Data Assimilation Approach Research Articles

Combining neural networks and data assimilation to enhance the spatial impact of Argo floats in the Copernicus Mediterranean biogeochemical model

Abstract. Biogeochemical-Argo (BGC-Argo) float profiles provide substantial information on key vertical biogeochemical dynamics and have been successfully integrated in biogeochemical models via data assimilation approaches. Although BGC-Argo assimilation results have been encouraging, data scarcity remains a limitation with respect to their effective use in operational oceanography. To address availability gaps in the BGC-Argo profiles, an observing system experiment (OSE) that combines a neural network (NN) and data assimilation (DA) was performed here. A NN was used to reconstruct nitrate profiles, starting from oxygen profiles and associated Argo variables (pressure, temperature, and salinity), while a variational data assimilation scheme (3DVarBio) was upgraded to integrate BGC-Argo and reconstructed observations in the Copernicus Mediterranean operational forecast system (MedBFM). To ensure the high quality of oxygen data, a post-deployment quality control method was developed with the aim of detecting and eventually correcting potential sensors drift. The Mediterranean OSE features three different set-ups: a control run without assimilation; a multivariate run with assimilation of BGC-Argo chlorophyll, nitrate, and oxygen; and a multivariate run that also assimilates reconstructed observations. The general improvement in the skill performance metrics demonstrated the feasibility of integrating new variables (oxygen and reconstructed nitrate). Major benefits have been observed with respect to reproducing specific biogeochemical-process-based dynamics such as the nitracline dynamics, primary production, and oxygen vertical dynamics. The assimilation of BGC-Argo nitrate corrects a generally positive bias of the model in most of the Mediterranean areas, and the addition of reconstructed profiles makes the corrections even stronger. The impact of enlarged nitrate assimilation propagates to ecosystem processes (e.g. primary production) at a basin-wide scale, demonstrating the importance of the assimilation of BGC-Argo profiles in forecasting the biogeochemical ocean state.

Real-time data assimilation for the thermodynamic modeling of cryogenic storage tanks

The thermal management of cryogenic storage tanks requires advanced control strategies to minimize the boil-off losses produced by heat leakages and sloshing-enhanced heat and mass transfer. This work presents a data-assimilation approach to calibrate a 0D thermodynamic model for cryogenic fuel tanks from data collected in real time from multiple tanks. The model combines energy and mass balance between three control volumes (the ullage vapor, the liquid, and the solid tank) with an Artificial Neural Network (ANN) for predicting the heat transfer coefficients from the current tank state.The proposed approach combines ideas from traditional data assimilation and multi-environment reinforcement learning, where an agent’s training (model assimilation) is carried out simultaneously on multiple environments (systems). The real-time assimilation uses a mini-batch version of the Limited-memory Broyden–Fletcher–Goldfarb–Shanno with bounds (L-BFGS-B) and adjoint-based gradient computation for solving the underlying optimization problem. The approach is tested on synthetic datasets simulating multiple tanks undergoing different operation phases (pressurization, hold, long-term storage, and sloshing). The results show that the assimilation is robust against measurement noise and uses it to explore the parameter space further. Moreover, the work shows that simultaneously sampling from multiple environments accelerates the assimilation.

Development of a multi-level factorial data assimilation approach for groundwater contaminant sources identification

The ensemble Kalman filter (EnKF) is recognized as a widely used approach for groundwater contamination sources (GCSs) parameters identification. The identification accuracy is affected by the quantification of sources of uncertainty (such as random disturbances on model inputs and measurements) in the assimilation process, but few studies have revealed the contributions of different sources of uncertainty on identification accuracy. To this end, this study developed an innovative multi-level factorial data assimilation (MFDA) approach, which integrates ensemble Kalman filtering and multi-level factorial analysis, to comprehensively reveal the impact of sources of uncertainty on the GCSs parameters identification accuracy for the first time. Not only did it explore the direct impact of individual sources of uncertainty on the GCSs parameters identification accuracy, more importantly, it also revealed the composite ones from multi-parameter interactions among these sources of uncertainty. The developed MFDA approach quantified the contributions of multiple sources of uncertainty, including model input data error (i.e. precipitation), model parameter error (i.e. hydraulic conductivity), contaminant concentration measurements error, and ensemble size. And the feasibility of the developed approach was verified by two hypothetical numerical case studies. The results indicated that: i) it was critically important to reduce the contamination concentration measurement errors to improve GCSs parameter identification accuracy. ii) model parameter and model input data were not sensitive to the identification accuracy. iii) the interaction between sources of uncertainty significantly affects the identification accuracy, which illustrated the interaction cannot be ignored in the identification process. Overall, this study highlights that the developed MFDA approach represents a promising solution for improving GCSs parameters identification accuracy.

Estimating the time-evolving refractivity of a turbulent medium using optical beam measurements: a data assimilation approach

In applications such as free-space optical communication, a signal is often recovered after propagation through a turbulent medium. In this setting, it is common to assume that limited information is known about the turbulent medium, such as a space- and time-averaged statistic (e.g., root-mean-square), but without information about the state of the spatial variations. It could be helpful to gain more information if the state of the turbulent medium can be characterized with the spatial variations and evolution in time described. Here, we propose to investigate the use of data assimilation techniques for this purpose. A computational setting is used with the paraxial wave equation, and the extended Kalman filter is used to conduct data assimilation using intensity measurements. To reduce computational cost, the evolution of the turbulent medium is modeled as a stochastic process. Following some past studies, the process has only a small number of Fourier wavelengths for spatial variations. The results show that the spatial and temporal variations of the medium are recovered accurately in many cases. In some time windows in some cases, the error is large for the recovery. Finally, we discuss the potential use of the spatial variation information for aiding the recovery of the transmitted signal or beam source.

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.

Convergence in simulating global soil organic carbon by structurally different models after data assimilation.

Current biogeochemical models produce carbon-climate feedback projections with large uncertainties, often attributed to their structural differences when simulating soil organic carbon (SOC) dynamics worldwide. However, choices of model parameter values that quantify the strength and represent properties of different soil carbon cycle processes could also contribute to model simulation uncertainties. Here, we demonstrate the critical role of using common observational data in reducing model uncertainty in estimates of global SOC storage. Two structurally different models featuring distinctive carbon pools, decomposition kinetics, and carbon transfer pathways simulate opposite global SOC distributions with their customary parameter values yet converge to similar results after being informed by the same global SOC database using a data assimilation approach. The converged spatial SOC simulations result from similar simulations in key model components such as carbon transfer efficiency, baseline decomposition rate, and environmental effects on carbon fluxes by these two models after data assimilation. Moreover, data assimilation results suggest equally effective simulations of SOC using models following either first-order or Michaelis-Menten kinetics at the global scale. Nevertheless, a wider range of data with high-quality control and assurance are needed to further constrain SOC dynamics simulations and reduce unconstrained parameters. New sets of data, such as microbial genomics-function relationships, may also suggest novel structures to account for in future model development. Overall, our results highlight the importance of observational data in informing model development and constraining model predictions.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.

Comparison of Met Office regional model soil moisture with COSMOS‐UK field‐scale in situ observations

AbstractThe UK Met Office state‐of‐the‐art, deterministic, convection‐permitting, coupled land‐atmosphere, regional weather forecasting system, known as the UKV or UK Variable resolution model (Tang et al. Meteorological Applications, 2013; 20:417–426), has been operational since 2015. Science updates are regularly made to the UKV land surface data assimilation scheme when those updates improve predictions of screen temperature and humidity, since these quantities have a direct impact on atmospheric states and weather forecasts. Less attention has been paid to whether UKV soil moisture analyses are close to independent, in‐situ soil moisture observations, partly because it is difficult to make meaningful comparisons between 1.5 km2 gridded model outputs and traditional point sensor measurements. Soil moisture is recognized to be important when hydrological forecasts for runoff and rivers are required. This is because soil moisture controls the extent to which rainfall can infiltrate the soil, and the amount of surface runoff affects the timing of peak river flows (Ward & Robinson, Principles of Hydrology. McGraw‐Hill Publishing Company; 2000; Singh et al. Water Resources Research, 2021, 57, e2020WR028827). Gómez et al. (Remote Sensing, 2020; 12:3691) report benefits to river flow forecasts when using soil moisture data assimilation in the UKV system instead of a daily downscaled product from the Met Office global model. The Met Office measures soil temperature and soil moisture at Cardington (Osborne & Weedon, Journal of Hydrometeorology, 2021, 22:279–295); there is no other UK Met Office site at which soil moisture is measured. In this study, we use field‐scale (~200 m radius) soil moisture measurements from the UK Centre for Ecology and Hydrology's (UKCEH's) COSMOS‐UK network to provide independent verification and analysis of UKV soil moisture during summer 2018, an unusually dry period in the United Kingdom. We find that the match to COSMOS‐UK soil moisture observations is generally good, and that changes made to the land data assimilation approach during a recent operational upgrade had a generally beneficial impact on UKV soil moisture analyses under very dry conditions.

Assimilation of Geophysics-Derived Spatial Data for Model Calibration in Geologic CO2 Sequestration

Summary Uncertainty in geological models usually leads to large uncertainty in the predictions of risk-related system properties and/or risk metrics (e.g., CO2 plumes and CO2/brine leakage rates) at a geologic CO2 storage site. Different types of data (e.g., point measurements from monitoring wells and spatial data from 4D seismic surveys) can be leveraged or assimilated to reduce the risk predictions. In this work, we develop a novel framework for spatial data assimilation and risk forecasting. Under the U.S. Department of Energy’s National Risk Assessment Partnership (NRAP), we have developed a framework using an ensemble-based data assimilation approach for spatial data assimilation and forecasting. In particular, we took CO2 saturation maps interpreted from 4D seismic surveys as inputs for spatial data assimilation. Three seismic surveys at Years 1, 3, and 5 were considered in this study. Accordingly, three saturation maps were generated for data assimilation. The impact from the level of data noise was also investigated in this work. Our results show increased similarity between the updated reservoir models and the “ground-truth” model with the increased number of seismic surveys. Predictive accuracy in CO2 saturation plume increases with the increased number of seismic surveys as well. We also observed that with the increase in the level of data noise from 1% to 10%, the difference between the updated models and the ground truth does not increase significantly. Similar observations were made for the prediction of CO2 plume distribution at the end of the CO2 injection period by increasing the data noise.

Direct assimilation of radar reflectivity using an ensemble 3DEnVar approach to improve analysis and forecasting of tornadic supercells over eastern China

AbstractAn ensemble three‐dimensional ensemble‐variational (3DEnVar) data assimilation (En3DA) approach that directly assimilates radar reflectivity was developed based on the Weather Research and Forecasting model data assimilation system. This system adopts radar reflectivity as the control variable to avoid the need for a tangent linear and adjoint of the observation operator. Flow‐dependent covariance was introduced via ensemble forecasts updated by a group of 3DEnVar. The performance of the En3DA system was examined for two selected cases of high‐impact severe tornadic supercells over China. Results for both cases indicated that the structure of the storms in terms of intensity, coverage, and associated low‐level mesocyclones were analysed more accurately when using the En3DA approach than when adopting the 3DVar method. Hydrometeor analysis showed that En3DA provided a more physically reasonable increment of hydrometeors compared to 3DVar, especially for the graupel mixing ratio. Furthermore, the En3DA forecast was better than the 3DVar forecast throughout the forecast period for both studied cases. En3DA produced smaller errors in terms of intensity and location for supercell forecasts with respect to reflectivity and reflectivity swaths. Furthermore, the quantitative forecast skill of radar reflectivity was improved using En3DA. Errors in the wind, temperature, and water vapor forecast fields produced by En3DA were also reduced compared to those of 3DVar. Diagnostics revealed that En3DA predicted an enhanced low‐level cold pool and stronger outflows in the forward‐flank downdraft and the rear‐flank downdraft regions, which are important for tornadogenesis.

Expanding Mars’s Climate Modeling: Interpretable Machine Learning for Modeling Mars Science Laboratory Relative Humidity

For the past several decades, numerous attempts have been made to model the climate of Mars, with extensive studies focusing on the planet’s dynamics and climate. While physical modeling and data assimilation approaches have made significant progress, uncertainties persist in comprehensively capturing the complexities of the Martian climate. We propose a novel approach to Martian climate modeling by leveraging machine-learning techniques that have shown remarkable success in Earth climate modeling. Our study presents a deep neural network designed to model relative humidity in Gale crater, as measured by NASA’s Mars Science Laboratory “Curiosity” rover. By utilizing meteorological variables produced by the Mars Planetary Climate Model, our model accurately predicts relative humidity with a mean error of 3% and an R 2 score of 0.92 over the range of relative humidity compared. Furthermore, we present an approach to predict quantile ranges of relative humidity, catering to applications that require a range of values. To address the challenge of interpretability associated with machine-learning models, we utilize an interpretable model architecture and conduct an in-depth analysis of its decision-making processes. We find that our neural network can model relative humidity at Gale crater using a few meteorological variables, with the monthly mean surface H2O layer, planetary boundary layer height, convective wind speed, and solar zenith angle being the primary contributors. In addition to providing an efficient method for modeling climate variables on Mars, this approach can also be utilized to expand on current data sets by filling spatial and temporal gaps in observations.

A Multi-step Data Assimilation Framework to Investigate the Effect of Measurement Uncertainty in the Reduction of Water Distribution Network Model Errors

Water distribution network (WDN) models are a common decision support tool for understanding the behavior and performance of WDNs, aiding in the planning and management of WDN systems. The increasing availability of real-time data has recently promoted the exploration of Data Assimilation (DA) techniques to improve these models. However, flow, pressure and demand data are uncertain, particularly due to sensor characteristics such as precision and noise. An open question is to what extent DA can still improve hydraulic models when the data used to this end is uncertain. This paper proposes a three-step Ensemble Kalman Filter based DA approach for WDNs (3-EnKF-WDN), building on previous approaches, and advancing in two main fronts: the use of extended period simulation, and the use of pressure-dependent demand (PDD) analysis. Different scenarios considering uncertain sensor data, with varied precision and noise, are applied to two networks of different sizes, representative of real-world WDNs. The computational demand of the 3-EnKF-WDN method is also assessed. Results show that increasing sensor’s precision and decreasing the noise in state measurements reduce model error, as expected. However, we also found that model errors: 1) are reduced more effectively by using 3-EnKF-WDN than by increasing sensors’ precision; 2) are not reduced if certain noise thresholds are surpassed; 3) can be reduced without assimilating demand data if the WDNs are fully monitored with head sensors in all the nodes and flow sensors in all the links.

Inferring Global Ocean Mass Increase From Tide Gauges Network With Climate Models

AbstractOcean mass increase contributes to global sea level rise, and plays an important role in understanding climate change. Here, we develop a data assimilation approach that enables the inference of ocean mass increase from global tide gauge network. This approach incorporates outputs from climate models and sea level fingerprints caused by water mass changes over land areas. The results suggest a trend of 2.15 ± 0.72 mm/yr for ocean mass increase over the period 1993–2022, which closes the global sea level budget with estimates of thermosteric sea level rise. Furthermore, the inferred ocean mass increase offers an insight into the causes of sea level rise since 1950. These findings emphasize the significance of climate models, in addition to simulating sea level changes, they contribute to understanding causes of sea level rise over the past decades.

Extending the utility of space-borne snow water equivalent observations over vegetated areas with data assimilation

Abstract. Snow is a vital component of the earth system, yet no snow-focused satellite remote sensing platform currently exists. In this study, we investigate how synthetic observations of snow water equivalent (SWE) representative of a synthetic aperture radar remote sensing platform could improve spatiotemporal estimates of snowpack. We use a fraternal twin observing system simulation experiment, specifically investigating how much snow simulated using widely used models and forcing data could be improved by assimilating synthetic observations of SWE. We focus this study across a 24∘×37∘ domain in the western USA and Canada, simulating snow at 250 m resolution and hourly time steps in water year 2019. We perform two data assimilation experiments, including (1) a simulation excluding synthetic observations in forests where canopies obstruct remote sensing retrievals and (2) a simulation inferring snow distribution in forested grid cells using synthetic observations from nearby canopy-free grid cells. Results found that, relative to a nature run, or assumed true simulation of snow evolution, assimilating synthetic SWE observations improved average SWE biases at maximum snowpack timing in shrub, grass, crop, bare-ground, and wetland land cover types from 14 %, to within 1 %. However, forested grid cells contained a disproportionate amount of SWE volume. In forests, SWE mean absolute errors at the time of maximum snow volume were 111 mm and average SWE biases were on the order of 150 %. Here the data assimilation approach that estimated forest SWE using observations from the nearest canopy-free grid cells substantially improved these SWE biases (18 %) and the SWE mean absolute error (27 mm). Simulations employing data assimilation also improved estimates of the temporal evolution of both SWE and runoff, even in spring snowmelt periods when melting snow and high snow liquid water content prevented synthetic SWE retrievals. In fact, in the Upper Colorado River region, melt-season SWE biases were improved from 63 % to within 1 %, and the Nash–Sutcliffe efficiency of runoff improved from −2.59 to 0.22. These results demonstrate the value of data assimilation and a snow-focused globally relevant remote sensing platform for improving the characterization of SWE and associated water availability.

Strong Extratropical Impact on Observed ENSO

Abstract Previous studies have indicated that the extratropics can influence ENSO via specific processes. However, it is still unclear to what extent ENSO is influenced by the extratropics in observation. Now we assess this issue by applying the regional data assimilation (RDA) approach in an advanced model, the GFDL CM2.1. Our study confirms a strong extratropical impact on observed ENSO. Quantitatively, the extratropical atmospheric variability poleward of 20° explains 56% of the observed variance of ENSO and greatly influences ∼67% of observed El Niño events during 1969–2008. This extratropical impact is still significant even as far as poleward of 30°. Furthermore, the impact from the southern extratropics is slightly stronger than that from the northern extratropics, partly caused by the Pacific ITCZ location north of the equator and different mixed-layer depth along the northern Pacific meridional mode (NPMM) and the southern Pacific meridional mode (SPMM). Our study further shows that all of three super El Niño events, those in 1972/73, 1982/83, and 1997/98, are influenced greatly by both hemispheric extratropics, with NPMM and SPMM interfering constructively, while most weak and moderate El Niño events are triggered by only one hemispheric extratropics, with NPMM and SPMM interfering destructively. Besides the extratropical Pacific influence on ENSO via NPMM/SPMM, the extratropics also has a potential impact on ENSO by influencing other tropical oceans and then by interbasin interactions.

A Novel Deep Learning Approach for Data Assimilation of Complex Hydrological Systems

AbstractIn hydrological research, data assimilation (DA) is widely used to fuse the information contained in process‐based models and observational data to reduce simulation uncertainty. However, many popular DA methods are limited by low computational efficiency or their reliance on the Gaussian assumption. To address these limitations, we propose a novel DA method called DA(DL), which leverages the capabilities of DL to model non‐linear relationships and recognize complex patterns. DA(DL) first generates a large volume of training data from the prior ensemble, and then trains a DL model to update the system knowledge (e.g., model parameters in this study) from multiple predictors. For highly non‐linear models, an iterative form of DA(DL) can be implemented. Additionally, strategies of data augmentation and local updating are proposed to enhance DA(DL) for problems involving small ensemble size and the equifinality issue, respectively. In two hydrological DA cases involving Gaussian and non‐Gaussian distributions, DA(DL) shows promising performance compared to two ensemble smoother methods, that is, ES(K) and ES(DL), which respectively apply the Kalman‐ and DL‐based updates. Potential improvements to DA(DL) can be made by designing better DL model architectures, imposing physical constraints to the training of the DL model, and further updating other important variables like model states, forcings and error terms.

ModE-RA: a global monthly paleo-reanalysis of the modern era 1421 to 2008

The Modern Era Reanalysis (ModE-RA) is a global monthly paleo-reanalysis covering the period between 1421 and 2008. To reconstruct past climate fields an offline data assimilation approach is used, blending together information from an ensemble of transient atmospheric model simulations and observations. In the early period, ModE-RA utilizes natural proxies and documentary data, while from the 17th century onward instrumental measurements are also assimilated. The impact of each observation on the reconstruction is stored in the observation feedback archive, which provides additional information on the input data such as preprocessing steps and the regression-based forward models. The monthly resolved reconstructions include estimates of the most important climate fields. Furthermore, we provide a reconstruction, ModE-RAclim, which together with ModE-RA and the model simulations allows to disentangle the role of observations and model forcings. ModE-RA is best suited to study intra-annual to multi-decadal climate variability and to analyze the causes and mechanisms of past extreme climate events.

Evaluation of data assimilation strategies on improving the performance of crop modeling based on a novel evapotranspiration assimilation framework

Recently, data assimilation (DA) has garnered significant attention. Integration of DA approaches and crop models could diminish model uncertainties and improve the precision of model simulations. While previous research extensively focused on assimilating leaf area index (LAI) or soil moisture (SM), the feasibility and effectiveness of assimilating evapotranspiration (ET) have been rarely explored. In this study, we proposed a novel framework of ET assimilation. Then, together with commonly assimilated LAI and SM, we evaluated the performance of this new method in simulating the key indicators (i.e., LAI and ET in daily and interannual scales, and the crop yield) based on the long-term eddy covariance observations and well-calibrated crop model. DA strategies we utilized to evaluate consist of two approaches (i.e., Ensemble Kalman filter (EnKF) and EnKF with simultaneous state-parameter estimation (EnKF-SSPE)) and combinations of three assimilated observations (i.e., LAI, SM, and ET).Our results demonstrate that joint assimilation of LAI and ET with EnKF-SSPE performs best for wheat while joint assimilation of SM and ET with EnKF-SSPE is the best for maize. For a single observation, LAI and ET play a dominant role in DA for wheat and maize, respectively. This is because the interannual variability of wheat growth is primarily influenced by agricultural management (e.g., cultivar change) and can be represented by LAI. For maize which is mostly rainfed, water stress usually occurs. Therefore, ET, with its ability to reflect the water stress status, proves to be effective. EnKF-SSPE outperforms EnKF, exhibiting potential in revealing the parameter evolution during long-term crop modeling, especially when crop cultivars are regularly renewed. This study evaluates different observations and methods through DA based on a newly proposed sequential ET assimilation framework, which might be illuminating for future applications of DA.

Sensor placement for data assimilation of turbulence models using eigenspace perturbations

We present an approach to sensor placement for turbulent mean flow data assimilation in the context of Reynolds-averaged Navier–Stokes (RANS) simulations. It entails generating a spatial uncertainty map through the eigenspace perturbations (ESPs) of the baseline turbulence model (e.g., the k−ω shear stress transport model) to quantify the epistemic structural errors in the model. A novel greedy search algorithm is proposed to place sensors targeting regions of highest uncertainty in the spatial uncertainty map generated from ESP. The algorithm is computationally efficient (e.g., computational cost negligible compared to a RANS solution) and is both easy to implement and tune. It involves two hyper-parameters (a constraint to avoid sensor clustering and the number of sensors) which we investigate in-depth. A variational (adjoint-based) data assimilation approach is used for flow reconstruction. The proposed strategy was tested on three two-dimensional wall-bounded flows (Reynolds number ranging 5.6×103–9.36×105) involving flow separation and reattachment. For the wall-mounted hump case, we found that data assimilation using 33 sensors with our proposed sensor placement algorithm reduced the average velocity prediction error by 60% vs 38% with a simple uniform placement of sensors. Furthermore, we found that we could achieve 61% error reduction using our algorithm with only three sensors. Notably, in all tested cases, the error reduction using our method for sensor placement was close in accuracy to the instances where the entire flow field data were used for flow reconstruction, which involved two to three orders of magnitude more data points than the placed sensors.

Can We Intercalibrate Satellite Measurements by Means of Data Assimilation? An Attempt on LEO Satellites

AbstractLow Earth Orbit satellites offer extensive data of the radiation belt region, but utilizing these observations is challenging due to potential contamination and difficulty of intercalibration with spacecraft measurements at Highly Elliptic Orbit that can observe all equatorial pitch‐angles. This study introduces a new intercalibration method for satellite measurements of energetic electrons in the radiation belts using a Data assimilation (DA) approach. We demonstrate our technique by intercalibrating the electron flux measurements of the National Oceanic and Atmospheric Administration (NOAA) Polar‐orbiting Operational Environmental Satellites (POES) NOAA‐15,‐16,‐17,‐18,‐19, and MetOp‐02 against Van Allen Probes observations from October 2012 to September 2013. We use a reanalysis of the radiation belts obtained by assimilating Van Allen Probes and Geostationary Operational Environmental Satellites observations into 3‐D Versatile Electron Radiation Belt (VERB‐3D) code simulations via a standard Kalman filter. We compare the reanalysis to the POES data set and estimate the flux ratios at each time, location, and energy. From these ratios, we derive energy and L* dependent recalibration coefficients. To validate our results, we analyze on‐orbit conjunctions between POES and Van Allen Probes. The conjunction recalibration coefficients and the data‐assimilative estimated coefficients show strong agreement, indicating that the differences between POES and Van Allen Probes observations remain within a factor of two. Additionally, the use of DA allows for improved statistics, as the possible comparisons are increased 10‐fold. Data‐assimilative intercalibration of satellite observations is an efficient approach that enables intercalibration of large data sets using short periods of data.