Abstract

This study develops a new variance-based uncertainty assessment framework to investigate the individual and combined impacts of various uncertainty sources on future extreme floods. The Long Ashton Research Station Weather Generator (LARS-WG) approach is used to downscale multiple general circulation models (GCMs), and the dynamically dimensioned search approximation of uncertainty approach is used to quantify hydrological model uncertainty. Extreme floods in a region in northeastern China are studied for two future periods: near term (2046–65) and far term (2080–99). Six GCMs and three emission scenarios (A1B, A2, and B1) are used. Results obtained from this case study show that the 500-yr flood magnitude could increase by 4.5% in 2046–65 and by 6.4% in 2080–99 in terms of median values; in worst-case scenarios, it could increase by 63.0% and 111.8% in 2046–65 and 2080–99, respectively. It is found that the combined effect of GCMs, emission scenarios, and hydrological models has a larger influence on the discharge uncertainties than the individual impacts from emission scenarios and hydrological models. Further, results show GCMs are the dominant contributor to extreme flood uncertainty in both 2046–65 and 2080–99 periods. This study demonstrates that the developed framework can be used to effectively investigate changes in the occurrence of extreme floods in the future and to quantify individual and combined contributions of various uncertainty sources to extreme flood uncertainty, which can guide future efforts to reduce uncertainty.

1. Introduction

Extreme floods have drawn increasing attention in recent years and pose a huge risk to environment and society in many parts of the world (Hirabayashi et al. 2013; Ward et al. 2013; Arnell and Gosling 2014; Koirala et al. 2014; Qi et al. 2016c). Extreme floods usually have long return periods (e.g., 100 years), and research has shown that climate change can have a high impact on the frequency of extreme floods (Arnell and Gosling 2014; Qin and Lu 2014). However, there is a lack of understanding on how the variability of simulated future extreme floods is affected by various uncertainties in data and models in the chain from climate models to hydrological models.

In assessment of future extreme floods, uncertainties from different sources must be taken into consideration, such as greenhouse gas emission scenarios, general circulation models (GCMs), downscaling techniques, and hydrological simulations. Emission scenarios, which are needed to drive GCMs, are based on assumptions of social, economic, and technological developments and thus have large uncertainties. Four emission scenario families—A1, A2, B1, and B2—are often used to represent emission uncertainties (IPCC 2014). The A1 scenario family describes a future world of very rapid economic growth, global population that peaks in the middle of twenty-first century, and rapid introduction of new efficient technologies. Within the A1 family, A1B represents a balanced use of energy across all sources. The A2 scenario family describes a very heterogeneous world. B1 describes a sustainable world with rapid change in economic structures. B2 describes a world in which the emphasis is on local solutions. Many GCMs have been developed and used; for example, the Coupled Model Intercomparison Project (CMIP) implements more than 15 GCMs (Lobell et al. 2007). The combined use of different GCMs can be attributed to the need to mitigate the insufficient human knowledge about the extreme complexity of climate systems. Because of the coarse resolutions of GCMs, many downscaling approaches have been developed to obtain high-resolution data, such as statistical downscaling (Wilby et al. 1998; Murphy 1999), dynamic downscaling (Giorgi and Mearns 1991; Murphy 1999), and weather generators (Racsko et al. 1991; Semenov and Barrow 1997; Semenov 2008; Liu et al. 2009; Semenov and Stratonovitch 2010). In addition, hydrological simulation uncertainty could have a significant influence because of insufficient human knowledge about hydrological processes and model parameters (Beven and Binley 1992; Maggioni et al. 2012; Tian et al. 2012; Zhang et al. 2013).

Different weather generators have been used as a downscaling approach and compared in the evaluation of extreme events within the context of climate change. For example, Wilby et al. (1998) compared weather generators and an artificial neural network approach and concluded that weather generators could fit daily precipitation statistics well and yield better results than the neural network approach. Semenov et al. (1998) compared two popular weather generators: Weather Generator (WGEN; Richardson 1981) and Long Ashton Research Station Weather Generator (LARS-WG; Semenov and Barrow 1997), and suggested that LARS-WG tends to match the observed data more closely because it uses more complex distributions for weather variables. Semenov (2008) evaluated LARS-WG in terms of extreme events and found that the normal distribution assumption for daily temperature may be inadequate. As a consequence, Semenov and Stratonovitch (2010) upgraded LARS-WG by replacing the normal distribution with an empirical distribution. Several validation studies of LARS-WG have revealed the upgrade is effective (Semenov and Stratonovitch 2010; Qin and Lu 2014).

Most recently, Qin and Lu (2014) combined emission scenarios, GCMs, LARS-WG, and a hydrological model to simulate extreme floods and found that the 200-yr flood magnitude could increase in a southern China basin in the future. Although the study by Qin and Lu (2014) considered GCM and emission scenario uncertainties, an important uncertainty source—hydrological model uncertainty—was omitted. Many studies have revealed that hydrological model uncertainty can be significant and should be considered, even though simulations using the best-fitted model parameters are highly accurate (Beven and Binley 1992; Freer et al. 1996; Beven and Freer 2001; He et al. 2015). It is essential, therefore, to take hydrological model uncertainty into account in extreme flood evaluation.

The individual and combined contributions of various uncertainty sources of GCMs, emission scenarios, and hydrological models to the overall uncertainty in extreme floods should be quantified because this is very important to guide future efforts to reduce extreme flood uncertainty. In this study, the combined effect represents the residual impacts of different uncertainty sources apart from individual impacts in the nonlinear uncertainty propagation process from climate models to hydrological models. Efforts have been made to quantify the respective influences of GCMs, downscaling methods, and hydrological models on water resources and extreme hydrological events (Wilby and Harris 2006; Minville et al. 2008; Kay et al. 2009; Steinschneider et al. 2012; Teng et al. 2012; Bosshard et al. 2013). Previous research, however, did not quantify the combined effect of different sources, except the study of Bosshard et al. (2013), which found that the combined effect of GCMs, downscaling approaches, and hydrological models has considerable impacts on discharges and different flow quantiles. However, more research is needed to investigate the combined effect in a chain of climate change impact assessments, in particular for future extreme flood prediction, which has a profound implication for design and management of water projects.

The overall aim of this research is to investigate the individual and combined impacts of uncertainty sources from GCMs, emission scenarios, and hydrological models on future extreme floods using a new assessment framework based on the variance-based sensitivity analysis approach (ANOVA; Bosshard et al. 2013). In this framework, the LARS-WG approach is used to downscale multiple GCMs, and a widely used computationally efficient hydrological model—TOPMODEL—is used for continuous flow simulations (Beven and Kirkby 1979), in which the dynamically dimensioned search approximation of uncertainty (DDS-AU; Tolson and Shoemaker 2008) approach is used to quantify TOPMODEL uncertainty. In the framework, the respective uncertainty sources, including their combined effects, can be explicitly quantified. To demonstrate the new framework, a midscale catchment in northeastern China is selected. Six GCMs and three emission scenarios—A1B, A2, and B1—are used.

The paper is organized as follows. Section 2 introduces the case study river basin and data. The newly developed framework is described in detail in section 3, including LARS-WG, TOPMODEL uncertainty quantification, and the ANOVA approach. Results and discussion, including changes in future extreme floods and uncertainty source quantification, are presented in section 4. Conclusions are presented in section 5.

2. Case study river basin and data

a. Biliu basin

Northeastern China, one of the most populous areas in China, plays an important role in food production for supporting the livelihood of the population and is a significant industrial region as well. This region frequently suffers from extreme floods that pose a threat to the regional sustainable development. Thus, this study is carried out in a river basin, the Biliu basin, in northeastern China to investigate extreme flood predictions under climate change.

The Biliu basin, located in a coastal region between the Bohai Sea and the Huanghai Sea, covers an area of 2814 km2, from 39.54° to 40.35°N in latitude and 122.29° to 122.92°E in longitude (Fig. 1). This basin is characterized by a temperate, monsoon marine climate, with summer (July–September) being the major rainy season. The average annual precipitation is 746 mm, and the average annual temperature is 10.6°C. The basin average elevation is 240 m, with a maximum of 985 m in the northern mountainous region and a minimum of 4.5 m in the southern part. The detailed information of the Biliu basin is obtained from gauge-based observations from the Biliu reservoir administration.

Fig. 1.

The distribution of rain gauges, a discharge gauge, and meteorological gauges in Biliu basin, Liaoning province, northeastern China.

Fig. 1.

The distribution of rain gauges, a discharge gauge, and meteorological gauges in Biliu basin, Liaoning province, northeastern China.

b. Observed data and discharge accuracy criterion

There are 11 rain gauges and one flow gauge in the Biliu basin. Observed daily discharge and rainfall data are available from 1978 to 2011. Meteorological data from three gauge stations nearby are available from 1978 to 2011 for daily minimum/maximum temperature and sunshine hour. These data were used as inputs to LARS-WG.

In discharge simulations, Nash–Sutcliffe efficiency (NSE) is used as a metric of model performance as it has been commonly used to assess the accuracy of discharge simulations (Tian et al. 2006; Mou et al. 2008; Zhang et al. 2013; Qi et al. 2015, 2016a,b). This criterion is also recommended in the flood forecasting handbook in China (People’s Republic of China 2008). NSE is calculated as follows:

 
formula

where Qpi and Qti are simulated and observed daily flows at time i, respectively, and is the mean of observed flows. A perfect fit should have an NSE value of one.

3. Uncertainty assessment framework

Figure 2 shows a flowchart of the newly developed framework for uncertainty assessment. The key processes are described below. First, meteorological data are collected, including observed daily precipitation, minimum/maximum temperature, and solar radiation, and their empirical distributions are calculated; the emission scenarios and GCMs are then selected. The distributions are represented using empirical functions, that is, histograms. Second, LARS-WG is used to downscale GCM outputs to generate daily data, including rainfall, minimum/maximum temperature, and solar radiation. The data are generated for baseline and future time periods. The baseline data are generated randomly from the meteorological data distributions, and the future period data are derived according to the generated baseline period data and GCM-projected changes. For example, if the minimum January temperature is predicted to increase by 1.5°C in 2050, then 1.5°C is added to the baseline data in order to calculate the minimum January temperature in 2050. This is the same approach used by Semenov and Stratonovitch (2010). Third, the generated data are used as the input data of a hydrological model—TOPMODEL—to simulate discharges, and hydrological model uncertainties are quantified using a stochastic global optimization algorithm DDS-AU (Tolson and Shoemaker 2008). Fourth, flood frequency analysis is conducted using simulated discharge data, and this process is repeated with randomly generated baseline data from the meteorological data distributions until the simulated baseline data can bracket observed floods. Note that, in LARS-WG, different random seeds for empirical meteorological distributions are used in the iterations in order to generate data corresponding well to observed data, and the same random seeds are used for the baseline and future periods. Fifth, a variance-based sensitivity analysis approach is used to quantify the individual contributions of GCMs, emission scenarios, TOPMODEL uncertainty parameters, and their combined effects to the overall uncertainties in simulated extreme floods.

Fig. 2.

Flowchart of the developed uncertainty assessment framework. The boxes correspond to five processes of the proposed framework; the diamond corresponds to an evaluation of the flood frequency analysis uncertainty in the baseline period; and the parallelograms correspond to generated data from LARS-WG and uncertainty quantification results.

Fig. 2.

Flowchart of the developed uncertainty assessment framework. The boxes correspond to five processes of the proposed framework; the diamond corresponds to an evaluation of the flood frequency analysis uncertainty in the baseline period; and the parallelograms correspond to generated data from LARS-WG and uncertainty quantification results.

LARS-WG, TOPMODEL parameter uncertainty, assessment of LARS-WG, and TOPMODEL combination and uncertainty quantification approach are explained in detail in sections 3ad, respectively.

a. LARS-WG

LARS-WG was developed by Racsko et al. (1991) and has been updated recently (Semenov and Barrow 1997; Semenov 2007; Semenov and Stratonovitch 2010). LARS-WG applies empirical distributions to fit wet spell length, dry spell length, precipitation amount, minimum temperature, maximum temperature, and solar radiation. The empirical distributions are used to generate meteorological data. In LARS-WG, if solar radiation is not available, sunshine duration data can be used to estimate it on the basis of an algorithm developed by Rietveld (1978). LARS-WG can also estimate evaporation data using the Priestley–Taylor equation. Using LARS-WG, meteorological data with a selected length under climate change can be generated (Semenov et al. 1998; Semenov 2008; Semenov and Stratonovitch 2010).

In LARS-WG, version 5.5, 15 GCMs used in the Intergovernmental Panel on Climate Change (IPCC) assessment report are included (IPCC 2007, 2014), and three emission scenarios (A1B, A2, and B1) and three future periods (2011–30, 2046–65, and 2080–99) are used because they are used in most of the GCMs. More detailed information on the 15 GCMs, the specific emission scenarios, and the specific future periods for each GCM can be found in the study by Semenov and Stratonovitch (2010). It should be noted that some of these GCMs are not available for all three emission scenarios and for all three future periods. Thus, the selection of a GCM is based on whether it can cover the future periods and emission scenarios of interest. In this study, we investigate the changes of extreme floods under the three emission scenarios for 2046–65 and 2080–99. Therefore, six GCMs were selected and listed in Table 1, in which the GCM research institutes, countries, names, and resolutions are shown.

Table 1.

GCMs, emission scenarios, and investigated time periods in this study. Time periods are baseline (B; 1978–2011), T1 (2046–65), and T2 (2080–99).

GCMs, emission scenarios, and investigated time periods in this study. Time periods are baseline (B; 1978–2011), T1 (2046–65), and T2 (2080–99).
GCMs, emission scenarios, and investigated time periods in this study. Time periods are baseline (B; 1978–2011), T1 (2046–65), and T2 (2080–99).

Because the resolutions of the GCMs used in this study are at least 1.4° × 1.4° and are larger than the Biliu basin, basin-averaged data (from 1978 to 2011) were used in LARS-WG to calculate meteorological data distributions. The basin-averaged data are calculated using the inverse distance weighting approach.

b. TOPMODEL and its uncertainty quantification

TOPMODEL is a physically based model of basin hydrology that attempts to combine the advantages of a simple lumped parameter model with distributed effects (Beven and Kirkby 1979). Fundamental to TOPMODEL’s parameterization are three assumptions: 1) saturated-zone dynamics can be approximated by successive steady-state representations, 2) hydrological gradients of the saturated zone can be approximated by the local topographic surface slope, and 3) the transmissivity profile whose form declines exponentially with increasing vertical depth of the water table or storage is spatially constant. More detailed descriptions of TOPMODEL and its mathematical formulation can be found in Beven and Kirkby (1979). TOPMODEL has been popularly utilized in many studies across the world (Blazkov and Beven 1997; Bastola et al. 2008; Bouilloud et al. 2010; Qi et al. 2016a,b) because of its relatively simple model structure. There are six parameters in TOPMODEL, and they are described in Table 2. As shown in Table 2, all the TOPMODEL parameters are related to soil or basin topography. These parameters are not affected by climate change and thus are assumed to be stationary (Cameron et al. 2000; Smith et al. 2014). In this study, the parameter ranges were defined according to the previous literature (Qi et al. 2016a,b).

Table 2.

TOPMODEL parameters.

TOPMODEL parameters.
TOPMODEL parameters.

The input data of TOPMODEL include basin-averaged precipitation, evaporation, and topographic data that can be estimated from digital elevation data. The digital elevation data were obtained from the NASA Shuttle Radar Topography Mission with a resolution of 30 m × 30 m (Rabus et al. 2003). Because reliable evaporation data are only available from January 2000 to December 2007, parameter uncertainty from the six TOPMODEL parameters was quantified using DDS-AU on the basis of this time period. The evaporation data were obtained from a water and energy budget–based distributed biosphere hydrological model that was carefully calibrated using observed discharges and Moderate Resolution Imaging Spectroradiometer (MODIS) land surface temperature data (Wan 2008). More detailed descriptions about the processes obtaining the evaporation data can be found in the study by Qi et al. (2015).

DDS-AU is implemented using multiple independent optimization trials of the dynamically dimensioned search stochastic global optimization algorithm (Tolson and Shoemaker 2007). Tolson and Shoemaker (2008) demonstrated that DDS-AU outperforms other approaches in efficiency and therefore was selected in this study to quantify TOPMODEL simulation uncertainty. NSE was used as the objective function to derive the uncertainty bounds and a threshold of 0.7 was used in this study, which generated 128 behavioral parameter sets. Such a threshold was selected based on a trial and error approach to make sure that the resulting uncertainty bounds are not too wide and observed discharges are also bracketed by uncertainty bounds. Figure 3 shows the behavioral TOPMODEL parameter sets. Each dot represents a behavioral parameter set. The values on the x axis represent TOPMODEL parameters and their values. It can be seen that many parameter values are acceptable: their corresponding NSE values are larger than 0.7. It should be noted that the behavioral simulations are results of combined effects of all the behavioral parameter sets, and all these behavioral parameter sets should be considered in TOPMODEL uncertainty quantification.

Fig. 3.

Behavioral TOPMODEL parameter sets using an NSE threshold value of 0.7. Each dot represents a behavioral parameter set.

Fig. 3.

Behavioral TOPMODEL parameter sets using an NSE threshold value of 0.7. Each dot represents a behavioral parameter set.

Predictive uncertainty bounds are constructed on the basis of the simulation results of behavior parameter sets. Note that other sources of uncertainty such as input data and model structure could be considered for producing predictive uncertainty bounds. However, these are not considered in this study as observed rainfall data and reliable evaporation based on water and energy budgets were used as inputs to TOPMODEL, and previous studies have shown that the structure of TOPMODEL is suitable for the Biliu basin (Qi et al. 2016a,b). When there are no reliable evaporation data, other approaches, for example, the Priestley–Taylor equation, could be used, and in this situation the uncertainty parameters of TOPMODEL can represent the uncertainty in evaporation (Beven and Binley 1992).

The lower and upper uncertainty bounds resulting from the 128 behavioral parameter sets are shown in Fig. 4 with peak discharges indicated with circles. It can be seen that all the observed peak discharges are between the lower and upper bounds, except for the flood peak in 2004. Although the flood peak in 2004 is out of the uncertainty bounds, it is very close to the upper uncertainty bound. These results indicate the selected uncertainty parameters can represent the hydrological simulation uncertainty.

Fig. 4.

TOPMODEL uncertainty quantification for discharges from 2000 to 2007 with peak discharges indicated with circles.

Fig. 4.

TOPMODEL uncertainty quantification for discharges from 2000 to 2007 with peak discharges indicated with circles.

c. Assessment of LARS-WG and TOPMODEL simulations

The calculated meteorological data distributions in the baseline period were used to generate 1000-yr data including rainfall and evaporation. These generated data were then used as inputs to TOPMODEL to simulate discharges. To assess LARS-WG and TOPMODEL simulations, flood frequencies using the 1000-yr simulated discharges and observed data will be compared. Figure 5 shows the comparison results. Return periods are shown on the x axis, and discharges are shown on the y axis. Four return periods ranging from 8 to 34 years are shown. The uncertainty bounds in flood frequency are generated from the 128 behavioral TOPMODEL parameter sets. The annual maximum data were used in the frequency analysis. It can be seen that the simulated discharge frequencies completely bracket the frequencies from observations. This reveals that the combination of LARS-WG and TOPMODEL can represent flood frequencies well.

Fig. 5.

Comparison of observed and simulated flood frequencies. The simulated flood frequencies are from TOPMODEL and LARS-WG downscaled data on the basis of baseline scenario. The simulation uncertainty bounds represent values between min and max estimation.

Fig. 5.

Comparison of observed and simulated flood frequencies. The simulated flood frequencies are from TOPMODEL and LARS-WG downscaled data on the basis of baseline scenario. The simulation uncertainty bounds represent values between min and max estimation.

d. Uncertainty quantification

The total ensemble uncertainty M is the variance of extreme floods predicted. To relate M to the uncertainty sources, the superscripts j, k, and l in represent a combination of TOPMODEL uncertainty parameter set j, GCM k, and emission scenario l. In this study, j varies from 1 to 128, k varies from 1 to 6, and l varies from 1 to 3. Details of the quantification are explained in the following sections. The chain in which TOPMODEL uncertainty parameters, GCMs, and emission scenarios are combined is shown in Fig. 6.

Fig. 6.

Combinations of emission scenarios, GCMs, and TOPMODEL uncertainty parameters. The details of GCMs are shown in Table 1.

Fig. 6.

Combinations of emission scenarios, GCMs, and TOPMODEL uncertainty parameters. The details of GCMs are shown in Table 1.

It has been argued that the ANOVA approach (Zwiers 1987, 1996) is based on a biased variance estimator that underestimates the variance when a small sample size is used (Bosshard et al. 2013). To reduce the bias effects on uncertainty contribution quantification, a subsampling method proposed by Bosshard et al. (2013) was used in this study. This subsampling method selects two samples from the largest sample set and generates a new sample set to be used for ANOVA. In this study, we selected two TOPMODEL parameter sets out of all the 128 sets, and the total number of combinations is C(128, 2) = 8128. With this sampling the superscript j in calculating was replaced with , which is a 2 × 8128 matrix as follows:

 
formula

Based on ANOVA, the total sum of squares (SST) can be divided into sums of squares due to the individual and combined effect:

 
formula

where SSA is the uncertainty contribution of TOPMODEL uncertainty parameters, SSB is the uncertainty contribution of GCMs, SSC is the contribution of emission scenarios, and SSI is the contribution of their combined effect.

The terms can be estimated using the subsampling procedure as follows (SSI is computed as the residual; Bosshard et al. 2013):

 
formula
 
formula
 
formula
 
formula
 
formula

where the minus symbol in the superscript parentheses indicates the averaging over the particular index. Variable H is the number of TOPMODEL uncertainty parameter sets (128 in this study), K is the number of GCMs (six in this study), and L is the number of emission scenarios (three in this study). Then the contribution of uncertainty sources to the overall uncertainty of is calculated as follows:

 
formula
 
formula
 
formula
 
formula

where , , , and have values between 0 and 1 and represent uncertainty contributions from TOPMODEL parameters, GCMs, emission scenarios, and combined effects, respectively. Variable I equals 8128 in this study. As shown in Eqs. (9)(12), the subsampling approach is necessary because it guarantees that every contributor has the same denominator I. The same denominator is used to make sure that the intercomparisons among the contributions from TOPMODEL uncertainty parameter, GCMs, emission scenarios, and combined effects are not affected by their different sampling numbers. The combined effect represents the influence from simultaneous variations among all the three uncertainty variables. It should be noted that the uncertainty quantification approach takes all sources together, and it does not repeat ANOVA for each source.

4. Results

a. Changes in extreme floods

Figure 7 shows the boxplots of extreme floods for three time periods: baseline, 2046–65, and 2080–99. The boxplots are generated from 18 scenarios (three emission scenarios for each of the six GCMs) and 128 TOPMODEL uncertainty parameter sets. The annual maximum discharge data from 1000-yr daily scale simulations were used to calculate the frequencies. The upper and lower ends indicate the highest and lowest discharges, and an uncertainty bound indicates the interval between the upper and lower ends. They are illustrated using the 500-yr return period discharges in the 2080–99 period.

Fig. 7.

Boxplots of extreme floods for three time periods: baseline, 2046–65, and 2080–99. The boxplots are generated from 18 scenarios (three emission scenarios for each of the six GCMs) and 128 TOPMODEL uncertainty parameter sets.

Fig. 7.

Boxplots of extreme floods for three time periods: baseline, 2046–65, and 2080–99. The boxplots are generated from 18 scenarios (three emission scenarios for each of the six GCMs) and 128 TOPMODEL uncertainty parameter sets.

Compared with the baseline case, the 2046–65 period shows a slight increase in median values and a significant increase in uncertainty bounds; for example, for 500-yr floods, the median increases by 4.5% and the upper end increases by 63.0%. Such large uncertainties indicate that it is extremely difficult to precisely estimate a flood value with a return period of interest. Similarly, compared with the baseline, in the 2080–99 case, median values increase slightly, but upper ends and uncertainty bounds increase significantly (the upper end increases by 111.8%). This indicates that more severe extreme floods could occur; for example, for 500-yr floods, the median could increase by 6.4%. Such increases in extreme flood magnitude could pose severe risk to flood defense infrastructures, and this suggests that the current flood defense standard may need to be upgraded for adaptation to future climate. In both the 2046–65 and 2080–99 cases, within the uncertainty bounds floods could be much larger than the medians, which are close to the lower bounds.

Comparing 2046–65 and 2080–99, it can be seen that the upper ends become greater and lower ends become smaller in 2080–99. This means that the uncertainty becomes larger with the increase of projection time. The increasing uncertainty bounds from 2046–65 to 2080–99 may be because projection uncertainties in emission scenarios and GCMs increase.

Figure 8 shows the boxplots of extreme floods under different emission scenarios. It can be seen that, in the 2046–65 case, the uncertainty bounds of the A1B scenario are larger than those of the A2 and B1 scenarios. However, in the 2080–99 case, the A2 scenario generates the largest uncertainty bounds among the three scenarios. These results indicate that scenario assumption influence is much stronger in the 2080–99 case than in the 2046–65 case. In addition, comparing the 2046–65 and 2080–99 cases, it can be seen that the B1 emission scenario always generates less severe extreme floods. This may be because the B1 emission scenario assumes the future world is sustainable with rapid changes in economic structures and more efforts in introducing clean technologies.

Fig. 8.

Boxplots of extreme floods for three future time periods: baseline, 2046–65, and 2080–99 in the three emission scenarios. In each panel, the boxplots are generated from six GCMs and 128 TOPMODEL uncertainty parameter sets.

Fig. 8.

Boxplots of extreme floods for three future time periods: baseline, 2046–65, and 2080–99 in the three emission scenarios. In each panel, the boxplots are generated from six GCMs and 128 TOPMODEL uncertainty parameter sets.

b. Uncertainty source quantification

Figure 9 shows uncertainty source quantification results for different return period extreme floods in two different future time periods: 2046–65 and 2080–99.

Fig. 9.

Uncertainty contribution for floods with return periods ranging from 8 to 500 years in time periods 2046–65 and 2080–99. The uncertainty contributions are represented using stripes with different colors.

Fig. 9.

Uncertainty contribution for floods with return periods ranging from 8 to 500 years in time periods 2046–65 and 2080–99. The uncertainty contributions are represented using stripes with different colors.

In the 2046–65 case, it can be seen that the GCMs contribute most of the uncertainty in all the return periods. The TOPMODEL parameters contribute less than the combined effect of TOPMODEL parameters, GCMs, and emission scenarios, but more than the emission scenarios. It should be noted that contributions only represent relative influence but not absolute impacts; therefore, the near-zero contribution of emission scenarios does not mean there is no influence, but means the influence is relatively smaller than others. Compared with the results in 2046–65, in 2080–99 the contributions of GCMs and emission scenarios increase, while the contributions of TOPMODEL parameters and combined effect decrease; GCMs are still the dominant uncertainty contributor. This information indicates that the longer the projection time, the larger the contributions from GCMs and emission scenarios. Developing more sophisticated and accurate GCMs, therefore, is a major challenge to reducing the uncertainty in flood predictions. Also, the above information indicates that hydrological model uncertainty has an important influence on projected extreme floods; thus, hydrological model uncertainty ought to be considered in research on climate change impacts on extreme floods.

The above contribution results are consistent with the analysis in Fig. 8. For example, Fig. 8 shows, in the 2046–65 case, that the influence of emission scenarios is relatively smaller than the 2080–99 case. This is clearly illustrated in Fig. 9.

Previous studies, for example, Prudhomme and Davies (2009) and Kay et al. (2009), have shown the uncertainty of GCMs is significant. Their results are consistent with our research. In our study, however, we also revealed that the combined effect of hydrological model parameters, GCMs, and emission scenarios can have significant influence. This information is extremely important because if the combined effect is neglected, the individual influences of GCMs, emission scenarios, and hydrological model parameters could be overestimated. This information is quantitatively revealed for the first time, according to the best of the authors’ knowledge, and may be very beneficial for climate change impact studies.

The uncertainty contributions are varying; for example, in 2046–65, parameter contribution varies from 4.0% to 9.0%, GCM contribution varies from 70.9% to 75.5%, and combined effect varies from 18.7% to 20.7%. These results suggest that the uncertainty contribution quantification should be conducted for return periods of interest independently from other return periods.

c. Discussion

Compared with the study by Qin and Lu (2014), which considered only the uncertainties in GCMs and emission scenarios for flood frequency analysis under climate change, the new framework in our study uses DDS-AU to consider the hydrological model uncertainty. As shown in our results, hydrological model uncertainty accounts for up to 9.0% of the variance while emission uncertainty accounts for up to 4.0% only; therefore, considering hydrological model uncertainty is very essential.

Compared with previous research that endeavored to quantify extreme flood uncertainty under climate change (Prudhomme et al. 2003; Wilby and Harris 2006; Minville et al. 2008; Najafi et al. 2011; Steinschneider et al. 2012; Teng et al. 2012), in this research, a variance decomposition approach was incorporated into the extreme flood uncertainty quantification, and therefore the individual contributions and combined effects of different uncertainty sources can be quantitatively compared, revealing the most important uncertainty sources to the overall variance of floods.

It should be noted that the uncertainty in downscaling was not considered in the uncertainty influence intercomparison in this study, though it can be incorporated in the new framework. This is because the simulated floods using LARS-WG downscaled data are in good agreement with observed data (shown in Fig. 5). In this study, a midscale basin was used to demonstrate the proposed uncertainty quantification framework, and some of the results in this study may not be transferable to other sizes/types of catchments, for example, the changes of extreme flood magnitude in future periods and the influence of uncertainty sources. However, the proposed new framework can be applied to other sizes/types of catchments. In addition, although TOPMODEL has been used in our case study, this model can be replaced with other hydrological models that are appropriate to describe catchment hydrological processes. Also, different hydrological models can be included in the new framework, which will allow for the consideration of the model structural uncertainty.

Note that a threshold value of 0.7 is used for NSE in this research, resulting in a total of 128 behavioral parameter sets. The value is selected to represent the hydrological simulation uncertainty, that is, most of the observed discharges are bracketed by the uncertainty bounds and there is only one exception (the 2004 peak discharge) in this case study. The NSE threshold value will have an effect on the uncertainty contributions, but it should be selected using the above principle, reflecting an appropriate level of model predictive uncertainty.

The ANOVA approach assumes independence among different uncertainty samples. The selected GCMs may be interdependent because of the similarity in model structures. However, as Bosshard et al. (2013) revealed, the dependence among GCMs could be diminished in discharge-related investigation.

In this research, the GCM data are from CMIP4, because currently the LARS-WG model can be used to downscale CMIP4 data only. In the future, the CMIP5 data could be included in the proposed framework when they can be downscaled using LARS-WG or other methods.

5. Conclusions

This study presents a variance-based uncertainty assessment framework to quantify the individual and combined impacts of uncertainty sources from GCMs, emission scenarios, and hydrological models on future extreme floods. This framework was applied to the Biliu River basin, northeastern China, and the following results are presented.

First, a more comprehensive uncertainty assessment framework that quantifies different uncertainty sources from GCMs, emission scenarios, and hydrological models is developed. This framework provides very useful information on the variations of future extreme floods and on respective and combined uncertainty contributions of GCMs, emission scenarios, and hydrological models.

Second, it is found that the combined effects of GCMs, emission scenarios, and hydrological models have significant impacts on extreme floods in future periods and could be larger than those of emission scenarios alone. This result implies that the individual influences of GCMs, emission scenarios, and hydrological model uncertainty on extreme floods could be overestimated if the combined effects are neglected.

Third, in both the 2046–65 and 2080–99 periods, GCMs are the dominant contributor to extreme flood uncertainty. This implies that the uncertainty in future extreme floods could be significantly reduced only when the accuracy of GCMs is improved.

The proposed framework should be tested on other sizes/types of case studies to investigate the changes of extreme flood magnitude in future periods and the influence of uncertainty sources. In addition, other uncertainty sources, such as different hydrological models, and nonstationary hydrological model parameters that can be affected by future climate change, should be incorporated into the proposed framework.

Acknowledgments

This study was supported by the National Natural Science Foundation of China (Grants 51320105010, 51279021, 91547116, and 41571022). The first author gratefully acknowledges the financial support provided by the China Scholarship Council. The authors are deeply indebted to the editors and three anonymous reviewers for their valuable time and suggestions that greatly improved the quality of this paper. The data of Biliu basin were obtained from the Biliu reservoir administration.

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