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Analytic Techniques

Spatial Models in Scholarship and Decision Support

What is a Model?

Any sort of representation may serve as a model. We often make drawings to identify critical aspects of a thing; diagrams to express relationships among ideas. The real things in the world are usually too difficult to manipulate or to share, so we deal with representations and treat them as frameworks for discussing real things and phenomena we hope to understand better. In the world of GIS these representations originate in a number of ways. We may have an aerial photograph that is a record of the reflectivity of places on the ground at a particular time. Or we may be a map of property parcels that has been digitized from a paper map or surveyed by a party of people on the ground. When we get very good with GIS, we may make more complicated models that involve the combination of many different GIS datasets and create new GIS layers, that may (or may not) help us to learn something useful about a place. In any case, whether we are using a single Aerial photo or a complex set of GIS layers and procedures, we need to understand how data represents the real world if we hope to understand the world through data.

The diagram below is an example of what Patrick Geddes called a Thinking Machine. This framework provides the critical phases of developing ideas about places and spatial processes using data and logical transformations. This framework is useful for understanding how, or whether, a map or model might be used successfully to support assertions and decisions and how to effectively document and share models for reuse and improvement.

Purposeful Abstractions

We seek to answer practical questions by combining information with ideas. At the same time we are aware that some answers may be useful while other answers may be rubbish. We have to learn to judge one from the other. Once we have informed ourselves and developed some degree of confidence, we have to share our new understanding with others. These details of are the basis of scholarship and decision support.

Questions and Purposes

A clear statement of Purpose is key to understanding a map or a model. Our purpose for modeling may be to explore a question about the way a place performs. We may want to generate some new information that will provide needed background for making a decision. In an academic setting our purpose may be to learn something about the suitibility of specific datasets for specific applications and to learn something about the ways that places may be represented with models. The statement of purpose provides the basis for evaluating the work. Defining the purpose of an investigation is an art that can make your task reasonable and interesting or foolish and impossible waste of time.

Conceptual Models and Data Models

It is good to be able to organize ideas and facts. These are the raw material of understanding. An example of a fact may be that there are wetlands located within our area of interest. An example of an idea may be that wetlands may be affected by land that is nearby. This logical chain of facts and ideas is a Conceptual Model. The conceptual model can be decomposed into individual concepts that may regard the existence of some entitiy or of some relationship. In our simple model, one of our concepts regards entities: Wetlands; and another a relationship: Land Near Wetlands. The factual components of a conceptual model may be represented with Data and the relationships may be represented with software Procedures. A procedure may transform data using some assumptions, for example recategorizing observed categories of land cover to some index of runnoff potential, or by transfroming elevation to slope. Alternatively we may use procedures to deduce locical associations among entities in different datasets, including simple Portrayal of land use and wetlands shaded with meaningful color on a map. A procedure might infer new information about relationships such as tabulating for a givenm scenario, the area of land that is within a distance of wetlands or of wetlands that are down-slope from land having some sort of runoff potential. Data Models are organizations of data and procedures that represent the entities and relationships of a conceptual model.

It is often the case that the formation of questions and purposes and the exploration of conceptual models and the discovery of data resources and procedures is an on-going cyclical process. The questions and purposes for a study being adjusted as we learn more about the situation, and the affordances and weaknesses of tools and data.

Useful Knowledge, Critical Evaluation and Understanding

As we strive to develop our understanding, we should be mindful of the fact that the world is a very complex and dynamic place. Any facts that we try to represent with data are likely to be out of date, incomplete, imprecise, and to a degree erroneous. The software procedures that we use to simulate associations among facts are very rarely perfect simulations of relationships in the real world. Our conceptual models are almost always gross simplifications of relality. So we can comfortably say that all data and all models are inaccurate. The more important question is whether our conceptual models, data and our procedures are accurate enough to create information useful for our stated purpose. For example, if our purpose is to explore a particular set of relationships, the fact that our data are old will not be important -- provided that each layer is of a similar vintage. Our stated purpose provides the context for evaluating whether our data and procedures reflect the concepts in our model well enough. Very often, the study of a place through modeling is not so useful for generating answers as it is for helping us to sharpen our question.

Though we may be sure that data and models may be erroneous, it is the hallmark of well-considered research to have an understanding of the likely magnitude and direction of the errors we expect. These matters are discussed in more detail in the page, Critique of Data, Metadata and Referencing Systems.

Each dataset and each procedure that we employ constitutes a model in itself -- with its own independent purposes and methodologies. Each of these needs to be understood through its Metadata (data about data) or documentation in order that we may judge the Fitness of a procedure or dataset as a representation of the ideal concepts of our conceptual model. Logically following the fitness of the individual datasets and procedures in our model will lead us to an understanding of how how errors may propogate in the new information we create. Our work may be judged according to the utility of our map or model for predicting accurately enough to support a decision with some degree of confidence. Even if our model is judged to be not useful (as most models are, when we are learning how to make them) the process of model making and critical evaluation will lead us and our successors to a better understanding of how our data or simulation procedures or conceptual models ought to be improved. In this sense, it is possible that your model may produce useful understanding even if the model itself does not achieve a high degree of confidence. The most important aspect of all of this is that we understand what we are doing and communicate this well.

Portrayal, Documentation and Credibility

All of this modeling has the ultimate aim of informing ourselves and sharing information with others. Portrayal of data is one more aspect of transformation and association of data. Visual juxtaposition of portrayed data in maps, charts and 3d visualizations are operations that allow a great deal of new information to be created in our minds and in the minds of our audience. In these operations, it is just as easy to create false or confusing information as it is to communicate a valid new idea. There is a lot of science and philosophy concerning the ways that graphical portrayal of information may or may not be effective in communicating an idea. This is discussed in more detail in Elements of Cartographic Style. A critical aspect of portrayal is that in portraying data as maps, 3d models, diagrams or charts, we may be effective in informing ourselves and communicating something useful, or we may be effective in confusing ourselves and communicating the fact that we do not understand what we are presenting as "Facts." The clarity, conciseness and consideration built into a model's portrayal and documentation is a critical factor in determining whether it is useful or perhaps even harmful.

Replicability and Experimental Simulation Models

A collection of data may represent a state of things, and relationships among these things may be discovered through associative procedures. Thus, models may perform as a platform for controlled experiments. We may take our data as a representation of some state of a system as it existed at time 0. We could make a copy of this schema, and change it by adding and removing some representations or changing their attributes to represent another condition that reflects an alternative future scenario. The alternative scenario may be transformed and portrayed in maps or in three dimensional models that may allow us to understand something about the alternative, before and after. For example, we might take our land cover data as representing an existing condition, and them modify it to explore a proposed change. This new model might be used to estimate the amount and quality of runoff that might enter wetlands, before and after.

Experimenting with models in areas where we know that our data are very good can be useful, especially for trying to understand whether the model would provide useful results where the data are not so good. Running a model while swapping out datasets of known variation in quality can help us to do sensitivity analysis that may help us to better general understanding of the applicability of a model in areas of different data quality. This sort of Sensitivity Analysis can be very useful for understanding models and modeling.

Scholarship: Collective Refinement of Questions and Models

We may think of the process of understanding a place as a strictly personal endeavor that begins and ends with us. Alternatively, we might think of our work as a contribution to a collaborative, continuing effort. There are a couple of ways that our work can multiply with the work of others: At the beginning, while we are formulating questions and conceptual models, we may study prior work and make use of lessons that have already learned. At the other end of our oproject, we may do a good job of documenting our on lessons learned, and organize our models and data in such a way that they may be re-used by our collaborators to study alternate approaches to the same landscape problem, or apply our conceptual and data models to completely new landscapes. This is how the collective learning machine known as scholarship and science is evolving in the information age. See Structure for a Place-Based Data collecton for more information about organizing a data model for sharing and collaboration.


References

In lecture, the relationships among these concepts may be demonstrated with one of the following sample datasets: