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Model Error (model + error)
Selected AbstractsNon-linearity and error in modelling soil processesEUROPEAN JOURNAL OF SOIL SCIENCE, Issue 1 2001T. M. Addiscott Summary Error in models and their inputs can be propagated to outputs. This is important for modelling soil processes because soil properties used as parameters commonly contain error in the statistical sense, that is, variation. Model error can be assessed by validation procedures, but tests are needed for the propagation of (statistical) error from input to output. Input error interacts with non-linearity in the model such that it contributes to the mean of the output as well as its error. This can lead to seriously incorrect results if input error is ignored when a non-linear model is used, as is demonstrated for the Arrhenius equation. Tests for non-linearity and error propagation are suggested. The simplest test for non-linearity is a graph of the output against the input. This can be supplemented if necessary by testing whether the mean of the output changes as the standard deviation of the input increases. The tests for error propagation examine whether error is suppressed or exaggerated as it is propagated through the model and whether changes in the error in one input influence the propagation of another. Applying these tests to a leaching model with rate and capacity parameters showed differences between the parameters, which emphasized that statements about non-linearity must be for specific inputs and outputs. In particular, simulations of mean annual concentrations of solute in drainage and concentrations on individual days differed greatly in the amount of non-linearity revealed and in the way error was propagated. This result is interpreted in terms of decoherence. [source] Model error and sequential data assimilation: A deterministic formulationTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008A. Carrassi Abstract Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first-order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short-time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white-noise assumption. The universal short-time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Society [source] Constrained least squares methods for estimating reaction rate constants from spectroscopic dataJOURNAL OF CHEMOMETRICS, Issue 1 2002Sabina Bijlsma Abstract Model errors, experimental errors and instrumental noise influence the accuracy of reaction rate constant estimates obtained from spectral data recorded in time during a chemical reaction. In order to improve the accuracy, which can be divided into the precision and bias of reaction rate constant estimates, constraints can be used within the estimation procedure. The impact of different constraints on the accuracy of reaction rate constant estimates has been investigated using classical curve resolution (CCR). Different types of constraints can be used in CCR. For example, if pure spectra of reacting absorbing species are known in advance, this knowledge can be used explicitly. Also, the fact that pure spectra of reacting absorbing species are non-negative is a constraint that can be used in CCR. Experimental data have been obtained from UV-vis spectra taken in time of a biochemical reaction. From the experimental data, reaction rate constants and pure spectra were estimated with and without implementation of constraints in CCR. Because only the precision of reaction rate constant estimates could be investigated using the experimental data, simulations were set up that were similar to the experimental data in order to additionally investigate the bias of reaction rate constant estimates. From the results of the simulated data it is concluded that the use of constraints does not result self-evidently in an improvement in the accuracy of rate constant estimates. Guidelines for using constraints are given. Copyright © 2002 John Wiley & Sons, Ltd. [source] Significance of Modeling Error in Structural Parameter EstimationCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2001Masoud Sanayei Structural health monitoring systems rely on algorithms to detect potential changes in structural parameters that may be indicative of damage. Parameter-estimation algorithms seek to identify changes in structural parameters by adjusting parameters of an a priori finite-element model of a structure to reconcile its response with a set of measured test data. Modeling error, represented as uncertainty in the parameters of a finite-element model of the structure, curtail capability of parameter estimation to capture the physical behavior of the structure. The performance of four error functions, two stiffness-based and two flexibility-based, is compared in the presence of modeling error in terms of the propagation rate of the modeling error and the quality of the final parameter estimates. Three different types of parameters are used in the parameter estimation procedure: (1) unknown parameters that are to be estimated, (2) known parameters assumed to be accurate, and (3) uncertain parameters that manifest the modeling error and are assumed known and not to be estimated. The significance of modeling error is investigated with respect to excitation and measurement type and locations, the type of error function, location of the uncertain parameter, and the selection of unknown parameters to be estimated. It is illustrated in two examples that the stiffness-based error functions perform significantly better than the corresponding flexibility-based error functions in the presence of modeling error. Additionally, the topology of the structure, excitation and measurement type and locations, and location of the uncertain parameters with respect to the unknown parameters can have a significant impact on the quality of the parameter estimates. Insight into the significance of modeling error and its potential impact on the resulting parameter estimates is presented through analytical and numerical examples using static and modal data. [source] Optimal asset allocation for a large number of investment opportunitiesINTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT, Issue 1 2005Hans Georg Zimmermann This paper introduces a stock-picking algorithm that can be used to perform an optimal asset allocation for a large number of investment opportunities. The allocation scheme is based upon the idea of causal risk. Instead of referring to the volatility of the assets time series, the stock-picking algorithm determines the risk exposure of the portfolio by concerning the non-forecastability of the assets. The underlying expected return forecasts are based on time-delay recurrent error correction neural networks, which utilize the last model error as an auxiliary input to evaluate their own misspecification. We demonstrate the profitability of our stock-picking approach by constructing portfolios from 68 different assets of the German stock market. It turns out that our approach is superior to a preset benchmark portfolio. Copyright © 2005 John Wiley & Sons, Ltd. [source] A parameter-reduced volterra model for dynamic RF power amplifier modeling based on orthonormal basis functionsINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2007M. Isaksson Abstract A nonlinear dynamic behavioral model for radio frequency power amplifiers is presented. It uses orthonormal basis functions, Kautz functions, with complex poles that are different for each nonlinear order. It has the same general properties as Volterra models, but the number of parameters is significantly smaller. Using frequency weighting the out-of-band model error can be reduced. Using experimental data it was found that the optimal poles were the same for different input powers and for the different nonlinear orders. The optimal poles were also the same for direct and inverse models, which could be explained theoretically to be a general property of nonlinear systems with negligible linear memory effects. The model can be used as either a direct or inverse model with the same model error for power amplifiers with negligible linear memory effects. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007. [source] A Calibrated, High-Resolution GOES Satellite Solar Insolation Product for a Climatology of Florida Evapotranspiration,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 6 2009Simon J. Paech Paech, Simon J., John R. Mecikalski, David M. Sumner, Chandra S. Pathak, Quinlong Wu, Shafiqul Islam, and Taiye Sangoyomi, 2009. A Calibrated, High-Resolution GOES Satellite Solar Insolation Product for a Climatology of Florida Evapotranspiration. Journal of the American Water Resources Association (JAWRA) 45(6):1328-1342. Abstract:, Estimates of incoming solar radiation (insolation) from Geostationary Operational Environmental Satellite observations have been produced for the state of Florida over a 10-year period (1995-2004). These insolation estimates were developed into well-calibrated half-hourly and daily integrated solar insolation fields over the state at 2 km resolution, in addition to a 2-week running minimum surface albedo product. Model results of the daily integrated insolation were compared with ground-based pyranometers, and as a result, the entire dataset was calibrated. This calibration was accomplished through a three-step process: (1) comparison with ground-based pyranometer measurements on clear (noncloudy) reference days, (2) correcting for a bias related to cloudiness, and (3) deriving a monthly bias correction factor. Precalibration results indicated good model performance, with a station-averaged model error of 2.2 MJ m,2/day (13%). Calibration reduced errors to 1.7 MJ m,2/day (10%), and also removed temporal-related, seasonal-related, and satellite sensor-related biases. The calibrated insolation dataset will subsequently be used by state of Florida Water Management Districts to produce statewide, 2-km resolution maps of estimated daily reference and potential evapotranspiration for water management-related activities. [source] A two-scale model for liquid-phase epitaxyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2009Ch. Eck Abstract We study a model for liquid-phase epitaxy that is based on a continuum description of the transport processes in the liquid and a Burton,Cabrera,Frank (BCF) model for the growth of the solid by epitaxy. In order to develop a model that is capable to incorporate structures of a very small scale in the solid phase within a computation for a technically relevant macroscopic length scale, we apply homogenization methods. The result of the homogenization procedure is a two-scale model that consists of macroscopic equations for fluid flow and solute diffusion in the fluid volume, coupled to microscopic BCF models for the evolution of the microstructure in the solid phase. The obtained two-scale model is justified by an estimate for the model error that is valid under appropriate assumptions on the regularity of the solutions. This estimate is proved for a phase field approximation of the BCF model. Copyright © 2008 John Wiley & Sons, Ltd. [source] Ensemble data assimilation with the CNMCA regional forecasting systemTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 646 2010Massimo Bonavita Abstract The Ensemble Kalman Filter (EnKF) is likely to become a viable alternative to variational methods for the next generation of meteorological and oceanographic data assimilation systems. In this work we present results from real-data assimilation experiments using the CNMCA regional numerical weather prediction (NWP) forecasting system and compare them to the currently operational variational-based analysis. The set of observations used is the same as the one ingested in the operational data stream, with the exception of satellite radiances and scatterometer winds. Results show that the EnKF-based assimilation cycle is capable of producing analyses and forecasts of consistently superior skill in the root mean square error metric than CNMCA operational 3D-Var. One of the most important issues in EnKF implementations lies in the filter tendency to become underdispersive for practical ensemble sizes. To combat this problem a number of different parametrizations of the model error unaccounted for in the assimilation cycle have been proposed. In the CNMCA system a combination of adaptive multiplicative and additive background covariance inflations has been found to give adequate results and to be capable of avoiding filter divergence in extended assimilation trials. The additive component of the covariance inflation has been implemented through the use of scaled forecast differences. Following suggestions that ensemble square-root filters can violate the gaussianity assumption when used with nonlinear prognostic models, the statistical distribution of the forecast and analysis ensembles has been studied. No sign of the ensemble collapsing onto one or a few model states has been found, and the forecast and analysis ensembles appear to stay remarkably close to the assumed probability distribution functions. Copyright © 2010 Royal Meteorological Society [source] A robust formulation of the ensemble Kalman filter,THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 639 2009S. J. Thomas Abstract The ensemble Kalman filter (EnKF) can be interpreted in the more general context of linear regression theory. The recursive filter equations are equivalent to the normal equations for a weighted least-squares estimate that minimizes a quadratic functional. Solving the normal equations is numerically unreliable and subject to large errors when the problem is ill-conditioned. A numerically reliable and efficient algorithm is presented, based on the minimization of an alternative functional. The method relies on orthogonal rotations, is highly parallel and does not ,square' matrices in order to compute the analysis update. Computation of eigenvalue and singular-value decompositions is not required. The algorithm is formulated to process observations serially or in batches and therefore easily handles spatially correlated observation errors. Numerical results are presented for existing algorithms with a hierarchy of models characterized by chaotic dynamics. Under a range of conditions, which may include model error and sampling error, the new algorithm achieves the same or lower mean square errors as the serial Potter and ensemble adjustment Kalman filter (EAKF) algorithms. Published in 2009 by John Wiley and Sons, Ltd. [source] Model error and sequential data assimilation: A deterministic formulationTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008A. Carrassi Abstract Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first-order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short-time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white-noise assumption. The universal short-time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Society [source] Model-error estimation in 4D-VarTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 626 2007Yannick Trémolet Abstract Current operational implementations of 4D-Var rely on the assumption that the numerical model representing the evolution of the atmospheric flow is perfect, or at least that model errors are small enough (relative to other errors in the system) to be neglected. This paper describes a formulation of weak-constraint 4D-Var that removes that assumption by explicitly representing model error as part of the 4D-Var control variable. The consequences of this choice of control variable for the implementation of incremental 4D-Var are discussed. It is shown that the background-error covariance matrix cannot be used as an approximate model-error covariance matrix. Another model-error covariance matrix, based on statistics of model tendencies, is proposed. Experimental results are presented. They show that this approach to accounting for and estimating model error captures some known model errors and improves the fit to observations, both in the analysis and in the background, but that it also captures part of the observation bias. We show that the model error estimated in this approach varies rapidly, and cannot be used to correct medium- or long-range forecasts. We also show that, because it relies on the tangent linear assumption for the entire assimilation window, the incremental formulation of weak-constraint 4D-Var is not the most suitable formulation for long assimilation windows. Copyright © 2007 Royal Meteorological Society [source] Accounting for an imperfect model in 4D-VarTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621 2006Yannick Tr'emolet Abstract In most operational implementations of four-dimensional variational data assimilation (4D-Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D-Var. We present three approaches for the formulation of weak-constraint 4D-Var: estimating explicitly a model-error forcing term, estimating a representation of model bias or, estimating a four-dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D-Var are discussed. We show that 4D-Var with an additional model-error representation as part of the control variable is essentially an initial-value problem and that its characteristics are very similar to that of strong constraint 4D-Var. Taking the four-dimensional state as the control variable, however, leads to very different properties. In that case, weak-constraint 4D-Var can be interpreted as a coupling between successive strong-constraint assimilation cycles. A possible extension towards long-window 4D-Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society [source] Tropical Pacific Ocean model error covariances from Monte Carlo simulationsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 613 2005O. Alves Abstract As a first step towards the development of an Ensemble Kalman Filter (EnKF) for ocean data assimilation in the tropical oceans, this article investigates a novel technique for explicitly perturbing the model error in Monte Carlo simulations. The perturbation technique involves perturbing the surface zonal stress. Estimates of the characteristics of the wind stress errors were obtained from the difference between zonal wind fields from the NCEP and ECMWF re-analyses. In order to create random zonal wind stress perturbations, an EOF analysis was performed on the intraseasonally time-filtered difference between the two re-analysis products. The first 50 EOFs were retained and random wind stress fields for each ensemble member were created by combining random amounts of each EOF. Ensemble runs were performed using a shallow-water model, with both short forecasts and long simulations. Results show covariance patterns characteristic of Kelvin wave and Rossby wave dynamics. There are interesting differences between covariances using short forecasts and those using long simulations. The use of the long simulations produced non-local covariances (e.g. negative covariances between east and west Pacific), whereas short forecasts produced covariances that were localized by the time it takes Kevin and Rossby waves to travel over the forecast period and the scales of spatial covariance in the wind stress errors. The ensembles of short forecasts produced covariances and cross-covariances that can be explained by the dynamics of equatorial Rossby and Kevin waves forced by wind stress errors. The results suggest that the ensemble generation technique to explicitly represent the model error term can be used in an EnKF. Copyright © 2005 Royal Meteorological Society [source] Can error source terms in forecasting models be represented as Gaussian Markov noises?THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 609 2005C. Nicolis Abstract The repercussions of model error on the long term climatological means and on the variability around them are analysed. The extent to which a stochastic representation of error source terms provides a universal correcting mechanism is addressed. General relations are derived linking the model error to the climatological means and the variability properties of a forecasting model subjected to a correcting Gaussian Markov noise on the basis of moment equations associated with Fokker,Planck and Liouville type equations. These relations are implemented in a variety of models giving rise to regular and to chaotic solutions. As it turns out, forecasting models fall into distinct universality classes differing in their response to the effect of noise according to the structure of the Jacobian and the Hessian matrices of the model phase-space velocity. It is concluded that different trends may exist in which the ,correcting' noise tends to depress or, on the contrary, amplify the model error. Copyright © 2005 Royal Meteorological Society. [source] A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models,THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 572 2001T. N. Palmer Abstract Conventional parametrization schemes in weather and climate prediction models describe the effects of subgrid-scale processes by deterministic bulk formulae which depend on local resolved-scale variables and a number of adjustable parameters. Despite the unquestionable success of such models for weather and climate prediction, it is impossible to justify the use of such formulae from first principles. Using low-order dynamical-systems models, and elementary results from dynamical-systems and turbulence theory, it is shown that even if unresolved scales only describe a small fraction of the total variance of the system, neglecting their variability can, in some circumstances, lead to gross errors in the climatology of the dominant scales. It is suggested that some of the remaining errors in weather and climate prediction models may have their origin in the neglect of subgrid-scale variability, and that such variability should be parametrized by non-local dynamically based stochastic parametrization schemes. Results from existing schemes are described, and mechanisms which might account for the impact of random parametrization error on planetary-scale motions are discussed. Proposals for the development of non-local stochastic-dynamic parametrization schemes are outlined, based on potential-vorticity diagnosis, singular-vector analysis and a simple stochastic cellular automaton model. [source] DISTURBANCE REJECTION USING AN ILC ALGORITHM WITH ITERATION VARYING FILTERSASIAN JOURNAL OF CONTROL, Issue 3 2004M. Norrlöf ABSTRACT An Iterative Learning Control disturbance rejection approach is considered and it is shown that iteration variant learning filters can asymptotically give the controlled variable zero error and zero variance. Convergence is achieved with the assumption that the relative model error is less than one. The transient response of the suggested ILC algorithm is also discussed using a simulation example. [source] CLONING DATA: GENERATING DATASETS WITH EXACTLY THE SAME MULTIPLE LINEAR REGRESSION FITAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009S. J. Haslett Summary This paper presents a simple computational procedure for generating ,matching' or ,cloning' datasets so that they have exactly the same fitted multiple linear regression equation. The method is simple to implement and provides an alternative to generating datasets under an assumed model. The advantage is that, unlike the case for the straight model-based alternative, parameter estimates from the original data and the generated data do not include any model error. This distinction suggests that ,same fit' procedures may provide a general and useful alternative to model-based procedures, and have a wide range of applications. For example, as well as being useful for teaching, cloned datasets can provide a model-free way of confidentializing data. [source] A Probabilistic Framework for Bayesian Adaptive Forecasting of Project ProgressCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 3 2007Paolo Gardoni An adaptive Bayesian updating method is used to assess the unknown model parameters based on recorded data and pertinent prior information. Recorded data can include equality, upper bound, and lower bound data. The proposed approach properly accounts for all the prevailing uncertainties, including model errors arising from an inaccurate model form or missing variables, measurement errors, statistical uncertainty, and volitional uncertainty. As an illustration of the proposed approach, the project progress and final time-to-completion of an example project are forecasted. For this illustration construction of civilian nuclear power plants in the United States is considered. This application considers two cases (1) no information is available prior to observing the actual progress data of a specified plant and (2) the construction progress of eight other nuclear power plants is available. The example shows that an informative prior is important to make accurate predictions when only a few records are available. This is also the time when forecasts are most valuable to the project manager. Having or not having prior information does not have any practical effect on the forecast when progress on a significant portion of the project has been recorded. [source] Error analysis for the evaluation of model performance: rainfall,runoff event time series dataHYDROLOGICAL PROCESSES, Issue 8 2005Edzer J. Pebesma Abstract This paper provides a procedure for evaluating model performance where model predictions and observations are given as time series data. The procedure focuses on the analysis of error time series by graphing them, summarizing them, and predicting their variability through available information (recalibration). We analysed two rainfall,runoff events from the R-5 data set, and evaluated 12 distinct model simulation scenarios for these events, of which 10 were conducted with the quasi-physically-based rainfall,runoff model (QPBRRM) and two with the integrated hydrology model (InHM). The QPBRRM simulation scenarios differ in their representation of saturated hydraulic conductivity. Two InHM simulation scenarios differ with respect to the inclusion of the roads at R-5. The two models, QPBRRM and InHM, differ strongly in the complexity and number of processes included. For all model simulations we found that errors could be predicted fairly well to very well, based on model output, or based on smooth functions of lagged rainfall data. The errors remaining after recalibration are much more alike in terms of variability than those without recalibration. In this paper, recalibration is not meant to fix models, but merely as a diagnostic tool that exhibits the magnitude and direction of model errors and indicates whether these model errors are related to model inputs such as rainfall. Copyright © 2004 John Wiley & Sons, Ltd. [source] Robust fault estimation of uncertain systems using an LMI-based approachINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2008Euripedes G. Nobrega Abstract General recent techniques in fault detection and isolation (FDI) are based on H, optimization methods to address the issue of robustness in the presence of disturbances, uncertainties and modeling errors. Recently developed linear matrix inequality (LMI) optimization methods are currently used to design controllers and filters, which present several advantages over the Riccati equation-based design methods. This article presents an LMI formulation to design full-order and reduced-order robust H, FDI filters to estimate the faulty input signals in the presence of uncertainty and model errors. Several cases are examined for nominal and uncertain plants, which consider a weight function for the disturbance and a reference model for the faults. The FDI LMI synthesis conditions are obtained based on the bounded real lemma for the nominal case and on a sufficient extension for the uncertain case. The conditions for the existence of a feasible solution form a convex problem for the full-order filter, which may be solved via recently developed LMI optimization techniques. For the reduced-order FDI filter, the inequalities include a non-convex constraint, and an alternating projections method is presented to address this case. The examples presented in this paper compare the simulated results of a structural model for the nominal and uncertain cases and show that a degree of conservatism exists in the robust fault estimation; however, more reliable solutions are achieved than the nominal design. Copyright © 2008 John Wiley & Sons, Ltd. [source] Impartial graphical comparison of multivariate calibration methods and the harmony/parsimony tradeoffJOURNAL OF CHEMOMETRICS, Issue 11-12 2006Forrest Stout Abstract For multivariate calibration with the relationship y,=,Xb, it is often necessary to determine the degrees of freedom for parsimony consideration and for the error measure root mean square error of calibration (RMSEC). This paper shows that degrees of freedom can be estimated by an effective rank (ER) measure to estimate the model fitting degrees of freedom and the more parsimonious model has the smallest ER. This paper also shows that when such a measure is used on the X-axis, simultaneous graphing of model errors and other regression diagnostics is possible for ridge regression (RR), partial least squares (PLS) and principal component regression (PCR) and thus, a fair comparison between all potential models can be accomplished. The ER approach is general and applicable to other multivariate calibration methods. It is often noted that by selecting variables, more parsimonious models are obtained; typically by multiple linear regression (MLR). By using the ER, the more parsimonious model is graphically shown to not always be the MLR model. Additionally, a harmony measure is proposed that expresses the bias/variance tradeoff for a particular model. By plotting this new measure against the ER, the proper harmony/parsimony tradeoff can be graphically assessed for RR, PCR and PLS. Essentially, pluralistic criteria for fairly valuating and characterizing models are better than a dualistic or a single criterion approach which is the usual tactic. Results are presented using spectral, industrial and quantitative structure activity relationship (QSAR) data. Copyright © 2007 John Wiley & Sons, Ltd. [source] Variation mode and effect analysis: an application to fatigue life predictionQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 2 2009Pär Johannesson Abstract We present an application of the probabilistic branch of variation mode and effect analysis (VMEA) implemented as a first-order, second-moment reliability method. First order means that the failure function is approximated to be linear around the nominal values with respect to the main influencing variables, while second moment means that only means and variances are taken into account in the statistical procedure. We study the fatigue life of a jet engine component and aim at a safety margin that takes all sources of prediction uncertainties into account. Scatter is defined as random variation due to natural causes, such as non-homogeneous material, geometry variation within tolerances, load variation in usage, and other uncontrolled variations. Other uncertainties are unknown systematic errors, such as model errors in the numerical calculation of fatigue life, statistical errors in estimates of parameters, and unknown usage profile. By treating also systematic errors as random variables, the whole safety margin problem is put into a common framework of second-order statistics. The final estimated prediction variance of the logarithmic life is obtained by summing the variance contributions of all sources of scatter and other uncertainties, and it represents the total uncertainty in the life prediction. Motivated by the central limit theorem, this logarithmic life random variable may be regarded as normally distributed, which gives possibilities to calculate relevant safety margins. Copyright © 2008 John Wiley & Sons, Ltd. [source] The potential of variational retrieval of temperature and humidity profiles from Meteosat Second Generation observationsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 638 2009F. Di Giuseppe Abstract The quality of temperature and humidity retrievals from the infrared Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensors on the geostationary Meteosat Second Generation (MSG) satellites is assessed by means of a one-dimensional variational algorithm. The study is performed with the aim of improving the spatial and temporal resolution of available observations to feed analysis systems designed for high-resolution regional-scale numerical weather prediction (NWP) models. The non-hydrostatic forecast model COSMO in the ARPA-SIMC operational configuration is used to provide background fields. Only clear-sky observations over sea are processed. An optimized one-dimensional variational set-up comprised of two water-vapour and three window channels is selected. It maximizes the reduction of errors in the model backgrounds while ensuring ease of operational implementation through accurate bias correction procedures and correct radiative transfer simulations. The 1Dvar retrieval quality is first quantified in relative terms, employing statistics to estimate the reduction in the background model errors. Additionally the absolute retrieval accuracy is assessed by comparing the analysis with independent radiosonde observations. The inclusion of satellite data brings a substantial reduction in the warm and dry biases present in the forecast model. Moreover it is shown that the use of the retrieved profiles generated by the 1Dvar in the COSMO nudging scheme can locally reduce forecast errors. Copyright © 2009 Royal Meteorological Society [source] Model error and sequential data assimilation: A deterministic formulationTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 634 2008A. Carrassi Abstract Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modelled on the basis of simple assumptions such as bias, white noise, and first-order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behaviour of model errors in marked contrast with previous approaches. This new scheme is applied in the context of a spatially distributed system proposed by Lorenz. First, it is found that, for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short-time dynamics of the estimation error covariance. Second, the deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained compared with the classical white-noise assumption. The universal short-time quadratic law for the evolution of the model error covariance matrix seems very promising for modelling estimation error dynamics in sequential data assimilation. Copyright © 2008 Royal Meteorological Society [source] Model-error estimation in 4D-VarTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 626 2007Yannick Trémolet Abstract Current operational implementations of 4D-Var rely on the assumption that the numerical model representing the evolution of the atmospheric flow is perfect, or at least that model errors are small enough (relative to other errors in the system) to be neglected. This paper describes a formulation of weak-constraint 4D-Var that removes that assumption by explicitly representing model error as part of the 4D-Var control variable. The consequences of this choice of control variable for the implementation of incremental 4D-Var are discussed. It is shown that the background-error covariance matrix cannot be used as an approximate model-error covariance matrix. Another model-error covariance matrix, based on statistics of model tendencies, is proposed. Experimental results are presented. They show that this approach to accounting for and estimating model error captures some known model errors and improves the fit to observations, both in the analysis and in the background, but that it also captures part of the observation bias. We show that the model error estimated in this approach varies rapidly, and cannot be used to correct medium- or long-range forecasts. We also show that, because it relies on the tangent linear assumption for the entire assimilation window, the incremental formulation of weak-constraint 4D-Var is not the most suitable formulation for long assimilation windows. Copyright © 2007 Royal Meteorological Society [source] The role of the basic state in the ENSO,monsoon relationship and implications for predictabilityTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 607 2005A. G. Turner Abstract The impact of systematic model errors on a coupled simulation of the Asian summer monsoon and its interannual variability is studied. Although the mean monsoon climate is reasonably well captured, systematic errors in the equatorial Pacific mean that the monsoon,ENSO teleconnection is rather poorly represented in the general-circulation model. A system of ocean-surface heat flux adjustments is implemented in the tropical Pacific and Indian Oceans in order to reduce the systematic biases. In this version of the general-circulation model, the monsoon,ENSO teleconnection is better simulated, particularly the lag,lead relationships in which weak monsoons precede the peak of El Niño. In part this is related to changes in the characteristics of El Niño, which has a more realistic evolution in its developing phase. A stronger ENSO amplitude in the new model version also feeds back to further strengthen the teleconnection. These results have important implications for the use of coupled models for seasonal prediction of systems such as the monsoon, and suggest that some form of flux correction may have significant benefits where model systematic error compromises important teleconnections and modes of interannual variability. Copyright © 2005 Royal Meteorological Society [source] Ridge regression in two-parameter solutionAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 6 2005Stan Lipovetsky Abstract We consider simultaneous minimization of the model errors, deviations from orthogonality between regressors and errors, and deviations from other desired properties of the solution. This approach corresponds to a regularized objective that produces a consistent solution not prone to multicollinearity. We obtain a generalization of the ridge regression to two-parameter model that always outperforms a regular one-parameter ridge by better approximation, and has good properties of orthogonality between residuals and predicted values of the dependent variable. The results are very convenient for the analysis and interpretation of the regression. Numerical runs prove that this technique works very well. The examples are considered for marketing research problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||||||||