1 Introduction
It is widely accepted that the most
certain impact of future climate change is an increase in temperature
across the globe, particularly in the Northern Hemisphere (IPCC, 2007,
2013). Global warming is expected to intensify the hydrological cycle
and alter evapotranspiration, with consequences for water resources
(Abbaspour et al., 2009; Arnell, 1999, 2004; Piao et al., 2010; Thompson
et al., 2013; Vörösmarty et al., 2000), ecosystem services
(Hoegh–Guldberg and Bruno, 2010; Matthews and Quesne, 2009; Preston et
al., 2002), and feedback to regional and global climates (Jung et al.,
2010). Assessment of the hydrologic impacts of future climate change
over large domains are commonly performed by coupling atmospheric
climate projections from global climate models (GCMs) and regional
climate models (RCMs) with land–surface schemes and hydrological models
(e.g., Alfieri et al., 2015; Chen et al., 2011a, 2011b, 2017; Deepashree
et al., 2010; Gädeke et al., 2014; Habets et al., 2013; Jha and
Gassman., 2014; Kay et al., 2009; Lu et al., 2018; Maurer and Duffy,
2005; Stephens et al., 2018; Wu et al., 2014, 2015; Xu et al., 2013;
Zhang et al., 2011).
Uncertainty is inevitable and important for numerical models, especially
for the complex hydrological models with future climate change impacts
(Kay et al., 2009; Neuman, 2003; Refsgaard et al., 2007). Uncertainties
arise from variant sources, including unpredictable future conditions,
lack of knowledge or data of the system, and variability in the natural
characteristics (Neuman, 2003; Refsgaard et al., 2007; Rubin et al.,
2010; Tartakovsky, 2013). For the future impacts of climate change, GCMs
and greenhouse gas emission scenarios (GGESs) are generally considered
to be the two major uncertain factors influencing the assessment of
hydrologic systems (Chen et al., 2011a, 2011b; Kay et al., 2009; Liu et
al., 2013; Minville et al., 2008; Thompson et al., 2013; Wilby and
Harris, 2006; Wu et al., 2015; Xu et al., 2013).
In addition to the uncertainty in GCMs and GGESs, other sources of
uncertainty, such as hydrological model uncertainty and parametric
uncertainty, were also found to be important for the hydrological impact
assessments. For example, Chen et al. (2011b, 2013) and Teutschbein et
al. (2011) noted that the dynamical and statistical approaches for
quantifying the impacts of climate change on hydrological systems are
considerably influenced by uncertainty. Wilby (2005) investigated the
impact of climate change on the monthly flows of the Thames by
considering the effect of hydrological model parameters and showed that
parameter uncertainty from the hydrological model is comparable in size
to the GGES uncertainty. Jiang et al. (2007) investigated the
hydrological impacts of climate change in the Dongjiang basin in
southern China by comparing six hydrological models, and the results
emphasized a large difference in modeling hydrological variables (e.g.,
runoff, evapotranspiration, and soil moisture). This finding has been
confirmed by Najafi et al. (2011), who suggested that hydrologic model
selection is necessary when assessing hydrologic climate change impacts.
The estimation for the importance of different uncertainty sources in
climate and hydrological model systems is essential for modelers and
managers, a sensitivity analysis is required for this estimation
process. In the uncertainty viewpoint, sensitivity analyses focus on
quantifying the uncertainty from different uncertain model inputs that
contribute to the model predictions (Dai and Ye., 2015; Saltelli et al.,
2010). Among the previous studies that have investigated the uncertainty
of climate hydrological models, the majority of sensitivity analysis
works mainly involve qualitative comparison, and these works only
provided the general ranking of uncertainty sources according to the
range of probability density functions (PDF) or cumulative distribution
function (CDF) of model outputs (Chen et al., 2011b, 2013; Dobler et
al., 2012; Nóbrega et al., 2011; Satish et al., 2011; Teng et al.,
2012). These studies showed that the uncertainty induced by GCMs is
generally large and the most important one for dramatically influencing
the model predictions (e.g., Bosshard et al., 2013; Déqué et al., 2007;
Fowler and Ekstrom,
2009;
Hattermann et al., 2018; Kay et al., 2009; Habets et al., 2013; Minville
et al., 2008; Shen et al., 2018; Su et al., 2017; Prudhomme and Davies,
2009).
Recently, the accurate quantification of different uncertainty sources
in hydrological models has been
popularized through the advanced
variance–based global sensitivity analysis method. This methodology has
been widely used in different hydrological and climate models because of
its advantage of model independence and capability of providing
mathematically rigorous and accurate measurements for the importance of
different model uncertainty sources (Chu–Agor et al. 2011; Saltelli,
2000; Song et al., 2015). For example, Vetter et al. (2017) has applied
the variance–based method to quantify the importance of three different
uncertainty sources (emission scenarios, climate models, and
hydrological models) with a study domain of 12 river basins over 6
continents, which is a comprehensive study on a large spatial scale.
However, the conventional variance–based global sensitivity analysis
method ignores the dependence or deterministic relationships of
different uncertainty sources and fails to consider combinations of
model uncertain inputs based on their characteristics (Dai et al.,
2017a, 2017b, 2019).
To overcome these shortcomings, Dai et al. (2017a, b) has developed a
more advanced hierarchical sensitivity analysis methodology which
integrated the variance–based sensitivity analysis method with the
hierarchical uncertainty framework, and this new methodology was capable
of grouping different model uncertainty sources and considering the
dependence relationships among these uncertain inputs. The new
hierarchical sensitivity analysis was tested in a complex groundwater
reactive transport model (Dai et al., 2017a) and has been proven to
provide useful and solid information for modelers about the importance
of uncertain model inputs. This study proposed a new variance–based
sensitivity analysis framework in hydrologic climate model systems on
the basis of Dai et al. (2017a, b). Particularly, for the first time,
this new hierarchical sensitivity analysis framework has been improved
and modified to be suitable for a climate hydrologic modeling system by
considering all different sources of uncertainty.
By using the new hierarchical sensitivity analysis framework, this paper
conducts a comprehensive and quantitative sensitivity analysis of the
climate–influenced hydrological model implemented at the basin scale
using continuous simulations of river flows. All possible uncertainty
sources in a hydrological model system under climate change, including
the alternative GGESs and GCMs, multiple hydrological models and variant
parameters, are all considered in this research. Two hierarchical
sensitivity analysis frameworks were implemented: the four–layer
sensitivity analysis framework considering GGESs, GCMs, hydrological
models and parameters, and the three–layer sensitivity analysis
framework considering GGESs, GCMs and hydrological parameters. Two model
outputs related to flooding were selected as the outputs of interest:
river discharge and surface runoff. Four different sources of
uncertainty: future alternative GGESs, multiple plausible GCMs, two
different hydrological models, and variant hydrological model parameters
are quantified. By providing a pilot example of uncertainty quantization
in climate–influenced hydrological models, we aim to (1) identify the
relative contribution of the uncertainty sources to the model outputs
and (2) test the spatio–temporal variations of general sources of
uncertainty in hydrological predictions in the context of climate
change. The framework used in this study is mathematically rigorous and
general, and can be applied to a wide range of hydrologic and
environmental models that consider climate change, which improves our
understanding of how climate influences the hydrological system.