Uncertainties In Initial Conditions Research Articles

Bearings-only tracking with iterated extended risk sensitive filter

This paper concerns the application of an iterated extended risk sensitive filter (IERSF) to target tracking problems. The relative merits of IERSF vis-a-vis the extended risk sensitive filter (ERSF) for a bearings-only tracking problem using root mean square error (RMSE) and robustness with uncertainty in initial condition are explored. An ERSF weakness, specifically an accumulation error in the computation of innovation steps due to approximating nonlinear functions at a recently available prior estimate, is presented. By using the IERSF with proper tuning of risk factor and local iteration, the filtering divergence may be overcome, and a stable, robust, and unbiased estimation is satisfactorily obtained. With numerical simulation results, the tracking performance of IERSF is compared with the performance of ERSF and extended Kalman filter. The IERSF results in reduced estimation error without much of an increase in burden of the associated computational algorithm.

Multivariate nonlinear ensemble prediction of daily chaotic rainfall with climate inputs

The basic characteristic of a chaotic system is its sensitivity to the infinitesimal changes in its initial conditions. A limit to predictability in chaotic system arises mainly due to this sensitivity and also due to the ineffectiveness of the model to reveal the underlying dynamics of the system. In the present study, an attempt is made to quantify these uncertainties involved and thereby improve the predictability by adopting a multivariate nonlinear ensemble prediction. Daily rainfall data of Malaprabha basin, India for the period 1955-2000 is used for the study. It is found to exhibit a low dimensional chaotic nature with the dimension varying from 5 to 7. A multivariate phase space is generated, considering a climate data set of 16 variables. The chaotic nature of each of these variables is confirmed using false nearest neighbor method. The redundancy, if any, of this atmospheric data set is further removed by employing principal component analysis (PCA) method and thereby reducing it to eight principal components (PCs). This multivariate series (rainfall along with eight PCs) is found to exhibit a low dimensional chaotic nature with dimension 10. Nonlinear prediction employing local approximation method is done using univariate series (rainfall alone) and multivariate series for different combinations of embedding dimensions and delay times. The uncertainty in initial conditions is thus addressed by reconstructing the phase space using different combinations of parameters. The ensembles generated from multivariate predictions are found to be better than those from univariate predictions. The uncertainty in predictions is decreased or in other words predictability is increased by adopting multivariate nonlinear ensemble prediction. The restriction on predictability of a chaotic series can thus be altered by quantifying the uncertainty in the initial conditions and also by including other possible variables, which may influence the system. (C) 2011 Elsevier B.V. All rights reserved.

Evaluation of an ocean data assimilation system for Chinese marginal seas with a focus on the South China Sea

Data assimilation is a powerful tool to improve ocean forecasting by reducing uncertainties in forecast initial conditions. Recently, an ocean data assimilation system based on the ensemble optimal interpolation (EnOI) scheme and HYbrid Coordinate Ocean Model (HYCOM) for marginal seas around China was developed. This system can assimilate both satellite observations of sea surface temperature (SST) and along-track sea level anomaly (SLA) data. The purpose of this study was to evaluate the performance of the system. Two experiments were performed, which spanned a 3-year period from January 1, 2004 to December 30, 2006, with and without data assimilation. The data assimilation results were promising, with a positive impact on the modeled fields. The SST and SLA were clearly improved in terms of bias and root mean square error over the whole domain. In addition, the assimilations provided improvements in some regions to the surface field where mesoscale processes are not well simulated by the model. Comparisons with surface drifter trajectories showed that assimilated SST and SLA also better represent surface currents, with drifter trajectories fitting better to the contours of SLA field than that without assimilation. The forecasting capacity of this assimilation system was also evaluated through a case study of a birth-and-death process of an anticyclone eddy in the Northern South China Sea (NSCS), in which the anticyclone eddy was successfully hindcasted by the assimilation system. This study suggests the data assimilation system gives reasonable descriptions of the near-surface ocean state and can be applied to forecast mesoscale ocean processes in the marginal seas around China.

Robust stochastic control based on imprecise probabilities

AbstractThis paper deals with the optimal quadratic control problem for non Gaussian discrete-time linear stochastic systems from the perspective of imprecise probabilities. The adopted philosophy is to use a convex set of probability distributions to characterize the imprecision in the knowledge about the probabilistic relationships present in the system to be controlled. In particular, an uncertain system model, named Linear Gaussian Vacuous Mixture (LGVM), in which disturbances and initial state uncertainty are described as convex combinations (mixtures) of nominal Gaussian distributions and unknown vacuous distributions, is adopted. A novel control approach is then derived, according to a worst-case paradigm, by minimizing the upper expectation of a finite-horizon quadratic cost functional with respect to all admissible probability distributions and exploiting a receding horizon strategy. Simulation experiments demonstrate its robustness in presence of large unexpected impulsive disturbances.

Estimating Climatically Relevant Singular Vectors for Decadal Predictions of the Atlantic Ocean

Abstract A key aspect in designing an efficient decadal prediction system is ensuring that the uncertainty in the ocean initial conditions is sampled optimally. Here one strategy for addressing this issue is considered by investigating the growth of optimal perturbations in the third climate configuration of the Met Office Unified Model (HadCM3) global climate model (GCM). More specifically, climatically relevant singular vectors (CSVs)—the small perturbations of which grow most rapidly for a specific set of initial conditions—are estimated for decadal time scales in the Atlantic Ocean. It is found that reliable CSVs can be estimated by running a large ensemble of integrations of the GCM. Amplification of the optimal perturbations occurs for more than 10 yr, and possibly up to 40 yr. The identified regions for growing perturbations are found to be in the far North Atlantic, and these perturbations cause amplification through an anomalous meridional overturning circulation response. Additionally, this type of analysis potentially informs the design of future ocean observing systems by identifying the sensitive regions where small uncertainties in the ocean state can grow maximally. Although these CSVs are expensive to compute, ways in which the process could be made more efficient in the future are identified.

Superposition of three sources of uncertainties in operational flood forecasting chains

One of the less known aspects of operational flood forecasting systems in complex topographic areas is the way how the uncertainties of its components propagate and superpose when they are fed into a hydrological model. This paper describes an experimental framework for investigating the relative contribution of meteorological forcing uncertainties, initial conditions uncertainties and hydrological model parameter uncertainties in the realization of hydrological ensemble forecasts. Simulations were done for a representative small-scale basin of the Swiss Alps, the Verzasca river basin (186 km 2). For seven events in the time frame from June 2007 to November 2008 it was possible to quantify the uncertainty for a five-day forecast range yielded by inputs of an ensemble numerical weather prediction (NWP) model (COSMO-LEPS, 16 members), the uncertainty in real-time assimilation of weather radar precipitation fields expressed using an ensemble approach (REAL, 25 members), and the equifinal parameter realizations of the hydrological model adopted (PREVAH, 26 members). Combining the three kinds of uncertainty results in a hydrological ensemble of 10,400 members. Analyses of sub-samples from the ensemble provide insight in the contribution of each kind of uncertainty to the total uncertainty. The results confirm our expectations and show that for the operational simulation of peak-runoff events the hydrological model uncertainty is less pronounced than the uncertainty obtained by propagating radar precipitation fields (by a factor larger than 4 in our specific setup) and NWP forecasts through the hydrological model (by a factor larger than 10). The use of precipitation radar ensembles for generating ensembles of initial conditions shows that the uncertainty in initial conditions decays within the first 48 hours of the forecast. We also show that the total spread obtained when superposing two or more sources of uncertainty is larger than the cumulated spread of experiments when only one uncertainty source is propagated through the hydrological model. The full spread obtained from uncertainty superposition is growing non-linearly.

Optimal guidance for reentry vehicles based on indirect Legendre pseudospectral method

Development of a feasible guidance scheme for reentry vehicles is a challenge because of its significant nonlinearity and multi-constraints. A method for the implementation of three-degree-of-freedom guidance for constrained reentry vehicle is presented in the paper. First, the constrained trajectory is generated by Legendre pseudospectral method (LPM) and then the feasibily of the trajectory is validated. Based on the obtained reference trajectory, the guidance problem is converted into a trajectory state regulation problem which is a linear time varying system. A robust state feedback guidance law is generated in real time using indirect Legendre pseudospectral feedback method. Finally, simulation results illustrate that the overall guidance scheme can lead to a very accurately controlled flight with all the constraints satisfied even in the presence of initial state uncertainty.

Nonlinear Estimation of Hypersonic State Trajectories in Bayesian Framework with Polynomial Chaos

This paper presents a nonlinear estimation algorithm to estimate state trajectories of a hypersonic vehicle with initial condition uncertainty. Polynomial chaos theory is used to predict the evolution of state uncertainty of the nonlinear system, and a Bayesian estimation algorithm is used to estimate the posterior probability density function of the nonlinear random process. The nonlinear estimation algorithm is then applied to the hypersonic reentry of a spacecraft in Martian atmosphere. Its performance is compared with estimators based on an extended Kalman filtering and unscented Kalman filtering framework. It is observed that for the particular application, the proposed estimator outperforms extended Kalman filtering and unscented Kalman filtering, highlighting its need in the current scenario.

Quantifying uncertainty, variability and likelihood for ordinary differential equation models

BackgroundIn many applications, ordinary differential equation (ODE) models are subject to uncertainty or variability in initial conditions and parameters. Both, uncertainty and variability can be quantified in terms of a probability density function on the state and parameter space.ResultsThe partial differential equation that describes the evolution of this probability density function has a form that is particularly amenable to application of the well-known method of characteristics. The value of the density at some point in time is directly accessible by the solution of the original ODE extended by a single extra dimension (for the value of the density). This leads to simple methods for studying uncertainty, variability and likelihood, with significant advantages over more traditional Monte Carlo and related approaches especially when studying regions with low probability.ConclusionsWhile such approaches based on the method of characteristics are common practice in other disciplines, their advantages for the study of biological systems have so far remained unrecognized. Several examples illustrate performance and accuracy of the approach and its limitations.

WRF/Chem‐MADRID: Incorporation of an aerosol module into WRF/Chem and its initial application to the TexAQS2000 episode

The Model of Aerosol Dynamics, Reaction, Ionization and Dissolution (MADRID) with three improved gas/particle mass transfer approaches (i.e., bulk equilibrium (EQUI), hybrid (HYBR), and kinetic (KINE)) has been incorporated into the Weather Research and Forecast/Chemistry Model (WRF/Chem) (referred to as WRF/Chem‐MADRID) and evaluated with a 5‐day episode from the 2000 Texas Air Quality Study (TexAQS2000). WRF/Chem‐MADRID demonstrates an overall good skill in simulating surface/aloft meteorological parameters and chemical concentrations of O3 and PM2.5, tropospheric O3 residuals, and aerosol optical depths. The discrepancies can be attributed to inaccuracies in meteorological predictions (e.g., overprediction in mid‐day boundary layer height), sensitivity to meteorological schemes used (e.g., boundary layer and land‐surface schemes), inaccurate total emissions or their hourly variations (e.g., HCHO, olefins, other inorganic aerosols) or uncounted wildfire emissions, uncertainties in initial and boundary conditions for some species (e.g., other inorganic aerosols, CO, and O3) at surface and aloft, and some missing/inactivated model treatments for this application (e.g., chlorine chemistry and secondary organic aerosol formation). Major differences in the results among the three gas/particle mass transfer approaches occur over coastal areas, where EQUI predicts higher PM2.5 than HYBR and KINE due to improperly redistributing condensed nitrate from chloride depletion process to fine PM mode. The net direct, semi‐direct, and indirect effects of PM2.5 decrease domainwide shortwave radiation by 11.2–14.4 W m−2 (or 4.1–5.6%) and near‐surface temperature by 0.06–0.14°C (or 0.2–0.4%), lead to 125 to 796 cm−3 cloud condensation nuclei at a supersaturation of 0.1%, produce cloud droplet numbers as high as 2064 cm−3, and reduce domainwide mean precipitation by 0.22–0.59 mm day−1.

Ozone predictabilities due to meteorological uncertainties in the Mexico City basin using ensemble forecasts

Abstract. The purpose of the present study is to investigate the sensitivity of ozone (O3) predictions in the Mexico City Metropolitan Area (MCMA) to meteorological initial uncertainties and planetary boundary layer (PBL) parameterization schemes using state-of-the-art meteorological and photochemical prediction models through ensemble forecasts. The simulated periods (3, 9, 15 and 29 March 2006) represent four typical meteorological episodes ("South-Venting", "O3-North", "O3-South" and "Convection-North", respectively) in the Mexico City basin during the MCMA-2006/MILAGRO campaign. Our results demonstrate that the uncertainties in meteorological initial conditions have significant impacts on O3 predictions, including peak time O3 concentrations ([O3]), horizontal and vertical O3 distributions, and temporal variations. The ensemble spread of the simulated peak [O3] averaged over the city's ambient monitoring sites can reach up to 10 ppb. The increasing uncertainties in meteorological fields during peak O3 period contribute to the largest unpredictability in O3 simulations, while the impacts of wind speeds and PBL height on [O3] are more straightforward and important. The magnitude of the ensemble spreads varies with different PBL schemes and meteorological episodes. The uncertainties in O3 predictions caused by PBL schemes mainly come from their ability to represent the mixing layer height; but overall, these uncertainties are smaller than those from the uncertainties in meteorological initial conditions.

Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems

This paper deals with stochastic spectral methods for uncertainty propagation and quantification in nonlinear hyperbolic systems of conservation laws. We consider problems with parametric uncertainty in initial conditions and model coefficients, whose solutions exhibit discontinuities in the spatial as well as in the stochastic variables. The stochastic spectral method relies on multi-resolution schemes where the stochastic domain is discretized using tensor-product stochastic elements supporting local polynomial bases. A Galerkin projection is used to derive a system of deterministic equations for the stochastic modes of the solution. Hyperbolicity of the resulting Galerkin system is analyzed. A finite volume scheme with a Roe-type solver is used for discretization of the spatial and time variables. An original technique is introduced for the fast evaluation of approximate upwind matrices, which is particularly well adapted to local polynomial bases. Efficiency and robustness of the overall method are assessed on the Burgers and Euler equations with shocks.

Uncertainty propagation in puff-based dispersion models using polynomial chaos

Atmospheric dispersion is a complex nonlinear physical process with numerous uncertainties in model parameters, inputs, source parameters, initial and boundary conditions. Accurate propagation of these uncertainties through the dispersion models is crucial for a reliable prediction of the probability distribution of the states and assessment of risk. A simple three-dimensional Gaussian puff-based dispersion model is used as a test case to study the effect of uncertainties in the model parameters and initial conditions on the output concentration. A polynomial chaos based approach is used to numerically investigate the evolution of the model output uncertainties due to initial condition and parametric uncertainties. The polynomial chaos solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large nonlinear systems with a relatively small number of uncertainties.

수치예보모형을 이용한 역학적 규모축소 기법을 통한 농업기후지수 모사

본 연구에서는 기상예측 모형을 이용하여 상세한 농업기후지수를 모사하고자 하였다. 이를 위해서 NCEP/NCAR 재분석 자료를 지역기후모형인 WRF의 초기 및 경계조건으로 하여 2002년 3월부터 7년간 상세한 기후 자료를 생산하고, 이렇게 구한 기후 자료를 통계적 보정을 거쳐 계통적 오차를 제거함으로써 그 기간의 기후를 재현하였으며 이를 이용하여 상세한 농업기후지수로 생산하였다. 수치 실험을 통해 생산된 상세 지역기후자료는 대순환 모형이 모사할 수 없는 남한의 복잡한 지형적 구조와 전체적인 관측 공간 패턴을 모사하였다. 통계적 보정은 모형결과가 관측에 비해 과소모사 되던 경향을 제거함으로써 보다 상세하고 관측에 가까운 시 공적 기후자료의 생산을 가능하게 하였다. 이렇게 모사된 기후 자료를 이용하여 식물온도 출 현초일, 작물온도 출현초일, 벼 이앙기의 저온 출현율, 종상일 등의 농업기후지수들에 대한 상세한 분포를 생산하였다. 보정 전 모형 결과에서는 계통적 오차인 모형의 기온 과소모사 경향에 의해 전반적인 유효온도와 종상일이 늦게 출현하였으며, 저온 출현율의 빈도가 높게 나타났다. 보정 후 모형 결과에서는 계통적 오차의 보정에 의해 유효온도 <TEX>$10^{\circ}C$</TEX> 출현일을 제외한 유효 온도 출현일과 종상일이 앞당겨졌으며, 저온 출현일 빈도가 감소하였다. 보정 후 모형 결과에서 유도된 유 효온도 <TEX>$10^{\circ}C$</TEX> 출현일은 보정 전 모형결과보다 3일 늦게 모사되고 있으나 보정 전 모형 결과에서 모사하지 못한 지역적 특징을 모사하고 있어 국지적으로 나타나는 작물온도 출현초일의 세부적인 패턴을 이해하는데 유용한 결과라고 판단된다. 모형의 결과로 유도된 농업기후지수는 복잡한 지역적 편차를 가지면서 정량적 정성적으로 관측에서 유도한 결과와 유사하게 나타났다. 반면 통계적 보정을 적용하여도 중부 논농사 지대의 작물온도 출현초일은 여전히 잘 모사되지 못하고 있는데 이는 모형의 결과가 계통적 오차 이외에도 또 다른 불확실성에 의한 문제를 내제하고 있음을 보여주는 결과이다. 향후 물리적 모수화 과정의 개선, 역학적 규모축소방법의 최적화 그리고 통계적 보정 방법의 다양한 적용을 통해 보다 향상된 농업기후지수를 생산할 수 있을 것으로 판단된다. 이러한 실험 결과는 농업 경영자들에게 상세 농업기후지수 분포의 이해를 도와줄 뿐만 아니라 본 연구의 실험 방식이 농업 예측에 활용될 경우 장기 예측 및 기후변화에 따른 예측을 위한 정보에 긴요하게 사용될 수 있을 것으로 생각된다. A regional climate model (RCM) can be a powerful tool to enhance spatial resolution of climate and weather information (IPCC, 2001). In this study we conducted dynamical downscaling using Weather Research and Forecasting Model (WRF) as a RCM in order to obtain high resolution regional agroclimate indices over the Korean Peninsula. For the purpose of obtaining detailed high resolution agroclimate indices, we first reproduced regional weather for the period of March to June, 2002-2008 with dynamic downscaling method under given lateral boundary conditions from NCEP/NCAR (National Centers for Environmental Prediction/National Center for Atmospheric Research) reanalysis data. Normally, numerical model results have shown biases against observational results due to the uncertainties in the modelis initial conditions, physical parameterizations and our physical understanding on nature. Hence in this study, by employing a statistical method, the systematic bias in the modelis results was estimated and corrected for better reproduction of climate on high resolution. As a result of the correction, the systematic bias of the model was properly corrected and the overall spatial patterns in the simulation were well reproduced, resulting in more fine-resolution climatic structures. Based on these results, the fine-resolution agro-climate indices were estimated and presented. Compared with the indices derived from observation, the simulated indices reproduced the major and detailed spatial distributions. Our research shows a possibility to simulate regional climate on high resolution and agro-climate indices by using a proper downscaling method with a dynamical weather forecast model and a statistical correction method to minimize the model bias.

A strategy for perturbing surface initial conditions in LAMEPS

AbstractThe lack or inadequate representation of uncertainties in the surface initial conditions (ICs) affects the quality of ensemble forecast, in particular the near surface temperature and precipitation. In this paper, a strategy for perturbing surface ICs in limited area model ensemble prediction system, noncycling surface breeding (NCSB) is proposed. The strategy combines short‐range surface forecasts driven by perturbed atmospheric forcing and the breeding method for generating the perturbation to surface ICs. NCSB is implemented and tested in Aire Limitée Adaptation dynamique Développement InterNational‐limited area ensemble forecasting (ALADIN‐LAEF). Statistical verification demonstrates that the application of NCSB improves the ALADIN‐LAEF 2m temperature and precipitation forecast. Positive impacts are also obtained for temperature and specific humidity in the lower atmosphere. Copyright © 2010 Royal Meteorological Society

Analysis study on perturbation energy and predictability of heavy precipitation in South China

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.

Polynomial Chaos-Based Analysis of Probabilistic Uncertainty in Hypersonic Flight Dynamics

In this paper, we present a novel computational framework for analyzing the evolution of the uncertainty in state trajectories of a hypersonic air vehicle due to the uncertainty in initial conditions and other system parameters. The framework is built on the so-called generalized polynomial chaos expansions. In this framework, stochastic dynamical systems are transformed into equivalent deterministic dynamical systems in higher dimensional space. Here, the evolution of uncertainty due to initial condition, ballistic coefficient, lift over drag ratio, and atmospheric density is analyzed. The problem studied here is related to the Mars entry, descent, and landing problems. We demonstrate that the polynomial chaos framework is able to predict evolution of uncertainty, in hypersonic flight, with the same order of accuracy as the Monte-Carlo methods but with more computational efficiency.

Sensitivity of cloud‐resolving precipitation simulations to uncertainty of vertical structures of initial conditions

AbstractSensitivity of precipitation simulations to the uncertainty of vertical structure of initial temperature or water vapour conditions is examined in this study by conducting a series of two‐dimensional cloud‐resolving model simulations. The perturbation experiments are perturbed by either initial temperature or initial water vapour in different vertical layers and are compared with the control experiment. The perturbations of initial temperature and water vapour are significantly smaller than observed temperature and water vapour errors. The results show that the precipitation simulations are much affected by these small perturbations of initial temperature and water vapour conditions when the spatial and temporal scales are less than 500 km and 4 hours respectively. The zonal scales of the precipitation simulations sensitive to uncertainty of initial temperature conditions are significantly smaller when the initial temperature is perturbed in the upper troposphere than when it is perturbed in the lower troposphere. The precipitation simulations are insensitive to the uncertainty of vertical profiles of initial water vapour conditions. Copyright © 2010 Royal Meteorological Society

Modelling population processes with random initial conditions

Population dynamics are almost inevitably associated with two predominant sources of variation: the first, demographic variability, a consequence of chance in progenitive and deleterious events; the second, initial state uncertainty, a consequence of partial observability and reporting delays and errors. Here we outline a general method for incorporating random initial conditions in population models where a deterministic model is sufficient to describe the dynamics of the population. Additionally, we show that for a large class of stochastic models the overall variation is the sum of variation due to random initial conditions and variation due to random dynamics, and thus we are able to quantify the variation not accounted for when random dynamics are ignored. Our results are illustrated with reference to both simulated and real data.

Nearly perfect fluid in Au + Au collisions at RHIC

In the Israel–Stewart's theory of dissipative hydrodynamics, we have analysed the STAR data on ϕ meson production in Au+Au collisions at s=200 GeV. From a simultaneous fit to ϕ mesons multiplicity, mean pT and integrated v2, we obtain a phenomenological estimate of QGP viscosity, η/s=0.07±0.03±0.14, the first error is due to the experimental uncertainty in STAR measurements, the second reflects the uncertainties in initial and final conditions of the fluid.