L INTRODUCTIONSatellites and other modern technologies today provide abundant information about spatial

variations in many kinds of resources . Although the demand for geographic information is grow-ing continually, in many cases it is only the start of a user's needs. The outputs from geographicinformation systems (GIS) often need to be used as inputs to spatially explicit models . One might,for example, wish to use maps of soils, cultivation and past productivity to forecast regional cropproduction, or to use maps of fuel loadings and of land use to assess fire hazard and risk .

A common shortcoming ofmost existing GISs is that they do not provide modelling capability ;many are really automated cartography . To be more effective, GISs need to link spatial infor-mation with process models, particularly ones that simulate processes across an entire map .Likewise modelling systems usually do not provide the flexibility to select or explore their out-puts. In large part these problems stem from the difficulties associated with developing simula-tion models .

In this account we outline the design of a generic landscape modelling system ("MOSAIC")that we are developing . The aim of this project is to simplify landscape modelling by providingprogramming languages and modelling tools that relate directly to landscapes and landscapeprocesses .

In previous work [3]-[7], we concluded that to simplify model development, modelling lan-guages need to consist of terms and concepts that relate to the system being modelled, ratherthan computational details. Furthermore, because simplicity and flexibility are competingdemands in modelling, these terms and concepts need to be based on paradigms that are validand useful for a wide range of phenomena . Here we show how these ideas can be applied in thecontext of landscape modelling. The generic landscape modelling system MOSAIC resolves theabove problem by providing a hierarchy of object-oriented languages [10],[14], whose semanticsrange from concepts associated with landscapes in general, to particular landscape systems, suchas crops, hydrology, and ecosystem dynamics .

2 . MODELLING LANDSCAPESThere are two fundamental ways of representing features in a landscape : one can store a list

of locations, noting the features associated with each location ; or else one can store a list of fea-tures, noting the location and properties of each feature . In a GIS, these two representations areassociated with raster data (e.g. satellite images) and vector data (e.g. map contours), respective-ly. Depending on the problem, models may need to be based on either of these representations,or on some combination of the two . For instance, a vegetation model may employ pixel-based

0378-4754/90/53.50 0 1990, IMACS/Elscvicr Science Publishers B .V. (North-Holland)

Mathematics and Computers in Simulation 32 (1990) 237-242North-Holland

A GENERIC APPROACH TO LANDSCAPE MODELLING

D.G . GREEN, R .E. REICHELT *, J_ van der LAANand B.W. MACDONALDEcosystem Dynamics Group, Research School of Biological Sciences, Australian National University .Canberra, ACT, Australia

237

tional

* Australian Institute of Marine Science, Townsville MSO, QLD, Australia 4.810,

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maps to provide data about soils and other landscape features, but represent plant populationsas lists of objects .

The concept of cellular automata provides a valid theoretical basis for models of manylandscape processes (Fig. 1). A cellular automaton is an array of identically programmedautomata that can interact with one another [18],[19] . Cellular automata models of landscapesconsist of fixed arrays in which each cell represents an area of the land surface [2]-[7] . The statesassociated with each cell correspond to environmental features, such as coral cover or topog-raphy. This approach is compatible with both pixel-based satellite imagery and with quadrat-based field observations . It also enables processes that involve movement through space (e.g.fire, dispersal) to be modelled in "natural" fashion .

Despite their conceptual simplicity, cellular automata are capable of a rich variety of be-haviour [18] . This variety arises because the cells interact . Many processes cause sites in alandscape to interact with one another and change the behaviour of the system as a whole . Forexample, seed dispersal causes clumps of vegetation to form, thus counteracting competition andpromoting the persistence of established plant communities .

FIGURE 1Examples of landscape modelling, drawn from work by the authors: (a) simulated spread of a Crown-of-Thorns out-break (black shading), using a digitized satellite image of a coral reef,, (b) bushfire scenario, showing a fire-front(black shading) threatening a town; (c) vegetation patches arising from simulated dispersal; (d) pixel map of vegeta-tion zones along the NSW-Victoria border region (1 km scale), for input to models of regional vegetation change .

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Many biological phenomena are best represented, not as a single cellular automaton, butrather as sets of distinct cellular automata that interact with one another . For example, it isclearly desirable to distinguish organisms from their environment [8] and to represent sessileorganisms (e.g. plants, corals) separately from motile organisms (e.g. herbivores, starfish). It isalso desirable to distinguish processes that happen on vastly different time or spatial scales . Forinstance, in a model of forest dynamics a fire is best represented as a growing collection of burn-ing fuel cells (Fig . 1), each of which corresponds to (and affects) a cell in the forest grid [2] . Modelsof behaviour [161 call for cellular automata in which the cells correspond to individual animals,with the relationships between cells variable and reflecting either the changing spatial locationsof the animals, or else the social structure of a group. "Turtle geometry" [11] provides an excel-lent starting point for modelling animal movement through space .

The processing speed of landscape models is generally limited by convolution . Here convolu-tion means that the outcome of a process at a given point depends on properties of some neigh-bourhood of the point. Dispersal, mentioned above, is one example of a convolution process . Agreat many landscape processes (e .g . fire spread, animal movement) need to be represented asconvolutions. With convolution, the processing time increases exponentially with the size of theneighbourhood considered, except on vector or array processors [12] . Raster-based models dealwith convolution in a very straightforward fashion : one simply scans all cells that lie within somedistance of the target cell . With vector-based models, one has to either scan through the entirelist of objects, or else maintain a list of "neighbours" for each object . This approach has the ad-vantages that it deals only with "relevant" objects or locations, and that neighbourhoods can bedefined equally well for non-spatial characteristics (e.g . genotype). On the other hand, maintain-ing and processing large lists can be difficult and time-consuming .

3 . SYNTACTIC MODELLINGThe development of simulation models has usually been a long and difficult task . The root

cause of this difficulty is that computing languages are conceptually far-removed from the sys-tems that they are used to represent. This conceptual gap has led to simulation being regardedin a static way. Thus much effort is usually devoted to calibrating and testing a single model,rather than exploring the merits of different models .

We have argued [4],[5] that the answer to this problem lies in designing programming lan-guages around concepts that relate directly to the systems being modelled, rather than detailsof the computation - the ideal simulation language is one in which the terms and concepts usedto model a process are the same as those used regularly in studying or thinking about the process .Languages oriented towards particular applications are becoming common in all areas ofprogramming .

Syntactic approaches have been applied to modelling natural resources [8] . For instance,Noble and Slatyer [10] devised what is effectively a graph grammar to describe a plant com-munity classification scheme based on "vital attributes" of the organisms and on the variousdynamic relationships that can occur. We have employed simple languages as "front-ends" oncomputer simulations of spatial models (Fig . 1) of coral reefs and of forest dynamics [4],[5],[6] .This practice provides a simple way of changing the setup for particular model runs and makesthe simulation models very flexible indeed . The lists of commands used to set up a model alsoprovide a concise summary of the assumptions and parameter values used .

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System control:

<model>

--a

MODEL <world> <problem> RUN [ ; <model> ; . . .) END.<world>

--*

<space> <time> <features> <processes>

Space and time :<space>

-*

SPACE <scale> {, <scale> . . .} ;<scale>

-*

<name> <minimum> <maximum> <interval> <boundary><boundary>

-*

wrap I absorb I reflect<time>

-+

TIME <scale> { ; <scale> ; . . . } ;<feature>

-->

<map> <path> I <attribute> I <classes><map>

4

MAP <name> <type> <initial state> ;<type>

-4

continuous discrete ( I Interval = <number> )<set>

-*

SET <name> = ( <name>, <name> , . . . ) ;<initial state>

-->

flie = <filename> I patchy Irandom = <mean>, <sd> I uniform = <value>

<path>

-.

PATH <name> ( <attribute>, . . . } ;<attribute>

-->

ATTRIBUTE <name> <type> <initial state> ;<classes>

-s

<class> { <class> , . . . )<class>

-->

CLASS <name> : <subclasses> ;<subclasses>

-->

<name> ( , <name> . . . }

Processes:<processes>

-#

<process> { ; <process> ; . . .I<process>

-->

PROCESS <name> <definition><definition>

4

<transition> (<definition> , . . . )<state change>

->

IF <condition> THEN <process> ;<transition>

->

<name> -> <name> ;<condition>

-4

<variable> <relation> <algebraic expression>( <connective> <condition> )

FIGURE 2Partial definition ofan object-oriented landscape modelling language in Backaus-Naur notation. Reserved wordsand symbols are given in boldface capitals . The symbols < > denote a language contruct; : :- indicates a defini-I ion ;( ) indicate possible repetitions ;[ I indicate optional syntax ; and I separates alternatives . Several intuitive-ly obvious terms (in italics) have been left undefined for simplicity.

4. THE MOSAIC HIERARCHY

There is a trade-off between flexibility and simplicity in the design of modelling languages .The more flexible a language is the more difficult it is to learn and use . On the other hand, a lan-guage can be made simpler to use only by making it more specific to a particular type of system .A solution to this dilemma is to use an object-oriented approach .

As the name implies, object-oriented languages [12],[17] define models in terms of the ob-jects being modelled. Most importantly, they permit hierarchical classes of objects to be defined,so that concepts and procedures defined for a particular class also apply to any subclass . For ex-ample, rules about the behaviour of the class "animals" would apply to any subclass such as"lions" or "starfish" . It is thus possible to construct what are, in effect, hierarchies of languagesdirected at increasingly specialized applications . The advantage of this approach is that at thetop level (e.g . crop modelling), models are defined in languages that relate directly to the system

D. G. Green et a!. / Landscape modelling

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concerned, but if a model requires concepts not embodied in that language, then the modellercan define new concepts and procedures using a lower-level language . For example, bushfiresare represented explicitly by the concept of fire at the vegetation dynamics level, butfire is a spe-cial case of the more general concept of an epidemic disturbance at the landscape dynamics level,and this is turn is a special case of a convolution process at the cellular automaton level .

Of fundamental to object-oriented definitions are the primary concepts with which new termsare defined. Our experience at building interfaces for a variety of spatially explicit models (e .g.Fig. 1) has revealed concepts that are common to many applications. We have distilled these con-cepts into a specification for a general landscape modelling language (Fig . 2). This langaugeprovides a foundation on which to build more specific syntax. Our approach is to structure theconcepts within modules directed at particular applications. If the tools within a module proveinadequate for a particular purpose, then the modeller can resort to tools at a lower level to fillthe gaps. For example, a hydrology module would contain explicit definitions and assumptionsabout water-tables, channels, gravimetric flow, etc . If a particular hydrology model needs to usea new or different process, then it can be defined in terms of the more general terms and proces-ses provided in the landscape module .

5. IMPLEMENTATIONWe plan to implement versions of the MOSAIC system on a variety of machines, initially

PCs, Vaxes and ANU's Fujitsu VP-100 supercomputer [15] .The user interface of a spatial modelling system needs to incorporate GIS capability . A GIS

is needed for inputs to a model in order to be able to select and prepare input maps and otherdata. Likewise, the outputs from spatially explicit models are so rich in information that theyreally need to be examined in the manner of a GIS . Moreover, for many purposes it is importantto be able to view selected items of information as the model runs . For instance, in running amodel of crop production, details such as total production in selected areas can be read off a mapof the final state of the region, whereas in scenarios such as changing land-use strategy, un-known effects can best be detected by viewing selected maps during the model run . Therefore areally flexible spatial modelling system needs to incorporate a flexible enquiry system .

An important facet of the design for the MOSAIC system are direct links between the simula-tion module and two sorts of expert system. The first of these systems would provide a user in-terface for setting up models [1] and for linking them with appropriate GIS data . The secondwould provide an intelligent monitor to observe model runs and to identify and record importantfeatures. This approach has already been used successfully in ecological modelling [9] .

The twin problems of speed and memory capacity often arise in modelling landscapes . Al-though GISs regularly deal in images of (say) more than 1 Mbyte in size, these images are usual-ly not held in dynamic memory, but are read from files and filtered as they are passed to thescreen. Landscape models, on the other hand, may need to access several maps repeatedly. Thesophistication that models can achieve is therefore limited by the memory capacity of the machineon which they runs . Even supercomputers have finite capacity to deal with multiple large maps .

242 D. G. Green ei at. / Landscape modelling

G CONCLUSIONThe MOSAIC system provides a framework within which a large range of environmental

processes can be modelled quickly and easily. Moreover, expert system "front-ends" for particularappplications can further simplify model and problem specification by freeing users from theneed to use the syntax directly. We plan to implement several versions of the core modellingroutines, so that the same set of modelling languages can be used on a range of machines, fromPCs to supercomputers.

REFERENCES[1] Deutsch, T., Gyorgyi, L . and Futo, I., Integrating an expert system and a simulation model : a case

study, in Artifical intelligence, expert systems and languages in modelling and simulation, editedby Kulikowski, C .A ., Huber, R.M. and Ferrate, G.A ., Elsevier, Amsterdam, pp . 213-218,1988.

[21 Green, D .G., Simulated fire spread in discrete fuels . Ecol. Model. 20, 21-32, 1983 .[3] Green, D.G., Simulated effects of fire, dispersal and spatial pattern on competition within forest

mosaics . Vegetatio to appear, 1989 .[4] Green, D.G. and Bradbury, R.H., Ecological languages and modelling . Ecol. Model., to appear .[5] Green, D.G., Bradbury, R.H ., and Bainbridge, S ., Embodiment of formal languages . Math . Comput .

Simul. 30,39-44,1987.[6] Green, D.G., Bradbury, R.H ., and Reichelt, R.E., Formal languages and biological pattern. J. Infer.

Deductive Biol . 5, 47-66, 1986 .[71 Green, D.G ., House, A.P.N. & House, S.M ., Simulating spatial patterns in forest ecosystems . Maths

Comput. Simul. 27,191-198,1985 .[8] Muetzelfeldt, R.I ., Towards an ecologically-oriented simulation language . In: S.E. Jorgensen

(Editor), State-of-the-Art in Ecological Modelling. Pergamon Press, New York, pp . 771-787,1978 .[9] Hogeweg, P. and Hesper, B ., Two predators and one prey in a patchy environment : an application

of MICMAC modelling. J. Theoret. Biol . 93,411-432,1981 .[10] Noble, I.R. and Slatyer, R.O ., The use of vital attributes to predict successional changes in plant

communities subject to recurrent disturbance . Vegetatio 43, 5-21, 1980 .[11] Papert, S ., Uses of technology to enhance education . LOGO Memo no. 8, M .I.T. AI Laboratory, Bos-

ton, 1973 .[12] Pierret-Golbreich, C ., Object-centred knowledge representation for modelling in biology, inArtifi-

cal intelligence, expert systems and languages in modelling and simulation, edited by Kulikowski,C.A., Huber, R.M. and Ferrate, G.A ., Elsevier, Amsterdam, pp . 207-211, 1988.

[131 Reichelt, R.E., Bainbridge, S. and Green, D.G., Crown-of-Thorns dispersal in the Great Barrier Reef- a simulation study . Math . Comput. Simul. 30,145-150,1988 .

[141 Reichelt,R.E., Green,D.G. & Bradbury,R .H., Discrete simulation of cyclone effect on the spatial pat-tern and community structure of a coral reef. Proc . 5th Int. Coral ReefSymposium, Tahiti. Vol. 3,pp. 337-342,1985 .

[15] Stockwell,D.R&Green,D.G.,Parallelandvectorprocessingandecologicalsimulation,Thisvolume,1989 .

[161 Westman, R.S ., Environmental languages and the functional basis of behaviour. In: B.A. Hazlett(Editor), Quantitative Methods in the Study ofAnimal Behaviour . Academic Press, New York, pp .145-201,1977 .

[171 Wegner, P., Object-oriented programming - learning the language. Byte 14(3), 245-253, 1989 .[181 Wilson, G., The life and times of cellular automata . New Scientist 120,44-49,1988 .[191 Wolfram, S ., Cellular automata as models of complexity . Nature 31 1, 419-424,1984 .