scholarly journals Use of a Maximum Entropy Method as a Regularization Technique during the Retrieval of Trace Gas Profiles from Limb Sounding Measurements

2006 ◽  
Vol 23 (12) ◽  
pp. 1657-1667 ◽  
Author(s):  
J. Steinwagner ◽  
G. Schwarz ◽  
S. Hilgers
Keyword(s):  
Maximum Entropy ◽  
Random Noise ◽  
A Priori ◽  
Michelson Interferometer ◽  
Simulated Data ◽  
Optimal Estimation ◽  
Initial Guess ◽  
Entropy Method ◽  
Trace Gas ◽  
Regularization Techniques

Abstract The retrieval of trace gas profiles from radiance measurements of limb sounding instruments represents an inverse problem: vertical profiles of mixing ratios have to be extracted from sequences of horizontally measured radiances recorded by a spectrometer. Typically, these retrievals are plagued by random noise and systematic errors, necessitating the use of regularization techniques during inversion calculations. In the following, the use of selected maximum entropy operators as a regularization tool is discussed and their performance with conventional optimal estimation and Tikhonov-type regularization techniques is compared. The main gain with the proposed maximum entropy operators is that no a priori knowledge is needed; a reasonable initial guess profile is fully sufficient. The approach is verified by using simulated data of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument, an infrared Fourier transform spectrometer flown on the European Envisat mission.

scholarly journals Level 2 processor and auxiliary data for ESA Version 8 final full mission analysis of MIPAS measurements on ENVISAT

2021 ◽  
Author(s):  
Piera Raspollini ◽  
Enrico Arnone ◽  
Flavio Barbara ◽  
Massimo Bianchini ◽  
Bruno Carli ◽  
...  
Keyword(s):  
Spectroscopic Data ◽  
A Priori ◽  
Michelson Interferometer ◽  
Temporal Stability ◽  
Optimal Estimation ◽  
Initial Guess ◽  
Atmospheric Composition ◽  
Data Set ◽  
Auxiliary Data ◽  
Level 2

Abstract. High quality long-term data sets of altitude-resolved measurements of the atmospheric composition are important because they can be used both to study the evolution of the atmosphere and as a benchmark for future missions. For the final ESA reprocessing of MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) on ENVISAT (ENViromental SATellite) data, numerous improvements were implemented in the level 2 (L2) processor Optimised Retrieval Model (ORM) version 8.22 (V8) and its auxiliary data. The implemented changes involve all aspects of the processing chain, from the modelling of the measurements with the handling of the horizontal inhomogeneities along the line of sight to the use of the Optimal Estimation for retrieving the minor species, from a more sensitive approach to detect the spectra affected by clouds to a refined method for identifying low quality products. Improvements in the modelling of the measurements were obtained also with an update of the used spectroscopic data and of the databases providing the a priori knowledge of the atmosphere. The HITRAN_mipas_pf4.45 spectroscopic database was finalised with new spectroscopic data verified with MIPAS measurements themselves, while recently measured cross-sections were used for the heavy molecules. The so-called IG2 data set, containing the climatology used by MIPAS L2 processor to generate the initial guess and interfering species profiles when the retrieved profiles from previous scans are not available, was improved taking into account the diurnal variation of the profiles defined using climatologies from both measurements and models. Horizontal gradients were generated using ECMWF ERA-Interim data closest in time and space to the MIPAS data. Further improvements in the L2 V8 products derived from the use of the L1b V8 products, which were upgraded to reduce the instrumental temporal drift and to handle the abrupt changes in the calibration gain. The improvements introduced into the ORM V8 L2 processor and its upgraded auxiliary data, together with the use of the L1b V8 products, lead to the generation of the MIPAS L2 V8 products that are characterised by an increased accuracy, better temporal stability, and a greater number of retrieved species.

scholarly journals Application of tomographic inversion in studying airglow in the mesopause region

1998 ◽  
Vol 16 (10) ◽  
pp. 1180-1189 ◽  
Author(s):  
T. Nygrén ◽  
M. J. Taylor ◽  
M. S. Lehtinen ◽  
M. Markkanen
Keyword(s):  
Gravity Waves ◽  
Random Noise ◽  
A Priori ◽  
Lower Thermosphere ◽  
Vertical Plane ◽  
Simulated Data ◽  
Altitude Range ◽  
Priori Information ◽  
Two Stages ◽  
Atmospheric Gravity

Abstract. It is pointed out that observations of periodic nightglow structures give excellent information on atmospheric gravity waves in the mesosphere and lower thermosphere. The periods, the horizontal wavelengths and the phase speeds of the waves can be determined from airglow images and, using several cameras, the approximate altitude of the luminous layer can also be determined by triangulation. In this paper the possibility of applying tomographic methods for reconstructing the airglow structures is investigated using numerical simulations. A ground-based chain of cameras is assumed, two-dimensional airglow models in the vertical plane above the chain are constructed, and simulated data are calculated by integrating the models along a great number of rays with different elevation angles for each camera. After addition of random noise, these data are then inverted to obtain reconstructions of the models. A tomographic analysis package originally designed for satellite radiotomography is used in the inversion. The package is based on a formulation of stochastic inversion which allows the input of a priori information to the solver in terms of regularization variances. The reconstruction is carried out in two stages. In the first inversion, constant regularization variances are used within a wide altitude range. The results are used in determining the approximate altitude range of the airglow structures. Then, in the second inversion, constant non-zero regularization variances are used inside this region and zero variances outside it. With this method reliable reconstructions of the models are obtained. The number of cameras as well as their separations are varied in order to find out the limitations of the method.Key words. Tomography · Airglow · Mesopause · Gravity waves

Fine-scale mapping of fish distribution from commercial catch and effort data using maximum entropy tomography

1998 ◽  
Vol 55 (5) ◽  
pp. 1220-1227 ◽  
Author(s):  
M Vignaux ◽  
G A Vignaux ◽  
S Lizamore ◽  
D Gresham
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Simulated Data ◽  
Real Data ◽  
Entropy Method ◽  
Fish Distribution ◽  
Bayesian Maximum Entropy ◽  
Commercial Catch ◽  
Trawl Fishery ◽  
Distribution Of Fish

We present a technique for mapping the spatial distribution of fish using commercial catch and effort data. The relative fish density can be estimated at scales smaller than the length of the unit of effort, such as a tow, by using a Bayesian maximum entropy method. This can take advantage of the fact that the tows cross to give information about the density in those areas. This is a novel application of a well-tested technique that has been used in other fields such as astronomical imaging. Its utility and robustness is demonstrated both on simulated data and on real data from the trawl fishery on spawning hoki off the west coast of the South Island of New Zealand.

scholarly journals A Rain-Rate Retrieval Algorithm for Attenuated Radar Measurements

2010 ◽  
Vol 49 (3) ◽  
pp. 381-393 ◽  
Author(s):  
Prabhat K. Koner ◽  
Alessandro Battaglia ◽  
Clemens Simmer
Keyword(s):  
Rain Rate ◽  
Least Squares Method ◽  
A Priori ◽  
Estimation Method ◽  
Optimal Estimation ◽  
Retrieval Algorithm ◽  
W Band ◽  
Regularization Techniques ◽  
Radar Measurements ◽  
Regularized Total Least Squares

Abstract A dynamic regularization scheme for rain-rate retrievals from attenuated radar measurements is presented. Most regularization techniques, including the optimal estimation method, use the state-space parameters to regularize the problem, which will always lead to a bias in the solution. To avoid this problem the authors introduce an evolutionary regularization technique, which is based on the spatial derivative of the measured reflectivity profile and allows for a bias-free global solution. The regularization strength is determined by the quadratic eigenvalue solution using the regularized total least squares method. With the new method, the authors perform a retrieval of rain-rate profiles from simulated measurements of a nadir-pointing W-band (94 GHz) radar, in a configuration similar to the cloud radar employed on CloudSat. The simulations assume that multiple scattering is negligible and only liquid hydrometeors are taken into account. The authors compare the results of this method with the outcome of an optimal estimation method and demonstrate that their method is superior in terms of reliability, correlation coefficient, and dispersion to the optimal estimation method for layers experiencing high values of attenuation; therefore, the a priori bias typical for optimal estimation solutions is avoided.

scholarly journals Retrieval of macrophysical cloud parameters from MIPAS: algorithm description

2011 ◽  
Vol 4 (4) ◽  
pp. 683-704 ◽  
Author(s):  
J. Hurley ◽  
A. Dudhia ◽  
R. G. Grainger
Keyword(s):  
A Priori ◽  
Michelson Interferometer ◽  
Optimal Estimation ◽  
Single Scattering ◽  
Stratospheric Aerosol ◽  
Retrieval Algorithm ◽  
Cloud Detection ◽  
Retrieval Process ◽  
Error Sources ◽  
Cloud Parameters

Abstract. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) onboard ENVISAT has the potential to be particularly useful for studying high, thin clouds, which have been difficult to observe in the past. This paper details the development, implementation and testing of an optimal-estimation-type retrieval for three macrophysical cloud parameters (cloud top height, cloud top temperature and cloud extinction coefficient) from infrared spectra measured by MIPAS. A preliminary estimation of a parameterisation of the optical and geometrical filling of the measurement field-of-view by cloud is employed as the first step of the retrieval process to improve the choice of a priori for the macrophysical parameters themselves. Preliminary application to single-scattering simulations indicates that the retrieval error stemming from uncertainties introduced by noise and by a priori variances in the retrieval process itself is small – although it should be noted that these retrieval errors do not include the significant errors stemming from the assumption of homogeneity and the non-scattering nature of the forward model. Such errors are preliminarily and qualitatively assessed here, and are likely to be the dominant error sources. The retrieval converges for 99% of input cases, although sometimes fails to converge for vetically-thin (<1 km) clouds. The retrieval algorithm is applied to MIPAS data; the results of which are qualitatively compared with CALIPSO cloud top heights and PARASOL cloud opacities. From comparison with CALIPSO cloud products, it must be noted that the cloud detection method used in this algorithm appears to potentially misdetect stratospheric aerosol layers as cloud. This algorithm has been adopted by the European Space Agency's "MIPclouds" project.

scholarly journals Envisat MIPAS measurements of CFC-11: retrieval, validation, and climatology

2008 ◽  
Vol 8 (2) ◽  
pp. 4561-4602 ◽  
Author(s):  
L. Hoffmann ◽  
M. Kaufmann ◽  
R. Spang ◽  
R. Müller ◽  
J. J. Remedios ◽  
...  
Keyword(s):  
Large Scale ◽  
Lower Stratosphere ◽  
A Priori ◽  
Michelson Interferometer ◽  
Optimal Estimation ◽  
Atmospheric Conditions ◽  
Data Set ◽  
Mixing Ratios ◽  
Priori Information ◽  
The Individual

Abstract. From July 2002 to March 2004 the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) aboard the European Space Agency's Environmental Satellite (Envisat) measured nearly continuously mid infrared limb radiance spectra. These measurements are utilised to retrieve the global distribution of the chlorofluorocarbon CFC-11 by applying a new fast forward model for Envisat MIPAS and an accompanying optimal estimation retrieval processor. A detailed analysis shows that the total retrieval errors of the individual CFC-11 volume mixing ratios are typically below 10% and that the systematic components are dominating. Contribution of a priori information to the retrieval results are less than 5 to 10%. The vertical resolution of the observations is about 3 to 4 km. The data are successfully validated by comparison with several other space experiments, an air-borne in-situ instrument, measurements from ground-based networks, and independent Envisat MIPAS analyses. The retrieval results from 425 000 Envisat MIPAS limb scans are compiled to provide a new climatological data set of CFC-11. The climatology shows significantly lower CFC-11 abundances in the lower stratosphere compared with the Reference Atmospheres for MIPAS (RAMstan V3.1) climatology. Depending on the atmospheric conditions the differences between the climatologies are up to 30 to 110 ppt (45 to 150%) at 19 to 27 km altitude. Additionally, time series of CFC-11 mean abundance and variability for five latitudinal bands are presented. The observed CFC-11 distributions can be explained by the residual mean circulation and large-scale eddy-transports in the upper troposphere and lower stratosphere. The new CFC-11 data set is well suited for further scientific studies.

scholarly journals Rapid quantitative pharmacodynamic imaging with Bayesian estimation

2015 ◽  
Author(s):  
Jonathan M. Koller ◽  
M. Jonathan Vachon ◽  
G. Larry Bretthorst ◽  
Kevin J. Black
Keyword(s):  
Random Noise ◽  
A Priori ◽  
Simulated Data ◽  
Previous Method ◽  
Proof Of Concept ◽  
Computationally Efficient ◽  
Primate Brain ◽  
Simulation Testing ◽  
Novel Method ◽  
Improved Accuracy

ABSTRACTWe recently described rapid quantitative pharmacodynamic imaging, a novel method for estimating sensitivity of a biological system to a drug. We tested its accuracy in simulated biological signals with varying receptor sensitivity and varying levels of random noise, and presented initial proof-of-concept data from functional MRI (fMRI) studies in primate brain. However, the initial simulation testing used a simple iterative approach to estimate pharmacokinetic-pharmacodynamic (PKPD) parameters, an approach that was computationally efficient but returned parameters only from a small, discrete set of values chosen a priori.Here we revisit the simulation testing using a Bayesian method to estimate the PKPD parameters. This improved accuracy compared to our previous method, and noise without intentional signal was never interpreted as signal. We also reanalyze the fMRI proof-of-concept data. The success with the simulated data, and with the limited fMRI data, is a necessary first step toward further testing of rapid quantitative pharmacodynamic imaging.

A new method for NMR data inversion based on double-parameter regularization

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. JM39-JM49 ◽  
Author(s):  
Jiangfeng Guo ◽  
Ranhong Xie ◽  
Youlong Zou ◽  
Guowen Jin ◽  
Lun Gao ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Regularization Parameter ◽  
Signal To Noise Ratio ◽  
Simulated Data ◽  
Entropy Method ◽  
Petroleum Exploration ◽  
Tight Sandstone ◽  
Nmr Data ◽  
Parameter Regularization

Nuclear magnetic resonance (NMR) technology plays a significant role in petroleum exploration. NMR data can be processed using inversion methods to reflect the relaxation information of all the components. We have developed a new double-parameter regularization (DPR) method for the inversion of NMR data, whose regularization terms consist of Tikhonov regularization and maximum entropy regularization. The objective function for the DPR method was solved using the Levenberg-Marquardt method, the proportional coefficient of the regularization parameter was obtained using an iteration procedure, and the optimum regularization parameter of the DPR method was selected using an S-curve. The relationship between the optimum regularization parameter and the signal-to-noise ratio (S/N) of the data was evaluated. Moreover, we compared the results of the NMR inversion obtained from the norm smooth method, the maximum entropy method, and the DPR method for simulated data. We evaluated how the proportional coefficient of the regularization parameter affected the inverted [Formula: see text] distributions and processed field NMR log data for a tight sandstone reservoir using the DPR method. The results indicated that the optimum regularization parameter for the DPR method gradually decreases with increasing data S/N. The accuracy is higher for the DPR method than for the norm smooth method and the maximum entropy method under low-S/N conditions. It is of great importance to select the proportional coefficient for the DPR method. The inverted [Formula: see text] distributions are similar for the DPR method and the norm smooth method when the proportional coefficient is small, and this is similar for the DPR method and the maximum entropy method when the proportional coefficient is large.

On the Challenges of Tomography Retrievals of a 2D Water Vapor Field Using Ground-Based Microwave Radiometers: An Observation System Simulation Experiment

2015 ◽  
Vol 32 (1) ◽  
pp. 116-130 ◽  
Author(s):  
Véronique Meunier ◽  
David D. Turner ◽  
Pavlos Kollias
Keyword(s):  
Boundary Layer ◽  
Water Vapor ◽  
Turbulent Boundary Layer ◽  
Covariance Matrix ◽  
A Priori ◽  
Simulated Data ◽  
Optimal Estimation ◽  
Estimation Algorithm ◽  
Observation System ◽  
Microwave Radiometers

AbstractTwo-dimensional water vapor fields were retrieved by simulated measurements from multiple ground-based microwave radiometers using a tomographic approach. The goal of this paper was to investigate how the various aspects of the instrument setup (number and spacing of elevation angles and of instruments, number of frequencies, etc.) affected the quality of the retrieved field. This was done for two simulated atmospheric water vapor fields: 1) an exaggerated turbulent boundary layer and 2) a simplified water vapor front. An optimal estimation algorithm was used to obtain the tomographic field from the microwave radiometers and to evaluate the fidelity and information content of this retrieved field.While the retrieval of the simplified front was reasonably successful, the retrieval could not reproduce the details of the turbulent boundary layer field even using up to nine instruments and 25 elevation angles. In addition, the vertical profile of the variability of the water vapor field could not be captured. An additional set of tests was performed using simulated data from a Raman lidar. Even with the detailed lidar measurements, the retrieval did not succeed except when the lidar data were used to define the a priori covariance matrix. This suggests that the main limitation to obtaining fine structures in a retrieved field using tomographic retrievals is the definition of the a priori covariance matrix.

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