2 Prerequisites

In order to use this cookbook you need the following information, usually provided with the data product (the spherical harmonic coefficients):

common symbol(s)	meaning
$GM$	value of the gravity-mass constant in m$^3$/s$^2$
	for the reference ellipsoid
$a$	value of the semi-major axis of the reference ellipsoid in meters
$GM_{\mathrm{g}}$, $a_{\mathrm{g}}$	the same for the geopotential model (subscript g)
$f$	flattening parameter of the reference ellipsoid or equivalently
$b$	value of the semi-minor axis of the reference ellipsoid in meters
$\omega$	angular velocity of the Earth's rotation in 1/s
$\bar{C}_{n,m}$, $\bar{S}_{n,m}$	the fully normalized spherical harmonic coefficients
	(or Stokes' coefficients) of the gravity model.

The parameters $GM$, $a$, $f$ (or $b$), and $\omega$ define the reference ellipsoid. This reference ellipsoid for the geoid undulations must be exactly the same as the one used for the altimetry data product. If you do not have this information directly from the provider of the data product your geoid undulation will most likely be wrong, so make sure to ask the authors of the altimetry data to provide you with this information.

Often, the satellite altimetry product and the spherical harmonic coefficients refer to different permanent tide systems. You have to know which tide systems are used so that you can correctly convert between them (see below).

Furthermore, you need the geographic, or equally, the geodetic coordinates of the location(s) where you want to compute the geoid height. We will denote the geographic latitude by $\varphi$ and the longitude by $\lambda$.