scholarly journals A method to derive the Site Atmospheric State Best Estimate (SASBE) of ozone profiles from radiosonde and passive microwave data

2015 ◽  
Vol 8 (3) ◽  
pp. 3399-3422 ◽  
Author(s):  
E. Maillard Barras ◽  
A. Haefele ◽  
R. Stübi ◽  
D. Ruffieux
Keyword(s):  
Brightness Temperature ◽  
A Priori ◽  
A Priori Information ◽  
Data Set ◽  
Ozone Data ◽  
Best Estimate ◽  
Vertical Range ◽  
Ozone Profile ◽  
Atmospheric State ◽  
Priori Information

Abstract. We present a method to derive the site atmospheric state best estimate (SASBE) of the ozone profile combining brightness temperature spectra around the 142 GHz absorption line of ozone measured by the microwave radiometer SOMORA and ozone profiles measured by the radiosonde (RS). The SASBE ozone profile is obtained using the radiosonde ozone profile as a priori information in an optimal estimation retrieval of the SOMORA radiometer. The resulting ozone profile ranges from ground up to 65 km altitude and makes optimal use of the available information at each altitude. The high vertical resolution of the radiosonde profile can be conserved and the uncertainty of the SASBE is well defined at each altitude. A SASBE ozone profile dataset has been generated for Payerne, Switzerland, with a temporal resolution of 3 profiles a week for the time period ranging from 2011 to 2013. The relative difference of the SASBE ozone profiles to the AURA/MLS ozone profiles lies between −3 to 6% over the vertical range of 20–65 km. Above 20 km, the agreement between the SASBE and AURA/MLS ozone profiles is better than the agreement between the operational SOMORA ozone data set and AURA/MLS. Below 20 km the SASBE ozone data are identical to the radiosonde measurements. The same method has been applied to ECWMF-ERA interim ozone profiles and SOMORA data to generate a SASBE dataset with a time resolution of 4 profiles per day. These SASBE ozone profiles agree between −4 and +8% with AURA/MLS. The improved agreement of the SASBE datasets with AURA/MLS above 20 km demonstrates the benefit of better a priori information in the retrieval of ozone from brightness temperature data.

scholarly journals Ozone profile smoothness as a priori information in the inversion of limb measurements

2004 ◽  
Vol 22 (10) ◽  
pp. 3411-3420 ◽  
Author(s):  
V. F. Sofieva ◽  
J. Tamminen ◽  
H. Haario ◽  
E. Kyrölä ◽  
M. Lehtinen
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Priori Information ◽  
Ozone Profile ◽  
Stellar Occultation ◽  
Atmospheric Profiles ◽  
Priori Information ◽  
Typical Measurement

Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.

scholarly journals Smoothing error pitfalls

2014 ◽  
Vol 7 (4) ◽  
pp. 3301-3319 ◽  
Author(s):  
T. von Clarmann
Keyword(s):  
Covariance Matrix ◽  
Error Propagation ◽  
A Priori ◽  
A Priori Information ◽  
Atmospheric Variability ◽  
True State ◽  
Statistical Sense ◽  
Atmospheric State ◽  
The Difference ◽  
Priori Information

Abstract. The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by the so-called smoothing error. In this paper it is shown that the concept of the smoothing error is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state. The idea of a sufficiently fine sampling of this reference atmospheric state is untenable because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully talk about temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the involved a priori covariance matrix has been evaluated on the comparison grid rather than resulting from interpolation. This is, because the undefined component of the smoothing error, which is the effect of smoothing implied by the finite grid on which the measurements are compared, cancels out when the difference is calculated.

scholarly journals Towards the retrieval of tropospheric ozone with the Ozone Monitoring Instrument (OMI)

2015 ◽  
Vol 8 (2) ◽  
pp. 671-687 ◽  
Author(s):  
T. Mielonen ◽  
J. F. de Haan ◽  
J. C. A. van Peet ◽  
M. Eremenko ◽  
J. P. Veefkind
Keyword(s):  
Radiative Transfer ◽  
Covariance Matrix ◽  
Tropospheric Ozone ◽  
Surface Albedo ◽  
A Priori ◽  
Stray Light ◽  
Retrieval Algorithm ◽  
A Priori Information ◽  
Ozone Profile ◽  
Priori Information

Abstract. We have assessed the sensitivity of the operational Ozone Monitoring Instrument (OMI) ozone profile retrieval algorithm to a number of a priori and radiative transfer assumptions. We studied the effect of stray light correction, surface albedo assumptions and a priori ozone profiles on the retrieved ozone profile. Then, we studied how to modify the algorithm to improve the retrieval of tropospheric ozone. We found that stray light corrections have a significant effect on the retrieved ozone profile but mainly at high altitudes. Surface albedo assumptions, on the other hand, have the largest impact at the lowest layers. Choice of an ozone profile climatology which is used as a priori information has small effects on the retrievals at all altitudes. However, the usage of climatological a priori covariance matrix has a significant effect. Based on these sensitivity tests, we made several modifications to the retrieval algorithm: the a priori ozone climatology was replaced with a new tropopause-dependent climatology, the a priori covariance matrix was calculated from the climatological ozone variability values, and the surface albedo was assumed to be linearly dependent on wavelength in the 311.5–330 nm channel. As expected, we found that the a priori covariance matrix basically defines the vertical distribution of degrees of freedom for a retrieval. Moreover, our case study over Europe showed that the modified version produced over 10% smaller ozone abundances in the troposphere which reduced the systematic overestimation of ozone in the retrieval algorithm and improved correspondence with Infrared Atmospheric Sounding Instrument (IASI) retrievals. The comparison with ozonesonde measurements over North America showed that the operational retrieval performed better in the upper troposphere/lower stratosphere (UTLS), whereas the modified version improved the retrievals in the lower troposphere and upper stratosphere. These comparisons showed that the systematic biases in the OMI ozone profile retrievals are not caused by the a priori information but by some still unidentified problem in the radiative transfer modelling. Instead, the a priori information pushes the systematically wrong ozone profiles towards the true values. The smaller weight of the a priori information in the modified retrieval leads to better visibility of tropospheric ozone structures, because it has a smaller tendency to damp the variability of the retrievals in the troposphere. In summary, the modified retrieval unmasks systematic problems in the radiative transfer/instrument model and is more sensitive to tropospheric ozone variation; that is, it is able to capture the tropospheric ozone morphology better.

Particle swarm optimization of 2D magnetotelluric data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. E125-E141 ◽  
Author(s):  
Francesca Pace ◽  
Alessandro Santilano ◽  
Alberto Godio
Keyword(s):  
Inverse Problem ◽  
Particle Swarm Optimization ◽  
A Priori ◽  
Particle Swarm ◽  
Stability And Convergence ◽  
Real Field ◽  
A Priori Information ◽  
Data Set ◽  
Swarm Optimization ◽  
Priori Information

We implement the particle swarm optimization (PSO) algorithm for the two-dimensional (2D) magnetotelluric (MT) inverse problem. We first validate PSO on two synthetic models of different complexity and then apply it to an MT benchmark for real-field data, the COPROD2 data set (Canada). We pay particular attention to the selection of the PSO input parameters to properly address the complexity of the 2D MT inverse problem. We enhance the stability and convergence of the solution of the geophysical problem by applying the hierarchical PSO with time-varying acceleration coefficients (HPSO-TVAC). Moreover, we parallelize the code to reduce the computation time because PSO is a computationally demanding global search algorithm. The inverse problem was solved for the synthetic data both by giving a priori information at the beginning and by using a random initialization. The a priori information was given to a small number of particles as the initial position within the search space of solutions, so that the swarming behavior was only slightly influenced. We have demonstrated that there is no need for the a priori initialization to obtain robust 2D models because the results are largely comparable with the results from randomly initialized PSO. The optimization of the COPROD2 data set provides a resistivity model of the earth in line with results from previous interpretations. Our results suggest that the 2D MT inverse problem can be successfully addressed by means of computational swarm intelligence.

A COMBINATION SCHEME FOR FUZZY CLUSTERING

2002 ◽  
Vol 16 (07) ◽  
pp. 901-912 ◽  
Author(s):  
EVGENIA DIMITRIADOU ◽  
ANDREAS WEINGESSEL ◽  
KURT HORNIK
Keyword(s):  
A Priori ◽  
Fuzzy Cluster ◽  
A Priori Information ◽  
Cluster Validity ◽  
Data Set ◽  
Cluster Algorithms ◽  
Combination Scheme ◽  
Priori Information ◽  
Theoretical Considerations ◽  
Structurally Stable

In this paper we present a voting scheme for fuzzy cluster algorithms. This voting method allows us to combine several runs of cluster algorithms resulting in a common partition. This helps us to tackle the problem of choosing the appropriate clustering method for a data set where we have no a priori information about it. We mathematically derive the algorithm from theoretical considerations. Experiments show that the voting algorithm finds structurally stable results. Several cluster validity indexes show the improvement of the voting result in comparison to simple fuzzy voting.

Structurally tailored 3D anisotropic controlled-source electromagnetic resistivity inversion with cross-gradient criterion and simultaneous model calibration

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. E387-E402 ◽  
Author(s):  
Max A. Meju ◽  
Randall L. Mackie ◽  
Federico Miorelli ◽  
Ahmad Shahir Saleh ◽  
Roger V. Miller
Keyword(s):  
Field Data ◽  
A Priori ◽  
Calibration Data ◽  
A Priori Information ◽  
Data Set ◽  
Low Contrast ◽  
Controlled Source ◽  
Low Resistivity ◽  
Band Limited ◽  
Priori Information

Geologic interpretation of 3D anisotropic resistivity models from conventional marine controlled-source electromagnetic (CSEM) data inversion faces difficulties in low-resistivity contrast sediments and structurally complex environments that typify the new frontiers for hydrocarbon exploration. Currently, the typically reconstructed horizontal resistivity [Formula: see text] and vertical resistivity [Formula: see text] models often have conflicting depth structures that are difficult to explain in terms of subsurface geology, and the resulting resistivities may not be close to the true formation resistivities required for estimating reservoir parameters. We have investigated the concept that an objective geologically oriented or structurally tailored inversion can be achieved by requiring that the cross-product of the gradient of horizontal resistivity and the gradient of the vertical resistivity is equal to zero at significant geologic boundaries. We incorporate this boundary-shape criterion in our 3D inverse problem formulations, implemented within nonlinear model-space and conjugate-gradient contexts, for cases in which a priori calibration data from wells and/or seismically derived subsurface boundaries are available and for cases in which these are lacking. The resulting fit-for-purpose solutions serve to better analyze the peculiarity of a given data set. We applied these algorithms to synthetic and field CSEM data sets representing a fold-thrust environment with low-resistivity and low-contrast sediments. The resulting [Formula: see text] and [Formula: see text] models from cross-gradient joint inversion of synthetic data of appropriate frequency bandwidth without a priori information are structurally similar and consistent with the test models, whereas those from the inversions of band-limited field data are consistent with the available seismic and resistivity well-log data. This particular approach will thus be useful for lithologic correlation in frontier regions with limited a priori information using broadband CSEM data. For these band-limited field data, we found that the anisotropic bulk resistivities of the low-contrast sediments are better determined by incorporating a priori calibration data from triaxial resistivity logs and seismic horizons.

Reconstruction of borehole radar images by a modified f–k migration

2020 ◽  
Vol 221 (3) ◽  
pp. 1626-1634
Author(s):  
Jianjian Huo ◽  
Binzhong Zhou ◽  
Qing Zhao ◽  
Iain M Mason
Keyword(s):  
Final Section ◽  
Early Stage ◽  
A Priori ◽  
A Priori Information ◽  
Data Set ◽  
Radar Images ◽  
Imaging Tool ◽  
Bedding Planes ◽  
Borehole Radar ◽  
Priori Information

SUMMARY Borehole radar (BHR) is an effective imaging tool. It can be used to detect and map faults, fractures, folds, domes, partings and mine workings. Most BHRs have azimuthally omnidirectional radiation patterns. The echoes sensed by such BHRs may come from any direction. Considering a radar in a straight borehole that passes through a stack of flat reflection planes, V-shaped events or crosses appear on the time section. One of the arms of each cross is a real image while the other is an ambiguity of known origin. Directional ambiguities such as these obstruct efforts to interpret the data. In this paper, we address this difficulty by using a modified f–k migration algorithm to translate crosses into lines on the final section that are consistent with a priori information about for example bedding. Compared with conventional strategies, for example migration + f–k dip filter, this approach integrates the two separated processes into one and is straightforward, computationally effective and simple to implement. The method is demonstrated using a synthetic model and a real BHR field data set. It allows the interpreter to use a priori information about fault swarms or plausible bedding planes at an early stage. The reconstructed BHR image helps the search for geological anomalies such as fractures, partings, domes and rolls that could be a hazard for mining.

scholarly journals Inversion of phase times for hypocenters and shallow crustal velocities, Mojave Desert, California

1979 ◽  
Vol 69 (2) ◽  
pp. 387-396 ◽  
Author(s):  
James A. Hileman
Keyword(s):  
Mojave Desert ◽  
Velocity Structure ◽  
A Priori ◽  
Relative Importance ◽  
Local Velocity ◽  
A Priori Information ◽  
Linear Least Squares ◽  
Data Set ◽  
Velocity Models ◽  
Priori Information

abstract Phase times for an ensemble of 20 aftershocks of the June 1, 1975, Galway Lake earthquake were inverted to determine hypocenters and local velocity structure simultaneously. A maximum likelihood formulation of linear, least-squares inversion was used so that the data were weighted according to their estimated variances. A trade-off parameter controlled the relative importance of the RMS error and the amount by which the model changed at each iteration. Individual aftershocks must be selected so that a wide variety of travel paths are represented. Initial trials disclosed that careful constraints are necessary for allowed changes in station delays. Fixed velocity boundaries, based on a priori information, were used for each of several starting models, and only layer velocities were allowed to vary. Each of the trials indicated that shallow crustal velocities in the vincinity of Galway Lake are somewhat lower than those of the usual velocity models. The velocities are not strongly constrained by this data set, but the results are consistent with a subsequent, detailed refraction survey by other workers. Mapping the travel-time surface in time-depth-distance space helps clarify the limitations inherent in a given problem.

3-D inversion of magnetic data

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 394-408 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Objective Function ◽  
A Priori ◽  
Magnetic Data ◽  
A Priori Information ◽  
Data Set ◽  
Earth Models ◽  
Priori Information ◽  
Model Region ◽  
D Model ◽  
Physical Realizability

We present a method for inverting surface magnetic data to recover 3-D susceptibility models. To allow the maximum flexibility for the model to represent geologically realistic structures, we discretize the 3-D model region into a set of rectangular cells, each having a constant susceptibility. The number of cells is generally far greater than the number of the data available, and thus we solve an underdetermined problem. Solutions are obtained by minimizing a global objective function composed of the model objective function and data misfit. The algorithm can incorporate a priori information into the model objective function by using one or more appropriate weighting functions. The model for inversion can be either susceptibility or its logarithm. If susceptibility is chosen, a positivity constraint is imposed to reduce the nonuniqueness and to maintain physical realizability. Our algorithm assumes that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only. All minimizations are carried out with a subspace approach where only a small number of search vectors is used at each iteration. This obviates the need to solve a large system of equations directly, and hence earth models with many cells can be solved on a deskside workstation. The algorithm is tested on synthetic examples and on a field data set.

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