2.5 Calculation of Sensitivity Indices by Latin Hypercube Sampling
A conventional approach to the variance estimation in Eqs. (6) and (8) is the Monte Carlo (MC) method. However, conventional MC sampling is computationally expensive, especially for the high dimensional models used in this research. To reduce the unaffordable computational cost, more efficient Latin hypercube sampling (LHS) method was used to generate the random parameter samples in this research (Helton and Davis., 2003; McKay et al., 1979). This method divides the ranges of them model parameters into n disjointed intervals with equal probability 1/n from which one value is sampled randomly in each interval.
Assuming that we have k alternative greenhouse gas emission scenarios, l plausible global climate models under each emission scenario, j plausible hydrological models under each global climate model and n LHS generated parameter sets, the partial variance caused by parametric uncertainty can be estimated as:
, (9)
where is the weight of model under global climate model and greenhouse gas emission scenario satisfying, and is the weight of the global climate models satisfying, and is the weight of the greenhouse gas emission scenario satisfying. Similarly, the partial variances of the hydrological models, global climate models and greenhouse gas emission scenarios can be calculated as:
,(10)
, (11)
.(12)
Based on Eqs. (9)–(12), the sensitivity indices defined in Eq. (6) and Eq. (8) (three–layer hierarchical framework) can be evaluated.
3Study Area and Data Sets
3.1Study Area
The study area is located in the upstream area of the Beijiang River, which is the second largest tributary of the Pearl River, southern China, and accounts for 73% of the Beijiang River basin with a drainage area of 34097 km2. The area consists of four major rivers: the Wujiang River, the Zhenjiang River, the Wengjiang River, and the Lianjiang River (Figure 2). The Hengshi hydrological station is the discharge station in the study basin (Figure 2). The study basin is located in the tropical and subtropical climate zones, with the flood season (April–September) precipitation accounting for approximately 70–80% of the annual precipitation. Due to the sufficient precipitation, high humidity and climate warming, the study catchment has often experienced extreme floods (e.g., June and August 1994, June 1998, June 2005, and July 2006) in the past few decades and will likely encounter more severe flooding in the next few decades (Wu et al., 2014; 2015).