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  • View in gallery

    Location map of the (a) Manicouagan-5 and (b) Hanjiang watersheds. The upstream part of the Hanjiang watershed was used in this study and its outlet (Danjiangkou) is noted with a green triangle.

  • View in gallery

    Methodological steps for the evaluation of bias correction methods using natural climate variability as a baseline. The 10 members of a climate model are given by mb1–mb10.

  • View in gallery

    Estimation of natural climate variability for (a),(b) daily precipitation and (c),(d) temperature (average of maximum and minimum temperatures) in terms of (left) mean and (right) standard deviation, at the annual and seasonal scale for observations and four climate models over the Manicouagan-5 watershed. The first bar of each histogram represents the natural climate variability of observations, whereas the other four bars represent the natural variability of four GCMs (CanCM4, CNRM-CM5, CSIRO Mk3.6.0, and HadCM3).

  • View in gallery

    Portrait diagram of precipitation biases in terms of units of natural variability for raw climate model outputs and bias-corrected time series for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. The precipitation time series are corrected with four bias correction approaches (LS, LOCI, DT, and DBC). The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. In (j), different groups of metrics are shown (I = mean of all days, II = mean of wet day, III = standard deviation of all days, IV = standard deviation of wet days, V = quantiles of all days, VI = quantiles of wet days, and VII = metrics of precipitation occurrence), as presented in Table 2.

  • View in gallery

    Portrait diagram of minimum temperature biases in terms of units of natural variability for raw climate model outputs and bias-corrected time series for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. The temperature time series are corrected with four bias correction approaches (LS, LOCI, DT, and DBC). The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. Groups I–III in (h) represent mean, standard deviation, and quantiles of temperature, respectively, as presented in Table 2.

  • View in gallery

    Mean hydrographs simulated using observed (OBS), raw GCM-simulated, and four bias correction methods’ corrected precipitation, and maximum and minimum temperatures for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. Mean hydrographs simulated using 10 runs of CanCM4 and observed precipitation and temperatures are also presented for comparison. (Please note the different scales on the y axis.)

  • View in gallery

    Portrait diagram of streamflow biases in terms of units of natural variability simulated by raw climate model outputs and bias-corrected time series for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. Four bias correction approaches (LS, LOCI, DT, and DBC) are used for precipitation and temperatures. The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. Groups I–IV in (j) represent mean, standard deviation, quantiles, and other aspects (time variables and frequency of high and low flows) of daily streamflow, as presented in Table 2.

  • View in gallery

    Portrait diagram of streamflow biases in terms of units of natural variability simulated by raw climate model outputs and bias-corrected time series for both (left) calibration (1961–80) and (right) validation (1981–2000) periods over the Hanjiang watershed. Four bias correction approaches (LS, LOCI, DT, and DBC) are used for precipitation and temperatures. The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. Groups I–IV in (j) represent mean, standard deviation, quantiles, and other aspects (time variables and frequency of high and low flows) of daily streamflow, as presented in Table 2.

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Using Natural Variability as a Baseline to Evaluate the Performance of Bias Correction Methods in Hydrological Climate Change Impact Studies

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  • 1 State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan, China
  • | 2 Ouranos Consortium, Montreal, Quebec, Canada
  • | 3 École de technologie supérieure, Université du Québec, Montreal, Quebec, Canada
  • | 4 École de technologie supérieure, and Centre pour l'étude et la simulation du climat à l'échelle régionale, Université du Québec, Montreal, Quebec, Canada
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Abstract

Postprocessing of climate model outputs is usually performed to remove biases prior to performing climate change impact studies. The evaluation of the performance of bias correction methods is routinely done by comparing postprocessed outputs to observed data. However, such an approach does not take into account the inherent uncertainty linked to natural climate variability and may end up recommending unnecessary complex postprocessing methods. This study evaluates the performance of bias correction methods using natural variability as a baseline. This baseline implies that any bias between model simulations and observations is only significant if it is larger than the natural climate variability. Four bias correction methods are evaluated with respect to reproducing a set of climatic and hydrological statistics. When using natural variability as a baseline, complex bias correction methods still outperform the simplest ones for precipitation and temperature time series, although the differences are much smaller than in all previous studies. However, after driving a hydrological model using the bias-corrected precipitation and temperature, all bias correction methods perform similarly with respect to reproducing 46 hydrological metrics over two watersheds in different climatic zones. The sophisticated distribution mapping correction methods show little advantage over the simplest scaling method. The main conclusion is that simple bias correction methods appear to be just as good as other more complex methods for hydrological climate change impact studies. While sophisticated methods may appear more theoretically sound, this additional complexity appears to be unjustified in hydrological impact studies when taking into account the uncertainty linked to natural climate variability.

Corresponding author address: Jie Chen, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 299 Bayi Road, Wuchang Distinct, Wuhan, Hubei 430072, China. E-mail: jiechen@whu.edu.cn

Abstract

Postprocessing of climate model outputs is usually performed to remove biases prior to performing climate change impact studies. The evaluation of the performance of bias correction methods is routinely done by comparing postprocessed outputs to observed data. However, such an approach does not take into account the inherent uncertainty linked to natural climate variability and may end up recommending unnecessary complex postprocessing methods. This study evaluates the performance of bias correction methods using natural variability as a baseline. This baseline implies that any bias between model simulations and observations is only significant if it is larger than the natural climate variability. Four bias correction methods are evaluated with respect to reproducing a set of climatic and hydrological statistics. When using natural variability as a baseline, complex bias correction methods still outperform the simplest ones for precipitation and temperature time series, although the differences are much smaller than in all previous studies. However, after driving a hydrological model using the bias-corrected precipitation and temperature, all bias correction methods perform similarly with respect to reproducing 46 hydrological metrics over two watersheds in different climatic zones. The sophisticated distribution mapping correction methods show little advantage over the simplest scaling method. The main conclusion is that simple bias correction methods appear to be just as good as other more complex methods for hydrological climate change impact studies. While sophisticated methods may appear more theoretically sound, this additional complexity appears to be unjustified in hydrological impact studies when taking into account the uncertainty linked to natural climate variability.

Corresponding author address: Jie Chen, State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 299 Bayi Road, Wuchang Distinct, Wuhan, Hubei 430072, China. E-mail: jiechen@whu.edu.cn

1. Introduction

The impacts of climate change on watershed hydrology have drawn increasing attention in the environmental and water resources communities (Arnell et al. 2001; Bates et al. 2008; IPCC 2013). Reliable estimates of the potential climate change impacts on hydrology rely on high-resolution and high-quality climate projections. General circulation models (GCMs) [or Earth system models (ESMs)] are the major tools providing climate change information for impact studies. However, GCM outputs are generally considered too coarse to be used as direct inputs in hydrological models for assessing the climate change impacts on hydrology. In addition, GCM outputs (e.g., precipitation and temperature) usually exhibit systematic and sometimes large biases relative to the corresponding observations (Maraun et al. 2010; Mearns et al. 2012; Sillmann et al. 2013). Nested regional climate models (RCMs) that use GCM lateral boundary conditions improve the climate simulations in many aspects, especially in terms of the representation of mesoscale atmospheric processes for producing local variables such as precipitation (Feser et al. 2011; Di Luca et al. 2012; Evans and McCabe 2010; Tselioudis et al. 2012; Lucas-Picher et al. 2013). However, RCM simulations are still prone to biases and still have shortcomings in terms of their direct use in finescale impact studies. For example, compared to same-scale observations, most RCMs tend to underestimate heavy precipitation and to overestimate the occurrence of light precipitation and wet-day frequency (Murphy 1999; Fowler et al. 2007). Furthermore, RCM ensembles are still relatively small compared to GCMs and might not allow a full exploration of uncertainty.

To overcome the above limitations of climate model outputs, several bias correction approaches have been developed (Ines and Hansen 2006; Sharma et al. 2007; Christensen et al. 2008; Mpelasoka and Chiew 2009; Piani et al. 2010; Themeßl et al. 2012; Johnson and Sharma 2012) and implemented in climate change impact studies (Chen et al. 2011a, 2013a; Teutschbein and Seibert 2012; Eisner et al. 2012; Ahmed et al. 2013). These bias correction methods can be classified as simple mean-based scaling (e.g., Schmidli et al. 2006; Chen et al. 2013b) and as sophisticated distribution-based mapping (e.g., Mpelasoka and Chiew 2009; Themeßl et al. 2012). Mean-based scaling involves correcting all climate events within a certain time scale (e.g., monthly or seasonal) using a constant correction factor. In contrast, distribution-based mapping corrects the higher moment of the distribution using parametric and nonparametric methods. Quantile mapping is one of the most common distribution-based correction methods and generally performs better than mean-based scaling. For example, Themeßl et al. (2011) compared seven statistical and bias correction methods in downscaling RCM daily precipitation and found that the quantile mapping method outperformed all other methods. Teutschbein and Seibert (2013) evaluated the performance of six bias correction methods for correcting RCM precipitation and temperature under a nonstationary climate (using two contrasting historical periods to represent the reference and future climates). Their study indicated that the distribution mapping method performed better than the mean-based scaling method for nonstationary climates, even though bias correction cannot completely remove the biases of climate model simulations over the validation period. Lafon et al. (2013) compared the performance of four bias correction methods (linear, nonlinear, gamma-based quantile mapping, and empirical quantile mapping) and found that all four methods could robustly correct the first and second moments of the precipitation distribution, while the performance in correcting the third and fourth distribution moments depended on the choice of the bias correction method and the calibration period.

The performance of bias correction methods were also tested in terms of their effects on hydrological modeling and climate change impact studies. For example, Teutschbein and Seibert (2012) tested a set of bias corrections methods (four methods for precipitation and three methods for temperature) for assessing climate change impacts on hydrology for both historical and future periods and found that all seven bias correction methods were capable of reducing the biases of RCM simulations for impact studies. However, the distribution mapping performed better than the mean-based scaling, especially in representing the hydrological extremes. Chen et al. (2013b) compared the performance of six bias correction methods for hydrological modeling over 10 watersheds dispersed across different climate regions of Canada and the contiguous United States. Their results indicated that the performance of hydrological modeling depends on the choice of a bias correction method and the location of a watershed, even though distribution-based mapping generally outperformed mean-based scaling.

Generally speaking, most studies have shown that bias correction methods are able to reduce biases to a certain degree and that distribution-based mapping outperforms mean-based scaling. However, a few recent studies have concluded that distribution-based mapping has a limited advantage over mean-based scaling. For example, White and Toumi (2013) compared the two classes of methods to bias-corrected GCM data prior to downscaling with an RCM and found the mean-based scaling method to be more reliable and accurate than the quantile mapping method. Wang et al. (2016) tested an ensemble of 10 empirical methods (five change factor methods and five bias correction methods) for statistically downscaling GCM precipitation and temperature using a pseudoreality approach by taking one climate simulation as a reference to correct other climate simulations. This study showed that sophisticated bias correction methods only have advantages with respect to reproducing the high-order statistics of precipitation and temperature.

A crucial assumption of all bias correction approaches is that the biases of climate model outputs are stationary. In other words, the biases of climate model simulations are supposed to be constant over historical and future periods. However, climate is strongly dominated by natural variability. The uncertainty related to natural climate variability can be comparable or even larger than that related to climate change signals, especially for the less-distant future (Deser et al. 2012a; Fatichi et al. 2014). In particular, the uncertainty due to natural climate variability is unlikely to be reduced with the improvement of climate model structure and more understanding of the natural climate system (Deser et al. 2012a). Natural climate variability necessarily introduces some level of nonstationarity in climate model biases. A recent study (Chen et al. 2015) showed that the biases of climate-model-simulated precipitation are different over two historical periods, simply because of natural climate variability.

The observed biases between climate model outputs and observations are the sum of two main components: different climate sensitivity due to model structure (the model and the real world react differently to the same forcing) and natural variability. Bias correction schemes can account for the first component, whereas the second one is irreducible, as shown in Chen et al. (2015).

Thus, the natural climate variability should be taken into account for climate change impact studies when using a bias correction method. In other words, one should not necessarily expect a bias correction method to completely remove biases for a climate model simulation. If the remaining biases of the corrected time series for the validation/future period are within the range of the natural climate variability, the bias correction method should be considered reliable and accurate for climate change impact studies. This is better explained by considering the various members of a climate model ensemble. Since postprocessing of a GCM is done to correct the biases due to scale mismatch, model structure, and climate sensitivity, it follows that all members of an ensemble should be corrected using the exact same factors. To bias correct individual members of an ensemble differently (as has been done in a few studies) is hard to justify since it treats members of an ensemble just as if they originated from different climate models. Doing so will bring all members of the ensemble very close to the observations, thus removing the all-important natural climate variability information. Correcting all members differently is akin to saying that there is no value in climate model ensembles and occults the irreducible impact of natural climate variability in our ability (or inability) to bias correct climate model outputs.

Accordingly, this study evaluates the performance of bias correction methods in assessing climate change impacts on hydrology using natural variability as a baseline. Four common bias correction methods ranging from simple linear scaling to sophisticated quantile mapping are tested. The natural climate variability is estimated by a 10-member ensemble of a GCM.

2. Study and data

a. Study area

The study was conducted over two large watersheds (Manicouagan-5 and Hanjiang watersheds) in two completely different climatic regimes (Fig. 1). The Manicouagan-5 is a temperate-climate, snowfall-dominated watershed located in the center of the province of Quebec, Canada, whereas the Hanjiang watershed is a monsoon-rainfall-dominated watershed located in south-central China. The methodological choice of using two widely different watersheds was made to evaluate the potential watershed dependence of conclusions drawn from this study. Additional details on both watersheds are presented below.

Fig. 1.
Fig. 1.

Location map of the (a) Manicouagan-5 and (b) Hanjiang watersheds. The upstream part of the Hanjiang watershed was used in this study and its outlet (Danjiangkou) is noted with a green triangle.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

1) Manicouagan-5 watershed

Manicouagan-5 covers 24 610 km2 of mostly forested area, which is the biggest subbasin of the Manicouagan catchment. It has a moderately hilly topography with a maximum elevation of 952 m MSL and a minimum elevation of 350 m MSL at the watershed outlet. Logging is the only important industrial activity over the watershed, and population density is extremely low. The watershed drains into the Manicouagan-5 reservoir, which is a 2000-km2 annular reservoir within an ancient eroded impact crater. The watershed ends at the Daniel-Johnson Dam, the largest buttressed multiple-arch dam in the world. The average annual precipitation over the watershed is 930 mm, of which about 45% is snowfall. Precipitation is fairly evenly distributed throughout the year. The average maximum and minimum temperatures (Tmax and Tmin) between 1961 and 2000 were 2.3° and −8.0°C, respectively. The daily mean discharge of the Manicouagan-5 River is about 530 m3 s−1. Snowmelt peak discharge usually occurs in May, with a multiyear average of about 2200 m3 s−1.

2) Hanjiang watershed

The Hanjiang watershed is located in south-central China and is one of the largest tributaries of the Yangtze River watershed. The Hanjiang River originates from the south side of the Qinling Mountain and joins the Yangtze River in the city of Wuhan. The Hanjiang watershed is composed of several tributaries draining a surface of approximately 159 000 km2. The catchment above the Danjiangkou reservoir is used in this study and has a surface area of 89 540 km2. The Danjiangkou reservoir serves as a water source for the middle route of the South-to-North Water Diversion Project. The watershed has a subtropical monsoon climate with a mean annual precipitation of about 840 mm. Most precipitation occurs between April and October, resulting in high flows over this period, whereas the remainder of the year sees little precipitation and much lower flows. The average Tmax and Tmin between 1961 and 2000 were 19.8° and 10.0°C, respectively. The daily mean discharge of the Hanjiang River is about 1150 m3 s−1.

b. Datasets

This study uses the observed and climate-model-simulated daily precipitation, Tmax, and Tmin over both watersheds. Observations and climate model simulations used in this study both cover the 1961–2005 period for the Manicouagan-5 watershed and the 1961–2000 period for the Hanjiang watershed. The different calibration and validation periods between both watersheds are related to the availability of streamflow data. The observed precipitation, Tmax, and Tmin for the Manicouagan-5 watershed were taken from the Hutchinson et al. (2009) dataset, which was obtained by interpolating station data to a 10-km grid using a thin plate smoothing spline surface fitting method (Hutchinson et al. 2009). Discharge data for Manicouagan-5 watershed were obtained from mass balance calculations at the dam and provided by Hydro-Québec. The station meteorological data for the Hanjiang watershed were taken from the China Meteorological Data Sharing Service System. The streamflow time series for the Hanjiang watershed was provided by the Bureau of Hydrology of the Changjiang Water Resources Commission. The climate model simulations were taken from the database of phase 5 of the Coupled Model Intercomparison Project (CMIP5). Thirty-one GCMs from 15 modeling centers were selected to adequately represent the model uncertainty (Table 1). Since Manicouagan-5 and Hanjiang are both large watersheds, several grid boxes within and surrounding the watershed were averaged to a single time series using the Thiessen polygon method for both precipitation and temperature. All observed data grid points within the watershed were also averaged.

Table 1.

Basic information of the selected CMIP5 models.

Table 1.

3. Methodology

a. Bias correction methods

Four methods ranging from simple scaling to sophisticated distribution mapping are used to correct biases for daily precipitation, Tmax, and Tmin simulated by 31 GCMs: linear scaling (LS), local intensity scaling (LOCI), daily translation (DT), and daily bias correction (DBC). Since the original version of LOCI only involves the correction of precipitation (occurrence and amounts), the temperature is corrected using a variance scaling approach developed by Chen et al. (2011a), but it is still labeled as LOCI in this study. Since all of these bias correction methods were also used in Chen et al. (2013a,b), they are only briefly described here. More details can be found in those two articles and their references. The four methods can be classified into mean-based approaches (LS and LOCI) and distribution-based approaches (DT and DBC). The mean-based approaches utilize constant monthly correction factors for both their precipitation and temperature time series, while distribution-based approaches correct precipitation and temperature distributions based on monthly correction factors that vary as a function of the distribution quantiles. Alternatively, the four methods can also be classified into approaches with (LOCI and DBC) and without (LS and DT) correction of the wet-day frequency of precipitation. Compared to LS, which only corrects mean precipitation and temperature, LOCI also corrects the wet-day frequency of precipitation and the variance of temperature. DT and DBC share the same algorithm in correcting precipitation amounts and temperature, but the latter also corrects the wet-day frequency. A 0.1-mm precipitation threshold was used to determine dry and wet days. To make a fair comparison, a day with a precipitation amount of less than 0.1 mm is considered as a dry day for GCM-simulated precipitation. Both observed and GCM-simulated precipitation and temperatures are divided into calibration (1961–85 for Manicouagan-5 and 1961–80 for Hanjiang) and validation (1986–2005 for Manicouagan-5 and 1981–2000 for Hanjiang) periods. All of the bias correction methods are calibrated on the first period and applied to the second period on a monthly basis.

b. Hydrological model

To study the impact of bias correction on hydrological variables, a hydrological model must be used. The hydrological simulations in this study were carried out using the Hydro-Québec hydrological model HSAMI (Fortin 2000). HSAMI is a lumped, conceptual rainfall–runoff model that has been used to forecast natural inflows for over 20 years. It is used by Hydro-Québec for streamflow forecasting on nearly 100 watersheds with surface areas ranging from 160 to 69 195 km2. It was also used as an impact model in several climate change impact studies (Minville et al. 2008; Chen et al. 2011a,b, 2012; Poulin et al. 2011; Arsenault et al. 2013; Lucas-Picher et al. 2015). HSAMI has 23 parameters, with two accounting for evapotranspiration, six for snowmelt, 10 for vertical water movement, and five for horizontal water movement. Vertical flows are simulated with four interconnected linear reservoirs including snow on the ground, surface water, and unsaturated and saturated zones. Horizontal flows are routed through one linear reservoir and two-unit hydrographs. The unit hydrograph shapes are based on a two-parameter gamma distribution density function. Both unit hydrographs are then computed and converted into streamflows for the whole watershed. Snow accumulation, snowmelt, soil freezing/thawing, and evapotranspiration are taken into account in this model. Model calibration was done automatically using the Covariance Matrix Adaptation Evolution Strategy (CMAES) (Hansen and Ostermeier 1996, 2001), following the work of Arsenault et al. (2014).

The basin-averaged minimum required daily input data for HSAMI are Tmax, Tmin, and liquid and solid precipitations. The liquid and solid precipitations are partitioned based on the mean temperature. If the mean temperature is ≥2°C, all precipitation is rainfall, if the mean temperature is ≤−2°C, all precipitation is solid. Otherwise, precipitation is linearly partitioned between snow and rainfall. Cloud cover fraction and snow water equivalent can also be used as inputs, if available. A natural inflow or discharge time series is also needed for proper calibration and validation. Model calibration and validation was performed on both watersheds using a typical split-sample approach. The optimal parameter set was chosen based on the Nash–Sutcliffe criteria (Nash and Sutcliffe 1970). The chosen set of parameters yielded Nash–Sutcliffe criteria values of 0.845 (calibration) and 0.828 (validation) for the Manicouagan-5 watershed and 0.814 (calibration) and 0.806 (validation) for the Hanjiang watershed.

c. Verification method

The performance of bias correction methods in hydrological impact studies will be evaluated using natural variability as a baseline. Specifically, the remaining biases of corrected climate model simulations and their simulated hydrological regimes will be expressed in units of natural variability. As mentioned earlier, natural climate variability can be used as a threshold to determine whether or not climate model outputs are biased.

The proposed method consists of three steps for evaluating all four bias correction methods (Fig. 2). The first step involves the estimation of the natural climate variability. One way of estimating the natural climate variability would be to use a very long time series of observed historical data. If the time series are long enough and do not contain the signal of anthropogenic forcing such as greenhouse gas and aerosols, climate statistic variation over different periods can be considered as a manifestation of natural variability. However, there are very few time series long enough to consider such an approach, and none available over the chosen watershed. Alternatively, natural climate variability can be approximately estimated using a multimember ensemble of a climate model. In such ensembles, members only differ in the conditions used to initialize the climate model. Model structure, atmospheric forcing, and climate sensitivity are identical. When using the climate model multimember ensemble, the intermember variability can be considered as an approximation of the natural climate variability. This approach has been used in a few other studies (e.g., Chen et al. 2011b; Deser et al. 2012a,b).

Fig. 2.
Fig. 2.

Methodological steps for the evaluation of bias correction methods using natural climate variability as a baseline. The 10 members of a climate model are given by mb1–mb10.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

To test the reliability of this method, the natural climate variability estimated from GCM multimember ensembles was compared against observed time series for the Manicouagan-5 watershed. In other words, the intermember variability of GCM ensembles was compared against the temporal variability of the observed time series. The observed precipitation and temperature (average of Tmax and Tmin) cover the period 1951–2010. A Mann–Kendall test performed over this period showed no significant trends for both annual precipitation and temperature at the significance level of P = 0.01, so no detrending was performed. There is a warming trend present in the last two decades for Tmax and in the last decade for Tmin, but its contribution is not sufficient to result in a significant trend for mean temperature over the whole 1951–2010 period. To estimate the natural variability using the observed time series, the 1951–2010 period was divided into five 20-yr periods (1951–70, 1961–80, 1971–90, 1981–2000, and 1991–2010). The range of variability for the five periods was evaluated in terms of mean and standard deviation of daily precipitation and temperature at the annual and seasonal scales. Four GCM 10-member ensembles (CanCM4, CNRM-CM5, CSIRO Mk3.6.0, and HadCM3) were also used to estimate natural variability. For each GCM, ten 20-yr periods (the 1961–80 period for each member) were selected and the same statistics (mean and standard deviation) were computed. This is far from being a perfect comparison since the number of 20-yr periods is different between datasets, and there are period overlaps in the observed data. Ultimately, the goal of this comparison is to ensure that using GCM outputs to estimate natural variability is a reasonable approach.

Figure 3 presents the natural climate variability in terms of the mean and standard deviation of precipitation and temperature estimated using both datasets. Even though differences can be observed between the two methods, overall, the multimember ensemble is a reasonable approach to represent the observed natural variability over this watershed. In addition, the four GCMs display a similar natural climate variability for both precipitation and temperature. From these results, it was decided to use just a single ensemble (CanCM4) to quantify the natural climate variability. Natural variability was quantified as the range of values from all members of the ensemble. For example, the mean annual precipitation for the 1961–2005 period for the 10 members of CanCM4 varies between 1016 and 1060 mm. Thus, the natural variability for this specific statistic is defined as 44 mm.

Fig. 3.
Fig. 3.

Estimation of natural climate variability for (a),(b) daily precipitation and (c),(d) temperature (average of maximum and minimum temperatures) in terms of (left) mean and (right) standard deviation, at the annual and seasonal scale for observations and four climate models over the Manicouagan-5 watershed. The first bar of each histogram represents the natural climate variability of observations, whereas the other four bars represent the natural variability of four GCMs (CanCM4, CNRM-CM5, CSIRO Mk3.6.0, and HadCM3).

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

The second methodological step involves framing current observations within a plausible range due to natural climate variability. It is clear that the observed climate of the recent past is only one of many possible realizations. There is no way to characterize this realization that could be hot, cold, dry, humid, or close to the median of all possible realizations. However, assuming that the estimated range of natural variability is reasonable, recent past climate could be as much as one unit of natural variability above (if the current realization is at the low end) or below (if the current realization is at the high end) the recent past climatic value. This is an important methodological choice since narrowing this range—for example, to half a unit of natural variability above and below—would provide better discrimination among postprocessing methods, but at the expense of underestimating natural variability. For example, the observed mean annual precipitation is 912 mm for the Manicouagan-5 watershed. With the natural climate variability estimated using the CanCM4 ensemble, the Manicouagan-5 watershed mean annual precipitation could vary between 868 (912 − 44) and 956 mm (912 + 44).

The third step involves expressing all of the remaining biases of postprocessed precipitation and temperature in terms of units of natural climate variability. If the remaining bias is within the range of natural variability, it is considered as “no apparent bias.” If the remaining bias is outside the range of natural climate variability, there is a significant remaining bias. For example, if the remaining bias of postprocessed mean annual precipitation over the validation period is within 44 mm of the observed value, this is labeled as having no apparent bias for this specific statistic. If the remaining bias is 66 mm, it can be expressed as having a bias of 0.5 units of natural variability [(66 − 44)/44].

To evaluate the performance of bias correction methods in assessing hydrological impacts, the natural variability first has to be estimated for hydrological variables. Natural hydrological variability is defined by considering the 10 flow discharge time series obtained by using the 10-member ensemble of CanCM4 as inputs to the hydrological model. Since climate model outputs are too biased to be used as direct inputs in hydrological models, the DBC method is applied to all 10 members of CanCM4 with a two-step procedure. First, the daily bias correction factors are estimated based on one member of CanCM4 with a median change in both annual mean precipitation and temperature for the calibration period. Second, all 10 members of CanCM4 are corrected based on the correction factors estimated by the median member for both the calibration and the validation periods. As discussed earlier, using the same correction factors for all members is fundamental for preserving the natural climate variability information obtained from the ensemble. By using this approach, natural climate variability can be transferred to the hydrological regime. One problem of this approach is that the median member of precipitation may not be the median of temperature. In this study, an approximate median member for both precipitation and temperature was selected for each watershed. Ongoing work indicates that hydrological modeling results are rather insensitive to the choice of a given member on which to base the bias correction scheme.

For hydrological modeling results, the plausible range of observed hydrological statistics was also estimated as much as one negative and positive unit of natural hydrological variability. To avoid the biases of hydrological model outputs, observed streamflows are represented by simulated discharge using observed precipitation and temperature rather than by measured flows at the watershed outlet. Finally, the remaining biases of hydrological variables are expressed in terms of units of natural variability for both the calibration and the validation periods.

d. Data analysis

All four bias correction methods are first calibrated using GCM-simulated precipitation and temperature for the calibration period, and then they are applied to the validation period. The corrected GCM simulations are then used to drive the HSAMI hydrological model to obtain hydrological simulations for both periods. The bias correction methods’ performances are then evaluated based on their ability to reproduce the observed precipitation, temperature, and streamflow statistics for both calibration and validation periods using natural variability as a baseline. The performance of these four bias correction methods is expressed using the portrait diagram in Gleckler et al. (2008), in which different colors indicate the remaining biases of precipitation, temperature, and streamflow in terms of the natural variability units. The portraits are arranged such that the columns are labeled by the evaluation metrics for precipitation, temperature, or streamflow, and the rows by the GCMs (identifier in Table 1). The evaluation metrics presented in Table 2 are used to evaluate the performance of bias correction methods with respect to reproducing the observed mean, standard deviation, and distribution. The mean and standard deviation are calculated for the entire time series and also on a monthly basis. The distribution is represented by 11 quantiles of the entire distribution. For precipitation, all metrics are calculated based on all-day precipitation, as well as wet-day precipitation. In addition, six metrics [wet-day frequency and mean, standard deviation, and extreme (quantile 0.99) of wet- and dry-day spells] are included to evaluate the correction in precipitation occurrence. Nine additional metrics are also included for evaluating hydrological simulations. They consist of three time variables (time to peak discharge, and the times to the beginning and to the end of flood), and 10-, 20-, and 50-yr return periods of high flow (quantile 0.95) and low flow (quantile 0.05). According to the hydrological regime, the high-flow period is defined as April–June for the Manicouagan-5 watershed and April–October for the Hanjiang watershed, and the low-flow period is defined as July–November for the Manicouagan-5 watershed and November–March for the Hanjiang watershed. In total, 81, 37, and 46 evaluation metrics are used for precipitation, temperature, and hydrology, respectively. The 81 metrics for precipitation are classified into seven groups (noted as I–VII in Table 2): all-day means, wet-day means, all-day standard deviations, wet-day standard deviations, all-day quantiles, wet-day quantiles, and metrics of precipitation occurrence. The 37 metrics for temperature are classified into three groups (noted as I–III in Table 2): all-day means, all-day standard deviations, and all-day quantiles. The 46 metrics for hydrology are classified into four groups (noted as I–IV in Table 2): all-day means, all-day standard deviations, all-day quantiles, and all other metrics (time variables and frequency of high and low flows).

Table 2.

Evaluation metrics for precipitation (PCP), temperature (T), and streamflow (std dev = standard deviation and Q10, Q20, and Q50 represent 10-, 20-, and 50-yr return periods, respectively) in different groups (labeled I–VII). For precipitation, metrics are evaluated twice with one for all-day precipitation (PCP1) and the other for wet-day precipitation (PCP2). All metrics are numbered with a numerical value from 1 to 81 for precipitation, 1 to 37 for temperature, and 1 to 46 for hydrology.

Table 2.

4. Results

a. Climate simulation

Figure 4 presents the portrait diagram of biases in terms of natural variability units for raw GCM-simulated precipitation and when postprocessed with the four bias correction methods over both the calibration and validation periods. Since similar results are obtained for both watersheds, only results for the Manicouagan-5 watershed are presented in Fig. 4 for illustration. The y axis represents the 31 GCMs used in this study and the x axis displays the 81 evaluation metrics, grouped in terms of mean, standard deviation, distribution, and precipitation occurrence (separated by solid vertical lines). Additionally, the mean, standard deviation, and distribution metrics are further grouped for all-day precipitation and wet-day precipitation (separated by dashed vertical lines).

Fig. 4.
Fig. 4.

Portrait diagram of precipitation biases in terms of units of natural variability for raw climate model outputs and bias-corrected time series for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. The precipitation time series are corrected with four bias correction approaches (LS, LOCI, DT, and DBC). The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. In (j), different groups of metrics are shown (I = mean of all days, II = mean of wet day, III = standard deviation of all days, IV = standard deviation of wet days, V = quantiles of all days, VI = quantiles of wet days, and VII = metrics of precipitation occurrence), as presented in Table 2.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

Prior to evaluating the bias correction methods, all GCMs are first evaluated using natural variability as a baseline over both calibration and validation periods. When evaluating GCMs, the differences between raw GCM simulations and observations in evaluation metrics are all expressed in terms of natural variability units. The raw data results clearly show that all GCMs generate biased precipitation outputs for at least some precipitation metrics, even though some GCMs perform much better than others (Figs. 4a,b). A white color means that the bias is smaller than the natural climate variability (no apparent bias), whereas colored areas show biases larger than natural climate variability (true biases). Looking at Figs. 4g–j, it is clear that all bias correction methods can remove the biases of all-day mean precipitation at the annual and monthly scales for the calibration period. However, slight biases still remain over the validation period. The LOCI and DBC methods both remove the wet-day precipitation mean biases, because the wet-day frequency is specifically considered by these two methods. With the exception of all-day mean, the LS method poorly reproduces all other metrics. In particular, considerable negative biases remain for the mean, standard deviation, and distribution metrics of wet-day precipitation for both the calibration and validation periods. These biases occur because GCMs usually overestimate wet-day frequency. This is also the reason why LS-corrected precipitation shows exactly the same biases as the raw GCMs in terms of the metrics of the precipitation occurrence. Similar results are also observed when using the DT method (Figs. 4g,h). Furthermore, this is also the reason why the negative biases remain for small and medium quantiles of wet-day precipitation when using the LS and DT methods.

The standard deviation of all-day and wet-day precipitation is reasonably well corrected when using the LOCI, DT, and DBC methods for the calibration period, even though the latter two methods perform better. However, the standard deviation of LS-corrected precipitation remains biased. The remaining biases over the validation period are larger than those over the calibration period. This is especially true for the wet-day frequency. For example, both the LOCI and DBC methods correct wet-day frequency, as indicated by the “no apparent bias” for the calibration period (white color). However, considerable positive biases remain for the validation period, as all 10 members of CanCM4 simulate too many wet days (precipitation occurs almost every day) for both the calibration and validation periods. This situation makes it very difficult for the bias correction methods to produce outputs that are within this very narrow range of natural variability. For the calibration period, the DBC method performs the best. Over the validation period, however, the LOCI method is just as good.

Figure 5 presents the portrait diagram of the biases for raw GCM-simulated and bias-corrected Tmin for both the calibration and validation periods over the Manicouagan-5 watershed. The bias correction methods’ performance is evaluated by their ability to reproduce 37 metrics representing the mean, standard deviation, and distribution of temperature. Since the DT and DBC use the same algorithm for correcting temperature biases, they are both shown on a single graph. Because very similar results are obtained for both Tmax and Tmin, Fig. 5 only presents the Tmin results. Once again, the raw GCMs’ temperature outputs have considerable biases. All of the bias correction methods do a reasonably good job of reducing temperature bias. In particular, the DT method completely removes all biases for the chosen metrics over the calibration period. The LS method only corrects mean temperature biases; it fails to correct standard deviation and distribution-based metrics. The LOCI method corrects both the mean and standard deviation of Tmin; thus, those metrics are reasonably well reproduced for the calibration period. However, a slight bias remains for the distribution-based metrics, as the distribution is not specifically corrected. The DT method completely removes all biases for the chosen metrics over the calibration period. However, biases remain for the validation period. Even though all bias correction methods are capable of reducing the temperature biases to a certain degree, the performance depends on the choice of bias correction method. LOCI and DT generally perform better than the LS method. However, there is no obvious difference between the LOCI and DT methods.

Fig. 5.
Fig. 5.

Portrait diagram of minimum temperature biases in terms of units of natural variability for raw climate model outputs and bias-corrected time series for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. The temperature time series are corrected with four bias correction approaches (LS, LOCI, DT, and DBC). The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. Groups I–III in (h) represent mean, standard deviation, and quantiles of temperature, respectively, as presented in Table 2.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

b. Hydrological modeling

The raw and postprocessed GCM daily precipitation and temperature time series were both used to drive the hydrological model and generate streamflows. Since modeling results were similar for both watersheds, Fig. 6 only presents the simulated mean hydrographs for both the calibration and the validation periods over the Manicouagan-5 watershed. Two envelopes are shown in each graph. The light gray envelope regroups all GCM runs, including the first run of CanCM4, whereas the dark gray envelope represents the 10-run CanCM4 ensemble. The mean hydrograph envelope obtained from raw GCM simulations displays a large uncertainty over both the calibration and the validation periods (Figs. 6a,b). This large envelope is the result of the various biases present in the raw precipitation and temperature GCM time series. All four bias correction methods are able to significantly reduce precipitation and temperature biases, and this translates into a narrower uncertainty envelope for the hydrological simulations over both the calibration and the validation periods. The difference between bias correction methods is smaller in this case than for the driving precipitation and temperature time series, with the exception of the LS method, which is clearly inferior for the spring flood. All methods perform better for the calibration period than over the validation period. The results presented in Fig. 6 tend to indicate that the apparent advantages of more complex postprocessing techniques do not translate well to the hydrological world.

Fig. 6.
Fig. 6.

Mean hydrographs simulated using observed (OBS), raw GCM-simulated, and four bias correction methods’ corrected precipitation, and maximum and minimum temperatures for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. Mean hydrographs simulated using 10 runs of CanCM4 and observed precipitation and temperatures are also presented for comparison. (Please note the different scales on the y axis.)

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

To better explore this finding, the four bias correction methods are also evaluated in the hydrological world by using 46 hydrological metrics for both watersheds, just as was done for precipitation and temperature. Figures 7 and 8 present the portrait diagrams of simulated hydrological metrics for the Manicouagan-5 and Hanjiang watersheds, respectively. These 46 metrics are classified into four groups that represent, respectively, the mean, standard deviation, distribution, and other key hydrological metrics such as the return period of extreme flow events (see Table 2 for a description). Figures 7 and 8 show that using raw GCM simulations results in poorly simulated hydrological metrics. In other words, the biases of simulated streamflow are much larger than the natural variability for all metrics. When using raw GCM outputs, the hydrological simulations for the Hanjiang watershed are worse than those for the Manicouagan-5 watershed. This is because GCM precipitation and temperature are more biased for the former than the latter (results not shown).

Fig. 7.
Fig. 7.

Portrait diagram of streamflow biases in terms of units of natural variability simulated by raw climate model outputs and bias-corrected time series for both (left) calibration (1961–85) and (right) validation (1986–2005) periods over the Manicouagan-5 watershed. Four bias correction approaches (LS, LOCI, DT, and DBC) are used for precipitation and temperatures. The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. Groups I–IV in (j) represent mean, standard deviation, quantiles, and other aspects (time variables and frequency of high and low flows) of daily streamflow, as presented in Table 2.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

Fig. 8.
Fig. 8.

Portrait diagram of streamflow biases in terms of units of natural variability simulated by raw climate model outputs and bias-corrected time series for both (left) calibration (1961–80) and (right) validation (1981–2000) periods over the Hanjiang watershed. Four bias correction approaches (LS, LOCI, DT, and DBC) are used for precipitation and temperatures. The numbers on the y axis correspond to the climate model identifier in Table 1, whereas the numbers on the x axis correspond to the evaluation metric identifier in Table 2. Groups I–IV in (j) represent mean, standard deviation, quantiles, and other aspects (time variables and frequency of high and low flows) of daily streamflow, as presented in Table 2.

Citation: Journal of Hydrometeorology 17, 8; 10.1175/JHM-D-15-0099.1

All bias correction methods applied to GCM precipitation and temperature outputs resulted in hydrological simulations with a better representation of the chosen 46 metrics, especially for the Hanjiang watershed. Over the Manicouagan-5 watershed, the two quantile-based methods (DT and DBC) performed slightly better than the mean-based methods (LS and LOCI) for the calibration period. The LS method performed the worst, although the differences are much smaller than for precipitation and temperature. All bias correction methods have a similar performance for the calibration period over the Hanjiang watershed. In other words, the mean-based methods are comparable to the quantile-based methods in terms of producing climate simulations for hydrological modeling. In particular, all bias correction methods perform better for the Hanjiang watershed than the Manicouagan-5 watershed, even though raw GCM simulations more poorly represent the hydrological metrics for the former than the latter. This is because the range of natural variability is larger for the Hanjiang watershed. Over the validation period, there appears to be virtually no difference among the four methods for the Manicouagan-5 watershed. For the Hanjiang watershed, the complex distribution mapping methods perform slightly better than mean-based scaling methods in terms of some hydrological metrics (e.g., quantiles of daily streamflow) but do worse for other metrics (e.g., mean and standard deviation of April streamflows). The DT and DBC methods behave similarly over the validation period, which indicates that correcting for the GCM drizzle effect is not needed for hydrological impact studies.

5. Discussion and conclusions

The use of climate model outputs in climate change impact studies is hindered by simulation biases resulting from scale mismatch, model structure, and climate sensitivity. Several bias correction methods with different levels of complexity have been developed and proposed throughout the years to deal with this problem. The performance of bias correction methods has been evaluated and compared in several studies. However, most of the existing studies base their evaluation of method performance only on the ability to reduce biases in model precipitation and temperature time series. Two important aspects are often overlooked in that type of evaluation. The first is natural variability and how neglecting its effect could impact our vision of bias correction performance. The second aspect covers the transferability of the bias reduction to the impact world, such as hydrology in this case. This paper looked at both of these aspects.

This study suggests using natural variability as a baseline to evaluate bias correction methods in assessing climate change impacts on hydrology. This approach is a more reasonable way to compare method performance since it specifically takes into account the concept that biases are not constant, even over short time scales (Chen et al. 2015), because of the inherent chaotic nature of the climatic system. Without such consideration, the more complex methods are more likely to be judged as the best. The rationale behind this approach is twofold. First, if a climate model bias is smaller than the estimated range of natural variability, then that model should be considered as unbiased or with no apparent bias. Bias correcting this model’s outputs to zero serves no scientific purpose and may in fact be detrimental by removing the physical structure between the various time series subjected to correction. Second, this approach serves as a benchmark for the evaluation of a bias correction method’s performance. If the bias of a given metric is within the range of natural variability after correction (for both the calibration and validation periods), the bias correction method is deemed reliable. One of the important ways to achieve this is to adequately estimate the natural variability. There are two main ways of estimating natural climate variability. The first approach makes use of long historical records and compares different metrics over several subperiods. However, the historical record is usually too short to accurately estimate the natural climate variability in most parts of the world. This is especially the case for Canada and China, where most weather stations were set up in the second half of the twentieth century. The second one, commonly done by climate modeling groups, consists of running a climate model with different initial conditions to produce an ensemble of climate simulations (e.g., Deser et al. 2012a,b). A basic comparison over the Manicouagan-5 watershed indicates that a GCM multimember ensemble can be an appropriate proxy for estimating the real-world natural climate variability. Since this comparison has been performed on a single watershed, additional validation would be needed at other locations to generalize this conclusion. In addition, the comparison performed in this paper (Fig. 3) is not perfect since the number of years was larger in the GCM ensemble than in the historical record. In addition, comparing different GCM members should, in theory, provide a wider range of natural variability, since ocean circulation, which is a key driving force behind climate variability, is likely to vary more between GCM members than for the continuous historical record. Accordingly, one might expect the natural variability of the observed record (not the almost 50 years in this case) to be smaller than the value estimated from the GCM ensemble method, and not a comparable value as observed in Fig. 3. This could mean that either natural variability is underestimated by the GCMs or that 50 years is sufficient to properly sample the main modes of variability. Since this study was performed over a single watershed, it is also possible that this result is an outlier and that further studies on natural climate variability should be conducted elsewhere, preferably in the presence of long time series.

Under the proposed natural variability framework, four bias correction methods with different levels of complexity were tested. These four methods ranged from simple mean-based scaling to relatively sophisticated distribution mapping methods. The four methods could also be classified into two groups that correct (or not) wet-day frequency. Other bias correction methods could have been added. However, these four methods include the most common classes of method used to bias correct climate model outputs. As such, the results of this study should be robust enough to be transferred to other approaches.

The results indicate that for climate model outputs, the bias reduction performance depends on both the choice of a bias correction method and on the evaluation metric. Quite predictably, the four tested methods perform as a function of the nature of their correcting algorithms. The mean-based methods perform relatively well at removing biases in mean values, but they fail at reproducing more complex statistics such as standard deviations and the distribution of quantiles. The distribution mapping methods perform much better in that respect. These results are consistent with those of other studies. However, using natural variability as a baseline significantly reduces the performance difference between methods. As such, the apparent advantages of more complex methods become harder to see over the validation period. For example, the mean-based LOCI method performs very similarly to the DBC methods over the validation period, whereas the former is clearly better over the calibration period. This suggests that the conclusions of many existing studies may have been tainted in favor of more complex methods by simply neglecting the nonstationarity of biases. Nonstationarity only gets more problematic for climate change studies, since for future periods, it is not only affected by natural climate variability, but also by differences in climate sensitivities between climate models and the real Earth system.

This paper also looked at the impact of bias-correcting GCM outputs after they are transferred to the impact study world. More specifically, it looks at how the biases of climate model outputs are transferred to the hydrological regime of the two watersheds. Similarly to many other studies, the results clearly show that the bias correction of precipitation and temperature time series is indeed necessary to generate the proper hydrological regime. Overall, the advantage of distribution mapping methods is hard to see over both the calibration and validation periods. They do not perform any better (or worse) over the Manicouagan-5 watershed. The sophisticated methods perform slightly better than mean-based scaling for distribution-based metrics over the Hanjiang watershed, but they perform worse for some other metrics, such as mean and standard deviation of April streamflows. This indicates the climate variables can be overcorrected when using the sophisticated bias correction methods. The worse performance for April streamflows is a good example, as this is the month that bridges the dry and wet seasons. As such, the hydrology appears to be more sensitive to the bias of precipitation inputs. The reason why distribution mapping approaches appear to have little to no advantage over mean-based methods for hydrological modeling is a difficult question to answer. There are likely two components to this behavior. First, GCM precipitation and temperature time series are corrected separately, whereas they are physically coherent variables inside the climate model. Indeed, bias correction can destroy this coherency, which has been a key argument against bias-correcting GCM outputs. The second component is linked to the well-known nonlinear behavior of impact models. This is particularly the case for hydrological models in which subtle modifications to the time series of precipitation and temperature can result in significant hydrological changes. In the case of both watersheds, it appears that the advantages of the more complex methods, which are apparent to some extent in precipitation and temperature time series, get lost when transferred to the hydrological world.

Based on the results of this study, it appears that it may not always be necessary to favor sophisticated bias correction methods over simple ones for hydrological impact studies, especially when taking into account natural variability as a physical limitation to methods of ever-increasing complexity. On the other hand, there are also no downsides to use the more complex methods, apart from more CPU time and more coding time. An important limitation of this study is that it only looked at the impacts on streamflows. Streamflows result from the spatial integration of various nonlinear physical processes combining precipitation and temperature. In such a case, the benefits of more complex postprocessing schemes may be lost, or at least attenuated through this spatial integration. It is possible that other impact studies (e.g., agriculture) may be more sensitive to postprocessing methods, even when taking into account natural variability. In addition, the use of complex postprocessing methods appears to have few downsides for hydrological impact studies, and they perform better than simple methods in terms of producing climate projections. However, results suggest that simple postprocessing methods are very likely adequate for many types of impact studies and that older studies should not be discounted on the basis of the postprocessing method used to correct climate model biases.

To estimate natural variability of hydrological variables, a bias correction procedure was applied to all members of a climate model. This procedure may impact the native natural variability present in the climate models, and this impact may be method dependent. The use of one member to estimate the correction factors and subsequent application to all other members is expected to mostly preserve the native natural variability, but this should be further studied in future work. While results from only one hydrological model were presented in the paper, the proposed framework was also tested with other hydrological models. Results indicate that the conclusions of this study are not sensitive to the choice of a hydrological model. The results obtained from this work are different from previous studies (e.g., Teutschbein and Seibert 2012, 2013; Chen et al. 2013b) that showed that distribution mapping performed better than mean-based scaling for hydrological simulation. These previous studies did not take into account the effects of natural climate variability when evaluating bias correction methods. In other words, while it is always possible to improve the absolute difference between corrected climate simulations and observations with more complex methods, if the gain is within the range of natural variability, it is not real. One conclusion is that more complex methods appear to be correcting details that are buried within the uncertainty due to natural climate variability. A good example of this is the correction of the drizzle effect, which has no effect on this hydrological impact study.

Bias correction methods are needed to reduce climate model output biases for climate change impact studies, even though such methods have been criticized and suffer from the nonstationarity problem (e.g., Maraun et al. 2010; Maraun 2013; Ehret et al. 2012; Chen et al. 2013b, 2015). While the direct use of dynamically downscaled raw regional climate outputs has been successful in a few studies of hydrological impact studies (e.g., Chen et al. 2011b, 2013b), most of the time bias correction is unavoidable for climate change impact studies, especially when using GCM outputs with low spatial resolutions. However, the choice of a postprocessing method should consider the inherent physical limitations due to the uncertainty linked to natural climate variability.

Acknowledgments

This work was partially supported by the Thousand Youth Talents Plan from the Organization Department of CCP Central Committee (Wuhan University, China, Grant 600400008), the National Natural Science Foundation of China (Grant 51525902), the Key Program of the National Natural Science Foundation of China (Grant 51539009), the Natural Science and Engineering Research Council of Canada (NSERC), Hydro-Québec, and the Ouranos Consortium on Regional Climatology and Adaption to Climate Change. The authors would like to acknowledge the contributions of the World Climate Research Programme Working Group on Coupled Modelling and the climate modeling groups listed in Table 1 for making available their respective model outputs. The authors wish to thank Rio-Tinto-Alcan and Hydro-Québec for providing the datasets for the Manicouagan-5 watershed, and the China Meteorological Data Sharing Service System and the Bureau of Hydrology of the Changjiang Water Resources Commission for providing the dataset for the Hanjiang watershed. The authors would also like to thank the anonymous reviewers, whose insightful comments helped improve this paper.

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