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.

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.

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 Structural uncertainty in air mass factor calculation for NO<sub>2</sub> and HCHO satellite retrievals

2017 ◽  
Vol 10 (3) ◽  
pp. 759-782 ◽  
Author(s):  
Alba Lorente ◽  
K. Folkert Boersma ◽  
Huan Yu ◽  
Steffen Dörner ◽  
Andreas Hilboll ◽  
...  
Keyword(s):  
Surface Albedo ◽  
Trace Gas ◽  
Retrieval Algorithm ◽  
Structural Uncertainty ◽  
Ancillary Data ◽  
Air Mass ◽  
Cloud Parameters ◽  
Uncertainty Estimates ◽  
Satellite Retrievals ◽  
Mass Factor

Abstract. Air mass factor (AMF) calculation is the largest source of uncertainty in NO2 and HCHO satellite retrievals in situations with enhanced trace gas concentrations in the lower troposphere. Structural uncertainty arises when different retrieval methodologies are applied within the scientific community to the same satellite observations. Here, we address the issue of AMF structural uncertainty via a detailed comparison of AMF calculation methods that are structurally different between seven retrieval groups for measurements from the Ozone Monitoring Instrument (OMI). We estimate the escalation of structural uncertainty in every sub-step of the AMF calculation process. This goes beyond the algorithm uncertainty estimates provided in state-of-the-art retrievals, which address the theoretical propagation of uncertainties for one particular retrieval algorithm only. We find that top-of-atmosphere reflectances simulated by four radiative transfer models (RTMs) (DAK, McArtim, SCIATRAN and VLIDORT) agree within 1.5 %. We find that different retrieval groups agree well in the calculations of altitude resolved AMFs from different RTMs (to within 3 %), and in the tropospheric AMFs (to within 6 %) as long as identical ancillary data (surface albedo, terrain height, cloud parameters and trace gas profile) and cloud and aerosol correction procedures are being used. Structural uncertainty increases sharply when retrieval groups use their preference for ancillary data, cloud and aerosol correction. On average, we estimate the AMF structural uncertainty to be 42 % over polluted regions and 31 % over unpolluted regions, mostly driven by substantial differences in the a priori trace gas profiles, surface albedo and cloud parameters. Sensitivity studies for one particular algorithm indicate that different cloud correction approaches result in substantial AMF differences in polluted conditions (5 to 40 % depending on cloud fraction and cloud pressure, and 11 % on average) even for low cloud fractions (<  0.2) and the choice of aerosol correction introduces an average uncertainty of 50 % for situations with high pollution and high aerosol loading. Our work shows that structural uncertainty in AMF calculations is significant and that it is mainly caused by the assumptions and choices made to represent the state of the atmosphere. In order to decide which approach and which ancillary data are best for AMF calculations, we call for well-designed validation exercises focusing on polluted conditions in which AMF structural uncertainty has the highest impact on NO2 and HCHO retrievals.

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 Information Value Measure for Optimization of Flexible Diagnosis Programs of Technical Objects

2019 ◽  
Vol 18 (6) ◽  
pp. 1434-1461 ◽  
Author(s):  
Evgeniy Kopkin ◽  
Igor Kobzarev
Keyword(s):  
A Priori ◽  
Technical Condition ◽  
Diagnostic Information ◽  
Information Value ◽  
Technical State ◽  
A Posteriori ◽  
Automated Systems ◽  
Maximum Value ◽  
Diagnostic Signs ◽  
The Difference

Existing methods of calculating of the value of diagnostic information circulating in the automated systems of monitoring of technical condition of objects do not take into account "losses" ("gains") resulting from making “wrong” decisions when identifying this state. The purpose of the work is to develop an algorithm that allows to solve the problem of recognizing the technical state of the object being analyzed by means of dynamic programming, the value of the diagnostic information as an optimized indicator being used. The solution to the optimization problem of a diagnostic procedure is based on the use of a measure of the information value proposed by R. L. Stratonovich. It is modified according to the subject area of the technical diagnostics and in the case when the diagnostic features presented in the form of intervals on the real numerical axis are used. The maximum value of the diagnostic information is achieved by minimizing the average "losses" (maximizing the average "gains") obtained when performing tests of diagnostic signs in the process of recognizing the technical condition of an object. To solve the problem, a recurrent expression possessing a scientific novelty has been proposed. It allows to calculate the value of the information obtained when performing tests of diagnostic signs in each of the analyzed information states of the diagnostic process. In the process of the diagnostics program implementation when recognizing the technical condition of the object both “losses” and “winnings” are possible. The difference between their a priori and a posteriori means values characterizes the value of the diagnostic information numerically. The magnitude of the information value indication depends on the probabilities of the results of the diagnostic signs checks and is proportional to the difference between the a posteriori and a priori probabilities of achieving the diagnostic goal. By using the proposed solution, it is possible to synthesize the flexible diagnostics program that is optimal according to the maximum value of diagnostic information in the form of a oriented graph or sets of tests in proper sequence of their execution. This is necessary in order to recognize the specific technical state in which the object is located. The implementation of the algorithm developed is possible in the software and algorithmic support of the automated systems for monitoring the state of complex technical objects.

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 Atmospheric composition and thermodynamic retrievals from the ARIES airborne FTS system – Part 1: Technical aspects and simulated capability

2013 ◽  
Vol 6 (6) ◽  
pp. 10833-10887 ◽  
Author(s):  
S. M. Illingworth ◽  
G. Allen ◽  
S. Newman ◽  
A. Vance ◽  
F. Marenco ◽  
...  
Keyword(s):  
Evaluation System ◽  
Degrees Of Freedom ◽  
Retrieval System ◽  
A Priori ◽  
Atmospheric Composition ◽  
Trace Gas ◽  
Technical Aspects ◽  
System Part ◽  
Priori Information ◽  
The Uk

Abstract. In this study we present an assessment of the retrieval capability of the Airborne Research Interferometer Evaluation System (ARIES); an airborne remote sensing Fourier Transform Spectrometer (FTS) operated on the UK Facility for Airborne Atmospheric Measurement (FAAM) aircraft. Simulated optimally-estimated-retrievals of partial column trace gas concentrations, and thermodynamic vertical profiles throughout the troposphere and planetary boundary layer have been performed here for simulated infrared spectra representative of the ARIES system. We also describe the operational and technical aspects of the pre-processing necessary for routine retrieval from the FAAM platform and the selection and construction of a priori information. As exemplars of the capability of the ARIES retrieval system, simulated retrievals of temperature, water vapour (H2O), carbon monoxide (CO), ozone (O3), and methane (CH4), and their corresponding sources of error and potential vertical sensitivity, are discussed for ARIES scenes across typical global environments. The maximum Degrees of Freedom for Signal (DOFS) for the retrievals, assuming a flight altitude of 7 km, were: 3.99, 2.97, 0.85, 0.96, and 1.45 for temperature, H2O, CO, O3, and CH4, respectively for the a priori constraints specified. Retrievals of temperature display significant vertical sensitivity (DOFS in the range 2.6 to 4.0 across the altitude range) as well as excellent simulated accuracy, with the vertical sensitivity for H2O also extending to lower altitudes (DOFS ranging from 1.6 to 3.0). It was found that the maximum sensitivity for CO, O3, and CH4 was approximately 1–2 km below the simulated altitudes in all scenarios. Comparisons of retrieved and simulated-truth partial atmospheric columns are used to assess the capability of the ARIES measurement system. Maximum mean biases (and bias standard deviations) in partial columns (i.e. below aircraft total columns) were found to be: +0.06 (±0.02 at 1σ) %, +3.95 (±3.11)%, +3.74 (±2.97)%, −8.26 (±4.64)% and +3.01 (±2.61)% for temperature, H2O, CO, O3, and CH4 respectively, illustrating that the retrieval system performs well compared to an optimal scheme. The maximum total a posteriori retrieval errors across the partial columns were also calculated, and were found to be 0.20%, 22.57%, 18.22%, 17.61%, and 16.42% for temperature, H2O, CO, O3, and CH4 respectively.

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