Spherical coordinate system

About: Spherical coordinate system is a research topic. Over the lifetime, 2663 publications have been published within this topic receiving 41853 citations.

An Energy and Angular-Momentum Conserving Vertical Finite-Difference Scheme and Hybrid Vertical Coordinates

Abstract: An energy and angular-momentum conserving vertical finite-difference scheme is introduced for a general terrain-following vertical coordinate which is a function of pressure and its surface value. A corresponding semi-implicit time scheme is also defined. These schemes am used to compare the usual sigma coordinate with the hybrid coordinate which reduces to pressure above a fixed level and with a modified hybrid coordinate which tends uniformly to pressure at upper levels. Error in the representation of the stratospheric pressure gradient over steep orography can be significantly reduced by use of the hybrid coordinate but the semi-implicit scheme is less stable. The modified hybrid coordinate offers a useful compromise.

A new magnetic coordinate system for conjugate studies at high latitudes

Abstract: Studying magnetically conjugate phenomena at very high latitudes requires a magnetic coordinate system that is smooth and well defined at the geographic poles In addition, it should provide for accurate comparisons at different altitudes In this report the authors present a variation on the corrected geomagnetic coordinate system that is well defined and smooth over the entire globe It provides an analytic expression relating geographic coordinates, including altitude, to the magnetic coordinates The coordinate system is produced by tracing magnetic field lines using the IGRF85 reference magnetic field model with time derivatives updating the model to 1988 An expansion of the relationship in terms of spherical harmonics has been determined, which then provides the required well-defined and smooth relationship over the entire globe Independent expansions for different altitudes show a smooth functional relationship of the coefficients of the expansion with altitude, and therefore simple interpolation schemes can be used to provide an appropriate expansion at any altitude between 0 km and approximately 600 km By reversing the process, the inverse expansions relating the magnetic coordinates to geographic coordinates have also been determined The effects of the seasonal variation in the Sun's declination along with the variation in the Sun's declinationmore » along with the variation in the Sun's apparent position due to the eccentricity of the Earth's orbit result in a variation of nearly 1 hour of magnetic local time for a fixed UT over the course of a year In many applications this variation may be important and should be included when presenting data in terms of magnetic latitude and MLT« less