General geomorphometry, derivatives of altitude, and descriptive statistics

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Abstract
In the application of multivariate statistics to geographic problems, too little critical attention is paid to questions of operational definition and sampling. Many of the operational definitions used in geomorphometry are extremely poor as measures of the intended concepts. General geomorphometry deals with surface altitude, gradient, distance and area, often in combination as in hypsometry, which relates area to altitude. General geomorphometry has a long history among European geographers. The automation of geomorphometry involves using electronic computers to process digital data representing the earth’s surface. The availability of machine-readable altitude data in either form has profound implications for geomorphometry. The availability of altitude matrices is particularly suggestive, since it facilitates the rationalisation of general geomorphometry, with derivatives of altitude as the unifying concept. Review of the literature of general geomorphometry shows that all of its parameters may be defined in terms of altitude.

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