A conceptual model is an abstract representation designed to articulate the processes operating in a system of interest. A conceptual model may take narrative form and use words to describe the system at hand, but with their long spatial science tradition, geographers have frequently drawn on geometry and graphical forms of visual representation to render their conceptual models. For instance, Figure 12.1 provides a schematic diagram of the physical processes involved in maintaining the earth's radiation balance, popularly known as 'the greenhouse effect'. While the phrase 'greenhouse effect' relies on the physical analogy between the earth's atmosphere and a glass greenhouse, this schematic diagram doesn't work by positing an analogy to something else, as Hesse's definition of modelling as analogy building suggests. Rather, it
seeks to conceptualize how the fundamental laws of physics apply in the particular case of the earth's atmosphere. From this perspective, the work of modelling is at once theoretical, helping to flesh out theory and make it more explicit and applicable, and experimental: manipulating model phenomena so as to test their correspondence to theory and to independent observations of the phenomena they are models of.
Despite the important role of conceptual modelling in linking theory to data, conceptual models can be difficult to apply empirically because they do not specify parameter values and boundary conditions. It is only by specifying the magnitude of the flows depicted in Figure 12.1 that our model of the greenhouse effect can be applied specifically to planet Earth rather than to Venus, for example. Without such empirical specification, this conceptual model can neither be tested against independent observations nor used in an applied context to generate precise predictions that might inform subsequent policy decisions. To those two ends, many geographers seek to convert their conceptual models into mathematical ones. But that move is by no means universal. As we discuss in the second part of this chapter, fierce debates about the philosophy of theory testing and the politics of applied science have led other geographers to resist mathematical modelling.
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