Multi-scale effects on spatial metrics in global water resources data: Implications to water stress

This dissertation examines theoretical concepts of geographic scale using empirical tests of multi-scale gridded water-availability, water use and population data and its derivatives like stress/scarcity (vulnerability) for the Missouri, Ganges and Danube River Basins. The two broad objectives of this study are to: (1) Test the effects of scale on mean and spatial variation of water resources and population data and develop a scaling function; and (2) Apply the results to measures of water resources vulnerability at multiple scales and examine patterns spatially. Competing and conflicting hypotheses were presented about expected relationships and empirically tested. Fine-resolution raster and vector geospatial datasets were aggregated to coarser grid sizes using the geographic information system (GIS) tool. Grid cell means and standard deviations were computed at each scale on SPSS 16.0 and SAS 9.2 and these values were tested for trends to develop scaling functions. Statistical correlations were also computed between water resources variables such as water use and population at different scales, and the correlation coefficients and measures of spatial autocorrelation were tested for trends with scale.;Results show that means and measures of variability in unscaled variables, like freshwater supply, water use, and population, increase at coarser scales. This is contrary to common assumptions of decreasing variability as grid-cell size (scale) increases. Moreover, these increases in mean cell values and variability with scale show strong, non-linear trends. Power-scaling relationships were consistent in all river basins under different climatic regimes and suggest predictable behaviors with scale for these variables. In contrast, variables that are scaled to area or population (e.g., population density or water availability per capita), behaved quite differently. Means cell values appear unrelated to scale while variability shows a tendency to decrease with scale. The trends for correlation coefficients between variables were erratic and sometimes contrary to common assumptions. Correlograms for spatial autocorrelation showed scale effects, however, the results were not readily intuitive.;Empirical and theoretical results for both of the measures of vulnerability - criticality ratio and Falkenmark index - were tested. Results suggest that these metrics computed for mean annual values are scale independent. When unscaled variables like water availability, use, and population are ratioed, their dependency on scale is lost. This implies that, for a particular river basin, average water resources vulnerability computed at one scale should apply to all scales. Populations and areas under various degrees of vulnerability are computed and mapped showing the location and heterogeneity in water stress and scarcity distributions.