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Home , Figure of the Earth

The measurement of everything

Image:IGM from the shape of the to that of a statue

Fernando Sansò

1 Academic authorities, ladies and gentlemen, dear friends and colleagues,

I am sure that you all expect me to start this talk by saying how much I’m honoured and happy to be here. And indeed, I’m profoundly honoured to be awarded a “laurea honoris causa” by the University of Aristoteles and happy to be here, celebrating more than me, more than my modest personal contribution to a science, the new greening of this science in itself, the old lady, , born together with the theory of mechanics and astronomy developed by the great scientists of the XVII, XVIII century, now regenerated into a young beautiful lady with her feet on the blossoming ground of the virtual representation of the of our everyday world and its head high in space, looking down to the earth and its global evolution and even further to the moon and the planets. This science with a modern name is called Geodesy and , at least here in Greece, certainly in Italy and in many other countries, though not everywhere. But I will return later on this point.

So let me start with the title of my talk “The measurement of every thing; from the shape of the earth to that of a statue”. The two key words here are “measuring and shape”. One could define Geodesy and Geomatics to be the science of measuring and modelling the geometry of the world at all scales, from planetary down to the scale of a small manufact, or even to the single cell of a leaving body. Measuring means translating our perception of reality into numbers, with a modern word we could say digitizing. Modelling, in a physical conceptual environment, means building a logical system composed by a certain number of quantities bound one to the other by a system of mathematical relations, such that knowing one part of the quantities through the measurements we can arrive at predicting the other quantities.

2 Without observations a model is just a mathematical game, a nice toy maybe, but disconnected from reality. Without a model you cannot even think of performing a measurement; this is a deep concept that was taught to me by P.Caldirola, my teacher of theoretical physics, one of the pupils of the school of Enrico Fermi. Think that already the world digitizing is an interesting anthropomorphic “model” meaning making a one to one correspondence of a group of objects with the fingers in my hands.

But let us make a small example of different nature: we want to prove that the measure of the distance between two points A and B is just 3 meters, having available a ruler 1 meter long. And then you know that all what I have to do is

to report my ruler three times along the line from A to B as in the figure.

Yet this elementary experiment is based on quite fundamental hypotheses (model), namely:

• that it is possible to draw a unique straight line through A and B, what a mathematician would call a , • that A and B are not moving while I am measuring, • that my ruler is so stiff that it does not change its length when I report it on the line AB .

3 By the way, before I continue with more pertinent examples, let me make a remark that we shall use later on: this “scientific activity” of the human bride is not so different, after all, to other activities of cultural nature, for instance the production of art. Also when we create an artistic “object” we start from the experience , the sensation, the feeling and use a model, a language specific of the artistic object we want to create, be it a poem, a painting or a sculpture, and we predict, verify whether we succeed in communicating the message, the emotion we want to convey through it. And notice; with no feeling there is no art, only dry technique; with no language there is no art; with a wrong prediction of the effect of communication there is no art. A poem could be sincere, written in a “proper” language, yet unable to generate feeling into the audience.

We come back now to some other examples much closer to Geodesy and Geomatics. One is the measurement of the of earth according to Erathostenes. The idea, illustrated by the Figure, is that if on the same day and even at the same hour in the day, at noon, in S (Syene), the modern Aswuan, we have no shadow of the column , while in A (Alessandria) we have the shortest shadow in the year measurement

A R a S εεε

4 so that S and A are on a (model) on the same meridian (model) then we can use the arc a (measurement) and the angle ε (measurement) to derive R (model) as a R = . ε

Another example much more related to an engineering problem, is the measurement of the height of a bell tower, without climbing it. The idea is shown in Figure

S

b h O a D

where the problem is solved by the principle of similarity of two triangles and we can see that by measuring a, b, D we can derive h as a proportion b h = ⋅ D a

Consider how many hypotheses (model) are implied by this simplistic reasoning:

5 • that the tower is vertical, for static reasons, • that the square (a, b) is disposed with b along the vertical, • that the vertical direction in 0 is parallel to that through S, • that the line of sight of 0A is a straight line.

As simple as they are these examples can already illustrate one of the distinctive characters of Geodesy and Geomatics considered as a science; mathematical models in this discipline are never considered to be right or wrong rather they are considered to have a certain degree of likelihood, to contain a certain quantity of truth, to be able to explain reality in a certain bounded and identifiable environment. I would say that a fuzzy logic or, if you like a Bayesian view point on learning models from experiments is naturally cast into the genetic structure of Geodesy and Geomatics, because we are so much used to treat measurements at the limits of the technical capability, that we are aware that any improvement in our instrumentation, by lowering the background noise, reveals new unexpected and reach relations between quantities previously not considered into our models.

Let me try to illustrate this concept through the history of one of the most classical fields of geodesy; that of determination of the figure of the earth. Of the spherical model of Erathostenes we already said. Incredibly enough it took 2000 years before scientists could be able to reason effectively on the shape of the earth in terms of models and measurements. The models was drawn in XVIII century from the intuition of Pierre Simon Laplace that the earth was formed by “the same gravitational forces that had spun the solar system out of a disk of luminous nebular dust”. According to the work of Alexis Claude Clairaut on self- gravitating bodies (1743) the model was that of an ellipsoid of revolution.

6 It will not enter into the interesting history of the expeditions organized by the French Academy of Sciences to measure the length of arcs of meridians, in Ecuador (Charles-Marie de La Condamine, Louis Godin, ), in Lapland (Pierre Louis Moreau de Maupertuis) and in France itself, among which I want to recall the one organized by Jean Baptiste Delambre and Pierre-François-André Méchain (1792-99).

But let me only report about an interview of Jean Dominique Cassini (the fourth in the family that directed the Observatoire de Paris over one century) with King Louis XVI, to explain why it was necessary a new measurement of the arc of meridian in France: “my father and grandfather’s instruments could but measure to within 15 seconds of arc, the instrument of Monsieur Borda here can measure to within one second”. So it took more or less one century of discussions on models, measurements and their accuracy to decide that the shape of the earth was that of an ellipsoid of revolution, what is nowadays well know from dynamics and even obvious if we look at the earth from space.

7 Yet the earth surface is not that of an ellipsoid. The thing is obvious on continents, where topographic irregularities are part of our common experience, but even oceans, with their smooth surface, averaged with respect to short periodic motions (tides and waves) are not following exactly the shape of an ellipsoid because , generated by a somewhat irregular distribution of masses inside the planet, impresses on the ocean the shape of an equipotential surface; what is called the . In order to survey the oceanic surface we have nowadays available measurements from bearing a radar altimeter that allows the reconstruction of the mean sea surface with an accuracy to within few centimeters.

And in this way we have understood that the actual mean sea surface can be far away from the geoid by meters, as predicted by the oceanographic models, when permanent oceanic currents, like the Gulf Stream or the Kuroshyo, are taken into account.

8 So we have to distinguish from the gravimetric shape of the earth, the geoid, and its geometric surface, namely the mean sea surface on the ocean and the topography on the earth. In order to identify the geoid, geodesy is realizing satellite gravity missions that will ultimately allow us to know the geoid with centimetric accuracy.

This has a large impact on the knowledge of the system earth. On ocean the difference between sea surface and geoid will provide a basic information to test and assess oceanographic circulation models. And remember that oceans transport 30-40% of the heat on the earth surface, thus determining the long term dynamics of climatic changes. On the continents the height of the topography on the geoid is a basic information to understand geodynamic processes like plate dynamics, subsidence, belts creation and so forth. But how to “measure” the geometric shape of the earth on continental areas? Geodesy is providing one basic piece of the game, namely positioning of individual points. This, that once upon a time was done by painful and lengthy triangulations, is nowadays done by satellite positioning, namely by GPS, the American positioning system, by GLONASS, the

9 Russian positioning system and, hopefully, in future by GALILEO, the European positioning system. Not to be forgotten the Chinese system BEIDOU, on its way of realization. All these systems allow to pin up points in space in a unified world wide reference system, in technical terms one should say to geo-reference points, to within few centimeters in a few minutes of measurements, at least when supported by suitable ground services. The other basic piece of the game, and we are entering now in Geomatics, is provided by the earth surface by suitable sensors. This can be done from space by radar, but in this case the accuracy goes down to the level of several meters with a ground resolution of ~ 100m; yet the SRTM radar mission has provided a unified digital model of the terrain over the whole planet. Other interferometric radar techniques are more adapt to monitor time variations of the earth surface height; yet, these are very valuable observations to control the land surface for the sake of safety of the society, with respect to a number of natural hazards (e.g. landslides, vulcanic eruptions, bradyseism etc.). But from space we can even look at the earth in an optical range to construct high resolution images (now at the resolution level of some decimeters). Once images are georeferenced, by using ground points of known coordinates, and rectified they automatically become real time updated maps of an invaluable importance for the control and planning of land use. And the same thing can be done by airborne instruments (photogrammetry) when we want to increase accuracy and resolution. In this task photogrammetry is supported by the capability of positioning by GPS the moving platform, by means of a so called system. A variant of this system can be used as well on any kind of vehicles (ships, cars etc..) to support their navigation.

1 Let us stop here one minute and try to answer a specific question; why are we so keen to know accurately where we are and how the space in which we move is done? Why are we not satisfied with a simple knowledge of what is next door or in the other street etc.? The answer is that in its technological economical and social development the human species is getting in a closer and closer contact all over the world because of its capability of communicating and moving fastly from one side to the other of the earth. On the same time the society is increasing enormously the use of natural resources from water to oil, from coal to wood, from corn to rice and so forth. Therefore there is an increasing need of knowing, in our fast and global interrelation, our position as well as that of our partners, and the space in which we move because this is a primary resource of our life and because we need to make it safe and we need to plan our action towards a sustainable development, without cutting the tree on which we are sitting.

So we need to know where we are and the space surrounding us exactly as we need to know what time is it. And we need it at different accuracy and resolution levels depending from our targets. When we want to plan a flight for instance from Milan to Thessaloniki we typically need our position to within 10 meters, but in the landing phase the position of the plane and the digital model of the landing strip have to be accurate to a decimeter, if we have to land steered by an automatic machine in a very foggy weather. Of course we should never do like that taxi driver that a few months ago, in the Netherlands, splashed into the channel because he was believing too much in his GPS! To make a few other examples, take a robot used in agriculture to plough automatically a field. Here again you need a decimetric accuracy if you want to do a well ordered job. Or think of the

1 hydrological model of a basin, which is so important in predicting floods. Here you need a very detailed and accurate digital model of the terrain and even you need to know the percentage of the ground occupied by the vegetation and possibly the kind of trees and bushes and possibly the moisture of the soil and so forth and so forth. All this information can be derived by observing the topographic surface by different sensors, what in geomatics is called remote sensing. In this respect it seems interesting to mention a relatively new technical achievement: the possibility of measuring a distance by a laser without reflectors, i.e. exploiting only the roughness of natural surfaces that send back a signal to the instrument with sufficient power to be detected. This is called a laser scanner. The instrument works usually with centimetric accuracy or better, depending from the nature of the surface surveyed, with a resolution up to 10.000 points per square meter. And you can see in the figures how it can be used, in different contexts, reproducing surfaces from an airborne instrument, or surveying manufacts with terrestrial instruments. As you can see on this cloud of points one can further drape an optical image, thus obtaining a result which is on the same time metrically reliable, nice and realistic to look at. Look for instance how fine is the survey of this famous bronze horse of the San Marco Basilica in Venice.

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(credits: Monti, Brumana et al, Elab 3DPOLI, LARIFO)

And indeed once everything has been measured-digitized we can collect the information, reproduce the objects and work on them; we can even navigate in a virtual city or build new houses, roads etc. So here we meet the concept that spatial information can then be manipulated by computers and we are at the origin of the word Geomatics, so much reminiscent of the other word Informatics. Let me strengthen once more that transforming our perception of the world into numbers allows us to properly archive this information in a safe form (consider that there are archiving procedures which are much more robust against degradation in time than any material, e.g. marble), to represent it any time we need, to study the relation between various quantities and last but not least to implement virtual projects, being able to evaluate the final effect before we do them in reality.

1 Even more it becomes a tool for understanding, preserving and repairing objects of cultural heritage.

Let me present you the example of the sculpture of Laokoon, credited to Polidoro. The sculpture has been retrieved in Rome, in the home of Nerone, with a broken arm and a debate five centuries long was initiated on how should have been the lost arm. One can see an interpretation by Benvenuto Cellini in the Figure and the solution that nowadays is considered as correct.

Imagine how many people could work on such a problem in XVI century, implying that they had to travel to Rome, and how many can contribute to that debate nowadays just using internet tools!

Now that we have finished this kind of tourist tour on Geodesy and Geomatics let us return to the heart of the problem. We have seen a wealth of observation techniques used in geodesy and geomatics and mentioned a number of mathematical models necessary to manipulate and use such, a kind of information. But is there really a science, that we can conventionally call Geodesy and Geomatics, or there is only a puzzle of different techniques, patching together pieces of different sciences?

1 Let me find a help for the answer in a paper by Max Planck of 1908, entitled “The unification of the physical image of the world”. Planck says “if you want to know the level reached by a science in its development, the best index is the way in which its fundamental concepts are defined and its internal parts are delimited”. And further on, after recalling that geometry was born from the need of measuring the fields, mechanics from the need of working machines, acoustic and optics from our physilogical sensations, he concludes “...we can say that up to now theoretical physics shows a strong trend to creating a unitary system, getting rid of its anthropomorphic origin...”

So, supported by such a high concept my answer to the above question is: yes, we are developing a science with its object and its parts; the determination of positions and surfaces from the scale of the planet down to the scale of a statue and all related fields starting from gravity to arrive nowadays to ocean circulation etc.; a science developing its original methods, remembering that statistics, in particular least squares and likelihood theory, was born to treat geodetic data, and nowadays from gravity field approximation to image analysis, a bunch of unified new tools, in particular random fields theory, are offered to the data analyst to build integrated and unified models; a science with its specific tools of representation and diffusion of the results, of course borrowed from informatics but reinterpreted with a such a strong degree of novelty that there is a new field in informatics considered to have the dignity of an independent branch, that of Geographic Information Systems.

Not to many schools in the world look upon our subject with this unified concept but certainly this happens here in Thessaloniki and

1 this vision is shared, since many years with my own school in Italy. And it is for this specific reason that I am particularly happy to be here today for this party of Geodesy and Geomatics.

Let me hope that in future our common vision will prevail continuing to produce with the younger generation new scientific achievements strengthening this greek-italian geodetic alliance.

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