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.