Composite Drought Indices of Monotonic Behaviour for Assessing Potential Impact of Climate Change to a Water Resources System

Abstract

In this study, innovative drought indices are developed to accurately quantify the characteristics of drought events and their possible impacts to the water resources system of the Tsengwen Reservoir of Taiwan. We applied a monotonic test to three fundamental single drought indices, namely reliability, vulnerability and resilience, to demonstrate that indices showing non-monotonic behaviour can potentially give misleading information regarding the effects of drought to water resources systems. We further tested two newly proposed single drought indices, Vul _system and Res _weighted , to the study site, of which Vul _system showed monotonic behaviour but Res _weighted still behaved non-monotonically, even though in a suppressed manner. Next, we proposed and tested three composite drought indices, sustainability index (SI), drought risk index (DRI) and the water shortage index (WSI), of which only the WSI behaved monotonically. As a result, WSI was applied to investigate the potential impact of climate change to the future drought risk of the study site. On the basis of WSI values derived from runoffs simulated by the modified HBV and a reservoir operation (water balance) model driven with 18 sets of climate changes scenarios of IPCC (2007) statistically downscaled using the MarkSim GCM model, it seems that there is a 20 % chance that climate change impact could lead to more severe droughts in the study site. However, under the combined impact of climate change and the effect of sedimentation to the Tsengwen Reservoir, which could decrease its storage capacity by about 12 % (i.e., s = 0.88), it seems more severe drought impacts will increase to 2/3 of the 18 test cases. Lastly, a direct relationship was developed between WSI and the multifractal strength, which implies that runoff data with a stronger multifractal strength could lead to more severe droughts and vice versa.

Appendix

For a time series, x, divided into N/r intervals of equal length, the box probability of the jth interval, P _r (i), is the probability of a sample being found in a box of a specified domain, and the scaling exponent, λ(q), is the q ^th moment of the box probability, ${\displaystyle \sum_{i=1}^{N/r}{P}_r}{(i)}^q={r}^{\lambda (q)}$, where λ(q) is the slope of the LHS versus r on a log-log plot. For a multifractal process, the slope λ(q) varies with r. Next, a Legendre transformation is often performed on λ(q) to produce the multifractal spectrum, of which its width is the multifractal strength of x.