A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction

The authors apply the technique of conditional nonlinear optimal perturbations (CNOPs) as a means of providing initial perturbations for ensemble forecasting by using a barotropic quasi-geostrophic (QG) model in a perfect-model scenario. Ensemble forecasts for the medium range (14 days) are made from the initial states perturbed by CNOPs and singular vectors (SVs). 13 different cases have been chosen when analysis error is a kind of fast growing error. Our experiments show that the introduction of CNOP provides better forecast skill than the SV method. Moreover, the spread-skill relationship reveals that the ensemble samples in which the first SV is replaced by CNOP appear superior to those obtained by SVs from day 6 to day 14. Rank diagrams are adopted to compare the new method with the SV approach. The results illustrate that the introduction of CNOP has higher reliability for medium-range ensemble forecasts.     

Application and Characteristic Analysis of the Moist Singular Vector in GRAPES-GEPS

The singular vector (SV) initial perturbation method can capture the fastest-growing initial perturbation in a tangent linear model (TLM). Based on the global tangent linear and adjoint model of GRAPES-GEPS (Global/Regional Assimilation and Prediction System—Global Ensemble Prediction System), some experiments were carried out to analyze the structure of the moist SVs from the perspectives of the energy norm, energy spectrum, and vertical structure. The conclusions are as follows: The evolution of the SVs is synchronous with that of the atmospheric circulation, which is flow-dependent. The moist and dry SVs are located in unstable regions at mid-to-high latitudes, but the moist SVs are wider, can contain more small- and medium-scale information, and have more energy than the dry SVs. From the energy spectrum analysis, the energy growth caused by the moist SVs is reflected in the relatively small-scale weather system. In addition, moist SVs can generate perturbations associated with large-scale condensation and precipitation, which is not true for dry SVs. For the ensemble forecasts, the average anomaly correlation coefficient of large-scale circulation is better for the forecast based on moist SVs in the Northern Hemisphere, and the low-level variables forecasted by the moist SVs are also improved, especially in the first 72 h. In addition, the moist SVs respond better to short-term precipitation according to statistical precipitation scores based on 10 cases. The inclusion of the large-scale condensation process in the calculation of SVs can improve the short-term weather prediction effectively.     

The Optimized Short-Range Ensemble Forecast Based on Singular Vector Calculations

In ensemble forecast,by summing up ensemble members,filtering the uncertainty,and retaining the common component,the ensemble mean with a better result can be achieved.However,the filtering works only when the initial perturbation develops nonlinearly.If the initial perturbation propagates in a linear space,the positive and negative members will counteract,leading to little difference between ensemble mean and control forecast and finally insignificant ensemble result.In 1 2-day ensemble forecast,based on singular vector (SV) calculations,to avoid this insignificance,the counteracting members originated from the same SV are advised not to put into the ensemble system together;the only candidate should be the one with the better forecast.Based on the ingredient analysis of initial perturbation development,a method to select ensemble members is presented in this paper,which can fulfill the above requirement.The regional model MM5V1 of NCAR/PSU (National Center for Atmosphere Research/Pennsylvania State University) and its corresponding tangent adjoint model are used.The ensemble spread and forecast errors are calculated with dry energy norm.Two mesoscale lows on the Meiyu front along the Yangtze River are examined.According to the analysis of the perturbation ingredient,among couples of counteracting members from different SVs,those members performing better always have smaller or greater spread compared with other members.Following this thinking,an optimized ensemble and an inferior ensemble are identified.The ensemble mean of the optimized ensemble is more accurate than that of the inferior ensemble,and the former also performs better than the traditional ensemble with positive and negative members simultaneously.As for growth of the initial perturbation,those initial perturbations originated from the summed SVs grow more quickly than those from the single SV,and they enlarge the range of spread of the ensemble effectively,thus leading to better performance of ensemble members.     

基于总能量模的GRAPES全球模式奇异向量扰动研究

以发展基于奇异向量技术为初值扰动的GRAPES全球集合预报系统为目的,在GRAPES模式及其干动力框架下的切线性、伴随模式基础上开展了以总能量模为权重算子的奇异向量计算技术研究,建立奇异向量的计算求解模块,并通过奇异向量检验方法和切线性近似方法验证了奇异向量求解的正确性.通过对中高纬度的GRAPES奇异向量水平结构的线性演变分析,证实了在最优时间间隔内GRAPES奇异向量能够快速增长,并能描述中高纬度大气的斜压不稳定特征.分析在初始时刻和最优化时间间隔时刻的GRAPES奇异向量总能量及其分量(动能和势能)的垂直分布特征,发现在中高纬度区域,GRAPES奇异向量能够描述对流层不同层次的斜压不稳定增长特征.     

An approximate energy cycle for inter-member variability in ensemble simulations of a regional climate model

The presence of internal variability (IV) in ensembles of nested regional climate model (RCM) simulations is now widely acknowledged in the community working on dynamical downscaling. IV is defined as the inter-member spread between members in an ensemble of simulations performed by a given RCM driven by identical lateral boundary conditions (LBC), where different members are being initialised at different times. The physical mechanisms responsible for the time variations and structure of such IV have only recently begun to receive attention. Recent studies have shown empirical evidence of a close parallel between the energy conversions associated with the time fluctuations of IV in ensemble simulations of RCM and the energy conversions taking place in weather systems. Inspired by the classical work on global energetics of weather systems, we sought a formulation of an energy cycle for IV that would be applicable for limited-area domain. We develop here a novel formalism based on local energetics that can be applied to further our understanding IV. Prognostic equations for ensemble-mean kinetic energy and available enthalpy are decomposed into contributions due to ensemble-mean variables (EM) and those due to deviations from the ensemble mean (IV). Together these equations constitute an energy cycle for IV in ensemble simulations of RCM. Although the energy cycle for IV was developed in a context entirely different from that of energetics of weather systems, the exchange terms between the various reservoirs have a rather similar mathematical form, which facilitates some interpretations of their physical meaning.     

Evaluation of Precipitation Indices over North America from Various Configurations of Regional Climate Models

This study presents the evaluation of simulations from two new Canadian regional climate models (RCMs), CanRCM4 and CRCM5, with a focus on the models’ skill in simulating daily precipitation indices and the Standardized Precipitation Index (SPI). The evaluation was carried out over the past two decades using several sets of gridded observations that partially cover North America. The new Canadian RCMs were also compared with four reanalysis products and six other RCMs. The different configurations of the Canadian RCM simulations also permit evaluation of the impact of different spatial resolutions, atmospheric drivers, and nudging conditions. The results from the new Canadian models show some improvement in precipitation characteristics over the previous Canadian RCM (CRCM4), but these differ with the seasons. For winter, CanRCM4 and CRCM5 have better skill than most other models over all of North America. For the summer, CRCM5 0.44° performs best over the United States, while CRCM4 has the best skill over Canada. Good skill is exhibited by CanRCM4 and CRCM4 in simulating the 6-month SPI over the Prairies and the western US Corn Belt. In general, differences are small between runs with or without large-scale spectral nudging; differences are small when different boundary conditions are used.     

GRAPES-GEPS全球集合预报系统湿奇异向量的时空尺度敏感性研究

湿奇异向量（Moist Singular Vectors,简称MSVs）是包含了湿物理切线性过程计算得到的奇异向量。研究MSVs对最优化时间间隔（optimization time interval,简称OTI）及模式水平分辨率的敏感性对提高集合预报效果至关重要。本文基于中国气象局数值预报中心自主研发的全球/区域同化和预报系统（Global/Regional Assimilation and Prediction System,简称GRAPES）——全球集合预报系统（Global ensemble prediction system,简称GEPS）业务版本研究了4组不同时空尺度（不同OTI和水平分辨率）下的MSVs,从能量模、能量谱、空间剖面等方面分析热带外MSVs特征,并从等压面变量评分、降水评分、降水概率预报等方面评估不同初值的集合预报效果。结果表明:提高MSVs水平分辨率可使其扰动具有较大的增长率,缩短OTI后MSVs能量向上传播的趋势更明显,并可以在中尺度范围产生较大SVs扰动。不同OTI下初始MSVs相似性较低,结构差异较大。从集合预报的结果来看,OTI为24 h试验的集合扰动能量增长较大,集合离散度在预报的0～96 h有明显提升,特别是2 m温度,且近地面要素的outlier评分也有明显改进。进一步分析发现,提高水平分辨率和缩短OTI的MSVs能够提高降水概率预报,而降水评分显示,同一水平分辨率下,OTI越短评分越好,但是提高MSVs的水平分辨率并不一定会提升小雨到中雨量级的降水评分。     

Can ensembles of regional climate model simulations improve results from sensitivity studies?

Intrinsic variability (IV) in regional climate models (RCMs) is often assumed to be small because at climatological timescales, the model solutions tend to be dominated by the model??s lateral boundary conditions. Recent studies have indicated that this IV may actually be large in certain instances for some variables. Direct interpretation of anomalies from RCM sensitivity studies relies on the assumption that differences between model simulations are entirely due to a physical forcing. However, if IV is as large or larger than the physical signal, then this assumption is violated. Using a 20 member ensemble of RCM simulations, we verify that IV of precipitation within a RCM can be large enough to violate the sensitivity study assumption, and we show that generating ensembles of simulations can help reduce the level of IV. We also present two indicators that can rule out the influence of IV when it is ambiguous whether anomalies within a sensitivity study are due to the sensitivity perturbation or whether they are due to IV.     

Sensitivity of the CRCM atmospheric and the Gulf of St. Lawrence Ocean‐Ice models to each other

Abstract

The sensitivity of the Canadian Regional Climate Model (CRCM), developed at the Université du Québec à Montréal, and the Gulf of St. Lawrence Ocean Model (GOM), developed at the Institut Maurice‐ Lamontagne, to each other is tested with an ensemble of simulations over eastern Canada from 1 November 1989 to 31 March 1990. The goal of this study is to investigate the interaction of the CRCM and GOM with respect to each other's forcing fields. In the first part of the experiment, a series of simulations were performed using an iterative strategy, where both models run separately and alternately, using variables from the other model to supply the needed forcing fields for the computation of surface fluxes. The runs are iterated several times over the same period from the output of the previous run to allow the atmosphere and the ocean to interact several times with each other and to study the evolution of the solutions from one iteration to the next. In the second part of the experiment, a two‐way coupled simulation is performed over the same period. The results indicate that on a monthly or longer timescale, the CRCM is not very sensitive to the details of the oceanic fields from GOM, except locally over the Gulf of St. Lawrence (GSL). However, GOM is quite sensitive to the differences in atmospheric fields from the CRCM. The results of several iterations converge to a unique solution, suggesting that the CRCM and GOM reach equilibrium with respect to each other's forcing fields. Furthermore, the results of the coupled run also converge to this same solution.     

GRAPES全球奇异向量方法改进及试验分析

基于总能量模的奇异向量扰动常用于构造集合预报的初始条件。以建立GRAPES（Global and Regional Assimilation PrEdiction System）全球集合预报系统为目的,基于前期研发的GRAPES全球模式奇异向量方法,在GRAPES全球切线性模式和伴随模式2.0版的框架下,开展了引入线性化边界层方案来改善奇异向量结构,并提高奇异向量计算效率的研究。通过连续试验,从奇异向量的扰动能量结构、扰动能量谱及扰动空间分布等方面,综合分析改进GRAPES全球奇异向量的结构及演变特征。试验结果表明,改进后的GRAPES奇异向量方法有效抑制了之前扰动能量在近地面层不合理的快速增长,同时,奇异向量最优扰动的结构更客观地体现了中高纬度区域大气初始条件中的斜压不稳定扰动及其演变,如在初始时刻奇异向量扰动能量主要位于对流层中层,并呈现出随高度向西倾斜的大气斜压特征;经过线性化演变,扰动能量向较大水平尺度转移,并在垂直结构上表现出向对流层高层上传及向对流层低层下传的特征等。针对GRAPES奇异向量迭代求解中伴随模式计算耗时为主的情况,改进伴随模式中广义共轭余差方案的调用方式,并采用大内存存储法来提高其计算效率,进而将奇异向量总计算时间缩短了25%。总之,改进后的GRAPES奇异向量方法,可应用于构建面向业务应用的GRAPES全球集合预报系统。      

Gradient in the climate change signal of European discharge predicted by a multi-model ensemble

In order to perform hydrological studies on the PRUDENCE regional climate model (RCM) simulations, a special focus was put on the discharge from large river catchments located in northern and central Europe. The discharge was simulated with a simplified land surface (SL) scheme and the Hydrological Discharge (HD) model. The daily fields of precipitation, 2 m temperature and evapotranspiration from the RCM simulations were used as forcing. Therefore the total catchment water balances are constrained by the hydrological cycle of the different RCMs. The validation of the simulated hydrological cycle from the control simulations shows that the multi-model ensemble mean is closer to the observations than each of the models, especially if different catchments and hydrological variables are considered. Therefore, the multi-model ensemble mean can be used to largely reduce the uncertainty that is introduced by a single RCM. This also provides more confidence in the future projections for the multi-model ensemble means. The scenario simulations predict a gradient in the climate change signal over Northern and Central Europe. Common features are the overall warming and the general increase of evapotranspiration. But while in the northern parts the warming will enhance the hydrological cycle leading to an increased discharge, the large warming, especially in the summer, will slow down the hydrological cycle caused by a drying in the central parts of Europe which is accompanied by a reduction of discharge. The comparison of the changes predicted by the multi-model ensemble mean to the changes predicted by the driving GCM indicates that the RCMs can compensate problems that a driving GCM may have with local scale processes or parameterizations.     

GRAPES全球集合预报初始条件及模式物理过程不确定性方法研究

为描述GRAPES全球模式初始条件的不确定性,基于适合集合预报应用的GRAPES全球奇异向量技术,依据大气初始误差符合正态分布的特征,采用高斯取样奇异向量来构造全球集合预报初始扰动,在此基础上建立了GRAPES全球集合预报系统(GRAPES-GEPS)。利用GRAPES全球同化分析场,对采用初始扰动的GRAPES-GEPS连续试验预报结果进行检验和分析。结果表明:GRAPES-GEPS中高度场、风场及温度场预报的集合离散度能有效快速增加,集合平均均方根误差与集合离散度的关系合理;相对控制预报的均方根误差,集合平均的预报优势在预报中期非常显著。为进一步体现GRAPES-GEPS中模式物理过程的不确定性,发展了模式物理过程倾向随机扰动技术(SPPT)。试验结果表明:SPPT方案的应用有效提高了GRAPES-GEPS在南、北半球和热带地区等压面要素预报的集合离散度,同时一定程度减小了集合平均误差,进而改进了集合平均误差与集合离散度的关系,其中SPPT方案在热带地区的改进最为显著。本文发展的基于奇异向量的初始扰动方法和模式扰动SPPT方案在中国气象局2018年12月业务化运行的GRAPES-GEPS中得到了应用。     

Impacts of Spectral Nudging on the Sensitivity of a Regional Climate Model to Convective Parameterizations in East Asia

The sensitivity of a regional climate model (RCM) to cumulus parameterization (CUPA) schemes in modeling summer precipitation over East Asia has been investigated by using the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (PSU-NCAR MM5). The feasibility of physical ensemble and the effect of interior (spectral) nudging are also assessed. The RCM simulations are evaluated against the NCEP/NCAR reanalysis data and NCEP/CPC precipitation data for three summers (JJA) in 1991, 1998, and 2003. The results show that the RCM is highly sensitive to CUPA schemes. Different CUPA schemes cause distinctive characteristics in the modeling of JJA precipitation and the intraseasonal (daily) variability of regional precipitation. The sensitivity of the RCM simulations to the CUPA schemes is reduced by adopting the spectral nudging technique, which enables the RCM to reproduce more realistic large-scale circulations at the upper levels of the atmosphere as well as near the surface, and better precipitation simulation in the selected experiments. The ensemble simulations using different CUPA schemes show higher skills than individual members for both control runs and spectral nudging runs. The physical ensemble adopting the spectral nudging technique shows the highest downscaling skill in capturing the general circulation patterns for all experiments and improved temporal distributions of precipitation in some regions.     

Evaluation of the internal variability and estimation of the downscaling ability of the Canadian Regional Climate Model for different domain sizes over the north Atlantic region using the Big-Brother experimental approach

The ability of a nested model to accurately simulate the subarctic climate is studied here. Two issues have been investigated: Model??s internal variability (IV) and the impact of domain size (DS). For this purpose we combine the ??perfect model?? approach, Big-Brother Experiment (BBE) (Denis et al. in Clim Dyn 18:627?C646, 2002) with the ensemble of simulations. The advantage of this framework is the possibility to study small-scale climate features that constitute the main added value of RCM. The effects of the DS on result were studied by employing two Little-Brother (LB) domain sizes. IV has been evaluated by introducing small differences in initial conditions in an ensemble of 20 simulations over each LB. Results confirm previous findings that the IV is more important over the larger domain of integration. The temporal evolution over two domain sizes is rather different and depends strongly on the synoptic situation. Small-scales solution over the larger domain diverges freely from the boundary forcing in some periods. Over the smaller domain, the amplitude of small-scale transient eddies is systematically underestimated, especially at higher altitude characterized by the strongest winds along the storm tracks. Over the larger domain, the amplitude of small-scale transient eddies is better represented. However, the weaker control by the lateral boundaries over the larger domain results in solutions with large internal variability. As a result, the ensemble average strongly underestimates the transient-eddy variance due to partial destructive interference of individual ensemble member solutions.     

Climate and climate change in western canada as simulated by the Canadian regional climate model

Abstract

A þrst climate simulation performed with the novel Canadian Regional Climate Model (CRCM) is presented. The CRCM is based on fully elastic non‐hydrostatic þeld equations, which are solved with an efþcient semi‐implicit semi‐Lagrangian (SISL) marching algorithm, and on the parametrization package of subgrid‐scale physical effects of the second‐generation Canadian Global Climate Model (GCMII). Two 5‐year integrations of the CRCM nested with GCMII simulated data as lateral boundary conditions are made for conditions corresponding to current and doubled CO₂ scenarios. For these simulations the CRCM used a grid size of 45 km on a polar‐stereographic projection, 20 scaled‐height levels and a time step of 15 min; the nesting GCMII has a spectral truncation of T32, 10 hybrid‐pressure levels and a time step of 20 min. These simulations serve to document: (1) the suitability of the SISL numerical scheme for regional climate modelling, (2) the use of GCMII physics at much higher resolution than in the nesting model, (3) the ability of the CRCM to add realistic regional‐scale climate information to global model simulations, and (4) the climate of the CRCM compared to that of GCMII under two greenhouse gases (GHG) scenarios.     

GRAPES全球模式静力平衡奇异向量改进及应用试验

采用线性化物理过程方案的GRAPES全球模式奇异向量在进行非线性模式积分时会有部分奇异向量出现崩溃问题,这说明奇异向量结构可能存在扰动变量之间不协调之处,需要对奇异向量扰动的计算方法优化,进而改进基于奇异向量的集合预报初值扰动,提高GRAPES全球集合预报效果。基于原有的GRAEPS全球奇异向量计算方法,在求解奇异向量时,对气压扰动的处理进行改进,将初始时刻的气压扰动分量通过位温扰动根据静力平衡关系导出获得,其他保持一致,发展了静力平衡奇异向量改进方法。基于有两个台风过程的个例（2019年8月8日12时（世界时））,分别采用原奇异向量方法和静力平衡奇异向量改进方法进行热带气旋目标区奇异向量的计算求解,并进行相应奇异向量的非线性模式积分,对比分析奇异向量非线性积分的稳定性。进而,对比分析奇异向量求解方法改进前、后热带气旋奇异向量的结构特征和初值扰动特征,开展了集合预报试验,评估改进后的奇异向量求解方法对GRAPES全球集合预报系统预报性能的影响。试验结果表明,静力平衡奇异向量改进方法通过产生协调的气压扰动和位温扰动场,解决了奇异向量非线性积分崩溃的问题,消除了原来不利于积分稳定性的气压扰动过于局地化的小尺度结构。静力平衡奇异向量改进方法对奇异向量中位温扰动分量和纬向风扰动分量结构影响较小,使得气压扰动分量的大值区位于台风附近,更好地描述热带气旋初值不确定性,与位温扰动分量的分布更加协调。采用静力平衡奇异向量改进方法,可以提高GRAPES全球集合预报在北半球和南半球等压面要素集合预报技巧和中国地区24 h累计降水概率预报技巧,增大台风路径集合离散度。      

The impact of atmospheric nonlinearities on the fastest growth of ENSO prediction error

In this paper we explore the impact of atmospheric nonlinearities on the optimal growth of initial condition error of El Niño and the Southern Oscillation (ENSO) prediction using singular vector (SV) analysis. This is performed by comparing and analyzing SVs of two hybrid coupled models (HCMs), one composed of an intermediate complexity dynamical ocean model coupled with a linear statistical atmospheric model, and the other one with the same ocean model coupled with a nonlinear statistical atmosphere. Tangent linear and adjoint models for both HCMs are developed. SVs are computed under the initial conditions of seasonal background and actual ENSO cycle simulated by the ocean model forced with the real wind data of 1980–1999. The optimization periods of 3, 6 and 9 months are individually considered. The results show that the first SVs in both HCMs are very similar to each other, characterized by a central east-west dipole pattern spanning over the entire tropical Pacific. The spatial patterns of the leading SV in both HCMs are not sensitive to optimization periods and initial time. However, the first singular value, indicating the optimal growth rate of prediction error, displays considerable differences between the two HCMs, indicating a significant impact of atmospheric nonlinearities on the optimal growth of ENSO prediction error. These differences are greater with increasing optimization time, suggesting that the impact of atmospheric nonlinearities on the optimal growth of prediction error becomes larger for a longer period of prediction.     

Mid-twenty-first century warm season climate change in the Central United States. Part I: regional and global model predictions

A regional climate model (RCM) constrained by future anomalies averaged from atmosphere–ocean general circulation model (AOGCM) simulations is used to generate mid-twenty-first century climate change predictions at 30-km resolution over the central U.S. The predictions are compared with those from 15 AOGCM and 7 RCM dynamic downscaling simulations to identify common climate change signals. There is strong agreement among the multi-model ensemble in predicting wetter conditions in April and May over the northern Great Plains and drier conditions over the southern Great Plains in June through August for the mid-twenty-first century. Projected changes in extreme daily precipitation are statistically significant over only a limited portion of the central U.S. in the RCM constrained with future anomalies. Projected changes in monthly mean 2-m air temperature are generally consistent across the AOGCM ensemble average, North American Regional Climate Change Assessment Program RCM ensemble average, and RCM constrained with future anomalies, which produce a maximum increase in August of 2.4–2.9 K over the northern and southern Great Plains and Midwest. Changes in extremes in daily 2-m air temperature from the RCM downscaled with anomalies are statistically significant over nearly the entire Great Plains and Midwest and indicate a positive shift in the warm tail of the daily 2-m temperature distribution that is larger than the positive shift in the cold tail.     

Combining climatological and participatory approaches for assessing changes in extreme climatic indices at regional scale

This paper combines the climatological and societal perspectives for assessing future climatic extremes over Kangasabati River basin in India using an ensemble of four high resolution (25 km) regional climate model (RCM) simulations from 1970 to 2050. The relevant extreme indices and their thresholds are defined in consultation with stakeholders and are then compared using RCM simulations. To evaluate the performance of RCM in realistically representing atmospheric processes in the basin, model simulations driven with ERAInterim global re-analysis data from 1989 to 2008 are compared with observations. The models perform well in simulating seasonality, interannual variability and climatic extremes. Future climatic extremes are evaluated based on RCM simulations driven by GCMs, for present (1970–1999) and for the SRES A1B scenario for future (2021–2050) period. The analysis shows an intensification of majority of extremes as projected by future ensemble mean. The study suggests that there is a marked consistency in stakeholder observed changes in climate extremes and future predicted trends.     

初始扰动振幅和集合样本数对CNOPs集合预报的影响

初始扰动振幅的大小和集合样本数对于集合预报取得更高预报技巧具有重要意义。本文将正交条件非线性最优扰动方法（orthogonal conditional nonlinear optimal perturbations,简称CNOPs）应用于概念模型Lorenz-96模式探讨了初始扰动振幅和集合样本数对集合预报技巧的影响,从而为使用更复杂模式进行集合预报提供指导。结果表明,由于CNOPs扮演了非线性系统中的最优初始扰动,从而使得当初始扰动振幅小于初始分析误差的大小时,CNOPs集合预报获得更高的预报技巧,并且CNOPs集合预报的最高预报技巧总是高于奇异向量法（singular vectors,简称SVs）集合预报的最高预报技巧。结果还表明,CNOPs集合预报倾向于具有一个合适的样本数时,达到最高技巧。更好的集合离散度——预报误差关系和更为平坦的Talagrand图（Talagrand diagram）进一步证明了CNOPs集合预报系统的可靠性,从而夯实了上述结果的合理性。因此,针对CNOPs集合预报,本文认为采用一个适当小于初始分析误差的初始扰动振幅和一个合适的集合样本数,有利于CNOPs集合预报达到最高预报技巧。