scholarly journals A Sampling Method for Quantifying the Information Content of IASI Channels

2017 ◽  
Vol 145 (2) ◽  
pp. 709-725 ◽  
Author(s):  
Alison Margaret Fowler
Keyword(s):  
Data Assimilation ◽  
Mutual Information ◽  
Information Content ◽  
Degrees Of Freedom ◽  
Sampling Method ◽  
Channel Selection ◽  
Variational Data Assimilation ◽  
State Variables ◽  
Highly Nonlinear ◽  
Linearization Errors

There is a vast amount of information about the atmosphere available from instruments on board satellites. One example is the Infrared Atmospheric Sounding Interferometer (IASI) instrument, which measures radiances emitted from Earth’s atmosphere and surface in 8461 channels. It is difficult to transmit, store, and assimilate such a large amount of data. A practical solution to this has been to select a subset of a few hundred channels based on those that contain the most useful information. Different measures of information content for objective channel selection have been suggested for application to variational data assimilation. These include mutual information and the degrees of freedom for signal. To date, the calculation of these measures of information content has been based on the linear theory that is at the heart of operational variational data assimilation. However, the retrieval of information about the atmosphere from the satellite radiances can be highly nonlinear. Here, a sampling method for calculating the mutual information that is free from assumptions about the linearity of the relationship between the observed radiances and the state variables is examined. It is found that large linearization errors can indeed lead to large discrepancies in the value of mutual information. How this new estimate of information content can be used in channel selection is addressed, with particular attention given to the efficiency of the new method. It is anticipated that accounting for the nonlinearity in the channel selection will be beneficial when using nonlinear data assimilation methods currently in development.

scholarly journals Optimal solution error covariance in highly nonlinear problems of variational data assimilation

2012 ◽  
Vol 19 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. Shutyaev ◽  
I. Gejadze ◽  
G. J. M. Copeland ◽  
F.-X. Le Dimet
Keyword(s):  
Nonlinear Dynamics ◽  
Data Assimilation ◽  
Optimal Solution ◽  
Nonlinear Problems ◽  
Variational Data Assimilation ◽  
Model Parameters ◽  
Efficient Computation ◽  
Viscous Term ◽  
Highly Nonlinear ◽  
The Cost

Abstract. The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

scholarly journals Hybridizing sequential and variational data assimilation for robust high-resolution hydrologic forecasting

2016 ◽  
Author(s):  
Felipe Hernández ◽  
Xu Liang
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Sequential Data ◽  
State Variables ◽  
Hydrologic Modelling ◽  
Multi Objective ◽  
High Resolution Models ◽  
Computational Resources ◽  
Traditional Approaches

Abstract. There are two main frameworks for the estimation of initial states in geophysical models for real-time and forecasting applications: sequential data assimilation and variational data assimilation. However, modern high-resolution models offer challenges, both in terms of indeterminacy and computational requirements, which render most traditional methods insufficient. In this article we introduce a hybrid algorithm called OPTIMISTS which combines advantageous features from both of these data assimilation perspectives. These features are integrated with a multi-objective approach for selecting ensemble members to create a probabilistic estimate of the state variables, which promotes the reduction of observational errors as well as the maintenance of the dynamic consistency of states. Additionally, we propose simplified computations as alternatives aimed at reducing memory and processor requirements. OPTIMISTS was tested on two models of real watersheds, one with over 1,000 variables and the second with over 30,000, on two distributed hydrologic modelling engines: VIC and the DHSVM. Our tests, consisting of assimilating streamflow observations, allowed determining which features of the traditional approaches lead to more accurate forecasts while at the same time making an efficient use of the available computational resources. The results also demonstrated the benefits of the coupled probabilistic/multi-objective approach, which proved instrumental in reducing the harmful effects of overfitting – especially on the model with higher dimensionality.

scholarly journals Optimal Ensemble-Based Selection of Channels from Advanced Sounders in the Presence of Cloud

2015 ◽  
Vol 143 (9) ◽  
pp. 3754-3773 ◽  
Author(s):  
Stefano Migliorini
Keyword(s):  
Data Assimilation ◽  
Degrees Of Freedom ◽  
General Procedure ◽  
Channel Selection ◽  
Merit Function ◽  
Correlated Errors ◽  
Optimal Ensemble ◽  
Imperfect Knowledge ◽  
Definition Of ◽  
Observation Uncertainty

Abstract This study aims to illustrate a general procedure based on well-known information theory concepts to select the channels from advanced satellite sounders that are most advantageous to assimilate both in clear-sky and overcast conditions using an ensemble-based estimate of forecast uncertainty. To this end, the standard iterative channel selection method, which is used to select the most informative channels from advanced infrared sounders for operational assimilation, was revisited so as to allow its use with measurements that have correlated errors. The method was here applied to determine a 24-humidity-sensitive-channel set that is small in size relative to a total of 8461 channels that are available on the Infrared Atmospheric Sounding Interferometer (IASI) on board the EUMETSAT Polar System MetOp satellites. The selected channels can be used to perform all-sky data assimilation experiments, in addition to those currently used for operational data assimilation of IASI data at ECMWF. Care was taken to include in the observation uncertainty used for channel selection the contributions arising from imperfect knowledge of the concentration of contaminants (except for cloud) in a given spectral channel. Also, (cumulative) weighting functions that provide a vertically resolved picture of the (total) number of degrees of freedom for signal expressed by a given set of measurements were introduced, which allows for the definition of a novel channel selection merit function that can be used to select measurements that are most sensitive to variations of a given parameter over a given atmospheric region (e.g., in the troposphere).

scholarly journals A three-dimensional variational data assimilation system for multiple aerosol species with WRF/Chem and an application to PM<sub>2.5</sub> prediction

2012 ◽  
Vol 12 (5) ◽  
pp. 13515-13552 ◽  
Author(s):  
Z. Li ◽  
Z. Zang ◽  
Q. B. Li ◽  
Y. Chao ◽  
D. Chen ◽  
...  
Keyword(s):  
Los Angeles ◽  
Data Assimilation ◽  
Three Dimensional ◽  
Variational Data Assimilation ◽  
Metal Species ◽  
Individual Species ◽  
Size Distributions ◽  
State Variables ◽  
Background Error ◽  
Mass Concentrations

Abstract. A three-dimensional variational data assimilation (3-DVAR) algorithm for aerosols in a WRF/Chem model is presented. The WRF/Chem model uses the MOSAIC (Model for Simulating Aerosol Interactions and Chemistry) scheme, which explicitly treats eight major species (elemental/black carbon, organic carbon, nitrate, sulfate, chloride, ammonium, sodium, and the sum of other inorganic, inert mineral and metal species) and represents size distributions using a sectional method with four size bins. The 3-DVAR scheme is formulated to take advantage of the MOSAIC scheme in providing comprehensive analyses of specie concentrations and size distributions. To treat the large number of state variables associated with the MOSAIC scheme, this 3-DVAR algorithm first determines the analysis increments of the total mass concentrations of the eight species, defined as the sum of the mass concentrations across all size bins, and then distributes the analysis increments over four size bins according to the background error variances. The number concentrations for each size bin are adjusted based on the ratios between the mass and number concentrations of the background state. This system has been applied to the analysis and prediction of PM2.5 in the Los Angeles basin during the CalNex 2010 field experiment, with assimilation of surface PM2.5 and speciated concentration observations. The results demonstrate that the data assimilation significantly reduces the errors in comparison with a down scaling simulation and improved forecasts of the concentrations of PM2.5 as well as individual species for up to 24 h. Some implementation difficulties and limitations of the system are also discussed.

scholarly journals Controller Design for the Rotational Dynamics of a Quadcopter

2019 ◽  
Vol 38 (2) ◽  
pp. 269-274
Author(s):  
Rabia Rashdi ◽  
Zeeshan Ali ◽  
Javed Rahman Larik ◽  
Liaquat Ali Jamro ◽  
Urooj Baig
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Controller Design ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Euler Method ◽  
State Variables ◽  
Nonlinear Controller ◽  
Nonlinear Dynamic Model ◽  
Highly Nonlinear

Researchers have shown their interests in establishing miniature flying robots to be utilized for, both, commercial and research applications. This is due to that fact that there appears to be a huge advancement in miniature actuators and sensors which depend on the MEMS (Micro Electro-Mechanical Systems) NEMS (Nano-Electro Mechanical Systems). This research underlines a detailed mathematical model and controller design for a quadcopter. The nonlinear dynamic model of the quadcopter is derived from the Newton-Euler method and Euler Lagrange method. The motion of a quadcopter can be classified into two subsystems: a rotational subsystem (attitude and heading) and translational subsystem (altitude and x and y motion). The rotational system is fully actuated whereas translational subsystem is under actuated. However, a quadcopter is 6 DOF (Degrees of Freedom) under actuated system. The controller design of a quadcopter is difficult due to its complex and highly nonlinear mathematical model where the state variables are strongly coupled and contain under actuated property. Nonlinear controller such as SMC (Sliding Mode Controller) is used to control altitude, yaw, pitch, and roll angles.Simulation results show that the robustness of the SMC design gives a better way to design a controller with autonomous stability flight with good tracking performance and improved accuracy without any chattering effect. The system states are following the desired trajectory as expected.

scholarly journals How much information do extinction and backscattering measurements contain about the chemical composition of atmospheric aerosol?

2016 ◽  
Author(s):  
Michael Kahnert ◽  
Emma Andersson
Keyword(s):  
Inverse Problem ◽  
Standard Deviation ◽  
Chemical Composition ◽  
Data Assimilation ◽  
Information Content ◽  
Shannon Entropy ◽  
Degrees Of Freedom ◽  
Singular Values ◽  
Related Model ◽  
Observation Operator

Abstract. We theoretically and numerically investigate the problem of assimilating lidar observations of extinction and backscattering coefficients of aerosols into a chemical transport model. More specifically, we consider the inverse problem of determining the chemical composition of aerosols from these observations. The main questions are how much information the observations contain to constrain the particles' chemical composition, and how one can optimise a chemical data assimilation system to make maximum use of the available information. We first quantify the information content of the measurements by computing the singular values of the observation operator. From the singular values we can compute the number of signal degrees of freedom and the reduction in Shannon entropy. For an observation standard deviation of 10 %, it is found that simultaneous measurements of extinction and backscattering allows us to constrain twice as many model variables as extinction measurements alone. The same holds for measurements at two wavelengths compared to measurements at a single wavelength. However, when we extend the set of measurements from two to three wavelengths then we observe only a small increase in the number of signal degrees of freedom, and a minor change in the Shannon entropy. The information content is strongly sensitive to the observation error; both the number of signal degrees of freedom and the reduction in Shannon entropy steeply decrease as the observation standard deviation increases in the range between 1 and 100 %. The right singular vectors of the observation operator can be employed to transform the model variables into a new basis in which the components of the state vector can be divided into signal-related and noise-related components. We incorporate these results in a chemical data assimilation algorithm by introducing weak constraints that restrict the assimilation algorithm to acting on the signal-related model variables only. This ensures that the information contained in the measurements is fully exploited, but not over-used. Numerical experiments confirm that the constrained data assimilation algorithm solves the inverse problem in a way that automatises the choice of control variables, and that restricts the minimisation of the costfunction to the signal-related model variables.

scholarly journals The Land Variational Ensemble Data Assimilation fRamework: LaVEnDAR

2019 ◽  
Author(s):  
Ewan Pinnington ◽  
Tristan Quaife ◽  
Amos Lawless ◽  
Karina Williams ◽  
Tim Arkebauer ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Land Surface ◽  
Time Window ◽  
Variational Data Assimilation ◽  
Surface Model ◽  
State Variables ◽  
Maize Crop ◽  
Area Index ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Abstract. The Land Variational Ensemble Data Assimilation fRamework (LaVEnDAR) implements the method of Four-Dimensional Ensemble Variational data assimilation for land surface models. Four-Dimensional Ensemble Variational data assimilation negates the often costly calculation of a model adjoint required by traditional variational techniques (such as 4DVar) for optimising parameters/state variables over a time window of observations. In this paper we implement LaVEnDAR with the JULES land surface model. We show the system can recover seven parameters controlling crop behaviour in a set of twin experiments. We run the same experiments at the Mead continuous maize FLUXNET site in Nebraska, USA to show the technique working with real data. We find that the system accurately captures observations of leaf area index, canopy height and gross primary productivity after assimilation and improves posterior estimates of the amount of harvestable material from the maize crop by 74 %. LaVEnDAR requires no modification to the model that it is being used with and is hence able to keep up to date with model releases more easily than other data assimilation methods.

An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation

SPE Journal ◽  
2007 ◽  
Vol 12 (04) ◽  
pp. 438-446 ◽  
Author(s):  
Yaqing Gu ◽  
Dean S. Oliver
Keyword(s):  
Porous Media ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Forecasting ◽  
Weather Prediction ◽  
Flow In Porous Media ◽  
Petroleum Reservoir ◽  
State Variables ◽  
Highly Nonlinear

Summary The dynamical equations for multiphase flow in porous media are highly nonlinear and the number of variables required to characterize the medium is usually large, often two or more variables per simulator gridblock. Neither the extended Kalman filter nor the ensemble Kalman filter is suitable for assimilating data or for characterizing uncertainty for this type of problem. Although the ensemble Kalman filter handles the nonlinear dynamics correctly during the forecast step, it sometimes fails badly in the analysis (or updating) of saturations. This paper focuses on the use of an iterative ensemble Kalman filter for data assimilation in nonlinear problems, especially of the type related to multiphase ow in porous media. Two issues are key:iteration to enforce constraints andensuring that the resulting ensemble is representative of the conditional pdf (i.e., that the uncertainty quantification is correct). The new algorithm is compared to the ensemble Kalman filter on several highly nonlinear example problems, and shown to be superior in the prediction of uncertainty. Introduction For linear problems, the Kalman filter is optimal for assimilating measurements to continuously update the estimate of state variables. Kalman filters have occasionally been applied to the problem of estimating values of petroleum reservoir variables (Eisenmann et al. 1994; Corser et al. 2000), but they are most appropriate when the problems are characterized by a small number of variables and when the variables to be estimated are linearly related to the observations. Most data assimilation problems in petroleum reservoir engineering are highly nonlinear and are characterized by many variables, often two or more variables per simulator gridblock. The problem of weather forecasting is in many respects similar to the problem of predicting future petroleum reservoir performance. The economic impact of inaccurate predictions is substantial in both cases, as is the difficulty of assimilating very large data sets and updating very large numerical models. One method that has been recently developed for assimilating data in weather forecasting is ensemble Kalman filtering (Evensen 1994; Houtekamer and Mitchell 1998; Anderson and Anderson 1999; Hamill et al. 2000; Houtekamer and Mitchell 2001; Evensen 2003). It has been demonstrated to be useful for weather prediction over the North Atlantic. The method is now beginning to be applied for data assimilation in groundwater hydrology (Reichle et al. 2002; Chen and Zhang 2006) and in petroleum engineering (Nævdal et al. 2002, 2005; Gu and Oliver 2005; Liu and Oliver 2005a; Wen and Chen 2006, 2007; Zafari and Reynolds 2007; Gao et al. 2006; Lorentzen et al. 2005; Skjervheim et al. 2007; Dong et al. 2006), but the applications to state variables whose density functions are bimodal has proved problematic (Gu and Oliver 2006). For applications to nonlinear assimilation problems, it is useful to think of the ensemble Kalman filter as a least squares method that obtains an averaged gradient for minimization not from a variational approach but from an empirical correlation between model variables (Anderson 2003; Zafari et al. 2006). In addition to providing a mean estimate of the variables, a Monte Carlo estimate of uncertainty can be obtained directly from the variability in the ensemble.

Considerations on Parameter and State Estimation with Ensemble Data Assimilation Methods – A Case Study with a Nonlinear Oscillator

2020 ◽  
Author(s):  
Arundhuti Banerjee ◽  
Femke Vossepoel
Keyword(s):  
Data Assimilation ◽  
The State ◽  
State Variables ◽  
Model Framework ◽  
Time Period ◽  
Highly Nonlinear ◽  
Using Data ◽  
Variable Errors ◽  
Parameter Values

&lt;p&gt;This study investigates the effect of erroneous parameter values for state and parameter estimation using data assimilation. The numerical model chosen for this study solves the van der Pol equation, a second-order differential equation that can be used to simulate oscillatory processes, such as earthquakes. In the model, discrepancies in the parameter values can have a significant influence on the forecasted states of the model, which is even more significant if its behaviour is highly nonlinear. When observations of the state variables are assimilated to update the parameters along with the state variables, this improves the quality of the state forecasts. The results suggest that corrections in the model parameter not only recover the actual parameter values but also reduce state-variable errors after a certain time period. However, data assimilation that updates the state variables but not the parameter can lead to erroneous estimates as well as forecasts of the oscillation. Since the study is performed on a simplified nonlinear model framework, the consequences of these results for data assimilation in more realistic models remains to be investigated.&lt;/p&gt;

scholarly journals A three-dimensional variational data assimilation system for multiple aerosol species with WRF/Chem and an application to PM<sub>2.5</sub> prediction

2013 ◽  
Vol 13 (8) ◽  
pp. 4265-4278 ◽  
Author(s):  
Z. Li ◽  
Z. Zang ◽  
Q. B. Li ◽  
Y. Chao ◽  
D. Chen ◽  
...  
Keyword(s):  
Los Angeles ◽  
Data Assimilation ◽  
Three Dimensional ◽  
Variational Data Assimilation ◽  
Metal Species ◽  
Individual Species ◽  
Size Distributions ◽  
State Variables ◽  
Background Error ◽  
Mass Concentrations

Abstract. A three-dimensional variational data assimilation (3-DVAR) algorithm for aerosols in a WRF/Chem model is presented. The WRF/Chem model uses the MOSAIC (Model for Simulating Aerosol Interactions and Chemistry) scheme, which explicitly treats eight major species (elemental/black carbon, organic carbon, nitrate, sulfate, chloride, ammonium, sodium and the sum of other inorganic, inert mineral and metal species) and represents size distributions using a sectional method with four size bins. The 3-DVAR scheme is formulated to take advantage of the MOSAIC scheme in providing comprehensive analyses of species concentrations and size distributions. To treat the large number of state variables associated with the MOSAIC scheme, this 3-DVAR algorithm first determines the analysis increments of the total mass concentrations of the eight species, defined as the sum of the mass concentrations across all size bins, and then distributes the analysis increments over four size bins according to the background error variances. The number concentrations for each size bin are adjusted based on the ratios between the mass and number concentrations of the background state. Additional flexibility is incorporated to further lump the eight mass concentrations, and five lumped species are used in the application presented. The system is evaluated using the analysis and prediction of PM2.5 in the Los Angeles basin during the CalNex 2010 field experiment, with assimilation of surface PM2.5 and speciated concentration observations. The results demonstrate that the data assimilation significantly reduces the errors in comparison with a simulation without data assimilation and improved forecasts of the concentrations of PM2.5 as well as individual species for up to 24 h. Some implementation difficulties and limitations of the system are discussed.

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