DISCRETE GLOBAL GRIDS：RETROSPECT AND PROSPECT

Michael F.Goodchild

（CenterforSpatialStudiesandDepartmentofGeography，UniversityofCalifornia，SantaBarbara，CA 93106－4060，USA）

DISCRETE GLOBAL GRIDS：RETROSPECT AND PROSPECT

Michael F.Goodchild

（CenterforSpatialStudiesandDepartmentofGeography，UniversityofCalifornia，SantaBarbara，CA93106－4060，USA）

Discrete global grids provide a means of rasterizing the curved surface of the Earth.They form the basic data models for digital globes，and thus enable the vision of Digital Earth.The author reviews the history of discrete global grids and Digital Earth，and the first generation of implementations，exemplified by Google Earth.Digital Earth challenges us to provide effective communication of information about the surface and near-surface of the Earth to the scientific community and the general public，but the first generation falls short of this vision in several respects，most notably the lack of an ability to simulate future states based on models of social and environmental processes.A summary is presented of previous work on a vision for the next generation of Digital Earth.

Discrete Global Grids（DGG）;Global Spatial Grid（GSG）;Geographic Information Systems（GIS）;Digital Earth;Digital Globe

Chinese Library Classification：P208 Document Code：A Article ID：1672－0504（2012）01－0001－06

1 INTRODUCTION

Rasters play a critically important role in many forms of human activity.We capture photographs by recording incoming light levels on rectangular arrays of sensors，and display the outputs of computers and personal electronic devices as rectangular arrays of light and color.Rasters form the basis of images of Earth captured from space or from the air，and used for mapping or as input to models of the Earth system′s dynamics.Yet rasters are inherently twodimensional and flat，and it is impossible，with a few exceptions，to tile any curved surface with identical，non-overlapping elements.Thus any application of imaging to the curved surface of the Earth must encounter and deal with the distortions inherent in map projections.Projections can be conformal，the scale at any point being the same in all directions，and thus able to preserve small shapes;they can preserve a limited subset of distances;but they cannot preserve all distances.Map projections are inherently difficult to comprehend，and are responsible for some of the problems people encounter with technologies such as geographic information systems（GIS）.

A model globe presents none of the problems of map projections，portraying a scaled Earth with no more distortion than is inherent in the measurement and production processes.Traditionally globes have been of limited value because they are difficult to produce，transport，and store，and can only present the globe as a whole with very limited detail.The world′s largest globe，according to the Guiness Book of World Records，measures a mere 12.6 m，or approximately one millionth of the size of the real globe.Yet in a digital system a three-dimensional globe is as easy to represent as a two-dimensional map，with no limits to spatial resolution.Moreover，a user who is able to manipulate the globe，rotating it and zooming in to greater detail，perceives the object being manipulated as truly three-dimensional.Digital globes have thus attracted great attention ever since the necessary 3D graphics capabilities became part of the functionality of the standard personal computer，beginning around 2001.Perhaps the best known is Google′s Earth，originally developed by Keyhole as Earthviewer.

A discrete global grid（DGG）is defined as a partitioning of the surface of the globe into approximately identical tiles（Sahr，White，and Kimerling，2003）［1］.A digital globe should support zooming，from perhaps 10 km resolution to 1 m or better，and thus the discrete global grid should be hierarchical and nested，each tile at one level being divided into subtiles at the next level using a simple，universal rule.Discrete global grids are normally considered to be partitions of the two-dimensional Earth surface，but it is a simple extension to think of threedimensional partitions of a solid Earth and atmosphere.

Only five partitions of the surface of a solid have the property that each element is identical.These are known as the five Platonic solids：the tetrahedron of four triangles，the cube of six squares，the octahedron of eight triangles，the dodecahedron of 12 pentagons，and the icosahedron of 20 triangles.But subdividing the tiles of a Platonic solid produces a solid that is non-Platonic，so although many DGGs are based on Platonic solids at their coarsest resolution，finer resolutions yield tiles that are unequal.

Clearly a DGG should strive for tiles that are as equal as possible in shape and area at any level.However，many other factors influence the suitability of a DGG，including computational performance.Kimerling et al.（1999）［2］present a set of criteria for the evaluation of DGGs that emphasize geometric rather than performance properties.

While it is always possible to draw vector data on a digital globe，connecting points with great-circle arcs，it is essential to use a raster approach to rendering the globe as a solid with recognizable features.Thus services such as Google Earth combine a raster-like representation of the appearance of the Earth′s surface with the ability to superimpose points，lines，and areas defined by vectors.

The purpose of this paper is to provide a highlevel summary of progress to date on DGGs and the digital globes they enable，with an emphasis on the latter.The next section discusses progress to date，using the vision of Digital Earth as a benchmark.This is followed by a section on prospects，and on updating the vision of Digital Earth as a basis for a next generation.

2 DIGITAL EARTH IN RETROSPECT

Digital replicas of real systems are attractive for many reasons.From a practical perspective，a digital replica allows virtual experiments that avoid intervention，and may produce faster results.Thus a digital representation of a city′s transportation system allows planners to examine the implications of events and planning decisions;a digital cadaver allows medical students to learn physiology without dissecting real bodies;and a digital airplane allows engineers to investigate designs prior to actual construction.A Digital Earth is similarly attractive，if only because it would allow researchers to investigate the impacts of factors such as increased atmospheric CO2without incurring all of the consequences of actual climate change.In arguing for the development of a Digital Earth，Gore（1992）［3］was more concerned with data access：if all of the available and relevant data sets were organized into a single package，scientists and the general public would have a much better window onto what is known about the Earth′s environment.His ideas were expanded and elaborated in a 1998 speech （portal.opengeospatial.org/files/？artifact-id＝6210）that laid out a vision for Digital Earth，and led to the establishment of a Digital Earth office in NASA（the National Aeronautics and Space Administration）and the funding of several exploratory projects to build prototypes.

From the perspective of 1998，Gore′s vision of a child exploring a virtual reality，zooming in to greater detail and enjoying a"magic carpet ride"over the Earth，sounded like science fiction.The Earth′s surface has 5×1014 elements at 1 m resolution，or 0.5 petabytes if an average of only 1 byte is used to describe each element.But by 2001，when Keyhole′s Earthviewer was launched to the general public，it had become possible to achieve Gore′s magic carpet ride and real-time zoom.Several factors contributed to this very rapid improvement of technology.First，broadband Internet access had become far more prevalent.Second，the typical personal computer now had the necessary graphics engine by default，largely because of video gaming.Third，developers had realized that pre-computing a hierarchy of tiles and sending them to the client when needed would make it possible to avoid the performance issues associated with computing and rendering on the client.Fourth，some clever level-of-detail management was employed，with finer detail in the center of view and coarser detail on the periphery.Fifth，the launch of fine-resolution imaging satellites，and investments in color aerial photography，meant that the necessary data for the base layer was now abundant，much of it in the public domain.Finally，Google′s publication of the Earth API（Application Programming Interface）and NASA′s decision to make the World Wind source-code available led to the rapid development of thousands of third-party applications.

This first generation of Digital Earth was enormously successful in many respects，most obviously since it enabled many aspects of the Gore vision.It showed that the vision could be implemented using a simple personal computer，a broadband connection，and a simple browser or thin client.The third spatial dimension could be handled，by raising or lowering objects relative to the ellipsoid.The technology was very user-centric，with a user interface that was easy to learn，free，and fun to use.The publication of the API and KML（Keyhole Markup Language）meant that almost anyone could explore personalized applications.From the perspective of today，it is clear that the first generation had an enormous impact，engaging the average person as never before in exploring a detailed representation of the planet，and playing a significant part in the emergence of a neogeography （Turner，2006）［4］in which the citizen is engaged as both consumer and producer of geographic information.

On the other hand，there were several significant gaps in the first generation′s implementation of Gore′s Digital Earth vision.First，the first generation focused on the surface and near-surface，treating the third spatial dimension as an extension above and below the surface，and offering little in the way of support for studies of the solid Earth or the atmosphere，or volumetric representations of the oceans.Second，the base data employed by Google Earth and other private-sector digital globes could be used only for visualization because of the terms under which it was licensed，falling short therefore of the Gore vision of a data-distribution mechanism.

A third missed opportunity lay in the potential use of digital globes as engines for simulation.In principle it should be possible to use the digital globe′s DGG as a finite-element mesh （Topping et al.，2004）［5］，to enable modeling and prediction of dynamic phenomena such as the atmosphere or ocean circulation through the solution of partial differential equations.In this way，digital globes could become mechanisms for communicating knowledge not only about how the Earth looks today，but about how it might look in the future.More broadly，digital globes could fill an important gap in the communication of knowledge about the planet′s future，through an easy-to-use interface.In practice，some digital globes have come close to achieving that goal，but only as engines for visualization of simulations obtained using other platforms.

In reality at least four distinct versions of the Digital Earth vision can be discerned in the Gore speech.Most conspicuous，perhaps，is the vision of an immersive environment with its zooming and magic carpet ride.But Digital Earth is also a metaphor for supporting the processes of search，discovery，and retrieval of geographic information.The concept of a geolibrary（NRC，1999）［6］sees such processes as extensions of the traditional role of a library，but adding a crucial element that libraries are unable to provide：the ability to assemble all information about a given location，in other words，to answer the question"What have you got about there？" .Maguire and Longley（2005）［7］extend this concept to the geoportal，a Web site that can provide a single point of entry into distributed resources not only of geographic information，but also of the tools to manipulate，analyze，and model it.By using a digital globe as the basis of its user interface，a geoportal can provide a much more intuitive approach than the traditional search over files and folders that still dominate much information retrieval.

Third，Digital Earth can be seen as the mother of all databases，a vast，distributed collection of the exabytes of data that now exist about the Earth′s surface and near-surface.Such a database would need to be supported by consistent protocols and standards，and made accessible through the intuitive interfaces that characterize geolibraries and geoportals.And finally，Digital Earth can be seen as a collection not only of data，but of higher-level，more abstract knowledge about the Earth′s dynamics，and the processes that create and modify its surface and near-surface.Most data about the Earth are crosssectional time slices，providing facts but falling well short of providing understanding.Digital Earth in this fourth vision would provide a storehouse of the models that express scientific knowledge of Earth dynamics，allowing users to visualize the Earth′s future in an accessible package through an interface designed for Gore′s young child.It would be capable of displaying not only what the Earth looks like，but what it used to look like in the past，and what it is expected to look like in the future based on the best available scientific knowledge.

3 DIGITAL EARTH IN PROSPECT

Enormous changes have occurred in the world of computing since Gore′s speech was written in late 1997.The impacts of the Internet and Web have been profound，enabling social media such as Facebook.Personal devices have proliferated，offering a range of services that would have been inconceivable in 1997.Moreover there is every reason to believe that the rate of innovation will continue and even accelerate in the next few years.With respect to Digital Earth，therefore，two questions seem appropriate：What are the prospects for implementing the remaining parts of the Gore vision？，and How should the vision be updated？

Several discussions along these lines have occurred in the past few years.In 2008 the Vespucci Initiative organized a two-day specialist meeting in Florence，and developed a position paper（Craglia et al.，2008）［8］.Subsequently the International Society for Digital Earth held a two-day workshop in Beijing in March 2011，leading to further discussion at the biennial International Symposium on Digital Earth in Perth in August 2011，and to two draft pa-pers.In this section I summarize the main points of these discussions.

The Vespucci Institute specialist meeting produced an eight-point vision：

（1）Digital Earth must serve several distinct communities，each with their own needs and abilities.To scientists，the value of Digital Earth lies in its support for data discovery and retrieval，and for collaboration between investigators and across disciplines.To citizens，the value of Digital Earth lies in the easy access it provides to detailed representations of the Earth.Educators and policy-makers have their own special needs.Thus the new vision for Digital Earth should emphasize diversity，and the need for an infrastructure that supports multiple，connected digital globes through appropriate protocols and standards.

（2）Digital Earth should be driven by concern for the problems that affect humanity and that humans need to solve，such as the nine identified by the Group on Earth Observations（www.earthobservations.org）or the 11 identified by a recent report on the geographical sciences （NRC，2010）［9］.Google has shown how important a tool such as Google Earth can be in focusing on specific problems，such as the crisis in Darfur.In this vision，versions of Digital Earth could focus on hunger，or the spread of disease，or the state of the global economy，using appropriate visualizations to convey the state of knowledge in each area.

（3）Digital Earth should allow search through time and space，and over data obtained both from sensors and from human observers.One of its most important functions should be to search for analogous situations（Goodchild，2008）［10］："Find for me the places on Earth where conditions are similar to those at this location."The ability to search for analogs would have value in many activities，but is currently not well supported either in GIS or in the first generation of Digital Earth.

（4）Digital Earth should allow the user to ask questions about change，identifying areas of the Earth where the most rapid change is occurring in certain dimensions，or finding places where anomalous patterns are emerging.It should support such searches in both social and environmental domains.Again，such searches are not well supported either in the first generation or in GIS.This aspect of the vision reflects a desire on the part of the participants at the specialist meeting to draw a clear distinction between the functionality of Digital Earth and that of GIS.

（5）Digital Earth should provide access not only to data，but also to services and models.It should allow the user to investigate the impacts of policy decisions and scenarios，providing a powerful and comprehensive tool in support of science-based planning.In this sense Digital Earth is seen as reflecting the goals of geodesign （ESRI，2010）［11］，combining the ability to sketch and specify development scenarios with the ability to evaluate and assess impacts.

（6）Digital Earth should provide visualizations of a wide range of data types.The digital globes recreate the visual appearance of the Earth′s surface，allowing the user to navigate by recognizing features rather than by the more abstract concepts of latitude and longitude.But communication of more abstract data types that are not inherently visual，such as air temperature，is more difficult.Some of the most difficult data types to communicate are social：income or state of health，for example.The communication of such abstractions to the general user presents a research problem of major importance.

（7）The early years of the 21st Century saw a rapid proliferation of electronic media，from the laptop and desktop to a wide range of small，personal devices.While there has been some convergence in recent years：smart phones now support Web browsing，for example，the vision of Digital Earth should include a range of modalities and devices.It should be possible to use features of Digital Earth through voice communication and text as well as through the familiar visual interface.

（8）Finally，Digital Earth should be engaging，interactive，and exploratory，features that provided much of the attraction of Google Earth and other examples of the first generation.It should provide a collaborative environment that supports learning and scientific research across the full range of disci-plines.

Further details，including a discussion of the research that still needs to be done to enable aspects of this new vision，can be found in the published paper（Craglia et al.，2008）［8］.

4 CONCLUSIONS

The experience of the past seven years clearly demonstrates that a digital globe can capture the imagination and interest of a large fraction of the public，as well as of the scientific community.It can provide an attractive mechanism for communicating information about the state of the planet，for enhancing people′s interest in the planet，and for drawing attention to issues of major importance to humanity.The digital globes facilitate access to information about the surface and nearsurface of the Earth as never before.

Nevertheless digital globes suffer from the same novelty effect as any other technology：a quick ramping up of interest，followed by a long decline.This is clearly evident，for example，in the timeline available at Google Trends.What is needed to sustain interest is a constant invention and re-invention，with new ideas and new applications in a steady flow.Moreover the original motivation for Digital Earth，as expressed in the Gore speech and in statements associated with Google Earth，focused on the kinds of attractive exploration exemplified by the magic carpet ride，rather than on applications that would provide a solid business case.In an earlier paper I attempted to retro-fit such a business case，arguing for a set of use cases that would clearly identify the necessary functions.Some of these functions appear in Section 3，notably in Items 3 and 4 of the prospective vision.

All humans have an investment in the future of the planet：it is the only one we will ever have，and Digital Earth can provide an effective platform for experiments that should never be carried out on the real thing.A Digital Earth powered by simulation models that are grounded in good science can provide predictions of the impacts of policy decisions，and allow a reasoned argument for or against proposed developments.In this sense a Digital Earth seems essential to the future of humanity.

Moreover，the first generation of digital globes have clearly demonstrated the power of such platforms to provide communication between science and the citizen，using an attractive and easy-to-use interface to convey information.While these capabilities are currently quite limited，successful research on the communication of abstract concepts and data types has the potential to greatly expand the range of possibilities.

Digital globes have come a long way since 1998，when they required expensive，stand-alone graphics machines.The advances noted earlier have made possible what few in 1998 would have considered credible：pan and zoom across more than four orders of magnitude of resolution，at video-refresh rates，in a standard personal computer.The potential is much greater，however：integration of Digital Earth with social media，enabling collaboration on a vast scale;simulation of a wide range of processes，enabling visualization of predictions about the planet′s future;and analytic functions that implement novel methods of search over the planet′s surface.

I began this paper with a review of discrete global grids，the fundamental building blocks of a digital globe.To date，the full potential of DGGs has yet to be realized，especially in their potential role in providing the mesh for simulation models，and in their extension to three dimensions，allowing representation of the solid Earth and the upper levels of the atmosphere.Much more remains to be done in achieving the full capabilities of DGGs and global geometry，since it is easy to find examples of corner-cutting and simplification in the first generation.It is clear also that the next generation will need to address uncertainty，an endemic issue with geographic information but one that is almost completely overlooked in the current generation.Communication of uncertainty will be especially important in connection with any predictions or results of simulation.

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全球離散格網(wǎng)：回顧與展望

邁克爾F.古德切爾德
（美國加州大學圣芭芭拉分校地理系、空間研究中心，圣芭芭拉，美國CA93106－4060）

全球離散格網(wǎng)是數(shù)字球體表達的基本數(shù)據(jù)模型，它提供了一種柵格化表達地球彎曲表面的方法，催生了數(shù)字地球。該文回顧全球離散格網(wǎng)與數(shù)字地球的發(fā)展史，評析了以谷歌地球為代表的第一代數(shù)字地球的技術實現(xiàn)。在為科學界及社會公眾提供地表與近地表信息交流方面，數(shù)字地球的有效性面臨挑戰(zhàn)，第一代數(shù)字地球在很多方面存在不足，其中最顯著的缺陷是不能基于社會與環(huán)境過程模型模擬地球的將來狀態(tài)。展望未來，簡要分析了下一代數(shù)字地球應具有的基本特征。

全球離散格網(wǎng)（DGG）;全球空間格網(wǎng)（GSG）;地理信息系統(tǒng)（GIS）;數(shù)字地球;數(shù)字球體

Author introduction：Michael F.Goodchild，Professor of the Department of Geography，University of California（Santa Barbara），researches involve on Geography，GIS and Geoinformation Science.E－mail：good＠geog.ucsb.edu