Interactive visualization of 3D mantle convection

The current availability of thousands of processors at many high performance computing centers has made it feasible to carry out, in near real time, interactive visualization of 3D mantle convection temperature fields, using grid configurations having 10–100 million unknowns. We will describe the technical details involved in carrying out this endeavor, using the facilities available at the Laboratory of Computational Science and Engineering (LCSE) at the University of Minnesota. These technical details involve the modification of a parallel mantle convection program, ACuTEMan; the usage of client–server socket based programs to transfer upwards of a terabyte of time series scientific model data using a local network; a rendering system containing multiple nodes; a high resolution PowerWall display, and the interactive visualization software, DSCVR. We have found that working in an interactive visualizastion mode allows for fast and efficient analysis of mantle convection results.     

Ubiquitous interactive visualization of 3D mantle convection using a web-portal with Java and Ajax framework

We have developed a new strategy and espouse a novel paradigm for large-scale computing and real-time interactive visualization. This philosophy calls for intense interactive sessions for a couple of hours at a time at the expense of storing data on many disk drives during regular or heroic runs on massively parallel systems. We have already carried out successfully real-time volume-rendering visualization by employing hundreds of processors for a grid with over 25 million unknowns. Both Cartesian and spherical 3D mantle convection are visualized. The volume-rendered images are viewed on a large display device, with many panels holding around 13 million pixels. We will employ a software strategy involving an hierarchical rendering service, which will have as software an Ajax interface for interactive visualization of large data sets on many different platforms from desktop PC’s to hand-held devices, such as the OQO and the Nokia N-800. An option for stereo viewing is also implemented. We have installed a user interface as web application, using Java and Ajax framework in order to achieve over the Internet reasonable accessibility to our ongoing runs. Our goal is to expand the array of interactive devices, which will make it feasible to carry out ubiquitous visualization and monitoring of large-scale simulations or onsite events and to allow for collaborations across oceans.     

Current Trends and Demands in Visualization in the Geosciences

Geosciences, along with many other disciplines in science and engineering, faces an exponential increase in the amount of data generated from observation, experiment and large-scale, high-resolution 3-D numerical simulations. In this communication we describe the fundamentals of visualization necessary to meet these challenges. We present several alternative methodologies such as 2D/3D feature extraction, segmentation methods, and flow topology, to help better understand the physical structure of the data. We use AMIRA from TGS to demonstrate our concepts. Examples are drawn from fields in computational fluid dynamics, 3-D mantle convection and seismic tomography. Finally, we present our perspective on the future of visualization.     

Volume rendering visualization of 3D spherical mantle convection with an unstructured mesh

We propose a new approach to utilize the algorithm of hardware-assisted visibility sorting (HAVS) in the 3D volume rendering of spherical mantle convection simulation results over unstructured grid configurations. We will also share our experience in using three different spherical convection codes and then taking full advantages of the enhanced efficiency of visualization techniques, which are based on the HAVS techniques and related transfer functions. The transfer function is a powerful tool designed specifically for editing and exploring large-scale datasets coming from numerical computation for a given environmental setting, and generates hierarchical data structures, which will be used in the future for fast access of GPU visualization facilities. This method will meet the coming urgent needs of real-time visualization of 3D mantle convection, by avoiding the demands of huge amount of I/O space and intensive network traffic over distributed parallel terascale or petascale architecture.     

A virtual voyage through 3D structures generated by chaotic mixing of magmas and numerical simulations: a new approach for understanding spatial and temporal complexity of magma dynamics

In this contribution, we present a virtual voyage through 3D structures generated by chaotic mixing of magmas and numerical simulations with the aim to highlight the power of 3D representations in the understanding of this geological phenomenon. In particular, samples of mixed juveniles from Salina island (Southern Italy) are reconstructed in 3D by serial lapping and digital montage and numerical simulations are performed by using a 3D chaotic dynamical system. Natural and simulated magma mixing structures are visualized by using several multimedia tools including animations and “virtual reality” models. It is shown that magma interaction processes can generate large spatial and temporal compositional heterogeneities in magmatic systems. The same topological structures are observed in both 3D reconstructed rock samples and chaotic numerical simulations, indicating that the mixing of magmas is governed by chaotic dynamics. The use of 3D multimedia models gives the opportunity to penetrate into magma mixing structures and to understand their significance in the context of magma dynamics. Such an approach is very powerful since multimedia tools can strongly capture the attention of the reader bringing him/her into an interactive and memorable geological experience.     

Capital taxation, long-run growth, and bequests

It has been shown that higher capital taxes can have a growth-enhancing effect when combined with a revenue-compensating cut in wage taxes or with an expansion in productivity-increasing public services. The present paper demonstrates that these results critically hinge on the existence of a bequest motive. It is shown that a wage-tax cut is no longer growth-enhancing when bequests are operative. By way of contrast, increasing productive public services may well boost growth. The theoretical findings are illustrated by numerical simulations based on US data.     

Visualization of multi-scale dynamics of hydrous cold plumes at subduction zones

Recent increases in the computational power of high-performance computing systems have led to a large gap between the high-resolution runs of numerical simulations—typically approaching 50–100 million tracers and 1–5 million grid points in two dimensions—and the modest resolution of 1–2 million pixels for conventional display devices. This technical problem is further compounded by the variety of fields produced by numerical simulations and the limited bandwidth available through the Internet in the course of collaborative ventures. We have developed a visualization system using the paradigm of web-based inquiry to address these mounting problems. We have employed, as a case study, a problem involving two-dimensional multi-scale dynamics of hydrous cold plumes at subduction zones. A Lagrangian marker method, in which the number of markers varies dynamically, is used to delineate the many different fields, such as temperature, viscosity, strain, and chemical composition. We found commercially available software to be insufficient for our visualization needs and so we were driven to develop a new set of tools tailored to high-resolution, multi-aspect, multi-scale simulations, and adaptable to many other applications in which large datasets involving tens of millions of tracers with many different fields are prevalent. In order to address this gap in visualization techniques, we have developed solutions for remote visualization and for local visualization. Our remote visualization solution is a web-based, zoomable image service (WEB-IS) that requires minimal bandwidth while allowing the user to explore our data through time, across many thermo–physical properties, and through different spatial scales. For local visualization, we found it optimal to use bandwidth-intensive, high-resolution display walls for performing parallel visualization in order to best comprehend the causal and temporal relationships between the multiple physical and chemical properties in a simulation.     

Secondary upwelling instabilities developed in high Rayleigh number convection: Possible applications to hot spots

We have conducted numerical experiments for mantle convection in an axisymmetrical spherical-shell geometry from Rayleigh numbers ranging from three million to 10 billion for a purely basal heating configuration. We focus on the development of secondary instabilities developed from plumes and compare them with laboratory experiments by Skilbeck and Whitehead (1978) and Whitehead, (1982). For Rayleigh numbers between around thirty million to one billion, a string of these secondary instabilities can develop from a single plume. Analysis of the spectrum of wavelength associated with the fold instabilities shows that there is a window in the Rayleigh number between around ten million and one bilion where these secondary folding instabilities would develop. These results, when applied to the upper mantle, may explain the formation of hot-spots in a turbulently convecting upper-mantle with a Rayleigh number greater than ten million.     

The growth of point source plumes at Rayleigh numbers up to 108 and Prandtl numbers up to 1000

Two-dimensional numerical simulations were conducted of the growth of thermal plumes from a point heat source at Rayleigh numbers up to 108 and Prandtl numbers up to 1000. Scaling the convection equations by the free fall velocity rather than the thermal diffusivity, increased the Prandtl number range available to numerical simulation by one order of magnitude from Prandtl number 100 to 1000. We present animations showing how the plumes grow with time for different Prandtl numbers. Plumes with Prandtl numbers around 7 (water) were found to be unstable to sinuous instabilities; whereas those at Prandtl numbers of 1000 had straight stems and fewer sinuous instabilities. Wavelet analysis was used to analyze the scales at which plumes initiated, and the scales at which sinuous instabilities occurred. The scale of both the plume structures and instabilities was found to decrease with Prandtl number.     

An Approach to a Visual Language for Convective Fluid Flows: Visualization of Geophysical Simulations

It was known that deep within numbers and binary data from simulations of geophysical convective flows resided various patterns. Two models of convective fluid flows were being considered. One was a model of two-dimensional (768 × 256) air convection with finite Prandtl number of one and Rayleigh number of 10⁸?10¹⁰, and another was a model of three-dimensional (up to 120 × 120 × 90) mantle convection with infinite Prandtl number and Rayleigh number of 10⁶?10⁸. Clearly, phenomena existed which superceded each individual dimensionless computer model to provide a piece of information regarding actual fluid flows. The problem was how to find, prove, and communicate these patterns and phenomena for convection simulations with gigabytes of data. In a search for such an analytical and communicative tool, the alternative of visualization was considered. The need for visualization was recognized and discussed. Then, utilizing both two- and three-dimensional models of high Rayleigh number convection, basic techniques of style and content were developed. Applications of the visualization techniques were designed utilizing IBM’s Data Explorer in order to create communicative images and movies, and after the applications, the problems of data storage and transfer became apparent. Throughout the process though, it became clear how important the language of vision actually could be in the geophysics community. In a field in which words such as plumes and internal waves have in ways replaced mathematics as the basic language for science, there is a need for another resource, another language-the visualization of convective fluid flows.     

Finite Prandtl number 2-D convection at high Rayleigh numbers

Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy “lithosphere”. We have conducted a systematic study on the variations of the convection style, as Prandtl numbers are varied from 7 to 100 at Rayleigh numbers 106 and 108. Numerical simulations show that changes in the Prandtl number could exert significant effects on the shear flow, the number of convection cells, the degree of layering in the convection, and the number and size of the plumes in the convecting fluid. We found that for a given Rayleigh number, the convection style can change from single cell to layered convection, for increasing Prandtl number from 7 to 100. These results are important for determining the surface deformation on the Jovian moon Europa. They also have important implications for surface heat flow on Europa, and for the interior heat transfer of the early Earth during its magma ocean phase. Electronic Supplementary Material is available if you access this article at http://dx.doi.org/10.1007/s10069-002-0004-4. On that page (frame on the left side), a link takes you directly to the supplementary material.     

Adaptation and Mitigation in Long-term Climate Policy

The paper analytically explores the optimal allocation of investments into mitigation and environmental adaptation against climate change damages at a macroeconomic level. The economic-environmental model is formulated as a social planner problem where adaptation and abatement investments are separate decision variables. The existence of a unique steady state is proven. A comparative static analysis of optimal investments leads to essential implications for associated long-term environmental policies. It is shown that the optimal policy mix between adaptation and mitigation is lower for countries with higher economic efficiency for all applicable parameter ranges. Data calibration and numerical simulations are provided to estimate practical validity of theoretical outcomes.     

Visualization of time-dependent dynamics of postglacial rebound

Postglacial rebound is a major geological process which plays an important role in many areas in the earth sciences. Up to now, most of the images derived from studies of the glacial isostatic adjustment phenomenon have been concerned with surface signatures, such as the uplift and gravity anomalies and not much attention has been paid on the dynamical responses in the mantle. We will make use of the 3D visualization package Amira to depict both the external and internal deformation histories of the transient viscoelastic flow inside the mantle induced by postglacial uplift. Of particularly great interest are the transient displacement fields and shear heating inside the mantle. This same visualization technology can be brought to bear in the future for visualizing tsunami waves in ocean basins excited by earthquakes, volcanic eruptions and InSAR images. We have also integrated the visualization results into the Google Earth virtual globe by combining this scheme with the Amira package to provide a better geographical and dynamical context.     

Space–time multiresolution atomistic visualization of MgO and MgSiO3 liquid data

First-principles molecular dynamics simulations of complex material systems such as geophysically relevant oxide and silicate liquids produce massive amounts of time-varying three-dimensional data for the atomic configurations. Given the high accuracy of these data, it is desirable to extract as much information hidden in the data as possible. In this paper, we elaborate on our recently proposed scheme to support interactive visualization at space–time multiresolution of the atomistic simulation data. Instead of just focusing on direct rendering of the given data, additional data (containing more quantitative and qualitative information) that usually have to be extracted by some other means are extracted and rendered on the fly. This allows us to gain better insight into the global as well as local spatio-temporal behavior of the data in the context of bonding, radial distribution, atomic coordination, clustering, structural stability and distortion, and diffusion. We illustrate such visualization for the simulation data on the liquid phases of MgO and MgSiO₃—the two most abundant components of Earth’s mantle. Our analysis shows that the structure and dynamics of both liquids change substantially with compression, with no discernible effects of temperature in most cases.     

Three-dimensional panel data models with interactive effects: Estimation and simulation

This paper considers three-dimensional panel data models with unobservable multiple interactive effects, which are potentially correlated with the covariates. We propose an iterated OLS (IOLS) approach for the estimation of the static model and an iterated GMM (IGMM) method for the dynamic model. Monte Carlo simulations illustrate that our methods perform well in finite samples.     

Regulation of Quality and the Ratchet Effect: Does Unverifiability Hurt the Regulator?

The paper considers a regulatory relationship in which the quality of the output produced by the firm may be hard to verify. When the regulators commitment power is unlimited, one finds that unverifiability always hurts the regulator. Here it is shown that this need no longer be the case if the regulators commitment power is limited. If unverifiability makes the regulator offer low-powered incentive schemes, the firms rent from having private information about the technology is reduced. In long-term relationships, such a reduction in the information rent mitigates the ratchet effect, and by means of numerical examples it is shown that this positive effect of unverifiability may dominate the standard static cost of unverifiability.     

Interactive Web-Based Map: Applications to Large Data Sets in the Geosciences

Current advances in computer hardware, information technology and data collection techniques have produced very large data sets in a wide variety of scientific and engineering disciplines. We must harness this opportunity to visualize and extract useful information from geophysical and geological data. We have taken the task of data mining by implementing a map-like approach over a web server for interrogating the data, using a client-server paradigm. The spatial-data is mapped onto a two-dimensional grid from which the user (client) can quiz the data with the map-interface as a user extension. The data is stored on the server, while the computational gateway separating the client and the server can be the front-end of an electronic publication, electronic classroom, a survey, or an e-business. We have used a combination of Java, Java3D, and Perl for processing the data and communicating between the client and the server. The user can interrogate the geospatial data over any particular region with arbitrary dimensions and then receive back relevant statistical analysis, such as the histogram plots and local statistics. We have applied this method for the following data sets: (1.) distribution of prime numbers (2.) two-dimensional mantle convection (3.) three-dimensional mantle convection (4.) high-resolution satellite reflectance data over multiple wavelengths (5.) molecular dynamics describing the flow of blood in narrow vessels. Using the map-interface, one can actually interrogate this data over the Internet.     

Tax policy and investment demand: A vintage approach

The effects of changes intax incentives for investment are investigated for a putty-clay vintage model in which replacement is an economic decision without requiring static expectations or steady-state growth. It is shown that, with a Cobb-Douglas ex ante production function, the effect on output and its price is identical with that in a non-vintage model with the same parameters. The effect on investment and employment is to introduce a long-run cyclical element. Some simulations for UK manufacturing show that even the direction of the short-run effect on investment and employment can be different dates.     

Optimal age‐dependent income taxation in a dynamic extensive model: The case for negative participation tax on young people

We consider optimal age‐dependent income taxation in a dynamic model where the labor‐leisure choice is the extensive margin, each household faces idiosyncratic shocks to labor productivity and a pecuniary cost to work, and there is no insurance market against the shocks. We show that the well‐known property of the optimal participation tax rate in the static model continues to hold in our dynamic economy, that is, the participation tax rates for some income groups with low consumption are likely negative. In dynamic models, the optimal participation tax rate depends on age and on labor income. Our numerical simulations suggest that a negative participation tax should be restricted to young households.     

Visualization and Analysis of Mixing Dynamical Properties in Convecting Systems with Different Rheologies

We analyzed and compared the mixing properties of 2-D mantle convection models. Two rheologically different models, Newtonian and non-Newtonian (power-law), were considered with both the line and field methods. The line method is based on monitoring of passive particles joined into lines, while the field method relies on the advection of a passive scalar field. Both visual and quantitative estimates revealed that the efficiency of the Newtonian mixing is greater than the non-Newtonian. A heterogeneity placed in the non-Newtonian convection forms horizontal structures, which may persist for at least 1 Ga on the upper-mantle scale. In addition, the non-Newtonian medium reveals a lesser amount of stretching of the lines than the Newtonian material. The rate of the Newtonian stretching fits well with an exponential dependence with time, while the non-Newtonian rheology shows the stretching rate close to a power-law dependence with time. In the Newtonian medium the heterogeneity is reorganized into two unstable vertical columns, while the non-Newtonian mixing favors horizontal structures. In the latter case, these structures are sufficiently stable in both the temporal and spatial planes to explain the mantle geochemical and geophysical heterogeneities. Due to the non-linear character of power-law rheology, the non-Newtonian medium offers a “natural” scale-dependent resistance to deformation, which prevents efficient mixing at the intermediate length scales.