On the determination of the predictability of a four-level geostrophic model using the effects of grid point numerical errors

Tellus ◽  
1977 ◽  
Vol 29 (6) ◽  
pp. 588-592
Author(s):  
P. J. EVERSON ◽  
J. C. PERFECT
Keyword(s):  
Grid Point ◽  
Numerical Errors

scholarly journals A wavefront orientation method for precise numerical determination of tsunami travel time

2013 ◽  
Vol 13 (11) ◽  
pp. 2863-2870 ◽  
Author(s):  
I. V. Fine ◽  
R. E. Thomson
Keyword(s):  
Travel Time ◽  
Grid Point ◽  
Point Pattern ◽  
Numerical Determination ◽  
Computationally Efficient ◽  
Tsunami Travel Time ◽  
Orientation Method ◽  
Huygens Principle ◽  
Improved Accuracy

Abstract. We present a highly accurate and computationally efficient method (herein, the "wavefront orientation method") for determining the travel time of oceanic tsunamis. Based on Huygens' Principle, the method uses an eight-point grid-point pattern and the most recent information on the orientation of the advancing wavefront to determine the time for a tsunami to travel to a specific oceanic location. The method is shown to provide improved accuracy and reduced anisotropy compared with the conventional multiple grid-point method presently in widespread use.

scholarly journals Accumulation in Antarctica and Greenland derived from passive-microwave data: a comparison with contoured compilations

1995 ◽  
Vol 21 ◽  
pp. 123-130 ◽  
Author(s):  
H. Jay Zwally ◽  
MARIO B. Giovinetto
Keyword(s):  
Field Data ◽  
Grid Point ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Hyperbolic Function ◽  
West Antarctica ◽  
The Mean ◽  
The Antarctic ◽  
Mass Accumulation

The annual rate of net mass accumulation at the surface in the Antarctic and Greenland ice sheets is determined from firn emissivity based on Nimbus-5 ESMR and Nimbus-7 THIR data. In this study the determinations are limited to the areas of dry-snow facies and are based on a hyperbolic function of emissivity. Two coefficients of the function are selected for particular regions of each ice sheet after a comparison with field data selected for their reliability (82 stations in East Antarctica, 69 stations in West Antarctica and 89 stations in Greenland). Derived accumulation values are produced for grid-point locations 100 km apart which cover 56–94% of the dry-snow areas and 32–58% of the accumulation areas of each ice sheet. These values are compared with interpolated values obtained from the latest contoured compilations of field data. The means of derived values for East and West Antarctica are 12% and 39% larger, respectively, than the mean obtained from interpolated values, suggesting that the isopleth patterns as drawn in the compilation of field data lead to underestimates. The mean of derived values for Greenland is 5% smaller than the mean obtained from interpolated values, suggesting that the compilation of field data may lead to small overestimates that are within the error of determination and the variability of accumulation. Improving facies zonation and the determination of coefficients for the areas of upper percolation facies should improve these preliminary assessments.

scholarly journals A Modified Kwee van Woerden Algorithm with Reliable Error-Estimates

2020 ◽  
Author(s):  
Hans J. Deeg
Keyword(s):  
Error Estimates ◽  
Fundamental Problem ◽  
Space Mission ◽  
Original Method ◽  
External Input ◽  
Light Curves ◽  
Improved Method ◽  
Timing Error ◽  
Numerical Errors

The Kwee van Woerden (KvW) method for the determination of eclipse minimum times has been a staple in eclipsing binary research for decades, due its simplicity and independence of external input parameters. However, its estimates of the timing error have been known to be of low reliability. During the analysis of very precise photometry of CM Draconis eclipses from TESS space mission data, KvW’s original equation for the timing error estimate produced numerical errors, which evidenced a fundamental problem in this equation. This contribution introduces an improved way to calculate the timing error with the KvW method. A code that implements this improved method, together with several further updates over the original method is presented as well. An example application on the CM Draconis light curves from TESS is given, where we show that its timing error estimates of about 1 second are in excellent agreement with error estimates obtained by other means.

scholarly journals A study of periodic potentials based on quadratic splines

2018 ◽  
Vol 29 (08) ◽  
pp. 1850067 ◽  
Author(s):  
M. Gadella ◽  
L. P. Lara
Keyword(s):  
Schrödinger Equation ◽  
Variational Method ◽  
Schrodinger Equation ◽  
Algebraic Equations ◽  
Energy Bands ◽  
One Dimensional ◽  
Numerical Errors ◽  
Periodic Potentials ◽  
Quadratic Splines

In this paper, we discuss a method based on a segmentary approximation of solutions of the Schrödinger equation by quadratic splines, for which the coefficients are determined by a variational method that does not require the resolution of complicated algebraic equations. The idea is the application of the method to one-dimensional periodic potentials. We include the determination of the eigenvalues up to a given level, and therefore an approximation to the lowest energy bands. We apply the method to concrete examples with interest in physics and discussed the numerical errors.

scholarly journals Guaranteed detection of the singularities of 3R robotic manipulators

2016 ◽  
Vol 7 (1) ◽  
pp. 31-38
Author(s):  
R. Benoit ◽  
N. Delanoue ◽  
S. Lagrange ◽  
P. Wenger
Keyword(s):  
Interval Analysis ◽  
Collision Detection ◽  
Robotic Manipulators ◽  
Joint Space ◽  
Detection Algorithm ◽  
Numerical Errors ◽  
Points Of Interest ◽  
Kinematic Behaviour ◽  
Kinematic Properties

Abstract. The design of new manipulators requires the knowledge of their kinematic behaviour. Important kinematic properties can be characterized by the determination of certain points of interest. Important points of interest are cusps and nodes, which are special singular points responsible for the non-singular posture changing ability and for the existence of voids in the workspace, respectively. In practice, numerical errors should be properly tackled when calculating these points. This paper proposes an interval analysis based approach for the design of a numerical algorithm that finds enclosures of points of interest in the workspace and joint space of the studied robot. The algorithm is applied on 3R manipulators with mutually orthogonal joint axes. A pre-processing collision detection algorithm is also proposed, allowing, for instance, to check for the accessibility of a manipulator to its points of interest. Through the two proposed complementary algorithms, based on interval analysis, this paper aims to provide a guaranteed way to obtain a broad characterisation of robotic manipulators.

Determination of the Relative Precision of Atoms in a Macromolecular Structure

1998 ◽  
Vol 54 (3) ◽  
pp. 391-399 ◽  
Author(s):  
Genfa Zhou ◽  
Junfeng Wang ◽  
Eric Blanc ◽  
Michael S. Chapman
Keyword(s):  
Electron Density ◽  
Grid Point ◽  
Real Space ◽  
Positional Error ◽  
Electron Densities ◽  
Isomorphous Replacement ◽  
Temperature Factors ◽  
Improved Methods

Several real-space indices and temperature factors are compared with respect to their correlation with atomic positional error and their ability to indicate atoms and residues with the worst of subtle errors. The best index, r ED, is a correlation coefficient between model and map electron densities, similar to one proposed earlier, but incorporating two improvements. Firstly, resolution is accounted for explicitly by calculating the model electron density by Fourier transformation of resolution-truncated scattering factors. Secondly, the deviation between model and map electron densities is assigned to neighboring atoms according to their contribution to the electron density of each grid point. With maps of various qualities, r ED is the single index with best correlation to atomic error with grouped or individual atoms, and it is the most reliable indicator of poor residues. With poorer omit maps, imprecision of individual atoms is best diagnosed by a combination of low r ED or high B factor. With the improved methods, 60–70% of the least precise atoms can detected in a fully refined structure. Similarly, 40–80% of the least precise atoms of an unrefined model can be detected by comparison with an isomorphous replacement map. This is useful in assessing and improving the quality of a model, but not sufficient to confidently validate all atoms of a structure at sub-atomic resolution.

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