The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 160

the ellipsoid is related to the normal gravity potential; thus N or can be determined

by the disturbing potential T. With derivations omitted, the formula is given by:

ʶ

T 0
ʳ 0

N ¼ , ð 4 : 47 Þ

where T 0 is the disturbing potential on the geoid and ʳ 0 is the normal gravity value

on the normal ellipsoid. Similarly, we have:

T p
ʳ m

ʶ ¼ , ð 4 : 48 Þ

where T p is the disturbing potential at the Earth's surface and ʳ m is the integral mean

of the normal gravity along line segment P 0 P (see Fig. 4.12 ).

4.4.3 Grid Models of Height Anomaly or Geoid Height

The grid model of height anomaly is a discrete numerical representation of height
anomaly within a certain range. It is an aggregation of height anomaly values of all
the equidistant grid points within this range, stored in the database in the form of
graticule data structure. This structure divides the geographical area covered by the
database into regular trapezoid grids based on longitude and latitude lines (see
Fig. 4.13 ) and uses the grid area or the vertical and horizontal intersection of grid
lines as the node to store the corresponding height anomaly values at the intersec-
tion or the average height anomaly values within the grid area.
For example, dividing a 1:1,000,000 map sheet into 240 360 equidistant

trapezoid grids based on directions in which the longitude and latitude lines run
according to a 1 0

1 0 field range, each grid can be numbered as 00001-86400,
from left to right by rows and from top to bottom by columns (similar to the
international subdividing method).
A multilevel grid structure can be used in grid models. Grids at different levels
have different distance intervals. The smaller the grid, the more precise the contin-
uous height anomaly can be. For example, we can divide the database building area
into different regions according to the known data distribution, and different
regions use grids with different distance intervals.
To establish the grid model of height anomaly over an area is to divide this area
into equidistant regular grid cells according to the longitude and latitude lines, and
then calculate the height anomaly of each grid node using a certain method
according to the known height anomaly within the area (e.g., GPS-leveling points).
When using a height anomaly grid model, one first needs to identify the grid cell
in which the point lies and then use bilinear interpolation according to the height
anomaly of the four grid intersections to calculate the height anomaly of the point.