TOPO-EUROPE - 2.2.5. High-performance computing

2.2.5. High-performance computing and time-dependent Earth models

Topical and Capacity Computing

Earth processes are complex and highly non-linear. Computational modelling has therefore become one of the most important tools to advance their understanding. Due to the dramatic advances in modern high-performance computing, great advances can be expected in our ability to model seismic wave propagation, rupture and fault dynamics, deformation of the lithosphere, or solid-state flow in the Earth’s mantle. Combined with an unprecedented wealth of observational data becoming available from ground, airborne and space-borne monitoring this bodes well for pushing forward the frontiers of our understanding of the fundamental processes that govern large-scale tectonic activity on Earth.

Earth models rank among the most challenging calculations computational physicists can perform today. Difficulties arise from the wide range of spatial and temporal scales that must be resolved. For example, failure processes in the brittle crust along plate margins may extend over distances of a few 10 km, while the plates themselves are embedded in a global circulation system of the Solid Earth with length-scales on the order of 10,000 km. Likewise, if we take global seismic wave propagation calculations performed at a dominant period of 5 sec as an example, there are up to 100 billion degrees of freedom. This translates into 10-100 Terabytes of main memory and weeks of integration time. Such requirements tax even the largest supercomputers in Europe.

Fig. 14. Tectonic High Performance Simulator (Tethys) with 150 Processors, 150 Gbytes main memory and sustained performance for Earth System models in excess of 300 Gflops. This topical computing system is available to TOPO-EUROPE (courtesy H.P. Bunge).

Reflecting the range of scales and the heavy computational burden it is easy to see that Earth models exceed the limitations of the largest high-performance computing system currently available to the European scientific community at national and European supercomputer centres. In addition to a tremendous demand in terms of the capability of computing systems (essentially the size of a computer) there is a rapidly growing demand in terms of the capacity (the amount of computing time or cycles actually available to a user) of the systems. Said differently, while there has been great progress at the highest end of supercomputing over the past decade there is a significant gap between local computing resources, such as desktop computers, and high-end systems. Measured against the leading systems, such as the Earth Simulator, the gap now spans close to four orders of magnitude in processing speed and main memory. To ease the limitations in computing capacity, several groups in TOPO-EUROPE are now at the forefront of installing state-of-the-art modelling infrastructures based on clusters of high-end PCs. These innovative mid-range parallel computer systems exploit the cost-advantage of mass-produced PCs and deliver superior price/performance. They are well suited to supply the computation capacity required for Earth simulations. Typical clusters comprise any number of processors from, say, a few tens to several hundred. For example, Munich University employs a new Earth modelling cluster with 150 processors, which ranks among the largest tectonic simulators in Europe (Note: a similar cluster at Caltech employs 2000 processors). This cluster is optimized for key-applications, including seismic wave-propagation and tectonic simulations that perform at high efficiency. Earth modelling clusters are distinctly topical. We anticipate a strong role for capacity and topical computing in TOPO-EUROPE and note that TOPO-EUROPE will have advanced new facilities, as for example the Munich Earth cluster (see Fig. 14), at its disposal. Some of the calculations that can be performed on such systems include:

Tectonic and lithospheric modelling
Modelling of seismic wave propagation
Mass-redistribution in the Solid-Earth system
Global circulation models of the Earth’s mantle
Glacial rebound models

Time-dependent Earth Models and Data-Assimilation

Geophysical modelling has greatly benefited from the advent of modern parallel computers. Focusing on the Earth's mantle, resources on topical computers are now sufficient to model its global flow pattern with a near-Earth-like convective vigour in 3D spherical geometry. To take the next step and model the geologic evolution of mantle flow and continental tectonics requires the use of sophisticated data-assimilation techniques. These techniques will be brought to bear in TOPO-EUROPE primarily to overcome fundamental problems inherent to initial conditions. In other words, we don’t know how to properly start geodynamic and tectonic simulation from some assumed initial conditions in the past, because these conditions are essentially unknown.

There are important reasons for trying to use data-assimilation techniques in TOPO-EUROPE and to overcome the initial-condition problem of tectonic modelling. Continental platform stratigraphy and marine transgressions were to a large part controlled by temporal changes of the Earth's dynamic topography in response to mantle convection. The current topographic elevation of southern Africa and the narrowness of its continental shelves are indicative of tectonic uplift that is probably supported by lower mantle flow. The dynamic origin of the South African topography is entirely consistent with independent evidence from seismic tomography, imaging a low velocity anomaly in the mantle beneath southern Africa. Similarly, dynamic processes in the deep Earth may have controlled the low topography of Europe during the Late Cretaceous.

Fig. 15. Cut-away of the 3D temperature field for a mantle circulation model seen from the Pacific hemisphere (GEMLAB: Geodynamic Earth Model of Los Alamos and Berkeley). The model was obtained by imposing the 119-Ma through present-day plate motion record, reflecting the history of subduction beneath the north-western Pacific. Blue is cold and red is hot. The upper 50 km of the mantle are removed in order to show the convective planform. Present-day plate boundaries are drawn for geographic reference (after Bunge et al., 1998).

From an algorithmic point of view data-assimilation is usually implemented either by sequential filtering or by global smoothing methods. In sequential filtering the model is integrated forward in time for the period for which observations are available. Whenever an instant is reached for which observations are available, the model is `updated' or `corrected'. The model is then restarted from the updated state and the process repeated until all available information has been used. This approach is now well established in global mantle convection studies, in which it is used to compute so-called mantle circulation models (Fig. 15) from past plate motion reconstructions.

We expect that sequential data-assimilation will play an important role in TOPO-EUROPE in bringing theoretical and observational communities together. Sequential data assimilation is well adapted to geodynamic modelling studies, because it performs a constant update on the model state and uses each new observation for correcting the latest model state. There is, however, a fundamental drawback. Owing to the sequential character of the assimilation, each individual observation is used only once, thus influencing only the forward state of the model. Information propagates from the past into the future, whilst no information is carried back into the past. We anticipate that this limitation will be of disadvantage in tectonic studies, as we have far more detailed knowledge on the present state of the system than on its past state. To overcome this limitation, TOPO-EUROPE will explore more powerful data-assimilation algorithms capable of carrying information back in time. Within the framework of the TOPO-EUROPE project, one of the most important datasets on deep mantle flow and large-scale tectonic processes will come from tomographic imaging studies of the Earth's interior.

Fig. 16. (a) Cut-away of the 3-D temperature initial condition field for the reference mantle circulation model (see text) seen from the Pacific hemisphere. The model is obtained by imposing (assimilating) mid-Mesozoic plate motions (c) until quasi steady-state is reached. Blue is cold, and red is hot and the linear color scale ranges from 0 to 2300 °C. The upper 100 km of the mantle are removed to show the convective planform. Narrow hot zones near the surface reflect passive mantle upwelling at the Izanagi (IZA), Farallon (FA), Pacific (PA) and Phoenix (PH) spreading centers. The cold downwelling in the cross-sectional view under the northwestern Pacific results from subduction of the Izanagi and Farallon plates. (b) Same as (a) but after 100 Myr of present-day plate motion (d) have been imposed. (c) Map of plate boundaries and velocities for the 119–100 Myr stage from Lithgow-Bertelloni and Richards (1998). The ancient Izanagi, Farallon and Phoenix plates occupy most of the Pacific Basin. (d) Same as (c) but for the present-day from Gordon and Jurdy (1986). The Izanagi, Farallon and Phoenix plates have largely disappeared (after Bunge et al., 2003).

Tomographic images provide important constraints on present and past mantle flow that can be linked explicitly to the evolution of topography and large-scale tectonic activity via a data assimilation approach involving variational methods. In this approach a numerical adjoint code and the forward model are solved jointly in an iterative procedure. Variational data-assimilation is a familiar tool in numerical weather prediction and oceanographic models, where it has resulted in dramatically improved model forecasts. Importantly, synthetic tests of variational data-assimilation in mantle circulation and tectonic models show similar improvements in forecast accuracy. Results show that deformation can be reconstructed backward into the Late Cretaceous. Figure 16 shows a snapshot of the 3D temperature field in a data-assimilation model of the mantle for the past 100 million years. Unfortunately, 3D modelling of mantle convection when combined with powerful numerical adjoint techniques comes at a heavy computational price. Weeks of integration time are necessary to solve such problems even on some of the most powerful parallel machines currently in use at national computing centres.

Feedback between Topography and Plate Tectonics

While it is generally assumed that plate tectonics and topography are linked through driving and resisting forces along plate boundaries, details of this linkage are not very well understood. Although buoyancy forces associated with subduction zones provide a significant driving force for plate convergence, the relative magnitudes of other driving and resisting forces are less clear, as are the main factors controlling long term changes in plate motions. The ability to consider past as well as present plate motions in the context of TOPO-EUROPE will provide important constraints, since changes in plate motion are necessarily driven by changes in one or more of the key driving forces, as can be inferred from independent data.

Fig. 17. Present-day subduction plane and plate base stresses inferred from a simulation for the Nazca and South American plates. Colour scale indicates stress magnitude in MPa. Plate boundaries are in black, Andes topographic elevation contours in grey. Resisting stresses along the subduction plane are comparable to plate driving shear traction of the mantle, particularly beneath highly elevated regions in the central Andes (after Iaffaldano et al., 2006).

An important analogue region for TOPO-EUROPE is South America, and more specifically the development of high topography in the Andes (see also section 3.8). Groups in TOPO-EUROPE have constructed a model that explicitly links global mantle convection and lithosphere models to infer plate motion changes in this region as far back as Miocene times. These calculations accurately predict the observed slowdown in convergence rates during the last 10 My and link it to the contemporaneous rise of the high Andes. This suggests that surface topography generated at convergent margins may have a strong bearing on plate motions (Fig. 17). The topographic load of large mountain belts and plateaus appears to absorb a significant amount of the available plate driving forces by increasing the coupling between the subducting and overriding plates. As such, this model may be applied and further evaluated in TOPO-EUROPE studies addressing the evolution of European orogenic belts, for which a large number of kinematic constraints will become available both from the analysis of past plate motions as from geodetic measurements on temporal variations of plate movements. These constraints will permit to model the relative contribution of different plate driving forces (Ziegler, 1993).