Impact Of Model Errors Research Articles

Ensemble-based sensitivity analysis of track forecasts of typhoon In-fa (2021) without and with model errors in the ECMWF, NCEP, and CMA ensemble prediction systems

Ensemble-based sensitivity analysis (ESA) has been widely applied to identifying and investigating the sources of forecast uncertainty in tropical cyclone (TC) track. The standard ESA used in most preceding studies involves calculating the time-lagged covariance of ensemble perturbations by removing the ensemble mean. This method primarily focuses on the influence of initial errors. However, such studies ignore two critical dimensions of ESA. One is how ensemble sensitivity is influenced by the varying forecast performance across different ensemble prediction systems (EPSs). Secondly, the impact of model errors on forecast uncertainties remains unaddressed. An in-depth examination of these two aspects provides a more comprehensive understanding of the factors contributing to TC track uncertainties.This study employed the standard ESA to analyze and compare the sources of uncertainty in the track forecast of Typhoon In-fa (2021) in three representative operational EPSs. Our findings reveal that the EPS's specific performance in ensemble spread markedly influence ensemble sensitivity. We identified that variations in the shape and location of key synoptic systems, such as the western Pacific subtropical high and monsoon trough, across ensemble members were notably distinct. These variations played a significant role in shaping the uncertainty for In-fa's track forecast within each system. Furthermore, we introduced a modified ESA to better account for the influence of model errors on TC track uncertainties. The modified ESA, when applied to ensembles with substantial systematic deviations, predominantly reflects the impact of model errors on track forecast inaccuracies, offering a notably different perspective compared to the standard ESA. Significance statementEnsemble-based sensitivity analysis (ESA) serves as an effective method for identifying the origins of forecast uncertainty in tropical cyclone (TC) tracks. Most preceding studies based on the standard ESA have predominantly concentrated on examining key physical processes within individual ensemble prediction system (EPS) and the impact of initial condition uncertainties. They often overlook the dependence of the ensemble sensitivity on the varying forecast performance of EPSs, as well as the impact of model errors on sensitivity assessment. This study revealed that the ensemble forecasts across different EPSs exhibit different performance in terms of ensemble spread in the shape and location of primary weather systems. This variability significantly contributes to the uncertainty in TC track forecasts through diverse processes. Furthermore, this research introduced a modified ESA, which effectively identifies the impact of model systematic deviations on TC track forecast errors. This approach along with the standard ESA provide a more comprehensive and nuanced analysis of the forecast error sensitivity associated with both initial condition and model related uncertainties.

Identification of human-structure interaction from full-scale observations: The impact of modeling errors

Identification of human-structure interaction from full-scale observations: The impact of modeling errors

Multivariate ensemble sensitivity analysis applied for an extreme rainfall over Indian subcontinent

Ensemble sensitivity analysis (ESA) uses sample statistics of ensemble forecasts to estimate relationships between forecast metrics and initial conditions. The ensemble sensitivity analysis is often considered as a simple univariate regression as it includes an approximation of analysis covariance matrix with corresponding diagonal elements. In this work, univariate ensemble sensitivity is extended to multivariate ensemble sensitivity that incorporates the contribution from the full covariance matrix in the sensitivity calculations. The performance of multivariate ensemble sensitivity over univariate is examined for meso- and convective scale ensemble forecasts of a heavy rainfall event that happened over the Chennai city in India in December 2015. The ensemble forecasts and analyses are generated using the Advanced Research - Weather Research and Forecasting (WRF) model Data Assimilation Research Testbed (DART) based Ensemble Kalman Filter (EnKF). Multivariate ensemble sensitivity shows organized sensitivity patterns, while the sensitivity values are found to be broadly distributed in univariate ensemble sensitivity. Both the methods are validated using a perturbed initial condition approach, and the results indicate that the multivariate ensemble sensitivity method is effective in predicting the forecast response closest to the actual model response compared to the univariate ensemble sensitivity. The impact of model error on sensitivity calculations is examined by generating a new set of ensembles that uses the Stochastic Kinetic Energy Backscatter Scheme (SKEBS). In the presence of added model error, the forecast response estimated by multivariate using SKEBS ensembles compares better with the actual response. It is found that the performance of the multivariate approach depends on the optimal choice of localization radius, and if insufficient localization is applied, the spurious long-distance correlation contaminates the performance of the multivariate ensemble sensitivity method. The impact of various forecast lead times on the univariate and multivariate ensemble sensitivity analysis indicates that responses using multivariate ensemble sensitivity are more accurate than univariate, especially at longer lead times when nonlinearity becomes significant. The performance of univariate and multivariate methods in convection-permitting scale is examined by using the high-resolution ensemble forecasts, and it is found that the multivariate sensitivity with localization substantially improves the estimates in finer scales.

Precise orbit and Earth parameter determination supported by LEO satellites, inter-satellite links and synchronized clocks of a future GNSS

The paper presents results of precise orbit and Earth parameter determination based on full-scale simulations of a potential future GNSS, with the name of Kepler, recently proposed by the German Aerospace Center. The space segment of the system consists of 24 Galileo-like Medium Earth Orbit (MEO) satellites and 6 Low Earth Orbit (LEO) satellites equipped with ultra-stable optical clocks. All spacecraft carry terminals for two-way optical inter-satellite links (ISLs) enabling high-rate data communication, constellation-wide clock synchronization and precise absolute ranging. The clock synchronization is assumed to create an extremely stable reference time scale based on ensemble of the optical clocks. A series of simulation scenarios are defined, starting from the Galileo constellation as benchmark, and gradually incorporating additional features including LEOs, ISLs and synchronized clocks to assess the impact on orbits, singnal-in-space range errors (SiSREs) and a geodetic quality Earth parameters like polar coordinates, length of day (LOD) and geocenter coordinates. Precise orbit determination (POD) is done at the observation level using the same standards and setups as in real data processing with ground network containing up to 18 stations. The MEO SiSRE, the most relevant to navigation applications, obtained for the Kepler constellation with perfect models and 18 ground stations was found to be 0.009 cm, 160 times better than 1.4 cm found for Galileo. It was demonstrated, that for operational POD for the Kepler system the ground network can be significantly reduced to only two stations if Earth rotation parameters are to be estimated, or to just one otherwise. A SiSRE value of 0.037 cm was obtained with two stations, and 0.018 cm with one station. For more realistic results a number of modeling errors are being considered. These concern observations – multipath, GNSS code hardware delays and ISL range biases, the dynamics – solar radiation pressure (SRP), gravity field, air drag, MEO antenna thrust, Earth tide potential, and the geometry – ocean loading and phase center offsets (PCOs) of space GNSS antennas. Any other satellite and station equipment contribution to mismodeling has been disregarded. It is shown, that for the Kepler the modeling errors are clearly visible in ISL observation residuals, in contrast to Galileo case, where they are to a large extent absorbed by the large number of estimated clock parameters. This was exploited to efficiently mitigate the dynamic modeling errors by estimation of empirical accelerations. With this setup the MEO SiSRE of 5 cm was obtained for Galileo and 0.3 cm, 0.4 cm and 0.7 cm for Kepler with 18, two and one ground station, respectively. The key to obtaining such low values are ISLs and synchronized satellite clocks. In the Kepler constellation with a single ground station the ISL range biases (RBs) up to 5 mm and 20 mm increase the SiSRE to 0.74 cm and 1.67 cm. Estimation of the ISL RBs is not recommended in the presence of modeling errors since they are significantly biased, which leads to increase of SiSRE to 2.2 cm. The Earth parameter determination, based on global network of 124 observing IGS stations, also benefits significantly from the Kepler constellation. The initial results show that the impact of modeling errors on Earth parameters can, as with POD, be effectively reduced in the Kepler system. The 30 cm error in integrated LOD, which has an impact on UT1-UTC, obtained for Galileo due to combined modeling errors could be reduced to 0.5 cm for the Kepler system. The same is true for the Z-coordinate of the geocenter, whose 14 mm error in the MEO-only solution could be reduced to 0.2 mm in the Kepler solution. The Earth parameters completely free of bias are obtained when the number of the modeling errors is reduced to only two: MEO SRP and PCOs. The ISL range biases up to 5 mm were found to have negligible impact on the estimated EPs. The largest differences (up to 0.2 mm) are found for UT1-UTC, for all other parameters they do not exceed 0.02 mm. The estimation of PCOs, being an integral part of Earth parameter determination, also benefits enormously from the Kepler design. It was demonstrated, that using only ten days of data they could be estimated with millimeter accuracy for MEOs and sub-millimeter accuracy for LEOs in all three spacial directions even in the presence of ISL range biases of up to 5 mm. Such accuracy of PCOs is not achievable with the Galileo constellation.

Three-dimensional traction microscopy with a fiber-based constitutive model

Tractions exerted by cells on their surroundings play an important role in many biological processes including stem cell differentiation, tumorigenesis, cell migration, cancer metastasis, and angiogenesis. The ability to quantify these tractions is important in understanding and manipulating these processes. Three-dimensional traction force microscopy (3DTFM) provides reliable means of evaluating cellular tractions by first measuring the displacement of fluorescent beads in response to these tractions in the surrounding matrix, and then using this measurement to compute the tractions. However, most applications of 3DTFM assume that the surrounding extra-cellular matrix (ECM) is non-fibrous, despite the fact that in many natural and synthetic environments the ECM contains a significant proportion of fibrous components. Motivated by this, we develop a computational approach for determining tractions, while accounting for the fibrous nature of the ECM. In particular, we make use of a fiber-based constitutive model in which the stress contains contributions from a distribution of nonlinear elastic fibers and a hyperelastic matrix. We solve an inverse problem with the nodal values of the traction vector as unknowns, and minimize the difference between a predicted displacement field, obtained by solving the equations of equilibrium in conjunction with the fiber-based constitutive model, and the measured displacement field at the bead locations. We employ a gradient-based minimization method to solve this problem and determine the gradient efficiently by solving for the appropriate adjoint field. We apply this algorithm to problems with experimentally observed cell geometries and synthetic, albeit realistic, traction fields to gauge its sensitivity to noise, and quantify the impact of using an incorrect constitutive model: the so-called model error. We conclude that the approach is robust to noise, yielding about 10% error in tractions for 5% displacement noise. We also conclude that the impact of model error is significant, where using a nonlinear exponential hyperelastic model instead of the fiber-based model, can lead to more than 100% error in the traction field. These results underline the importance of using appropriate constitutive models in 3DTFM, especially in fibrous ECM constructs.

Data Assimilation in Hydrologic Routing: Impact of Model Error and Sensor Placement on Flood Forecasting

AbstractDiverse hydrologic and hydraulic models of varying complexities have been proposed in the past few decades to accurately predict the water levels and discharges along rivers. Among them, th...

Hedging of Asian options under exponential Lévy models: computation and performance

In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Lévy model by deriving backward recursive integrals for the price sensitivities of the option. The procedure is applied to the analysis of the performance of the delta and delta–gamma hedges in an incomplete market; particular attention is paid to the hedging error and the impact of model error on the quality of the chosen hedging strategy. The numerical analysis shows the impact of jump risk on the hedging error of the option position, and the importance of including traded options in the hedging portfolio for the reduction of this risk.

Impact of Model Errors of Burst Capacity Models on the Reliability Evaluation of Corroding Pipelines

AbstractThis paper quantifies the impact of model error associated with the burst capacity model on the probability of burst of corroding oil and gas pipelines due to the internal pressure. Three burst pressure models that are widely used in the pipeline industry, namely the B31G Modified, det norske veritas (DNV), and pipeline corrosion failure criterion (PCORRC) models, are considered in the analyses. The time-dependent probabilities of burst of three hypothetical examples, which are representative of the oil and gas transmission pipelines in the United States, are evaluated by using the first-order reliability method (FORM) to carry out the comparative study. The analysis results indicate that the model error has a substantial effect on the burst probability evaluated. The probabilities of burst evaluated by considering the model error can be several orders of magnitude higher than those evaluated by ignoring the model error. The results underscore the critical importance of including the model error a...

Evaluation of Asian Option Greeks by Convolution

In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Levy model by deriving backward recursive integrals for the price sensitivities of the option. The procedure is applied to the analysis of the performance of the delta and delta-gamma hedges in an incomplete market; particular attention is paid to the hedging error and the impact of model error on the quality of the chosen hedging strategy. The numerical analysis shows the impact of jump risk on the hedging error of the option position, and the importance of including traded options in the hedging portfolio for the reduction of this risk.

Ancillary service impact on outpatient scheduling

The paper aims to provide a simulation optimization solution to improve patient scheduling that accounts for varying ancillary service time such as x-ray to minimize patient wait time. The two-step approach is to: identify patients' needs for ancillary services while scheduling appointments; and propose an algorithm to determine ancillary service time via simulation optimization. The main aim is to provide sufficient time between arrival at the clinic and the actual examination time for a patient to complete pre-visit activities without contributing significantly to patient wait time. Two case studies are included to demonstrate the approach. Triaging at the appointment-scheduling time saves an average 17 minutes for physician's first consultation in a clinic day, and a 7 percent reduction on current average patient wait time for case 1. Case 2 results in a 9 percent reduction on average patient wait time. The scheduled ancillary service time depends on the frequency and the ancillary service time, and appointment slot design. One limitation is the impact of modeling error on the account of ancillary service times and the modeling assumptions. The proposed approach provides a studying method for clinic staff to account for ancillary services prior to physicians' visits for a better patient care. Two case studies demonstrated the practicability and promising results on reducing patient waiting. This article presents a unique approach to considering the required ancillary services in outpatient scheduling system that minimizes patient wait times. The approach will strengthen the existing scheduling methods to allow the time for ancillary services.

Joint Impact of Forecast Tendency and State Error Biases in Ensemble Kalman Filter Data Assimilation of Inner-Core Tropical Cyclone Observations

Abstract In this study the properties and causes of systematic errors in high-resolution data assimilation of inner-core tropical cyclone (TC) observations were investigated using the Hurricane Weather Research and Forecasting (HWRF) Ensemble Data Assimilation System (HEDAS). Although a recent study by Aksoy et al. demonstrated overall good performance of HEDAS for 83 cases from 2008 to 2011 using airborne observations from research and operational aircraft, some systematic errors were identified in the analyses with respect to independent observation-based estimates. The axisymmetric primary circulation intensity was underestimated for hurricane cases and the secondary circulation was systematically weaker for all cases. The diagnostic analysis in this study shows that the underestimate of primary circulation was caused by the systematic spindown of the vortex core in the short-term forecasts during the cycling with observations. This tendency bias was associated with the systematic errors in the secondary circulation, temperature, and humidity. The biases were reoccurring in each cycle during the assimilation because of the inconsistency between the strength of primary and secondary circulation during the short-term forecasts, the impact of model error in planetary boundary layer dynamics, and the effect of forecast tendency bias on the background error correlations. Although limited to the current analysis the findings in this study point to a generic problem of mutual dependence of short-term forecast tendency and state estimate errors in the data assimilation of TC core observations. The results indicate that such coupling of errors in the assimilation would also lead to short-term intensity forecast bias after the assimilation for the same reasons.

On the Angular Resolution Limit for Array Processing in the Presence of Modeling Errors

In this correspondence, we study the impact of modeling errors on the angular resolution limit (ARL) for two closely spaced sources in the context of array processing. Particularly, we follow two methods based on the well-known Lee and Smith's criteria using the Cramer-Rao lower bound (CRB) to derive closed-form expressions of the ARL with respect to (w.r.t.) the error variance. We show that, as the signal-to-noise ratio increases, the ARL does not fall into zero (contrary to the classical case without modeling errors) and converge to a fixed limit depending on the method for which we give a closed-form expression. One can see that at high SNR, the ARL in the Lee and Smith sense are linear as a function of the error variance. We also investigate the influence of the array geometry on the ARL based on the Lee's and Smith's criteria.

Impact of model errors in convective transport on CO source estimates inferred from MOPITT CO retrievals

Estimates of surface fluxes of carbon monoxide (CO) inferred from remote sensing observations or free tropospheric trace gas measurements using global chemical transport models can have significant uncertainties because of discrepancies in the vertical transport in the models, which make it challenging to unequivocally relate the observations back to the surface fluxes in the models. The new Measurement of Pollution in the Troposphere (MOPITT) version 5 retrievals provide greater sensitivity to lower tropospheric CO over land relative to the previous versions and are, therefore, useful for evaluating vertical transport in models. We have assimilated the new MOPITT CO retrievals, using the Goddard Earth Observing System (GEOS)‐Chem model, to study the influence of vertical transport errors on inferred CO sources. We compared the source estimates obtained by assimilating the CO profiles, the column amounts, and the surface level retrievals for June–August 2006. The three different inversions produced large differences in the source estimates in regions of convection and strong CO emissions. The inversion using the CO profiles suggested an 85% increase in emissions in India/Southeast Asia, which exacerbated the model bias in the lower and middle troposphere, whereas using the surface level retrievals produced a 37% decrease in Indian/Southeast Asian emissions, which exacerbated the underestimate of CO in the upper troposphere. Globally, the inversion with the surface retrievals suggested a 22% reduction in emissions from the a priori estimate of 161 Tg CO/month (from combustion and the oxidation of biogenic volatile organic compounds), averaged in June–August 2006. The analysis results were validated with independent surface CO measurements from NOAA Global Monitoring Division (GMD) network and upper troposphere CO measurements from the Civil Aircraft for the Regular Investigation of the Atmosphere Based on an Instrumented Container (CARIBIC). We found that the inversion with the surface retrievals agreed best with surface CO data but produced the largest discrepancy with the CARIBIC aircraft data in the upper troposphere, suggesting the influence of vertical transport errors in the model. Our results show that the comparison of the a posteriori CO distributions obtained from the inversions using the surface and profile retrievals provides a means of characterizing the potential impact of the vertical transport biases on the source estimates and the CO distribution.

The Elephant in the Room: Model Error and Solvency Regulation

I present a brief practitioner-focused discussion of model error in the context of insurance solvency regulation. Particular focus is on the impact of model error on the interraction of regulators and regulated firms.

ECMWF seasonal forecast system 3 and its prediction of sea surface temperature

The latest operational version of the ECMWF seasonal forecasting system is described. It shows noticeably improved skill for sea surface temperature (SST) prediction compared with previous versions, particularly with respect to El Nino related variability. Substantial skill is shown for lead times up to 1 year, although at this range the spread in the ensemble forecast implies a loss of predictability large enough to account for most of the forecast error variance, suggesting only moderate scope for improving long range El Nino forecasts. At shorter ranges, particularly 3–6 months, skill is still substantially below the model-estimated predictability limit. SST forecast skill is higher for more recent periods than earlier ones. Analysis shows that although various factors can affect scores in particular periods, the improvement from 1994 onwards seems to be robust, and is most plausibly due to improvements in the observing system made at that time. The improvement in forecast skill is most evident for 3-month forecasts starting in February, where predictions of NINO3.4 SST from 1994 to present have been almost without fault. It is argued that in situations where the impact of model error is small, the value of improved observational data can be seen most clearly. Significant skill is also shown in the equatorial Indian Ocean, although predictive skill in parts of the tropical Atlantic are relatively poor. SST forecast errors can be especially high in the Southern Ocean.

Targeting of observations for accidental atmospheric release monitoring

In the event of an accidental atmospheric release of radionuclides from a nuclear power plant, accurate real-time forecasting of the activity concentrations of radionuclides is acutely required by the decision makers for the preparation of adequate countermeasures. Yet, the accuracy of the forecasted plume is highly dependent on the source term estimation. Inverse modelling and data assimilation techniques should help in that respect. However the plume can locally be thin and could avoid a significant part of the radiological monitoring network surrounding the plant. Deploying mobile measuring stations following the accident could help to improve the source term estimation. In this paper, a method is proposed for the sequential reconstruction of the plume, by coupling a sequential data assimilation algorithm based on inverse modelling with an observation targeting strategy. The targeting design strategy consists in seeking the optimal locations of the mobile monitors at time t + 1 based on all available observations up to time t. The performance of the sequential assimilation with and without targeting of observations has been assessed in a realistic framework. It focuses on the Bugey nuclear power plant (France) and its surroundings within 50 km from the plant. The existing surveillance network is used and realistic observational errors are assumed. The targeting scheme leads to a better estimation of the source term as well as the activity concentrations in the domain. The mobile stations tend to be deployed along plume contours, where activity concentration gradients are important. It is shown that the information carried by the targeted observations is very significant, as compared to the information content of fixed observations. A simple test on the impact of model error from meteorology shows that the targeting strategy is still very useful in a more uncertain context.

Case Article—Introductory Integrative Cases on Airline Revenue Management

This case article summarizes two case series. Each case series includes three subcases and has an associated teaching note. These six short cases introduce many of the concepts that underlie the practice of airline revenue management: protection levels, overbooking, customer buy-up and buy-down behavior, network controls, bid prices, and the spiral-down effect. The cases are integrative in the sense that they reinforce many of the fundamental concepts taught in business programs, such as the formulation of statistical models, customer segmentation, the meaning of shadow prices in optimization, and the impact of model errors on real-world decisions. The cases also use many of the basic skills and tools taught in business programs: data analysis and forecasting, simulation, and optimization. By applying these tools, the cases move students quickly beyond the standard newsvendor-style formulation of the revenue management problem. Because the cases require students to apply these tools to interesting and relatively complex revenue management problems, the tools themselves gain more credibility among the students. Case Teaching Note: Interested Instructors please see the Instructor Materials page for access to the restricted materials. To maintain the integrity and usefulness of cases published in ITE, unapproved distribution of the case teaching notes and other restricted materials to any other party is prohibited.

The Influence of Atmospheric Noise and Uncertainty in Ocean Initial Conditions on the Limit of Predictability in a Coupled GCM

Abstract The influence of atmospheric stochastic forcing and uncertainty in initial conditions on the limit of predictability of the NCEP Climate Forecast System (CFS) is quantified based on comparisons of idealized identical twin prediction experiments using two different coupling strategies. In the first method, called the interactive ensemble, a single oceanic general circulation model (GCM; the Modular Ocean Model version 3 of GFDL) is coupled to the ensemble average of multiple realizations (in this case six ensemble members) of an atmospheric GCM (NCEP Global Forecast System). In the second method the standard CFS is used. The interactive ensemble is specifically designed to reduce the internal atmospheric dynamic fluctuations that are unrelated to the sea surface temperature anomalies via ensemble averaging at the air–sea interface, whereas in the standard CFS, the atmospheric noise (i.e., stochastic forcing) plays an active role in the evolution of the coupled system. In the identical twin experiments presented here, the perfect model approach is taken, thereby explicitly excluding the impact of model error on the estimate of the limit of predictability. The experimental design and the analysis separately consider how uncertainty in the ocean initial conditions (i.e., initial condition noise) versus uncertainty as the forecast evolves (i.e., noise due to internal dynamics of the atmosphere) impact estimates of the limit of predictability. Estimates of the limit of predictability are based on both deterministic measures (ensemble spread and root-mean-square error) and probabilistic measures (relative operating characteristics). The analysis examines both oceanic and atmospheric variables in the tropical Pacific. The overarching result is that noise in the initial condition is the primary factor limiting predictability, whereas noise as the forecast evolves is of secondary importance.

Variational Assimilation of Tropical Atmosphere‐Ocean and expendable bathythermograph data in the Hamburg Ocean Primitive Equation ocean general circulation model, adjusting the surface fluxes in the tropical ocean

A four‐dimensional variational method has been developed that assimilates expandable bathythermograph and Tropical Atmosphere‐Ocean subsurface temperature data into the Hamburg Ocean Primitive Equation model. The method decreases the misfit between model and observed ocean temperatures by adjusting the surface forcing. The main goal of the assimilation scheme is to improve ocean analyses in the tropical Pacific. As a first study, only wind stress is adjusted in the assimilation. In two identical twin experiments it is demonstrated that the scheme works well in the equatorial Pacific. The scheme is capable of reducing errors in the ocean analysis that originate either from the wind stress forcing or the initial state. The impact of model errors on the data assimilation is investigated in a experiment with real observations. In this experiment the temperature innovations near the equator are comparable to those of an optimal interpolation data assimilation scheme.

On the predictability of regional oceanic jet stream: The impact of model errors at the inflow boundary

When a jet is simulated in a fine-resolution regional model with inflow and outflow boundaries, its dynamical behavior depends crucially on the specified inflow boundary condition (IBC). Our primary goals are (1) to explore the model's ability to simulate the jet when the IBC is approximately known, (2) to examine the dynamical propagation and growth of the IBC errors in both space and time, and (3) to assess the relative usefulness of different types of data used to specify the IBC. This paper represents the results of an ensemble of 30 IBC-perturbed experiments derived from the Semi-Spectral Primitive Equation Model (SPEM). It is found that the system is very sensitive to the IBC perturbation, particularly in the velocity component. Evaluation of the evolution of both ensemble-mean error variance and anomaly correlation shows that the system's predictability limits are reached at 64 days for the streamfunction (ψ) field, 43 days for the density (ρ) field at the surface, and 50 days for the p field at the thermocline level. The longer predictability in the ψ field is mainly due to the use of the rigid-lid approximation, which filters out small-scale and hence unpredictable barotropic waves. A much shorter local predictability for all fields occurs in the domain's central area, where the jet is most unstable and where the richest dynamical activity is concentrated. We also analyze the ensemble mean fields and the ensemble distribution of the jet-axis positions from the 30 IBC-perturbed simulations. The major results are: (1) the ensemble mean field exhibits a better representation of the reference jet than a single simulation, because the averaging procedure smooths out small-scale fluctuations for which there is little simulation skill left; (2) the least number of realizations necessary to constitute a usable ensemble lies between 12 and 20; (3) the distribution of jet-axis positions is Gaussian within 60 days and then becomes non-Gaussian and excursive. In addition, the difference of jet axis positions between the ensemble mean and the reference is not statistically distinguishable until 30 days. However, it deviates with time and becomes statistically significant at 60 days. Additional experiments are performed to help clarify (1) the difference between the present and traditional predictability known as the sensitivity to initial conditions, (2) the relative impact of velocity and density perturbations on the jet simulation, and (3) the minimum strength of the IBC perturbation that cause the jet system to be unpredictable.