scholarly journals Effects of <i>a priori</i> profile shape assumptions oncomparisons between satellite NO<sub>2</sub> columns and model simulations

2020 ◽  
Author(s):  
Matthew J. Cooper ◽  
Randall V. Martin ◽  
Daven K. Henze ◽  
Dylan B. A. Jones
Keyword(s):  
Shape Factor ◽  
A Priori ◽  
Trace Gas ◽  
A Posteriori ◽  
A Priori Information ◽  
Profile Shape ◽  
Satellite Retrievals ◽  
Mass Factor ◽  
The Difference ◽  
Priori Information

Abstract. A critical step in satellite retrievals of trace gas columns is the calculation of the air mass factor (AMF) used to convert observed slant columns to vertical columns. This calculation requires a priori information on the shape of the vertical profile. As a result, comparisons between satellite-retrieved and model-simulated column abundances are influenced by the a priori profile shape. We examine how differences between the shape of the simulated and a priori profile can impact the interpretation of satellite retrievals by performing an adjoint-based 4D-Var assimilation of synthetic NO2 observations for constraining NOx emissions. We use the GEOS-Chem Adjoint model to perform assimilations using a variety of AMFs to examine how a posteriori emission estimates are affected if the AMF is calculated using an a priori shape factor that is inconsistent with the simulated profile. In these tests, an inconsistent a priori shape factor increased errors in a posteriori emissions estimates by up to 80 % over polluted regions. As the difference between the simulated profile shape and the a priori profile shape increases, so do the corresponding assimilated emission errors. This reveals the importance of using simulated profile information for AMF calculations when comparing that simulated output to satellite retrieved columns.

scholarly journals Effects of a priori profile shape assumptions on comparisons between satellite NO<sub>2</sub> columns and model simulations

2020 ◽  
Vol 20 (12) ◽  
pp. 7231-7241
Author(s):  
Matthew J. Cooper ◽  
Randall V. Martin ◽  
Daven K. Henze ◽  
Dylan B. A. Jones
Keyword(s):  
Shape Factor ◽  
A Priori ◽  
Trace Gas ◽  
A Posteriori ◽  
Profile Shape ◽  
Satellite Retrievals ◽  
Mass Factor ◽  
The Difference ◽  
Priori Information ◽  
Mean Square Errors

Abstract. A critical step in satellite retrievals of trace gas columns is the calculation of the air mass factor (AMF) used to convert observed slant columns to vertical columns. This calculation requires a priori information on the shape of the vertical profile. As a result, comparisons between satellite-retrieved and model-simulated column abundances are influenced by the a priori profile shape. We examine how differences between the shape of the simulated and a priori profiles can impact the interpretation of satellite retrievals by performing an adjoint-based four-dimensional variational (4D-Var) assimilation of synthetic NO2 observations for constraining NOx emissions. We use the GEOS-Chem adjoint model to perform assimilations using a variety of AMFs to examine how a posteriori emission estimates are affected if the AMF is calculated using an a priori shape factor that is inconsistent with the simulated profile. In these tests, an inconsistent a priori shape factor increased root mean square errors in a posteriori emission estimates by up to 30 % for realistic conditions over polluted regions. As the difference between the simulated profile shape and the a priori profile shape increases, so do the corresponding assimilated emission errors. This reveals the importance of using simulated profile information for AMF calculations when comparing that simulated output to satellite-retrieved columns.

NUMERICAL SOLUTION OF TWO-DIMENSIONAL PROBLEMS OF THERMOVISCOELASTICITY

2021 ◽  
Vol 335 (1) ◽  
pp. 60-64
Author(s):  
M. Bukenov ◽  
Ye. Mukhametov
Keyword(s):  
A Priori ◽  
Elastic Collision ◽  
Qualitative Behavior ◽  
Stress Profile ◽  
Two Dimensional ◽  
A Priori Information ◽  
Deformable Solids ◽  
Methods Of Calculation ◽  
The Difference ◽  
Priori Information

This paper considers the numerical implementation of two-dimensional thermoviscoelastic waves. The elastic collision of an aluminum cylinder with a two-layer plate of aluminum and iron is considered. In work [1] the difference schemes and algorithm of their realization are given. The most complete reviews of the main methods of calculation of transients in deformable solids can be found in [2, 3, 4], which also indicates the need and importance of generalized studies on the comparative evaluation of different methods and identification of the areas of their most rational application. In the analysis and physical interpretation of numerical results in this work it is also useful to use a priori information about the qualitative behavior of the solution and all kinds of information about the physics of the phenomena under study. Here is the stage of evolution of contact resistance of collision – plate, stress profile.

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 Impact of nonlinearity on changing the a priori of trace gas profile estimates from the Tropospheric Emission Spectrometer (TES)

2008 ◽  
Vol 8 (12) ◽  
pp. 3081-3092 ◽  
Author(s):  
S. S. Kulawik ◽  
K. W. Bowman ◽  
M. Luo ◽  
C. D. Rodgers ◽  
L. Jourdain
Keyword(s):  
Total Error ◽  
A Priori ◽  
Trace Gas ◽  
Minor Effect ◽  
A Priori Information ◽  
Linear Estimate ◽  
Common Prior ◽  
Non Linear ◽  
Priori Information ◽  
A Minor

Abstract. Non-linear maximum a posteriori (MAP) estimates of atmospheric profiles from the Tropospheric Emission Spectrometer (TES) contains a priori information that may vary geographically, which is a confounding factor in the analysis and physical interpretation of an ensemble of profiles. One mitigation strategy is to transform profile estimates to a common prior using a linear operation thereby facilitating the interpretation of profile variability. However, this operation is dependent on the assumption of not worse than moderate non-linearity near the solution of the non-linear estimate. The robustness of this assumption is tested by comparing atmospheric retrievals from the Tropospheric Emission Spectrometer processed with a uniform prior with those processed with a variable prior and converted to a uniform prior following the non-linear retrieval. Linearly converting the prior following a non-linear retrieval is shown to have a minor effect on the results as compared to a non-linear retrieval using a uniform prior when compared to the expected total error, with less than 10% of the change in the prior ending up as unbiased fluctuations in the profile estimate results.

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 Detection of Jumps Parameters in Economic Processes(the Case of Modelling Profitability)

2018 ◽  
Vol 7 (4.3) ◽  
pp. 488 ◽  
Author(s):  
O. V. Poliarus ◽  
Y. O. Poliakov ◽  
I. L. Nazarenko ◽  
Y. T. Borovyk ◽  
M. V. Kondratiuk
Keyword(s):  
A Priori ◽  
Machine Building ◽  
Building Industry ◽  
A Posteriori ◽  
A Priori Information ◽  
Parameter Change ◽  
Economic Process ◽  
Intense Noise ◽  
Priori Information ◽  
Economic Nature

A new method of parameters jumps detection in economic processes is presented. A jump of the economic process parameter must be understood as a rapid parameter change for a time that does not exceed the period of process registration.  A system of stochastic differential equations for a posteriori density probability of a jump is synthesized. The solution of the system is the probability of a parameter jump, the estimation and variance of the jump in the presence of a priori information under conditions of noise influence. The simulation results are conducted for profitability of machine building industry of Kharkiv region, Ukraine. The system provides detection of jump parameters, even in conditions of intense noise of economic nature. To increase the probability of finding jumps it is necessary to have a priori information.  

scholarly journals Statistical Ranging of Orbits for Trans-Neptunian Objects

2002 ◽  
Vol 12 ◽  
pp. 255-256 ◽  
Author(s):  
J. Virtanen ◽  
K. Muinonen ◽  
E. Bowell
Keyword(s):  
Phase Space ◽  
A Priori ◽  
Posteriori Probability ◽  
A Posteriori ◽  
A Priori Information ◽  
A Posteriori Probability ◽  
Uncertainty Prediction ◽  
Absolute Magnitudes ◽  
Priori Information

AbstractWe consider initial determination of orbits for trans-neptunian objects (TNOs), a topical theme because of the rapidly growing TNO population and the challenges in recovering lost TNOs. We apply the method of initial phase-space ranging of orbits to the poorly observed TNOs. The rigorous a posteriori probability density of the TNO orbital elements is examined using a Monte Carlo technique by varying the TNO topocentric ranges corresponding to the observation dates. We can optionally adopt a Bayesian approach to select the region of phase space containing the most plausible orbits. This is accomplished by incorporating semimajor axes, eccentricities, inclinations, and absolute magnitudes of multi-apparition TNOs as a priori information. The resulting a posteriori distributions permit ephemeris and ephemeris uncertainty prediction for TNO recovery observations.

Joint interpretation and uncertainty analysis of petrophysical properties in unconventional shale reservoirs

2015 ◽  
Vol 3 (1) ◽  
pp. SA33-SA49 ◽  
Author(s):  
Qinshan Yang ◽  
Carlos Torres-Verdín
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Estimation Method ◽  
Monte Carlo Algorithm ◽  
Posteriori Probability ◽  
Inversion Method ◽  
A Posteriori ◽  
A Priori Information ◽  
Core Data ◽  
Priori Information

Interpretation of hydrocarbon-bearing shale is subject to great uncertainty because of pervasive heterogeneity, thin beds, and incomplete and uncertain knowledge of saturation-porosity-resistivity models. We developed a stochastic joint-inversion method specifically developed to address the quantitative petrophysical interpretation of hydrocarbon-bearing shale. The method was based on the rapid and interactive numerical simulation of resistivity and nuclear logs. Instead of property values themselves, the estimation method delivered the a posteriori probability of each property. The Markov-chain Monte Carlo algorithm was used to sample the model space to quantify the a posteriori distribution of formation properties. Additionally, the new interpretation method allows the use of fit-for-purpose statistical correlations between water saturation, salt concentration, porosity, and electrical resistivity to implement uncertain, non-Archie resistivity models derived from core data, including those affected by total organic carbon (TOC). In the case of underdetermined estimation problems, i.e., when the number of measurements was lower than the number of unknowns, the use of a priori information enabled plausible results within prespecified petrophysical and compositional bounds. The developed stochastic interpretation technique was successfully verified with data acquired in the Barnett and Haynesville Shales. Core data (including X-ray diffraction data) were combined into a priori information for interpretation of nuclear and resistivity logs. Results consisted of mineral concentrations, TOC, and porosity together with their uncertainty. Eighty percent of the core data was located within the 95% credible interval of estimated mineral/fluid concentrations.

scholarly journals NUMERICAL SOLUTION OF TWO-DIMENSIONAL PROBLEMS OF THERMOVISCOELASTICITY

2021 ◽  
Vol 335 (1) ◽  
pp. 60-64
Author(s):  
M. Bukenov ◽  
Ye. Mukhametov
Keyword(s):  
A Priori ◽  
Elastic Collision ◽  
Qualitative Behavior ◽  
Stress Profile ◽  
Two Dimensional ◽  
A Priori Information ◽  
Deformable Solids ◽  
Methods Of Calculation ◽  
The Difference ◽  
Priori Information

This paper considers the numerical implementation of two-dimensional thermoviscoelastic waves. The elastic collision of an aluminum cylinder with a two-layer plate of aluminum and iron is considered. In work [1] the difference schemes and algorithm of their realization are given. The most complete reviews of the main methods of calculation of transients in deformable solids can be found in [2, 3, 4], which also indicates the need and importance of generalized studies on the comparative evaluation of different methods and identification of the areas of their most rational application. In the analysis and physical interpretation of numerical results in this work it is also useful to use a priori information about the qualitative behavior of the solution and all kinds of information about the physics of the phenomena under study. Here is the stage of evolution of contact resistance of collision – plate, stress profile.

scholarly journals Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. H19-H31 ◽  
Author(s):  
Knud Skou Cordua ◽  
Thomas Mejer Hansen ◽  
Klaus Mosegaard
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
A Priori ◽  
Waveform Inversion ◽  
Multiple Point ◽  
Full Waveform Inversion ◽  
A Posteriori ◽  
A Priori Information ◽  
Full Waveform ◽  
Priori Information

We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatiallycorrelated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

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