Network Representations of Critical Elements of Pressure Surfaces

TJ HE possibility and the desirability of a general spatial systems theory for geography that relates to principles of spatial structure and spatial process at terrestrial scales is a current concern. We have found certain general abstract geometric and topological properties of continuous and everywhere differentiable surfaces to be relevant, informative, productive of additional understandings, and springboards for incisive research in contexts as seemingly different as money, ideas, information, commodity, and population flows,' and the stream orders, hierarchies, and basin nestings of river systems.2 What we offer in this paper are simple extensions to aspects of atmospheric pressure systems. We begin with things about which we entertain fairly firm convictions. A sequence follows which is increasingly speculative but, we hope, also increasingly provocative, in the least pejorative sense of that word. We identify critical elements (points, paths, and areas) of atmospheric pressure surfaces, consider the roles of these elements in the context of flows in the atmosphere, reduce the surface to networks, codify the networks as matrices, and suggest computer-assisted operations on these matrices to produce not only descriptive indices of the connectivities in the system akin to conventional measures in meteorology but also "solutions" to flow problems like those having currency in social science. Final tests of the constructs will require the input of meteorologists concerning physical relationships in the system. A research objective might be to test whether the focusing and channeling of physical quantities from the system into greatly simplified network configurations involve only negligible losses of information so that relevant numerical solutions to simplified forms of the nonlinear partial differential equations of the system (using plausible approximations to initial conditions and boundary values) might be used in programming solutions for forecasting. A more realistic intermediate objective is to obtain critical review and also needed input with respect to atmospheric dynamics. Consider sea-level distribution of pressure for the Northern Hemisphere at a given moment, as illustrated in Figure I, with spatial variations shown by the very well known means of isobars. Each such isobar represents the intersection of an undulating constant-valued atmospheric pressure surface with the sea-level surface. Surfaces intersect along a line. Such a line traces out points of equal value of pressure on the surface on which the variation is to be displayed. Each such sea-level