Error Growth Research Articles

Effects of a simulated maritime shift schedule on vigilance, sleep, and sleepiness

ABSTRACT Shift work is associated with circadian misalignment, which causes sleep loss, impairs performance, and increases the risk of accidents. Shorter, more frequently shifting watch schedules, widely used in industries such as maritime operation, defense, and mining, may mitigate these risks by reducing shift length and providing sleep opportunities for all workers across the biological night. However, the effects of frequently shifting work on sleep and performance still need to be clarified. The current study investigated the vigilance, sleepiness, and sleep patterns of fifteen participants who lived in a controlled and confined laboratory that mimicked a maritime environment for 14 d following a simulating frequent shift schedule. The results of psychomotor vigilance tasks (PVT) suggest that this shift schedule may lead to an accumulation of vigilance detrimental across watch days, with both reaction speed impairment and error growth. Furthermore, the circadian phase significantly affects PVT performance, with the afternoon shift section showing relatively better performance. Overall, more working hours per day resulted in poorer PVT performance. As the shift progressed, total sleep duration reduced slightly, and wake after sleep onset (WASO) increased. Sleep during the biological night was generally longer than sleep in the daytime. Less on-watch time was linked to longer overall sleep duration. Additionally, although the subjective sleepiness obtained by the Karolinska Sleepiness Scale (KSS) varied insignificantly across days, the KSS score was negatively correlated with PVT performance. This research can serve as a foundation for developing countermeasures to mitigate frequently shifting schedules’ potentially detrimental effects and safety risks.

The importance of data assimilation components for initial conditions and subsequent error growth

The importance of data assimilation components for initial conditions and subsequent error growth

Representing uncertainty in limited-area data assimilating ocean models

A limited-area ocean prediction system is developed to acquire forecast error covariances related to uncertainty in atmospheric forcing and turbulent mixing using perturbed model parameters within an Ensemble Kalman Filter (EnKF). The system performs sequential data assimilation delivering realistic ocean state estimation and forecasts. It is initialised to observations using the EnKF, the hybrid-EnKF and Ensemble Optimal Interpolation (EnOI). It has higher resolution than the parent global model, includes tides and assimilates altimetric sea level anomaly to constrain the offshore mesoscale circulation. Dynamic ensemble spread introduced by parameter uncertainty shows agreement with error estimates obtained from forecast innovation statistics. Hybrid EnKF offers improvements to both EnKF and EnOI, having smaller analysis increments and forecast errors. The ensemble mean of the hybrid-EnKF is more accurate than any member due to the introduction of parameterised error which behaves as additive inflation in the hybrid EnKF system. This indicates the parameterisation acts as a non-linear filter for model forecast error growth. To demonstrate consistency, experiments are carried out for various regions that differ in their oceanographic situations. The hybrid EnKF data assimilation system enables practical use of dynamic ensembles that capture the flow dependent errors which are mixed with static or climatological covariances for situations where model error is systematically under-estimated.

Faster Bootstrapping via Modulus Raising and Composite NTT

FHEW-like schemes utilize exact gadget decomposition to reduce error growth and ensure that the bootstrapping incurs only polynomial error growth. However, the exact gadget decomposition method requires higher computation complexity and larger memory storage. In this paper, we improve the efficiency of the FHEWlike schemes by utilizing the composite NTT that performs the Number Theoretic Transform (NTT) with a composite modulus. Specifically, based on the composite NTT, we integrate modulus raising and gadget decomposition in the external product, which reduces the number of NTTs required in the blind rotation from 2(dg + 1)n to 2(⌈dg⌉/2 + 1)n. Furthermore, we develop a modulus packing technique that uses the Chinese Remainder Theorem (CRT) and composite NTT to bootstrap multiple LWE ciphertexts through one blind rotation process.We implement the bootstrapping algorithms and evaluate the performance on various benchmark computations using both binary and ternary secret keys. Our results of the single bootstrapping process indicate that the proposed approach achieves speedups of up to 1.7 x, and reduces the size of the blind rotation key by 50% under specific parameters. Finally, we instantiate two ciphertexts in the packing procedure, and the experimental results show that our technique is around 1.5 x faster than the two bootstrapping processes under the 127-bit security level.

Effects of Wind Stress Uncertainty on Short-Term Prediction of the Kuroshio Extension State Transition Process

Abstract Based on the conditional nonlinear optimal perturbation for boundary condition method and Regional Ocean Modeling System (ROMS), this study investigates the influence of wind stress uncertainty on predicting the short-term state transitions of the Kuroshio Extension (KE). The optimal time-dependent wind stress errors that lead to maximum prediction errors are obtained for two KE stable-to-unstable and two reverse transitions, which exhibit local multieddies structures with decreasing magnitude as the end time of prediction approaches. The optimal boundary errors initially induce small oceanic errors through Ekman pumping. Subsequently, these errors grow in magnitude as oceanic internal processes take effect, which exerts significant influences on the short-term prediction of the KE state transition process. Specifically, during stable-to-unstable (unstable-to-stable) transitions, the growing error induces an overestimation (underestimation) of the meridional sea surface height gradient across the KE axis, leading to the predicted KE state being more (less) stable. Furthermore, the dynamics mechanism analysis indicates that barotropic instability is crucial for the error growth in the prediction of both the stable-to-unstable and the reverse transition processes due to the horizontal shear of flow field. But work generated by wind stress error plays a more important role in the prediction of the unstable-to-stable transitions because of the synergistic effect of strong wind stress error and strong oceanic error. Eventually, the sensitive areas have been identified based on the optimal boundary errors. Reducing wind stress errors in sensitive areas can significantly improve prediction skills, offering theoretical guidance for devising observational strategies.

Stabilizing machine learning prediction of dynamics: Novel noise-inspired regularization tested with reservoir computing

Recent work has shown that machine learning (ML) models can skillfully forecast the dynamics of unknown chaotic systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (“climate”) can be produced by employing a feedback loop, whereby the model is trained to predict forward only one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this feedback can result in artificially rapid error growth (“instability”). One established mitigating technique is to add noise to the ML model training input. Based on this technique, we formulate a new penalty term in the loss function for ML models with memory of past inputs that deterministically approximates the effect of many small, independent noise realizations added to the model input during training. We refer to this penalty and the resulting regularization as Linearized Multi-Noise Training (LMNT). We systematically examine the effect of LMNT, input noise, and other established regularization techniques in a case study using reservoir computing, a machine learning method using recurrent neural networks, to predict the spatiotemporal chaotic Kuramoto–Sivashinsky equation. We find that reservoir computers trained with noise or with LMNT produce climate predictions that appear to be indefinitely stable and have a climate very similar to the true system, while the short-term forecasts are substantially more accurate than those trained with other regularization techniques. Finally, we show the deterministic aspect of our LMNT regularization facilitates fast reservoir computer regularization hyperparameter tuning.

Third-order exponential integrator for linear Klein–Gordon equations with time and space-dependent mass

Allowing for space- and time-dependence of mass in Klein–Gordon equations resolves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations. In this paper we propose a third-order exponential integrator, where the main idea lies in embedding the oscillations triggered by the possibly highly oscillatory component intrinsically into the numerical discretisation. While typically high oscillation requires appropriately small time steps, an application of Filon methods allows implementation with large time steps even in the presence of very high oscillation. This greatly improves the efficiency of the time-stepping algorithm. Proof of the convergence and its rate are nontrivial and require alternative representation of the equation under consideration. We derive careful bounds on the growth of global error in time discretisation and prove that, contrary to standard intuition, the error of time integration does not grow once the frequency of oscillations increases. Several numerical simulations are presented to confirm the theoretical investigations and the robustness of the method in all oscillatory regimes.

Impacts of Multiscale Components of Initial Perturbations on Error Growth Characteristics and Ensemble Forecasting Skill

Abstract To compare the roles of two kinds of initial perturbations in a convection-permitting ensemble prediction system (CPEPS) and reveal the effects of the differences in large-scale/small-scale perturbation components on the CPEPS, three initial perturbation schemes are introduced, including a dynamical downscaling (DOWN) scheme originating from a coarse-resolution model, a multiscale ensemble transform Kalman filter (ETKF) scheme, and a filtered ETKF (ETKF_LARGE) scheme. First, the comparisons between the DOWN and ETKF schemes reveal that they behave differently in many ways. Specifically, the ensemble spread and forecast error for precipitation in the DOWN scheme are larger than those in the ETKF; the probabilistic forecasting skill for precipitation in the DOWN scheme is better than that in the ETKF at small neighborhood radii, whereas the advantages of the ETKF begin to appear as the neighborhood radius increases; DOWN possesses better spread–skill relationships than ETKF and has comparable probabilistic forecasting skills for nonprecipitation. Second, the comparisons between DOWN and ETKF_LARGE indicate that the differences in the large-scale initial perturbation components are key to the differences between DOWN and ETKF. Third, the comparisons between ETKF and ETKF_LARGE demonstrate that the small-scale initial perturbations are important since they can increase the precipitation spread in the early times and decrease the forecast errors while simultaneously improving the probabilistic forecasting skill for precipitation. Given the advantages of the DOWN and ETKF schemes and the importance of both large-scale and small-scale initial perturbations, multiscale initial perturbations should be constructed in future research.

The Two- to Four-Day Predictability of Midlatitude Cyclones: Don’t Sweat the Small Stuff

Abstract We use convection-permitting idealized simulations of moist midlatitude cyclones to compare the growth of synoptic-scale perturbations derived from an adjoint model with the growth of equal-energy-norm, monochromatic-wavelength perturbations at the smallest resolved scale. For initial magnitudes comparable to those of initial-condition uncertainties in present-day data assimilation systems, the adjoint perturbations produce a “forecast bust,” significantly changing the intensity and location of the cyclone and its accompanying precipitation. In contrast, the small-scale-wave perturbations project strongly onto the moist convection, but the upscale growth from the random displacement of individual convective cells does not significantly alter the cyclone’s development nor its accompanying precipitation through 2–4-day lead times. Instead, the differences in convection generated at early times become negligible because the development of subsequent convection is driven by the mostly unchanged synoptic-scale flow. Reducing the perturbation magnitudes by factors of 10 and 100 demonstrates that nonlinear dynamics play an important role in the displacement of the cyclone by the full-magnitude adjoint perturbations, and that the upscale growth of small-magnitude, small-scale perturbations is too slow to significantly change the cyclone. These results suggest that a sensitive dependence on the synoptic-scale initial conditions, analogous to that of the Lorenz (1963) system, may be more relevant to 2–4-day midlatitude-cyclone forecast busts than the upscale error growth in the Lorenz (1969) model.

Can Artificial Intelligence‐Based Weather Prediction Models Simulate the Butterfly Effect?

AbstractWe investigate error growth from small‐amplitude initial condition perturbations, simulated with a recent artificial intelligence‐based weather prediction model. From past simulations with standard physically‐based numerical models as well as from theoretical considerations it is expected that such small‐amplitude initial condition perturbations would grow very fast initially. This fast growth then sets a fixed and fundamental limit to the predictability of weather, a phenomenon known as the butterfly effect. We find however, that the AI‐based model completely fails to reproduce the rapid initial growth rates and hence would incorrectly suggest an unlimited predictability of the atmosphere. In contrast, if the initial perturbations are large and comparable to current uncertainties in the estimation of the initial state, the AI‐based model basically agrees with physically‐based simulations, although some deficits are still present.

Deep Learning of Systematic Sea Ice Model Errors From Data Assimilation Increments

AbstractData assimilation is often viewed as a framework for correcting short‐term error growth in dynamical climate model forecasts. When viewed on the time scales of climate however, these short‐term corrections, or analysis increments, can closely mirror the systematic bias patterns of the dynamical model. In this study, we use convolutional neural networks (CNNs) to learn a mapping from model state variables to analysis increments, in order to showcase the feasibility of a data‐driven model parameterization which can predict state‐dependent model errors. We undertake this problem using an ice‐ocean data assimilation system within the Seamless system for Prediction and EArth system Research (SPEAR) model, developed at the Geophysical Fluid Dynamics Laboratory, which assimilates satellite observations of sea ice concentration every 5 days between 1982 and 2017. The CNN then takes inputs of data assimilation forecast states and tendencies, and makes predictions of the corresponding sea ice concentration increments. Specifically, the inputs are states and tendencies of sea ice concentration, sea‐surface temperature, ice velocities, ice thickness, net shortwave radiation, ice‐surface skin temperature, sea‐surface salinity, as well as a land‐sea mask. We find the CNN is able to make skillful predictions of the increments in both the Arctic and Antarctic and across all seasons, with skill that consistently exceeds that of a climatological increment prediction. This suggests that the CNN could be used to reduce sea ice biases in free‐running SPEAR simulations, either as a sea ice parameterization or an online bias correction tool for numerical sea ice forecasts.

Warm conveyor belts as amplifiers of forecast uncertainty

AbstractWarm conveyor belts (WCBs) are rapidly ascending air streams associated with extratropical cyclones. WCBs exert a substantial influence on the evolution of the large‐scale midlatitude flow and have previously been related to increased forecast uncertainty in case studies. This study provides a first systematic investigation of the role of WCBs for errors in medium‐range ensemble forecasts in the Atlantic–European region. The study is enabled through a unique data set, allowing for a Lagrangian detection of WCBs in three years of operational ensemble forecasts from the European Centre for Medium‐Range Weather Forecasts. By analysing the relationship between commonly used error metrics of variables that characterise the large‐scale flow and WCBs, the study aims to shed light on the question of the extent to which WCBs act as a source of forecast errors and as an amplifier of pre‐existing errors in a state‐of‐the‐art global operational numerical weather prediction model. We show that forecasts with high WCB activity are on average characterised by an amplified Rossby‐wave pattern and anticyclonic flow anomalies downstream. We find that the forecast skill is generally reduced when the WCB activity is high, and that WCB activity is particularly increased when the error growth is largest. To establish a causal relationship, we employ two composite approaches. The first focuses on the time of largest error growth and the second calculates normalised forecast error fields centered on WCB objects. Both approaches yield a consistent picture: anomalously high errors are initially associated with misrepresentations of an upstream trough. In regions of WCB ascent and outflow, the errors grow rapidly in terms of magnitude and scale and are projected onto the upper‐level large‐scale circulation. We also find indications that WCBs can cause errors even when the upstream flow is well represented. Notwithstanding, evidence is robust for WCBs acting as an amplifier of forecast uncertainty.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term (up to 30 days) predictions of Earth Rotation Parameters (ERPs) such as Polar Motion (PM: PMX and PMY) play an essential role in real-time applications related to high-precision reference frame conversion. Currently, least squares (LS) + auto-regressive (AR) hybrid method is one of the main techniques of PM prediction. Besides, the weighted LS + AR hybrid method performs well for PM short-term prediction. However, the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model. In this study, we have derived a modified stochastic model for the LS + AR hybrid method, namely the weighted LS + weighted AR hybrid method. By using the PM data products of IERS EOP 14 C04, the numerical results indicate that for PM short-term forecasting, the proposed weighted LS + weighted AR hybrid method shows an advantage over both the LS + AR hybrid method and the weighted LS + AR hybrid method. Compared to the mean absolute errors (MAEs) of PMX/PMY short-term prediction of the LS + AR hybrid method and the weighted LS + AR hybrid method, the weighted LS + weighted AR hybrid method shows average improvements of 6.61%/12.08% and 0.24%/11.65%, respectively. Besides, for the slopes of the linear regression lines fitted to the errors of each method, the growth of the prediction error of the proposed method is slower than that of the other two methods.

Influence of Physically Constrained Initial Perturbations on the Predictability of Mei-Yu Heavy Precipitation

Abstract Based on the conditional nonlinear optimal perturbation (CNOP) approach, the predictability of mei-yu heavy precipitation and its underlying physical processes is investigated. As an extension of our previous work, the practical predictability of heavy precipitation events is studied using more realistic initial perturbations than previously considered. The initial perturbation reflects certain physical connections among multiple variables, including zonal and meridional winds, potential temperature (T), and water vapor mixing ratio (Q). Two types of initial perturbations for the CNOP are identified, with similar spatial distributions but opposite signs and resulting effects. The accumulated precipitation is strengthened with mostly positive perturbations in the T and Q components for the CNOP and weakened by negative perturbations. Comparing downscaling (DOWN) perturbations and random perturbations (RPs) with the CNOP, it is found that the CNOP and DOWN perturbations exhibit particularly large- and mesoscale spatial structures, respectively, while the RPs yield a spatial distribution with mostly convective-scale features. Also, the CNOP results in the largest error growth and forecast uncertainty, especially for Q, followed by the DOWN perturbations; those in the RPs are the smallest. These results provide important implications for optimizing the initial perturbations of convection-permitting ensemble prediction systems, especially precipitation forecasts. Moreover, it is suggested that small-scale related variables, that is, those associated with vertical motion and microphysical processes, are much less predictable than thermodynamic variables, and the errors grow through distinct physical processes for the three types of initial perturbations, that is, those with flow-dependent features.

Double-time-scale non-probabilistic reliability-based controller optimization for manipulator considering motion error and wear growth

Motion error and wear growth are two crucial factors that determine the performance of the manipulator system. The two factors are distinct from the sensitivity to time and respectively indicate its control performance and lifespan level. In this paper, a double-time-scale non-probabilistic reliability (DTSNPR)-based optimization method, which considers time-sensitive factor motion error as time-dependent reliability (TDR) and time-insensitive factor clearance wear growth as time-independent reliability (TIR), is proposed to comprehensively evaluate and optimize the controller of the manipulator system in consideration of these multi-scale factors. Meanwhile, for a highly nonlinear response problem of a manipulator system, the adaptive subinterval collocation method (ASICM) which transfers the highly nonlinear uncertainty propagation problem into a sequence of small subintervals, is adopted to obtain the response range more precisely. The proposed DTSNPR-based optimization method is applied to three numerical manipulator systems and ensures each of them under a predefined level of reliability upon both motion error and wear growth. The results also indicate that the proposed ASICM owns an advantage over computational cost and precision, with only 0.4% error and 1% computational cost compared with the Monte-Carlo methods.

Development of Accurate Long-lead COVID-19 Forecast.

Coronavirus disease 2019 (COVID-19) will likely remain a major public health burden; accurate forecast of COVID-19 epidemic outcomes several months into the future is needed to support more proactive planning. Here, we propose strategies to address three major forecast challenges, i.e., error growth, the emergence of new variants, and infection seasonality. Using these strategies in combination we generate retrospective predictions of COVID-19 cases and deaths 6 months in the future for 10 representative US states. Tallied over >25,000 retrospective predictions through September 2022, the forecast approach using all three strategies consistently outperformed a baseline forecast approach without these strategies across different variant waves and locations, for all forecast targets. Overall, probabilistic forecast accuracy improved by 64% and 38% and point prediction accuracy by 133% and 87% for cases and deaths, respectively. Real-time 6-month lead predictions made in early October 2022 suggested large attack rates in most states but a lower burden of deaths than previous waves during October 2022 -March 2023; these predictions are in general accurate compared to reported data. The superior skill of the forecast methods developed here demonstrate means for generating more accurate long-lead forecast of COVID-19 and possibly other infectious diseases.

Multi factors-PredRNN based significant wave height prediction in the Bohai, Yellow, and East China Seas

IntroductionCurrently, deep-learning-based prediction of Significant Wave Height (SWH) is mostly performed for a single location in the ocean or simply relies on a single factor (SF). Such approaches have the disadvantage of lacking spatial correlations or dynamic complexity, leading to an inevitable growth of the prediction error with time.MethodsHere, attempting a solution, we develop a Multi-Factor (MF) data-driven 2D SWH prediction model for the Bohai, Yellow, and East China Seas (BYECS). Our model is developed based on a multi-channel PredRNN algorithm that is an improved deep-learning calculation of the ConvLSTM.ResultsIn our model, the MF of historical SWH, 10 m surface winds, ocean surface currents, bathymetries, and open boundaries are used to predict 2D SWH in the next 1-72h. Our modeled SWHs show the correlation coefficients as 0.98, 0.90, and 0.87 for the next 6h, 24h, and 72h, respectively.DiscussionAccording to the ablation experiments, winds are the dominant factor in the MF model and the memory-decoupling module is the key improvement of the PredRNN compared to the ConvLSTM. Furthermore, when the historical SWH is excluded from the input, the correlation coefficients remain around 0.95 in the 1-72h prediction due to the elimination of the error accumulation. It was worse than the MF-PredRNN with the historical SWH before 10h but better than it after 10h. Overall, for the prediction of SWH in the BYECS, our MF-PredRNN-based 2D SWH prediction model significantly improves the accuracy and extends the effective prediction time length.

An adjoint-free algorithm for conditional nonlinear optimal perturbations (CNOPs) via sampling

Abstract. In this paper, we propose a sampling algorithm based on state-of-the-art statistical machine learning techniques to obtain conditional nonlinear optimal perturbations (CNOPs), which is different from traditional (deterministic) optimization methods.1 Specifically, the traditional approach is unavailable in practice, which requires numerically computing the gradient (first-order information) such that the computation cost is expensive, since it needs a large number of times to run numerical models. However, the sampling approach directly reduces the gradient to the objective function value (zeroth-order information), which also avoids using the adjoint technique that is unusable for many atmosphere and ocean models and requires large amounts of storage. We show an intuitive analysis for the sampling algorithm from the law of large numbers and further present a Chernoff-type concentration inequality to rigorously characterize the degree to which the sample average probabilistically approximates the exact gradient. The experiments are implemented to obtain the CNOPs for two numerical models, the Burgers equation with small viscosity and the Lorenz-96 model. We demonstrate the CNOPs obtained with their spatial patterns, objective values, computation times, and nonlinear error growth. Compared with the performance of the three approaches, all the characters for quantifying the CNOPs are nearly consistent, while the computation time using the sampling approach with fewer samples is much shorter. In other words, the new sampling algorithm shortens the computation time to the utmost at the cost of losing little accuracy.

Super convergence analysis of fully discrete Hermite splines to simulate wave behaviour of Kuramoto–Sivashinsky equation

An improved collocation technique has been proposed to discretize the fourth-order multi-parameter non-linear Kuramoto -Sivashinsky (K-S) equation. The spatial direction has been discretized with quintic Hermite splines, whereas the temporal direction has been discretized with a weighted finite difference scheme. The fourth-order equation in space direction has been decomposed into second-order using space splitting by introducing a new variable. Space splitting has been proposed to improve the convergence of the approximate solution. The proposed equation has been analyzed on a uniform grid in both space and time directions. Error bounds for general order Hermite splines are established for fully discrete scheme. Stability analysis for the proposed scheme has also been discussed elaborately. Periodic and non periodic problems of K-S equation type have been discussed to study the technique. The error growth has been addressed by computing L2− norm and L∞− norm.

A probabilistic perspective on predictability of solar irradiance using bootstrapped correlograms and ensemble predictability error growth

Recently in “Correlogram, predictability error growth, and bounds of mean square er-ror of solar irradiance forecasts” [Renew. Sustain. Energy Rev. 167 (2022) 112736], a new measure of predictability, applicable to solar irradiance in particular, was proposed. That predictability measure is expressed as one minus the ratio of the smallest attainable and highest tolerable root mean square errors (RMSEs) for a specific forecasting situation. Whereas the smallest attainable RMSE can be derived from the predictability error growth (PEG) of a numerical weather prediction model, the highest tolerable RMSE is computed from the forecasts of a naïve standard of reference. Despite that proposal has pioneered our understanding on the predictability of solar irradiance, answers to some technical challenges remain opaque. One of those technical challenges is the lack of uncertainty quantification of the predictability estimate, which is what this work seeks to resolve. Two conceptions, namely, ensemble PEG and bootstrapped correlograms, are herein introduced to facilitate the probabilistic representations of the smallest attainable and highest tolerable RMSEs, respectively. It is found that the uncertainty in predictability estimates is very small as compared to the range over which predictability varies across climatic conditions and forecast horizons.