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Chinese Physics B 2014年第8期23卷 669-677页

作者：胡淑娟邱春雨张利云黄启灿于海鹏丑纪范 College of Atmospheric Sciences Lanzhou University School of Mathematics and Statistics Lanzhou University

model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.

关键词： numerical weather prediction model error past data inverse problem

An Online model Correction Method Based on an Inverse Problem:Part I—model error Estimation by Iteration

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Advances in Atmospheric Sciences 2015年第10期32卷 1329-1340页

作者： XUE Haile SHEN Xueshun CHOU Jifan State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences School of Atmospheric Sciences Lanzhou University Center for Numerical Prediction China Meteorological Administration

errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.

关键词： model error past data inverse problem error estimation model correction GRAPES-GFS

An Online model Correction Method Based on an Inverse Problem:PartⅡ——Systematic model error Correction

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Advances in Atmospheric Sciences 2015年第11期32卷 1493-1503页

An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors （MEs） in past intervals. Given the analyses, the ME in each interval （6 h） between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year （2001-2005） GRAPES- GFS （Global Forecast System of the Global and Regional Assimilation and Prediction System） error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.

关键词： model error past data inverse problem error estimation model correction GRAPES-GFS

R-Factor Analysis of Data Based on Population models Comprising R- and Q-Factors Leads to Biased Loading Estimates

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Open Journal of Statistics 2024年第1期14卷 38-54页

作者： André Beauducel Department of Psychology University of Bonn Bonn Germany

Effects of performing an R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. Although R-factor analysis of data based on a population model comprising R- and Q-factors is possible, this may lead to model error. Accordingly, loading estimates resulting from R-factor analysis of sample data drawn from a population based on a combination of R- and Q-factors will be biased. It was shown in a simulation study that a large amount of Q-factor variance induces an increase in the variation of R-factor loading estimates beyond the chance level. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.

关键词： R-Factor Analysis Q-Factor Analysis Loading Bias model error Multivariate Kurtosis

Synchronization of chaos using radial basis functions neural networks

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Journal of Systems Engineering and Electronics 2007年第1期18卷 83-88,100页

作者： Ren Haipeng Liu Ding School of Automation and Information Engineering Xi'an Univ. of Technology Xi'an 710048 P.R.China

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

关键词： Chaos synchronization Radial basis function neural networks model error Parameter perturbation Measurement noise.

A Forecast error Correction Method in Numerical Weather Prediction by Using Recent Multiple-time Evolution Data

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Advances in Atmospheric Sciences 2013年第5期30卷 1249-1259页

作者：薛海乐沈学顺丑纪范 School of Atmospheric Sciences Lanzhou University State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Center for Numerical Prediction China Meteorological Administration

The initial value error and the imperfect numerical model are usually considered as error sources of numerical weather prediction （NWP）. By using past multi-time observations and model output, this study proposes a method to estimate imperfect numerical model error. This method can be inversely estimated through expressing the model error as a Lagrange interpolation polynomial, while the coefficients of polyno- mial are determined by past model performance. However, for practical application in the full NWP model, it is necessary to determine the following criteria：（1） the length of past data sufficient for estimation of the model errors, （2） a proper method of estimating the term ＂model integration with the exact solution＂ when solving the inverse problem, and （3） the extent to which this scheme is sensitive to the observational errors. In this study, such issues are resolved using a simple linear model, and an advection diffusion model is applied to discuss the sensitivity of the method to an artificial error source. The results indicate that the forecast errors can be largely reduced using the proposed method if the proper length of past data is chosen. To address the three problems, it is determined that （1） a few data limited by the order of the corrector can be used, （2） trapezoidal approximation can be employed to estimate the ＂term＂ in this study; however, a more accurate method should be explored for an operational NWP model, and （3） the correction is sensitive to observational error.

关键词： numerical weather prediction past data model error inverse problem

Comparison of Constant and Time-variant Optimal Forcing Approaches in El Nio Simulations by Using the Zebiak–Cane model

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Advances in Atmospheric Sciences 2016年第6期33卷 685-694页

作者： Ben TIAN Wansuo DUAN Laboratory for Climate Studies National Climate CenterChina Meteorological AdministrationBeijing 100081 State Key Laboratory of Numerical modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029

model errors offset by constant and time-variant optimal forcing vector approaches （termed COF and OFV, respectively） are analyzed within the framework of E1 Nifio simulations. Applying the COF and OFV approaches to the well-known Zebiak-Cane model, we re-simulate the 1997 and 2004 E1 Nifio events, both of which were poorly degraded by a certain amount of model error when the initial anomalies were generated by coupling the observed wind forcing to an ocean com- ponent. It is found that the Zebiak-Cane model with the COF approach roughly reproduced the 1997 E1 Nifio, but the 2004 E1 Nifio simulated by this approach defied an ENSO classification, i.e., it was hardly distinguishable as CP-E1 Nifio or EP-E1 Nifio. In hoth E1 Nifio simulations, substituting the COF with the OFV improved the fit between the simulations and obser- vations because the OFV better manages the time-variant errors in the model. Furthermore, the OFV approach effectively corrected the modeled E1 Nifio events even when the observational data （and hence the computational time） were reduced. Such a cost-effective offset of model errors suggests a role for the OFV approach in complicated CGCMs.

关键词： ENSO simulation model error optimal forcing vector

Reliability of design approaches for axially loaded offshore piles and its consequences with respect to the North Sea

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Journal of Rock Mechanics and Geotechnical Engineering 2018年第6期10卷 1112-1121页

作者： Kirill A.Schmoor Martin Achmus Aligi Foglia Maik Wefer Institute for Geotechnical Engineering Leibniz University HannoverHannover30167Germany Fraunhofer Institute for Wind Energy Systems(IWES) Bremerhaven27572Germany

In the near future, several offshore wind farms are planned to be built in the North Sea. Therefore, jacket and tripod constructions with mainly axially loaded piles are suitable as support structures. The current design of axial bearing resistance of these piles leads to deviant results regarding the pile resistance when different design methods are adopted. Hence, a strong deviation regarding the required pile length must be addressed. The reliability of a design method can be evaluated based on a model error which describes the quality of the considered design method by comparing measured and predicted pile bearing resistances. However, only few pile load tests are reported with regard to the boundary conditions in the North Sea. This paper presents 6 large-scale axial pile load tests which were incorporated within a new model error approach for the current design methods used for the axial bearing resistance,namely API Main Text method and cone penetration test(CPT)-based design methods, such as simplified ICP-05, offshore UWA-05, Fugro-05 and NGI-05 methods. Based on these new model errors, a reliabilitybased study towards the safety was conducted by performing a Monte-Carlo simulation. In addition,consequences regarding the deterministic pile design in terms of quality factors were evaluated. It is shown that the current global safety factor(GSF) prescribed and the partial safety factors are only valid for the API Main Text and the offshore UWA-05 design methods; whereas for the simplified ICP-05,Fugro-05 and NGI-05 design methods, an increase in the required embedded pile length and thus in the GSF up to 2.69, 2.95 and 3.27, respectively, should be considered to satisfy the desired safety level according to DIN EN 1990 of b ? 3.8. Further, quality factors for each design method on the basis of all reliability-based design results were derived. Hence, evaluation of each design method regarding the reliability of the pile capacity prediction is possible.

关键词： Pile load test model error System reliability Global safety factors(GSFs) Quality factors

Effect of Stochastic MJO Forcing on ENSO Predictability

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Advances in Atmospheric Sciences 2011年第6期28卷 1279-1290页

作者：彭跃华段晚锁项杰 The State Key Laboratory of Numerical modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of Sciences Department of Military Oceanography Dalian Naval Academy Institute of Meteorology PLA University of Science and Technology

Within the frame of the Zebiak-Cane model,the impact of the uncertainties of the Madden-Julian Oscillation（MJO） on ENSO predictability was studied using a parameterized stochastic representation of intraseasonal *** results show that the uncertainties of MJO have little effect on the maximum prediction error for ENSO events caused by conditional nonlinear optimal perturbation（CNOP）;compared to CNOP-type initial error,the model error caused by the uncertainties of MJO led to a smaller prediction uncertainty of ENSO,and its influence over the ENSO predictability was not *** result suggests that the initial error might be the main error source that produces uncertainty in ENSO prediction,which could provide a theoretical foundation for the data assimilation of the ENSO forecast.

关键词： Madden-Julian Oscillation(MJO) El Nin o-Southern Oscillation(ENSO) conditional nonlinear optimal perturbation(CNOP) model error

The Role of Nonlinear Forcing Singular Vector Tendency error in Causing the"Spring Predictability Barrier"for ENSO

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Journal of Meteorological Research 2016年第6期30卷 853-866页

作者：段晚锁赵鹏胡均亚徐辉 State Key Laboratory of Numerical modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Meteorological Administration Training Center Beijing 100081 University of Chinese Academy of Sciences Beijing 100049

With the Zebiak-Cane model, the present study investigates the role of model errors represented by the nonlinear forcing singular vector （NFSV） in the ＂spring predictability barrier＂（SPB） phenomenon in ENSO prediction. The NFSV-related model errors are found to have the largest negative effect on the uncertainties of El Nino prediction and they can be classified into two types： the first is featured with a zonal dipolar pattern of SST anomalies （SSTA）, with the western poles centered in the equatorial central western Pacific exhibiting positive anomalies and the eastern poles in the equatorial eastern Pacific exhibiting negative anomalies; and the second is characterized by a pattern almost opposite to the first type. The first type of error tends to have the worst effects on El Nifio growth-phase predictions, whereas the latter often yields the largest negative effects on decaying-phase predictions. The evolution of prediction errors caused by NFSV- related errors exhibits prominent seasonality, with the fastest error growth in spring and/or summer; hence, these errors result in a significant SPB related to El Nifio events. The linear counterpart of NFSVs, the （linear） forcing singular vector （FSV）, induces a less significant SPB because it contains smaller prediction errors. Random errors cannot generate an SPB for El Nifio events. These results show that the occurrence of an SPB is related to the spatial patterns of tendency errors. The NFSV tendency errors cause the most significant SPB for El Nifio events. In addition, NFSVs often concentrate these large value errors in a few areas within the equatorial eastern and central-western Pacific, which likely represent those areas sensitive to El Nifio predictions associated with model errors. Meanwhile, these areas are also exactly consistent with the sensitive areas related to initial errors determined by previous studies. This implies that additional observations in the sensitive areas would not only improve the a

关键词： spring predictability barrier model error optimal perturbation El Nifio event