Error Growth Research Articles

Vehicle trajectory prediction and generation using LSTM models and GANs.

Vehicles' trajectory prediction is a topic with growing interest in recent years, as there are applications in several domains ranging from autonomous driving to traffic congestion prediction and urban planning. Predicting trajectories starting from Floating Car Data (FCD) is a complex task that comes with different challenges, namely Vehicle to Infrastructure (V2I) interaction, Vehicle to Vehicle (V2V) interaction, multimodality, and generalizability. These challenges, especially, have not been completely explored by state-of-the-art works. In particular, multimodality and generalizability have been neglected the most, and this work attempts to fill this gap by proposing and defining new datasets, metrics, and methods to help understand and predict vehicle trajectories. We propose and compare Deep Learning models based on Long Short-Term Memory and Generative Adversarial Network architectures; in particular, our GAN-3 model can be used to generate multiple predictions in multimodal scenarios. These approaches are evaluated with our newly proposed error metrics N-ADE and N-FDE, which normalize some biases in the standard Average Displacement Error (ADE) and Final Displacement Error (FDE) metrics. Experiments have been conducted using newly collected datasets in four large Italian cities (Rome, Milan, Naples, and Turin), considering different trajectory lengths to analyze error growth over a larger number of time-steps. The results prove that, although LSTM-based models are superior in unimodal scenarios, generative models perform best in those where the effects of multimodality are higher. Space-time and geographical analysis are performed, to prove the suitability of the proposed methodology for real cases and management services.

Causes and Consequences of Sea Ice Initialization Shock in Coupled NWP Hindcasts with the GC2 Climate Model

AbstractWe present a coupled retrospective forecast (hindcast) study using the Met Office Global Coupled Model, version 2 (GC2), in which we identify and mitigate causes of initialization shock that lead to rapid error growth in sea ice forecasts. Sea ice state variables and volume budget terms as a function of forecast lead time are evaluated relative to analyses from an uncoupled Met Office ocean–sea ice analysis system [Forecast Ocean Assimilation Model, version 13 (FOAMv13)]. Two sources of initialization shock are highlighted and addressed, both of which are related to effective differences in physics between the analysis system and coupled forecast model. The primary shock to sea ice state variables arises from the use of a salinity-independent freezing temperature for seawater in GC2 as opposed to a salinity-dependent formulation in FOAMv13. A secondary effect arises from differences in the sea ice roughness and hence air–ice drag in the GC2 forecast model compared to the FOAMv13 analysis system. Generalizing from the findings of this study, we suggest that using nonnative analyses as initial conditions for coupled numerical weather prediction (NWP) studies will likely make them prone to initialization shock in some model components, to the detriment of forecast skill. To reduce the undesirable impacts of initialization shock on short-range forecast skill noted in this study we would therefore recommend the use of initial conditions (analyses) physically consistent with the native model components of the coupled forecast model, a native coupled analysis likely being the optimal initialization method.

Observation impact metrics in NWP: A theoretical study. Part I: Optimal systems

AbstractTwo methods are widely used to assess the impact of observations in global numerical weather prediction (NWP): data denial experiments (DDEs) and the forecast sensitivity‐based observation impact (FSOI) method. A DDE measures the impact on forecast accuracy of removing an observation type from the system, whereas FSOI measures the amount by which an observation type reduces the short‐range forecast error (within a system containing all observation types). It is usually found, in global NWP experiments in which both methods are used, that the FSOI impact of a given observation type is greater than its DDE impact. The aim of this article is to present the theory behind the DDE and FSOI metrics that are commonly used and to explore factors that cause DDE and FSOI metrics to give different results. The general theory is presented for an optimal analysis and forecast system and then applied to a simple model with two state variables. To explain the commonly found result of FSOI impact greater than DDE impact, the following system properties are found to be important: mixing of information (and error) by the forecast model between state variables, the rate of forecast error growth, the presence of forecast model error, the way in which observational information is distributed between state variables and denied from them, and the presence of error in the data used for forecast verification. These results provide insight into why NWP systems are resilient to the removal of observational information; they are shown to be resilient if information is denied primarily from well‐observed variables but not when denied primarily from poorly observed variables.

A coupled finite volume and material point method for two-phase simulation of liquid–sediment and gas–sediment flows

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid–sediment mixtures) to dust kick-up below helicopter rotors (gas–sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g. the granular surface, elastic stress, etc.).Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures.

Adaptive Cardinal Heading Aided for Low Cost Foot-Mounted Inertial Pedestrian Navigation

The use of a low-cost MEMS-based Inertial Measurement Unit (IMU) provides a cost-effective approach for navigation purposes. Foot-mounted IMU is a popular option for indoor inertial pedestrian navigation, as a small and light MEMS-based inertial sensor can be tied to a pedestrian's foot or shoe. Without relying on GNSS or other external sensors to enhance navigation, the foot-mounted pedestrian navigation system can autonomously navigate, relying solely on the IMU. This is typically performed with the standard strapdown navigation algorithm in a Kalman filter, where Zero Velocity Updates (ZVU) are used together to restrict the error growth of the low-cost inertial sensors. ZVU is applied every time the user takes a step since there exists a zero velocity condition during stance phase. While velocity and correlated attitude errors can be estimated correctly using ZVUs, heading error is not because it is unobservable. In this paper, weextend our previous work to correct the heading error by aiding it using Multiple Polygon Areas (MPA) with adaptive weighting factor. We termed the approach as Adaptive Cardinal Heading Aided Inertial Navigation (A-CHAIN). We formulated an adaptive weighting factor applied to measurement noise to enhance measurement confidence. We then incorporated MPA heading into the algorithm, whereas multiple buildings with the same orientation are grouped together and assigned a specific heading information as a priori. Results shown that against the original CHAIN, the proposed Adaptive-CHAIN improved the position accuracy by more than five-fold.

Establishing the Suitability of the Model for Prediction Across Scales for Global Retrospective Air Quality Modeling.

The U.S. EPA is leveraging recent advances in meteorological modeling to construct an air quality modeling system to allow consistency from global to local scales. The Model for Prediction Across Scales-Atmosphere (MPAS-A or MPAS) has been developed by the National Center for Atmospheric Research (NCAR) as a global complement to the Weather Research and Forecasting model (WRF). Patterned after a regional coupled system with WRF, the Community Multiscale Air Quality (CMAQ) modeling system has been coupled within MPAS to explore global-to-local chemical transport modeling. Several options were implemented into MPAS for retrospective applications. Nudging-based data assimilation was added to support continuous simulations of past weather to minimize error growth that exists with a weather forecast configuration. The Pleim-Xiu land-surface model, the Asymmetric Convective Model 2 boundary layer scheme, and the Pleim surface layer scheme were added as the preferred options for retrospective air quality applications with WRF. Annual simulations were conducted using this EPA-enhanced MPAS configuration on two different mesh structures and compared against WRF. MPAS generally compares well with WRF over the conterminous United States. Errors in MPAS surface meteorology are comparable to WRF throughout the year. Precipitation statistics indicate MPAS performs slightly better than WRF. Solar radiation in MPAS is higher than WRF and measurements, suggesting fewer clouds in MPAS than WRF. Upper-air meteorology is well-simulated by MPAS, but errors are slightly higher than WRF. These comparisons lend confidence to use MPAS for retrospective air quality modeling and suggest ways it can be further improved in the future.

Two-Year Dynamical Predictions of ENSO Event Duration during 1954–2015

AbstractEl Niño and La Niña events show a wide range of durations over the historical record. The predictability of event duration has remained largely unknown, although multiyear events could prolong their climate impacts. To explore the predictability of El Niño and La Niña event duration, multiyear ensemble forecasts are conducted with the Community Earth System Model, version 1 (CESM1). The 10–40-member forecasts are initialized with observed oceanic conditions on 1 March, 1 June, and 1 November of each year during 1954–2015; ensemble spread is created through slight perturbations to the atmospheric initial conditions. The CESM1 predicts the duration of individual El Niño and La Niña events with lead times ranging from 6 to 25 months. In particular, forecasts initialized in November, near the first peak of El Niño or La Niña, can skillfully predict whether the event continues through the second year with 1-yr lead time. The occurrence of multiyear La Niña events can be predicted even earlier with lead times up to 25 months, especially when they are preceded by strong El Niño. The predictability of event duration arises from initial thermocline depth anomalies in the equatorial Pacific, as well as sea surface temperature anomalies within and outside the tropical Pacific. The forecast error growth, on the other hand, originates mainly from atmospheric variability over the North Pacific in boreal winter. The high predictability of event duration indicates the potential for extending 12-month operational forecasts of El Niño and La Niña events by one additional year.

A Stochastic Parameter Perturbation Method to Represent Uncertainty in a Microphysics Scheme

AbstractCurrent state-of-the art regional numerical weather forecasts are run at horizontal grid spacings of a few kilometers, which permits medium- to large-scale convective systems to be represented explicitly in the model. With the convection parameterization no longer active, much uncertainty in the formulation of subgrid-scale processes moves to other areas such as the cloud microphysical, turbulence, and land surface parameterizations. The goal of this study is to investigate experiments with stochastically perturbed parameters (SPP) within a microphysics parameterization and the model’s horizontal diffusion coefficients. To estimate the “true” uncertainty due to parameter uncertainty, the magnitudes of the perturbations are chosen as realistically as possible and not with a purposeful intent of maximal forecast impact as some prior work has done. Spatial inhomogeneities and temporal persistence are represented using a random perturbation pattern with spatial and temporal correlations. The impact on the distributions of various hydrometeors, precipitation characteristics, and solar and longwave radiation are quantified for a winter case and a summer case. In terms of upscale error growth, the impact is relatively small and consists primarily of triggering atmospheric instabilities in convectively unstable regions. In addition, small in situ changes with potentially large socioeconomic impacts are observed in the precipitation characteristics such as maximum hail size. Albeit the impact of introducing physically based parameter uncertainties within the bounds of aerosol uncertainties is small, their influence on the solar and longwave radiation balances may still have important implications for global model simulations of future climate scenarios.

On the sensitive areas for targeted observations in ENSO forecasting

Using the outputs from CMCC-CM in CMIP5 experiments, the authors identified sensitive areas for targeted observations in ENSO forecasting from the perspective of the initial error growth (IEG) method and the particle filter (PF) method. Results showed that the PF targets areas over the central-eastern equatorial Pacific, while the sensitive areas determined by the IEG method are slightly to the east of the former. Although a small part of the areas targeted by the IEG method also lie in the southeast equatorial Pacific, this does not affect the large-scale overlapping of the sensitive areas determined by these two methods in the eastern equatorial Pacific. Therefore, sensitive areas determined by the two methods are mutually supportive. When considering the uncertainty of methods for determining sensitive areas in realistic targeted observation, it is more reasonable to choose the above overlapping areas as sensitive areas for ENSO forecasting. This result provides scientific guidance for how to better determine sensitive areas for ENSO forecasting.摘要本研究分别从初始误差增长和粒子滤波同化的角度识别了ENSO预测的目标观测敏感区.结果表明:与粒子滤波同化方法确定的敏感区相比, 基于初始误差增长确定的敏感区位置稍微偏东, 且在东南太平洋也有分布, 但整体而言, 这两种方法确定的敏感区存在大范围重合区域, 是互为印证的.在实际目标观测中, 如果考虑使用确定敏感区方法的不确定性, 那么选择上述两种方法确定的敏感区的重合区域作为ENSO预测的目标观测敏感区将更为合理.

Error Growth Dynamics within Convection-Allowing Ensemble Forecasts over Central U.S. Regions for Days of Active Convection

AbstractError growth is investigated based on convection-allowing ensemble forecasts starting from 0000 UTC for 13 active convection events over central to eastern U.S. regions from spring 2018. The analysis domain is divided into the northwest (NW), northeast (NE), southeast (SE), and southwest (SW) quadrants (subregions). Total difference energy and its decompositions are used to measure and analyze error growth at and across scales. Special attention is paid to the dominant types of convection with respect to their forcing mechanisms in the four subregions and the associated difference in precipitation diurnal cycles. The discussions on the average behaviors of error growth in each region are supplemented by four representative cases. Results show that the meso-γ-scale error growth is directly linked to precipitation diurnal cycle while meso-α-scale error growth has a strong link to large-scale forcing. Upscale error growth is evident in all regions/cases but up-amplitude growth within its own scale plays different roles in different regions/cases. When large-scale flow is important (as in the NE region), precipitation is strongly modulated by the large-scale forcing and becomes more organized with time, and upscale transfer of forecast error is stronger. On the other hand, when local instability plays more dominant roles (as in the SE region), precipitation is overall less organized and has the weakest diurnal variations. Its associated errors at the γ and β scale can reach their peaks sooner and meso-α-scale error tends to rely more on growth of error with its own scale. Small-scale forecast errors are directly impacted by convective activities and have a short response time to convection while increasingly larger-scale errors have longer response times and delayed phase within the diurnal cycle.

Propagation of rays in 2D and 3D waveguides: A stability analysis with Lyapunov and reversibility fast indicators.

Propagation of rays in 2D and 3D corrugated waveguides is performed in the general framework of stability indicators. The analysis of stability is based on the Lyapunov and reversibility error. It is found that the error growth follows a power law for regular orbits and an exponential law for chaotic orbits. A relation with the Shannon channel capacity is devised and an approximate scaling law found for the capacity increase with the corrugation depth.

Stochastic Method of Discounted Cash Flows

The method of discounted cash flows (DCF) is one of the main and popular methods of economic assessment of business, which is used all over the world. However, the actual behavior of business projects evaluated by this method often differs from that predicted, and the difference can be tens of times.It should be noted that at present, the discounted cash flow method is a subject of extensive literature, but there are no analytical arguments for large discrepancies between the theory and practice of the method. The aim of the study is to provide a theoretical explanation of the forecasting errors inherent in the discounted cash flow method. The research method is related to the analysis of the traditional method of discounted cash flows, which shows that the key indicator that affects the final result is the net income for a certain period of time. Analyzing the economic content of the flows that appear in the formation of net income, we can conclude that for a trade-type enterprise, the cash flow of receipts associated with current operations is significantly random and, therefore, requires the use of stochastic description methods.The paper offers a mathematical model of the mentioned cash flow. It is assumed that the event associated with a purchase (cash receipt) is modeled on the time axis by a point with a random time of occurrence. Then, obviously, the number of points n that appear on a fixed time interval will be a random number. A justification is given for the fact that the point process is a Poisson random point process or simply a Poisson point process, in which the times of occurrence of points W1 ,W2 , ..., Wi and their number N(t) at time t are random variables. We introduce the function λ(t), which characterizes the average number of cash receipts (purchases) per unit of time. From an economic point of view, it is driven by consumer preferences of buyers, and from a mathematic point of view it is a function of the intensity of appearance of points of the Poisson process. The monetary values of purchases made by customers are described by random positive ui values which arise at the Wi moments of the occurrence of shopping events, simulate a random process of cash receipts at the enterprise.Introduction to the consideration of the random Poisson flow of business receipts and their values, which are also random positive values with an arbitrary probability distribution, is the key assumption of the work. The proposed approach allowed us to develop a stochastic model of the company’s revenues, generalize the method of discounted cash flows, obtain a number of simple ratios, and on this basis explain the growth of the method forecast error with an increase in the duration of the forecast horizon.New results of the study are the use of stochastic methods to describe business revenues and expressions obtained on this basis for the variance and standard deviation of the company’s net cash flow, depending on the number of forecasting periods. It is shown that the growth of the standard deviation of the net cash flow, i.e. the forecasting errors, is a fundamental feature of the method in this interpretation. For the initial estimates, a simple expression is obtained and corresponding graphs are given.In conclusion, it is noted that the presented graphs of the behavior of the standard deviation of the method estimates show that the estimate from below of the mentioned deviation slowly grows with an increase in the number of prediction periods and depends only on the number of periods. It is noted that this growth is calculated in relation to the first forecast period, which itself may contain errors, and it is determined only by consumer preferences. Of course, you can choose the forecast period not a month, but, for example, a year, but then the error of the first period will be significantly increased. Thus, this review makes it possible to explain some aspects of the growth of the error of the discounted cash flow method with the forecast time.

Self-Adaptive Asymmetrical Artificial Potential Field Approach Dedicated to the Problem of Position Tracking by Nonholonomic UAVs in Windy Enivroments

Abstract Artificial potential fields (APFs) are a popular method of planning and controlling the path of robot movement, including unmanned aerial vehicles (UAVs). However, in the case of nonholonomic robots such as fixed-wing UAVs, the distribution of velocity vectors should be adapted to their limited manoeuvrability to ensure stable and precise position tracking. The previously proposed local asymmetrical potential field resolves this issue, but it is not effective in the case of windy environments, where the UAV is unable to maintain the desired position and drifts due to the wind drift effect. This is reflected in the growth of position error, which, similar to the steady-state error in the best case, is constant. To compensate for it, the asymmetrical potential field approach is modified by extending definitions of potential function gradient and velocity vector field (VVF) with elements based on the integral of position tracking error. In the case of wind drift, the value of this integral increases over time, and lengths and orientations of velocity vectors will also be changed. The work proves that redefining gradient and velocity vector as a function of position tracking error integrals allows for minimisation of the position tracking error caused by wind drift.

Dependence of tropical cyclone intrinsic intensity variability on the large‐scale environment

AbstractThis study examines the dependence of tropical cyclone (TC) intrinsic intensity variability on the large‐scale environment. Using idealized simulations with the Hurricane Research and Forecasting (HWRF) model, the growth of TC intensity errors and the subsequent saturation of intensity errors at the mature stage are quantified for a range of environmental conditions. Among several factors, it is found that sea‐surface temperature (SST) and tropospheric static stability are the two main ones affecting the growth rate and saturation of TC intensity errors, with a larger error saturation at maximum intensity equilibrium and a faster error growth rate during rapid intensification for a warmer SST or less stable troposphere. Results from this study highlight the fundamental characteristics of TC intensity predictability, which appears to vary with environmental conditions, instead of being a universal measure for TCs in all ocean basins. These results also suggest a limit on TC intensity forecast accuracy that is governed by the large‐scale environment, which needs to be taken into consideration for future TC model development.

Non-convolutional second-order complex-frequency-shifted perfectly matched layers for transient elastic wave propagation

The numerical simulation of wave propagation in heterogeneous unbounded media using domain discretization techniques requires truncation of the physical domain: at the truncation boundary, Perfectly Matched Layers (PMLs) – buffers wherein wave attenuation is imposed – are often used to mimic outgoing wave motion and prevent waves from re-entering the interior computational domain. The PML’s wave-dissipative properties derive from a coordinate mapping concept, where the physical coordinate is mapped onto a frequency-dependent complex coordinate in the PML via a complex stretching function. The choice of the stretching function controls not only the spectral character and the absorptive properties of the PML, but also, more critically, the long-time stability when the computational domain-PML ensemble is used for transient wave simulations.The standard PML stretching function can lead to error growth, particularly when propagating waves impinge at grazing incidence on the truncation boundary. By contrast, a modification to the standard stretching function that has led to the Complex-Frequency-Shifted CFS-PML has been shown to alleviate the temporal instability. However, whereas PML formulations using the standard stretching function can lead to second-order in time semi-discrete forms, affording multifaceted benefits, all CFS-PML formulations to date require the evaluation of convolutions. In this paper, we discuss a new CFS-PML formulation that avoids the evaluation of convolutions, while preserving the second-order temporal character of elastic waves. It is shown that, upon spatial discretization, the CFS-PML can be completely described by a triad of stiffness, damping, and mass matrices, which can be readily incorporated into existing finite element codes originally designed for interior problems, to endow them with wave simulation capabilities on unbounded domains. Numerical experiments in the time-domain demonstrate the efficacy of the proposed approach; we also report long-time stability for problems involving waveguides and grazing wave incidence.

Evaluating Forecast Performance and Sensitivity to the GSI EnKF Data Assimilation Configuration for the 28–29 May 2017 Mesoscale Convective System Case

AbstractIn an effort to improve radar data assimilation configurations for potential operational implementation, GSI EnKF data assimilation experiments based on the operational system employed by the Center for Analysis and Prediction of Storms (CAPS) real-time Spring Forecast Experiments are performed. These experiments are followed by 6-h forecasts for an MCS on 28–29 May 2017. Configurations examined include data thinning, covariance localization radii and inflation, observation error settings, and data assimilation frequency for radar observations. The results show experiments that assimilate radar observations more frequently (i.e., 5–10 min) are initially better at suppressing spurious convection. However, assimilating observations every 5 min causes spurious convection to become more widespread with time, and modestly degrades forecast skill through the remainder of the forecast window. Ensembles that assimilate more observations with less thinning of data or use a larger horizontal covariance localization radius for radar data predict fewer spurious storms and better predict the location of observed storms. Optimized data thinning and horizontal covariance localization radii have positive impacts on forecast skill during the first forecast hour that are quickly lost due to the growth of forecast error. Forecast skill is less sensitive to the ensemble spread inflation factors and observation errors tested during this study. These results provide guidance toward optimizing the configuration of the GSI EnKF system. Among the DA configurations tested, the one employed by the CAPS Spring Forecast Experiment produces the most skilled forecasts while remaining computationally efficient for real-time use.

Construction of Explicit Symplectic Integrators in General Relativity. I. Schwarzschild Black Holes

Abstract Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for the long-term integration of N-body Hamiltonian systems in the solar system. However, the construction of explicit symplectic integrators is frequently difficult in general relativity because all variables are inseparable. Moreover, even if two analytically integrable splitting parts exist in a relativistic Hamiltonian, all analytical solutions are not explicit functions of proper time. Naturally, implicit symplectic integrators, such as the midpoint rule, are applicable to this case. In general, these integrators are numerically more expensive to solve than same-order explicit symplectic algorithms. To address this issue, we split the Hamiltonian of Schwarzschild spacetime geometry into four integrable parts with analytical solutions as explicit functions of proper time. In this manner, second- and fourth-order explicit symplectic integrators can be easily made available. The new algorithms are also useful for modeling the chaotic motion of charged particles around a black hole with an external magnetic field. They demonstrate excellent long-term performance in maintaining bounded Hamiltonian errors and saving computational cost when appropriate proper time steps are adopted.

Segregation of Forecast Errors in the Planetary Boundary Layer Parameterization Over the State of Odisha and Neighboring Regions in India During Summer Monsoon Season

Planetary boundary layer parametrization (PBL) is a key factor influencing weather forecast skills. This article provides a quantitative illustration of the segregation of forecast errors and their growth arising from different PBLs of the Weather Research and Forecasting (WRF) model. The systematic (root mean square) components of forecast errors arising from four different PBLs of the WRF over the state of Odisha (India) and its surrounding regions are elucidated. Error characterizations are carried out for the forecast lead time up to 96 h (day-4) for two contrasting monsoon seasons, i.e., 2013 (normal) and 2014 (deficit). A total of 1112 simulations are carried out for each initial condition, i.e., May 15 to September 29 for both monsoon seasons using four PBL schemes, i.e., Yonsei University (YSU), Mellor–Yamada–Nakanishi-Niino (MYNN), Asymmetric Convective Model version 2 (ACM2), and medium-range forecast (MRF). The overall results suggest the errors in thermodynamical variables (i.e., temperature and relative humidity) are large compared to the dynamical variable (i.e., wind). For the normal monsoon year (i.e., 2013), the MRF and MYNN exhibit the lowest root mean square error (RMSE) of temperature compared to ACM2 and YSU, whereas MRF (MYNN) shows the lowest (highest) error growth at 24–48 h (72–96 h). The deficit year (2014) has a higher temperature error compared to that of the normal monsoon year (2013), which might be due to frequent monsoon break periods. The spatial distribution of wind exhibits the lowest systematic error for MRF with lead time up to 48 h. The subsequent decrease (increase) of convergence (divergence) of error flux over northern Odisha and increase (decrease) of the same over southern Odisha suggests that the error propagation occurs from north to south. In general, both the convergence and divergence of error energy are found to be weak in MRF and MYNN, attributable to the lower error growth rate and hence the smaller systematic errors compared to ACM2 and YSU for both these monsoon seasons. It is also found that the systematic component of the linear (nonlinear) error growth rate is contributed by the physics (dynamics) components of the model. These findings will provide guidance for the model community and operational agencies to make an optimal choice of PBL parameterizations, particularly for the monsoon forecast.

Self-aided SINS for spiral-diving human-occupied vehicle in midwater

PurposeMotivated by the problems that the positioning error of strap-down inertial navigation system (SINS) accumulates over time and few sensors are available for midwater navigation, this paper aims to propose a self-aided SINS scheme for the spiral-diving human-occupied vehicle (HOV) based on the characteristics of maneuvering pattern and SINS error propagation.Design/methodology/approachFirst, the navigation equations of SINS are simultaneously executed twice with the same inertial measurement unit (IMU) data as input to obtain two sets of SINS. Then, to deal with the horizontal velocity provided by one SINS, a delay-correction high-pass filter without phase shift and amplitude attenuation is designed. Finally, the horizontal velocity after processing is used to integrate with other SINS.FindingsSimulation results indicate that the horizontal positioning error of the proposed scheme is less than 0.1 m when an HOV executes spiral diving to 7,000 meters under the sea and it is inherently able to estimate significant sensors biases.Originality/valueThe proposed scheme can provide a precise navigation solution without error growth for spiral-diving HOV on the condition that only IMU is required as a navigation sensor.

Fitting latent growth models with small sample sizes and non-normal missing data

This study investigates the performance of robust maximum likelihood (ML) estimators when fitting and evaluating small sample latent growth models with non-normal missing data. Results showed that the robust ML methods could be used to account for non-normality even when the sample size is very small (e.g., N < 100). Among the robust ML estimators, “MLR” was the optimal choice, as it was found to be robust to both non-normality and missing data while also yielding more accurate standard error estimates and growth parameter coverage. However, the choice “MLMV” produced the most accurate p values for the χ2 test statistic under conditions studied. Regarding the goodness of fit indices, as sample size decreased, all three fit indices studied (i.e., comparative fit index, root mean square error of approximation, and standardized root mean square residual) exhibited worse fit. When the sample size was very small (e.g., N < 60), the fit indices would imply that a proposed model fit poorly, when this might not be actually the case in the population.