Gravity potential (W):
Sum of the gravitational potential (V) and of the centrifugal potential (C) of the rotating Earth. Differences between two points may be observed by levelling.

Equipotential surface:
A surface where W is equal to a constant. Points on one such surface may be determined regionally with tide-gauges, which define regional mean sea-level.

Height datum:
Defined by the equipotential surface which best agrees with local mean sea-level calculated from tide-gauges for a specific time period.

Geoid:
Equipotential surface which approximates the global mean sea-level, i.e. a global set of tide-gauges and levelling bench-marks, after subtraction of the dynamic components. It can be considered as the hypothetical ocean at rest.

Mean Earth ellipsoid:
It is an ellipsoid of revolution, rotating with the Earth around its z-axis, and centred at the Earth’s centre of mass. It is determined as the surface which gives best fit in some sense to mean sea-level. The height above this ellipsoid, h, is measured along the normal to the ellipsoid. It is observed indirectly by satellite positioning (such as GPS) from the determined Cartesian co-ordinates (x, y, z).

Geoid height:
It is the height, N, of a point on the geoid with respect to the ellipsoid (it is positive above). Geoid height excursions amount to about + 90 and - 105 metres in the extremes. These are long-wavelength features (several thousand kilometres). Variations of shorter extensions (tens to hundreds of kilometres) have a magnitude of centimetres to one or a few metres.

Orthometric height:
It is the height, H, measured from the geoid along the plumbline; it is commonly called the height above mean sea-level. It is observed by levelling: the measurements (level differences and gravity) yield the geopotential number which is converted to metric units by dividing by the mean gravity along the plumbline. This is how the height system of most countries is established.

Gravity:
Is the magnitude, g, of the gradient of W at the Earth’s surface and of V in space. It may be observed by an absolute technique (e.g. in a free fall experiment) or relatively (as a difference) by a spring gravimeter.

Gravity gradients:
They are derivatives of the gravity vector, i.e. second-order derivatives of W at the Earth’s surface and of V in space. Certain linear combinations may be measured by a torsion-balance at Earth’s surface, and by forming differences of adjacent accelerometer measurements in space.

Normal gravity potential:
It is a model gravity potential, U, with the ellipsoid as an equipotential surface. It is used to calculate normal gravity, y.

Anomalous potential:
Is the difference T = W - U. It is small and allows linearisation, such as the Bruns equation N = T/y, which directly relates potential and geoid height. Measured quantities are frequently expressed as derivatives of T, such as the gravity gradients.

Gravity anomaly:
At any point of given latitude and orthometric height, the gravity anomaly Δ g is the value derived by subtracting measured and normal gravity ( Δ g = g - y) . The gravity y is calculated at a point with the ellipsoidal height put equal to the orthometric height.

Spherical harmonic coefficients:
The potential V (or T) may be expanded as an infinite series of spherical harmonic functions which are the spherical equivalent of Fourier series in a plane. The coefficients of the series are numbered according to degree and order, l and m respectively (m < l) , which corresponds to wave numbers in the plane. The zonal harmonics are those coefficients of order zero and correspond to averages of the potential in longitude. The other coefficients are called tesseral harmonics (sectorial when l = m).

Kaula’s rule:
For a given degree, the quadratic mean (over all orders) of the harmonic coefficients for the Earth decreases approximately like 10 ^-5 /l ² ; the square of this quantity is called degree variance and corresponds to the signal power spectrum density.

Global (geopotential) model:
Is a model of the Earth’s gravitational potential in the form of a set of spherical harmonic coefficients, truncated at a maximum degree and order L.