Scale invariance of water stress and scarcity indicators: Facilitating cross-scale comparisons of water resources vulnerability

Abstract

Several indicators are commonly used to measure the degree of water resources vulnerability (e.g., water stress and scarcity) in different populations and regions. Little is known, however, about how these indicators respond to changes in the scale of data used to derive them. Two of the most widely used water resources vulnerability metrics, conventionally computed for mean annual values at the country level are Falkenmark Index (FI) for per capita water availability and the Criticality Ratio (CR) for water use to availability. This study computes FI and CR values at a wide range of scales and tests for trends with scale in three river basins: Missouri (North America), Danube (Europe) and Ganges (South Asia) Basins. Gridded sub-continental hydro-climatic data sets at 0.5° resolution are used and aggregated at multiple scales from 0.5° to 5.0°. Analytical logic and empirical evidence show that mean grid-cell values of these vulnerability metrics are in fact scale-independent (scale-invariant) for a given basin. When unscaled variables like water availability and use are ratioed to variables that depend on area, such as population, their dependency on scale may be lost and they become spatially scaled variables. For example, grid-cell mean values of water availability are scale dependent, but grid-cell mean values of the ratio of water availability to population (i.e. FI) are not. This implies that, for a particular river basin, average water resources vulnerability computed by FI and CR at one scale should apply to all scales. This has tremendous implications to applied geographic studies of water resources, and is especially interesting since the unscaled variables used to derive the two indices are scale dependent and vary greatly with scale. The paper and findings highlight the multi-scale complexities of water resources and the geographic nature of water resources and vulnerability metrics.