A Dynamic Earth System: Rome, 15.11.2012 – Forum (anglais)

Australie/Pays Bas

Kurt Lambeck

Prix Balzan 2012 pour les sciences de la terre solide, particulièrement les contributions interdisciplinaires

Pour sa contribution exceptionnelle à la compréhension des relations entre le rebond post-glaciaire et les variations du niveau des mers. Ses découvertes ont marqué un tournant décisif pour les sciences du climat.

The Earth is a very dynamic body, as anyone living in Italy will have experienced in their lifetime. The planet is constantly stressed by internal thermally driven processes that periodically manifest themselves at the surface by earthquakes and volcanic eruptions. These processes also lead to slow – imperceptible on the human time scale – change that have given the planet its present shape. We are also only too aware of the dynamic nature of the atmosphere and oceans and together these internal and external forces of nature have shaped the planet as we observe it today.

Thus we see a planet that is undergoing constant change. This is perhaps not what I expected when I started university in Australia in the late 1950’s. There, and in subsequent post-graduate studies at the Technical University of Delft, the National technical University of Athens, and Oxford University, I trained as a geodesist, as a ‘measurer of the Earth’, with the goal of determining the planet’s shape and gravity field using the then new methods provided by the tracking of artificial satellites. In those days one was taught that the planet was basically fixed and that the occasional perturbations to the geodetic network were nuisances rather than a source of information on the planet’s response to the internal and external forces. That realisation, that the geodetic measurements could provide valuable insights into the dynamics of the Earth system took another decade to be widely accepted, driven by both the growing geological evidence for the new ‘continental drift’ or plate tectonics, and by rapidly improving satellite tracking and spacecraft technologies.

Planetary gravity fields
My earliest years as a post-doctoral researcher were focussed on understanding the Baker-Nunn camera network that was the most important civilian global network for the scientific tracking of satellites. This was in the United States at the Smithsonian Astrophysical Observatory in Cambridge, which at that time was the leading center for satellite geodesy studies. The satellite methods for positioning in those days, including the emerging ranging to satellites using lasers, were exceedingly cumbersome and imprecise compared with what is being achieved with lasers and GPS today but they produced the fundamental theory for orbital motions that still forms the core of today’s activities. My own contribution to this was to improve the positioning methods using the so-called ‘geometrical method’ that avoided the need for any information on the orbital dynamics. This was important at the time because both the knowledge of the forces acting on the satellite and the computational capabilities were limited. At the same time (late 1960’s) my then colleague, E.M. Gaposchkin, had honed his skills at orbit analyses for gravity perturbations and which yielded as a by-product additional estimates for tracking station coordinates. By combining the geometric and ‘dynamic’ methods and by incorporating terrestrial information on the gravity field – the foundations for which had been laid down earlier by W.M. Kaula – we were able to produce a global solution (the Smithsonian Standard Earth Model SE-II) that for the first time had significant geophysical consequences: that the variations in gravity as seen near the planet’s surface was closely related to the then emerging plate tectonics hypothesis. With time the plate tectonics model provided the underpinning of modern understanding of the evolution of the Earth and I note that this was recognized on two occasions by the Balzan Foundation: with awards to D.P. McKenzie, D.H. Mathews and F.J. Vine in 1981 and to X. LePichon in 2002.

What made our work particularly significant was that at that time virtually every geological and geophysical observation had gone into constructing the hypothesis and there were few independent measurements that could be used to test the hypothesis. Our gravity model provided one of the more important ones for that. Gravity was anomalously high over the convergent plate boundaries – most notably around the pacific – as well as over ‘hotspots’ or mantle plumes such as the Azores or Kerguelen; gravity was anomalously low over the older ocean basins and over old continental cratons. These correlations have been refined in subsequent work but for the next decade or so our SE-II provided a key constraint in the modelling of mantle convection and subduction processes. And, at the same time, the model achieved its original goals of becoming widely used by NASA and other space agencies for the orbit computation and prediction of a wide range of satellites.

I would summarize my own contribution to this model as having come from a good understanding of the accuracies of the observational data and the integration of different and distinctly different data so as to take account of the strengths and weaknesses of the individual contributions. The procedures we developed remained standards for the next decade or so and if the numerical results have now been superseded by newer space techniques and improved computational methods, all the essential long wavelength features of the planet’s gravity field established then remain valid today. For me, the importance of my work was to learn the value of understanding ones observational data base; the value of combining complementary data – sometimes from unexpected quarters – and that it was to lead me down a new path of geophysics.

The Earth’s deformation spectrum
The new SE-II solution also provided a civilian global coordinate reference frame that allowed continental geodetic datums to be interconnected and that provided a starting point for measuring the ‘drift’ of continents. Geodetic accuracies at that time had improved by about an order of magnitude, from a few tens of meters in 1960 to a few meters in 1970, still too low for observing these drifts on decadal time scales. But major improvements in tracking accuracies were occurring, particularly laser ranging and the electronic (Doppler) tracking systems, that had been the domain primarily of the US Navy, were becoming increasingly accessible to civilian users. Also, new methods were being explored for sensing the gravity field with satellite-borne instrumentation (radar altimeters, gravity gradiometers, and others) and computational methods and capacity was expanding rapidly. Thus by about 1970 I could be quite confident that within a few decades we would be able to observe the earth’s deformations at the centimetre level and that satellite geodesy would move from predominantly measuring the static earth to monitoring the planet’s dynamics. Thus this was a good time to focus on what could be done with the emerging geodetic data and I did that by moving to France to contribute to their growing satellite geodesy program, first at the Paris Observatory and later at the Institut de Physique du Globe and the University of Paris.

The spectrum of deformations of the earth can be described in terms of time and length scales and observed, in principle at least, using a wide range of methods and disciplines. At the very long time scales we have the tectonic plate motions on continental scales and the plate-margin deformations on more regional scales. On time scales of a few thousand years we have the response of the Earth’s surface and oceans to the deglaciation of the last large ice sheets. On annual and decadal scales we have the earth’s response to atmospheric and ocean mass redistributions and possibly to changes in the core’s magnetic field. On monthly to semidiurnal periods we have the tidal deformations of the planet and on time scales of hours to seconds we have the displacement fields associated with the earthquake stress cycle. Geological data provides most of the insight for the longer period phenomena while seismological data provides the insights at the very short period part of the spectrum. One problem in understanding this spectrum was, and still is, to understand the transition from essentially elastic and brittle behaviour of the crust and mantle at the one end to the essentially fluid behaviour of the mantle at the other. The geodetic data, at least partly, fills the gap in between.

Thus my goal circa 1970 was to examine each of these processes operating on different time and length scales and to arrive at a comprehensive understanding of the rheology of the planet such that one could begin to understand the response of the planet to any forcing. Grandiose plans are sure to fail. This one has, but much has been learnt on the journey!

Global scales: Planetary rotation and tides
One example concerned the Earth’s rotation. The periodic tidal force deforms the planet and modifies the inertia tensor such that the rotation rate will vary with fortnightly, monthly, semi-annual and longer periods. Thus measurements of these changes – and the improving satellite tracking methods also led to improvements in the planetary rotation measurements – should provide estimates of the earth’s rheological response at these periods. Does the earth, for example, lag the tide-raising potential and therefore show evidence for energy dissipation at these periods? But other processes contribute to the changes in the Earth’s rotation, including cyclic changes in the atmospheric angular momentum and ocean tides and the observations often tell us more about the fluid regimes than about the solid earth. What I, along with my colleague A. Cazenave, was able to do was to demonstrate that a very large part of the semi-annual and almost all of the annual changes in rotation were the result of the exchange of angular momentum between the solid earth and atmosphere over a wide range of periods, from a few days – at the then resolution of the data- to years. This has led to an ongoing program by others of calculating the atmospheric angular momentum from meteorological data and to strip this from the rotation data so that it becomes possible to examine the other contributions: is there a lag in the ocean tidal response or is any residual component the result of tidal energy dissipation in the mantle? The jury is still out but certainly with the vastly improved data sets now available, both meteorological and geodetic, the problem is worth revisiting.

Tides perturb not only the Earth’s rotation. Satellite motion is also affected by the associated gravitational changes and in 1974, in collaboration with G. Balmino and A. Cazenave, we developed a comprehensive orbital theory for the effects of solid-earth, ocean and atmospheric tides. One important side effect of this was the realisation that this orbital perturbation provided a direct estimate of the amount of energy dissipated in the oceans during a tidal cycle, without requiring a knowledge of the specific dissipation mechanisms. Thus these satellite estimates provide a powerful constraint on numerical models of tides but, more interestingly, they provide a constraint on the evolution of the lunar orbit: from the analysis of artificial satellite orbital perturbations we were able to quantify the distancing of the moon from the earth at a rate of a few cm/year. By identifying the major energy sink as being in the oceans, the extrapolation of the orbital evolution also becomes uncertain because of the changing ocean basin configurations back through time. This effectively solved the so-called ‘time-scale’ problem such that the orbit evolution was consistent with the Moon having formed in a close-earth environment at about the same time as the Earth itself.

I have recently returned to the question of reconstructing the ocean basins through the recent glacial cycles and looking at the changes in tidal dissipation and its consequences on the long-term evolution of the Earth-Moon system. Hopefully there will be some new results before I finally retire.

There are many other components in the spectrum of the earth’s variable rotation, occurring over a wide range of time scales and which provide insight into the dynamics and interactions within the Earth-ocean-atmosphere system. Their examination took me on a journey – in the footsteps of W.H. Munk and G.J.F. MacDonald – through palaeontology to unravel the length of day in Palaeozoic time, through discussions of archaeological and historical records in search of lunar observations, and through the earliest astronomical to the modern geodetic observations. This was discussed in my 1980 book, ‘The Earth’s Variable Rotation’. Since 1980, the observational database has expanded considerably and the noise spectrum has been much reduced such that new signals are appearing and a new review of the subject would be appropriate.

Regional scales: Lithospheric tectonics
In late 1977 I had returned to Australia to take up the position of Professor of Geophysics at the Australian National University (ANU), with an option of spending six months a year in France or the USA to pursue the space science component of my research. But that quickly proved impractical and I focussed increasingly on tectonic processes acting in the Earth’s crust and upper mantle, focussing on the shorter wavelength and longer time part of the earth-deformation spectrum. Initially this was through integrating the results of satellite altimetry analyses with geological and geophysical evidence to study the mechanisms by which seamounts and other large volcanic complexes were supported by the lithosphere, the outer layer of the planet capable of supporting stress differences on geological time scales. This was another case of where the geodetic results pointed to an interesting problem but where they provided insights – on the strength of the oceanic lithosphere and on the evolution of the stress state, for example – only when this information was combined with other geophysical and geological information.

These studies led to a search for examples where one could infer the strength of the continental lithosphere over different time scales using gravity observations. The Australian continent provides several such examples. Australia is mostly an ancient continent, well eroded with little topographic relief and well away from active plate boundaries. But it contains large and deep sedimentary basins that are essentially inconsistent with then geophysical conventions: they are not in isostatic equilibrium in any conventional sense and they did not form through extension of the lithosphere. Clearly new models of these intra-continental sedimentary basins were required and I was able to do this by introducing horizontal in-plane compressive driving stress, erosion and sedimentation as amplifiers of the deformation, and stress relaxation in the lithosphere, and which involved deformation within the entire crust and upper mantle. The origins of this model is in the 1958 book by W.A. Heiskanen and F.A. Vening Meinesz – for me an influential book from my undergraduate days but that has been very much ignored through the following decades – and I was able to test it in the mid-1980’s with some novel seismic experiments. At the time the principal success of the models was probably in uniting the geological community against it, leading to a renewed interest in the geological evolution and to new deep crustal seismic sounding and it is fair to add that the then novel aspects of the proposed basin formation process have found their way into modern models for continental tectonics.

Solid-fluid interactions: Sea level and ice sheets
1988 saw the publication of my second book, Geophysical Geodesy published by Oxford University Press. This was an attempt to convince the geodetic community to think of their experiments as one part of a much larger experiment of trying to understand the structure and evolution of the planet and of the importance of integrating the methods of conventional and satellite geodesy with geophysics, geology and the physics of the fluid regimes. This was a time when the technological advances of the earlier years were finally beginning to produce quantum leaps in accuracy and resolution of the geodetic measurements: The GPS system was in its development phase and rapid positioning at centimetre precisions was becoming a reality; the radio-astronomy tool of long-baseline interferometry had provided direct evidence for the motions of continents; the power of satellite altimetry for both geodesy and oceanography had been clearly demonstrated by the SEASAT satellite; and proto-types of the sensors that would revolutionize the ability to measure the Earth’s gravity field had been flown and tested.

Upon reflection it may appear odd to leave such a promising field at that time and I have no real explanation for doing so other than that I saw other interesting science problems that I thought I could contribute to. This included the question of sea level change during glacial cycles: the deformation of the earth and the concomitant rise and fall of sea level on millennium time scales, stressing the planet cyclically with load stresses of several tens of MPa that are similar to the stress differences associated with mantle convection. In starting out I was particularly fortunate to have had the very important inputs from two colleagues, M. Nakiboglu and M. Nakada to formulate the mathematical methodology, as well as from subsequent students and researchers to carry out field, laboratory and computational work.

The ‘glacial rebound’ phenomenon is about the response of the Earth to the changing ice loads as the planet oscillates between glacial and interglacial periods. This response includes sea-level change as water is taken out off (or added to) the oceans when ice sheets grow (or decay) – there is a rich geological record of such change extending back through several cycles – as well as an instrumental record for the past 100 or so years. It also includes the surface deformation in response to the changing load stresses and this has now been observed directly for the past decade or two using geodetic positioning methods. Furthermore there is the change in the gravity field as surface ice-water mass is redistributed and the earth deforms and this results in further perturbations in the motions of close-earth satellites as well as in the planet’s rotation. Different observational responses are sensitive to different parameters quantifying the rebound theory and it is a field where inter-disciplinarity is an absolute necessity if any progress is to be made.

The initial idea was to invert the observations of the response to estimate the mantle viscosity in the part of the spectrum between geodetic and geological frequencies. But, as always, the problem turned out to be more complex and the results were only as good as the a-priori assumptions made about the glacial load history, uncertainties that were almost as large, if not larger, as those in the a-priori knowledge of the mantle viscosity, and it was quickly learned that the focus had to be on improving the understanding of ice sheets as well.

The most important observational data set for glacial rebound comes from the geological record over time scales similar to that of the glacial cycles. This takes the form, for example, of the position of an old shoreline relative to the present shoreline. Thus it is a relative measurement and an elevated shoreline could mean that there has been a reduction of water in the oceans, that the land has been uplifted, or both. On a deformable Earth, the response to the growth and decay of ice sheets results in a complex spatial pattern of sea level change because of the changes to both the shape of the planet’s surface and its gravity field and there will be places where at any time relative sea level is seen to be falling while elsewhere it is seen to be rising at rates that are dependent on the mantle rheology and on the ice history – where was the ice, when was it there, and how much there was. A reasonable assumption is that we know when and where the ice sheets occurred, at least for the time since the last maximum glaciation. But there are no direct (or very few) observational constraints on the ice thickness through time. Thus the scientific challenge is, from incomplete and imperfect data sets, to infer both the earth response function and the ice sheet thickness, assuming that the history of the ice margins is known.

In principle this is a quite standard inverse formulation but its execution has been fraught with difficulties. But it is worth pursuing because, if it can be solved, it provides the best evidence we can have for the mantle properties that control mantle convection and the thermal evolution of the planet; because it would provide insights into the palaeo ice sheets and climate; and because it would provide the background signals to present day sea level change. The geological and geomorphological records of central Scandinavia or northern Canada around the Hudson Bay point to ongoing land uplift (or local sea level fall) in response to the removal of the ice load. But elsewhere the ocean floor is loaded by the meltwater and the sea floor subsides, dragging the coastlines down with it. The rebound process is a global phenomenon that continues today and into the future even if no further changes were to occur in the remaining ice sheets. As we recognized early on, in 1984, modern sea-level rise cannot be summarised by a single number of rise or fall and, like its palaeo counterpart, it will exhibits spatial variability.

Our approach to analysing the geological evidence has been to focus on regional solutions with a careful analysis of available field data and, where necessary, to complement existing information with new data. This has taken my students, colleagues, and not-often enough myself, to many parts of the world where the sea-level response was expected to be particularly sensitive to certain ice or earth parameters: including across Scandinavia, Greenland, the Mediterranean, several locations in Australia, Antarctica and most recently the Seychelles. This has been a slow process but has enabled us to develop inversion schemes of field data that permitted the largely unknown mantle viscosity to be determined despite the only partial knowledge of the past ice sheets. Thus we concluded that the mantle viscosity increased substantially with depth (by a factor of 20-50 between the average values for the upper and lower mantles). This is now widely accepted and has important consequences for modelling mantle convection. More challenging has been the determination of lateral variations in mantle viscosity and we have made some progress down this path by focussing on regional solutions rather than attempting a single global solution. The lateral variation in the average upper mantle viscosity that we infer is less than a factor of ten higher for the mantle beneath the ancient continents than for the mantle beneath young oceanic lithosphere. This is less than we expected from a-priori considerations of laboratory-based flow laws and lateral temperature variations inferred from surface heat-flow measurements and we do not yet have a satisfactory explanation.

The other significant result that we established early on, in 1988, was that the Antarctica ice sheet experienced a major reduction in volume (possibly as much as 20-25% of its volume) since the onset of the global deglaciation starting about 20,000 years ago. This was reached in an iterative process, first by analysing sea level data from locations far from former ice sheets to estimate the global change in ice volume, and subtracting from this ice volume estimates from local inversions for individual northern hemisphere ice sheets where the ice margin retreat is relatively well understood and where there is a reliable data base. We are now completing one further iteration in this process but the essential conclusions about the Antarctic ice sheet are seemingly inescapable even though glaciologists may not like them: that the Antarctic ice sheet was substantially larger at the time of the LGM, extending out to the shelf edge in most locations; that melting occurred after that of the northern hemisphere ice sheets; and ongoing melting until at least 2000-3000 years ago.

Our inversions on the northern hemisphere ice sheets have included, in chronological order, the British Isles, Scandinavia and arctic Eurasia, Greenland and North America. These models are for the time since the last glacial maximum except for Eurasia where we have been able to extend the inversions back to the penultimate glacial maximum about 140,000 years ago and including the onset of the last glacial cycle starting at ~ 115,000 years ago. The significance of the model results is that they are free of glaciological and climate assumptions so that they provide independent models for testing the driving forces of climate, or for testing feedbacks between climate and ocean circulation. This is an area ripe for speculations: for example, to initiate ice sheet growth in Arctic Russia at the start of the last glacial cycle, is global warming first required to disrupt the polar sea ice so as to produce atmospheric moisture in high and cold latitudes where currently precipitation is low? This is also an area where much more work is required before we can give much credence to such speculations.

As I have noted earlier, one of the features of our work has been the search for new data types. One example of this comes from the nearby fish tanks along the Tyrrhenian coast of Italy (and elsewhere in the Mediterranean) and constructed primarily during the Augustan period of the Roman Empire. I was led to these archaeological features by my two colleagues M. Anzidei (INGV) and F. Antonioli (ENEA) who, following a pioneering effort by M. Caputo (La Sapienza) several decades earlier, realized that these structures were no longer functional because of local sea level rise. What we were able to contribute through our glacial rebound modelling and assessment of tectonic contributions, was the conversion of these local observations to global inferences of sea level change over the past 2000 years. Then, by comparing these results with recent tide gauge records from nearby sites we were able to infer that the rise observed by the latter for about the last 100 years was in fact a recent phenomenon and that from ~2000 to ~100 years ago there had been little net change in ocean volume. While this does not identify the source of the most recent change in ocean volume, its coincidence with the onset of global industrialisation does point to an anthropogenic influence. We are now in the process of expanding our fish tank studies to other parts of the Mediterranean to establish a regional baseline for sea level 2000 years ago that can be used for separating the background geological contributions to sea level from the more recent human-driven contributions, for evaluating tectonic stability of the coastlines, and to provide an understanding of the functionality of other archaeological structures whose positions were controlled in some way by the sea level at the time of construction.

Whereto from here?

Humans have been aware off, and adjusted to, sea-level change throughout their existence. There have been times when coastal dwellers would have had to shift their camps regularly, either to avoid inundation as in the Persian Gulf before about 7000 years ago, or to move closer to the shore as in Scandinavia. Migratory routes will have been closed off and ocean crossings will have become wider and more dangerous. The development of successful models for sea level change through time does permit these changes to be quantified and hypotheses of human migrations to be tested. Could the fragmentation of a large near-shore island in the Aegean into the present archipelago that occurred around BC and at a time of rapid sea level rise be the origin of the Atlantis myth? Are the struggles of the Sumerian God Enki with the sea and the subsequent deluge an early explanation for the inundation of the Persian Gulf at a similar time? Further back in time, were there periods before the last glacial maximum when the Red Sea did not impose a major barrier to human movement out of Africa? These are questions where the physical and social sciences meet and that we are now able to begin to address quantitatively.

In summarizing some of my work over more years than I wish to count I have identified many loose ends and I have not achieved my goal of developing that elusive model for the Earth’s rheology to explain the response of the planet at all time and length scales. But in that journey we have identified many of the issues that need to be addressed by the next generation of researchers. I anticipate that the Balzan Prize will make a contribution to that.