Approximations to full equations as long as use in a GCM “Primitive Equations” Plus other equations How to solve equations Linear Advection Equation

Approximations to full equations as long as use in a GCM “Primitive Equations” Plus other equations How to solve equations Linear Advection Equation www.phwiki.com

Approximations to full equations as long as use in a GCM “Primitive Equations” Plus other equations How to solve equations Linear Advection Equation

Mannis, David, Co-Publisher/President has reference to this Academic Journal, PHwiki organized this Journal N.B. the ‘material derivative’, rate of change following the motion:

Jackson State Community College TN www.phwiki.com

This Particular University is Related to this Particular Journal

Approximations to full equations as long as use in a GCM r = a + z (a=radius of Earth) z a Coriolis in addition to metric terms proportional to can be ignored For large scales, vertical acceleration is small, hence vertical component becomes: “Primitive Equations” Plus other equations Continuity equation Ideal Gas Law First Law of Thermodynamics These equations can be shown to conserve energy, angular momentum, in addition to mass.

How to solve equations Few analytical solutions to full Navier-Stokes equations, in addition to only as long as fairly idealised problems. Hence need to solve numerically. At heart of all numerical schemes is a Taylor series expansion: Suppose we have an interval L, covered by N equally spaced grid points, xj=(j-1) x, then Re-arrange to give approximation as long as derivatives First order accurate: Second order accurate Fourth order accurate Linear Advection Equation Differential equation becomes following difference equation Second order accurate in both space in addition to time Centered time in addition to space scheme

Numerical Stability in addition to numerical solutions Schemes may be accurate but unstable: e.g. simple centred difference scheme as long as linear advection scheme will be stable only if Courant-Friedrichs-Levy number less than 1. Many schemes can have artificial (computational mode) All schemes distort true solution (e.g. change phase in addition to /or group speed) Some schemes fail to conserve properties of system (e.g. energy) Examples of Numerical Schemes More solutions

Staggered Grids Grids on Sphere Vertical Grid/Coordinates Hybrid coordinates

Mannis, David San Diego Community Newspaper Group Co-Publisher/President www.phwiki.com

Summary so far Dynamics of atmosphere ( in addition to ocean) governed by straight as long as ward physics Discretisation has problems but generally can be understood in addition to quantified. NO tuneable parameters so far NO need as long as knowledge of past in addition to only need present to initialise models. BUT

Mannis, David Co-Publisher/President

Mannis, David is from United States and they belong to San Diego Community Newspaper Group and they are from  San Diego, United States got related to this Particular Journal. and Mannis, David deal with the subjects like Local News; Regional News

Journal Ratings by Jackson State Community College

This Particular Journal got reviewed and rated by Jackson State Community College and short form of this particular Institution is TN and gave this Journal an Excellent Rating.