Uncertainties In Initial Conditions Research Articles

CONTROL AND ESTIMATION FOR A CLASS OF IMPULSIVE DYNAMICAL SYSTEMS

The nonlinear dynamical control system with uncertainty in initial states and parameters is studied. It is assumed that the dynamic system has a special structure in which the system nonlinearity is due to the presence of quadratic forms in system velocities. The case of combined controls is studied here when both classical measurable control functions and the controls generated by vector measures are allowed. We present several theoretical schemes and the estimating algorithms allowing to find the upper bounds for reachable sets of the studied control system. The research develops the techniques of the ellipsoidal calculus and of the theory of evolution equations for set-valued states of dynamical systems having in their description the uncertainty of set-membership kind. Numerical results of system modeling based on the proposed methods are included.

Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System

In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly accurate numerical computations over simulating guaranteed enclosures of all reachable states of a dynamic system model with bounded uncertainty in parameters and initial conditions, to the solution of global optimization tasks. By exploiting the fundamental enclosure properties of interval analysis, this paper aims at computing invariant sets of nonlinear closed-loop control systems. For that purpose, Lyapunov-like functions and interval analysis are combined in a novel manner. To demonstrate the proposed techniques for enclosing invariant sets, the systems examined in this paper are controlled via sliding mode techniques with subsequently enclosing the invariant sets by an interval based set inversion technique. The applied methods for the control synthesis make use of a suitably chosen Gröbner basis, which is employed to solve Bézout’s identity. Illustrating simulation results conclude this paper to visualize the novel combination of sliding mode control with an interval based computation of invariant sets.

Ensemble data assimilation and prediction of typhoon and associated hazards using TEDAPS: evaluation for 2015–2018 seasons

The initial condition accuracy is a major concern for tropical cyclone (TC) numerical forecast. The ensemble-based data assimilation techniques have shown great promise to initialize TC forecast. In addition to initial condition uncertainty, representing model errors (e.g. physics deficiencies) is another important issue in an ensemble forecasting system. To improve TC prediction from both deterministic and probabilistic standpoints, a Typhoon Ensemble Data Assimilation and Prediction System (TEDAPS) using an ensemble-based data assimilation scheme and a multi-physics approach based on Weather Research and Forecasting (WRF) model, has been developed in Shanghai Typhoon Institute and running realtime since 2015. Performance of TEDAPS in the prediction of track, intensity and associated disaster has been evaluated for the Western North Pacific TCs in the years of 2015–2018, and compared against the NCEP GEFS. TEDAPS produces markedly better intensity forecast by effectively reducing the weak biases and therefore the degree of underdispersion compared to GEFS. The errors of TEDAPS track forecasts are comparative with (slightly worse than) those of GEFS at longer (shorter) forecast leads. TEDAPS ensemble-mean exhibits advantage over deterministic forecast in track forecasts at long lead times, whereas this superiority is limited to typhoon or weaker TCs in intensity forecasts due to systematical underestimation. Four case-studies for three landfalling cyclones and one recurving cyclone demonstrate the capacities of TEDAPS in predicting some challenging TCs, as well as in capturing the forecast uncertainty and the potential threat from TC-associated hazards.

The Impact of Initial Condition and Warm Conveyor Belt Forecast Uncertainty on Variability in the Downstream Waveguide in an ECWMF Case Study

AbstractPerturbations to the potential vorticity (PV) waveguide, which can result from latent heat release within the warm conveyor belt (WCB) of midlatitude cyclones, can lead to the downstream radiation of Rossby waves, and in turn high-impact weather events. Previous studies have hypothesized that forecast uncertainty associated with diabatic heating in WCBs can result in large downstream forecast variability; however, these studies have not established a direct connection between the two. This study evaluates the potential impact of latent heating variability in the WCB on subsequent downstream forecasts by applying the ensemble-based sensitivity method to European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecasts of a cyclogenesis event over the North Atlantic. For this case, ensemble members with a more amplified ridge are associated with greater negative PV advection by the irrotational wind, which is associated with stronger lower-tropospheric southerly moisture transport east of the upstream cyclone in the WCB. This transport is sensitive to the pressure trough to the south of the cyclone along the cold front, which in turn is modulated by earlier differences in the motion of the air masses on either side of the front. The position of the cold air behind the front is modulated by upstream tropopause-based PV anomalies, such that a deeper pressure trough is associated with a more progressive flow pattern, originating from Rossby wave breaking over the North Pacific. Overall, these results suggest that more accurate forecasts of upstream PV anomalies and WCBs may reduce forecast uncertainty in the downstream waveguide.

Downstream influence of mesoscale convective systems. Part 2: Influence on ensemble forecast skill and spread

Ensemble forecasts are run operationally to determine the forecast uncertainty arising from initial condition, model physics and boundary condition uncertainty. However, global configuration ensembles, which use a convection parametrization scheme, may miss uncertainty because of the misrepresentation of intense convection by such schemes. Here, the impacts of the misrepresentation of mesoscale convective systems (MCSs) on downstream ensemble forecast skill and evolution are determined for a case study. MCS perturbations (calculated‐15 from the difference between outputs from convection‐parametrizing and convection‐permitting Met Office model configurations) are added to six members of a global configuration ensemble created by downscaling forecasts from the global version of the Met Office Global and Regional Ensemble Prediction System. For the first 36 hours, differences grow on the convective scale related to the MCSs, leading to systematic deepening of a developing UK cyclone, although there is damping of the perturbations found in root mean square difference calculations between the forecasts with and without the perturbations (particularly in mean sea level pressure). Subsequently, differences grow rapidly to the synoptic scale, and by five days impact the entire Northern Hemisphere. The MCS perturbations can have systematic effects on ensemble forecasts (e.g., a systematic displacement of a downstream cyclone is found), but, for this case, there is no discernible change in forecast skill as measured by the root mean square error of the ensemble means and the effects of the MCS perturbations are smaller than those generated by the initial condition perturbations. The spread of the combined ensemble (the two ensembles with and without the MCS perturbations) is larger than that of the individual ensembles. Thus, perturbing convection‐parametrizing models to include potential vorticity anomalies associated with MCSs represented in convection‐permitting forecasts, or idealized representations of them, produces alternative realizations from those generated by initial condition perturbations and has the potential to be useful operationally.

Practical Uncertainties in the Limited Predictability of the Record-Breaking Intensification of Hurricane Patricia (2015)

AbstractHurricane Patricia (2015) was a record-breaking tropical cyclone that was difficult to forecast in real time by both operational numerical weather prediction models and operational forecasters. The current study examines the potential for improving intensity prediction for extreme cases like Hurricane Patricia. We find that Patricia’s intensity predictability is potentially limited by both initial conditions, related to the data assimilation, and model errors. First, convection-permitting assimilation of airborne Doppler radar radial velocity observations with an ensemble Kalman filter (EnKF) demonstrates notable intensity forecast improvements over assimilation of conventional observations alone. Second, decreasing the model horizontal grid spacing to 1 km and reducing the surface drag coefficient at high wind speed in the parameterization of the sea surface–atmosphere exchanges is also shown to notably improve intensity forecasts. The practical predictability of Patricia, its peak intensity, rapid intensification, and the underlying dynamics are further investigated through a high-resolution 60-member ensemble initialized with realistic initial condition uncertainties represented by the EnKF posterior analysis perturbations. Most of the ensemble members are able to predict the peak intensity of Patricia, but with greater uncertainty in the timing and rate of intensification; some members fail to reach the ultimate peak intensity before making landfall. Ensemble sensitivity analysis shows that initial differences in the region beyond the radius of maximum wind contributes the most to the differences between ensemble members in Patricia’s intensification. Ensemble members with stronger initial primary and secondary circulations beyond the radius of maximum wind intensify earlier, are able to maintain the intensification process for longer, and thus reach a greater and earlier peak intensity.

Hydrological post-processing of streamflow forecasts issued from multimodel ensemble prediction systems

Hydrological simulations and forecasts are subject to various sources of uncertainties. Thiboult et al. (2016) constructed a 50,000-member great ensemble that ultimately accounts for meteorological forcing uncertainty, initial condition uncertainty, and structural uncertainty. This large 50,000-member ensemble can also be separated into sub-components to untangle the three main sources of uncertainties mentioned above. However, in Thiboult et al. (2016) model outputs were simply pooled together, considering equiprobable members. This paper studies the use of Bayesian model averaging (BMA) to post-process multimodel hydrological forecasts. BMA assigns multiple sets of weights on different models and may then generate more skillful and reliable probabilistic forecasts. BMA weights explicitly quantify the level of confidence one can have regarding each candidate hydrological model and lead to a predictive probabilistic density function (PDF) containing information about uncertainty. The BMA scheme improves the overall quality of forecasts mainly by maintaining the ensemble dispersion with the lead time. It also has the ability to improve the reliability and skill of multimodel systems that only include two sources of uncertainties that the 50,000-member great ensemble using all forecasting tools (i.e., multimodel, EnKF, and meteorological ensemble forcing) could predict jointly. Furthermore, Thiboult et al. (2016) showed that the meteorological forecasts they used were somehow biased and unreliable on some catchments. The BMA scheme is capable to improve the accuracy and reliability of the hydrological forecasts in that case as well.

Near surface ocean temperature uncertainty related to initial condition uncertainty

Contributions to climate uncertainty in the modeling of the near surface temperature of the ocean come from several sources: the knowledge of the initial state of the atmosphere, the inadequacy of a model to include or correctly represent all aspects of the dynamics, the uncertain knowledge of the initial state of the ocean and small-scale (or internal, “weather”) noise. This paper concentrates on the latter uncertainty, the uncertainty in the knowledge of the initial field, resulting in a map of the uncertainty of the near surface temperature field. To make the full estimate of this uncertainty, the outcomes from a relatively small, 30 member, ensemble were expanded using statistical emulators. The uncertainty varies in space and decreases in time. There are broad areas of similar uncertainty, consistent with uncertainties in the initial conditions and the variability in local processes. After 10 years, the average spatial uncertainty calculated from this expanded data set gives a range of +/− 0.4 ^{circ }C with 95% of the spatial areas having an uncertainty of less than +/− 0.9 ^{circ }C. When compared to other estimates of similar metrics, the map represents a lower bound on the uncertainty because this first experiment examines the ocean/ice system in isolation from feedbacks that occur between the atmosphere and the ocean. This uncertainty also does not include any contribution from the lack of knowledge about how a future state of the air/ocean system will be forced by changes in greenhouse gases.

Evaluation of the impact on European air traffic by uncontrolled reentering spacecraft with initial state uncertainty

The area of spaceflight, especially human space flight, experienced a change in the past decades. Due to the privatization of space flight, many advances were provided and human space flight was pushed forward. The number of spaceflight and spaceports has increased as well as the interest in space tourism. General feasibility studies of space tourism were performed by different authors considering safety aspects, planning or the integration of spacecraft into air traffic. An efficient and safe integration is mandatory to minimize the risk on human life and to sustain a steady air traffic. Nevertheless, an optimal integration of spacecraft into air traffic may be disturbed by unexpected happenings. Within this paper, a scenario is considered, where a spacecraft sustains malfunctions in the control mechanism just before reentering the atmosphere. The reentry is considered to be uncontrolled, whereas the initial state vector of the spacecraft is varied randomly. The resulting on-ground distribution is evaluated for an exemplary scenario and the impact on European air traffic is simplified estimated by the definition of a temporary flight restriction.

Sensitivity of Hail Precipitation to Ensembles of Uncertainties of Representative Initial Environmental Conditions From ECMWF

AbstractThe sensitivity of hail precipitation from an idealized hailstorm to realistic environmental uncertainties was investigated through ensembles of cloud‐resolving simulations using the Weather Research and Forecasting model, with initial condition perturbations derived from the European Centre for Medium‐Range Weather Forecasting (ECMWF) operational ensemble. The analyses revealed that hail precipitation rate was very sensitive to small initial environmental perturbations, particularly in thermodynamic variables. The hail precipitation rate was significantly positively correlated with perturbations to the initial potential temperature below 750 hPa and to water vapor mixing ratio above 750 hPa. These small initial perturbations led to subsequent substantial differences in hail precipitation as well as in characteristics of the parent storm (e.g., updraft velocity, diabatic heating, and microphysical processes), all of which play a key role in hail growth. The larger sensitivity of hail precipitation to thermodynamic rather than kinematic environmental initial condition perturbations persisted even when the magnitude of the perturbations was reduced to 10% of the realistic uncertainties derived from the ECMWF ensemble. In the ensemble with reduced‐amplitude initial perturbations, there was still a moderately strong positive correlation between hail precipitation rate and the initial perturbations of the thermodynamic variables. However, these sensitivities were nonlinear, suggesting that the intrinsic predictability of hail precipitation rate may be limited, even when environmental uncertainties are reduced to 10%, 1.0 × 10−3, and 1.0 × 10−5 of the currently realistic magnitude of initial condition uncertainty.

Mars entry trajectory planning using robust optimization and uncertainty quantification

Due to the existence of obvious uncertainties within Mars atmospheric entry, design and analysis of the optimal trajectory under uncertainties play a significant role in reducing flight risk and maintaining guidance performance and delivery accuracy. In this paper, using robust optimization strategy and uncertainty quantification technique, we developed an innovative approach for planning the Mars entry trajectory under uncertainties. The main contribution of this work is twofold: one is considering both dynamics parameter uncertainty and initial state uncertainty, and the other is simultaneously focusing on the reliability of constraint satisfaction and insensitivity of performance index towards uncertainties. First, Mars entry trajectory planning problem under uncertainties is formulated as a robust optimization problem. Second, the uncertainty propagation with regard to Mars entry dynamics is derived, and the quantification of objective function and constraints under uncertainties is conducted. Third, the robust trajectory optimization problem is transformed into an equivalent optimal control problem in the expanded higher-dimensional state space by polynomial chaos expansion, and the solution is obtained by the hp-adaptive pseudospectral method. Finally, the effectiveness of the proposed method is verified through two Mars entry optimal trajectory cases. And the obtained optimal trajectories are reliable and evidently robust to uncertainties compared to traditional deterministic optimization and reliability-based optimization.

Optimal Transport Based Tracking of Space Objects in Cylindrical Manifolds

In this paper, we examine the performance of satellite state estimation algorithms in the modified equinoctial coordinate system, defined on the cylindrical manifold of $\mathbb {R}^{5}\times \mathbb {S}$, where $\mathbb {R}$ is the space of reals and $\mathbb {S}$ denotes circular space. A comparison is made between an optimal transport based filter and ensemble Kalman filter algorithm in the context of satellite state estimation. The initial state joint probability density function is modeled in $\mathbb {R}^{5}\times \mathbb {S}$ using the Gauss von Mises distribution. The sensor noise for optimal transport filtering is modeled in the same manifold. The ensemble Kalman filter, by definition, requires the sensor noise to be Gaussian and is modeled in $\mathbb {R}^{6}$ for this problem. We observe that there is a clear advantage in using an optimal transport based filtering algorithm where we represent the initial condition uncertainty and sensor noise, in the cylindrical manifold. These two filtering algorithms are implemented on a simulated International Space Station orbit, with measurement at equal intervals. We compare two distinct scenarios in this simulation based study. In the first one, sensor noise characteristics are assumed to be known. For the second one, we present a new algorithm within the optimal transport framework with unknown sensor noise characteristics, a practical and relevant issue in the space-tracking problems. The optimal transport based algorithm provides more consistent and robust estimates compared to that of ensemble Kalman filter, in each of these scenarios.

Dynamical Seasonal Prediction of Tropical Cyclone Activity: Robust Assessment of Prediction Skill and Predictability

AbstractImproving the seasonal prediction of tropical cyclone (TC) activity demands a robust analysis of the prediction skill and the inherent predictability of TC activity. Using the resampling technique, this study analyzes a state‐of‐the‐art prediction system and offers a robust assessment of when and where the seasonal prediction of TC activity is skillful. We found that uncertainties of initial conditions affect the predictions and the skill evaluation significantly. The sensitivity of predictions to initial conditions also suggests that landfall and high‐latitude activity are inherently harder to predict. The lower predictability is consistent with the relatively low prediction skill in these regions. Additionally, the lower predictability is largely related to the atmospheric environment rather than the sea surface temperature, at least for the predictions initialized shortly before the hurricane season. These findings suggest the potential for improving the seasonal TC prediction and will help the development of the next‐generation prediction systems.

Generalized Polynomial Chaos Expansion Approach for Uncertainty Quantification in Small Satellite Orbital Debris Problems

This paper demonstrates the use of generalized polynomial chaos expansion for the propagation of uncertainties present in various dynamical models. Specifically, a sampling based non-intrusive approach using pseudospectral stochastic collocation is employed to obtain the coefficients required for the generalized polynomial chaos expansion. Various recently developed quadrature techniques are employed within the generalized polynomial chaos expansion framework in order to illustrate their efficacy. In addition to that, the paper also provides an efficient numerical quadrature technique to be used as a sampling technique in stochastic collocation to quantify the uncertainties which are governed by different distribution functions. Results are presented for the orbital motion of a 2U CubeSat subject to initial condition uncertainty and drag related parametric uncertainty demonstrating the accuracy and effectiveness of the proposed technique. Further, stochastic sensitivity analysis is performed to gain insight into the impact of uncertain variables on the evolution of the quantities of interest.

The Taiwan WRF Ensemble Prediction System: Scientific Description, Model-Error Representation and Performance Results

The Taiwan mesoscale ensemble prediction system (EPS) based on the Weather Research and Forecast model (WRF), also called WEPS, is designed to provide reliable ensemble forecasts for the East Asian region centered on Taiwan. The most skillful ensemble is obtained if model-uncertainty is represented in addition to initial condition uncertainty. A number of numerical prediction experiments are conducted to obtain the optimal configuration consisting of multiple physics-schemes, and two stochastic parameterization schemes: The Stochastic-Kinetic Energy Backscatter (SKEB) Scheme and the Stochastically Perturbed of Physics-Tendency (SPPT) scheme. The performance of the best configuration of WEPS is objectively verified against ECMWF reanalysis and a high-resolution simulation. Further analysis finds little impact of the stochastic schemes on quantitative precipitation forecasts and a single Typhoon case study. We conclude that for best performance over the East Asian domain, stochastic parameterizations alone are not sufficient to represent model-uncertainty and need to be augmented with a multi- physics suite.

What Is the Predictability Limit of Midlatitude Weather?

Abstract Understanding the predictability limit of day-to-day weather phenomena such as midlatitude winter storms and summer monsoonal rainstorms is crucial to numerical weather prediction (NWP). This predictability limit is studied using unprecedented high-resolution global models with ensemble experiments of the European Centre for Medium-Range Weather Forecasts (ECMWF; 9-km operational model) and identical-twin experiments of the U.S. Next-Generation Global Prediction System (NGGPS; 3 km). Results suggest that the predictability limit for midlatitude weather may indeed exist and is intrinsic to the underlying dynamical system and instabilities even if the forecast model and the initial conditions are nearly perfect. Currently, a skillful forecast lead time of midlatitude instantaneous weather is around 10 days, which serves as the practical predictability limit. Reducing the current-day initial-condition uncertainty by an order of magnitude extends the deterministic forecast lead times of day-to-day weather by up to 5 days, with much less scope for improving prediction of small-scale phenomena like thunderstorms. Achieving this additional predictability limit can have enormous socioeconomic benefits but requires coordinated efforts by the entire community to design better numerical weather models, to improve observations, and to make better use of observations with advanced data assimilation and computing techniques.

Analytical Predictive Guidance Algorithm Based on Single Ballistic Coefficient Switching for Mars Aerocapture

Aerocapture can significantly reduce the velocity increment required for a planetary orbital mission and reduce the amount of propellant needed. And it may be one of the key technologies necessary for large-scale space exploration missions in the future. In this paper, the analytical solution of aerocapture based on the piecewise variable ballistic coefficient is studied around the exploration of Mars. An aerocapture analytical predictive guidance algorithm for single ballistic coefficient switching is proposed. The terminal velocity after the ballistic coefficient switching can be obtained by analytical calculation in real time. The adaptive control of the switching time of the ballistic coefficient is realized. The simulation results show that the guidance algorithm is accurate and robust, which can effectively overcome the influence of atmospheric density error, aerodynamic parameter error, and initial state uncertainty.

Improvements in Forecasting Intense Rainfall: Results from the FRANC (Forecasting Rainfall Exploiting New Data Assimilation Techniques and Novel Observations of Convection) Project

The FRANC project (Forecasting Rainfall exploiting new data Assimilation techniques and Novel observations of Convection) has researched improvements in numerical weather prediction of convective rainfall via the reduction of initial condition uncertainty. This article provides an overview of the project’s achievements. We highlight new radar techniques: correcting for attenuation of the radar return; correction for beams that are over 90% blocked by trees or towers close to the radar; and direct assimilation of radar reflectivity and refractivity. We discuss the treatment of uncertainty in data assimilation: new methods for estimation of observation uncertainties with novel applications to Doppler radar winds, Atmospheric Motion Vectors, and satellite radiances; a new algorithm for implementation of spatially-correlated observation error statistics in operational data assimilation; and innovative treatment of moist processes in the background error covariance model. We present results indicating a link between the spatial predictability of convection and convective regimes, with potential to allow improved forecast interpretation. The research was carried out as a partnership between University researchers and the Met Office (UK). We discuss the benefits of this approach and the impact of our research, which has helped to improve operational forecasts for convective rainfall events.

Estimating the Intrinsic Limit of Predictability Using a Stochastic Convection Scheme

AbstractGlobal model simulations together with a stochastic convection scheme are used to assess the intrinsic limit of predictability that originates from convection up to planetary scales. The stochastic convection scheme has been shown to introduce an appropriate amount of variability onto the model grid without the need to resolve the convection explicitly. This largely reduces computational costs and enables a set of 12 cases equally distributed over 1 year with five ensemble members for each case, generated by the stochastic convection scheme. As a metric, difference kinetic energy at 300 hPa over the midlatitudes, both north and south, is used. With this metric the intrinsic limit is estimated to be about 17 days when a threshold of 80% of the saturation level is applied. The error level at 3.5 days roughly compares to the initial-condition uncertainty of the current ECMWF data assimilation system, which suggests a potential improvement of 3.5 forecast days through perfecting the initial conditions. Error-growth experiments that use a deterministic convection scheme show smaller errors of about half the size at early forecast times and an estimate of intrinsic predictability that is about 10% longer, confirming the overconfidence of deterministic convection schemes.

Unscented MPSP for Optimal Control of a Class of Uncertain Nonlinear Dynamic Systems

A new computationally efficient nonlinear optimal control synthesis technique, named as unscented model predictive static programming (U-MPSP), is presented in this paper that is applicable to a class of problems with uncertainties in time-invariant system parameters and/or initial conditions. This new technique is a fusion of two recent ideas, namely MPSP and Riemann–Stieltjes optimal control problems. First, unscented transform is utilized to construct a low-dimensional finite number of deterministic problems. The philosophy of MPSP is utilized next so that the solution can be obtained in a computational efficient manner. The control solution not only ensures that the terminal constraint is met accurately with respect to the mean value, but it also ensures that the associated covariance matrix (i.e., the error ball) is minimized. Significance of U-MPSP has been demonstrated by successfully solving two benchmark problems, namely the Zermelo problem and inverted pendulum problem, which contain parametric and initial condition uncertainties.