Search

Rossby‐wave packets (RWPs) along the midlatitude jet are a fundamental ingredient of extratropical dynamics. RWPs have been linked to enhanced atmospheric predictability and the occurrence of extreme weather events. We here investigate the predictability of Northern Hemispheric RWPs as physical entities, defined by enhanced values of the Rossby‐wave envelope field. Using a catalogue of RWPs identified and tracked in reanalysis data, we analyze RWP predictability in a 19‐year period of NOAA GEFSv12 reforecasts. Our analysis adopts the so‐called distance and amplitude score (DAS), a verification metric that avoids both the double‐penalty issue of field‐based verification of coherent features and the complications of an object‐based approach. Applied to the envelope field, forecast errors defined by this metric asymptote towards saturation, but do not completely reach saturation within the 10 days lead time available to this study. The growth rate of the median DAS is highest initially and decreases with lead time. This is a nontrivial result, because the underlying envelope field largely de‐emphasizes phase information, but still exhibits very similar error‐growth characteristics to fields that contain the full phase information. Variations in RWP predictability are dominated by the stage of the RWP life cycle, with higher predictability found for the propagation stage than the onset and decay stages. In addition, RWP predictability exhibits a seasonal cycle, with higher predictability in winter than in summer. Controlling for seasonality and the stage of the life cycle, we find that (i) high‐amplitude RWPs exhibit higher predictability than low‐amplitude RWPs up to 6 days lead time and (ii) there is a general pattern of relatively high predictability over Eurasia. Finally, predictability of the propagating stage is higher if forecasts are initialized after RWP onset than if initialized before onset. In this sense, RWP onset acts as a predictability barrier to the subsequent propagation stage. [ABSTRACT FROM AUTHOR]

Definition: This entry examines Lorenz's error growth models with quadratic and cubic hypotheses, highlighting their mathematical connections to the non-dissipative Lorenz 1963 model. The quadratic error growth model is the logistic ordinary differential equation (ODE) with a quadratic nonlinear term, while the cubic model is derived by replacing the quadratic term with a cubic one. A variable transformation shows that the cubic model can be converted to the same form as the logistic ODE. The relationship between the continuous logistic ODE and its discrete version, the logistic map, illustrates chaotic behaviors, demonstrating computational chaos with large time steps. A variant of the logistic ODE is proposed to show how finite predictability horizons can be determined, emphasizing the continuous dependence on initial conditions (CDIC) related to stable and unstable asymptotic values. This review also presents the mathematical relationship between the logistic ODE and the non-dissipative Lorenz 1963 model. [ABSTRACT FROM AUTHOR]

This entry examines Lorenz’s error growth models with quadratic and cubic hypotheses, highlighting their mathematical connections to the non-dissipative Lorenz 1963 model. The quadratic error growth model is the logistic ordinary differential equation (ODE) with a quadratic nonlinear term, while the cubic model is derived by replacing the quadratic term with a cubic one. A variable transformation shows that the cubic model can be converted to the same form as the logistic ODE. The relationship between the continuous logistic ODE and its discrete version, the logistic map, illustrates chaotic behaviors, demonstrating computational chaos with large time steps. A variant of the logistic ODE is proposed to show how finite predictability horizons can be determined, emphasizing the continuous dependence on initial conditions (CDIC) related to stable and unstable asymptotic values. This review also presents the mathematical relationship between the logistic ODE and the non-dissipative Lorenz 1963 model.

We consider the numerical analysis of the inchworm Monte Carlo method, which is proposed recently to tackle the numerical sign problem for open quantum systems. We focus on the growth of the numerical error with respect to the simulation time, for which the inchworm Monte Carlo method shows a flatter curve than the direct application of Monte Carlo method to the classical Dyson series. To better understand the underlying mechanism of the inchworm Monte Carlo method, we distinguish two types of exponential error growth, which are known as the numerical sign problem and the error amplification. The former is due to the fast growth of variance in the stochastic method, which can be observed from the Dyson series, and the latter comes from the evolution of the numerical solution. Our analysis demonstrates that the technique of partial resummation can be considered as a tool to balance these two types of error, and the inchworm Monte Carlo method is a successful case where the numerical sign problem is effectively suppressed by such means. We first demonstrate our idea in the context of ordinary differential equations, and then provide complete analysis for the inchworm Monte Carlo method. Several numerical experiments are carried out to verify our theoretical results. [ABSTRACT FROM AUTHOR]

The application of lateral boundary perturbations (LBPs) helps to restore dispersion in convection-allowing ensemble forecasts (CAEFs). However, the applicability of LBPs remains unclear because of the differences between convection systems. Short-range (24 h) ensemble forecasts are carried out to explore this issue with a strong-forcing (SF) case and a weak-forcing (WF) case in East China. The dependence of LBPs on the forcing types of severe convection is investigated regarding the forecast error growth caused by the lateral boundary conditions (LBCs). The results show that the LBPs mainly influence the SF case rather than the WF case, especially after a 12-h forecast. The large-scale errors dominate in the SF case because the change in the synoptic-scale system affects the forecast error evolution. In contrast, the large-scale errors are mainly derived from the upscaling of the small-scale errors in the WF case, indicating that using LBPs is only insufficient in such a case. In sensitivity experiments that vary the magnitude of LBPs from 10% to 150% of its original value, CAEFs demonstrate more sensitive to LBPs in the SF case than in the WF case, indicating that the WF case has intrinsically limited predictability. Overall, LBPs are more suitable for the SF case, while additional perturbations from other sources are required for CAEFs in the WF case because of the limits of intrinsic predictability. [ABSTRACT FROM AUTHOR]

The application of lateral boundary perturbations (LBPs) helps to restore dispersion in convection-allowing ensemble forecasts (CAEFs). However, the applicability of LBPs remains unclear because of the differences between convection systems. Short-range (24 h) ensemble forecasts are carried out to explore this issue with a strong-forcing (SF) case and a weak-forcing (WF) case in East China. The dependence of LBPs on the forcing types of severe convection is investigated regarding the forecast error growth caused by the lateral boundary conditions (LBCs). The results show that the LBPs mainly influence the SF case rather than the WF case, especially after a 12-h forecast. The large-scale errors dominate in the SF case because the change in the synoptic-scale system affects the forecast error evolution. In contrast, the large-scale errors are mainly derived from the upscaling of the small-scale errors in the WF case, indicating that using LBPs is only insufficient in such a case. In sensitivity experiments that vary the magnitude of LBPs from 10% to 150% of its original value, CAEFs demonstrate more sensitive to LBPs in the SF case than in the WF case, indicating that the WF case has intrinsically limited predictability. Overall, LBPs are more suitable for the SF case, while additional perturbations from other sources are required for CAEFs in the WF case because of the limits of intrinsic predictability.

Among all of the sources of tropical cyclone (TC) intensity forecast errors, the uncertainty of sea surface temperature (SST) has been shown to play a significant role. In the present study, we determine the SST forcing error that causes the largest simulation error of TC intensity during the entire simulation period by using the WRF model with time-dependent SST forcing. The SST forcing error is represented through the application of a nonlinear forcing singular vector (NFSV) structure. For the selected 12 TC cases, the NFSV-type SST forcing errors have a nearly coherent structure with positive (or negative) SST anomalies located along the track of TCs but are especially concentrated in a particular region. This particular region tends to occur during the specific period of the TCs life cycle when the TCs present relatively strong intensity, but are still intensifying just prior to the mature phase, especially within a TC state exhibiting a strong secondary circulation and very high inertial stability. The SST forcing errors located along the TC track during this time period are verified to have the strongest disturbing effect on TC intensity simulation. Physically, the strong inertial stability of TCs during this time period induces a strong response of the secondary circulation from diabatic heating errors induced by the SST forcing error. Consequently, this significantly influences the subsidence within the warm core in the eye region, which, in turn, leads to significant errors in TC intensity. This physical mechanism explains the formation of NSFV-type SST forcing errors. According to the sensitivity of the NFSV-type SST forcing errors, if one increases the density of SST observations along the TC track and assimilates them to the SST forcing field, the skill of TC intensity simulation generated by the WRF model could be greatly improved. However, this adjustment is most advantageous in improving simulation skill during the time period when TCs become strong but are still intensifying just prior to reaching full maturity. In light of this, the region along the TC track but in the time period of TC movement when the NFSV-type SST forcing errors occur may represent the sensitive area for targeting observation for SST forcing field associated with TC intensity simulation. [ABSTRACT FROM AUTHOR]

This study investigated the regime-dependent predictability using convective-scale ensemble forecasts initialized with different initial condition perturbations in the Yangtze and Huai River basin (YHRB) of East China. The scale-dependent error growth (ensemble variability) and associated impact on precipitation forecasts (precipitation uncertainties) were quantitatively explored for 13 warm-season convective events that were categorized in terms of strong forcing and weak forcing. The forecast error growth in the strong-forcing regime shows a stepwise increase with increasing spatial scale, while the error growth shows a larger temporal variability with an afternoon peak appearing at smaller scales under weak forcing. This leads to the dissimilarity of precipitation uncertainty and shows a strong correlation between error growth and precipitation across spatial scales. The lateral boundary condition errors exert a quasi-linear increase on error growth with time at the larger scale, suggesting that the large-scale flow could govern the magnitude of error growth and associated precipitation uncertainties, especially for the strong-forcing regime. Further comparisons between scale-based initial error sensitivity experiments show evident scale interaction including upscale transfer of small-scale errors and downscale cascade of larger-scale errors. Specifically, small-scale errors are found to be more sensitive in the weak-forcing regime than those under strong forcing. Meanwhile, larger-scale initial errors are responsible for the error growth after 4 h and produce the precipitation uncertainties at the meso-β-scale. Consequently, these results can be used to explain under-dispersion issues in convective-scale ensemble forecasts and provide feedback for ensemble design over the YHRB. [ABSTRACT FROM AUTHOR]

This study provides a process‐based perspective on the amplification of forecast uncertainty and forecast errors in ensemble forecasts. A case from the North Atlantic Waveguide and Downstream Impact Experiment that exhibits large forecast uncertainty is analysed. Two aspects of the ensemble behaviour are considered: (a) the mean divergence of the ensemble members, indicating the general amplification of forecast uncertainty, and (b) the divergence of the best and worst members, indicating extremes in possible error‐growth scenarios. To analyse the amplification of forecast uncertainty, a tendency equation for the ensemble variance of potential vorticity (PV) is derived and partitioned into the contributions from individual processes. The amplification of PV variance is, on average for the midlatitudes of the Northern Hemisphere, dominated by near‐tropopause dynamics. Locally, however, other processes can dominate the variance amplification, for example, in the region where tropical storm Karl interacts with the Rossby‐wave pattern during extratropical transition. In this region, the variance amplification is dominated by upper‐tropospheric divergence and tropospheric–deep interaction and is thereby mostly related to (moist baroclinic) cyclone development. The differences between the error growth in the best and worst ensemble members can, to a large part, be attributed to differences in the representation of cut‐off evolution around 3 days, which subsequently amplifies substantially in the highly nonlinear region of the Rossby‐wave pattern until 5 days. In terms of the processes, the differences in error growth are dominated by differences in the error growth by near‐tropopause dynamics. The approach presented provides flow‐dependent insight into the dynamics of forecast uncertainty and forecast errors and helps to understand better the different contributions of specific weather systems to the medium‐range amplification of ensemble spread. [ABSTRACT FROM AUTHOR]

The sensitivity of ensemble simulations of deep convective events in the southeastern United States to initial‐condition (IC) errors is examined by imposing idealized moisture perturbations at small and large scales. Four severe weather events are considered, ranging from a springtime frontal system to convection driven almost exclusively by daytime heating. Events with strong synoptic‐scale forcing were insensitive to the scale of IC errors, but weakly forced events exhibited greater sensitivity to small‐scale than large‐scale IC errors. Additional ensemble simulations of idealized convective systems suggest that the greater sensitivity to small‐scale IC errors of the weakly forced cases arises from their higher sensitivity to the strength and location of the first convective elements. Ensemble spread and predictability are characterized by two measures: the ratio of the perturbation kinetic energy (KE) about the ensemble mean to the background KE and the neighborhood‐based fractions skill score (FSS) of hourly precipitation with respect to that in an unperturbed reference simulation. For simulations of both observed events and idealized convective systems, the FSS appears to be a more discriminating indicator of differences in predictability between different convective events. [ABSTRACT FROM AUTHOR]

For practical applications, the long time behaviour of the error of numerical solutions to time-dependent partial differential equations is very important. Here, we investigate this topic in the context of hyperbolic conservation laws and flux reconstruction schemes, focusing on the schemes in the discontinuous Galerkin spectral element framework. For linear problems with constant coefficients, it is well-known in the literature that the choice of the numerical flux (e.g. central or upwind) and the selection of the polynomial basis (e.g. Gauß–Legendre or Gauß–Lobatto–Legendre) affects both the growth rate and the asymptotic value of the error. Here, we extend these investigations of the long time error to variable coefficients using both Gauß–Lobatto–Legendre and Gauß–Legendre nodes as well as several numerical fluxes. We derive conditions guaranteeing that the errors are still bounded in time. Furthermore, we analyse the error behaviour under these conditions and demonstrate in several numerical tests similarities to the case of constant coefficients. However, if these conditions are violated, the error shows a completely different behaviour. Indeed, by applying central numerical fluxes, the error increases without upper bound while upwind numerical fluxes can still result in uniformly bounded numerical errors. An explanation for this phenomenon is given, confirming our analytical investigations. [ABSTRACT FROM AUTHOR]

This study investigates the practical predictability of two simulated mesoscale convective systems (MCS1 and MCS2) within a state-of-the-art convection-allowing ensemble forecast system. The two MCSs are both controlled by the synoptic Meiyu-front but differ in mesoscale orographic forcing. An observation system simulation experiment (OSSE) setup is first built, which includes flow-dependent multiple-scale initial and lateral boundary perturbations and a 12-h 30-member ensemble forecast is thereby created. In combination with the difference total energy, the decorrelation scale and the ensemble sensitivity analysis, both forecast error evolution, precipitation uncertainties and meteorological sensitivity that describe the practical predictability are assessed. The results show large variabilities of precipitation forecasts among ensemble members, indicative of the practical predictability limit. The study of forecast error evolution shows that the error energy in the MCS1 region in which the convection is blocked by the Dabie Mountains exhibits a simultaneous peak pattern for all spatial scales at around 6 h due to strong moist convection. On the other hand, when large-scale flow plays a more important role, the forecast error energy in the MCS2 region exhibits a stepwise increase with increasing spatial scale. As a result of error energy growth, the precipitation uncertainties evolve from small scales and gradually transfer to larger scales, implying a strong relationship between error growth and precipitation across spatial scales, thus explaining the great precipitation variability within ensemble members. These results suggest the additional forcing brought by the Dabie Mountains could regulate the predictability of Meiyu-frontal convection, which calls for a targeted perturbation design in convection-allowing ensemble forecast systems with respect to different forcing mechanisms.

The "summer prediction barrier" (SPB) of SST anomalies (SSTA) over the Kuroshio-Oyashio Extension (KOE) refers to the phenomenon that prediction errors of KOE-SSTA tend to increase rapidly during boreal summer, resulting in large prediction uncertainties. The fast error growth associated with the SPB occurs in the mature-to-decaying transition phase, which is usually during the August-September-October (ASO) season, of the KOE-SSTA events to be predicted. Thus, the role of KOE-SSTA evolutionary characteristics in the transition phase in inducing the SPB is explored by performing perfect model predictability experiments in a coupled model, indicating that the SSTA events with larger mature-to-decaying transition rates (Category-1) favor a greater possibility of yielding a more significant SPB than those events with smaller transition rates (Category-2). The KOE-SSTA events in Category-1 tend to have more significant anomalous Ekman pumping in their transition phase, resulting in larger prediction errors of vertical oceanic temperature advection associated with the SSTA events. Consequently, Category-1 events possess faster error growth and larger prediction errors. In addition, the anomalous Ekman upwelling (downwelling) in the ASO season also causes SSTA cooling (warming), accelerating the transition rates of warm (cold) KOE-SSTA events. Therefore, the SSTA transition rate and error growth rate are both related with the anomalous Ekman pumping of the SSTA events to be predicted in their transition phase. This may explain why the SSTA events transferring more rapidly from the mature to decaying phase tend to have a greater possibility of yielding a more significant SPB. [ABSTRACT FROM AUTHOR]

Despite significant, steady improvements in the skill of medium-range weather predictionsystems over the past several decades, the accuracy of these forecasts are occasionally very poor.These forecast failures are referred to as “busts” or “dropouts”. The lack of a clear explanationfor bust events limits the development and implementation of strategies designed to reduce theiroccurrence. This study seeks to explore a flow regime where forecast busts occur over Europe inassociation with mesoscale convective systems over North America east of the Rocky Mountains.Our investigation focuses on error growth in the European Centre for Medium-Range WeatherForecasting’s (ECMWF’s) global model during the summer 2015 PECAN (Plains Elevated Convectionat Night) experiment. Observations suggest that a close, but varied interrelationship can occurbetween long-lived, propagating, mesoscale convection systems over the Great Plains and Rossbywave packets. Aloft, the initial error occurs in the ridge of the wave and then propagates downstreamas an amplifying Rossby wave packet producing poor forecasts in middle latitudes and, in somecases, the Arctic. Our results suggest the importance of improving the representation of organizeddeep convection in numerical models, particularly for long-lived mesoscale convective systems thatproduce severe weather and propagate near the jet stream.

We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved. [ABSTRACT FROM AUTHOR]

We assess the scale-dependent growth of forecast errors based on a 50-member global forecast ensemble from the European Centre for Medium Range Weather Forecasts. Simulated forecast errors are decomposed into scales and a new parametric model for the representation of the error growth is applied independently to every zonal wavenumber. In contrast to the standard fitting method, the new fitting function involves no time derivatives and provides the asymptotic values of the forecast errors as a function of the fitting parameters. The range of useful prediction skill, estimated as a scale where forecast errors exceed 60% of their asymptotic values is around 7 days on large scales and 2–3 days at 1000 km scale. The new model is easily transformed to the widely used model of Dalcher and Kalnay (1987) to discuss the scale-dependent growth as a sum of two terms, the so-called $ \alpha $ and $ \beta $ terms. Their comparison shows that at planetary scales their contributions to the growth in the first two days are similar whereas at small scales the $ \beta $ term describes most of a rapid exponential growth of errors towards saturation.

A systematic study of the intrinsic predictability of tropical cyclone (TC) intensity is conducted using a set of cloud-resolving model ensembles of Hurricane Earl (2010). The ensembles are perturbed with a stochastic kinetic-energy backscatter scheme (SKEBS) and started from identical initial conditions. Scale-dependent error growth is investigated by imposing stochastic perturbations with various spatial scales on the TC and its environment. Predictability limits (upper bound) are determined by computing the error magnitude associated with each component of the Fourier-decomposed TC wind fields at forecast times up to 7 days. Three SKEBS ensembles with different perturbation scales are used to investigate the effects of small-scale, mesoscale and large-scale uncertainties on the predictability of TC intensity. In addition, the influence of the environmental flow is investigated by perturbing the lateral boundary conditions. It is found that forecast errors grow rapidly on small scales (azimuthal wave numbers > 20), which saturate within 6-12 h in all four ensembles, regardless of perturbation scale. Errors grow relatively slower on scales corresponding to rain bands (wave numbers 2-5), limiting the predictability of these features to 1-5 days. Earl's mean vortex and the wave number-1 asymmetry are comparatively resistant to error growth and remain predictable for at least 7 days. Forecast uncertainty of the mean vortex and wave number-1 asymmetry is greater in the large-scale perturbation and perturbed lateral boundary condition ensembles. The results from this case indicate that the predictability of the mean vortex and wave number-1 asymmetry is predominately associated with the predictability of the large-scale environment, which is generally much longer than that of convective-scale processes within the TC. [ABSTRACT FROM AUTHOR]

A key attribute of a probabilistic forecast system is its reliability: the degree to which forecast probabilities agree with outcome frequencies. Here, we focus on short-lead-time (12 h) reliability in the nonlinear background forecasts of the Ensemble of Data Assimilations (EDA) from the European Centre for Medium-Range Weather Forecasts (ECMWF). A 'reliability budget', derived from consistency arguments, is used to separate the mean-squared departures of the ensemble mean (relative to observations) into bias, ensemble variance and observation-error contributions, along with a residual that indicates a deficiency in reliability. At these short lead times, the residual is found to be sensitive, in a local manner, to the assignment of observation errors and to the parametrization of 'stochastic physics', which accounts for the deficit in a model's error growth rate. In particular, the results highlight the importance of the stochastic physics parametrization to represent error growth rates fully in convective regions and suggest that current stochastic physics may be too active in subtropical anticyclones, where the mid-tropospheric meteorology is largely characterized by time-mean descent and radiative cooling. Other results demonstrate how the reliability budget can be used to tune observation errors, which leads to an improvement in diagnosed background reliability. Although there remains some ambiguity in the attribution of deficiencies, the budget represents a useful additional tool that can help stimulate improvements in model stochastic error representation and observation-error estimates. Such improvements should help facilitate the development of more reliable ensemble forecasts in future. [ABSTRACT FROM AUTHOR]

By performing perfect model predictability experiments in a coupled general circulation model from the point of view of initial error growth, it is demonstrated that there may exist a 'summer prediction barrier' (SPB) in the predictions of Pacific Decadal Oscillation-related sea surface temperature anomalies (PDO-related SSTA), which refers to the phenomenon that initial errors exhibit a significant season-dependent evolution, with the largest error growth occurring in the August-September-October (ASO) season. Due to the effect of the SPB, the prediction error of PDO-related SSTA events starts to grow rapidly during the ASO season and yields a positive (negative) prediction error for the warm (cold) events, essentially inducing a delay of the events. The SPB may be one of the main factors limiting the predictability of North Pacific sea surface temperature. The physical and dynamical mechanisms of the SPB are explored from two aspects: thermodynamics and dynamics. In terms of thermodynamics, we demonstrate that the fastest error growth of PDO-related SST cold (warm) events during the ASO season is mainly due to the largest anomalous release (absorption) of the latent heat flux in this season; while for dynamics, the effect of the vertical gradient of climatological mean sea temperature on the anomalous upwelling (downwelling) dominates the contribution of the dynamical temperature advections to the error growth of the PDO-related SST cold (warm) events during the ASO season. The anomalous release (absorption) of the latent heat flux and anomalous upwelling (downwelling) of the ocean currents are both related to the anomalous northwesterly or cyclonic (southeasterly or anticyclonic) wind over the PDO-related SSTA region, which indicates that the error growth associated with the SPB of PDO-related SST cold (warm) events is mainly driven by anomalous wind stress. The error growth associated with the SPB for PDO-related SSTA may also explain why the SSTA in the Kuroshio-Oyashio Extension is much less predictable than in other regions of the North Pacific, as shown by some state-of-the-art climate models. [ABSTRACT FROM AUTHOR]

This study seeks to quantify the predictability of different forecast variables at various scales through spectral analysis of the difference between perturbed and unperturbed cloud-permitting simulations of idealized moist baroclinic waves amplifying in a conditionally unstable atmosphere. The error growth of a forecast variable is found to be strongly associated with its reference-state (unperturbed) power spectrum and slope, which differ significantly from variable to variable. The shallower the reference state spectrum, the more spectral energy resides at smaller scales, and thus the less predictable the variable since the error grows faster at smaller scales before it saturates. In general, the variables with more small-scale components (such as vertical velocity) are less predictable, and vice versa (such as pressure). In higher-resolution simulations in which more rigorous small-scale instabilities become better resolved, the error grows faster at smaller scales and spreads to larger scales more quickly before the error saturates at those small scales during the first few hours of the forecast. Based on the reference power spectrum, an index on the degree of lack (or loss) of predictability (LPI) is further defined to quantify the predictive time scale of each forecast variable. Future studies are needed to investigate the scale- and variable-dependent predictability under different background reference flows, including real case studies through ensemble experiments. [ABSTRACT FROM AUTHOR]

The impact of both initial and parameter errors on the spring predictability barrier (SPB) is investigated using the Zebiak-Cane model (ZC model). Previous studies have shown that initial errors contribute more to the SPB than parameter errors in the ZC model. Although parameter errors themselves are less important, there is a possibility that nonlinear interactions can occur between the two types of errors, leading to larger prediction errors compared with those induced by initial errors alone. In this case, the impact of parameter errors cannot be overlooked. In the present paper, the optimal combination of these two types of errors [i.e., conditional nonlinear optimal perturbation (CNOP) errors] is calculated to investigate whether this optimal error combination may cause a more notable SPB phenomenon than that caused by initial errors alone. Using the CNOP approach, the CNOP errors and CNOP-I errors (optimal errors when only initial errors are considered) are calculated and then three aspects of error growth are compared: (1) the tendency of the seasonal error growth; (2) the prediction error of the sea surface temperature anomaly; and (3) the pattern of error growth. All three aspects show that the CNOP errors do not cause a more significant SPB than the CNOP-I errors. Therefore, this result suggests that we could improve the prediction of the El Niño during spring by simply focusing on reducing the initial errors in this model. [ABSTRACT FROM AUTHOR]

ABSTRACT A sensitivity study to perturbations in the initial conditions in a simulated evolution of a baroclinic wave using the Weather Research and Forecasting (WRF) regional model is discussed in this paper. With the goal of analysing the impacts of these perturbations in the context of weather forecast and also with the aim of exploring the presence of preferred directions of growth in the errors, two cases were analysed: an ideal experiment using a case study available from the WRF set-up and a simulation of a real evolution of a mid-latitude cyclone over Southeastern South America (SESA) and the Atlantic Ocean. In the ideal experiment two spatial structures were considered for the perturbations, random and sinusoidal noise, while for the real experiment only sinusoidal structures were considered. These perturbations were then applied to the initial conditions of temperature and zonal wind. Additionally, simulations with an increment in atmospheric moisture were performed for the real experiment. It was found in both real and ideal cases that the temperature errors tend to organize in a preferable direction of growth, although this direction changes depending on the case considered. Results also show that perturbations in temperature field lead to larger error than perturbing the zonal wind. Finally, the increment of moisture did not produce significant changes in the distribution or intensity of the errors in the real case. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach for the initialization of ensemble numerical forecasting: Dynamic Analogue Initialization (DAI). DAI assumes that the best model state trajectories for the past provide the initial conditions for the best forecasts in the future. As such, DAI performs the ensemble forecast using the best analogues from a full size ensemble. As a pilot study, the Lorenz63 and Lorenz96 models were used to test DAI's effectiveness independently. Results showed that DAI can improve the forecast significantly. Especially in lower-dimensional systems, DAI can reduce the forecast RMSE by ∼50% compared to the Monte Carlo forecast (MC). This improvement is because DAI is able to recognize the direction of the analysis error through the embedding process and therefore selects those good trajectories with reduced initial error. Meanwhile, a potential improvement of DAI is also proposed, and that is to find the optimal range of embedding time based on the error's growing speed. [ABSTRACT FROM AUTHOR]

In a previous study the author showed, using a toy model, that forecast performance using four-dimensional variational analysis (4D-Var) and an imperfect forecast model was dramatically improved by using a regularization matrix instead of a matrix estimating the true background-error covariance. This article carries out a theoretical analysis of this behaviour. The analysis first highlights the interpretation of short-window 4D-Var as a fixed lag smoother, which means that the control over model error growth exerted by observations late in the assimilation window is taken into account. It is then shown that, in a scalar case, the solution will converge to that of infinitely long-window weak-constraint 4D-Var where the same regularization constraint is applied at each subwindow. The optimum choice of regularization constraint is analyzed for the converged solution and is such that the regularization evolved by the model to the observation time equals the true error evolved to the observation time. The true error is controlled by the observation error regardless of the amount of model error provided that the optimum regularization is used. The same calculation is done for 3D-Var, showing that the true error is not so controlled and is typically larger. It is shown that the feedback between forecast-error growth and the choice of regularization constraint can have a strong effect on the optimal choice, as observed in the experiments. The results are consistent with setting the regularization equal to the background error calculated relative to the truth projected on to the model attractor, rather than the truth itself. In this context, the model attractor can be regarded as the model state closest to the truth that gives the correct time derivatives. [ABSTRACT FROM AUTHOR]

Using predictions for the sea surface temperature (SST) generated by a Flexible Global Ocean-Atmosphere-Land System model of IAP/LASG (FGOALS-g), the season-dependent predictability of SST anomalies for El Nino/La Nina events is investigated by analyzing the forecast error growth in an imperfect model scenario. The results indicate that, for the predictions through the spring season in the growth phase of El Nino events, the prediction errors induced by both initial errors and model errors tend to have a prominent season-dependent evolution and yield a prominent spring predictability barrier (SPB). For the decay-phase predictions of El Nino events, a less prominent season-dependent evolution of prediction errors and then a less prominent SPB are observed. For the growth- and decay-phase predictions of La Nina events, the prediction errors do not exhibit a significant season-dependent evolution and yield a less prominent SPB phenomenon. These results indicate that the SPB phenomenon depends remarkably on the ENSO events themselves, particularly the phases of the El Nino/La Nina events. We also report that the initial SST errors that correspond to a significant SPB for El Nino events tend to have the dominant modes in a large-scale dipolar pattern with negative anomalies in the equatorial central-western Pacific and positive anomalies in the eastern Pacific, or vice versa. We further demonstrate that the error growth related to a significant SPB for El Nino prediction generated by the FGOALS-g model can result from two dynamical mechanisms: in one case, the prediction errors grow in a manner similar to El Niño; in the other, the prediction errors develop with a tendency opposite to El Niño. Copyright © 2012 Royal Meteorological Society [ABSTRACT FROM AUTHOR]

Abstract: We examine how the estimation error grows with time when a mobile robot estimates its location from relative pose measurements without global position or orientation sensors. We show that, in both two-dimensional and three-dimensional space, both the bias and the variance of the position estimation error grows at most linearly with time asymptotically. Non-asymptotic bounds on the bias and variance are obtained, which provide insight into the mechanism of error growth. The bias is crucially dependent on the trajectory of the robot. Conclusions on the asymptotic growth rate of the bias continue to hold even with unbiased measurements or error-free translation measurements. Exact formulas for the bias and the variance of the position estimation error are provided for two specific two-dimensional trajectories–straight line and periodic. Experiments with a P3-DX wheeled robot and Monte Carlo simulations are provided to verify the theoretical predictions. A method to reduce the bias is proposed based on the lessons learned. [Copyright &y& Elsevier]

Sensitivity simulations are conducted in AREM (Advanced Regional Eta-Coordinate numerical heavy-rain prediction Model) for a torrential precipitation in June 2008 along South China to investigate the effect of initial uncertainty on precipitation predictability. It is found that the strong initial-condition sensitivity for precipitation prediction can be attributed to the upscale evolution of error growth. However, different modality of error growth can be observed in lower and upper layers. Compared with lower-level, significant error growth in the upper-layer appears over both convective area and high jet stream. It thus indicates that the error growth depends on both moist convection due to convective instability and the wind shear associated with dynamic instability. As heavy rainfall process can be described as a series of energy conversion, it reveals that the advection-term and latent heating serve as significant energy sources. Moreover, the dominant source terms of error-energy growth are nonlinearity advection (ADVT) and difference in latent heating (DLHT), with the latter being largely responsible for the rapid error growth in the initial stage. In this sense, the occurrence of precipitation and error-growth share the energy source, which implies the inherent predictability of heavy rainfall. In addition, a decomposition of ADVT further indicates that the flow-dependent error growth is closely related to the atmospheric instability. Thus the system growing from unstable flow regime has its intrinsic predictability. [ABSTRACT FROM AUTHOR]

Within a theoretical ENSO model, the authors investigated whether or not the errors superimposed on model parameters could cause a significant “spring predictability barrier” (SPB) for El Niño events. First, sensitivity experiments were respectively performed to the air-sea coupling parameter, α and the thermocline effect coefficient µ. The results showed that the uncertainties superimposed on each of the two parameters did not exhibit an obvious season-dependent evolution; furthermore, the uncertainties caused a very small prediction error and consequently failed to yield a significant SPB. Subsequently, the conditional nonlinear optimal perturbation (CNOP) approach was used to study the effect of the optimal mode (CNOP-P) of the uncertainties of the two parameters on the SPB and to demonstrate that the CNOP-P errors neither presented a unified season-dependent evolution for different El Niño events nor caused a large prediction error, and therefore did not cause a significant SPB. The parameter errors played only a trivial role in yielding a significant SPB. To further validate this conclusion, the authors investigated the effect of the optimal combined mode (i.e. CNOP error) of initial and model errors on SPB. The results illustrated that the CNOP errors tended to have a significant season-dependent evolution, with the largest error growth rate in the spring, and yielded a large prediction error, inducing a significant SPB. The inference, therefore, is that initial errors, rather than model parameter errors, may be the dominant source of uncertainties that cause a significant SPB for El Niño events. These results indicate that the ability to forecast ENSO could be greatly increased by improving the initialization of the forecast model. [ABSTRACT FROM AUTHOR]

The AREMv2.3 mesoscale numerical model is used to explore storm processes in South China during the pre-rainy season in 2006 by imposing perturbations on the initial fields of physical variables (temperature, humidity, and wind fields). Sensitivity experiments are performed to examine the impacts of initial uncertainties on precipitation, on the error growth, and on the predictability of mesoscale precipitation in South China. The primary conclusion is that inherent initial condition uncertainties can significantly limit the predictability of storm. The 24-h accumulated precipitation is most sensitive to temperature perturbations. Larger-amplitude initial uncertainties generally lead to larger perturbation energies than those with smaller amplitude, but these kinds of differences decrease with time monotonically so the mechanism for the growth of perturbation energy is nonlinear. The power spectra of precipitation differences indicate that predictability increases with accumulated time. This also indicates the difficulties faced for short-term, small-scale precipitation forecasting. [ABSTRACT FROM AUTHOR]

In a recent paper, Gutiérrez et al. (Nonlinear Process Geophys 15(1):109–114, ) introduced a new characterization of spatiotemporal error growth—the so called mean–variance logarithmic (MVL) diagram—and applied it to study ensemble prediction systems (EPS); in particular, they analyzed single-model ensembles obtained by perturbing the initial conditions. In the present work, the MVL diagram is applied to multi-model ensembles analyzing also the effect of model formulation differences. To this aim, the MVL diagram is systematically applied to the multi-model ensemble produced in the EU-funded DEMETER project. It is shown that the shared building blocks (atmospheric and ocean components) impose similar dynamics among different models and, thus, contribute to poorly sampling the model formulation uncertainty. This dynamical similarity should be taken into account, at least as a pre-screening process, before applying any objective weighting method. [ABSTRACT FROM AUTHOR]

Recently reported results indicate that small amplitude and small scale initial errors grow rapidly and subsequently contaminate short-term deterministic mesoscale forecasts. This rapid error growth is dependent on not only moist convection but also the flow regime. In this study, the mesoscale predictability and error growth of mei-yu heavy rainfall is investigated by simulating a particular precipitation event along the mei-yu front on 4–6 July 2003 in eastern China. Due to the multi-scale character of the mei-yu front and scale interactions, the error growth of mei-yu heavy rainfall forecasts is markedly different from that in middle-latitude moist baroclinic systems. The optimal growth of the errors has a relatively wide spectrum, though it gradually migrates with time from small scale to mesoscale. During the whole period of this heavy rainfall event, the error growth has three different stages, which similar to the evolution of 6-hour accumulated precipitation. Multi-step error growth manifests as an increase of the amplitude of errors, the horizontal scale of the errors, or both. The vertical profile of forecast errors in the developing convective system indicates two peaks, which correspond with convective instability and the moist physics. The error growth for the mei-yu heavy rainfall is concentrated inside the mei-yu front, and related to moist convective instability and scale interaction. [ABSTRACT FROM AUTHOR]