A height system is a one-dimensional coordinate system used to express the metric distance (height) of a point above a reference surface (i.e., the zero-height level). Traditionally, the reference surface is linked to the mean sea level and the heights are determined using geodetic levelling techniques. These techniques measure the distance between two equipotential or level surfaces of the Earth’s gravity field and provide the height along the curved plumb line. The mean sea level serving as the zero-height level is inferred from averaged tide gauge records over certain time intervals and the heights are determined along the so-called vertical or levelling networks. As the tide gauges register the local sea level and the vertical networks cover limited regions, these systems are known as local height systems. Presently, there are about hundred local and regional height systems in use, and they exhibit discrepancies with respect to each other up to 2 m.
The International Height Reference System (IHRS) is a global unified height system: the zero-height level is a global equipotential surface of the Earth’s gravity field and the vertical coordinate of any point on the Earth’s surface is the level difference with respect to that global equipotential surface. Heights referring to the IHRS are consistent globally and do not depend on the local sea levels. The realisation of the IHRS is the International Height Reference Frame (IHRF): a set of reference stations homogeneously distributed over the world and with known geopotential numbers or height values referring to the IHRS.
A prominent example of the importance of the IHRS/IHRF is the recent height determination of Mount Everest in 2020. Referring this height to the Chinese height system (e.g. in the figure above) or to the Nepalese height system (e.g. ) would produce different values, making difficult to decide which one is the appropriate one. To avoid discrepancies, the Chinese and Nepalese governments agreed to refer the new Mount Everest’s height to the IHRS/IHRF (e.g. ).