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Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact Bayesian formulae for the state estimation of high-dimensional systems. In this paper, an analytically tractable mathematical framework for continuous-in-time Lagrangian data assimilation is developed. It preserves the nonlinearity in the observational processes while approximating the forecast model of the underlying flow field using linear stochastic models (LSMs). A critical feature of the framework is that closed analytic formulae are available for solving the posterior distribution, which facilitates mathematical analysis and numerical simulations. First, an efficient iterative algorithm is developed in light of the analytically tractable statistics. It accurately estimates the parameters in the LSMs using only a small number of the observed tracer trajectories. Next, the framework facilitates the development of several computationally efficient approximate filters and the quantification of the associated uncertainties. A cheap approximate filter with a diagonal posterior covariance derived from the asymptotic analysis of the posterior estimate is shown to be skillful in recovering incompressible flows. It is also demonstrated that randomly selecting a small number of tracers at each time step as observations can reduce the computational cost while retaining the data assimilation accuracy. Finally, based on a prototype model in geophysics, the framework with LSMs is shown to be skillful in filtering nonlinear turbulent flow fields with strong non-Gaussian features. • Linear stochastic models are proposed to accelerate Lagrangian data assimilation. • An iterative algorithm is developed to estimate the parameters in the models. • The models are skillful in filtering nonlinear turbulent flow fields. • A novel random tracer selection strategy for data assimilation is proposed. [ABSTRACT FROM AUTHOR]

Knee pain is the most common and disabling symptom in Osteoarthritis (OA). Joint pain is a late manifestation of the OA. In earlier stages of the disease changes in joint structures are shown. Also, formation of bony osteophytes, cartilage degradation, and joint space reduction which are some of the most common, among others. The main goal of this study is to associate radiological features with the joint pain symptom. Univariate and multivariate studies were performed using Bioinformatics tools to determine the relationship of future pain with early radiological evidence of the disease. All data was retrieved from the Osteoarthritis Initiative repository (OAI). A case-control study was done using available data from participants in OAI database. Radiological data was assessed with different OAI radiology groups. We have used quantitative and semi-quantitative scores to measure two different relations between radiological data in three different time points. The goal was to track the appearance and prevalence of pain as a symptom. All predictive models were statistically significant (P ≤ 0,05), obtaining the receiving operating characteristic (ROC) curves with their respective area under the curves (AUC) of 0.6516, 0.6174, and 0.6737 for T-0, T-1 and T-2 in quantitative analysis. For semi-quantitative an AUC of 0.6865, 0.6486, and 0.6406 for T-0, T-1 and T-2. The models obtained in the Bioinformatics study suggest that early joint structure changes can be associated with future joint pain. An image based biomarker that could predict future pain, measured in early OA stages, could become a useful tool to improve the quality of life of people dealing OA. [ABSTRACT FROM AUTHOR]

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf’s joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h.

Since the prime days of stochastic hydrology back in 1960s, autoregressive (AR) and moving average (MA) models (as well as their extensions) have been widely used to simulate hydrometeorological processes. Initially, AR(1) or Markovian models with Gaussian noise prevailed due to their conceptual and mathematical simplicity. However, the ubiquitous skewed behavior of most hydrometeorological processes, particularly at fine time scales, necessitated the generation of synthetic time series to also reproduce higher-order moments. In this respect, the former schemes were enhanced to preserve skewness through the use of non-Gaussian white noise— a modification attributed to Thomas and Fiering (TF). Although preserving higher-order moments to approximate a distribution is a limited and potentially risky solution, the TF approach has become a common choice in operational practice. In this study, almost half a century after its introduction, we reveal an important flaw that spans over all popular linear stochastic models that employ non-Gaussian white noise. Focusing on the Markovian case, we prove mathematically that this generating scheme provides bounded dependence patterns, which are both unrealistic and inconsistent with the observed data. This so-called “envelope behavior” is amplified as the skewness and correlation increases, as demonstrated on the basis of real-world and hypothetical simulation examples.

The monthly maximum of the 24-h average time-series data of ambient air quality—sulphur dioxide (SO2), nitrogen dioxide (NO2) and suspended particulate matter (SPM) concentration monitored at the six National Ambient Air Quality Monitoring (NAAQM) stations in Delhi, was analysed using Box–Jenkins modelling approach (Box et al. ). Univariate linear stochastic models were developed to examine the degree of prediction possible for situations where only the past record of pollutant data are available. In all, 18 models were developed, three for each station for each of the respective pollutant. The model evaluation statistics suggest that considerably satisfactory real-time forecasts of pollution concentrations can be generated using the Box–Jenkins approach. The developed models can be used to provide short-term, real-time forecasts of extreme air pollution concentrations for the Air Quality Control Region (AQCR) of Delhi City, India. [ABSTRACT FROM AUTHOR]

Uncertainty-aware design and management of urban water systems lies on the generation of synthetic series that should precisely reproduce the distributional and dependence properties of residential water demand process (i.e., significant deviation from Gaussianity, intermittent behaviour, high spatial and temporal variability and a variety of dependence structures) at various temporal and spatial scales of operational interest. This is of high importance since these properties govern the dynamics of the overall system, while prominent simulation methods, such as pulse-based schemes, address partially this issue by preserving part of the marginal behaviour of the process (e.g., low-order statistics) or neglecting the significant aspect of temporal dependence. In this work, we present a single stochastic modelling strategy, applicable at any fine time scale to explicitly preserve both the distributional and dependence properties of the process. The strategy builds upon the Nataf's joint distribution model and particularly on the quantile mapping of an auxiliary Gaussian process, generated by a suitable linear stochastic model, to establish processes with the target marginal distribution and correlation structure. The three real-world case studies examined, reveal the efficiency (suitability) of the simulation strategy in terms of reproducing the variety of marginal and dependence properties encountered in water demand records from 1-min up to 1-h. [ABSTRACT FROM AUTHOR]

Since the prime days of stochastic hydrology back in 1960s, autoregressive (AR) and moving average (MA) models (as well as their extensions) have been widely used to simulate hydrometeorological processes. Initially, AR(1) or Markovian models with Gaussian noise prevailed due to their conceptual and mathematical simplicity. However, the ubiquitous skewed behavior of most hydrometeorological processes, particularly at fine time scales, necessitated the generation of synthetic time series to also reproduce higher-order moments. In this respect, the former schemes were enhanced to preserve skewness through the use of non-Gaussian white noise— a modification attributed to Thomas and Fiering (TF). Although preserving higher-order moments to approximate a distribution is a limited and potentially risky solution, the TF approach has become a common choice in operational practice. In this study, almost half a century after its introduction, we reveal an important flaw that spans over all popular linear stochastic models that employ non-Gaussian white noise. Focusing on the Markovian case, we prove mathematically that this generating scheme provides bounded dependence patterns, which are both unrealistic and inconsistent with the observed data. This so-called “envelope behavior” is amplified as the skewness and correlation increases, as demonstrated on the basis of real-world and hypothetical simulation examples. [ABSTRACT FROM AUTHOR]