# International Association of Geodesy

The International Association of Geodesy (IAG) is a constituent association of the International Union of Geodesy and Geophysics focusing on the science which measures and describes the Earth's shape, its rotation and gravity field.

## History

The precursors to the IAG were arc measurement campaigns. The IAG was founded in 1862 as the Mitteleuropäische Gradmessung (Central European Arc Measurement), later became the Europäische Gradmessung (European Arc Measurement) in 1867, the Internationale Erdmessung (Association Geodésique Internationale in French and "International Geodetic Association" in English) in 1886, and took its present name in 1946.
In 1832, Carl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram in the form of the CGS system (centimetre, gram, second). In 1836, he founded the Magnetischer Verein, the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the Magnetischer Verein would be followed by that of the Central European Arc Measurement (German: Mitteleuropaïsche Gradmessung) on the initiative of Johann Jacob Baeyer in 1863, and by that of the International Meteorological Organisation, whose president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).
As early as 1861, Johann Jacob Baeyer sent a memorandum to the King of Prussia recommending international collaboration in Central Europe with the aim of determining the shape and dimensions of the Earth. At the time of its creation, the association had sixteen member countries: Austrian Empire, Kingdom of Belgium, Denmark, seven German states (Grand Duchy of Baden, Kingdom of Bavaria, Kingdom of Hanover, Mecklenburg, Kingdom of Prussia, Kingdom of Saxony, Saxe-Coburg and Gotha), Kingdom of Italy, Netherlands, Russian Empire (for Poland), United Kingdoms of Sweden and Norway, as well as Switzerland. The Central European Arc Measurement created a Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer.
Baeyer's goal was a new determination of anomalies in the shape of the Earth using precise triangulations, combined with gravity measurements. This involved determining the geoid by means of gravimetric and leveling measurements, in order to deduce the exact knowledge of the terrestrial spheroid while taking into account local variations. To resolve this problem, it was necessary to carefully study considerable areas of land in all directions. Baeyer developed a plan to coordinate geodetic surveys in the space between the parallels of Palermo and Freetown Christiana (Denmark) and the meridians of Bonn and Trunz (German name for Milejewo in Poland). This territory was covered by a triangle network and included more than thirty observatories or stations whose position was determined astronomically. Bayer proposed to remeasure ten arcs of meridians and a larger number of arcs of parallels, to compare the curvature of the meridian arcs on the two slopes of the Alps, in order to determine the influence of this mountain range on vertical deflection. Baeyer also planned to determine the curvature of the seas, the Mediterranean Sea and Adriatic Sea in the south, the North Sea and the Baltic Sea in the north. In his mind, the cooperation of all the States of Central Europe could open the field to scientific research of the highest interest, research that each State, taken in isolation, was not able to undertake.
Friedrich Wilhelm Bessel using the method of least squares calculated from several arc measurements a new value for the flattening of the Earth, which he determined as ⁠1/299.15⁠. Errors in the method of calculating the length of the arc measurement of Delambre and Méchain were taken into account by Bessel when he proposed his reference ellipsoid in 1841. The definitive length of the Mètre des Archives had required a value for the non-spherical shape of the Earth, known as the flattening of the Earth. The Weights and Measures Commission adopted, in 1799, a flattening of ⁠1/334⁠ based on analysis by Pierre-Simon Laplace who combined the arc of Peru and the data of the meridian arc of Delambre and Méchain. Combining these two data sets Laplace succeeded to estimate the flattening anew and was happy to find the suitable value ⁠1/334⁠. It also fitted well with his estimate ⁠1/336⁠ based on 15 pendulum measurements Bessel's reference ellipsoid would long be used by geodesists. An even more accurate value was proposed in 1901 by Friedrich Robert Helmert according to gravity measurements performed under the auspices of the International Geodetic Association.
Seventeen years after Bessel calculated his ellipsoid of reference, some of the meridian arcs the German astronomer had used for his calculation had been enlarged. This was a very important circumstance because the influence of random errors due to vertical deflections was minimized in proportion to the length of the meridian arcs: the longer the meridian arcs, the more precise the image of the Earth ellipsoid would be. After the Struve Geodetic Arc measurement, it was resolved in the 1860s, at the initiative of Carlos Ibáñez e Ibáñez de Ibero, future president of both the International Geodetic Association and the International Committee for Weights and Measure, to remeasure the arc of meridian from Dunkirk to Formentera and to extend it from Shetland to the Sahara. This did not pave the way to a new definition of the metre because it was known that the theoretical definition of the metre had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an oblate spheroid, but which in detail differs from it so as to prohibit any generalization and any extrapolation from the measurement of a single meridian arc. In 1859, Friedrich von Schubert demonstrated that several meridians had not the same length, confirming an hypothesis of Jean Le Rond d'Alembert. He also proposed an ellipsoid with three unequal axes. In 1860, Elie Ritter, a mathematician from Geneva, using Schubert's data computed that the Earth ellipsoid could rather be a spheroid of revolution accordingly to Adrien-Marie Legendre's model. However, the following year, resuming his calculation on the basis of all the data available at the time, Ritter came to the conclusion that the problem was only resolved in an approximate manner, the data appearing too scant, and for some affected by vertical deflections, in particular the latitude of Montjuïc in the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of the repeating circle.
   The definition of the length of a metre in the 1790s was founded upon Arc measurements in France and Peru with a definition that it was to be 1/40 millionth of the circumference of the earth measured through the poles. Such were the inaccuracies of that period that within a matter of just a few years more reliable measurements would have given a different value for the definition of this international standard. That does not invalidate the metre in any way but highlights the fact that continuing improvements in instrumentation made better measurements of the earth's size possible.
It was well known that by measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he did not dare to admit this inaccuracy. This was later explained by clearance in the central axis of the repeating circle causing wear and consequently the zenith measurements contained significant systematic errors. Polar motion predicted by Leonhard Euler and later discovered by Seth Carlo Chandler also had an impact on accuracy of latitudes' determinations. Among all these sources of error, it was mainly an unfavourable vertical deflection that gave an inaccurate determination of Barcelona's latitude and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.
Spain and Portugal joined the European Arc Measurement in 1866. French Empire hesitated for a long time before giving in to the demands of the Association, which asked the French geodesists to take part in its work. It was only after the Franco-Prussian War, that Charles-Eugène Delaunay represented France at the Congress of Vienna in 1871. In 1874, Hervé Faye was appointed member of the Permanent Commission which was presided by Carlos Ibáñez e Ibáñez de Ibero.
The creation of the International Geodetic Association would mark the adoption of new scientific methods which allowed to take into account observational errors in science. It then became possible to accurately measure parallel arcs, since the difference in longitude between their ends could be determined thanks to the invention of the electrical telegraph. Furthermore, advances in metrology combined with those of gravimetry have led to a new era of geodesy. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all the measurements of terrestrial arcs and all determinations of the gravitational acceleration by means of pendulum.
Significant improvements in gravity measuring instruments must also be attributed to Bessel. He devised a gravimeter constructed by Adolf Repsold which was first used in Switzerland by Emile Plantamour, Charles Sanders Peirce and Isaac-Charles Élisée Cellérier (1818–1889), a Genevan mathematician soon independently discovered a mathematical formula to correct systematic errors of this device which had been noticed by Plantamour and Adolphe Hirsch. This would allow Friedrich Robert Helmert to determine a remarkably accurate value of ⁠1/298.3⁠ for the flattening of the Earth when he proposed his ellipsoid of reference.
This was also the result of the Metre Convention of 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following forerunners such as Ferdinand Rudolph Hassler later Carlos Ibáñez e Ibáñez de Ibero.
Since the metre was originally defined, each time a new measurement is made, with more accurate instruments, methods or techniques, it is said that the metre is based on some error, from calculations or measurements. When Carlos Ibáñez e Ibáñez de Ibero first president of both the International Geodetic Association and the International Committee for Weigths and Measures took part to the remeasurement and extension of the arc measurement of Delambre and Méchain, mathematicians like Legendre and Gauss had developed new methods for processing data, including the "least squares method" which allowed to compare experimental data tainted with observational errors to a mathematical model. Moreover the International Bureau of Weights and Measures would have a central role for international geodetic measurements as Charles Édouard Guillaume's discovery of invar minimized the impact of measurement inaccuracies due to temperature systematic errors. The Earth measurements thus underscored the importance of the scientific method at a time when statistics were implemented in geodesy. As a leading scientist of his time, Carlos Ibáñez e Ibáñez de Ibero was one of the 81 initial members of the International Statistical Institute (ISI) and delegate of Spain to the first ISI session (now called World Statistic Congress) in Rome in 1887.
In the 19th century, astronomers and geodesists were concerned with questions of longitude and time, because they were responsible for determining them scientifically and used them continually in their studies. The International Geodetic Association, which had covered Europe with a network of fundamental longitudes, took an interest in the question of an internationally-accepted prime meridian at its seventh general conference in Rome in 1883. Indeed, the Association was already providing administrations with the bases for topographical surveys, and engineers with the fundamental benchmarks for their levelling. It seemed natural that it should contribute to the achievement of significant progress in navigation, cartography and geography, as well as in the service of major communications institutions, railways and telegraphs. From a scientific point of view, to be a candidate for the status of international prime meridian, the proponent needed to satisfy three important criteria. According to the report by Carlos Ibáñez e Ibáñez de Ibero, it must have a first-rate astronomical observatory, be directly linked by astronomical observations to other nearby observatories, and be attached to a network of first-rate triangles in the surrounding country. Four major observatories could satisfy these requirements: Greenwich, Paris, Berlin and Washington. The conference concluded that Greenwich Observatory best corresponded to the geographical, nautical, astronomical and cartographic conditions that guided the choice of an international prime meridian, and recommended the governments should adopt it as the world standard. The Conference further hoped that, if the whole world agreed on the unification of longitudes and times by the Association's choosing the Greenwich meridian, Great Britain might respond in favour of the unification of weights and measures, by adhering to the Metre Convention.
The International Geodetic Association gained global importance with the accession of Chile, Mexico and Japan in 1888; Argentina and United-States in 1889; and British Empire in 1898. The convention of the International Geodetic Association expired at the end of 1916. It was not renewed due to the First World War. However, the activities of the International Latitude Service were continued through an Association Géodesique réduite entre États neutres thanks to the efforts of H.G. van de Sande Bakhuyzen and Raoul Gautier (1854–1931), respectively directors of Leiden Observatory and Geneva Observatory.
Before the Great War, there were quite a number of international associations active in this or that science or even in this or that specialized field of a given science. Among them, the most powerful and oldest was the International Geodesic Association where German influence predominated and which had its central office at the Prussian Geodetic Institute in Potsdam. During the war, many scientists were concerned with the means to be considered for resuming, at the end of hostilities, international scientific work. An essentially American and British idea was to group together the scientific unions relating to various disciplines under the authority of a Supreme Council. An international conference, which brought together in Brussels in July 1919 the scientists of the countries allied or associated in the fight against Germany and of a certain number of neutral states, created an International Science Council and various unions dependent on this Council; but, Geodesy, instead of being free and independent as before, was associated with the Geophysical Sciences in the International Union of Geodesy and Geophysics which first president was Charles Jean-Pierre Lallemand.

## Overview

At present there are 4 commissions and one inter-commission committee:
* Reference Frames
* Gravity Field
* Geodynamics and Earth Rotation
* Positioning & Applications
* Inter-commission Committee on Theory

## International Services

The twelve IAG Services are split into three general topic areas: geodesy (IERS, IDS, IGS, ILRS, and IVS), gravity (IGFS, ICGEM, IDEMS, ISG, IGETS and BGI) and sea level (PSMSL).
* International Gravimetric Bureau (French: Bureau Gravimétrique International) (BGI)
* International Center for Global Earth Models (ICGEM)
* International Digital Elevation Model Service (IDEMS)
* International DORIS Service (IDS)
* International Earth Rotation and Reference Systems Service (IERS)
* International Geodynamics and Earth Tide Service (IGETS)
* International Gravity Field Service (IGFS)
* International GNSS Service (IGS)
* International Laser Ranging Service (ILRS)
* International VLBI Service for Geodesy and Astrometry (IVS)
* International Service for the Geoid (ISG)
* Permanent Service for Mean Sea Level (PSMSL)
The Global Geodetic Observing System (GGOS) is the observing arm of the IAG that focuses on proving the geodetic infrastructure to measure changes in the earth's shape, rotation and mass distribution.
The International GNSS Service (IGS), part of GGOS, archives and processes GNSS data from around the world. IGS data is used in the 2021 reference frame (G2139) of WGS84.

### Journal

IAG sponsors the Journal of Geodesy, published by Springer.

### Awards

The IAG's awards for outstanding achievement in geodesy include the Guy Bomford Prize (inaugurated in 1975), the Levallois Medal (inaugurated in 1979), and the IAG Young Author's Award (inaugurated in 1993).