A simultaneous calibration and data assimilation (C/DA) to improve NRLMSISE00 using thermospheric neutral density (TND) from space-borne accelerometer measurements

2020 ◽  
Vol 224 (2) ◽  
pp. 1096-1115
Author(s):  
E Forootan ◽  
S Farzaneh ◽  
M Kosary ◽  
M Schmidt ◽  
M Schumacher
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Precise Orbit Determination ◽  
Low Earth Orbit ◽  
Model Parameters ◽  
Neutral Density ◽  
Incoherent Scatter ◽  
Drag Forces ◽  
Gravity Recovery ◽  
Limited Accuracy

SUMMARY Improving thermospheric neutral density (TND) estimates is important for computing drag forces acting on low-Earth-orbit (LEO) satellites and debris. Empirical thermospheric models are often used to compute TNDs for the precise orbit determination experiments. However, it is known that simulating TNDs are of limited accuracy due to simplification of model structure, coarse sampling of model inputs and dependencies to the calibration period. Here, we apply TND estimates from accelerometer measurements of the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE) missions as observations to improve the NRLMSISE-00 model, which belongs to the mass spectrometer and incoherent scatter family of models. For this, a novel simultaneous calibration and data assimilation (C/DA) technique is implemented that uses the ensemble Kalman filter and the ensemble square-root Kalman filter as merger. The application of C/DA is unique because it modifies both model-derived TNDs, as well as the selected model parameters. The calibrated parameters derived from C/DA are then used to predict TNDs in locations that are not covered by CHAMP and GRACE orbits, and forecasting TNDs of the next day. The C/DA is implemented using daily CHAMP- and/or GRACE-TNDs, for which compared to the original model, we find 27 per cent and 62 per cent reduction of misfit between model and observations in terms of root mean square error and Nash coefficient, respectively. These validations are performed using the observations along the orbital track of the other satellite that is not used in the C/DA during 2003 with various solar activity. Comparisons with another empirical model, that is, Jacchia-Bowman, indicate that the C/DA results improve these quality measurements on an average range of 50 per cent and 60 per cent, respectively.

How can Thermospheric Neutral Density (TND) estimates from CHAMP and GRACE accelerometer observations be used to improve empirical models?

2020 ◽  
Author(s):  
Ehsan Forootan ◽  
Saeed Farzaneh ◽  
Mona Kosary ◽  
Maike Schumacher
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Orbit Determination ◽  
Ensemble Kalman Filter ◽  
Precise Orbit Determination ◽  
Accurate Estimation ◽  
Neutral Density ◽  
Square Root ◽  
Precise Orbit ◽  
Leo Satellites

<p>An accurate estimation of the Thermospheric Neutral Density (TND) is important to compute drag forces acting on Low-Earth-Orbit (LEO) satellites and debris. Empirical thermospheric models are often used to compute TNDs (along-track of LEO satellites) for the Precise Orbit Determination (POD) experiments. However, recent studies indicate that the TNDs of available models do not perfectly reproduce TNDs derived from accelerometer observations. In this study, we use TND estimates from the Challenging Minisatellite Payload (CHAMP) and Gravity Recovery and Climate Experiment (GRACE) missions and merge them with the NRLMSISE00 from the Mass Spectrometer and Incoherent Scatter family. The integration is implemented by applying a simultaneous Calibration and Data Assimilation (C/DA) technique. The application of C/DA is advantageous since it uses model equation to interpolate and extrapolate TNDs that are not covered by CHAMP and GRACE. It also modifies the model's selected parameters to simulate TNDs that are closer to those of CHAMP and GRACE. The C/DA of this study is implemented daily using CHAMP- and/or GRACE-TNDs, while using the Ensemble Kalman Filter (EnKF) and Ensemble Square-Root Kalman Filter (EnSRF) as merger. Compared to the original model, on average, we found 27% (in the range of 2% to 56%) improvements in the estimation of TNDs. In addition, the results of the C/DA are compared with the TND outputs of the JB2008 model along the CHAMP and GRACE orbits, whose results indicate that the daily C/DA outputs are 60% closer to the observed TNDs (that are not used for the C/DA). Overall, our assessment indicates that EnSRF results in more realistic TND simulation and prediction compared to those derived from EnKF. We show that the improved TND estimates of this study will be beneficial for Precise Orbit Determination (POD) studies.  </p><p><strong>Keywords: </strong>Thermosphere, Calibration and Data Assimilation (C/DA), NRLMSISE00, Ensemble Kalman Filter (EnKF), Ensemble Square-Root Kalman Filter (EnSRF)</p>

scholarly journals An empirical model (CH-Therm-2018) of the thermospheric mass density derived from CHAMP

2018 ◽  
Author(s):  
Chao Xiong ◽  
Hermann Lühr ◽  
Michael Schmidt ◽  
Mathis Bloßfeld ◽  
Sergei Rudenko
Keyword(s):  
Empirical Model ◽  
Solar Minimum ◽  
Mass Density ◽  
Precise Orbit Determination ◽  
Wave Pattern ◽  
Magnetic Activity ◽  
Low Earth Orbit ◽  
Naval Research ◽  
Champ Satellite ◽  
Incoherent Scatter

Abstract. Thermospheric drag is the major non-gravitational perturbation acting on Low Earth Orbit (LEO) satellites at altitudes up to 1000 km. The drag depends on the thermospheric density, which is a key parameter in the planning of LEO missions, e.g. their lifetime, collision avoidance, precise orbit determination, as well as orbit and re-entry prediction. In this study, we present an empirical model, named CH-Therm-2018, of the thermospheric mass density derived from 9-year (from August 2000 to July 2009) accelerometer measurements at altitude from 460 to 310 km, from the CHAllenging Minisatellite Payload (CHAMP) satellite. The CHAMP dataset is divided into two 5-year periods with 1-year overlap (from August 2000 to July 2005 and from August 2004 to July 2009), to represent the high-to-moderate and moderate-to-low solar activity conditions, respectively. The CH-Therm-2018 model is a function of seven key parameters, including the height, solar flux index, season (day of year), magnetic local time, geographic latitude and longitude, as well as magnetic activity represented by the solar wind merging electric field. Predictions of the CH-Therm-2018 model agree well with the CHAMP observations (disagreements within ±20 %), and show different features of thermospheric mass density during solar activities, e.g. the March-September equinox asymmetry and the longitudinal wave pattern. We compare the CH-Therm-2018 predictions with the Naval Research Laboratory Mass Spectrometer Incoherent Scatter Radar Extended (NRLMSISE-00) model. The result shows that CH-Therm-2018 better predicts the density evolution during the last solar minimum (2008-2009) than the NRLMSISE-00 model. By comparing the Satellite Laser Ranging (SLR) observations of the ANDE-Pollux satellites during August-September 2009, we estimate 6-h scaling factors of thermospheric mass density and obtain a median value of 1.27 ± 0.60, indicating that our model, on average, slightly underestimates the thermospheric mass density at solar minimum.

Scale factors of the thermospheric neutral density – a comparison of SLR and accelerometer solutions

2021 ◽  
Author(s):  
Lea Zeitler ◽  
Armin Corbin ◽  
Kristin Vielberg ◽  
Sergei Rudenko ◽  
Anno Löcher ◽  
...  
Keyword(s):  
Time Resolution ◽  
Aerodynamic Drag ◽  
Precise Orbit Determination ◽  
Neutral Density ◽  
Observation Data ◽  
Accelerometer Data ◽  
Scale Factors ◽  
Weather Events ◽  
Leo Satellites ◽  
Gravity Recovery

<p>The aerodynamic drag depending on the neutral density of the thermosphere is the largest non-gravitational force that decelerates Low Earth Orbiting (LEO) satellites with altitudes lower than 1000 km.  Consequently, the knowledge of the thermospheric neutral density is of crucial importance for many applications in geo-scientific investigations, such as precise orbit determination (POD), re-entry prediction, manoeuvre planning or satellite lifetime predictions. The accuracy of existing thermosphere models depends on observation data of the thermosphere, which are quite sparse. Evaluations of different thermosphere models indicate considerable differences, especially for time epochs of severe space weather events. Hence, an improvement of thermosphere models is absolutely necessary.</p><p>In this study, discrepancies between the empirical thermosphere model NRLMSISE-00 and the results of two geodetic observation techniques are discussed. For this purpose, two approaches are applied to calculate scale factors between the modelled density from the NRLMSISE-00 model and those from geodetic techniques. The first approach applies the POD of LEO satellites to estimate scale factors with a time resolution of 12 hours derived from Satellite Laser Ranging (SLR) tracking measurements. The SLR missions used here include the spherical satellites Starlette, Westpac, Blits, Stella and Larets. As our second approach, scale factors are computed by evaluating the aerodynamic acceleration using the on-board accelerometer data of the Challenging Mini-satellite Payload (CHAMP) mission and the Gravity Recovery and Climate Experiment (GRACE) mission. Here, the time resolution of scale factors is fixed to be 12 hours to be comparable with the first approach. Finally, we investigate the resulting scale factors from the above mentioned satellites at various altitudes, e.g. 960 km for Starlette and 400 km for GRACE. Especially, the temporal variation as well as the altitude dependency of the scale factors will be discussed.</p>

scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

2018 ◽  
Vol 25 (4) ◽  
pp. 731-746 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Particle Filter ◽  
Reservoir Modeling ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Initial Ensemble ◽  
Leading Mode ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable Markov chain Monte Carlo (MCMC) methods are computationally expensive. Sequential ensemble methods such as ensemble Kalman filters and particle filters provide a favorable alternative. However, ensemble Kalman filter has an assumption of Gaussianity. Ensemble transform particle filter does not have this assumption and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimations in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ ensemble transform particle filter (ETPF) and ensemble transform Kalman filter (ETKF) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). The large number of uncertain parameters is of particular interest for subsurface reservoir modeling as it allows us to parameterize permeability on the grid. We prove that the updated parameters obtained by ETPF lie within the range of an initial ensemble, which is not the case for ETKF. We examine the performance of ETPF and ETKF in a twin experiment setup, where observations of pressure are synthetically created based on the known values of parameters. For a small number of uncertain parameters (one and five) ETPF performs comparably to ETKF in terms of the mean estimation. For a large number of uncertain parameters (2500) ETKF is robust with respect to the initial ensemble, while ETPF is sensitive due to sampling error. Moreover, for the high-dimensional test problem ETPF gives an increase in the root mean square error after data assimilation is performed. This is resolved by applying distance-based localization, which however deteriorates a posterior estimation of the leading mode by largely increasing the variance due to a combination of less varying localized weights, not keeping the imposed bounds on the modes via the Karhunen–Loeve expansion, and the main variability explained by the leading mode. A possible remedy is instead of applying localization to use only leading modes that are well estimated by ETPF, which demands knowledge of which mode to truncate.

Data Assimilation of Coupled Fluid Flow and Geomechanics Using the Ensemble Kalman Filter

SPE Journal ◽  
2010 ◽  
Vol 15 (02) ◽  
pp. 382-394 ◽  
Author(s):  
Haibin Chang ◽  
Yan Chen ◽  
Dongxiao Zhang
Keyword(s):  
Fluid Flow ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Material Properties ◽  
Ensemble Kalman Filter ◽  
Oil Field ◽  
Reservoir Rock ◽  
Model Parameters ◽  
Stress Strain ◽  
Reservoir Flow

Summary In reservoir history matching or data assimilation, dynamic data, such as production rates and pressures, are used to constrain reservoir models and to update model parameters. As such, even if under certain conceptualization the model parameters do not vary with time, the estimate of such parameters may change with the available observations and, thus, with time. In reality, the production process may lead to changes in both the flow and geomechanics fields, which are dynamically coupled. For example, the variations in the stress/strain field lead to changes in porosity and permeability of the reservoir and, hence, in the flow field. In weak formations, such as the Lost Hills oil field, fluid extraction may cause a large compaction to the reservoir rock and a significant subsidence at the land surface, resulting in huge economic losses and detrimental environmental consequences. The strong nonlinear coupling between reservoir flow and geomechanics poses a challenge to constructing a reliable model for predicting oil recovery in such reservoirs. On the other hand, the subsidence and other geomechanics observations can provide additional insight into the nature of the reservoir rock and help constrain the reservoir model if used wisely. In this study, the ensemble-Kalman-filter (EnKF) approach is used to estimate reservoir flow and material properties by jointly assimilating dynamic flow and geomechanics observations. The resulting model can be used for managing and optimizing production operations and for mitigating the land subsidence. The use of surface displacement observations improves the match to both production and displacement data. Localization is used to facilitate the assimilation of a large amount of data and to mitigate the effect of spurious correlations resulting from small ensembles. Because the stress, strain, and displacement fields are updated together with the material properties in the EnKF, the issue of consistency at the analysis step of the EnKF is investigated. A 3D problem with reservoir fluid-flow and mechanical parameters close to those of the Lost Hills oil field is used to test the applicability.

One-Dimensional Soil Moisture Simulation Using Ensemble Kalman Filter

2012 ◽  
Vol 212-213 ◽  
pp. 177-180
Author(s):  
Xiao Lei Fu ◽  
Zhong Bo Yu ◽  
Yu Li ◽  
Hai Shen Lv ◽  
Di Liu ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Soil Layer ◽  
Model Parameters ◽  
Deep Soil ◽  
One Dimensional ◽  
Initial Soil Moisture ◽  
Initial Soil

Data assimilation is a method which integrates model and observation. In hydrology, ensemble Kalman filter (EnKF) as a sequential data assimilation method is often used to correct model parameters, thus improve the simulated accuracy. In this study, we conduct one numerical experiment to predict soil moisture using the one-dimensional soil moisture system based on ensemble Kalman filter and Simple Biosphere (SiB2) Model at Meilin study area, China. The simulated period is divided into two parts: 0-60h and 60-240h. The results show that EnKF is an efficient method in assimilating the soil moisture, especially in soil surface layer and deep soil layer; in addition, the efficiency of EnKF depends on the selection of initial soil moisture profile. With different initial soil moisture profiles, the performance of EnKF is different at the first few assimilated time, but with time grows, it can improve the simulated accuracy significantly.

scholarly journals Comparison of accelerometer data calibration methods used in thermospheric neutral density estimation

2018 ◽  
Vol 36 (3) ◽  
pp. 761-779 ◽  
Author(s):  
Kristin Vielberg ◽  
Ehsan Forootan ◽  
Christina Lück ◽  
Anno Löcher ◽  
Jürgen Kusche ◽  
...  
Keyword(s):  
Solar Activity ◽  
Radiation Pressure ◽  
Precise Orbit Determination ◽  
High Solar Activity ◽  
Neutral Density ◽  
Accelerometer Data ◽  
The Earth ◽  
Calibration Methods ◽  
Leo Satellites ◽  
Gravity Recovery

Abstract. Ultra-sensitive space-borne accelerometers on board of low Earth orbit (LEO) satellites are used to measure non-gravitational forces acting on the surface of these satellites. These forces consist of the Earth radiation pressure, the solar radiation pressure and the atmospheric drag, where the first two are caused by the radiation emitted from the Earth and the Sun, respectively, and the latter is related to the thermospheric density. On-board accelerometer measurements contain systematic errors, which need to be mitigated by applying a calibration before their use in gravity recovery or thermospheric neutral density estimations. Therefore, we improve, apply and compare three calibration procedures: (1) a multi-step numerical estimation approach, which is based on the numerical differentiation of the kinematic orbits of LEO satellites; (2) a calibration of accelerometer observations within the dynamic precise orbit determination procedure and (3) a comparison of observed to modeled forces acting on the surface of LEO satellites. Here, accelerometer measurements obtained by the Gravity Recovery And Climate Experiment (GRACE) are used. Time series of bias and scale factor derived from the three calibration procedures are found to be different in timescales of a few days to months. Results are more similar (statistically significant) when considering longer timescales, from which the results of approach (1) and (2) show better agreement to those of approach (3) during medium and high solar activity. Calibrated accelerometer observations are then applied to estimate thermospheric neutral densities. Differences between accelerometer-based density estimations and those from empirical neutral density models, e.g., NRLMSISE-00, are observed to be significant during quiet periods, on average 22 % of the simulated densities (during low solar activity), and up to 28 % during high solar activity. Therefore, daily corrections are estimated for neutral densities derived from NRLMSISE-00. Our results indicate that these corrections improve model-based density simulations in order to provide density estimates at locations outside the vicinity of the GRACE satellites, in particular during the period of high solar/magnetic activity, e.g., during the St. Patrick's Day storm on 17 March 2015.

Effect of joint assimilation of GRACE and discharge observations on simulated water storages and fluxes

2020 ◽  
Author(s):  
Kerstin Schulze ◽  
Jürgen Kusche ◽  
Olga Engels ◽  
Petra Döll ◽  
Somayeh Shadkam ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Mississippi River ◽  
Water Resource Management ◽  
Water Cycle ◽  
Time Frame ◽  
Model Parameters ◽  
Hydrological Models ◽  
Realistic Representation ◽  
Single Data ◽  
Gravity Recovery

<p>Several applications, from water resource management to the prediction of extreme events, require a realistic representation of the global water cycle. Global hydrological models simulate continental water fluxes and individual storages. However, they poorly reproduce observations of discharge and total water storage anomalies (TWSA). To improve the realism of the simulations, TWSA derived from the Gravity Recovery and Climate Experiment (GRACE) mission are usually assimilated into hydrological models.<br>However, while assimilating GRACE-TWSA yields more realistic TWSA simulations, it is not clear how it affects the simulation of individual storages and fluxes. Therefore, assimilating discharge, in-situ or derived from satellite-altimetry, has been suggested to improve simulated discharge which is especially important for ungauged parts of basins.</p><p>In this study, we jointly assimilate GRACE-TWSA and discharge observations and, for the first time, simultaneously calibrate the model parameters in order to improve the simulation skills of the model beyond the observational time frame. For this, we couple the WaterGAP 2.2d model with the Parallel Data Assimilation Framework and apply an Ensemble Kalman Filter for the Mississippi River Basin from 2003 to 2016. Furthermore, we compare our results to single-data assimilation and validate them against discharge observations that were not used for calibration/assimilation. Additionally, we analyze the effect of the calibrated parameters on the model’s realism.</p>

scholarly journals Extracranial estimation of neural mass model parameters using the Unscented Kalman Filter

2017 ◽  
Author(s):  
Lara Escuain-Poole ◽  
Jordi Garcia-Ojalvo ◽  
Antonio J. Pons
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Neural Mass Model ◽  
Model Parameters ◽  
Mass Model ◽  
Imperfect Data ◽  
Non Invasive ◽  
Neural Mass ◽  
Eeg Recordings ◽  
The Brain

AbstractData assimilation, defined as the fusion of data with preexisting knowledge, is particularly suited to elucidating underlying phenomena from noisy/insufficient observations. Although this approach has been widely used in diverse fields, only recently have efforts been directed to problems in neuroscience, using mainly intracranial data and thus limiting its applicability to invasive measurements involving electrode implants. Here we intend to apply data assimilation to non-invasive electroencephalography (EEG) measurements to infer brain states and their characteristics. For this purpose, we use Kalman filtering to combine synthetic EEG data with a coupled neural-mass model together with Ary’s model of the head, which projects intracranial signals onto the scalp. Our results show that using several extracranial electrodes allows to successfully estimate the state and parameters of the neural masses and their interactions, whereas one single electrode provides only a very partial and insufficient view of the system. The superiority of using multiple extracranial electrodes over using only one, be it intra- or extracranial, is shown over a wide variety of dynamical behaviours. Our results show potential towards future clinical applications of the method.Author SummaryTo completely understand brain function, we will need to integrate experimental information into a consistent theoretical framework. Invasive techniques as EcoG recordings, together with models that describe the brain at the mesoscale, provide valuable information about the brain state and its dynamical evolution when combined with techniques coming from control theory, such as the Kalman filter. This method, which is specifically designed to deal with systems with noisy or imperfect data, combines experimental data with theoretical models assuming Bayesian inference. So far, implementations of the Kalman filter have not been suited for non-invasive measures like EEG. Here we attempt to overcome this situation by introducing a model of the head that allows to transfer the intracranial signals produced by a mesoscopic model to the scalp in the form of EEG recordings. Our results show the advantages of using multichannel EEG recordings, which are extended in space and allow to discriminate signals produced by the interaction of coupled columns. The extension of the Kalman method presented here can be expected to expand the applicability of the technique to all situations where EEG recordings are used, including the routine monitoring of illnesses or rehabilitation tasks, brain-computer interface protocols, and transcranial stimulation.

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