Impacts of bias nonstationarity of climate model outputs on hydrological simulations

Bias correction methods are based on the assumption of bias stationarity of climate model outputs. However, this assumption may not be valid, because of the natural climate variability. This study investigates the impacts of bias nonstationarity of climate models simulated precipitation and temperature on hydrological climate change impact studies. The bias nonstationarity is determined as the range of difference in bias over multiple historical periods with no anthropogenic climate change for four different time windows. The role of bias nonstationarity in future climate change is assessed using the signal-to-noise ratio as a criterion. The results show that biases of climate models simulated monthly and annual precipitation and temperature vary with time, especially for short time windows. The bias nonstationarity of precipitation plays a great role in future precipitation change, while the role of temperature bias is not important. The bias nonstationarity of climate model outputs is ampli ﬁ ed when driving a hydrological model for hydrological simulations. The increase in the length of time window can mitigate the impacts of bias nonstationarity for stream ﬂ ow projections. Thus, a long time period is suggested to be used to calibrate a bias correction method for hydrological climate change impact studies to reduce the in ﬂ uence of natural climate variability.


INTRODUCTION
The assessment of climate change impacts on the hydrological cycle has been widely investigated during recent years (Graham et  for the future period used as inputs of hydrological models for hydrological impact studies. However, the coarse resolution of GCMs does not meet the need of high resolution for the hydrological models (Maraun et al. ). In parallel, GCMs are imperfect representations of reality with systematic biases found between climate model simulations and observations. To resolve these problems, a number of downscaling methods have been developed during the last two decades. Especially, bias correction becomes a standard procedure when using regional climate model ( During recent years, bias correction methods are also commonly used for GCM's outputs. Since the resolution of climate model outputs is lower than that of observations, bias correction methods also act as downscaling methods.
The usually used bias correction methods range from simple mean-based scaling to sophisticated distributionbased mapping and multivariate or/and multisite correction.
The commonly used bias correction methods are usually based on an assumption that biases of climate models outputs are stationary. In other words, these bias correction methods assume climate models outputs present the same biases in magnitude and direction between historical and future periods. However, this assumption may not be valid, as pointed out in a few recent studies (e.g. Buser

Maraun () verified the bias stationary assumption in
RCMs for European seasonal mean temperature and precipitation sums using a pseudo-reality approach, which considers one climate model as pseudo observation to compare with other climate models simulations. The results showed that biases are relatively stable in general, but bias nonstationarity was identified in some regions where changes in potentially relevant physical variables are significant. This study was conducted in the climate model world, the transferability to real world needs to be further investigated. To test the bias nonstationarity in real-world climate, Chen et al. () compared the biases between climate models simulations and corresponding observations over two historical periods. The results showed that biases of climate models simulated precipitation are nonstationary even for two close historical periods, while temperature biases are relatively stationary. This study attributed the bias nonstationarity of precipitation to natural climate variability (multi-decadal climate variability). A similar study was also carried out by Wang et al. (), who tested bias nonstationarity of precipitation in the eastern United States determined by a skill score, which compares the errors of a downscaling method over validation period with the errors of observations between calibration and validation periods. The results show that precipitation biases are nonstationary at most of the stations, especially for the annual extreme precipitation. Taking

Study area
The case study was conducted at the Hanjiang River basin The GCM-simulated daily precipitation and maximum and minimum temperatures were extracted from the database of CMIP5. In order to capture the uncertainty related to climate models, 17 GCMs were used in this study (Table 1)  method first detects the trend and breakpoint using the Mann-Kendall test (Mann ; Kendall ). If a trend exists, it is removed for the period after the breakpoint using a linear method. To preserve the seasonality, the detrending method was applied for each month, respectively.

Calculation of difference in bias
After detrending, the variation of observed and GCM-simulated precipitation and temperature within the 1901-2000 period is considered to be only attributed to the natural climate variability. Since natural climate variability is inherently complex and manifests itself over various temporal and spatial scales, this study only investigates its impacts on bias correcting climate model outputs over decadal and multi-decadal temporal and watershed spatial scales. In order to investigate the impacts of natural climate variability at the temporal scale, the 100-year precipitation and temperature time series are divided into several independent decadal and multi-decadal periods. The time window consists of 10, 20, 33 and 50 years for the 100year period. For example, when the time window is 20 years, the 100-year period is divided into five 20-year periods (1901-1920, 1921-1940, 1941-1960, 1961-1980 and 1981-2000). The first period of each time window (e.g. 1901-1910 for 10-year window) is used as the baseline period.
For each decadal or multi-decadal period, the biases of GCM-simulated monthly and annual precipitation (BP) and temperature (BT) relative to observations are calculated using Equations (1) and (2), respectively:  RB is calculated based on the differences in bias among multiple periods using Equation (3): where DB max and DB min indicate the maximum and minimum values of differences in bias between historical periods and the baseline period, respectively. The outliers were removed when calculating the RB to ensure the reasonability of estimation. The outliers are detected if they are larger than Q 75 þ 1.5 × (Q 75 -Q 25 ) or smaller than Q 25 -  (4) and (5): where j indicates the number of decadal or multi-decadal periods from 2001 to 2100, and subscript b indicates the baseline period (e.g. 1901-1910, 1901-1920, 1901-1933 or 1901-1950). These precipitation and temperature time series without detrending were used to retain climate change tendency.
Then, SNR is calculated as the absolute ratio of CCS and RB for both monthly and annual precipitation and temperature. If the CCS is relatively smaller than the RB, e.g. the SNR being smaller than 1, the RB is considered to have large impacts on future climate changes and their hydrological impacts and vice versa.

Hydrological modeling
The hydrological simulations were carried out using a lumped hydrological model named as the Two-Parameter Monthly Water Balance Model (Xiong & Guo ). It is a simple and monthly lumped rainfall-runoff model with only two physical parameters. The first parameter is c, which represents a coefficient to take account of the effect of the time scale change. The second parameter is SC, which represents the field capacity of a watershed. The monthly runoff (Q) was simulated using Equations (6) and (7): where t indicates the number of months, E and EP indicate the monthly actual and potential evapotranspiration, The observed monthly streamflow was used to model calibration (1961-1980) and validation (1981-2000).
Model calibration was done automatically using shuffled

RESULTS
Bias nonstationarity of precipitation and temperature  However, different results are observed for annual mean temperature. Even though the difference in bias varies with time, the anthropogenic climate change is significantly greater than the bias nonstationarity for annual mean temperature, especially for the future periods ( Figure 5(b)). In other words, even though the bias nonstationarity can affect the detection of the real anthropogenic climate change of annual mean temperature, the influence is limited.
Comparing to future climate change signal, the temperature bias can be considered as stationary. However, for the first The SNR of precipitation and temperature is also calculated at monthly scale. Figure 6 shows are less important in the wet season than in the dry season.
Therefore, the impacts of bias nonstationarity in the dry season need to be paid more attention than in the wet season and annual scale. In terms of the mean monthly temperature (Figure 6(b)), the SNR from May to November is larger than other months for the mid and far future, and the maximum values of the SNR present between May and August over each decadal or multi-decadal period. In addition, the comparison of the SNR between annual and monthly temperature shows that the SNR at the monthly scale is smaller than that at the annual scale, especially for short time windows, while for the 50-year window, the SNR between June and October is comparable to or even larger than that at the annual scale. In the near future , the SNR in each month is comparable to or smaller than one for the short time window, because of the weak climate change signal.

Propagation of bias nonstationarity in hydrology
The propagation of bias nonstationarity of climate models simulated precipitation and temperature in hydrology is investigated by running a hydrological model over the Hanjiang watershed. Figure

Uncertainty of baseline observations
In this study, the CRU dataset was used as the baseline to calculate the bias of GCM-simulated precipitation and temperature.
The CRU data is gridded data obtained by interpolating gauged precipitation and temperature to regular grids. Due to limited gauges used for interpolation, the CRU dataset may also be biased. In order to investigate the uncertainty related to the baseline dataset, another dataset produced by the University of Delaware (version 4.01, available at www.esrl.noaa.gov/ psd/data/gridded/data.UDel_AirT_Precip.html), with a spatial resolution of 0.5 from 1901 to 2000, the same as the CRU dataset, is also used to estimate the difference in bias between each historical period and the baseline period. Figure 10 shows the difference in bias for mean annual precipitation and temperature obtained from CRU and the University of Delaware (USA) dataset for 10-, 20-, 33-and 50-year windows. Similarly, the difference in bias varies with time for all time windows.
Meanwhile, the range of difference in bias decreases with the extension of the time window. Generally, the range of difference in bias is similar for two datasets, even though the magnitude is not exactly the same.

Uncertainty of greenhouse gas emission scenarios
The role of bias nonstationarity on future climate changes may rely on greenhouse gas emission scenarios, as different scenarios predict different future climate change signal. All the above results are based on the scenario of RCP4.5. In order to investigate the uncertainty related to the greenhouse gas emission scenario, the climate change signal of mean annual precipitation and temperature predicted by RCP4.5 and RCP8.5 are compared ( Figure 11). The results showed that climate change signals predicted by RCP4.5 and RCP8.5 are comparable for precipitation, while the former is much smaller than the latter for temperature in terms of both median value and uncertainty related to GCMs for all time windows. Thus, the use of different greenhouse gas emission scenarios would not change the conclusion that the role of precipitation bias nonstationarity is important in future precipitation change.
However, the impacts of temperature bias nonstationarity may depend on emission scenarios. For a high emission scenario (e.g. RCP8.5), the bias nonstationarity will become even less important, while for a low emission scenario (e.g.

RCP4
.5), it may become important for near future periods.

Methods to estimate natural climate variability
For the historical period, the difference in bias between two periods is caused by natural climate variability, because the anthropogenic climate change is pre-removed. Thus, to investigate the role of bias nonstationarity in future climate change, the range of bias is defined as 'noise', i.e. the difference between maximum and minimum values of biases across multiple periods with outliers deleted. An alternative approach using the standard deviation of bias over multiple periods can also be used to estimate natural climate variability. Table 2

Future work
This study only investigated the bias nonstationarity of precipitation and temperature for the historical period. Thus, the bias nonstationarity only resulted from natural climate variability.
However, for a future period, bias nonstationarity resulted