Uncertainties In Initial Conditions Research Articles

Stochastic high‐order internal model‐based adaptive TILC with random uncertainties in initial states and desired reference points

SummaryMany practical batch processes operate repetitively in industry and lack intermediate measurements for the interested process variables. Moreover, the initial states as well as the desired product objective often vary with different runs because of the existence of many uncertainties in practice. This work proposes a novel adaptive terminal iterative learning control method to deal with random uncertainties in desired terminal points and initial states. The run‐varying initial states are formulated by a stochastic high‐order internal model, which is further incorporated into the controller design. The desired terminal output is run dependent and is directly compensated like a feedback term in the controller. Only the system output at the endpoint of an operation is utilized to update the control signal. An estimation algorithm is designed to update the system Markov parameters as a whole. No explicit model information is involved in the controller design; thus, the proposed method is data driven and can be applied to nonlinear systems directly. Both the theoretical analysis and the simulation studies demonstrate the effectiveness of the proposed approach under random initial states and iteration‐varying referenced terminal points. Copyright © 2016 John Wiley & Sons, Ltd.

Angles-only relative navigation and closed-loop guidance for spacecraft proximity operations

This research investigates angles-only relative navigation and closed-loop guidance algorithm for spacecraft mid-range orbital proximity operations when the orbital maneuver allows for range observability. Emphasis and contribution are on developing angles-only relative navigation and guidance coupling algorithm in the context of Clohessy–Wiltshire and Tschauner–Hempel dynamics. Observability analysis of the relative state is done and the general mathematical expression of the observable condition is obtained. Coupling relationship between the angles-only relative navigation and the multi-pulse sliding guidance is discussed and its analytic expression is derived. A novel closed-loop guidance scheme is designed based on the coupling relationship and unscented kalman filter. Two-body Monte Carlo simulations are conducted to evaluate the validity and test the performance of the closed-loop system. The sensitivities of the navigation and guidance accuracy to the line-of-sight angles accuracy, initial separation and initial state uncertainties, number of pulses, and dynamics are presented and discussed.

An Efficient Method to Correct Under-Dispersion in Ensemble Streamflow Prediction of Inflow Volumes for Reservoir Optimization

Ensemble streamflow prediction (ESP) has been widely used to gain insight on possible future inflows to hydropower reservoirs. However underestimation of climate, model structure and initial condition uncertainty often leads to under-dispersed ESP forecasts. In this paper, we present a novel approach called “Hindcast-mode Uncertainty Estimation” (HUE) to efficiently add variability in ESP forecasts to reduce their under-dispersion. The method was tested on a Canadian catchment used by Rio Tinto – Aluminium division to produce hydropower for their aluminium smelting plants. This project was focused on correcting long-term predictions of freshet runoff volumes to optimize drawdown volumes, with up to 6 months of lead time. It was found that by adding an error term to the hydrological model’s snow water equivalent (SWE) state variable at the time of forecast in hindcasting mode, the resulting simulation could be forced to perfectly reproduce the freshet runoff volume. This error term was computed for all years on record which enabled modeling of the error’s distribution. This distribution can then be sampled from to add noise to the model’s SWE at the start of a new ESP forecast. Results show that the current winter ESP forecasts are strongly under-dispersed for the freshet runoff volume estimation and that the proposed method is able to widen the ESPs to correct the under-dispersion problem. This was validated by using Talagrand diagrams which shifted from a U-shape (prior to HUE) to a uniform distribution (with HUE). The project objectives of correcting the ESP forecast’s under-dispersion in spring runoff estimations was thus attained with minimal effort, bypassing the need to perform more complex ensemble data assimilation techniques.

A Comparison of Two Ensemble Generation Methods Using Oceanic Singular Vectors and Atmospheric Lagged Initialization for Decadal Climate Prediction

Abstract The sensitivity of ensemble spread and forecast skill scores of decadal predictions to details of the ensemble generation is investigated by incorporating uncertainties of ocean initial conditions using ocean singular-vector-based (OSV) perturbations. Results are compared to a traditional atmospheric lagged initialization (ALI) method. Both sets of experiments are performed using the coupled MPI-ESM model initialized from the GECCO2 ocean synthesis. The OSVs are calculated from a linear inverse model based on a historical MPI-ESM run. During the first three lead years, the sea surface temperature spread from ALI hindcasts appears to be strongly underestimated, while OSV hindcasts show a more realistic spread. However, for later lead times (the second pentad of hindcasts), the spread becomes overestimated for large areas of the ocean in both ensembles. Yet, for integrated measures such as the North Atlantic SST and Atlantic meridional overturning circulation, the spread of OSV hindcasts is overestimated at initial time and reduces over time. The spread reliability measures are shown to be sensitive to the choice of the verification dataset. In this context, it is found that HadISST tends to underestimate the variability of SST as compared to Reynolds SST and satellite observations. In terms of forecast skill for surface air temperature, SST, and ocean heat content, OSV hindcasts show improvement over ALI hindcasts over the North Atlantic Ocean up to lead year 5.

Quantifying initial and wind forcing uncertainties in the Gulf of Mexico

This study aims at analyzing the combined impact of uncertainties in initial conditions and wind forcing fields in ocean general circulation models (OGCM) using polynomial chaos (PC) expansions. Empirical orthogonal functions (EOF) are used to formulate both spatial perturbations to initial conditions and space-time wind forcing perturbations, namely in the form of a superposition of modal components with uniformly distributed random amplitudes. The forward deterministic HYbrid Coordinate Ocean Model (HYCOM) is used to propagate input uncertainties in the Gulf of Mexico (GoM) in spring 2010, during the Deepwater Horizon oil spill, and to generate the ensemble of model realizations based on which PC surrogate models are constructed for both localized and field quantities of interest (QoIs), focusing specifically on sea surface height (SSH) and mixed layer depth (MLD). These PC surrogate models are constructed using basis pursuit denoising methodology, and their performance is assessed through various statistical measures. A global sensitivity analysis is then performed to quantify the impact of individual modes as well as their interactions. It shows that the local SSH at the edge of the GoM main current—the Loop Current—is mostly sensitive to perturbations of the initial conditions affecting the current front, whereas the local MLD in the area of the Deepwater Horizon oil spill is more sensitive to wind forcing perturbations. At the basin scale, the SSH in the deep GoM is mostly sensitive to initial condition perturbations, while over the shelf it is sensitive to wind forcing perturbations. On the other hand, the basin MLD is almost exclusively sensitive to wind perturbations. For both quantities, the two sources of uncertainty have limited interactions. Finally, the computations indicate that whereas local quantities can exhibit complex behavior that necessitates a large number of realizations, the modal analysis of field sensitivities can be suitably achieved with a moderate size ensemble.

The method of distributions for dispersive transport in porous media with uncertain hydraulic properties

AbstractPredictions of solute transport in subsurface environments are notoriously unreliable due to aquifer heterogeneity and uncertainty about the values of hydraulic parameters. Probabilistic framework, which treats the relevant parameters and solute concentrations as random fields, allows for quantification of this predictive uncertainty. By providing deterministic equations for either probability density function or cumulative distribution function (CDF) of predicted concentrations, the method of distributions enables one to estimate, e.g., the probability of a contaminant's concentration exceeding a safe dose. We derive a deterministic equation for the CDF of solute concentration, which accounts for uncertainty in flow velocity and initial conditions. The coefficients in this equation are expressed in terms of the mean and variance of concentration. The accuracy and robustness of the CDF equations are analyzed by comparing their predictions with those obtained with Monte Carlo simulations and an assumed beta CDF.

Accounting for three sources of uncertainty in ensemble hydrological forecasting

Abstract. Seeking more accuracy and reliability, the hydrometeorological community has developed several tools to decipher the different sources of uncertainty in relevant modeling processes. Among them, the ensemble Kalman filter (EnKF), multimodel approaches and meteorological ensemble forecasting proved to have the capability to improve upon deterministic hydrological forecast. This study aims to untangle the sources of uncertainty by studying the combination of these tools and assessing their respective contribution to the overall forecast quality. Each of these components is able to capture a certain aspect of the total uncertainty and improve the forecast at different stages in the forecasting process by using different means. Their combination outperforms any of the tools used solely. The EnKF is shown to contribute largely to the ensemble accuracy and dispersion, indicating that the initial conditions uncertainty is dominant. However, it fails to maintain the required dispersion throughout the entire forecast horizon and needs to be supported by a multimodel approach to take into account structural uncertainty. Moreover, the multimodel approach contributes to improving the general forecasting performance and prevents this performance from falling into the model selection pitfall since models differ strongly in their ability. Finally, the use of probabilistic meteorological forcing was found to contribute mostly to long lead time reliability. Particular attention needs to be paid to the combination of the tools, especially in the EnKF tuning to avoid overlapping in error deciphering.

Intrinsic Predictability of the 20 May 2013 Tornadic Thunderstorm Event in Oklahoma at Storm Scales

AbstractUsing a high-resolution convection-allowing numerical weather prediction model, this study seeks to explore the intrinsic predictability of the severe tornadic thunderstorm event on 20 May 2013 in Oklahoma from its preinitiation environment to initiation, upscale organization, and interaction with other convective storms. This is accomplished through ensemble forecasts perturbed with minute initial condition uncertainties that were beyond detection capabilities of any current observational platforms. It was found that these small perturbations, too small to modify the initial mesoscale environmental instability and moisture fields, will be propagated and evolved via turbulence within the PBL and rapidly amplified in moist convective processes through positive feedbacks associated with updrafts, phase transitions of water species, and cold pools, thus greatly affecting the appearance, organization, and development of thunderstorms. The forecast errors remain nearly unchanged even when the initial perturbations (errors) were reduced by as much as 90%, which strongly suggests an inherently limited predictability for this thunderstorm event for lead times as short as 3–6 h. Further scale decomposition reveals rapid error growth and saturation in meso-γ scales (regardless of the magnitude of initial errors) and subsequent upscale growth into meso-β scales.

On the robustness of near term climate predictability regarding initial state uncertainties

A set of four ensemble simulations has been designed to assess the relative importance of atmospheric, oceanic, and deep ocean initial state uncertainties, as represented by spatial white noise perturbations, on seasonal to decadal prediction skills in a perfect model framework. It is found that a perturbation mimicking random oceanic uncertainties have the same impact as an atmospheric-only perturbation on the future evolution of the ensemble after the first 3 months, even if they are initially only located in the deep ocean. This is due to the fast (1 month) perturbation of the atmospheric component regardless of the initial ensemble generation strategy. The divergence of the ensemble upper-ocean characteristics is then mainly induced by ocean–atmosphere interactions. While the seasonally varying mixed layer depth allows the penetration of the different signals in the thermocline in the mid-high latitudes, the rapid adjustment of the thermocline to wind anomalies followed by Kelvin and Rossby waves adjustment dominates the growth of the ensemble spread in the tropics. These mechanisms result in similar ensemble distribution characteristics for the four ensembles design strategy at the interannual timescale.

Validation of RELAP5 model of experimental test rig simulating the natural convection in MTR research reactors

Abstract In an attempt to understand the built-up of natural circulation in MTR pool type upward flow research reactors after loss of power, an experimental test rig was built to simulate the loop of natural circulation in MTR reactors. The test rig consisting of two vertically oriented branches, in one of them the core is simulated by two rectangular, electrically heated, parallel channels. The other branch simulates the part of the return pipe that participates in the development of core natural circulation. In the first phase of the work, many experimental runs at different conditions of channel's power and branch's initial temperatures are performed. The channel's coolant and surface temperatures were measured. The measurements and their interpretation were published by the first three authors. In the present work the thermal hydraulic behavior of the test rig is complemented by theoretical analysis using RELAP5 Mod 3.3 system code. The analysis consisting of two parts; in the first part RELAP5 model is validated against the measured values and in the second part some of the other not measured hydraulic parameters are predicted and analyzed. The test rig is typically nodalized and an input dick is prepared. In spite of the low pressure of the test rig, the results show that RELAP5 qualitatively predicts the thermal hydraulic behaviour and the accompanied phenomenon of flow inversion of such facilities. Quantitatively, there is a difference between the predicted and measured values especially the channel's surface temperature. This difference may be return to the uncertainties in initial conditions of experimental runs, the position of the thermocouples which buried inside the heat structure, and the heat transfer package in RELAP5.

Relative Reachable Domain for Spacecraft with Initial State Uncertainties

The reachable domain is a geometric description of the maneuverability of a spacecraft under control and/or measurement uncertainties. In this paper, the reachable domain concept is introduced into the field of satellite relative motion and termed the relative reachable domain. The relative reachable domain geometrically represents the effects of the initial control and/or measurement uncertainties on relative motion. A general method is developed to find the envelope of the coplanar relative reachable domain for arbitrary reference orbits, by evaluating the extremal values of the potentially accessible radius with respect to a given reference position. The relative reachable domain formulations are analytically expressed for circular reference orbits. It is shown that the relative reachable domain is a convenient tool for analyzing a variety of cluster flight mission problems. Several practical applications are suggested, including determining the upper bound on the separation distances among satellites. It is also shown that the relative reachable domain can be used for assessing the collision risk and that, in some situations, the relative reachable domain is more reliable than existing collision assessment methods. Numerical examples demonstrate the usefulness of the proposed method for finding the relative reachable domain and show that the analytical calculation of the relative reachable domain is accurate even in the case of noncoplanar perturbed motion.

Improving High-Resolution Weather Forecasts Using the Weather Research and Forecasting (WRF) Model with an Updated Kain–Fritsch Scheme

Abstract Efforts to improve the prediction accuracy of high-resolution (1–10 km) surface precipitation distribution and variability are of vital importance to local aspects of air pollution, wet deposition, and regional climate. However, precipitation biases and errors can occur at these spatial scales due to uncertainties in initial meteorological conditions and/or grid-scale cloud microphysics schemes. In particular, it is still unclear to what extent a subgrid-scale convection scheme could be modified to bring in scale awareness for improving high-resolution short-term precipitation forecasts in the WRF Model. To address these issues, the authors introduced scale-aware parameterized cloud dynamics for high-resolution forecasts by making several changes to the Kain–Fritsch (KF) convective parameterization scheme in the WRF Model. These changes include subgrid-scale cloud–radiation interactions, a dynamic adjustment time scale, impacts of cloud updraft mass fluxes on grid-scale vertical velocity, and lifting condensation level–based entrainment methodology that includes scale dependency. A series of 48-h retrospective forecasts using a combination of three treatments of convection (KF, updated KF, and the use of no cumulus parameterization), two cloud microphysics schemes, and two types of initial condition datasets were performed over the U.S. southern Great Plains on 9- and 3-km grid spacings during the summers of 2002 and 2010. Results indicate that 1) the source of initial conditions plays a key role in high-resolution precipitation forecasting, and 2) the authors’ updated KF scheme greatly alleviates the excessive precipitation at 9-km grid spacing and improves results at 3-km grid spacing as well. Overall, the study found that the updated KF scheme incorporated into a high-resolution model does provide better forecasts for precipitation location and intensity.

The Sensitivity of Heavy Precipitation to Horizontal Resolution, Domain Size, and Rain Rate Assimilation: Case Studies with a Convection-Permitting Model

The Australian Community Climate and Earth-System Simulator (ACCESS) is used to test the sensitivity of heavy precipitation to various model configurations: horizontal resolution, domain size, rain rate assimilation, perturbed physics, and initial condition uncertainties, through a series of convection-permitting simulations of three heavy precipitation (greater than 200 mm day−1) cases in different synoptic backgrounds. The larger disparity of intensity histograms and rainfall fluctuation caused by different model configurations from their mean and/or control run indicates that heavier precipitation forecasts have larger uncertainty. A cross-verification exercise is used to quantify the impacts of different model parameters on heavy precipitation. The dispersion of skill scores with control run used as “truth” shows thatthe impacts of the model resolution and domain size on the quantitative precipitation forecast are not less than those of perturbed physics and initial field uncertainties in these not intentionally selected heavy precipitation cases. The result indicates that model resolution and domain size should be considered as part of probabilistic precipitation forecasts and ensemble prediction system design besides the model initial field uncertainty.

Atmospheric and Oceanic Contributions to Irreducible Forecast Uncertainty of Arctic Surface Climate

Abstract Uncertainty of Arctic seasonal to interannual predictions arising from model errors and initial state uncertainty has been widely discussed in the literature, whereas the irreducible forecast uncertainty (IFU) arising from the chaoticity of the climate system has received less attention. However, IFU provides important insights into the mechanisms through which predictability is lost and hence can inform prioritization of model development and observations deployment. Here, the authors characterize how internal oceanic and surface atmospheric heat fluxes contribute to the IFU of Arctic sea ice and upper-ocean heat content in an Earth system model by analyzing a set of idealized ensemble prediction experiments. It is found that atmospheric and oceanic heat flux are often equally important for driving unpredictable Arctic-wide changes in sea ice and surface water temperatures and hence contribute equally to IFU. Atmospheric surface heat flux tends to dominate Arctic-wide changes for lead times of up to a year, whereas oceanic heat flux tends to dominate regionally and on interannual time scales. There is in general a strong negative covariance between surface heat flux and ocean vertical heat flux at depth, and anomalies of lateral ocean heat transport are wind driven, which suggests that the unpredictable oceanic heat flux variability is mainly forced by the atmosphere. These results are qualitatively robust across different initial states, but substantial variations in the amplitude of IFU exist. It is concluded that both atmospheric variability and the initial state of the upper ocean are key ingredients for predictions of Arctic surface climate on seasonal to interannual time scales.

Ensemble Prediction of the Dispersion of Volcanic Ash from the 13 February 2014 Eruption of Kelut, Indonesia

AbstractA meteorological ensemble prediction system that represents uncertainties in both initial conditions and model formulations is coupled with a modified version of the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model. This coupled dispersion ensemble prediction system (DEPS) is used to generate a 24-member ensemble forecast of the dispersion of the volcanic ash cloud produced by the 13 February 2014 eruption of Kelut, Indonesia. Uncertainties in the volcanic ash source are not represented. For predictions up to 12 h from the start of the eruption, forecasts from the deterministic control member and from the DEPS both show very good qualitative agreement with satellite observations. By 18–24 h the DEPS forecast shows better qualitative agreement with observations than does the deterministic forecast. Although composited fields such as the ensemble mean and probability present information concisely, experiments here show that it is very important to also consider results from individual member forecasts in order to identify features that may be underrepresented. For example, an area of relatively high ash concentration that was forecast by most of the members was not particularly evident in the composited fields because the location of this feature was highly variable between member forecasts. To fully understand a DEPS forecast, it is necessary to consider both atmospheric column load and concentration fields, individual member forecasts, and a range of thresholds in computing and interpreting probabilities.

A new application of conditional nonlinear optimal perturbation approach to boundary condition uncertainty

AbstractThe conditional nonlinear optimal perturbation (CNOP) approach was mainly used to investigate the effects of the uncertainties in initial condition and model parameters on model results. This study presents a new application of the CNOP approach to the investigation of the effects of boundary condition uncertainty. Specifically, we first give the general formulation of the CNOP approach for uncertainties of initial and boundary conditions and model parameters. The method is then applied to analyze the effects of nutrient perturbations at the bottom boundary of the water column on the modeled deep chlorophyll maximum (DCM) using an ocean ecosystem model. The results show that nutrient perturbations at the bottom boundary have significant impacts on the modeled DCM. Interestingly, the approach also reveals that nonlinear processes play important roles in the evolution of phytoplankton perturbations caused by nutrient perturbations at the bottom boundary. This implies that the CNOP approach is useful for investigating the effects of boundary condition uncertainty.

The early geodynamic evolution of Mars-type planets

It is not clear whether Mars once possessed active tectonics, yet the question is critical for understanding the thermal evolution of Mars, and the origin and longevity of its early dynamo. To address these issues, we have coupled mantle flow simulations, together with parameterized core evolution models, to simulate the early evolution of Mars-like planets, and constrain the influence of early mobile-lid tectonics on core evolution. We have explored a wide parameter suite, encapsulating a range of uncertainties in initial conditions, rheological parameters, and surface strength. We present successful models that experience early mobile-lid behaviour, with a later transition into a stagnant-lid mode, which reproduce core dynamo histories similar to the magnetic history of early Mars.

J/ψproduction and suppression in high-energy proton-nucleus collisions

We apply a Color Glass Condensate+Non-Relativistic QCD (CGC+NRQCD) framework to compute $J/\psi$ production in deuteron-nucleus collisions at RHIC and proton-nucleus collisions at the LHC. Our results match smoothly at high $p_\perp$ to a next-to-leading order perturbative QCD + NRQCD computation. Excellent agreement is obtained for $p_\perp$ spectra at RHIC and LHC for central and forward rapidities, as well as for the normalized ratio $R_{pA}$ of these results to spectra in proton-proton collisions. In particular, we observe that the $R_{pA}$ data is strongly bounded by our computations of the same for each of the individual NRQCD channels; this result provides strong evidence that our description is robust against uncertainties in initial conditions and hadronization mechanisms.

Irreducible uncertainty in near-term climate projections

Model simulations of the next few decades are widely used in assessments of climate change impacts and as guidance for adaptation. Their non-linear nature reveals a level of irreducible uncertainty which it is important to understand and quantify, especially for projections of near-term regional climate. Here we use large idealised initial condition ensembles of the FAMOUS global climate model with a 1 %/ year compound increase in CO2 levels to quantify the range of future temperatures in model-based projections. These simulations explore the role of both atmospheric and oceanic initial conditions and are the largest such ensembles to date. Short-term simulated trends in global temperature are diverse, and cooling periods are more likely to be followed by larger warming rates. The spatial pattern of near-term temperature change varies considerably, but the proportion of the surface showing a warming is more consistent. In addition, ensemble spread in inter-annual temperature declines as the climate warms, especially in the North Atlantic. Over Europe, atmospheric initial condition uncertainty can, for certain ocean initial conditions, lead to 20 year trends in winter and summer in which every location can exhibit either strong cooling or rapid warming. However, the details of the distribution are highly sensitive to the ocean initial condition chosen and particularly the state of the Atlantic meridional overturning circulation. On longer timescales, the warming signal becomes more clear and consistent amongst different initial condition ensembles. An ensemble using a range of different oceanic initial conditions produces a larger spread in temperature trends than ensembles using a single ocean initial condition for all lead times. This highlights the potential benefits from initialising climate predictions from ocean states informed by observations. These results suggest that climate projections need to be performed with many more ensemble members than at present, using a range of ocean initial conditions, if the uncertainty in nearterm regional climate is to be adequately quantified.

Stochastic Discrete Equation Method (sDEM) for two-phase flows

A new scheme for the numerical approximation of a five-equation model taking into account Uncertainty Quantification (UQ) is presented. In particular, the Discrete Equation Method (DEM) for the discretization of the five-equation model is modified for including a formulation based on the adaptive Semi-Intrusive (aSI) scheme, thus yielding a new intrusive scheme (sDEM) for simulating stochastic two-phase flows. Some reference test-cases are performed in order to demonstrate the convergence properties and the efficiency of the overall scheme. The propagation of initial conditions uncertainties is evaluated in terms of mean and variance of several thermodynamic properties of the two phases.