.
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
9.
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
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11.
ABSTRACT The impact of both initial and parameter errors on the spring predictability barrier （SPB） is investigated using the Zebiak Cane model （ZC model）. Previous studies have shown that initial errors contribute more to the SPB than parameter errors in the ZC model. Although parameter errors themselves are less important, there is a possibility that nonlinear interactions can occur between the two types of errors, leading to larger prediction errors compared with those induced by initial errors alone. In this case, the impact of parameter errors cannot be overlooked. In the present paper, the optimal combination of these two types of errors [i.e., conditional nonlinear optimal perturbation （CNOP） errors] is calculated to investigate whether this optimal error combination may cause a more notable SPB phenomenon than that caused by initial errors alone. Using the CNOP approach, the CNOP errors and CNOP-I errors （optimal errors when only initial errors are considered） are calculated and then three aspects of error growth are compared： （1） the tendency of the seasonal error growth; （2） the prediction error of the sea surface temperature anomaly; and （3） the pattern of error growth. All three aspects show that the CNOP errors do not cause a more significant SPB than the CNOP-I errors. Therefore, this result suggests that we could improve the prediction of the E1 Nifio during spring by simply focusing on reducing the initial errors in this model. 相似文献
12.
Theoretical Basis and Application of an Analogue- Dynamical Model in the Lorenz System 总被引：2，自引：0，他引：2
The theoretical basis and application of an analogue-dynamical model (ADM) in the Lorenz system
is studied. The ADM can effectively combine statistical and dynamical methods in which the small disturbance
of the current initial value superimposed on the historical analogue reference state can be regarded as a
prediction objective. Primary analyses show that under the condition of appending disturbances in model
parameters, the model errors of ADM are much smaller than those of the pure dynamical model (PDM).
The characteristics of predictability on the ADM in the Lorenz system are analyzed in phase space by
conducting case studies and global experiments. The results show that the ADM can quite effectively
reduce prediction errors and prolong the valid time of the prediction in most situations in contrast
to the PDM, but when model errors are considerably small, the latter will be superior to the former.
To overcome such a problem, the multi-reference-state updating can be applied to introduce the
information of multi-analogue and update analogue and can exhibit exciting performance in the ADM. 相似文献
13.
数值天气预报和气候预测的可预报性问题 总被引：29，自引：7，他引：29
考察由初始状态误差和模式中参数误差所引起的预报结果的不确定性。提出了数值天气预报与气候预测中三类可预报性问题，即，最大可预报时间，最大预报误差，初值与参数的最大允许误差。然后将这三类问题化成了对应的非线性优化问题，给出了处理此类非线性优化问题的思路，并且有数值方法对Lorenz模型研究了这三类问题。 相似文献
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15.
Xiaoran ZHUANG Jinzhong MIN Liu ZHANG Shizhang WANG Naigeng WU Haonan ZHU 《大气科学进展》2020,37(8):893-911
This study investigated the regime-dependent predictability using convective-scale ensemble forecasts initialized with different initial condition perturbations in the Yangtze and Huai River basin(YHRB) of East China. The scale-dependent error growth(ensemble variability) and associated impact on precipitation forecasts(precipitation uncertainties) were quantitatively explored for 13 warm-season convective events that were categorized in terms of strong forcing and weak forcing. The forecast error growth in the strong-forcing regime shows a stepwise increase with increasing spatial scale,while the error growth shows a larger temporal variability with an afternoon peak appearing at smaller scales under weak forcing. This leads to the dissimilarity of precipitation uncertainty and shows a strong correlation between error growth and precipitation across spatial scales. The lateral boundary condition errors exert a quasi-linear increase on error growth with time at the larger scale, suggesting that the large-scale flow could govern the magnitude of error growth and associated precipitation uncertainties, especially for the strong-forcing regime. Further comparisons between scale-based initial error sensitivity experiments show evident scale interaction including upscale transfer of small-scale errors and downscale cascade of larger-scale errors. Specifically, small-scale errors are found to be more sensitive in the weak-forcing regime than those under strong forcing. Meanwhile, larger-scale initial errors are responsible for the error growth after 4 h and produce the precipitation uncertainties at the meso-β-scale. Consequently, these results can be used to explain underdispersion issues in convective-scale ensemble forecasts and provide feedback for ensemble design over the YHRB. 相似文献
16.
It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic(or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics—namely, the global and local attractor radii(GAR and LAR, respectively)—are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach2~(1/2) with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases. 相似文献
17.
In south China, warm-sector rainstorms are significantly different from the traditional frontal rainstorms due to complex mechanism, which brings great challenges to their forecast. In this study, based on ensemble forecasting, the high-resolution mesoscale numerical forecast model WRF was used to investigate the effect of initial errors on a warmsector rainstorm and a frontal rainstorm under the same circulation in south China, respectively. We analyzed the sensitivity of forecast errors to the... 相似文献
18.
初始扰动对一次华南暴雨预报的影响的研究 总被引：2，自引：1，他引：1
本文选取了2006年华南前汛期的一次暴雨过程, 采用AREMv2.3中尺度数值模式进行数值模拟, 分别在模式初始场的物理量场 (温度场、 风场、 湿度场) 上加扰动, 分析不同物理量场上的扰动对降水预报的影响, 以及物理量预报误差和扰动能量的增长情况。同时, 通过本个例讨论误差增长与湿对流的关系, 扰动振幅对误差增长的影响和华南区域的中尺度降水的可预报性问题。数值试验结果表明: 初始时刻不同物理量场加实际振幅的正态分布的随机扰动时, 对降水的影响是不同的。对于24小时降水预报, 温度场对降水的影响最大。误差的增长与湿对流不稳定有着密切的关系。小尺度小振幅误差增长很快, 而且是非线性增长。这意味着短期的较小尺度降水的可预报性很小。与大振幅扰动相比, 小振幅扰动造成的误差较小。但是小振幅扰动的迅速发展, 很快就会对降水预报造成较大的影响。因此, 只能有限地提高预报质量, 而且由于扰动非线性增长很快, 在预报时间的提前上, 不会有太大的改善。 相似文献
19.
Estimating the Predictability of the Quasi-Biweekly Oscillation Using the Nonlinear Local Lyapunov Exponent Approach 
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下载免费PDF全文 The quasi-biweekly oscillation (QBWO) is a major intraseasonal variability (ISV) in the tropics. Based on bandpass-filtered outgoing longwave radiation (OLR) and wind field data, the predictability limits of the QBWO in boreal summer and boreal winter are investigated using the nonlinear local Lyapunov exponent (NLLE) approach The analysis shows that the evolution of the mean error growth of the QBWO in boreal summer and the evolution of the mean error growth in boreal winter are comparable Both curves exhibit rapid growth in the initial stage followed by a slowly fluctuating, ascending trend before saturation is reached. As a result, the potential predictability limits for the boreal summer QBWO are very close to those for the boreal winter QBWO, with a lead time of approximately three weeks. Given the current limitations in the simulation and prediction of ISV, including the QBWO, the results of this study provide a useful reference for assessing the predictability of the QBWO using model simulations. 相似文献
20.
数值模式初值的敏感性程度对四维同化的影响 总被引：3，自引：0，他引：3
用著名的Ｌｏｒｅｎｚ系统作了共轭变分同化的数值试验。发现随着模式对初值敏感性程度的增加，用这种方法得到和模式相协调的初始场愈来愈困难，直到某些情况下的完全失败。这表明四维同化和可预报期限是联系在一起的。另一方面，随着方程不精确程度的增加，变分同化的效果愈来愈差，直到所做的预报无任何意义可言。如果在做变分同化的同时对模式参数也进行反演，就可使得基于Ｌｏｒｅｎｚ系统所做的预报效果大大提高。 相似文献