The Combined Effect of Initial Error and Model Error on ENSO Prediction Uncertainty Generated by the Zebiak-Cane Model

Initial errors and model errors are the source of prediction errors. In this study, the authors compute the conditional nonlinear optimal perturbation （CNOP）-type initial errors and nonlinear forcing singular vector （NFSV）- type tendency errors of the Zebiak-Cane model with respect to El Nifio events and analyze their combined effect on the prediction errors for E1 Nino events. The CNOP- type initial error （NFSV-type tendency error） represents the initial errors （model errors） that have the largest effect on prediction uncertainties for E1 Nifio events under the perfect model （perfect initial conditions） scenario. How- ever, when the CNOP-type initial errors and the NFSV- type tendency errors are simultaneously considered in the model, the prediction errors caused by them are not am- plified as the authors expected. Specifically, the predic- tion errors caused by the combined mode of CNOP-type initial errors and NFSV-type tendency errors are a little larger than those caused by the NFSV-type tendency er- rors. This fact emphasizes a need to investigate the opti- mal combined mode of initial errors and tendency errors that cause the largest prediction error for E1 Nifio events.     

What Kind of Initial Errors Cause the Severest Prediction Uncertainty of EI Nino in Zebiak-Cane Model

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.     

Is Model Parameter Error Related to a Significant Spring Predictability Barrier for El Nio events？ Results from a Theoretical Model

Within a theoretical ENSO model, the authors investigated whether or not theerrors superimposed on model parameters could cause a significant ``springpredictability barrier' (SPB) for El Nino events. First, sensitivityexperiments were respectively performed to the air--sea coupling parameter,α and the thermocline effect coefficient μ. The results showed that theuncertainties superimposed on each of the two parameters did not exhibit anobvious season-dependent evolution; furthermore, the uncertainties caused avery small prediction error and consequently failed to yield a significantSPB. Subsequently, the conditional nonlinear optimal perturbation (CNOP)approach was used to study the effect of the optimal mode (CNOP-P) of theuncertainties of the two parameters on the SPB and to demonstrate that theCNOP-P errors neither presented a unified season-dependent evolution fordifferent El Nino events nor caused a large prediction error, andtherefore did not cause a significant SPB. The parameter errors played onlya trivial role in yielding a significant SPB. To further validate thisconclusion, the authors investigated the effect of the optimal combined mode(i.e. CNOP error) of initial and model errors on SPB. The resultsillustrated that the CNOP errors tended to have a significantseason-dependent evolution, with the largest error growth rate in thespring, and yielded a large prediction error, inducing a significant SPB.The inference, therefore, is that initial errors, rather than modelparameter errors, may be the dominant source of uncertainties that cause asignificant SPB for El Nino events. These results indicate that theability to forecast ENSO could be greatly increased by improving theinitialization of the forecast model.     

What Kind of Initial Errors Cause the Severest Prediction Uncertainty of El Nino in Zebiak-Cane Model

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 El Nino events in the ZC model,the predictions tend to yield false alarms due to the uncertainties caused by CNOP.For the relatively strong El Nino events,the ZC model largely underestimates their intensities.Also,our results suggest that the error growth of El Nino 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 diffcult.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.     

云可分辨模式中误差的增长和传播对定量降水可预报性的影响

Limitations in the predictability of quantitative precipitation forecasting （QPF） that arise from initial errors of small amplitude and scale are investigated by means of real-case high-resolution （cloud-resolving） numerical weather prediction （NWP） integrations. The case considered is the hail and wind disaster that occurred in Sichuan on 8 April 2005. A total of three distinct perturbation methods are used. The results suggest that a tiny initial error in the temperature field can amplify and influence the weather in a large domain, changing the 12-h forecasted rainfall by as much as one-third of the original magnitude. Furthermore, the comparison of the perturbation methods indicates that all of the methods pinpoint the same region （the heavy rainfall areas in the control experiment） as suffering from limitations in predictability. This result reveals the important role of nonlinearity in severe convective events.     

A Case Study of the Error Growth and Predictability of a Meiyu Frontal Heavy Precipitation Event

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.     

初始扰动对一次华南暴雨预报的影响的研究

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。     

Three-Dimensional Structure of Optimal Nonlinear Excitation for Decadal Variability of the Thermohaline Circulation

The decadal variability of the North Atlantic thermohaline circulation（THC） is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures： the perturbations are mainly in the northwestern basin at a depth ranging from 1500 to 3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the decadal THC variations in the tangent linear and nonlinear models show remarkably different characteristics, suggesting the importance of nonlinear processes in the decadal variability of the THC.     

不同模式误差方案在集合Kalman滤波土壤湿度同化中的比较试验

本文主要目的是探讨不同模式误差方案在土壤湿度同化中的性能。基于集合Kalman滤波同化方法和AVIM (Atmosphere-Vegetation Interaction Model) 陆面模式, 利用理想试验对膨胀因子方案 (Covariance Inflation, 简称CI)、 直接随机扰动方案 (Direct Random Disturbance, 简称DRD)、 误差源扰动方案 (Source Random Disturbance, 简称SRD) 等3种模式误差方案的同化效果进行了比较, 讨论了各方案在不同观测误差、 观测层数、 观测间隔情况下的同化性能。试验结果表明在观测误差估计完全准确的情况下, 3种方案都能获得较好的同化效果, 并且SRD方案相对于真值的均方根误差最小。当观测误差估计不准确时, SRD方案的同化效果仍能基本得以保持, 而CI和DRD方案则对观测误差估计更为敏感, 同化效果下降明显。当同化多层观测时, CI和DRD方案由于难以保持不同层观测之间的匹配关系, 同化结果反而变差, 而SRD方案能有效协调同化多层观测, 增加观测层后同化结果有了进一步的改善。当观测时间间隔较大时, CI和DRD方案的同化效果显著下降; 而SRD方案由于包含了一定的误差订正功能, 在观测稀疏时仍能保持较好的同化效果。     

均生函数残差预报模型在降水预报中的试验研究

在均生函预报模型的基础上,利用其残差数据序列对均生函数预报模型进行校正,提出了均生函数残差预报模型。运用两种模型对百色市6、7、8月月降雨量进行了历史样本拟合,并进行独立地样本预报试验。预报结果发现,均生函数残差预报模型对原有模型在预报精度上都有一定的改进,取得了较好的预报效果。同时,利用M ann-K enda ll法和Y am am oto法,可以明确突变开始的时间,指出突变区域,使待报时段与建模资料处在同一气候阶段则预报效果更为理想。     

On the Application of a Genetic Algorithm to the Predictability Problems Involving \"On-Off\" Switches

The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation (CNOP) method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on-off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the ad- joint method. In this study, we attempted to apply a genetic algorithm (GA) to the CNOP method, named GA-CNOP, to solve the predictability problems involving on-off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on-off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.     

Time-Dependent Solutions to the Fokker-Planck Equation of Maximum Reduced Air-Sea Coupling Climate Model

1. IntroductionAir-sea interaction is an important physical pro-cess in the climate system. Because oceans occupy twothirds of the earth's surface, and have a tremendousthermal inertia, oceans exert an extremely importantinfluence on atmospheric motion, and the air-sea inter-action becomes a core item of climate change studies.Contrarily, the atmosphere constrains the motion ofseawater through wind drifts and heat transfer. Withregard to the hotspot problem of global warming, theocean is a mos…     

两种四维奇异值分解同化方法的比较及误差分析

4DSVD是最近提出的一种新的资料同化方法。目前还存在一些需要解决的问题,比如如何选取样本,如何得到支撑大气吸引子的基向量以及选取基向量的个数问题等等。作者利用奇异值分解(SVD)与经验正交函数分解(EOF)两种方法来获得支撑大气吸引子的基向量,推导了基于这两种方法的4DSVD分析场的理论公式,并用简单的数值试验比较了基于这两种方法的4DSVD分析场的空间相关系数和误差,初步分析了分析场与基向量个数的关系以及与样本选取的关系和分析误差的来源及各种误差对分析误差影响的相对大小。结果表明,用SVD方法作为获得支撑大气吸引子基向量的方法得到的分析场较EOF方法稳定,分析场与基向量个数有密切关系,观测误差、模式误差和观测代表性误差是分析误差的主要来源,且其引起的分析误差随着基向量个数增多而增大。     

Assessing the Impacts of Eurasian Snow Conditions on Climate Predictability with a Global Climate Model

On the basis of two ensemble experiments conducted by a general atmospheric circulation model (Institute of Atmospheric Physics nine-level atmospheric general circulation model coupled with land surface model, hereinafter referred to as IAP9L_CoLM), the impacts of realistic Eurasian snow conditions on summer climate predictability were investigated. The predictive skill of sea level pressures (SLP) and middle and upper tropospheric geopotential heights at mid-high latitudes of Eurasia was enhanced when improved Eurasian snow conditions were introduced into the model. Furthermore, the model skill in reproducing the interannual variation and spatial distribution of the surface air temperature (SAT) anomalies over China was improved by applying realistic (prescribed) Eurasian snow conditions. The predictive skill of the summer precipitation in China was low; however, when realistic snow conditions were employed, the predictability increased, illustrating the effectiveness of the application of realistic Eurasian snow conditions. Overall, the results of the present study suggested that Eurasian snow conditions have a significant effect on dynamical seasonal prediction in China. When Eurasian snow conditions in the global climate model (GCM) can be more realistically represented, the predictability of summer climate over China increases.     

高空探测资料气球漂移的计算方法

随着数值模式的不断发展,探空气球的漂移偏差越来越不可忽视。为了提高高空观测数据的质量,减小在探测过程中由于气球漂移造成探测资料在空间上的误差,中国气象局提出一套探空、测风报的空间、时间扩充编码方案。该文从探空雷达探测系统、探测原理分析出发,介绍了该方案计算方法,并用个例说明方案的使用方法及业务应用前景。     

赤道高频纬向风强迫对ENSO事件强度的影响

ENSO强度的影响因子是一个具有争议性的问题.作者探讨了一种理想的赤道高频纬向风强迫对ENSO强度的影响.将该问题转化为一类关于模式参数扰动的非线性最优化问题;基于所用的理论ENSO模式,研究了赤道高频纬向风强迫在调制ENSO强度中的角色.结果表明,对于E1 Ni(n)o和La Ni(n)a事件,存在两类外强迫,一类促进E1 Ni(n)o事件的发展却抑制La Ni(n)a事件的发展,另一类则抑制E1 Ni(n)o而促进La Ni(n)a事件的发展.这两类外强迫的主要区别在于初始相位的不同.相位决定了外强迫对ENSO事件是促进的还是抑制的,而外强迫的振幅和周期则决定了外强迫影响ENSO强度的大小.这些外强迫主要是通过海洋波动对斜温层深度的调节来影响ENSO事件的强度的.     

Possible Sources of Forecast Errors Generated by the Global/Regional Assimilation and Prediction System for Landfalling Tropical Cyclones. Part Ⅱ: Model Uncertainty

This paper investigates the possible sources of errors associated with tropical cyclone (TC) tracks forecasted using the Global/Regional Assimilation and Prediction System (GRAPES). In Part I, it is shown that the model error of GRAPES may be the main cause of poor forecasts of landfalling TCs. Thus, a further examination of the model error is the focus of Part II. Considering model error as a type of forcing, the model error can be represented by the combination of good forecasts and bad forecasts. Results show that there are systematic model errors. The model error of the geopotential height component has periodic features, with a period of 24 h and a global pattern of wavenumber 2 from west to east located between 60°S and 60°N. This periodic model error presents similar features as the atmospheric semidiurnal tide, which reflect signals from tropical diabatic heating, indicating that the parameter errors related to the tropical diabatic heating may be the source of the periodic model error. The above model errors are subtracted from the forecast equation and a series of new forecasts are made. The average forecasting capability using the rectified model is improved compared to simply improving the initial conditions of the original GRAPES model. This confirms the strong impact of the periodic model error on landfalling TC track forecasts. Besides, if the model error used to rectify the model is obtained from an examination of additional TCs, the forecasting capabilities of the corresponding rectified model will be improved.