The key 1990s challenge in environmental modelling has been to create models with sophisticated spatio-temporal representational structures matching the problem domain which can generate testable predictions about the functioning of environmental systems. Many researchers have considered geographic information systems (GIS) when coupled with environmental models to be suitable for this purpose and have adopted them in a wide range of studies (Goodchild, Parks and Steyaert 1993). However, it is clear that the use of GIS places constraints on the representational scope of the coupled system: GIS are two dimensional, layer based, geometry-indexed systems and are often difficult to link to existing environmental models as Livingstone and Raper (1994) have shown. In summary, GIS are often difficult to couple to environmental models, and, if this is achieved the representational compromises required are prejudicial to the overall aims of environmental modelling.
This scenario seems to require some new thinking on the design of environmental modelling systems. Raper and Livingstone (1995) have argued that the design of an integrated system should be driven by the nature of the environmental system and its spatio-temporal structure and set out the design of an object-oriented geomorphological modelling system called OOgeomorph. Underlying the OOgeomorph design is a computer-aided software engineering (CASE) environment capable of building data models which directly implement entities and functional or spatio-temporal relationships derived from any source theory. OOgeomorph was used to represent the May and Tanner (1973) theory of coastal evolution in an integrated 4D modelling framework.
This paper has two main aims: firstly, to briefly describe the OOgeomorph model and its implementation for a coastal geomorphological theory; and, secondly to explore the implications of the OOgeomorph design and its representation of space and time for populating models with data and carrying out subsequent analysis.
The driving philosophy behind the development of OOgeomorph has been to create a system that is suitable for formulating and testing theories within a geomorphological research context. Two fundamental points were realised (Raper and Livingstone 1994), firstly that the system needed to be capable of handling spatio-temporal representations and secondly that the system should not impose a restrictive, proprietary data model. These observations resulted in a number of general design approaches to be adopted in the implementation of OOgeomorph. These can be summarised as follows:
Design Approach 1
The separation of proposed geomorphological models from the observed or derived data that is used to populate these models.
This approach is consistent with the 'layered' philosophy of the Universal Geographic Information eXecutive (UGIX) system design proposed by Raper and Bundock (1993) which ensures that the low-level data structures of the stored data do not exert any influence on the structure of the geomorphological representation. A conventional GIS or other spatial database, the Geomorphological Spatial Database or GSD (figure 1), can therefore be used as a repository for observed data required by OOgeomorph. The GSD could be any form of spatial database ranging in sophistication from ASCII files of x,y,z coordinates to a fully topologically structured GIS.
The data in the GIS is 'mapped' onto the models under test by the creation of two class structures. Firstly, a class structure called 'geomorph_system' which represents a testable model; and secondly, a class structure called 'geomorph_info' which implements a generic representation of the observed data. The classes in 'geomorph_info' can be regarded as metadata which describes the associated data and encapsulate the translation mechanisms required to extract it from the GSD. The 'geomorph_info' classes are therefore a layer that separates a high-level geomorphological data model from a low level GIS data model and are decomposed according to the form of the data rather than the form of the geomorphological representation.
Figure 1 System Architecture - source Raper and Livingstone (1995)
Design Approach 2
The structure of the data model should be organised according to geomorphological concepts.
Since there is no way of knowing in advance what organising concepts a particular geomorphologist will select then the structure of the data model needs to be flexible. This resulted in the adoption of what could be termed a customisable CASE approach to enable the creation of a model structure which follows a set of user-defined principles. These user-defined principles are equated by the authors to the adoption of a 'meta-theory' which determines the nature of a set of 'basic level categories' to be used as a starting point for the construction of the geomorphological data model. In the rest of the paper these 'basic level categories' will be be considered to be processes, forms and materials in accordance to some kind of geomorphological 'meta-theory'. In a full implementation of OOgeomorph it would be possible to define a different configuration of 'basic level categories' before creating the data model by defining instances of the class 'geomorph_system' - this, however, is not discussed any further here.
The 'basic level categories' can be used by a geomorphologist to create specific sets of 'process', 'form' and 'material' classes relevant to the investigation or environment, the idea being that a number of different class structures can be investigated without having to redefine the underlying spatial database. Theories or conventions can be used to determine which variables or 'observables' are relevant to the geomorphological phenomena under investigation and the range of values allowed for each used as a criteria for 'geomorphological object-creation'. In OOgeomorph a geomorphological object is known as a 'phenomenon instance', in that it is an instance of an aggregated class made up of collected observables of the process, form and material classes. This approach ensures that geomorphological phenomena are not forced into a taxonomic hierarchy (as in some GIS designs) based upon geometric descriptions of their state at a particular point in space-time, but rather that they are assembled from the spatio-temporal coincidence of relevant process, form and material observables according to user-defined criteria.
Design Approach 3
Geomorphological observables should be referenced to four dimensions and be capable of overlapping with each other.
Each observable, such as wave approach angle or surface elevation, is valid over a spatio-temporal region determined by the conditions under which the measurements were collected or variables defined. Initially a convention has been adopted whereby this region is decomposed into its spatial and temporal components; a 'time of knowing' and a 'location of knowing'. Both these references and the value of the observable being measured constitute its attributes. These attributes are derived from the data described in 'geomorph_info' and may be in a variety of different spatial data formats. The idea behind the creation of the 'time of knowing' and 'place of knowing' attribute is to make the spatio-temporal information reconcilable. The next step is to define a phenomenon class as an aggregation of relevant attributes, organised according to specified observables, each of which 'know' where they are derived from and have associated methods to enable geographical processing tasks to be performed according to the functionality of the GSD. Any additional processing tasks required would need to be added to OOgeomorph.
The concept of time currently adopted in OOgeomorph equates to the concept of 'valid time' considered by Worboys (1994) and others. The 'time of knowing' is a point in time (recorded as a clock time and date) when each observable of process, form and material can be known. This idea needs to be extended so as to acknowledge that measurements have a estimable 'range of applicability' prior to modelling or analysis. This extension might be in the form of extending the point into a one-dimensional bounded region or by the addition of an associated validity method eg a probability distribution. Any phenomenon instance is therefore a collection of process, form or material observables (figure 2) each with its own space-time reference which may be disjunct, overlapping or identical.
In a typical scenario phenomenon class may be defined by the aggregation of three process observables, two form observables and three material observables (i.e. eight in all). If these observables themselves have a value, a 'time of knowing' and a 'place of knowing', then there will be at least 24 process, form or material attributes associated with a PI. The spatio-temporal structure of each PI and the set of PIs in the phenomenon class is entirely in the hands of the geomorphologist, since each of the eight process, form and material observables can have a different spatio-temporal extent. This design means that PI's are spatially and temporally heterogeneous ranging from highly observation-dependent forms ('over this space at this time' ) to infinite steady forms ('always, everywhere' ). An implication of this design is that PI's of widely differing 'scales' are created and compared rendering the concept much less important. The key control over scale is, therefore, the granularity of the theory governing selection of process, form and material observables.
It is an explicit design aim for OOgeomorph that such complex expressions be facilitated as it permits the storage together of geomorphological phenomena considered comparable as a working hypothesis, though they may be both spatially and temporally disjunct and have differing values for their process, form or material observables. Any differences can then be examined using tools created to compare the PI's under objective conditions.
Figure 2 Structure of Phenomenon Instances (PI's) - source Raper and Livingstone (1995)
Design Approach 4
To permit the assignment of behaviour, expressed as mathematical models, to data about geomorphological phenomena.
Given that a phenomenon instance (PI) is likely to be spatially and temporally heterogeneous it is necessary to implement a set of tools to operate on PI's. Such tools can be implemented as operations 'encapsulated' with the phenomenon sub-class. An important class of these tools involves interpolation. Many proprietary GIS have spatial interpolation procedures and, as long as the GSD permits external command processing all of these are available to OOgeomorph either before or after the creation of the PI's. Since PI's are objects existing in a spatio-temporal framework then if one is to create integral 4D objects to represent dynamic geomorphological phenomena, eg coastal spits, that can be related to other PI's then a set of formal 4D interpolation operations are required. The definition of interpolation operations is just part of a wider set of tasks including the specification of 4D object-object relations and the identification of characteristic 4D forms so that a 4D object language can be used to formalise 4D operations.
Operations relevant to OOgeomorph include:
generation of new PI's by creating new observables according to mathematical/statistical models;
temporal and/or spatial interpolation to harmonise the space-time bounds of observables;
temporal and/or spatial generalisation when PI's vary slowly over space and time.
To indicate the use of the OOgeomorph design an example is given here that is based upon the May and Tanner theory of coastal cell development. It has been created to test some of the hypotheses about the spatio-temporal development of coastal cells which Carter (1988) advanced, in this case with specific reference to medium term coastal development.
The first stage is to identify the concepts in the theory and which of the 'basic-level categories' they belong to (Table 1).
Form Category Process Category Material Category Internal points Wave energy E Unconsolidated sediment Erosion Wave crest approach angle a Deposition Longshore wave power PL High spring tide level Sediment discharge Qs Low spring tide level
Table 1 Concepts used in the coastal cell theory as formulated by Carter (1988) - source Raper and Livingstone (1995)
The next stage requires that the observables, consisting of values or types with discrete four dimensional spatio-temporal referencing, used to define or model these concepts be defined as classes in one of the 'basic level categories' (Table 2). The key issue in this procedure is the granularity of the representation i.e. the spatio-temporal region over which these observables are valid. In most cases the theory should provide a definition of the granularity of representation such that the temporal and spatial domains can be identified.
Figure 3 Basic relationships of the May and Tanner theory (a-e are 'internal points')
In this case the May and Tanner theory provides concepts of granularity in the form of the 'internal points' of the coastal cell, which themselves represent minima and maxima of longshore wave energy power flux within the cell. To implement this representation it was decided use measurable shoreline cross-sections at-a-time the spacing and frequency of measurement defining the granularity of the study. Shoreline cross-sections are normal to wave run-up and tidal fluxes and therefore offer versatile 'candidates' for the internal points. They also offer appropriate ways to discretise the other concepts in the theory such as sediment flux, angle of approach for wave crests and material properties.
Form observables Process observables Material observables Candidate point Wave crest approach angle a Sediment type High spring tide level Longshore wave energy power PL Low spring tide level Sediment discharge Qs
Table 2 Form, process and material observables for the coastal cell representation in OOgeomorph - source Raper and Livingstone (1995)
Observables in table 2 have an internal structure in the form of the following attributes:
Value of attribute {Char * } an alphanumeric value for the attribute
Time-of-knowing {Char * } clock time and date
Place-of-knowing {Geom * } a series of points defining a shoreline cross-section
The phenomenon class - a data model of a coastal cell , will have 21 'attributes' organised into sets of three and a phenomenon instance will consist of many observable instances. In order to actually test the validity of a coastal cell model and to parameterise the model from empirical observation requires the extension of the model to include methods associated with either the observable classes or the phenomenon class - suitable spatio-temporal interpolation methods are an important requirement for this part of the model. For example:
Since the cross sections may not always be taken in the same place nearest neighbour cross-sections in space over time need to be identified. A simple solution is to select nearest subsequent time then nearest spatial distance. However it is entirely possible that the cross-section from a slightly later survey but in a more similar spatial location may be more suitable - if suitable units can be derived eg from consideration of controlling processes, then a 4D distance can be used with dimension [L][T]. [L] in distance units [T] in time units.
The result of this operation is to create a new, derived, observable which can be added to the definition of the phenomenon class if required i.e. net shoreline change.
Identifying internal points 'a' to 'e'
Since it is difficult to determine longshore wave energy power (PL) directly (Carter 1988), this operation requires secondary evidence to identify candidate points. Approaches include those based upon wave refraction modelling and beach elevation/sediment type variation alongshore. Candidate points can also be proposed from evidence of erosion and deposition recorded in the previously created net shoreline change observable.
Defining the boundaries of features such as spits
One of the main aims behind the design of OOgeomorph is to enable the definition of features such as spits including statements about their boundaries. Features such as spits are modelled as phenomenon instances (PI's) or sub-sets of the observable instances that make up a PI. The boundary of a spit over space and either at or over a particular period of time is derived from the cartesian product of all the time and places of knowing of the observables that make up the spit. Such a boundary is a set of possibly spatially and temporally disjoint regions, it is proposed that an initial spatio-temporal interpolation would define the 4D equivalent of a convex hull around these regions. The state of the spit boundary at a particular time would then be approximated by a 3D cross-section.
The result of this operation would be a new phenomenon instance, possibly constituting a sub-set of another PI. It allows the geomorphologist to define the boundaries of features such as spits by using morphometric analysis of slope angles and other observable values and to use information such as tide levels as delimiters. The geometry resulting from such an operation is associated with a phenomenon instance and allows vectors of movement to be computed between successive states of a spit's boundary.
The structuring created by OOgeomorph makes it possible to execute four dimensional 'range queries' which look for space-time coincidences. In studying the evolution of coastal cells, typical questions which take the form of a range query include:
Where do rates of movement for feature boundaries defined by an operation on the PI's reach their maximum and when?
When do the candidates for internal points differ most in longshore terms when defined by differing criteria?
All the above operations and queries are designed to be carried out on any set of phenomenon instances defined in the study zone. The existence of this kind of system will make it possible to carry out such queries on many different phenomenon instance sets defined using different tools. The authors have been collecting the data required to instantiate this representation for the Scolt Head barrier island (in North Norfolk, England) at regular intervals over the last five years and are engaged in the implementation of this data model for this field site.
OOgeomorph has been designed to allow modellers considerable flexibility in the way that observables are spatially and temporally referenced. This was considered necessary since the variables in many environmental models are spatially and temporally heterogeneous and each may discretised from a continuous external reality differently. Kemp (1993) considered this problem at length and argued that the solution was to express all variables in (discrete) field form such that all modelled variables could be determined for the same locations at the same successive times. Kemp suggested that the process of expressing the variables in field form should, therefore, be documented and encapsulated with the datasets at the time of creation. However, she notes that 'this information must be deduced and appended by the modeller him- or herself who, it is hoped understands at least a little about the nature and sampling of the phenomenon being represented' (p121). OOgeomorph has been designed, firstly, to permit a wider range of discretisations than those involving the expression of all variables over a single field associated with a single time, and, secondly to make the assignment of variables to spatial and temporal ranges fully explicit within the modelling process.
In OOgeomorph each observable has its own spatio-temporal attributes viz. location (x, x,y or x,y,z sets) and time-of-knowing (year/month/day & hours/seconds). The spatial referencing may be one, two or three dimensional in nature and describes the position at which the observable's value is measured. The temporal referencing is a one dimensional point reference to the time at which the observable's value is known. Hence, as a minimum, the OOgeomorph design requires that the observable's value plus its location and time be known or stated as an assumption, and stored as attributes of the observable class. Instances of observables may not necessarily overlap in time and space if they are measured in the field rather than being co-located by assumption or by implication of other models. To illustrate the different design approach taken by OOgeomorph the spatial and temporal structure of a series of typical environmental modelling problems are considered below for two of the model types distinguished by Burrough (1996).
Firstly, 'rule-based models' relate states of variables using logic and set operations e.g. IF salt marsh elevation is greater than or equal to spring tide level THEN the marine sedimentation rate equals zero. In such an example the resulting state is assumed to hold for all locations where the initial state is true. The range of meaning can be extended by using fuzzy set membership values. In a conventional environmental model linked to a GIS the known marsh elevations would be discretised as a field; any values in the field greater than the height of the spring tide would be selected and written out as a new field corresponding to null marine sedimentation. In OOgeomorph 'elevation' would be implemented as an 'observable' with attributes of location (x,y,z) and time-of-knowing while spring tide level would have attributes of location (z) and time-of-knowing (in this case predicted days and times). The logical model would be implemented as a method in OOgeomorph and would generate a new attribute of null marine sedimentation for any elevation point higher than the value of tide level as a query. Note that by making the calculation of the level of spring tide a method, the OOgeomorph approach could also generate output for any particular spring tide level without creating a new field. OOgeomorph would also not require that scattered values of elevation be converted into a discrete field-based surface model to implement the model.
Secondly, deterministic physical (or mathematical) models relate variables through mathematical relationships e.g. the May and Tanner (1973) theory of coastal cell evolution used in Raper and Livingstone (1995) which relates wave crest convergence at the shoreline to the distribution of wave power along the shoreline. By taking the first derivatives of the rate of change of longshore wave power, the points of maximum and minimum wave power can be determined, and through them the rates and locations of erosion and deposition along the shoreline can be calculated. In a conventional environmental model linked to a GIS, the wave convergence and the distribution of wave power would have to be calculated outside the GIS for an idealised x axis corresponding to the shoreline. By discretising the rate of change of longshore wave power at a user-specified interval, offsets from the shoreline of a particular time could be calculated. In a vector GIS the 'offsets' would be drawn as lines and connected to form a predicted future shoreline. In OOgeomorph observables for convergence, longshore wave power and shoreline would be given value, location (x) and time-of- knowing attributes. Methods to determine longshore wave power from convergence and erosion/deposition from rate of change of longshore wave power would operate on instances with a shared time and generate new instances of the shoreline observable at user defined x intervals. By taking this approach OOgeomorph allows the integration of all the calculations in the same system and can automatically carry out the calculations for any specified time. It would also be possible in OOgeomorph to creat an observable called 'actual shoreline' which could automatically be compared with a 'predicted shoreline' over any time interval.
In each of the above cases the comparison of the 'conventional' approach with the 'OOgeomorph' approach specifies an idealised procedure: in normal modelling practice the situation is often much less clear cut and many 'pre-processing' operations are required to harmonise the spatial and temporal limits, resolution and symmetry of the discretisation of the variables. For example, some variables will be sampled at a point and the value generalised to be representative of an area e.g. records from a gauging station (climatic or geomorphic processes). Conversely, some variables will be sampled simultaneously over an area creating a field of values which are summarised to generate a single point (e.g. remote sensing of wave height). Similarly, sparse temporal measurements may need to be generalised to cover unmeasured periods (e.g. elevation surveys), or, samples may be taken at frequent intervals leading to the need to summarise values (e.g. recording of water levels using a chart recorder). The spatial and temporal heterogeneity may also involve an assymetry in summarising or generalising operations: hence, there may be spatial constraints on the operations in a particular direction or temporal constraints over a particular period
Facilities for spatio-temporal 'interpolation' (an expression used here to cover summarising and generalising operations) should, therefore, be built into environmental modelling systems and tools designed to document their use. It is suggested here that one way to manage the spatial and temporal heterogeneity of the variables is to record the 'range of applicability' of both the location and time-of- knowing attributes by creating using two additional attributes. Spatially, this 'range of applicability' could be a radius around a point, a buffer around a line or polygon, a vertical range or a resolution change limit for a field. Temporally, the 'range of applicability' could be a period of time which is symmetrical or assymmetrical around the temporal point.
Such 'range of applicability' attributes when added to the basic spatial and temporal attributes would greatly facilitate a variety of forms of spatio-temporal 'interpolation' in OOgeomorph. Firstly, by using simple queries the 'range of applicability' for a set of variables could be explored to check their comparability in spatial and temporal domains. If the set has a single outlier in range terms, methods can be constructed for that variable to recalculate summarisation or generalisation operations on the raw data so as to harmonise the range with the other variables aggregated into the phenomenon class. Similarly, if the set of 'ranges of applicability' for a group of observables being entered into an algebraic expression is highly heterogeneous in nature then methods can be developed to define a commensurable spatial and temporal range for all the observables.
Spatio-temporal interpolation can also be applied to the domain of the variable instances as well as the spatial and temporal domains of the variables themselves. When variables can be considered to be evidence (either singly or jointly) for the existence of some geoscientific phenomenon the spatio- temporal distribution of the instances may be of critical importance. At present few if any modelling systems can represent, manipulate or visualise such data. The design of OOgeomorph makes it possible to pose four dimensional range queries to determine the bounding limits of any phenomenon. Such limits correspond to a four dimensional envelope or 'hypercuboid'. In the case of a study of the rate and style of change of coastal forms the configuration of such an envelope is of considerable interest since its four dimensional form and structure may be correlated with the energy inputs to the system.
However, the structure of the available instances may be deficient in some respect. For example, certain observations may be missing or there may be errors associated with them. In this case it may be necessary to interpolate observations lying spatially and temporally 'between' observations at known locations. OOgeomorph can be used to locate space-times where there are no observations and the nearest observations to the 'empty' area. Currently the authors are developing heuristics for the interpolation of points for coastal surveys that it was not possible to carry out for logistical reasons.
The key implication of the research carried out in this paper is that by adopting a new spatial database design that assigns four dimensional coordinates to all 'observables', a range of environmental modelling operations can be carried out within one system without the need for the low level coupling of a model and a GIS. Chief amongst these operations are the ability to establish the 'range of applicability' of variables that are to be related in a formal modelling statement and the ability to interpolate gaps in spatio-temporal observation data.
Implementation work on the OOgeomorph system is under way within the framework of a UK Ministry of Agriculture, Fisheries and Food (Coastal and Flood Defence Division) research project on coastal spits and nesses. The resulting system will be used to manage field collected and simulation- generated data on the spatio-temporal behaviour of these landforms and to enable the testing of hypotheses on the driving processes.
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Jonathan Raper# and David Livingstone*
#Department of Geography, Birkbeck College, Univ. of London 7-15 Gresse Street, London, W1P 2LL, UK
tel. +44 171 631 6470 fax. +44 171-631 6498 j.raper@geog.bbk.ac.uk
*School of Geography, Kingston University, Penrhyn Rd, Kingston, KT1 2EE, UK
tel. +44 181 547 2000 [2021] d.livingstone@kingston.ac.uk