Extreme precipitations measured by radar

2021 ◽  
Author(s):  
András Bárdossy ◽  
Geoff Pegram
Keyword(s):  
Reduction Factor ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Large Area ◽  
Area Reduction ◽  
Polar Coordinate ◽  
Radar Measurements ◽  
Stationary Conditions ◽  
The Mean ◽  
Block Sizes

<p>Radar measurements provide information on precipitation in space and time. They do not measure precipitation but reflectivity. The transformation to precipitation is not straightforward.  The result is that different, partly random, partly systematic errors may occur.  Radar precipitation pixels are usually considered to measure the mean over a large area of 500 x 500 m. However the measurement itself is represented in polar coordinates and is subsequently transformed to a Cartesian system. As the measurements in the polar coordinate system deliver areal averages corresponding to different block sizes this is likely to have an effect on the estimates of the true precipitation values. This particularly applies to extremes. In the outer circles of the radar scan the blocks are bigger, and thus the measurements deliver areal extremes where a kind of area reduction factor is the result of the resolution. In order to investigate the influence of this on the extremes two numerical simulation examples were considered. Results from a long high resolution simulation using the String of Beads model applied with data from South Africa, and of a copula based direct simulation, are analysed and presented. The results show that the extremes towards the outer ring of the radar observations may, under stationary conditions, be reduced by up to 20 %.</p>

scholarly journals Determination of Ship Approach Parameters in the Polar Coordinates System

2014 ◽  
Vol 96 (1) ◽  
pp. 1-8
Author(s):  
Andrzej Banachowicz ◽  
Adam Wolski
Keyword(s):  
Coordinate System ◽  
Target Position ◽  
Geometric Interpretation ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Polar Coordinate ◽  
Radar Measurements ◽  
Cartesian Coordinate ◽  
Radar Antenna

Abstract An essential aspect of the safety of navigation is avoiding collisions with other vessels and natural or man made navigational obstructions. To solve this kind of problem the navigator relies on automatic anti-collision ARPA systems, or uses a geometric method and makes radar plots. In both cases radar measurements are made: bearing (or relative bearing) on the target position and distance, both naturally expressed in the polar coordinates system originating at the radar antenna. We first convert original measurements to an ortho-Cartesian coordinate system. Then we solve collision avoiding problems in rectangular planar coordinates, and the results are transformed to the polar coordinate system. This article presents a method for an analysis of a collision situation at sea performed directly in the polar coordinate system. This approach enables a simpler geometric interpretation of a collision situation

Additional Separated-Variable Solutions of the Biharmonic Equation in Polar Coordinates

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
I. H. Stampouloglou ◽  
E. E. Theotokoglou
Keyword(s):  
Fourth Order ◽  
Biharmonic Equation ◽  
Direct Determination ◽  
Additional Term ◽  
Elastic Solid ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Radial Coordinate ◽  
Displacement Fields ◽  
Polar Coordinate

From the biharmonic equation of the plane problem in the polar coordinate system and taking into account the variable-separable form of the partial solutions, a homogeneous ordinary differential equation (ODE) of the fourth order is deduced. Our study is based on the investigation of the behavior of the coefficients of the above fourth order ODE, which are functions of the radial coordinate r. According to the proposed investigation additional terms, φ¯−m(r,θ)(1≤m≤n) other than the usually tabulated in the Michell solution (1899, “On the Direct Determination of Stress in an Elastic Solid, With Application to the Theory of Plates,” Proc. Lond. Math. Soc., 31, pp. 100–124) are found. Finally the stress and the displacement fields due to each one additional term of φ¯−m(r,θ) are determined.

scholarly journals Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
R. K. Mohanty ◽  
Rajive Kumar ◽  
Vijay Dahiya
Keyword(s):  
Iterative Method ◽  
Spline Approximation ◽  
Cubic Spline ◽  
Poisson’S Equation ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Poisson's Equation ◽  
Polar Coordinate ◽  
Cylindrical Polar Coordinates ◽  
Diffusion Convection

Using nonpolynomial cubic spline approximation in x- and finite difference in y-direction, we discuss a numerical approximation of O(k2+h4) for the solutions of diffusion-convection equation, where k>0 and h>0 are grid sizes in y- and x-coordinates, respectively. We also extend our technique to polar coordinate system and obtain high-order numerical scheme for Poisson’s equation in cylindrical polar coordinates. Iterative method of the proposed method is discussed, and numerical examples are given in support of the theoretical results.

scholarly journals The Symplectic Method in Polar Coordinates for Linear Viscoelastic Materials

2015 ◽  
Vol 9 (1) ◽  
pp. 130-134
Author(s):  
W.X. Zhang ◽  
Y. Bai
Keyword(s):  
Analytical Form ◽  
Fundamental Solutions ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Symplectic Method ◽  
Polar Coordinate ◽  
Linear Viscoelastic ◽  
Annular Sector ◽  
Particular Solution ◽  
Variable Substitution

In this study, the symplectic method is applied to a two-dimensional annular-sector viscoelastic domain under the polar coordinate system. By applying variable separation approach, all fundamental solutions are derived in analytical form. Furthermore, using the method of variable substitution, lateral conditions are transformed into finding a particular solution for the governing equations, and this particular solution is derived with the use of eigensolution expansion. In the numerical example, the boundary condition problem is discussed in detail to analyze the stress response of viscoelastic solids.

The Shape of Space: Evidence for Spontaneous but Flexible Use of Polar Coordinates in Visuospatial Representations

2021 ◽  
pp. 095679762097237
Author(s):  
Sami R. Yousif ◽  
Frank C. Keil
Keyword(s):  
Spatial Representation ◽  
Spatial Scales ◽  
Human Mind ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
Spatial Tasks ◽  
Polar Coordinate ◽  
Visual Matching ◽  
2D Space

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing 2D space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which capture angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments, using a simple visual-matching paradigm, show that (a) representational format is recoverable from the errors that observers make in simple spatial tasks, (b) human-made errors spontaneously favor a polar coordinate system of representation, and (c) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence as well as work on spatial representation at other spatial scales.

Outlier detection by the EM algorithm for laser scanning in rectangular and polar coordinate systems

2015 ◽  
Vol 9 (3) ◽  
Author(s):  
Karl-Rudolf Koch ◽  
Boris Kargoll
Keyword(s):  
Em Algorithm ◽  
Coordinate System ◽  
Linear Model ◽  
Laser Scanning ◽  
Local Coordinate System ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
The Em Algorithm ◽  
Polar Coordinate

AbstractTo visualize the surface of an object, laser scanners determine the rectangular coordinates of points of a grid on the surface of the object in a local coordinate system. Vertical angles, horizontal angles and distances of a polar coordinate system are measured with the scanning. Outliers generally occur as gross errors in the distances. It is therefore investigated here whether rectangular or polar coordinates are better suited for the detection of outliers. The parameters of a surface represented by a polynomial are estimated in the nonlinear Gauss Helmert (GH) model and in a linear model. Rectangular and polar coordinates are used, and it is shown that the results for both coordinate systems are identical. It turns out that the linear model is sufficient to estimate the parameters of the polynomial surface. Outliers are therefore identified in the linear model by the expectation maximization (EM) algorithm for the variance-inflation model and are confirmed by the EM algorithm for the mean-shift model. Again, rectangular and polar coordinates are used. The same outliers are identified in both coordinate systems.

scholarly journals The shape of space: Evidence for spontaneous but flexible use of polar coordinates in visuospatial representations

2021 ◽  
Author(s):  
Sami Ryan Yousif ◽  
Frank Keil
Keyword(s):  
Spatial Representation ◽  
Dimensional Space ◽  
Spatial Scales ◽  
Human Mind ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Coordinate Systems ◽  
Spatial Tasks ◽  
Polar Coordinate ◽  
Visual Matching

What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing two-dimensional space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which captures angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments utilizing a simple ‘visual matching’ paradigm show that (1) representational format is recoverable from the errors observers make in simple spatial tasks; (2) human-made errors spontaneously favor a polar coordinate system of representation; and (3) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence, as well as work on spatial representation at other spatial scales.

scholarly journals Polar Transforms for ITK

2006 ◽  
Author(s):  
Jakub Bican
Keyword(s):  
Image Processing ◽  
Coordinate System ◽  
Polar Coordinates ◽  
Polar Coordinate System ◽  
Cartesian Coordinates ◽  
Polar Coordinate ◽  
2D Space

Polar transform is a geometric transform, that transforms points form cartesian coordinates to so-called polar coordinates. In case of 2D space, a point in polar coordinate system is addressed by radius and angle. In image processing, polar transform is usually used to convert rotations around the origin of polar coordinate system to translations.This submission contains the implementation of forward and inverse polar transforms in two very simple classes for the Insight Toolkit.

scholarly journals Probability Characteristics, Area Reduction, and Wind Directionality Effects of Extreme Pressure Coefficients of High-Rise Buildings

2021 ◽  
Vol 11 (15) ◽  
pp. 7121
Author(s):  
Shouke Li ◽  
Feipeng Xiao ◽  
Yunfeng Zou ◽  
Shouying Li ◽  
Shucheng Yang ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Pressure Coefficient ◽  
Wind Pressure ◽  
Extreme Pressure ◽  
Distribution Law ◽  
Distribution Fitting ◽  
Pressure Coefficients ◽  
High Rise ◽  
Area Reduction ◽  
The Mean

Wind tunnel tests are carried out for the Commonwealth Advisory Aeronautical Research Council (CAARC) high-rise building with a scale of 1:400 in exposure categories D. The distribution law of extreme pressure coefficients under different conditions is studied. Probability distribution fitting is performed on the measured area-averaged extreme pressure coefficients. The general extreme value (GEV) distribution is preferred for probability distribution fitting of extreme pressure coefficients. From the comparison between the area-averaged coefficients and the value from GB50009-2012, it is indicated that the wind load coefficients from GB50009-2012 may be non-conservative for the CAARC building. The area reduction effect on the extreme wind pressure is smaller than that on the mean wind pressure from the code. The recommended formula of the area reduction factor for the extreme pressure coefficient is proposed in this study. It is found that the mean and the coefficient of variation (COV) for the directionality factors are 0.85 and 0.04, respectively, when the orientation of the building is given. If the uniform distribution is given for the building’s orientation, the mean value of the directionality factors is 0.88, which is close to the directionality factor of 0.90 given in the Chinese specifications.

scholarly journals Mudrock Microstructure: A Technique for Distinguishing between Deep-Water Fine-Grained Sediments

Minerals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 653
Author(s):  
Shereef Bankole ◽  
Dorrik Stow ◽  
Zeinab Smillie ◽  
Jim Buckman ◽  
Helen Lever
Keyword(s):  
Grain Size ◽  
Deep Water ◽  
Sedimentary Facies ◽  
X Ray Diffraction ◽  
Weak Current ◽  
Large Area ◽  
Fine Grained ◽  
Mean Size ◽  
The Mean ◽  
Water Facies

Distinguishing among deep-water sedimentary facies has been a difficult task. This is possibly due to the process continuum in deep water, in which sediments occur in complex associations. The lack of definite sedimentological features among the different facies between hemipelagites and contourites presented a great challenge. In this study, we present detailed mudrock characteristics of the three main deep-water facies based on sedimentological characteristics, laser diffraction granulometry, high-resolution, large area scanning electron microscopy (SEM), and the synchrotron X-ray diffraction technique. Our results show that the deep-water microstructure is mainly process controlled, and that the controlling factor on their grain size is much more complex than previously envisaged. Retarding current velocity, as well as the lower carrying capacity of the current, has an impact on the mean size and sorting for the contourite and turbidite facies, whereas hemipelagite grain size is impacted by the natural heterogeneity of the system caused by bioturbation. Based on the microfabric analysis, there is a disparate pattern observed among the sedimentary facies; turbidites are generally bedding parallel due to strong currents resulting in shear flow, contourites are random to semi-random as they are impacted by a weak current, while hemipelagites are random to oblique since they are impacted by bioturbation.

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