International Journal of Geographical Information

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International Journal of Geographical Information Science

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A working prototype of a dynamic geographical information system Maria J. P. de Vasconcelos; António Gonçalves; Filipe X. Catry; José U. Paúl; Fernando Barros

To cite this Article de Vasconcelos, Maria J. P. , Gonçalves, António , Catry, Filipe X. , Paúl, José U. and Barros,

Fernando(2002) 'A working prototype of a dynamic geographical information system', International Journal of Geographical Information Science, 16: 1, 69 — 91 To link to this Article: DOI: 10.1080/13658810110095048 URL: http://dx.doi.org/10.1080/13658810110095048

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int. j. geographical information science, 2002 vol. 16, no. 1, 69± 91

Research Article A working prototype of a dynamic geographical information system* ´ NIO GONC MARIA J. P. DE VASCONCELOS1,2 , ANTO ¸ ALVES2 , ´ L2,3 and FERNANDO BARROS4 FILIPE X. CATRY3 , JOSE´ U. PAU 1 Centro de Cartogra a, Instituto de Investigaçaõ CientÌ´ ca Tropical, Travessa do Conde da Ribeira, No 9, 1300 Lisboa, Portugal;

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e-mail: [email protected] 2 Centro de Estudos Florestais, Departamento de Engenharia Florestal, ISA, Lisboa, Portugal 3 Centro Nacional de Informaçaõ Geogra´ ca, Lisboa Portugal 4 Departamento de Engenharia Informa´tica, Universidade de Coimbra, Coimbra, Portugal (Received 3 August 2000; accepted 2 June 2001) Abstract. The objective of this work is to develop a dynamic geographical information system (DGIS) applicable for the simulation of spatio-temporal phenomena. DGIS is designed and implemented as a dynamic raster GIS in a fully integrated systems strategy using theory of modelling and simulation, discrete event systems speci cations, and knowledge-based simulation methodologies. The approach accommodates the representations and operators of current GIS in a broader systems representation scheme that includes the constructs for handling continuous time, model base, multiple resolution, hierarchy, taxonomy, variable structure, and intelligent agents. DGIS is de ned as an endomorphic system that can be transformed by the user into diŒerent, application-speci c, spatial dynamic simulation environments depending on the models selected to t the various aspects of its structure. In this paper we describe the theory, methods, and technologies upon which the system is designed and implemented and discuss how it can support complex spatial simulations. To probe operational applicability, an instance of DGIS is generated: a re spread simulation environment, which is tested in the simulation of 15 real re events.

1.

Introduction The application of geographical information systems (GIS) to the simulation of spatial dynamic processes has been presented in many studies and it is a current topic of research (Egenhofer and Golledge 1998). However, all commercial GIS packages represent space and its attributes statically and are designed around a speci c abstraction of reality, which does not account for time and process. *Project 4037 PAMAF, Ministe´rio da Agricultura, do Desenvolvimento Rural e das Pescas. The work presented in this paper was developed while the rst author was a researcher at Centro Nacional de Informaçaõ Geogra´ ca, Lisbon, Portugal. Internationa l Journal of Geographica l Information Science ISSN 1365-881 6 print/ISSN 1362-308 7 online © 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/13658810110095048

M. J. P. de Vaconcelos et al.

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Consequently, the development of temporally explicit geographical information systems requires new and more encompassing models of reality that can expand the representation capabilities to a more complex worldview. In this context, the work presented here has the following objectives:


1. To propose an approach for the development of dynamic geographical information systems. 2. To produce one operational instance of that approach: a re spread simulation environment. 3. To test the validity of re spread simulations against real re events. We propose applying modelling and simulation theory (Zeigler 1976) and a set of methods known as knowledge-based simulation (Zeigler 1990) to design a system structure that supports the synthesis of many diŒerent application-speci c spatial simulation environments. The applicability of these concepts is illustrated by the development DGIS based on which a re spread simulation environment is obtained, applied, and tested in real re situations. The approach includes constructs for handling time, model base, multiple resolution, hierarchy, taxonomy, variable structure, and intelligent agents. Even though all of these constructs can be available in DGIS, the re spread simulation instance generated in this work uses a subset of the listed constructs: time handling, model base, hierarchy, taxonomy, and variable structure. The assumption behind DGIS is that every static spatial location can become a processor at any instant, and that active processors can also be deactivated at any instant. This entails that the simulation environment must be capable of supporting the dynamic transformation of static locations into spatial processors and vice versa, and that the simulations are performed on a continuous time base. Central to the development of DGIS is the work presented by Takeyama and Couclelis (1997), where it is demonstrate d that the attribute layering abstraction prevailing in GIS is isomorphic to that of a multivariate map, with every location (geo-unit ) seen as a set of multiple attributes. As illustrated in gure 1, we apply the interchangeability of the two representations, and use both representations of space simultaneously. This dual representation integrates spatial data models and spatial process models (Takeyama and Couclelis 1997 ).

Figure 1.

Alternative representations of space: as layers of attributes or as geo-units.

A prototyp e of a dynamic GIS

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The re spread simulation environment derived from DGIS is tested against real data on the propagation of a set of 15 forest res. The tests are set up through an experiment that is designed to study the match of simulated and real re spatial characteristics after given time intervals. There are two separate goals for the experiment that lead to two diŒerent types of presentation of results and discussion: (1) to demonstrate the applicability of the concepts, methods, and technologies presented for the design and development of a dynamic GIS; and (2) to evaluate the reliability of the re spread predictions. The ability to proceed with the second objective implies that the rst is also being accomplished. 2. Background 2.1. Modelling of spatial dynamic processes with GIS: re spread Dynamic modelling with GIS has been a major topic of interest in several application elds, especially in landscape ecology, ecology, and natural resource studies (Green et al. 1989, Costanza et al. 1990, Kelmelis 1993, Vasconcelos et al. 1993, Ball et al. 1996, Wu 1998 ). There has been increasing interest on developing the ability to model spatially explicit dynamic processes at several diŒerent aggregation levels, and on deriving the behaviour of higher level complex entities (such as a landscape or an ecosystem) based on the interaction of many lower-level, individualbased models (Couclelis 1985, 1989, di Castri and Hadley 1988, Houston et al. 1988, O’Neill et al. 1989, Pickett et al. 1989, Costanza et al. 1990, Vasconcelos et al. 1993, Clarke 1994, Burrough 1998, Wu 1998). Simulations of re spread using geographical information systems have been presented in many studies (Cohen et al. 1989, Ball and Guertin 1992, Vasconcelos and Guertin 1992, Clarke et al. 1994, Vasconcelos et al. 1995, Coleman and Sullivan 1996 ). However, the approaches proposed to date have two major drawbacks, which may be common to other application elds. The rst is the use of a loosely coupled systems strategy (Goodchild 1992a, Bennett 1997) where the GIS operations and the model calculations are performed in separate software packages, and the second is the lack of appropriate testing of simulation reliability. One of the many reasons for the use of loose coupling in simulations of re spread is the availability of re behaviour models (McArthur 1967, Rothermel 1972, Noble et al. 1980), some of which can be obtained as ready-to-run software (Andrews 1986, Finney and Ryan 1995 ). Most of these models estimate rate of spread and other re characteristics, given input values for fuel, weather, and topography of a homogeneous parcel of land. In this work we use Rothermel’s re behaviour model (Rothermel 1972, 1983) and some extensions available in the BEHAVE program (Andrews 1986 ). The variables used in this model are obtainable by mathematical expressions that depend on terrain, fuel, and weather, all of which can be represented as maps in a GIS. Given that calculations with Rothermel’s model have been validated for homogeneous conditions (Sneeuwjagt and Frandsen 1977, Wilgen et al. 1985) and our assumption of attribute homogeneity within each spatial unit represented in DGIS, we can consider that the values of re rate of spread calculated in each unit are valid. Thus, in our experiment we only test the accuracy of the re growth simulations. The accuracy of simulations performed in heterogeneous landscapes has been weakly tested, with most tests using a single re event (Vasconcelos and Guertin 1992, Coleman and Sullivan 1996). Testing re simulations is a di cult endeavour owing to the cost of both the simulation runs and the acquisition of data for

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validation. In our work we overcome the rst problem; however the collection of data for testing has been a very time-consuming process and this is the reason why our testing sample is composed of only 15 re events. 2.2. Requirements of spatio-tempora l information systems There is already a considerable body of work where the desirable characteristics of truly spatio-tempora l systems are discussed and the possible avenues for development are pointed (Goodchild 1992a, Burrough and Frank 1995, Vasconcelos et al. 1995, Bennett 1997, Takeyama and Couclelis 1997, Burrough 1998, Egenhofer and Colledge 1998, Wu 1998). As supported by several authors (e.g. Bennett 1997, Burrough 1998), data models for dynamic geographical systems should be thought of as a triplet comprising state, process, and relation or ow. Additionally, such systems should integrate enabling technologies, namely objects, agents, and modelbase management (Bennett 1997). Burrough (1998) focuses on process distribution over space and addresses a vast body of work on computation that has been covered by researchers working on partial diŒerential equations, nite state machines, cellular automata and their extensions. Of these, we highlight the work by Couclelis (1985, 1989) who was the rst to suggest that Zeigler’s theory of modelling and simulation (Zeigler 1976) could anchor the future development of spatial dynamic modelling environments. Smyth (1998) considers, as we do, that the incorporation of time and process in GIS is a geographical modelling problem that must be formally addressed. The idea is that a complete GIS modelling framework should be able to accommodate the many representations and levels of abstraction possible that correspond to diŒerent models of reality depending on the particular ontology under which they are conceived. A modelled world under a particular ontology is a microworld (Davis 1990) of the real world with its associated smallness in content and detail. By using this microworld concept in his idealized framework, Smyth (1998) is reproducing, in the geographical modelling context, the concepts of base model, lumped model, and experimental f rame of the general theory of modelling and simulation (Zeigler 1976, 1984, 1990). Burrough and Frank (1995) discuss how there is no single approach to spatial data handling that is su ciently generic for all possible applications. In the same line, Smyth (1998 ) argues that the entity view and the continuous eld view are not easily integrated and that it is di cult to separate the logic of a continuous eldbased microworld from its physics. We hope to illustrate that the entity view and the continuous view of the world can be integrated within the same system, and that by applying the representational constructs used in DEVS (see below) for specifying distributed autonomous systems (Zeigler 1990) we meet all the requirements mentioned above. We must clarify, however, that we only address the case of closed models (Smyth 1998 ). 2.3. DEVS The approach proposed with the development of DGIS is called KnowledgeBased Simulation (Zeigler 1990 ). It is based on the speci cation of modular, hierarchical, and object-oriented discrete event systems (Zeigler 1976, 1990 ), and it integrates arti cial intelligence knowledge representation schemes in a framework called DEVS (Zeigler 1990). DEVS knowledge representation scheme, the system entity structure (SES), is hierarchical and combines decomposition, coupling, and taxonomy (Zeigler



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1990 ). The entities in the SES refer to conceptual components of reality for which models may reside in a model base. A SES represents a family of models; the synthesis of a particular hierarchical model, expressed in a composition tree, is obtained by pruning the SES to represent a given situation. Pruning is the process by which modular models available in the model base are chosen and coupled according to the scheme provided by the SES. Each particular choice of models results in a speci c coupled-model, which is an instance of those many possible with that SES. In our work we have a system entity structure that represents a family of models: spatial models (to which spatial dynamic models belong ). The most basic models from which all others are built by coupling are called atomic models. Atomic models are speci ed in a dynamic discrete event formalism (Zeigler 1976); since DEVS models have closure under coupling (Zeigler 1984, 1990) all models created by coupling of atomic models also are discrete event models. A new form of coupled models is based on the concept of Dynamic Structure Network (Barros 1997). These network models have the ability to change their own structure during a simulation run, and this capability allows having on memory only those parts of the models that are currently in use, thus supporting the representation of larger models. Atomic models are stand-alone modular objects that are de ned as an 8-tuple of the form (Zeigler 1990): M 5 (X,S,q0 ,Y,t,d ,d ,l ) ext int

(1)

X is the input set, S is the sequential state set, q0 is the initial state, Y is the output set, t is the time advance function, d is the external transition function that ext computes the next state and transition time when external events arrive, d is the int internal transition function that computes the next state and time of transition when no messages arrive in input ports, l is the output function that generates an output just before an internal transition takes place. Two state variables are usually present: phase and sigma. In the absence of external events the model remains in the current phase for the time given by sigma. The discrete event formalism focuses on changes of variable values and generates time segments that are piecewise constant. When an external event, such as ignition of re, occurs the external transition function places the system in a new phase and sigma thus scheduling the next internal transition. The next state is computed on the basis of the present state, the input port and value, and the time elapsed in the current state. A DEVS model works as a timed state machine, so that the state of the system is changed by external or internal events with elapsed time. Discrete event models use a continuous state and a continuous time axis and diŒer from continuous models because only a nite number of state changes may occur within a nite time interval, depending on instantaneous events (Cho and Cho 1997). Dynamic Structure Networks are de ned by the 4-tuple (Barros 1998) DSDEN 5 (X ,Y ,g,M ) N N N g

(2)

where N is the network name, X is the set of network input values, Y is the set N N of network output values, g is the name of the dynamic network executive, M is g the model of the executive g.

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The model of the executive, is a modi ed atomic model de ned by the 9-tuple M 5 (X ,S ,q0, ,Y ,c,S* ,t ,d ,l ) (3) g g g g g g g g where c: S S* is the structure function, S* is the set of network structures. g A structure S × S* associated with the executive sequential state s , × S , is given by a jg g S 5 c(s , ) 5 (D , {M , }, {I , }, {Z , }) (4) j jg j ij ij ij where D is the set of component names associated with the executive sequential j state s , , for all i × D , M , is the model of component i, for all i × D n {g,N}, I , jg j ij j ij is set of components in uencers of i, for all i × D n {g}, Z , is the input function of j ij component i, Z is the output function of the network N. N, j The network structure is controlled by the executive, and can be changed whenever the executive changes its sequential state. These changes include the set of components, represented by set {M , }, and the interconnections among components ij represented by sets {I , } and {Z , }. The application of various forms of dynamic ij ij structure networks to the simulation of forest res can be found in Barros and Ball (1998) and Vasconcelos et al. (1995 ). One more concept used in our approach is that of endomorphism (Zeigler 1990 ): there are several diŒerent representations of space and its attributes embedded in the system, which are related to each other by abstraction. One of these models is external to the simulation processes and represents the real spatial area of concern ( layer mode representation) on which the dynamic component operates. The others are internal to the dynamic component and are employed in the simulations. Conceptualization of DGIS DGIS is a dynamic geographical information system that supports the construction of application-speci c spatial simulation environments. It is designed such that there is a variable set of spatial units, which can be lled with instances of the dynamic modular models stored in a model base. The modular models must be speci ed in DEVS formalism and instantiated to ll particular spatial and temporal positions. The number of instances and their spatial distribution varies during the simulations, which are driven by the ensemble of active units formalized in a dynamic structure network. The basic idea behind DGIS is that space is conceived as a set of spatially static potential automata exhaustively covering space. This set is de ned as a variable but nite network of distributed discrete event systems functioning in an emulation of parallel processing. The units of the network have a correspondence to the representations available in GIS: cells or vector objects, which are pairs of locations and associated values and can be denominated geo-units (Goodchild 1992b, Takeyama and Couclelis 1997). Owing to the discrete event nature of the systems speci cation used, starting a simulation does not require the de nition of time steps, nor does it entail that all locations are de ned as automata with synchronized, mandatory state transitions (as occur in cellular automata speci cations). Only locations directly addressed during the simulation are active, and state transitions occur on an individual basis at uneven, previously unde ned points in time. The progression through space of a phenomenon or entity can be represented by the diŒerent states the active geo-units take at varying instants in time. 3.


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DGIS is a modular system with the following main characteristics: The representations of space, attributes, and time are independent from the speci c models to be used in the simulations. Space can be simultaneously represented in two diŒerent and interchangeabl e manners: as a set of attribute layers and as a set of geo-units with multiple attributes. The geo-unit space representation is used exclusively for the simulations. If there are no processes being modelled, and only spatial operations are needed, then the traditional GIS layer operation mode is kept. The instances of the models used in the simulations drive the advance of time. The model/time-induced changes in the attributes of geo-units are accounted for, managed, and represented in the layer mode through another module, the controller, which is an executive that keeps an updated internal representation of geo-units. The dynamic models reside in a model base and are instantiated for activating the geo-units, which become distributed processors in the simulations. The geo-units can incorporate any instance of the models in the model base because the models are de ned in a modular discrete event systems formalism for which the geo-units are a template. The attributes in the map layers are descriptive variables of the instance models incorporated by the active geo-units (processors) and can be used as state variables upon activation. In our work the geo-units representation of space is conceived as a xed grid of cells. The topological invariance of this spatial representation facilitates the spatial referencing of every geo-unit. However, this is a simpli cation for prototype implementation. As described above, the system is conceived to work with locations and is thus independent of form, size, and spatial referencing mode of the implementation. At this stage, DGIS uses vector maps only in the layer representation mode. Figure 2 is a schematic representation of the structure of the system, which comprises three modules. The module Interface is external to the systems speci cation used for constructing DGIS. The two modules: MAP-Layers and MAP-Dynamic, are the two components of DGIS speci ed in DEVS formalism. The key piece is the Controller, which coordinates message passing between all components of the system. If the user requests exclusively spatial data calculations and manipulations, the Controller is passive and sends the messages received from the user to MAP-Layers keeping the geo-units representation inactive. In this case the system looks like a standard GIS. If a simulation is started, then the dynamic structure network (Controller /Geo-units) is activated, and updates (model or user driven) of the database layers are all mediated by the Controller. The neighbourhood shape of each geo-unit can be xed at the beginning of the simulation or it can be a part of the information content of the owing messages. 4. Formalization 4.1. T he system entity structure and composition tree The system entity structure used is shown in gure 3(a). DGIS is a coupled model with two modular components: MAP-Layers and MAP-Dynamic. MAP-Layers is the module that includes the spatial database as a set of attribute layers both in


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Figure 2. Schematic representation of the proposed system. There are three main modules: Map—Layers, Map—Dynamic, and Interface. Interface is external to the systems speci cations used for constructing DGIS and is adapted to the speci c application purpose: simulation of re spread.

cellular and in vector format, in a standard GIS representation of space. MAPDynamic is a dynamic structure network with two types of components: the Controller, an atomic model acting as the network executive, and an indeterminate number of similar entities called Geo-unit, represented in the network MAPGeounits. In this study we transform the SES into the composition tree shown in gure 3(b). The re simulation environment is generated by coupling the atomic models MAPLayers, CONTROLLER, and FIRE (which are the models available in the model base—see Appendix 1) according to the SES. This process generates MAP-Dynamic as a speci c instance of the dynamic structure networks possible with this SES, by specifying that each newly created Geo-unit is transformed into a Geo-FIREunit. Consequently, the spatio-tempora l structure of a dynamic GIS is in place, and generating a simulation environment for a particular phenomenon requires just one step: the selection and activation of the speci c discrete-event model each Geo-unit must embody. When the user, through input of an ignition location and respective time (external event) starts a simulation, the Controller goes through a state transition from passive to active, and one Geo-FIREunit is activated. The latter goes through a transient state and sends a message to the Controller with its calculated time-to-burn. Then the Geo-FIREunit goes through an internal transition and phase is set to burning and sigma to time-to-burn. Time-to-burn is calculated using Rothermel’s re spread model and variable values that correspond to the spatial attributes of the speci c cell location and to the weather conditions of the present time. Once time-to-burn has elapsed, the re can spread to neighbouring locations and the active Geo-FIREunit becomes inactive. The controller knows that that speci c active Geo-FIREunit has become inactive from its own internal representation of the processing units and it is responsible for its elimination and for the creation of



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Figure 3. (a) The system entity structure (SES) for DGIS. The denomination ‘dec’ stands for ‘decomposition’ and ‘spec’ for ‘specialization’. DGIS is composed of two entities MAPDynamic and MAP-Layers. MAP-Layers is the module that includes the spatial data base as a set of attribute layers. MAP-Dynamic is a dynamic structure network with two components, the Controller and MAP-Geounits. The Controller is an executive and MAP-Geounits is the Geo-units set with an undetermined number of elements represented by the three vertical lines. MAP-Layers and MAP-Dynamic are two representations of the same spatial reality. Geo-units are created and eliminated only when simulations take place, each with an identity that depends on the location it represents, and embodying an instance of a given model. The choice of models is given by those present in the model base (FIRE, FLOOD, WALK...). (b) The generic SES is transformed into a speci c composition tree, where Geo-units are speci ed (spec) to be Geo-FIREunits, thus generating one of the possible modelling environments represented by this SES, which we named Geofogo. The dashed light grey lines represent the uncertainty in the number of active Geo-FIRE at any instant.

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new Geo-FIREunits corresponding to the in uencees of the rst. Each newly active cell computes its respective time-to-burn, which varies from cell to cell and depends on the direction of maximum spread (calculated in the re behaviour model) and on the direction of contagion (see Vasconcelos et al. 1995 ). Therefore, in a running simulation, there is a variable set of geo-referenced active processors corresponding to the burning cells, which have asynchronous state transitions and a local internal clock, synchronized with a global simulation clock. 4.2. Software characteristics DGIS is a Windows-based dynamic GIS developed in a fully integrated systems strategy (Goodchild 1992a, Bennett 1997 ) using C1 1 . The particular composition tree of DGIS we apply in this study is named Geofogo, and its Graphical User Interface (GUI) was developed using Object Pascal. Geofogo is designed for simulation of forest re spread and for prediction of potential re behaviour. The GUI is adapted to the particular case of re growth simulation. It uses dropdown menus and pop-up windows, which are triggered both by the user and by the running simulations. There is a spatial toolbox, and a temporal toolbox. The spatial toolbox is similar to those found in many GISs. The temporal toolbox includes a simulation clock, and operations to introduce start time, next run interval, and/or total run time, and/or end time, a run button, a stop button, and a continue button. Spatial operations require that the simulation be stopped. However, once they are nished the simulations can continue with the updated spatial data. Weather data are input in tabular mode with each record also holding a eld with time. This eld indicates the instant on which the respective weather conditions are to be used in the simulations. The conditions prevail until the time of the next weather record matches the simulation clock or the user introduces a new weather record with the clock stopped and then clicks the ‘continue’ button. The system continuously provides the user with information related to the simulated res. There is information obtainable during the simulations and information that is only available when the simulations are nished. The progression of res through space is continuously displayed to the user in a movie-like mode and the clock runs on a continuous time base. The backdrop map can be changed at any time and there is no limit to the number of vector maps that can be overlaid on the running simulation. Since all objects in the spatial database (maps, cells, and records in tables) can have time as an attribute, it is possible for the user to determine at what instant each existent database object has been created. However, given that the simulations are performed on a continuous time base, it is impossible to save all the simulated sates of the system. Consequently, the user must specify at what instants should the database be appended with new time-indexed information. Even if no such instants are speci ed, the user can always recreate all previous states of the system by re-running the simulations to a desired point in time. 5. Application of Geofogo 5.1. Experiment design and data collection As a basic step for the application of Geofogo we evaluate the implementation of Rothermel’s re model under completely controlled conditions of fuel, weather, and topography (see Vasconcelos 1993 for details on procedures) . Then, we evaluate



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the reliability of the re-spread predictions by performing several comparisons between real res and simulated res. Our experimental scheme is stepwise and is shown in table 1. The reason for this stepwise approach is that we need to evaluate what are the conditions under which the simulations can be used. In fact, for re management and pressupression planning, where ‘what-if ’ scenarios are analysed, there is no need for the same type of accuracy as for real-time re ghting. Furthermore, in the latter case, it can be useful to know ahead of time what are the most likely re spread paths, even if the predicted forms are not exactly reproduced. Formal comparisons are performed for steps 2, 3, and 4. Step 1 has been visually evaluated and step 5 was discarded from the analysis owing to lack of data. The constant presence of smoke during the res and the topographic conditions of the study area made it almost impossible to register the correct re front positions and associated times on 1:25 000 topographic maps. To assess the accuracy of re area and shape simulations, we performed a t test on the pairwise values of total area burned and of the shape indices listed in table 1. To assess the coincidence of re shape locations we built contingency tables for each case with percentage correspondence of predicted burned cells versus really burned cells and with calculation of omission and commission errors. The study area selected for this study area corresponds to 22 municipalities in central Portugal. For this area, a geographic digital database was built using 1:25 000 topographic maps, in a Gauss-Kruge r projection. The cartographic database includes raster and vector maps of various themes and scales, and contains all the terrain and cover variables that are necessary for the calculations of re rate of spread (slope, aspect, and fuel). The spatial resolution of the raster database is 25 m. The choice of grid size was made based on the scale of those maps with the lowest spatial resolution: 1: 25 000. Fuel maps are described in terms of fuel models (Anderson 1982). A fuel model corresponds to a xed set of parameters, describing the structure and heat content Table 1.

Step 1 2 3 4

5

Stepwise scheme used in the experiment. Step number 5 was not performed formally due to lack of data; the progression of simulated res was inspected visually and informally compared with reality. Description Assess the agreement between the general direction of re propagation Assess the agreement between size of burns. Comparison of number of cells burned in reality and in the simulation Assess the agreement between nal re shapes. Compare the following shape indices(1) : Form ratio, Circularity, Orientation, and Elongation Assess the agreement between geographical position. Analyse a contingency table where omission and commission errors are calculated relatively to the real burned cells Assess the agreement between intermediate re positions through the main re spread paths

Comparison type Direction Area Final shape Location

Progression

(1) Formulas for the shape indices can be found in URL: http://www.microimages.com/ refman/html/prock010.htm


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of each vegetation patch, which is used in the calculations of re rate of spread. There are 13 standard fuel models developed for the vegetation types of the USA. Since there are no fuel models speci cally developed for the Mediterranean-type vegetation present in central Portugal, we used the correspondences to the standard fuel models reported by ICONA (no date) for ecologically similar regions in Spain. To create the fuel model maps we used 1:10 000 false colour aerial photography from 1995 and eld checking. During two re seasons (1996 and 1997), eld teams collected data on re events. For each sampled re we recorded the varying meteorological conditions during the re (10-minute interval measurements of wind speed and direction, relative humidity, and temperature), and the re spatial characteristics with a global positioning system (GPS): ignition location, re perimeter, and when possible sequences of re front positions. The data were later compiled and digitized for use in Geofogo and for the comparisons of simulations with reality. Of the res monitored in the eld, 15 have enough data to be used in the comparisons. 5.2. Simulations There are several aspects in the occurrence of forest res and in the respective simulations that have to be confronted so that the limitations of the described experiment are clear: (a) To perform the simulations we use the ignition locations and the approximate times of ignition reported in the Forest Service records. When this information is not available we use parts of large res for which we have collected one or more re front positions with associated time. (b) The calculations performed with Rothermel’s model predict re spread under natural conditions and do not account for the reductions of re rate of spread resulting from re ghting actions. Consequently, this model does not predict the end of a re, unless it results from natural combinations of weather and fuel that prevent burning form occurring. This implies that the user stops the simulations at the containment time reported in the Forest Service records. The exact instant for the extinction of a forest re is di cult to establish. There are many procedures associated with the containment and extinction of res, during which the re is still burning at low indeterminate rates. The duration of these procedures is variable and is not accurately registered by the re ghting personnel. (c) There are real burned areas (mapped two or three days after the re with a GPS) that include re-ignition and re- ghting situations after the res are considered extinct. These episodes are usually of short duration, but correspond to unknown intervals of time and weather conditions. Keeping the above-mentione d limitations in mind, and considering that part of those sources of error may be absorbed by the resolution (25 m) of the spatial database, we set up the simulations by indicating the weather tables, and an ignition point, line, or area and ignition date and time. Then, the simulation clock is started and the spreading re is continuously shown on the screen along with the running time, and the corresponding weather conditions. The simulations can be stopped and re-initiated to update the fuel maps and/or change the map-layer on which the re is displayed. Vector layers (e.g. with the location of roads) can be overlaid at any point.


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Results and discussion Geofogo has been applied operationally to the simulation of forest res. Besides the common di culties and iterations in obtaining a good graphical user interface, there were no di culties with the simulations for which the appropriate data were in place. The simulations are shown on screen with continuous motion of the re fronts along with a continuous clock that reports time exclusively at event moments (e.g. ignition of new cells).


6.

6.1. T he Experiment Figure 4 and table 2 summarize the results of the experiment. Some res are very small (see table 2) and thus the 25 m resolution grid structure of the spatial database becomes evident in the illustration. These res appear to have a diŒerent scale of analysis. However, this is just the result of the need of magni cation for illustration purposes, since all res were simulated using the same spatial database and scale. The comparison of real re paths and burned areas (thin line) with those of the respective simulations (grey area) shows an encouraging level of agreement. Of the 15 res used in this study, 11 reach step 4 of our experimental scheme. With the exception of three cases discussed below, all the most signi cant diŒerences in coincidence (> 40%) can be explained by the re ghting activities. In fact, those diŒerences correspond mostly to commission errors (areas that are predicted to burn and do not burn in reality), with omission errors comparatively low. Commission errors are generally associated with the progression in the simulation of speci c re perimeter sections that do not burn in reality because they have been fought (for example, the res of Sobral-10, and Fagilde-8). In these cases re shapes are poorly predicted but the coincidence of the simulated progression in the other perimeter sections is quite acceptable. There are several cases where simulations are performed for parts of a re. This is the case of Vila Mendo-3 where even though the re burned for two days, the simulations correspond to two periods of those days for which there are meteorological data available. Thus the nal simulated area is smaller than the actual burnt area. The analysis of shapes, shown in table 2, reveals that for those 11 res that reached step 4 of our experimental scheme, the values of the indices for the real and simulated sample are very comparable. However, we conclude that the shape indices we used are probably not the best for this study because of situations such as that of the Nesperido-6 re. This simulation is one of those that better matches the sequences of real re paths, with complex inversions in direction correctly reproduced. Additionally, the nal shapes of the simulated and real res are very similar (see gure 4). Nevertheless, the values of the shape indices for simulation and reality are signi cantly diŒerent. Of the four cases that did not reach level 4, two correspond to simulations that are completely diŒerent from reality (Encostas de Sa´-12 and Sra da Ouvida-4). The Cujo´-9 re corresponds to a simulation that shows coincident directions of spread but presents substantial omission errors, and the Fagilde-8 re shows a good correspondence between simulation and reality on all anks but one. The latter corresponds to a re line that was strongly fought and stopped with heavy equipment in reality, but spreads rapidly in the simulation. The analysis of the two cases with no correspondence between reality and simulation provides good insight over some of the issues that must be addressed in



82

Figure 4. Comparison of simulations with respective real res. The grey area corresponds to cells that burned out during the simulation. The dark grey cells in the perimeter of the burned area correspond to cells with re activity at the end of the simulation time.

PINOUCA

´ QUINA QUINTA da MA

MORTINHOS

´ ENCOSTAS de SA

POC ¸ O SANTIAGO

SOBRAL

´ CUJO

FAGILDE

NELA

NESPERIDO

ALMOFALA

Sra da OUVIDA

VILA MENDO

MEZIO

˜ SILVA

Fire events

Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated Real Simulated1 Simulated2 Real Simulated Real Simulated Real Simulated

Table 2.

281.4 229.6 170.0 181.7 482.0 404.5 70.0 67.0 163.8 210.2 74.0 56.2 15.3 29.9 6.4 22.8 34.0 41.1 11.3 19.7 10.1 17.2 245.6 72.6 345.9 8.3 13.8 180.8 189.4 31.9 42.5

Burned area ( ha)

56.7

84.1

85.1

91.1

48.2

90.4

75.8

24.2

5.4

91.7

80.7

80.1

61.8

264.7

103.7

11.8

42.4

80.7

14.4

17.7

5.4

90.1

93.9

59.0

92.2

91.8

64.1

85.9

15.0

69.6

89.2

76.2

% Commission coincidence error (%)

14.9

8.9

8.3

15.9

94.6

9.9

6.1

41.0

7.8

8.2

35.9

14.1

85.0

30.4

10.8

23.8

Omission error (%)

Contingency tables

0.483 0.588 0.664 0.667 0.405 0.489 0.365 0.529 0.297 0.336 0.272 0.212 0.336 0.570 0.282 0.582 0.257 0.324 0.559 0.595 0.494 0.479 0.313 0.322 0.504 0.230 0.317 0.543 0.462 0.441 0.623

Form ratio

Shape indices

0.643 0.756 0.748 0.856 0.561 0.775 0.573 0.755 0.547 0.602 0.493 0.426 0.469 0.649 0.447 0.713 0.456 0.544 0.690 0.795 0.710 0.602 0.617 0.612 0.675 0.479 0.515 0.694 0.654 0.658 0.740

106.590 106.804 100.072 87.309 63.320 85.149 57.554 95.475 56.496 65.046 61.752 42.549 43.824 74.924 49.387 97.093 40.788 63.822 82.818 89.318 78.353 113.798 97.442 88.203 100.060 61.319 56.460 78.682 64.254 79.482 95.027

0.824 0.975 0.938 0.985 0.862 0.678 0.700 0.911 0.670 0.580 0.818 0.569 0.889 0.862 0.748 0.880 0.804 0.733 0.945 0.783 0.889 0.792 0.482 0.504 0.656 0.675 0.456 0.945 0.864 0.824 0.939

Circularity Orientation Elongation

Summary of results: burned areas, contingency tables and shape indices.


A prototyp e of a dynamic GIS 83


84


future studies of this kind. It is worthwhile noting that in both cases, as in the Cujo´-9 re, the real re spreads on a single slope on the leeside of a mountain. In fact, the wind adjustments used in Geofogo are not prepared to deal with the eddy eŒects present in these situations. These eŒects can invert the direction of the wind promoting the presence of upslope winds at ame height that push the re in the opposite direction to the winds aloft (Pyne et al. 1996). This problem is particularly important because there are situations where the meteorological measurements where taken at some distance from the re. Three of the four mentioned cases where the simulations do not correctly reproduce reality are in this situation: they occurred on one slope on the leeside of the mountain and have no local meteorological measurements (measurements were taken at the nearest meteorological station). To illustrate how the weak modelling of the topographic eŒects on wind direction may be the reason for the simulation errors, we show the results of a simulation performed with a reversed wind direction for the case of Encostas de Sa´ in gure 4 (12a) and table 2. The results of pairwise t tests (a 5 0.05) applied in the re samples (including the 15 sampled cases) indicate that we can accept that the real res and the simulated res are not signi cantly diŒerent for items: area burned, orientation, and elongation. We believe these results are encouraging for we tried to model an extremely complex phenomenon. The propagation of forest res is controlled by the interaction of a vast set of variables that are di cult to quantify and represent spatially. We should keep in mind that the possible sources of error are manifold (data collection, digital map representation of the variables, re spread model, and simulation process) and that the errors associated exclusively with the simulation process cannot be isolated here. Given this, it would be unrealistic to expect exact matches between real and simulated res. 6.2. T he system This study illustrated how diŒusion through space can be represented and simulated within a dynamic GIS. Since the homomorphism between discrete event representations and diŒerential equation representations has been demonstrate d (Zeigler et al. 2000) we can state that all spatial dynamic processes represented in the form of systems of diŒerential equations can potentially be simulated with DGIS. Additionally, as proven by Zeigler (1976) and discussed by Couclelis (1985, 1989 ), the implementation of distributed discrete event automata is a substantial extension of the widespread cellular automata formalizations. Consequently, all cellular automata implementations can also be represented and simulated in this system. The re example shown used 10-minute tabular weather data, with each record applied to the entire re area at the appropriate time. However, if available, spatially distributed weather data can be easily applied by having time-stamped weather map layers that are used by the active geo-units in the same way the other local attributes are. As shown, the ability to distribute calculations both in space and time, in an emulation of parallel processing, is important because it allows the simulation of complex spatial phenomena that require very large spatial data sets, in low-end computers. This may be a step towards achieving the desired goal: operational dynamic geographical information systems. It is important to note that not all constructs available in the proposed approach were employed in our re example. In fact, a xed dimension grid was used to represent space, only one type of atomic model was used to ll the active locations



85

in the simulations, and intelligent agents were not applied (even though endomorphism, which is an attribute of intelligent systems, was employed ). Realistic applications that could take advantage of all the constructs available would also require a set of validated process models and compatible cartographic and tabular databases. Since this is not easily obtained, further testing of DGIS may require several applications, each using a diŒerent subset of the mentioned constructs. The use of a SES to represent a family of models that can be unfolded to represent many diŒerent speci c models is not new in simulation. However, it has not been commonly used in the geographical modelling context. The SES can meet the need of representing diŒerent abstractions of the same spatial reality within the same system (Zeigler and Moon 1997 ) and can support the attachment of diŒerent user interfaces depending on the abstraction used for a particular application. For example, in our case study we had a model for FIRE in the model base. However, if other models existed, and as long as the coupling schemes were preserved, we could have used them in diŒerent composition trees that would support diŒerent simulations of the same res. These other models could correspond to lumped FIRE models applicable with coarser map or weather data. In the same line of reasoning we can have more elaborate SESs that include more than one dynamic structure network, thus supporting simultaneous simulations of the same phenomenon at diŒerent resolutions. The above concepts can be taken further. There may be diŒerent abstractions of MAP-Dynamic formalized as DEVS models in the model base that upon pruning result in a diŒerent modelling environment. For example, Geo-units could correspond to a vector representation in MAP-Layers. With this spatial representation the de nition, interaction, creation, and elimination of Geo-units during the running simulations obeys a more elaborate spatial referencing code and must include additional procedures for handling topology. However, the temporal functioning of the system relies on the exact same constructs as in the raster mode, with the controller processing and using a constantly updated internal representation of MAP-Geounits. 7.

Conclusions and future developments By showing an operational application to the simulation of forest res, we have demonstrate d that the concepts and methods used in the development of DGIS are usable for creating a spatio-tempora l modelling environment in GIS. DGIS can be directly used to simulate other processes of the same type with one single requirement: that new DEVS models are included in the model base. Once these models are available, the geo-units can incorporate them to drive the simulations. We performed a GIS-based simulation of a landscape level phenomenon relying on the behaviour and interaction of many lower level entities that can simultaneously process their respective local information. Moreover, the simulations run on a continuous time base (there are no prede ned time steps) and are performed using a low-end platform. The operational application of DGIS illustrates that the inclusion of a temporal dimension in GIS does not require that the currently used spatial data formats be dropped. By contrast, we incorporate those formats in a compatible real worldview that corresponds to a formal, physically based theory of modelling and simulation and to a set of proven knowledge representation schemes. The framework proposed uses endomorphs and embedded modelling and permits the realization of many


86


diŒerent microworlds of the real world based on the same main structure, which is convertible to diŒerent compositions of modular models. Further development of the re simulation environment generated with DGIS is mainly dependent on knowledge of the processes associated with the spread and containment of forest res. If those processes can be described by rules, functions, or other relation types, they can be encoded in atomic models and made available to DGIS through its model base. Nevertheless the re simulation environments now obtainable from DGIS, with continuous monitoring of re progression through time and space, may be used as surrogate laboratories for fuel and forest management and for producing projections that support decisions on allocation of resources in large re events. Additionally, DGIS can serve to test and monitor the performance of diŒerent re spread models encoded in DEVS formalism. Finally we would like to point out that a system such as DGIS can be developed within existing commercial GIS packages, some of which already have the tools for automatic generation of special purpose graphical user interfaces. The incorporation of the simulation capabilities presented here does not need to imply a computing overhead for the standard user, because the system would work exactly as a common GIS for those applications that do not require the more sophisticated simulation capabilities. Acknowledgments We would like to thank all participants of project PAMAF 4037 for their eŒorts in the eld campaigns, especially Patricia Vinagre, Tiago Oliveira and Manuela Baptista. We would also like to thank J. M. C. Pereira (Department of Foresty, Institute of Agronomy, Technical University of Lisbon), for the helpful discussions that led to the development of this work. We acknowledge the contribution of Rui Silva (Estaçaõ Florestal Nacional) and of the following institutions: Divisaõ de Protecçaõ da Floresta Contra Inceˆndios da Direcçaõ Geral das Florestas, Direcçaõ Regional de Agricultura da Beira Litoral (Zona Agra´ria de Daõ e Lafo˜es, e Direcçaõ de Serviços das Florestas); Centro de Coordenaçaõ Operacional dos Bombeiros Volunta´rios de Viseu (CCO Viseu); Centro de Prevençaõ e Detecçaõ de Inceˆndios Florestais (CPD03); Inspecçaõ Regional dos Bombeiros Volunta´rios da Regiaõ Centro and Instituto de Meteorologia. References Anderson, H. E., 1982, Aids to determining fuel models for estimating re behaviour. USDA Forest Service, Intermountain Forest and Range Experiment Station, General Technical Report INT-122. Andrews, P. L., 1986, Behave: Fire behavior prediction and fuel modelling system—BURN Subsystem, part1. USDA Forest Service, Intermountain Forest and Range Experiment Station, General Technical Report INT-194. Ball, G. L., and Guertin, D. P., 1992, Improved re growth modelling, International Journal of W ildland Fire, 2, 47–54. Ball, G. L., Zeigler, B. P., Schlitchting, R., Marefat, M., and Guertin, D. P., 1996, Problems of multi-resolution integration in dynamic simulation. In Proceedings of T hird International Conference/Workshop in Integrative GIS and Environmental Modelling, Santa Fe, New Mexico 21–25 January 1996. URL: http://www.ncgia.ucsb.edu/conf/SANTA_FECD_ROM/sf_papers/ball_george/ santafe.html Barros, F. J., 1997, Modelling formalisms for dynamic structure systems. ACM T ransactions on Modelling and Computer Simulation, 7, 501–515.



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Barros, F. J., 1998, Abstract simulators for the DSDE formalism. Proceedings of the 1998 W inter Simulation Conference, IEEE, Piscatah, 407–412. Barros, F. J., and Ball, G. L., 1998, Fire modelling using dynamic structure cellular automata. Proceedings of the III International Conference on Forest Fire Research, 879–888. Bennett, D. A., 1997, A framework for the integration of geographical information systems and model base management. International Journal of Geographical Information Science, 11, 337–357. Burrough, P. A., 1998, Dynamic modelling and geocomputation. In Geocomputation: A Primer, edited by P. Longley, S. M. Brooks, R. McDonnell and B. Macmillan (Chichester, New York: John Wiley and Sons), pp. 165–191. Burrough, P. A, and Frank, A. U., 1995, Concepts and paradigms in spatial information: are current geographical information systems truly generic? International Journal of Geographical Information Systems, 9, 101–116. Cho, H. J., and Cho Y. K., 1997, DEVS-Java Reference Guide (Arizona: Arti cial Intelligence and Simulation Research Group, Department of Electrical and Computer Engineering, University of Arizona). Clarke, K. C., Brass, J. A., and Riggan, P. J., 1994, A cellular automaton model of wild re propagation and extintion. Photogrametric Engeneering and Remote Sensing, 60, 1355–1367. Cohen, P. R., Greenberg, M. L., Hart, D. M., and Howe, A. E.,1989, Trial by re: understanding the design requirements for agents in complex environments. AI Magazine, Fall, 31–48. Coleman, J. R., and Sullivan, A. L.,1996, A real-time computer application for the prediction of re spread across Australian landscapes. Simulation, 67, 230–240. Costanza, R., Sklar, F. H., and White, M. L., 1990, Modelling coastal landscape dynamics. BioScience, 40, 91–107. Couclelis, H., 1985, Cellular worlds: a framework for modelling micro-macro dynamics. Environment and Planning A, 17, 585–596. Couclelis, H., 1989, Of mice and man: what rodent populations can teach us about complex spatial dynamics. Environment and Planning A, 20, 99–109. Couclelis, H., 1998, Aritostelian spatial dynamics in the age of geographic information systems, In Spatial and T emporal Reasoning in Geographic Information Systems, edited by Max J. Egenhofer and Reginald G. Golledge (Oxford: Oxford University Press), pp. 109–118. Davis, E., 1990, Representations of commonsense knowledge (San Mateo, CA: Morgan Kaufman). de Castri, F., and Hadley, M., 1988, Enhancing the credibility of ecology: interacting along and across hierachical scales. Geo-journal, 17, 5–35. Egenhofer, M. J., and Golledge, R. G., eds, 1998, Spatial and T emporal Reasoning in Geographic Information Systems (Oxford: Oxford University Press). Finney, M., and Ryan, K. C., 1995, Use of the FARSITE re growth model for re prediction in US National Parks. In Proceedings of the International Emergency Management and Engineering Conference, May 1995, Sifua Antipolis, France, San Diego, CA: SCS, pp. 183–189. Goodchild, M., 1992a, Integrating GIS and spatial data analysis: problems and possibilities. International Journal of Geographic Information Systems, 1, 203–220. Goodchild, M., 1992b, Geographical data modelling. Computers and Geosciences, 18, 401–408. Green, D. G., Reichelt, R. E., vander Laan, J., and MacDonald, B. W., 1989, A generic approach to landscape modelling. In Proceedings Eight Biennial Conference, Simulation Society of Australia, Brisbane: CSIRO, pp. 342–347. Houston, M., de Angelis, D., and Post, W., 1988, New computer models unify ecological theory. BioScience, 38, 682–691. ICONA (no date) Clave fotogra ca para la identi cacion de modelos de combustible. Ministe´rio de Agricultura Pesca y Alimentacion. Kelmelis, J., A., 1993, Terrestrial process research using a multi-scale geographic approach. Photogrammetric Engineering and Remote Sensing, 59, 971–976. McArthur, A. G., 1967, Fire behaviour in eucalypt forests. Report 107, Commonwealth of Australia Forest and Timber Bureau, Camberra.


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Noble, I. R., Bary, G. A. V., and Gill, A. M., 1980, McArthur’s re danger meters. Australian Journal of Ecology, 5, 201–203. Pickett, S. T., Kolasa, J., Armesto, J. J., and Collins, S. L., 1989, The ecological concept of disturbance and its expression at various hierarchical levels. Oikos, 54, 129–136. Pyne, S. J., Andrews, P. L., and Laven, R. D., 1996, Introduction to W ildland Fires (New York: John Wiley & Sons). Rothermel, R. C., 1972, A mathematical model for predicting re spread in wildland fuels. General Technical Report INT-115. Ogden UT USDA Forest Service, Intermountain Research Station. Rothermel, R. C., 1983, How to predict the spread and intensity of forest and range res. General Technical Report INT-143, USDA Forest Service, Intermountain Research Station. Smyth, C. S., 1998, A representational framework for geographic modelling. In Spatial and T emporal Reasoning in Geographic Information Systems, edited by M. J. Egenhofer and R. G. Golledge (Oxford: Oxford University Press), pp. 191–213. Sneeuwjagt, R. J., and Frandsen, W. H., 1977, Behavior of experimental grass res vs. predictions based on Rothermel’s re model. Canadian Journal of Forest Research, 7, 357–367. Takeyama, M., and Couclelis, H., 1997, Map dynamics: integrating cellular automata and GIS through Geo-Algebra. International Journal of Geographical Information Science, 11, 73–91. Wilgen, B. W. V., Maitre, D. C. L., and Kruger, F. J., 1985, Fire behavior in South African Fynbos (Macchia) vegetation and prediction from Rothermel’s re model. Journal of Applied Ecology, 22, 207–216. Wu, F., 1998, SimLand: a prototype to simulate land conversion through the integrated GIS and CA with AHP-derived transition rules. International Journal of Geographical Information Science, 12, 63–82. Vasconcelos, M. J. P., 1993, Modelling Spatial Dynamic Ecological Processes with DEVS— Scheme and Geographic Information Systems. PhD. Dissertation, Universirty of Arizona. Vasconcelos, M. J., and Guertin, D. P., 1992, FIREMAP-simulation of re growth with a geographic information system. International Journal of W ildland Fire, 2, 87–96. Vasconcelos, M. J. P., Zeigler, B. P., and Graham, L. A., 1993, Modelling multi-scale spatial ecological processes under the discrete event systems paradigm. L andscape Ecology, 8, 273–286. Vasconcelos, M. J. P., Pereira, J. M. C., and Zeigler, B. P., 1995, Simulation of re growth using discrete event hierarchical modular models. EARSeL Advances in Remote Sensing, 4, 54–62. Zeigler, B. P., 1976, T heory of Modelling and Simulation (New York: John Wiley). Zeigler, B. P., 1984, Multifaceted Modelling and Discrete Event Simulation (London: Academic Press). Zeigler, B. P., 1990, Object-oriented Simulation with Hierarchical Modular Models: Intelligent Agents and Endomorphic Systems (Boston: Academic Press). Zeigler, B. P., and Moon, Y., 1997, DEVS representation and aggregation of spatially distributed systems: speed-versus-error tradeoŒs. SCS T ransactions, 13, 179–189. Zeigler, B. P., Praehofer, H., and Kim, T. G., 2000, T heory of Modelling and Simulation. Integrating Discrete Event and Continuous Complex Dynamic Systems (San Diego: Academic Press).

Appendix 1 Pseudo-Code for atomic model FIRE State Variables Phase 5 passive Sigma 5 in nity Time-to-burn 5 0 Descriptive variables Attributes corresponding to this geo- re-unit location in the thematic-maps


89


External Transition Function Case phase is ‘passive Compute rate of spread using descriptive variables and input content (wind, temperature, and humidity) Compute time-to-burn (function of rate of spread, direction of maximum spread and direction of contagion) Set phase to ‘calculating Set sigma to 0 Case phase is ‘burning Compute new rate of spread from new input content (wind, temperature, and humidity) Compute new time-to-burn (function of elapsed time in phase burning and new rate of spread ) Set sigma to time-to-burn and phase to ‘burning Internal Transition Function Case phase is ‘calculating Set phase to ‘burning Set sigma to time-to-burn Case phase is ‘burning Passivate Output Function Case phase is ‘calculating output time-to-burn Pseudo-Code for atomic model CONT ROL L ER State Variables Phase 5 passive Sigma 5 in nite Initial-list 5 ( ) Processing-list 5 ((in nite-in nite)) Command 5 ( ) Mapname 5 ( ) Storephase 5 ( ) Store-time-of-next-event 5 in nite External Transition Function Case port is from-user Case content is init-geounit-ids Set phase to ’init Set initial-list to geounit-ids Set sigma to 0 Case content is GIS-operation Set command to GIS-operation Set phase to ’mapcalculate Set sigma to 0 Case content is Stop Set Storephase to phase Set Store-time-of-next-even t to sigmaÕ

e

90

M. J. P. de Vaconcelos et al. Update all id/time pairs in processing-list to id/(timeÕ Set phase to ’passive Set sigma to ’in nite

e)


Case content is Continuesimulation Set phase to storephase Set sigma to store-time-of-next-even t Case port is from-geounit and phase is ’init Insert content id/time in processing list Remove id from initial-list If initial-list is empty Set phase to ’processing Set sigma to minimum time of processing list pairs Else Hold-in ’init Case port is from-map-layers and phase is ’mapcalculate Set phase to ’mapready Set mapname to input-content Set sigma to 0 Internal Transition Function Case phase is ’init Hold-in ’init Case phase is ’mapready Set phase to ’passive Set sigma to in nite Case phase is ’mapcalculate Hold-in ’mapcalculate Case phase is ’processing Remove pair id/time from processing list Update all id/time pairs in processing-list to id/(timeÕ Set initial-list to neighbors of removed id Set phase to ’init Set sigma to 0 Else Continue

e)

Output Function Case phase is ’init output initial-list in port to-geounits Case phase is ’mapcalculate output command in port to-maplayers Case phase is ’mapready output mapname in port to-user Case phase is ’processing output nothing Pseudo-Code for atomic model MAP-L AY ERS State Variables Phase 5 passive Sigma 5 in nity Target-maps 5 none Target-maps-created-during-simulation 5 none


91


Descriptive Variables All thematic maps in the spatial data base External Transition Function If input port is from-controller and content is for-target-map s then Set target-maps to input content Make copy-of-target-map s in the database Update values of copy-of-target-map s in the database Set sigma to 0, phase to ‘control-wait, and target-maps to none If input port is controller and content is target-maps-create-during-simulatio n then Update values of target-maps-create-during-simulatio n Set sigma to 0 and phase to ‘control-wait If input port is from-user then Execute requested target-maps transformation Set sigma to 0, phase to ‘waiting, and target-maps to none Internal Transition Function Passivate Output Function Case phase is waiting output target-maps