Proposed Data Assimilation Research Articles

A framework of data assimilation for wind flow fields by physics-informed neural networks

Various types of measurement techniques, such as Light Detection and Ranging (LiDAR) devices, anemometers, and wind vanes, are extensively utilized in wind energy to characterize the inflow. However, these methods typically gather data at limited points within local wind fields, capturing only a fraction of the wind field’s characteristics at wind turbine sites, thus hindering detailed wind field analysis. This study introduces a framework using Physics-informed Neural Networks (PINNs) to assimilate diverse sensor data types. This includes line-of-sight (LoS) wind speed, velocity magnitude and direction, velocity components, and pressure. Moreover, the parameterized Navier–Stokes (N–S) equations are integrated as physical constraints, ensuring that the neural networks accurately represent atmospheric flow dynamics. The framework accounts for the turbulent nature of atmospheric boundary layer flow by including artificial eddy viscosity in the network outputs, enhancing the model’s ability to learn and accurately depict large-scale flow structures. The reconstructed flow field and the effective wind speed are in good agreement with the actual data. Furthermore, a transfer learning strategy is employed for the online deployment of pre-trained PINN, which requires less time than that of the actual physical flow. This capability allows the framework to reconstruct wind flow fields in real time based on live data. In the demo cases, the maximum error between the effective wind speed reconstructed online and the actual value at the wind turbine site is only 3.7%. The proposed data assimilation framework provides a universal tool for reconstructing spatiotemporal wind flow fields using various measurement data. Additionally, it presents a viable approach for the online assimilation of real-time measurements. To facilitate the utilization of wind energy, our framework’s source code is openly accessible.

Data assimilation with machine learning for dynamical systems: Modelling indoor ventilation

Data assimilation is a method of combining physical observations with prior knowledge (for instance, a computational simulation) in order to produce an improved estimate of the state of a system; that is, improved over what the physical observations or the computational simulation, alone, could offer. Recently, machine learning techniques have been deployed in order to address the significant computational burden that is associated with the procedures involved in data assimilation.In this paper we propose an approach that uses a non-intrusive reduced-order model (NIROM) as a surrogate for a high-resolution model thereby saving computational effort. The mismatch between observations and the surrogate model is propagated forwards and backwards in time in a manner similar to 4D-variational data assimilation methods. The observations and prior are reconciled in a new way which takes full advantage of the neural network used in the NIROM and also means that there is no need to form the sensitivities explicitly when propagating the mismatch. Instead, the observations are part of the input and output of the network. The key advantages of this data assimilation approach are its simplicity (as we can avoid differentiating the forward model and bypass the use of an optimisation method), and its ability to integrate with control and uncertainty quantification methodologies.Modelling the air quality in a school classroom is the test case for our demonstration. After comparing the proposed data assimilation approach with 4D Variational Data Assimilation, we investigate two scenarios. The first of these is a dual-twin type experiment, for which the proposed approach is shown to perform very well, and the second is a test case which assimilates predictions from the NIROM with observations collected from a classroom in Houndsfield Primary School.

Contaminant source and aquifer characterization: An application of ES-MDA demonstrating the assimilation of geophysical data

Contaminant source and aquifer characterization (CSAC) is critical in groundwater pollution evaluation and remediation. The ensemble smoother with multiple data assimilation (ES-MDA) is utilized to jointly identify contaminant source information and hydraulic conductivities by assimilating time-lapse electrical resistivity tomography (ERT) data. In a synthetic profile with a time-varying release history in a heterogeneous aquifer, we verify the performance of the proposed data assimilation framework. The results show that the CSAC problem could be handled by the proposed approach. The time-varying release history and the high permeability area can be identified with adequate time-lapse ERT measurements. Further reproduction of the evolution of the plume after CSAC also shows consistency with the reference plume. The poor conditioning inversion caused by the filter inbreeding is analyzed by comparing four scenarios with different apparent resistivity measurements. Furthermore, we also evaluate the impact of uncertainties in the petrophysical properties and geophysical observations on our data assimilation framework. The results show that the proposed ES-MDA data assimilation framework could provide a convincing inversion of the time-varying release history and hydraulic conductivities.

A Novel Data Assimilation-Based Real-Time State Estimation Method for Gas Influx Profiling During Riser Gas Events

AbstractRiser gas events during offshore drilling operations are hazardous and challenging to control. Therefore, knowledge of the gas influx sizes and distributions in a marine drilling riser is critical for the selection of riser gas handling methods and the estimation of risks of riser gas unloading. An extended Kalman filter-based data assimilation method is developed and evaluated for the real-time estimation of gas influx rates and void fraction distributions in a riser during riser gas handling. Full-scale experiments were conducted in this study for the evaluation of the proposed data assimilation method. An offshore well, which consists of a marine drilling riser and a wellbore below the subsea blowout preventer, was simulated by a 1572-m-deep experimental well. Real-time measurement data, including surface and downhole pressures, pump rates, and liquid outflow rates, were used to estimate the downhole gas influx rates using the Kalman filter. An online calibrated drift-flux model based on data assimilation is used to estimate the distributions of void fractions in the riser over time. The measurement data from a gas flowmeter and the distributed fiber-optic sensing were used to validate the estimation results, and satisfying performance was seen from the presented method. This study proposed a novel data assimilation-based state estimation method by maximizing the use of measurement data of different types from the available managed pressure drilling systems. This method enables the more accurate estimation and prediction of gas behaviors in a riser and helps to facilitate real-time decision-making during riser gas handling.

Regulating the time of the crop model clock: A data assimilation framework for regions with high phenological heterogeneity

in crop growth data assimilation systems, the mismatch between simulated and observed phenology significantly deteriorates the performance of crop growth modeling. This situation may be more severe for smallholder farmers-managed fields, where the phenological heterogeneity was high even when climate condition was relatively uniform. Previous studies investigated the non-sequential methods to retrospectively assimilate historical phenology observations. However, approaches to dynamically assimilating phenological measurements through sequential data assimilation methods remain unexplored one of the most intractable challenges of dynamic phenology assimilation is that a considerable proportion of model parameters and variables are entangled with phenology, therefore simply assimilating phenological measurements could disturb the model clock. This study aims to establish a robust crop data assimilation framework capable of assimilating phenological measurements in real time without disturbing the model clock the framework used an open-source version of the AquaCrop model to simulate crop growth and used the ensemble Kalman filter (EnKF) to assimilate observations sequentially. A parameter refresh method was proposed to restore the phenological consistency of model parameters after updating the phenology state. Assimilation strategies with different observation types and compositions of state vectors were designed after a global sensitivity analysis of model parameters. These strategies were evaluated through the Observing System Simulation Experiments (OSSE), and the selected strategies were tested in a real-world case. the results of the OSS Experiments show that the phenological mismatch problem greatly affects crop growth simulation, and this mismatch could not be narrowed effectively by assimilating non-phenological observations. Assimilating phenological measurements with the proposed parameters refresh method and assimilation strategies closed this mismatch and produced better performance compared to the Restart-EnKF method. In the real-world paddy rice case, assimilating phenology with the proposed strategies significantly improved yield estimation in low-yield plots (less than 4 ton/ha) compared to assimilating canopy cover (CC) alone, with an R2 increase from 0.07 to 0.48. Assimilating CC, biomass and phenology simultaneously produced the best yield estimation for all plots, with R2 = 0.57 and RMSE = 1.00 ton/ha. assimilating phenology under a consistent model clock significantly improved yield estimation when the phenological heterogeneity of plots was high. the results highlight the effectiveness and robustness of the established data assimilation framework for dynamic crop growth simulation, indicating the potentials of the proposed data assimilation framework for regional in-season crop modeling and yield forecasting.

Mean wind flow reconstruction of a high-rise building based on variational data assimilation using sparse pressure measurements

The paper investigates the applicability of the variational data assimilation approach to reconstruct three-dimensional wind flows around a high-rise building model, and provides guidelines towards an efficient reconstruction. The objective is to determine the best distributed control parameters based on the Reynolds-averaged-Navier–Stokes (RANS) model coupled with pressure data. The strategy considers a distributed additive forcing control parameter, acting on the momentum equation and/or the transport equation of turbulent dissipations, where the closure is performed. To avoid unphysical solutions and accelerate the optimization convergence a Sobolev gradient descent regularization is proposed and compared with penalty techniques. The proposed data assimilation framework is applied to a realistic wind engineering estimation problem combining sparse wall pressure measurements with a routinely used industrial three-dimensional RANS numerical code. Results demonstrate that wall-pressure data is a meaningful enough piece of information to recover accurately the wake flow extension. A hybrid control parameter on the transport of the dissipation and the momentum equations leads to very precise results, whereas the Sobolev gradient descent direction gives efficient regularization and a fast convergence. These findings can be useful for future application of such a data assimilation technique to wind engineering problems.

A new Kalman filter approach for structural parameter tracking: Application to the monitoring of damaging structures tested on shaking-tables

In this paper, a new data assimilation framework for correcting finite element models from datasets acquired on-the-fly in low-frequency dynamics is presented. An Unscented Kalman filter algorithm is coupled with a modified Constitutive Relation Error (mCRE) observer, leading to a Modified Dual Kalman Filter algorithm (MDKF). Built as a Hermitian data-to-model distance written in the frequency domain enriched with a CRE residual accounting for model bias, the mCRE functional has shown interesting assets for model updating purposes, in particular enhanced convexity and robustness to measurement noise. The proposed data assimilation strategy integrates the latter through a metric change in the measurement update equation. It thus differs from classical nonlinear Kalman filtering for parameter estimation as the comparison between measurements and model predictions is achieved through the mCRE functional itself. Besides, the calibration of MDKF internal parameters is facilitated by a set of general guidelines that ensure the performance of the algorithm. The methodology is applied to two earthquake engineering examples. The performances of MDKF are first assessed using synthetic measurements from a plane frame subjected to random ground acceleration. Actual measurements from the SMART2013 benchmark are then assimilated in a real-time context to monitor the eigenfrequency drop of a reinforced-concrete structure submitted to a sequence of gradually damaging shaking-table tests. The nice correlation with (i) data-driven identification results, and (ii) sequential mCRE-based model updating results, illustrates the relevance of this new approach and suggests promising use of MDKF for on-the-fly adaptive control prospects and applications involving data-to-model interaction.

A new data assimilation method of recovering turbulent mean flow field at high Reynolds numbers

This paper proposes a new data assimilation method for recovering the high-fidelity turbulent mean flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion (POD-Inversion) data assimilation method. Aiming at flows including shock wave discontinuities or separation at high angles of attack, the proposed method can reconstruct the high-fidelity mean flow field combined with experimental force coefficients. We firstly perform the POD analysis to turbulent eddy viscosity fields computed by the SA model and obtain base POD modes. Then the POD coefficients are optimized by global optimization algorithm coupling with computational fluid dynamics (CFD) solver. The high-fidelity turbulent mean flow fields are recovered by several main modes, which can dramatically reduce dimensions of the system. The effectiveness of the method is verified by cases of transonic flow around the RAE2822 airfoil at high Reynolds numbers and the separated flow around S809 airfoil at high angles of attack. The results demonstrate that the proposed data assimilation method can recover turbulent flow fields which optimally match the experimental data, and can significantly reduce the error of aerodynamic coefficients. Furthermore, the proposed method can provide high-fidelity mean field data to establish turbulence models based on machine learning.

Wheat growth monitoring and yield estimation based on remote sensing data assimilation into the SAFY crop growth model

Crop growth monitoring and yield estimate information can be obtained via appropriate metrics such as the leaf area index (LAI) and biomass. Such information is crucial for guiding agricultural production, ensuring food security, and maintaining sustainable agricultural development. Traditional methods of field measurement and monitoring typically have low efficiency and can only give limited untimely information. Alternatively, methods based on remote sensing technologies are fast, objective, and nondestructive. Indeed, remote sensing data assimilation and crop growth modeling represent an important trend in crop growth monitoring and yield estimation. In this study, we assimilate the leaf area index retrieved from Sentinel-2 remote sensing data for crop growth model of the simple algorithm for yield estimation (SAFY) in wheat. The SP-UCI optimization algorithm is used for fine-tuning for several SAFY parameters, namely the emergence date (D0), the effective light energy utilization rate (ELUE), and the senescence temperature threshold (STT) which is indicative of biological aging. These three sensitive parameters are set in order to attain the global minimum of an error function between the SAFY model predicted values and the LAI inversion values. This assimilation of remote sensing data into the crop growth model facilitates the LAI, biomass, and yield estimation. The estimation results were validated using data collected from 48 experimental plots during 2014 and 2015. For the 2014 data, the results showed coefficients of determination (R2) of the LAI, biomass and yield of 0.73, 0.83 and 0.49, respectively, with corresponding root-mean-squared error (RMSE) values of 0.72, 1.13 t/ha and 1.14 t/ha, respectively. For the 2015 data, the estimated R2 values of the LAI, biomass, and yield were 0.700, 0.85, and 0.61, respectively, with respective RMSE values of 0.83, 1.22 t/ha, and 1.39 t/ha, respectively. The estimated values were found to be in good agreement with the measured ones. This shows high applicability of the proposed data assimilation scheme in crop monitoring and yield estimation. As well, this scheme provides a reference for the assimilation of remote sensing data into crop growth models for regional crop monitoring and yield estimation.

A newly proposed data assimilation framework to enhance predictions for reflood tests

Data assimilation is the process that can enhance the predictions by adjusting the input parameters inside their uncertainties range. In this study, the predicted results of the reflood tests, which were simulated by the SPACE code, were examined using the data assimilation technique. Crucially, a newly proposed data assimilation framework, STARU (Sampling meThod for highly non-lineAR system Uncertainty analysis), was developed. To propose the new data assimilation framework, we combined a new accuracy evaluation method with the Monte Carlo sampling algorithm to enhance the predictions for such a complex system as reflooding phenomena (many input parameters and non-linear responses). Subsequently, the outcomes of STARU were compared with the performances of data assimilation in PAPIRUS, a toolkit with many functions and modules for uncertainty analysis, which was developed by Heo and Kim (2015). Conversely, STARU only focused on solving problems with many parameters and highly non-linear systems in which implementation of the Monte Carlo sampling method is required because of the complexity of the systems. The main objectives of developing STARU are to reduce the computation time and increase the acceptance rate of the data assimilation process for complex systems. Consequently, we found that STARU effectively enhanced the data assimilation results for the reflood tests with higher acceptance rates and faster convergence. Furthermore, better improvements and more stable convergence of the system states were also observed, which effectively facilitated the search process for the most sensitive physical models in the predictions. In the future, STARU may be suitable for implementation in the other complex problems to calibrate the models, examine the uncertainty propagation, and study the sensitivity analysis.

The Joint Assimilation of Remotely Sensed Leaf Area Index and Surface Soil Moisture into a Land Surface Model

This work tests the hypothesis that jointly assimilating satellite observations of leaf area index and surface soil moisture into a land surface model improves the estimation of land vegetation and water variables. An Ensemble Kalman Filter is used to test this hypothesis across the Contiguous United States from April 2015 to December 2018. The performance of the proposed methodology is assessed for several modeled vegetation and water variables (evapotranspiration, net ecosystem exchange, and soil moisture) in terms of random errors and anomaly correlation coefficients against a set of independent validation datasets (i.e., Global Land Evaporation Amsterdam Model, FLUXCOM, and International Soil Moisture Network). The results show that the assimilation of the leaf area index mostly improves the estimation of evapotranspiration and net ecosystem exchange, whereas the assimilation of surface soil moisture alone improves surface soil moisture content, especially in the western US, in terms of both root mean squared error and anomaly correlation coefficient. The joint assimilation of vegetation and soil moisture information combines the results of individual vegetation and soil moisture assimilations and reduces errors (and increases correlations with the reference datasets) in evapotranspiration, net ecosystem exchange, and surface soil moisture simulated by the land surface model. However, because soil moisture satellite observations only provide information on the water content in the top 5 cm of the soil column, the impact of the proposed data assimilation technique on root zone soil moisture is limited. This work moves one step forward in the direction of improving our estimation and understanding of land surface interactions using a multivariate data assimilation approach, which can be particularly useful in regions of the world where ground observations are sparse or missing altogether.

Research on assimilation simulation of chlorophyll a concentrations in a virtual geographic environment

AbstractChlorophyll a concentration is an important parameter for the characterization of water quality and reflects the degree of eutrophication and the algae content in water bodies. Based on the idea of integrating models, data and visualization to build virtual geographic environments (VGEs), this article proposes a data assimilation scheme based on particle filters to assimilate the concentration of chlorophyll a in a VGE. The VGE is based on a modular concept to design function plugins and perform water quality assimilation simulations and GIS visualization. We conducted assimilation experiments using buoy observation data and forecast chlorophyll a concentrations. During the assimilation stage, the root mean square error and average relative error are notably reduced. The assimilation results indicate that the proposed data assimilation method can significantly improve accuracy in the prediction of chlorophyll a concentrations. An assimilation case study indicates that the VGE can be effectively used in water environment pollution and dynamic process simulations.

Integrating deep learning-based data assimilation and hydrogeophysical data for improved monitoring of DNAPL source zones during remediation

Data assimilation techniques allow the integration of multi-source data with physical modeling of dense nonaqueous phase liquid (DNAPL) source zones to monitor their evolution in time and thereby improve remediation efforts. The DNAPL source zone is governed by multiphase physics and its architecture is usually highly irregular and nonstationary. Traditional data assimilation methods use stationary models to describe these nonstationary DNAPL saturation fields, leading to significant errors in the estimation of unknown source zone architectures (SZAs). In this study, we propose a geostatistical data assimilation method to improve performance monitoring of DNAPL remediation. We estimate the DNAPL SZA after parameterizing the DNAPL saturation field using a deep learning method instead of a stationary statistical model. First, we train a convolutional variational autoencoder (CVAE) network to capture the physics of DNAPL infiltration and depletion. Then, we incorporate the CVAE network within the Ensemble Kalman filter (EnKF) to resolve the evolving DNAPL SZA by assimilating time-lapse hydrogeophysical measurements (i.e., oscillatory hydraulic tomography, downgradient dissolved DNAPL concentration, and electrical resistivity tomography). To assess the proposed CVAE-EnKF framework's performance, we conducted numerical experiments with evolving DNAPL SZAs in a 2D heterogeneous aquifer. Results show that the proposed framework significantly improved DNAPL saturation estimates throughout the source zone over time, compared to the standard EnKF method. CVAE-EnKF reduced the estimation error of DNAPL mass remediated by 51% from EnKF, along with better predictions of source zone longevity. It also better captured the morphology and center/spread of mass of the evolving remediated portions of the source zone and provided better estimates of pooled-DNAPL mass. Furthermore, the CVAE-EnKF method is more stable and converges faster than EnKF alone. Overall, the proposed data assimilation framework can improve real-time monitoring of DNAPL remediation and risk analysis.

Training a convolutional neural network to conserve mass in data assimilation

Abstract. In previous work, it was shown that the preservation of physical properties in the data assimilation framework can significantly reduce forecast errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high-dimensional prediction systems as found in Earth sciences. We, therefore, propose using a convolutional neural network (CNN) trained on the difference between the analysis produced by a standard ensemble Kalman filter (EnKF) and the QPEns to correct any violations of imposed constraints. In this paper, we focus on the conservation of mass and show that, in an idealised set-up, the hybrid of a CNN and the EnKF is capable of reducing analysis and background errors to the same level as the QPEns.

A dual state-parameter updating scheme using the particle filter and high-spatial-resolution remotely sensed snow depths to improve snow simulation

Snow varies widely in space and time over high mountain regions. Accurately representing the spatial distribution of snow water equivalent (SWE) is critically important for improving our understanding of snow accumulation and melt processes. Despite its importance, in situ observations are lacking in poorly gauged regions such as the headwater region of the Yangtze River (HRYR). Traditional remotely sensed retrievals are highly uncertain due to the effect of cloudiness (e.g., optical remote sensing-derived snow cover area) and the coarse spatial resolution (e.g., passive microwave remote sensing-derived snow depth). Hydrological modeling is a powerful way to understand the snow processes, but uncertainty still exists due to model deficiency and errors of forcing data. Assimilating high-spatial-resolution remotely sensed snow data into a snowmelt model may be potentially valuable for more accurate snow predictions. In this study, a high-spatial-resolution remotely sensed snow depth data set (500 m, derived by integrating snow cover area, land surface temperature, and passive microwave brightness temperature products) was assimilated into a snowmelt model within a particle filter (PF) assimilation framework, which updates both model state variables and parameters simultaneously. After assimilation, the time series of basin-averaged SWE estimation showed an appreciable improvement with respect to the simulation with the traditional calibration (TC) method, in terms of the Nash-Sutcliffe efficiency (NSE) coefficient increased by ~ 10–20% and root‐mean‐square error (RMSE) decreased by ~ 7–18%. The PF approach also greatly improved the spatial distribution of SWE estimation with RMSE decreased by ~ 15–30%. The SWE estimation from the PF was also comparable or even better than that from another assimilation scheme, namely, the direct insertion. Comparison with in situ snowfall data indicated that the simulated snowfall from the PF outperformed the TC, with RMSE decreased by ~ 15–32% and correlation coefficient increased by ~ 58–83%. Furthermore, the evolution of parameters suggested the applicability of the PF method with spatially variable parameters. With spatiotemporally variable parameters in the PF, the snow model could perfectly simulate the actual snow distribution particularly over high elevation regions where the average temperature was lower than 0 °C, while fixed parameters in the TC cannot simulate the variable snow distribution. The proposed data assimilation framework has large potential of improving the accuracy of snow prediction across poorly gauged high mountain areas.

Physics-informed neural networks for multiphysics data assimilation with application to subsurface transport

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge because of the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a multiphysics-informed deep neural network machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual deep neural networks (DNNs) to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head and concentration) of a physical system. Next, we jointly train these DNNs by minimizing the loss function that consists of the governing equations residuals in addition to the error with respect to measurement data. We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for the joint inversion of these parameter and states in a steady-state advection–dispersion problem. We study the accuracy of the proposed data assimilation approach with respect to the data size (i.e., the number of measured variables and the number of measurements of each variable), DNN size, and the complexity of the parameter field. We demonstrate that the physics-informed DNNs are significantly more accurate than the standard data-driven DNNs, especially when the training set consists of sparse data. We also show that the accuracy of parameter estimation increases as more different multiphysics variables are inverted jointly.

A data assimilation approach for groundwater parameter estimation under Bayesian maximum entropy framework

Spatial heterogeneity in groundwater system introduces significant challenges in groundwater modeling and parameter calibration. In order to mitigate the modeling uncertainty, data assiilation methods have been applied in the parameter estimation by assessing the uncertainties from both groundwater model and observations. In practice, the observations from groundwater system can be limited, and furthermore, boundary conditions and hydrogeological parameters, such as hydraulic conductivity, can be uncertain and biased. In order to handle the uncertain observations, this study applied the Bayesian maximum entropy (BME) for a data assimilation approach that integrates groundwater model, MODFLOW, and a variety of observations with uncertainties. In BME, no distributional assumption is imposed in the uncertain observations. We conducted numerical simulation with datasets of hard data of heads and hydrogeological parameters, uncertain head data on boundary, and uncertain hydrogeological parameters, i.e., hydraulic conductivity and storage coefficient. Three numerical scenarios with differerent combinations of datasets were conducted. Results show that the proposed data assimilation approach can gradually improve the modeling performance in the sense of lower mean squared errors over time. Moreover, the inclusion of uncertain observations can further improve the efficiency and accuracy in parameter estimation and hydraulic head prediction.

A data assimilation framework for data-driven flow models enabled by motion tomography

Autonomous underwater vehicles (AUVs) have become central to data collection for scientific and monitoring missions in the coastal and global oceans. To provide immediate navigational support for AUVs, computational data-driven flow models described as generic environmental models (GEMs) construct a map of the environment around AUVs. This paper proposes a data assimilation framework for the GEM to update the map using data collected by the AUVs. Unlike Eulerian data, Lagrangian data along the AUV trajectory carry time-integrated flow information. To facilitate assimilation of Lagrangian data into the GEM, the motion tomography method is employed to convert Lagrangian data of AUVs into an Eulerian spatial map of a flow field. This process allows assimilation of both Eulerian and Lagrangian data into the GEM to be incorporated in a unified framework, which introduces a nonlinear filtering problem. Considering potential complementarity of Eulerian and Lagrangian data in estimating spatial and temporal characteristics of flow, we develop a filtering method for estimation of the spatial and temporal parameters in the GEM. The observability is analyzed to verify the convergence of our filtering method. The proposed data assimilation framework for the GEM is demonstrated through simulations using two flow fields with different characteristics: (i) a double-gyre flow field and (ii) a flow field constructed by using real ocean surface flow observations from high-frequency radar.

A Mesoscopic Traffic Data Assimilation Framework for Vehicle Density Estimation on Urban Traffic Networks Based on Particle Filters

Traffic conditions can be more accurately estimated using data assimilation techniques since these methods incorporate an imperfect traffic simulation model with the (partial) noisy measurement data. In this paper, we propose a data assimilation framework for vehicle density estimation on urban traffic networks. To compromise between computational efficiency and estimation accuracy, a mesoscopic traffic simulation model (we choose the platoon based model) is employed in this framework. Vehicle passages from loop detectors are considered as the measurement data which contain errors, such as missed and false detections. Due to the nonlinear and non-Gaussian nature of the problem, particle filters are adopted to carry out the state estimation, since this method does not have any restrictions on the model dynamics and error assumptions. Simulation experiments are carried out to test the proposed data assimilation framework, and the results show that the proposed framework can provide good vehicle density estimation on relatively large urban traffic networks under moderate sensor quality. The sensitivity analysis proves that the proposed framework is robust to errors both in the model and in the measurements.

Towards operational 3D-Var assimilation of chlorophyll Biogeochemical-Argo float data into a biogeochemical model of the Mediterranean Sea

The emerging availability of Biogeochemical-Argo (BGC-Argo) float data creates new opportunities to combine models and observations in investigations of the interior structures and dynamics of marine ecosystems. An existing variational data assimilation scheme (3DVarBio) has been upgraded and coupled with the Copernicus Marine Environment Monitoring Service biogeochemical model of the Mediterranean Sea to assimilate BGC-Argo chlorophyll profile observations. Our results show that the assimilation of BGC-Argo float data is feasible. Moreover, the proposed data assimilation framework provides significant corrections to the chlorophyll concentrations and is able to consistently re-adjust the shapes of chlorophyll profiles during surface blooms occurring in winter vertically mixed conditions, and in the case of the summer deep chlorophyll maxima.Sensitivity analysis and diagnostic metrics have been applied to evaluate the impact of assimilation and the relevance of different factors of the 3DVarBio method. A key factor is the observation error that has been tuned on a monthly basis to incorporate the representation error. Different frequencies of the assimilation cycle have been tested: daily or 3-day assimilation fosters the highest skill performances despite the reduced impacts and the increase of computational burden. Considering the present size of the BGC-Argo Mediterranean network (about 15 floats) and the estimated non-homogeneous correlation radius length scale (15.2 km on average), the chlorophyll assimilation can constrain the phytoplankton dynamics along the whole water column over an area up to 10% of the Mediterranean Sea.