Time-varying characteristics of saturated hydraulic conductivity in grassed swales based on the ensemble Kalman filter algorithm -A case study of two long-running swales in Netherlands.

Saturated hydraulic conductivity (Ks) of the filler layer in grassed swales are varying in the changing environment. In most of the hydrological models, Ks is assumed as constant or decrease with a clogging factor. However, the Ks measured on site cannot be the input of the hydrological model directly. Therefore, in this study, an Ensemble Kalman Filter (EnKF) based approach was carried out to estimate the Ks of the whole systems in two monitored grassed swales at Enschede and Utrecht, the Netherlands. The relationship between Ks and possible influencing factors (antecedent dry period, temperature, rainfall, rainfall duration, total rainfall and seasonal factors) were studied and a Multivariate nonlinear function was established to optimize the hydrological model. The results revealed that the EnKF method was satisfying in the Ks estimation, which showed a notable decrease after long-term operation, but revealed a recovery in summer and winter. After the addition of Multivariate nonlinear function of the Ks into hydrological model, 63.8% of the predicted results were optimized among the validation events, and compared with constant Ks. A sensitivity analysis revealed that the effect of each influencing factors on the Ks varies depending on the type of grassed swale. However, these findings require further investigation and data support.

Interpretable physiological forecasting in the ICU using constrained data assimilation and electronic health record data.

OBJECTIVE: Prediction of physiological mechanics are important in medical practice because interventions are guided by predicted impacts of interventions. But prediction is difficult in medicine because medicine is complex and difficult to understand from data alone, and the data are sparse relative to the complexity of the generating processes. Computational methods can increase prediction accuracy, but prediction with clinical data is difficult because the data are sparse, noisy and nonstationary. This paper focuses on predicting physiological processes given sparse, non-stationary, electronic health record data in the intensive care unit using data assimilation (DA), a broad collection of methods that pair mechanistic models with inference methods. METHODS: A methodological pipeline embedding a glucose-insulin model into a new DA framework, the constrained ensemble Kalman filter (CEnKF) to forecast blood glucose was developed. The data include tube-fed patients whose nutrition, blood glucose, administered insulins and medications were extracted by hand due to their complexity and to ensure accuracy. The model was estimated using an individual's data as if they arrived in real-time, and the estimated model was run forward producing a forecast. Both constrained and unconstrained ensemble Kalman filters were estimated to compare the impact of constraints. Constraint boundaries, model parameter sets estimated, and data used to estimate the models were varied to investigate their influence on forecasting accuracy. Forecasting accuracy was evaluated according to mean squared error between the model-forecasted glucose and the measurements and by comparing distributions of measured glucose and forecast ensemble means. RESULTS: The novel CEnKF produced substantial gains in robustness and accuracy while minimizing the data requirements compared to the unconstrained ensemble Kalman filters. Administered insulin and tube-nutrition were important for accurate forecasting, but including glucose in IV medication delivery did not increase forecast accuracy. Model flexibility, controlled by constraint boundaries and estimated parameters, did influence forecasting accuracy. CONCLUSION: Accurate and robust physiological forecasting with sparse clinical data is possible with DA. Introducing constrained inference, particularly on unmeasured states and parameters, reduced forecast error and data requirements. The results are not particularly sensitive to model flexibility such as constraint boundaries, but over or under constraining increased forecasting errors.

Analysis of COVID-19 in Japan with extended SEIR model and ensemble Kalman filter.

We introduce an extended SEIR infectious disease model with data assimilation for the study of the spread of COVID-19. In this framework, undetected asymptomatic and pre-symptomatic cases are taken into account, and the impact of their uncertain proportion is fully investigated. The standard SEIR model does not consider these populations, while their role in the propagation of the disease is acknowledged. An ensemble Kalman filter is implemented to assimilate reliable observations of three compartments in the model. The system tracks the evolution of the effective reproduction number and estimates the unobservable subpopulations. The analysis is carried out for three main prefectures of Japan and for the entire country of Japan. For these four communities, our estimated effective reproduction numbers are more stable than the corresponding ones estimated by a different method (Toyokeizai). We also perform sensitivity tests for different values of some uncertain medical parameters, like the relative infectivity of symptomatic/asymptomatic cases. The regional analysis results suggest the decreasing efficiency of the states of emergency.

Data-assimilation and state estimation for contact-based spreading processes using the ensemble kalman filter: Application to COVID-19.

The main aim of the present paper is threefold. First, it aims at presenting an extended contact-based model for the description of the spread of contagious diseases in complex networks with consideration of asymptomatic evolutions. Second, it presents a parametrization method of the considered model, including validation with data from the actual spread of COVID-19 in Germany, Mexico and the United States of America. Third, it aims at showcasing the fruitful combination of contact-based network spreading models with a modern state estimation and filtering technique to (i) enable real-time monitoring schemes, and (ii) efficiently deal with dimensionality and stochastic uncertainties. The network model is based on an interpretation of the states of the nodes as (statistical) probability densities samples, where nodes can represent individuals, groups or communities, cities or countries, enabling a wide field of application of the presented approach.

Fetal Electrocardiogram Extraction from the Mother's Abdominal Signal Using the Ensemble Kalman Filter.

Fetal electrocardiogram (fECG) assessment is essential throughout pregnancy to monitor the wellbeing and development of the fetus, and to possibly diagnose potential congenital heart defects. Due to the high noise incorporated in the abdominal ECG (aECG) signals, the extraction of fECG has been challenging. And it is even a lot more difficult for fECG extraction if only one channel of aECG is provided, i.e., in a compact patch device. In this paper, we propose a novel algorithm based on the Ensemble Kalman filter (EnKF) for non-invasive fECG extraction from a single-channel aECG signal. To assess the performance of the proposed algorithm, we used our own clinical data, obtained from a pilot study with 10 subjects each of 20 min recording, and data from the PhysioNet 2013 Challenge bank with labeled QRS complex annotations. The proposed methodology shows the average positive predictive value (PPV) of 97.59%, sensitivity (SE) of 96.91%, and F1-score of 97.25% from the PhysioNet 2013 Challenge bank. Our results also indicate that the proposed algorithm is reliable and effective, and it outperforms the recently proposed extended Kalman filter (EKF) based algorithm.

A meteorologically adjusted ensemble Kalman filter approach for inversing daily emissions: A case study in the Pearl River Delta, China.

The conventional Ensemble Kalman filter (EnKF), which is now widely used to calibrate emission inventories and to improve air quality simulations, is susceptible to simulation errors of meteorological inputs, making accurate updates of high temporal-resolution emission inventories challenging. In this study, we developed a novel meteorologically adjusted inversion method (MAEInv) based on the EnKF to improve daily emission estimations. The new method combines sensitivity analysis and bias correction to alleviate the inversion biases caused by errors of meteorological inputs. For demonstration, we used the MAEInv to inverse daily carbon monoxide (CO) emissions in the Pearl River Delta (PRD) region, China. In the case study, 60% of the total CO simulation biases were associated with sensitive meteorological inputs, which would lead to the overestimation of daily variations of posterior emissions. Using the new inversion method, daily variations of emissions shrank dramatically, with the percentage change decreased by 30%. Also, the total amount of posterior CO emissions estimated by the MAEInv decreased by 14%, indicating that posterior CO emissions might be overestimated using the conventional EnKF. Model evaluations using independent observations revealed that daily CO emissions estimated by MAEInv better reproduce the magnitude and temporal patterns of ambient CO concentration, with a higher correlation coefficient (R, +37.0%) and lower normalized mean bias (NMB, -17.9%). Since errors of meteorological inputs are major sources of simulation biases for both low-reactive and reactive pollutants, the MAEInv is also applicable to improve the daily emission inversions of reactive pollutants.

Ensemble-Based Assimilation of Satellite All-Sky Microwave Radiances Improves Intensity and Rainfall Predictions for Hurricane Harvey (2017).

Ensemble-based data assimilation of radar observations across inner-core regions of tropical cyclones (TCs) in tandem with satellite all-sky infrared (IR) radiances across the TC domain improves TC track and intensity forecasts. This study further investigates potential enhancements in TC track, intensity, and rainfall forecasts via assimilation of all-sky microwave (MW) radiances using Hurricane Harvey (2017) as an example. Assimilating Global Precipitation Measurement constellation all-sky MW radiances in addition to GOES-16 all-sky IR radiances reduces the forecast errors in the TC track, rapid intensification (RI), and peak intensity compared to assimilating all-sky IR radiances alone, including a 24-hr increase in forecast lead-time for RI. Assimilating all-sky MW radiances also improves Harvey's hydrometeor fields, which leads to improved forecasts of rainfall after Harvey's landfall. This study indicates that avenues exist for producing more accurate forecasts for TCs using available yet underutilized data, leading to better warnings of and preparedness for TC-associated hazards in the future.

Sequential Data Assimilation of the Stochastic SEIR Epidemic Model for Regional COVID-19 Dynamics.

Newly emerging pandemics like COVID-19 call for predictive models to implement precisely tuned responses to limit their deep impact on society. Standard epidemic models provide a theoretically well-founded dynamical description of disease incidence. For COVID-19 with infectiousness peaking before and at symptom onset, the SEIR model explains the hidden build-up of exposed individuals which creates challenges for containment strategies. However, spatial heterogeneity raises questions about the adequacy of modeling epidemic outbreaks on the level of a whole country. Here, we show that by applying sequential data assimilation to the stochastic SEIR epidemic model, we can capture the dynamic behavior of outbreaks on a regional level. Regional modeling, with relatively low numbers of infected and demographic noise, accounts for both spatial heterogeneity and stochasticity. Based on adapted models, short-term predictions can be achieved. Thus, with the help of these sequential data assimilation methods, more realistic epidemic models are within reach.

Multiple Target Tracking Based on Multiple Hypotheses Tracking and Modified Ensemble Kalman Filter in Multi-Sensor Fusion.

In multi-sensor fusion (MSF), the integration of multi-sensor observation data with different observation errors to achieve more accurate positioning of the target has always been a research focus. In this study, a modified ensemble Kalman filter (EnKF) is presented to substitute the traditional Kalman filter (KF) in the multiple hypotheses tracking (MHT) to deal with the high nonlinearity that always shows up in multiple target tracking (MTT) problems. In addition, the multi-source observation data fusion is also realized by using the modified EnKF, which enables the low-precision observation data to be corrected by high-precision observation data, and the accuracy of the corrected data can be calibrated by the statistical information provided by the EnKF. Numerical studies are given to demonstrate the effectiveness of our proposed method and the results show that the MHT-EnKF method can achieve remarkable enhancement in dealing with nonlinear movement variation and positioning accuracy for MTT problems in MSF scenario.

Assimilating flow and level data into an urban drainage surrogate model for forecasting flows and overflows.

It is crucial to be able to forecast flows and overflows in urban drainage systems to build good and effective real-time control and warning systems. Due to computational constraints, it may often be unfeasible to employ detailed 1D hydrodynamic models for real-time purposes, and surrogate models can be used instead. In rural hydrology, forecast models are usually built or calibrated using long historical time series of, for example, flow or level observations, but such series are typically not available for the ever-changing urban drainage systems. In the current study, we therefore used a fast, reservoir-based surrogate forecast model constructed from a 1D hydrodynamic urban drainage model. Thus, we did not rely directly on historical time series data. Forecast models should preferably be able to update their internal states based on observations to ensure the best initial conditions for each forecast. We therefore used the Ensemble Kalman filter to update the surrogate model before each forecast. Water level or flow observations were assimilated into the model either directly, or indirectly using rating curves. The model forecasts were validated against observed flows and overflows. The results showed that model updating improved the forecasts up to 2 h ahead, but also that updating using water level observations resulted in better flow forecasts than assimilation based on flow data. Furthermore, updating with water level observations was insensitive to changes in the noise formulation used for the Ensemble Kalman filter, meaning that the method is suitable for operational settings where there is often little time and data for fine-tuning.

State and Parameter Estimation from Observed Signal Increments.

The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.

Concrete ensemble Kalman filters with rigorous catastrophic filter divergence.

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catastrophic filter divergence, whereby ensemble-state estimates explode to machine infinity, despite the true state remaining in a bounded region. In this article we provide a breakthrough insight into the phenomenon, by introducing a simple and natural forecast model that transparently exhibits catastrophic filter divergence under all ensemble methods and a large set of initializations. For this model, catastrophic filter divergence is not an artifact of numerical instability, but rather a true dynamical property of the filter. The divergence is not only validated numerically but also proven rigorously. The model cleanly illustrates mechanisms that give rise to catastrophic divergence and confirms intuitive accounts of the phenomena given in past literature.

Integrating remotely sensed surface water extent into continental scale hydrology.

In hydrological forecasting, data assimilation techniques are employed to improve estimates of initial conditions to update incorrect model states with observational data. However, the limited availability of continuous and up-to-date ground streamflow data is one of the main constraints for large-scale flood forecasting models. This is the first study that assess the impact of assimilating daily remotely sensed surface water extent at a 0.1° × 0.1° spatial resolution derived from the Global Flood Detection System (GFDS) into a global rainfall-runoff including large ungauged areas at the continental spatial scale in Africa and South America. Surface water extent is observed using a range of passive microwave remote sensors. The methodology uses the brightness temperature as water bodies have a lower emissivity. In a time series, the satellite signal is expected to vary with changes in water surface, and anomalies can be correlated with flood events. The Ensemble Kalman Filter (EnKF) is a Monte-Carlo implementation of data assimilation and used here by applying random sampling perturbations to the precipitation inputs to account for uncertainty obtaining ensemble streamflow simulations from the LISFLOOD model. Results of the updated streamflow simulation are compared to baseline simulations, without assimilation of the satellite-derived surface water extent. Validation is done in over 100 in situ river gauges using daily streamflow observations in the African and South American continent over a one year period. Some of the more commonly used metrics in hydrology were calculated: KGE', NSE, PBIAS%, R2, RMSE, and VE. Results show that, for example, NSE score improved on 61 out of 101 stations obtaining significant improvements in both the timing and volume of the flow peaks. Whereas the validation at gauges located in lowland jungle obtained poorest performance mainly due to the closed forest influence on the satellite signal retrieval. The conclusion is that remotely sensed surface water extent holds potential for improving rainfall-runoff streamflow simulations, potentially leading to a better forecast of the peak flow.

A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment.

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

A general description of criticality in neural network models.

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.

Constraint optimization of an integrated production model utilizing history matching and production forecast uncertainty through the ensemble Kalman filter.

The calibration of reservoir models using production data can enhance the reliability of predictions. However, history matching often leads to only a few matched models, and the original geological interpretation is not always preserved. Therefore, there is a need for stochastic methodologies for history matching. The Ensemble Kalman Filter (EnKF) is a well-known Monte Carlo method that updates reservoir models in real time. When new production data becomes available, the ensemble of models is updated accordingly. The initial ensemble is created using the prior model, and the posterior probability function is sampled through a series of updates. In this study, EnKF was employed to evaluate the uncertainty of production forecasts for a specific development plan and to match historical data to a real field reservoir model. This study represents the first attempt to combine EnKF with an integrated model that includes a genuine oil reservoir, actual production wells, a surface choke, a surface pipeline, a separator, and a PID pressure controller. The research optimized a real integrated production system, considering the constraint that there should be no slug flow at the inlet of the separator. The objective function was to maximize the net present value (NPV). Geological data was used to model uncertainty using Sequential Gaussian Simulation. Porosity scenarios were generated, and conditioning the porosity to well data yielded improved results. Ensembles were employed to balance accuracy and efficiency, demonstrating a reduction in porosity uncertainty due to production data. This study revealed that utilizing a PID pressure controller for the production separator can enhance oil production by 59% over 20 years, resulting in the generation of 2.97 million barrels of surplus oil in the field and significant economic gains.

Prediction and control of cholera outbreak: Study case of Cameroon.

This paper deals with the problem of the prediction and control of cholera outbreak using real data of Cameroon. We first develop and analyze a deterministic model with seasonality for the cholera, the novelty of which lies in the incorporation of undetected cases. We present the basic properties of the model and compute two explicit threshold parameters R¯0 and R_0 that bound the effective reproduction number R0, from below and above, that is R_0≤R0≤R¯0. We prove that cholera tends to disappear when R¯0≤1, while when R_0>1, cholera persists uniformly within the population. After, assuming that the cholera transmission rates and the proportions of newly symptomatic are unknown, we develop the EnKf approach to estimate unmeasurable state variables and these unknown parameters using real data of cholera from 2014 to 2022 in Cameroon. We use this result to estimate the upper and lower bound of the effective reproduction number and reconstructed active asymptomatic and symptomatic cholera cases in Cameroon, and give a short-term forecasts of cholera in Cameroon until 2024. Numerical simulations show that (i) the transmission rate from free Vibrio cholerae in the environment is more important than the human transmission and begin to be high few week after May and in October, (ii) 90% of newly cholera infected cases that present the symptoms of cholera are not diagnosed and (iii) 60.36% of asymptomatic are detected at 14% and 86% of them recover naturally. The future trends reveals that an outbreak appeared from July to November 2023 with the number of cases reported monthly peaked in October 2023. An impulsive control strategy is incorporated in the model with the aim to avoid or prevent the cholera outbreak. In the first year of monitoring, we observed a reduction of more than 75% of incidences and the disappearance of the peaks when no control are available in Cameroon. A second monitoring of control led to a further reduction of around 60% of incidences the following year, showing how impulse control could be an effective means of eradicating cholera.

Coupling an agent-based model and an ensemble Kalman filter for real-time crowd modelling.

Agent-based modelling has emerged as a powerful tool for modelling systems that are driven by discrete, heterogeneous individuals and has proven particularly popular in the realm of pedestrian simulation. However, real-time agent-based simulations face the challenge that they will diverge from the real system over time. This paper addresses this challenge by integrating the ensemble Kalman filter (EnKF) with an agent-based crowd model to enhance its accuracy in real time. Using the example of Grand Central Station in New York, we demonstrate how our approach can update the state of an agent-based model in real time, aligning it with the evolution of the actual system. The findings reveal that the EnKF can substantially improve the accuracy of agent-based pedestrian simulations by assimilating data as they evolve. This approach not only offers efficiency advantages over existing methods but also presents a more realistic representation of a complex environment than most previous attempts. The potential applications of this method span the management of public spaces under 'normality' to exceptional circumstances such as disaster response, marking a significant advancement for real-time agent-based modelling applications.

Identification of factors impacting on the transmission and mortality of COVID-19.

This paper proposes a dynamic infectious disease model for COVID-19 daily counts data and estimate the model using the Langevinized EnKF algorithm, which is scalable for large-scale spatio-temporal data, converges to the right filtering distribution, and is thus suitable for performing statistical inference and quantifying uncertainty for the underlying dynamic system. Under the framework of the proposed dynamic infectious disease model, we tested the impact of temperature, precipitation, state emergency order and stay home order on the spread of COVID-19 based on the United States county-wise daily counts data. Our numerical results show that warm and humid weather can significantly slow the spread of COVID-19, and the state emergency and stay home orders also help to slow it. This finding provides guidance and support to future policies or acts for mitigating the community transmission and lowering the mortality rate of COVID-19.

A Stochastic Approximation-Langevinized Ensemble Kalman Filter Algorithm for State Space Models with Unknown Parameters.

Inference for high-dimensional, large scale and long series dynamic systems is a challenging task in modern data science. The existing algorithms, such as particle filter or sequential importance sampler, do not scale well to the dimension of the system and the sample size of the dataset, and often suffers from the sample degeneracy issue for long series data. The recently proposed Langevinized ensemble Kalman filter (LEnKF) addresses these difficulties in a coherent way. However, it cannot be applied to the case that the dynamic system contains unknown parameters. This article proposes the so-called stochastic approximation-LEnKF for jointly estimating the states and unknown parameters of the dynamic system, where the parameters are estimated on the fly based on the state variables simulated by the LEnKF under the framework of stochastic approximation Markov chain Monte Carlo (MCMC). Under mild conditions, we prove its consistency in parameter estimation and ergodicity in state variable simulations. The proposed algorithm can be used in uncertainty quantification for long series, large scale, and high-dimensional dynamic systems. Numerical results indicate its superiority over the existing algorithms. We employ the proposed algorithm in state-space modeling of the sea surface temperature with a long short term memory (LSTM) network, which indicates its great potential in statistical analysis of complex dynamic systems encountered in modern data science. Supplementary materials for this article are available online.