The statistical study of hydraulic geometry: A new direction for compositional data analysis |
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| Authors: | Gregory S Ridenour and John R Giardino |
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| Institution: | (1) Department of Geography, Texas A&M University, College Station, 77843-3147, Texas;(2) Present address: Social Sciences Department, University of Texas, 3900 University Blvd., 75701-6699 Tyler, Texas;(3) Departments of Geography and Geology, Texas A&M University, 77843-3147 College Station, Texas |
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| Abstract: | Hydraulic exponents and unit hydraulic exponents are unit-sum constrained, which requires that they be analyzed by statistical methods designed for compositional data. Though uncertainties remain regarding selection of the  best constraining operation and method of handling departures from the unit-sum constraint, neither category of uncertainty should be an impediment to the selection of the appropriate statistical methodology. In a small sample study, the hydraulic geometry of different types of streams were compared: (1) semi-arid: perennial vs. ephemeral; (2) tropical: Puerto Rico vs. West Malaysia; and (3) semi-arid vs. tropical (by pooling the previous data sets). All three comparisons revealed statistically significant differences in either logratio mean vectorsor logratio covariance matrices but not both. All six categories of data had logistic normal distributions. Because the derivatives at a given discharge of curvilinear hydraulic geometry relationships and hydraulic exponents on either side of the breakpoints of piecewise linear relationships are unit-sum constrained, they also can be studied by compositional methods. However, the compositional approach is limited in cases where distributions have large departures from logistic normality and for streams that have negative hydraulic exponents. |
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| Keywords: | hydraulic geometry unit hydraulic geometry derivative hydraulic geometry compositional data analysis unit-sum constraint ternary diagram logratio |
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