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).