On ℓ 1 -Regularization Under Continuity of the Forward Operator in Weaker Topologies

2018 ◽  
pp. 67-88
Author(s):  
Daniel Gerth ◽  
Bernd Hofmann
Keyword(s):  
Forward Operator

scholarly journals Focal transformation, an imaging concept for signal restoration and noise removal

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. A55-A59 ◽  
Author(s):  
A. J. Berkhout ◽  
D. J. Verschuur
Keyword(s):  
Input Data ◽  
Noise Removal ◽  
Point Of View ◽  
Data Interpolation ◽  
Signal Restoration ◽  
Physical Point ◽  
Seismic Processing ◽  
Promising Tool ◽  
Focal Area ◽  
Forward Operator

Interpolation of data beyond aliasing limits and removal of noise that occurs within the seismic bandwidth are still important problems in seismic processing. The focal transform is introduced as a promising tool in data interpolation and noise removal, allowing the incorporation of macroinformation about the involved wavefields. From a physical point of view, the principal action of the forward focal operator is removing the spatial phase of the signal content from the input data, and the inverse focal operator restores what the forward operator has removed. The strength of the method is that in the transformed domain, the focused signals at the focal area can be separated from the dispersed noise away from the focal area. Applications of particular interest in preprocessing are interpolation of missing offsets and reconstruction of signal beyond aliasing. The latter can be seen as the removal of aliasing noise.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

scholarly journals Development and application of a backscatter lidar forward operator for quantitative validation of aerosol dispersion models and future data assimilation

2017 ◽  
Vol 10 (12) ◽  
pp. 4705-4726 ◽  
Author(s):  
Armin Geisinger ◽  
Andreas Behrendt ◽  
Volker Wulfmeyer ◽  
Jens Strohbach ◽  
Jochen Förstner ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Volcanic Ash ◽  
Model Systems ◽  
Spherical Particles ◽  
Lidar Measurement ◽  
Backscatter Coefficient ◽  
Future Data ◽  
Sensitivity Studies ◽  
Ash Dispersion ◽  
Forward Operator

Abstract. A new backscatter lidar forward operator was developed which is based on the distinct calculation of the aerosols' backscatter and extinction properties. The forward operator was adapted to the COSMO-ART ash dispersion simulation of the Eyjafjallajökull eruption in 2010. While the particle number concentration was provided as a model output variable, the scattering properties of each individual particle type were determined by dedicated scattering calculations. Sensitivity studies were performed to estimate the uncertainties related to the assumed particle properties. Scattering calculations for several types of non-spherical particles required the usage of T-matrix routines. Due to the distinct calculation of the backscatter and extinction properties of the models' volcanic ash size classes, the sensitivity studies could be made for each size class individually, which is not the case for forward models based on a fixed lidar ratio. Finally, the forward-modeled lidar profiles have been compared to automated ceilometer lidar (ACL) measurements both qualitatively and quantitatively while the attenuated backscatter coefficient was chosen as a suitable physical quantity. As the ACL measurements were not calibrated automatically, their calibration had to be performed using satellite lidar and ground-based Raman lidar measurements. A slight overestimation of the model-predicted volcanic ash number density was observed. Major requirements for future data assimilation of data from ACL have been identified, namely, the availability of calibrated lidar measurement data, a scattering database for atmospheric aerosols, a better representation and coverage of aerosols by the ash dispersion model, and more investigation in backscatter lidar forward operators which calculate the backscatter coefficient directly for each individual aerosol type. The introduced forward operator offers the flexibility to be adapted to a multitude of model systems and measurement setups.

Improved impacts in observing system simulation experiments of radio occultation observations as a result of model and data assimilation changes

2020 ◽  
Author(s):  
L. CUCURULL ◽  
S. P. F. CASEY
Keyword(s):  
Data Assimilation ◽  
Radio Occultation ◽  
Weather Forecasting ◽  
Positive Impact ◽  
System Simulation ◽  
Weather Prediction ◽  
Wind Fields ◽  
Simulation Experiments ◽  
The Impact ◽  
Forward Operator

AbstractAs global data assimilation systems continue to evolve, Observing System Simulation Experiments (OSSEs) need to be updated to accurately quantify the impact of proposed observing technologies in weather forecasting. Earlier OSSEs with radio occultation (RO) observations have been updated and the impact of the originally proposed Constellation Observing Satellites for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) mission, with a high-inclination and low-inclination component, has been investigated by using the operational data assimilation system at NOAA and a 1-dimensional bending angle RO forward operator. It is found that the impact of the low-inclination component of the originally planned COSMIC-2 mission (now officially named COSMIC-2) has significantly increased as compared to earlier studies, and significant positive impact is now found globally in terms of mass and wind fields. These are encouraging results as COSMIC-2 was successfully launched in June 2019 and data have been recently released to operational weather centers. Earlier findings remain valid indicating that globally distributed RO observations are more important to improve weather prediction globally than a denser sampling of the tropical latitudes. Overall, the benefits reported here from assimilating RO soundings are much more significant than the impacts found in previous OSSEs. This is largely attributed to changes in the data assimilation and forecast system and less to the more advanced 1-dimensional forward operator chosen for the assimilation of RO observations.

Algebraic Methods for the Construction of Algebraic-Difference Equations With Desired Behavior

2018 ◽  
Vol 34 ◽  
pp. 1-17 ◽  
Author(s):  
Lazaros Moysis ◽  
Nicholas Karampetakis
Keyword(s):  
Difference Equations ◽  
Polynomial Matrix ◽  
Elementary Divisor ◽  
System Of Equations ◽  
Polynomial Matrices ◽  
Linear System Of Equations ◽  
System A ◽  
Auto Regressive ◽  
Algebraic Difference ◽  
Forward Operator

For a given system of algebraic and difference equations, written as an Auto-Regressive (AR) representation $A(\sigma)\beta(k)=0$, where $\sigma $ denotes the shift forward operator and $A\left( \sigma \right) $ a regular polynomial matrix, the forward-backward behavior of this system can be constructed by using the finite and infinite elementary divisor structure of $A\left( \sigma \right) $. This work studies the inverse problem: Given a specific forward-backward behavior, find a family of regular or non-regular polynomial matrices $A\left( \sigma \right) $, such that the constructed system $A\left( \sigma \right) \beta \left( k\right) =0$ has exactly the prescribed behavior. It is proved that this problem can be reduced either to a linear system of equations problem or to an interpolation problem and an algorithm is proposed for constructing a system satisfying a given forward and/or backward behavior.

Interpreting an evaluation of the ECMWF global model with CloudSat observations: ambiguities due to radar reflectivity forward operator uncertainties

2012 ◽  
Vol 138 (669) ◽  
pp. 2047-2065 ◽  
Author(s):  
Sabatino Di Michele ◽  
Maike Ahlgrimm ◽  
Richard Forbes ◽  
Mark Kulie ◽  
Ralf Bennartz ◽  
...  
Keyword(s):  
Global Model ◽  
Radar Reflectivity ◽  
Forward Operator

scholarly journals Evaluation of the COSMO model (v5.1) in polarimetric radar space – Impact of uncertainties in model microphysics, retrievals, and forward operator

2021 ◽  
Author(s):  
Prabhakar Shrestha ◽  
Jana Mendrok ◽  
Velibor Pejcic ◽  
Silke Trömel ◽  
Ulrich Blahak ◽  
...  
Keyword(s):  
Weather Prediction ◽  
Model Space ◽  
Polarimetric Radar ◽  
Surface Precipitation ◽  
The Difference ◽  
Microphysical Processes ◽  
Nwp Model ◽  
Two Parameters ◽  
Ice Water ◽  
Forward Operator

Abstract. Sensitivity experiments with a numerical weather prediction (NWP) model and polarimetric radar forward operator (FO) are conducted for a long-duration stratiform event over northwestern Germany, to evaluate uncertainties in the partitioning of the ice water content and assumptions of hydrometeor scattering properties in the NWP model and FO, respectively. Polarimetric observations from X-band radar and retrievals of hydrometeor classifications are used for comparison with the multiple experiments in radar and model space. Modifying two parameters (Dice and Tgr) responsible for the production of snow and graupel, respectively, was found to improve the synthetic polarimetric moments and simulated hydrometeor population, while keeping the difference in surface precipitation statistically insignificant at model resolvable grid scales. However, the model still exhibited a low bias in simulated polarimetric moments at lower levels above the melting layer (−3 to −13 °C) where snow was found to dominate. This necessitates further research into the missing microphysical processes in these lower levels (e.g., fragmentation due to ice-ice collisions), and use of more reliable snow scattering models to draw valid conclusions.

scholarly journals Bias correction in assimilation of AOD observations with WRF-Chem

2018 ◽  
Author(s):  
Anton Kliewer ◽  
Milija Zupanski ◽  
Qijing Bian ◽  
Sam Atwood ◽  
Yi Wang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Moving Average ◽  
Three Dimensional ◽  
Bias Reduction ◽  
Naval Research ◽  
Hygroscopic Growth ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
Non Gaussian ◽  
Forward Operator

Abstract. Accurate prediction and representation of three-dimensional aerosol distributions in the littoral (coastal) zone is both desired and difficult with many compounding factors contributing to this problem. To reduce uncertainty in forecasting in coastal regions, a coupled meteorological-aerosol data assimimilation (DA) system has been configured to include satellite observations of aerosol optical depth (AOD). These high-resolution observations are from newly-devised retrieval algorithms that utilize Moderate Resolution Imaging Spectroradiometer (MODIS) data to retrieve AOD over the coastal and turbid water surface. The Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) is combined with an ensemble-based DA system, the Maximum Likelihood Ensemble Filter (MLEF), to simulate a dust event over the Arabian Peninsula from 2016. The assimimilation of AOD observations required the development of a forward operator that converts model predictions into observation space. This operator, which incorporates hygroscopic growth of aerosol particles and determines extinction efficiency based via Mie theory, has a positive bias between the model guess and the retrieved AOD observations. In order to reduce this bias two different methods are proposed and evaluated. One is a moving average method employed throughout the case study while the other relies on a statistical re-sampling approach. The conclusion of these experiments, determined by a number of metrics including, but not limited to, root mean square (RMS) errors, an evaluation of the reduction in the cost function, and degrees of freedom for signal (DFS), indicate that the bias reduction scheme that accumulates bias information throughout the case study outperforms the method based on re-sampling. This conclusion is corroborated by inspection of the analysis increments from the DA process and by the innovations in observational space. An analysis of the non-Gaussian innovations resulting from the non-linear forward operator is also presented. This research is in support of a Multidisciplinary University Research Initiative (MURI) supported by the Office of Naval Research (ONR) with the primary goal of understanding aerosols in the littoral zone.

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