scholarly journals CONSTRUCTION AN OBSERVATION IN THE SHESTAKOV–SVIRIDYUK MODEL IN TERMS OF MULTIDIMENSIONAL “WHITE NOISE” DISTORTION

2020 ◽  
Vol 12 (4) ◽  
pp. 41-50
Author(s):  
M.A. Sagadeeva ◽  
Keyword(s):  
Experimental Data ◽  
White Noise ◽  
Measurement Problem ◽  
A Priori ◽  
Dynamic Measurement ◽  
Observation Data ◽  
Virtual Observation ◽  
Optimal Dynamic ◽  
The Difference ◽  
Priori Information

The Shestakov–Sviridyuk model is a mathematical model of a measuring unit used to reconstruct a dynamically distorted signal with the help of experimental data. This model is also called the optimal dynamic measurement problem. The theory of optimal dynamic measurement is based on the problem of minimizing the difference between the values of a virtual observation obtained using a computational model and experimental data, usually distorted by some disturbances. The article describes the Shestakov–Sviridyuk model of optimal dynamic measurement in terms of various types of disturbances. It focuses on the preliminary stage of the study of the optimal dynamic measurement problem, namely, the Pyt’ev–Chulichkov method for constructing observation data, i. e. converting experimental data to clean them from disturbances in the form of “white noise”, which is understood as the Nelson–Glicklich derivative of the multidimensional Wiener process. To use this method, a priori information on the properties of the functions describing the observation, is used.

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 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 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 Production Possibility Frontiers and Estimation of Competition Effects: The Use of A Priori Information on Biological Processes in Intercropping

1992 ◽  
Vol 28 (3) ◽  
pp. 351-368 ◽  
Author(s):  
Radha Ranganathan
Keyword(s):  
Experimental Data ◽  
Biomass Yield ◽  
Plant Density ◽  
A Priori ◽  
Biological Processes ◽  
A Priori Information ◽  
Production Frontier ◽  
Production Possibility ◽  
Competition Effects ◽  
Priori Information

SummaryProduction possibility frontiers contribute much to an economic evaluation of yield advantages from intercropping. The difficulty with estimating a production frontier empirically from experimental data is one of ascertaining that the fitted curve corresponds with the frontier. This problem has been overcome by deriving the frontier from a priori knowledge of the biological processes that determine the outcome in intercropping. The hyperbolic relationship between biomass yield and plant density, and the parameters that characterize the degree of intra-and inter-specific competition in intercropping are used in this paper to derive production possibility frontiers. The method is illustrated with data from three intercropping studies. A brief review of the two main methods used by researchers to evaluate the results of intercropping, and their limitations, is also presented.

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 An improved method using adaptive smoothing for GNSS tomographic imaging of ionosphere

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0250613
Author(s):  
Rushang Jia ◽  
Xumin Yu ◽  
Jianping Xing ◽  
Yafei Ning ◽  
Hecheng Sun
Keyword(s):  
A Priori ◽  
Simulated Data ◽  
Reconstruction Technique ◽  
Electron Content ◽  
Observation Data ◽  
A Priori Information ◽  
Improved Method ◽  
Adaptive Smoothing ◽  
Total Electron ◽  
Priori Information

Global navigation satellite system (GNSS) is a well-established sensors in the recent ionosphere research. By comparing with classical meteorological equipments, the GNSS application can obtain more reliable and precious ionospheric total electron content (TEC) result. However, the most used GNSS ionospheric tomography technique is sensitive to a priori information due to the sparse and non-uniform distribution of GNSS stations. In this paper, we propose an improved method based on adaptive Laplacian smoothing and algebraic reconstruction technique (ALS-ART). Compared with traditional constant constraints, this method is less dependent on a priori information and adaptive smoothing constraints is closer to the actual situation. Tomography experiments using simulated data show that reconstruction accuracy of ionospheric electron density using ALS-ART method is significantly improved. We also use the method to do the analysis of real observation data and compare the tomography results with ionosonde observation data. The results demonstrate the superiority and reliability of the proposed method compared to traditional constant constraints method which will further improve the capability of obtaining precious ionosphere TEC by using GNSS.

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.

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