PUBLICATIONS. Journal of Geophysical Research: Atmospheres

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1 PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE Key Points: Climate model biases are nonstationary over much of North America The difference in biases is comparable to the climate change signal The uncertainty of impacts may have been underestimated in most impact studies Correspondence to: J. Chen, Citation: Chen, J., F. P. Brissette, and P. Lucas-Picher (2015), Assessing the limits of bias-correcting climate model outputs for climate change impact studies, J. Geophys. Res. Atmos., 120, , doi:. Received 26 SEP 2014 Accepted 15 JAN 2015 Accepted article online 20 JAN 2015 Published online 12 FEB 2015 Assessing the limits of bias-correcting climate model outputs for climate change impact studies Jie Chen 1, François P. Brissette 1, and Philippe Lucas-Picher 1,2 1 École de Technologie Supérieure, Université du Québec, Montreal, Quebec, Canada, 2 Centre ESCER, Université du Québec à Montréal, Montreal, Quebec, Canada Abstract Bias correction of climate model outputs has emerged as a standard procedure in most recent climate change impact studies. A crucial assumption of all bias correction approaches is that climate model biases are constant over time. The validity of this assumption has important implications for impact studies and needs to be verified to properly address uncertainty in future climate projections. Using 10 climate model simulations, this study specifically tests the bias stationarity of climate model outputs over Canada and the contiguous United States (U.S.) by comparing model outputs with corresponding observations over two 20 year historical periods ( and ). The results show that precipitation biases are clearly nonstationary over much of Canada and the contiguous U.S. and where they vary over much shorter time scales than those normally considered in climate change impact studies. In particular, the difference in biases over two very close periods of the recent past are, in fact, comparable to the climate change signal between future ( ) and historical ( ) periods for precipitation over large parts of Canada and the contiguous U.S., indicating that the uncertainty of future impacts may have been underestimated in most impact studies. In comparison, temperature bias can be considered to be approximately stationary for most of Canada and the contiguous U.S. when compared with the magnitude of the climate change signal. Given the reality that precipitation is usually considered to be more important than temperature for many impact studies, it is advisable that natural climate variability and climate model sensitivity be better emphasized in future impact studies. 1. Introduction The Intergovernmental Panel on Climate Change stated that climate warming is unequivocal and the continued emission of greenhouse gases will cause further warming and changes in all components of the climate system [Intergovernmental Panel on Climate Change, 2013]. The assessment of climate change impacts mainly relies on climate model outputs, derived from either general circulation models (GCMs) (or Earth system models (ESMs)) or regional climate models (RCMs). However, climate model outputs are generally considered too biased to be used as direct inputs in environmental models for climate change impact studies [Sharma et al., 2007; Christensen et al., 2008; Maraun et al., 2010; Chen et al., 2013a]. To overcome this problem, several bias correction methods have been developed and used in hundreds of climate change impact studies [e.g., Chen et al., 2013b; Themeßl et al., 2011; Johnson and Sharma, 2011; Teutschbein and Seibert, 2012; Mpelasoka and Chiew, 2009]. However, there are many controversies in using the bias-corrected climate model outputs for climate change impact studies [Chen et al., 2013a; Ehret et al., 2012; Muerth et al., 2013; Maraun, 2013]. Most bias correction methods are criticized for impairing the inherent advantages of climate models by altering the spatial-temporal field consistency and the relations among variables, and because they violate conservation principles [Ehret et al., 2012]. Moreover, all bias correction approaches ranging from simple scaling to sophisticated distribution mapping are based on an assumption that climate model biases are stationary over time [Hewitson and Crane, 2006; Piani et al., 2010; Maraun, 2012; Maurer et al., 2013]. This assumption has been implicitly accepted in most climate change impact studies, and only a few verification studies have been conducted so far. The bias stationarity of climate model outputs is usually assessed based on the bias-corrected results. If the performance of a bias correction method in the validation period is as good as that in the calibration period, the bias of climate model outputs can be considered to be stationary over the test period. For example, Piani et al. [2010] validated a gamma distribution-based quantile mapping method for correcting RCM-simulated daily precipitation over Europe using a split sample approach (one historical period for CHEN ET AL American Geophysical Union. All Rights Reserved. 1123

2 calibrating the method and the other one for validation). The results showed that the bias correction method performs reasonably well not only for the mean but also for extremes. Terink et al. [2010] corrected RCM-simulated precipitation and temperature by fitting the mean and coefficient of variation of the observation and found that bias correction led to satisfactory results. The differences between RCM-simulated and observed precipitation and temperature decreased significantly, even though the corrected precipitation was less satisfactory for a few given periods. These studies imply that RCM biases are generally stationary over the historical periods. Maurer et al. [2013] specifically examined the bias stationarity of climate modelsimulated precipitation and temperature over historical periods for 20 individual grid boxes over North America. They found that on average, the GCM bias is statistically the same between two different sets of years for most locations. Teutschbein and Seibert [2013] also investigated the bias stationarity of RCM simulations by using two contrasting historical periods representing either the reference or the future climate. They tested the performance of six bias correction schemes over both periods. Their results indicated that the quantile mapping method showed the best performance for nonstationary conditions, even though none of the bias correction methods was able to completely remove the bias of climate model simulations over the validation period. Maraun [2012] proposed a pseudoreality approach by taking one climate model as a reference to correct another climate model. This method allows testing the bias stationarity assumption in a changing climate and found that biases are relatively stable for seasonal mean temperature and precipitation sums. However, there is no guarantee that results from the pseudoreality can be transferred to the real world [Maraun, 2012]. Even though bias correction approaches are capable of reducing the bias of climate model outputs to a certain extent, no bias correction approach can completely remove biases over a validation period, especially for higher-order statistics [Teutschbein and Seibert, 2012, 2013; Chen et al., 2013a]. Remaining biases may result in significant errors in climate change impact studies, especially when the projected climate change signal over historical and future periods is of the same order of magnitude or smaller than these biases. In particular, a more straightforward way to test bias stationarity consists of directly comparing model outputs with corresponding observations over two historical periods and without any bias correction. By directly comparing biases over the two time periods, there is no need to take into account the performance of correction schemes. Accordingly, this study tests the bias stationarity of climate model-simulated precipitation and temperature over Canada and the contiguous United States (U.S.) by comparing two consecutive 20 year periods ( and ). Additionally, the difference in bias over the two consecutive historical periodsisfurthercomparedwiththeclimate change signal of climate model simulations between reference ( ) and future ( ) periods. The difference in biases betweentwoperiodsiscalculatedasthe difference (relative for precipitation and absolute for temperature) of the biases between the climate model outputs and the corresponding observations for each 20 year period. If biases are not constant over two very close time periods, there is little hope they will be stationary for periods separated by 50 to 100 years, as is commonly done in climate change impact studies. Over a longer time period, natural climate variability and differences in climate sensitivities between the real climate and the climate model could result in an increased bias. Moreover, if biases are not stationary, the difference in bias can be compared to the climate change signal to assess the robustness of the signal. 2. Data and Methods 2.1. Data This study was conducted over Canada and the contiguous U.S. Both observed and climate model-simulated data were extracted for this region. Instead of using irregularly spaced station data, gridded daily precipitation and maximum and minimum temperatures (Tmax and Tmin) data sets were used in this study. The gridded data for Canada are the Hutchinson et al. [2009] 10 km data set created using a thin plate smoothing spline algorithm. In the U.S., the 5 km Santa Clara data set was used [Maurer et al., 2002; Livneh et al., 2013], which was gridded using the synergraphic mapping algorithm [Shepard, 1984]. These gridded data were derived from observed daily precipitation Tmax and Tmin from approximately 20,000 National Oceanic and Atmospheric Administration and Cooperative Observer (Co-op) stations. To consider the uncertainty related to climate models when verifying the bias stationarity hypothesis, eight different climate models with different spatial resolutions were selected for a total of 10 model runs. CHEN ET AL American Geophysical Union. All Rights Reserved. 1124

3 Table 1. General Information of All Climate Models in This Study Category Model Name Driver Resolution (Latitude Longitude) Abbreviation Source Number of Grid Boxes GCM RCM Canadian General Circulation Model (v3.1) Canadian Earth System Model (v2.5.4) Model for Interdisciplinary Research on Climate (v2.7.1) Model for Interdisciplinary Research on Climate Earth System Model (v2.7.1) Meteorological Research Institute-Coupled atmosphere-ocean global climate model (v2.5.9) Meteorological Research Institute Earth System Model (v2.8.1) Regional Climate Model (Ouranos and University of Quebec at Montreal, v4.2.3) Regional Climate Model (Canadian Centre for Climate Modelling and Analysis, v4) CGCM CanESM MIROC MIROC-ESM MRI-CGCM MRI-ESM CGCM CRCM4-C NCEP CRCM4-N loki.qc.ec.gc.ca/dai/dai-e.html# CanESM CanRCM CanRCM Specifically, precipitation, Tmax and Tmin from six global models and two regional models were used. Details about the models are presented in Table 1. The six global models consist of three GCMs (CGCM3, MIROC5, and MRI-CGCM3) and three ESMs (CanESM2, MIROC-ESM, and MRI-ESM1) with different spatial resolutions ranging between (latitude longitude) and The Earth system models can be considered as advanced versions of GCMs which contain more complex components such as the terrestrial carbon cycle. The two RCMs were developed by two different institutes in Canada. The CRCM4 was developed by the Ouranos Consortium and University of Quebec at Montreal. It was run at a spatial resolution of 45 km over the North American domain using version (CGCM3 pilot = simulation aev ) and version (National Centers for Environmental Prediction (NCEP) reanalysis pilot = simulation ade )[Music and Caya, 2007, 2009]. The CanRCM4 was developed by the Canadian Centre for Climate Modelling and Analysis. It was driven with the CanESM2 at its boundaries over two different resolutions (0.44 and 0.22 ). Daily data were used for all climate models. All the model data cover the period In addition, the CGCM3 model under the B1 greenhouse gases emission scenario also covers the period to allow for the comparison of biases against the climate change signal. Tmax and Tminwereaveragedtomeantemperatureforbothobservedandmodeled data. Consequently, from this point on, temperature will be used to simplify terminology Method In order to calculate the biases of climate model outputs for a specific grid box, the gridded time series of the observations were first averaged to each GCM and RCM grid scale. The bias of modeled precipitation (B P ) and temperature (B T ) was then calculated for all grid boxes and two historical periods ( and ) using equations (1) and (2). B P ¼ ðp mod P obs Þ=P obs (1) B T ¼ T mod T obs (2) where P mod and P obs, respectively, represent the modeled and observed precipitation and T mod and T obs, respectively, represent the modeled and observed temperature. The bias stationarity of climate model-simulated precipitation and temperature was first tested based on the performance of a bias correction method over a validation period. The bias correction method used in this study is a distribution mapping approach combining daily translation (DT) [Mpelasoka and Chiew, 2009] for CHEN ET AL American Geophysical Union. All Rights Reserved. 1125

4 Figure 1. (a d) Bias pattern of the Third Generation Canadian General Circulation Model (CGCM3)-simulated mean annual precipitation (PCP) and temperature (TMP) over two 20 year historical periods ( and ). MAV is the mean absolute value of biases across all grid boxes over Canada and the contiguous U.S. Figure 2. Bias pattern of the Third Generation Canadian General Circulation Model (CGCM3)-simulated mean winter precipitation (PCP) and temperature (TMP) over two 20 year historical periods ( and ). MAV is the mean absolute value of biases across all grid boxes over Canada and the contiguous U.S. CHEN ET AL American Geophysical Union. All Rights Reserved. 1126

5 Figure 3. Bias (relative error for precipitation and absolute error for temperature) of corrected mean annual and winter precipitation (PCP) and temperature (TMP) for the period. The bias correction was calibrated by the Third Generation Canadian General Circulation Model (CGCM3)-simulated daily precipitation and temperature for the period and applied to the period. MAV is the mean absolute value of biases across all grid boxes over Canada and the contiguous U.S. temperature and precipitation, as well as the local intensity scaling (LOCI) [Schmidli et al., 2006] for precipitation probability of occurrence. The bias correction method was calibrated over the period and then applied to the period. First, the LOCI method was used to correct the precipitation occurrence, insuring that the wet-day frequency of corrected precipitation at the calibration period is equal to that of the observed data at the same period. The DT method is then applied to correct the frequency distribution of precipitation amounts and temperature with 100 quantile divisions. The bias correction was conducted at the monthly scale. More details about this bias correction method can be found in Chen et al. [2013b]. The bias stationarity was also directly verified by comparing model outputs against corresponding observations over two historical periods. Based on biases calculated using equations (1) and (2), the difference in bias over the two historical periods was computed for all grid boxes. The difference in bias was then compared with the climate change signal in terms of mean (annual and seasonal) and extreme (95th percentile) values for both precipitation and temperature. The climate change signal was calculated using equation (3) for precipitation (CCS P ) and equation (4) for temperature (CCS T ). CCS P ¼ ðp mod P mod Þ=P mod (3) CCS T ¼ ðt mod T mod Þ (4) where P mod and P mod represent the climate model precipitation for the periods and , respectively. T represents the temperature. The bias stationarity of climate model outputs was also verified by using multimodel ensemble mean precipitation and temperature derived from 10 climate simulations. Since different climate models have different spatial resolutions, all models were first regridded to the CGCM3 grid scale using the nearest-neighbor interpolation method. The difference in bias was then calculated for each individual model and for all grid boxes. At the last step, the mean values of the difference in bias were calculated by averaging all 10 climate simulations. CHEN ET AL American Geophysical Union. All Rights Reserved. 1127

6 Figure 4. (a d) Difference in biases (DB) of mean annual precipitation (PCP) and temperature (TMP) (% for precipitation and C for temperature) over two 20 year historical periods ( and ) versus climate change signal (CCS) between reference ( ) and 20 year future ( ) periods for the Third Generation Canadian General Circulation Model (CGCM3) over North America. MAV is the mean absolute value of DB or CCS across all grid boxes over Canada and the contiguous U.S. The bias of climate model outputs, the difference in bias, and the climate change signal were investigated using the mean absolute value (MAV) as a metric. The MAV is defined as the mean value of the absolute difference over each grid box. The one-tailed paired t test was used to test the difference between the difference in bias and the climate change signal at the significant level of P = The spatial variability of bias nonstationarity was also investigated for mean annual and winter precipitation. All precipitation grid boxes over Canada and the U.S. were first classified into six groups according to the updated Köppen-Geiger climate classification [Kottek et al., 2006]. The MAV of difference in bias was then calculated for each group. Due to the data availability of RCMs and observations in Canada, the difference in bias was computed over two consecutive 20 year periods. In reality, 30 year periods have been more commonly used to define climatology as well as for climate change impact studies. In order to confirm that the use a 20 year period is adequate at capturing the natural climate variability, the procedure was also tested using two consecutive 30 year historical periods ( and ) for both mean annual precipitation and temperature derived from CGCM3. This analysis was only carried over the contiguous U.S. where longer observation time series are available. 3. Results 3.1. Bias Pattern of the Modeled Precipitation and Temperature Figure 1 presents the biases of CGCM3-simulated mean annual precipitation and temperature for and The results show that CGCM3 is biased for both precipitation and temperature with MAVs of 19.6% and 2.4 C, respectively, across all grid boxes and two time periods. The bias is especially large for the western U.S. and Canada, as the GCM experiences difficulties in mountainous areas. This can also be due to inadequacies in the observational data set due to the relatively sparse observational network in CHEN ET AL American Geophysical Union. All Rights Reserved. 1128

7 Figure 5. (a d) Difference in biases (DB) of mean winter precipitation (PCP) and temperature (TMP) (% for precipitation and C for temperature) over two 20 year historical periods ( and ) versus climate change signal (CCS) between reference ( ) and 20 year future ( ) periods for the Third Generation Canadian General Circulation Model (CGCM3) over North America. MAV is the mean absolute value of DB or CCS across all grid boxes over Canada and the contiguous U.S. mountainous areas. A larger bias in temperature is observed for Canada than the U.S., but this pattern is not observed for precipitation. Generally, both historical periods display a similar spatial pattern for both precipitation and temperature biases. However, the magnitude of the bias differs from one period to the next over many grid points, and especially for precipitation, even though this is not easily discernable when looking at Figure 1. The mean seasonal precipitation and temperature are more biased than the annual counterparts, especially for precipitation over western North America. Since the trends are similar for all seasons, only the results of CGCM3 for the winter season are presented in Figure 2. The MAV is 31.6% for precipitation and 3.5 C for temperature across all grid boxes and both time periods. Specifically, precipitation is more biased than the period for western Canada, while the opposite is observed for western and central U.S Bias-Corrected Precipitation and Temperature The bias correction method calibrated over the period was used to correct the CGCM3-simulated precipitation and temperature for the period. Figure 3 shows the bias (relative difference between corrected and observed precipitation and absolute difference for temperature) for the corrected mean annual and winter precipitation and temperature for the validation ( ) period. Since the bias for the calibration period is almost zero, results are not presented. Generally, the biases of CGCM3-simulated precipitation and temperature can be considerably reduced by using a bias correction method. The MAV of biases is reduced from 18.4% to 9.5% for mean annual precipitation and from 2.2 C to 0.6 C for mean annual temperature. For mean winter precipitation and temperature, the values, respectively, change from 29.7% to 16.0% and from 3.1 C and 1.3 C. The bias of the corrected mean annual precipitation and temperature is much smaller than that of winter values, especially for temperature. The remaining bias of corrected precipitation and temperature indirectly reflects the nonstationarity of climate model biases. CHEN ET AL American Geophysical Union. All Rights Reserved. 1129

8 Figure 6. (a d) Difference in biases (DB) of 95th percentile daily precipitation (PCP) and temperature (TMP) (% for precipitation and C for temperature) over two 20 year historical periods ( and ) versus climate change signal (CCS) between reference ( ) and 20 year future ( ) periods for the Third Generation Canadian General Circulation Model (CGCM3) over North America. MAV is the mean absolute value of DB or CCS across all grid boxes over Canada and the contiguous U.S Difference in Bias Over Two Historical Periods The differences in bias of the mean annual precipitation and temperature between and derived from the CGCM3 over Canada and the contiguous U.S. are presented in Figure 4. The bias of mean annual precipitation is clearly not stationary, with the difference in bias ranging from 55.2% to 34.7% for a MAV of 9.7% across Canada and the contiguous U.S. (Figure 1a). The second period ( ) is more biased than the first ( ) in central Canada, while the opposite is observed for the central and western U.S. (CGCM3 shows positive biases for both periods in these regions as presented in Figure 1). In comparison, the climate change signal for mean annual precipitation varies from 31.1% to 43.5% between and , with a MAV of 17.3% (Figure 4b). The difference in bias is greater than the climate change signal for a large number of grid boxes. This is especially striking for southern Canada and most of the U.S. In the U.S., the MAV of the climate change signal is equal to 6.2%, while it is 50% larger for the difference in bias (9.2%). The paired t test shows that the absolute value of the difference in bias is significantly larger than that of the climate change signal for the contiguous U.S. at the P = 0.05 level. These are robust results, considering that we are comparing differences in bias between two consecutive 20 year periods against the climate change signal for two 20 year horizons separated by 80 years. Compared to the climate change signal, the difference in bias is a relatively small source of uncertainty for mean annual temperature. The climate change signal averages 4.1 C, which is significantly larger than the 0.6 C average value of difference in bias over Canada and the contiguous U.S. While the climate change signal dominates the difference in bias for the period, this may not be the case for a less distant future horizon. The nonstationarity of precipitation and temperature biases is also observed at the seasonal scale and was found to be even larger than at the annual scale. Figure 5 presents the difference in bias versus the climate change signal for mean winter precipitation and temperature. In Figures 5a and 5b, the difference in bias of mean winter precipitation is comparable to or larger than the climate change signal for most of Canada and the contiguous U.S. Once again, this is especially true for southern Canada and the contiguous U.S. CHEN ET AL American Geophysical Union. All Rights Reserved. 1130

9 60 (a) Mean annual precipitation 40 Difference in bias (%) CGCM3 CanESM2 MIROC5 MIROC-ESM MRI-CGCM3 MRI-ESM1 CRCM4-C CRCM4-N CanRCM4-44 CanRCM4-22 MMEM (b) Mean winter precipitation 100 Difference in bias (%) CGCM3 CanESM2 MIROC5 MIROC-ESM MRI-CGCM3 MRI-ESM1 CRCM4-C CRCM4-N CanRCM4-44 CanRCM4-22 MMEM Figure 7. Box plot of the difference in biases (%) over two 20 year historical periods ( and ) for mean annual and winter precipitation derived from 10 climate model simulations and multimodel ensemble mean (MMEM). The number of grids for constructing each box plot was presented in Table 1. On each box, the central mark is the median, the edges of the box are the 25th and 75th percentiles, the whiskers extend to the most extreme datapoints that the algorithm considers to not be outliers, and the outliers are plotted individually. For plotting simplicity, several outliers of box plots constructed by the difference in bias have been omitted. Especially, the paired t test shows that the absolute value of the difference in bias is significantly larger than that of the climate change signal for the U.S. at P = However, for Canada, the former is significantly smaller than the latter. As was the case with annual temperature, temperature biases are mostly smaller than the climate change signal at the seasonal scale (Figures 5c and 5d), although there are regions where they are comparable, such as the eastern U.S. Similarly to the mean annual and seasonal precipitation, the bias of extreme daily precipitation is also not stationary, even though the difference in bias of extreme daily precipitation is slightly smaller than that of mean annual and winter precipitation (Figure 6a). The difference in bias ranges from 56.6% to 31.9% with a MAV of 9.1% across Canada and the contiguous U.S. The difference in bias in Canada is consistently larger than that in the contiguous U.S. with a MAV of 10.2% for the former and 6.7% for the latter. The climate change signal of extreme daily precipitation ranges from 30.3% to 36.6% between and with a MAV of 12.8%. Similarly, the climate change signal is stronger in Canada than in the U.S. with respective MAV equal to 15.2% and 7.8% (Figure 6b). The difference in bias is comparable to the climate change signal for southern Canada and most of the U.S. Again, the difference in bias is significantly larger than the climate change signal for the U.S., but not for Canada in terms of absolute values, when using the paired t test at the significant level of P = The bias of daily extreme temperature is relatively stationary (Figures 6c and 6d) as it is mostly smaller than the climate change signal. However, extreme daily temperature is more nonstationary than the mean annual and seasonal temperature with a MAV of 0.7 C, especially for central North America. The climate change signal is also stronger over this region than in other parts of Canada and the contiguous. Overall, the climate change signal for extreme temperature is weaker than for mean values. For example, the climate change signal of extreme temperature averages 2.6 C, which is considerably smaller than the 4.1 C for mean annual temperature. The aforementioned results have been verified for other global and regional climate models. In the latter case, biases were also verified when the RCM was driven with a reanalysis at its boundaries. To make for an CHEN ET AL American Geophysical Union. All Rights Reserved. 1131

10 3 (a) Mean annual temperature 2 Difference in bias ( o C) CGCM3 CanESM2 MIROC5 MIROC-ESM MRI-CGCM3 MRI-ESM1 CRCM4-C CRCM4-N CanRCM4-44 CanRCM4-22 MMEM (b) Mean winter temperature Difference in bias ( o C) CGCM3 CanESM2 MIROC5 MIROC-ESM MRI-CGCM3 MRI-ESM1 CRCM4-C CRCM4-N CanRCM4-44 CanRCM4-22 MMEM Figure 8. Box plot of the difference in biases ( C) over two 20 year historical periods ( and ) for mean annual and winter temperature derived from 10 climate model simulations and multimodel ensemble mean (MMEM). The number of grids for constructing each box plot was presented in Table 1. On each box, the central mark is the median, the edges of the box are the 25th and 75th percentiles, the whiskers extend to the most extreme datapoints that the algorithm considers to not be outliers, and the outliers are plotted individually. easier intercomparison, Figures 7 and 8 present box plots of the difference in bias of mean annual and winter precipitation and temperature for the outputs of six global models and two Canadian RCMs (CRCM4 and CanRCM4), as well as for the multimodel ensemble mean. Each box plot is built using all of the model grid boxes over Canada and the contiguous U.S. Several observations can be drawn from these two figures. While there are some minor differences, the results about the outputs of CGCM3 mentioned earlier can be extended to other climate models. The use of a more complex Earth system models had no impact on the biases nonstationarity. The advanced Earth system model may have advantages in terms of reducing the bias of its outputs but has little advantage in overcoming the bias nonstationarity. Increasing the resolution from GCM-scale to middle- and high-resolution RCMs also had little impact on the outputs. If anything, more variability was observed, which is not surprising considering the much larger number of grid boxes and considering that RCM grid boxes were not averaged to GCM grid boxes. This shows that the nonstationarity of biases is the result of natural climate variability embedded in the climate model nonlinear equations. However, driving CRCM4 with NCEP reanalysis somewhat improved bias stationarity, especially for temperature, which is not a surprising observation, since reanalysis (at least in theory) should track observations and, as a result, should have a more stationary bias. This property is somewhat transferred to the RCM, as it used NCEP reanalysis as its boundary conditions. Figure 9 presents the difference in bias for the multimodel ensemble mean precipitation and temperature at the annual and seasonal (winter) scales. Results observed for CGCM3 can mostly be extended to the multimodel ensemble mean. The multimodel ensemble mean precipitation and temperature biases display spatial patterns similar to that of CGCM3 at both the annual and seasonal scales. Specifically, the difference in bias for the multimodel ensemble mean annual precipitation ranges from 61.5% to 42.8% with a MAV of 12.4% across Canada and the contiguous U.S., which is even slightly larger than that of the CGCM3 simulated annual precipitation. Similarly to the individual CGCM3 model, the winter precipitation is more nonstationary than the annual precipitation witha22.5%differenceinbiasinterms of the MAV across Canada and the contiguous U.S. Temperature is also found to be relatively stationary for the multimodel ensemble mean at both the annual and winter scales. In the case of temperature, CHEN ET AL American Geophysical Union. All Rights Reserved. 1132

11 Figure 9. Difference in biases of multimodel ensemble mean annual and winter precipitation (PCP) and temperature (TMP) over two 20 year historical periods ( and ). MAV is the mean absolute value of difference in biases across all grid boxes over Canada and the contiguous U.S. Table 2. MAV of the Difference in Biases (%) a Source Model Northern CAN Western U.S. Central CAN Central U.S. Southern CAN Northern U.S. Southern U.S. Annual CGCM CanESM MIROC MIROC-ESM MRI-CGCM MRI-ESM CRCM4-C CRCM4-N CanRCM CanRCM Mean Winter CGCM CanESM MIROC MIROC-ESM MRI-CGCM MRI-ESM CRCM4-C CRCM4-N CanRCM CanRCM Mean a The MAV was calculated over two historical periods ( and ) for mean annual and winter precipitation derived from 10 climate model simulations over six climate classification of North America based on the updated Köppen-Geiger climate classification (CAN = Canada and U.S. = United States). CHEN ET AL American Geophysical Union. All Rights Reserved. 1133

12 Table 3. MAV of the DB Over Two 30 Year ( and ) and Two 40 Year ( and ) Historical Periods Versus That of the CCS Between the 30 Year Reference ( ) and Future ( ) Periods, as Well as the 40 Year Reference ( ) and Future ( ) Periods for Mean Annual Precipitation (%) and Temperature ( C) a Variable however, the multimodel ensemble mean is more stationary than that of the individual models. For example, the difference in bias of CGCM3 simulated annual temperature is 0.6 C in terms of the MAV, while this value decreases to 0.3 C for the multimodel ensemble mean. Box plots of the difference in bias of the multimodel ensemble mean precipitation (Figure 7) and temperature (Figure 8) are consistent with the results presented in Figure 9. The multimodel ensemble mean would normally be expected to be more stationary than any individual model. However, this study shows that this is not the case for precipitation. This is because all climate models apparently underestimate the natural variability of precipitation over the chosen time period. For example, the observed precipitation data suggest a 4.7% increase in mean annual precipitation from to over Canada and the contiguous U.S. However, climate models project smaller changes ranging from 0.5% to 3.9% with a MAV of 1.2%. These results may partly be due to an insufficient number of ensemble members, thus resulting in a biased ensemble mean. On the other hand, the bias of multimodel ensemble mean temperature is more stationary than any of the individual models. For example, the observed data suggest a 0.63 C increase in mean annual temperature over Canada and contiguous U.S. for the two historical periods, while climate models project increases in temperature ranging from 0.26 C to 1.14 C with a MAV of 0.58 C, which is very close to that of observed data. Table 2 presents the spatial variability of bias nonstationarity for mean annual and winter precipitation for all climate models. The difference in bias of mean precipitation is largest for Northern Canada, although it is not possible to discount potential observation biases due to extremely poor station coverage. Large differences in bias are also observed in the western U.S., possibly in part due to the complex surface elevation of this mountainous area. Precipitation is much more variable over mountainous areas, and climate models may have more difficulties at representing this variability. This is partly because subgrid processes are not explicitly represented at the climate model scale and because the topography cannot be adequately represented at the model scale. As mentioned earlier, deficiencies in the observational record over mountainous areas may also explain this behavior. The difference in bias is relatively small for central North America and especially over the southern U.S. where the topography is flat. However, it should be noted that the climate change signal is also weakest over the same region. The difference in bias was also compared against the climate change signal between the 30 year reference ( ) and future ( ) periods for the contiguous U.S. The MAV of the difference in biases versus that of the climate change signal is presented in Table 3 for CGCM3-simulated precipitation and temperature. Similarly to the 20 year period, the difference in bias of precipitation over the two consecutive 30 year periods is comparable to that of the climate change signal between the 30 yearlong future and reference periods for the contiguous U.S. For temperature, the climate change signal was again much larger than the difference in bias. Similar results (Table 3) were also obtained using 40 year horizons ( and for the recent past and for climate change). The difference in bias was particularly large for the 40 year horizon. However, this larger bias may simply be the result of the decreasing number of weather stations when going too far back in time. The use of larger time windows requires going further back in time and further increases the risk of having biases linked to differences in the observational network. Nonetheless, this indicates that results obtained using 20 year time slices appear to be robust. 4. Discussion and Conclusion 30 Year Period 40 Year Period DB CCS DB CCS PCP TMP a These data are simulated by the Third Generation Canadian General Circulation Model (CGCM3) over the contiguous United States. This study investigated the bias stationarity of climate model outputs a crucial assumption when using bias correction approaches for climate change impact studies. Prior to testing for bias stationarity, the annual and seasonal mean bias pattern of climate models (with results from CGCM3 presented in the paper) was CHEN ET AL American Geophysical Union. All Rights Reserved. 1134

13 presented for two 20 year historical periods for both precipitation and temperature. The results indicate that climate model precipitation and temperature outputs are biased. Both time periods display similar spatial patterns for precipitation and temperature bias, even though the magnitude of the bias is somewhat different for each period. The use of an appropriate bias correction method can remove almost all biases over the calibration period. However, when applied over the validation period, biases remain. These are relatively minor for temperature at the annual scale. However, remaining biases can reach up to 9.5% for mean annual precipitation and 16.0% for mean winter precipitation in terms of the MAV. The nonstationarity of biases has to be interpreted as a function of absolute bias values. For example, the nonstationarity component of temperature outputs is only a small part of the bias. In such cases, the nonstationarity is largely not problematic for impact studies. On the other hand, if bias nonstationarity is an important part of the bias, as is the case for precipitation, it has a potentially significant influence on the results of climate change impact studies. The nonstationarity of the biases and impact on impact studies can also be investigated by directly comparing the difference in bias over the two consecutive historical periods against the climate change signal between a future time horizon and the reference periods. If the difference in bias is comparable to or even larger than the climate change signal, this has very important implications on the uncertainty of impact studies. The results of this work indicate that climate model biases are not constant over a much shorter time horizon than most climate change impact studies for precipitation. Only one emission scenario (B1) was used to represent a possible future. Different results may be obtained in terms of the difference between the difference in bias and climate change signal when using other emission scenarios (e.g., A2 and A1B). However, the use of different scenarios (or different climate model) should not impact the conclusion about the nonstationarity of climate model biases. In particular, the typical 10 to 20% projected precipitation change in many impact studies [e.g., O Gorman, 2012; Chen et al., 2011a, 2011b; Piao et al., 2010] must be interpreted very carefully, especially in the presence of a small number of climate projections, since the climate change signal is possibly of the same magnitude (and smaller in some cases) as the uncertainty error brought in by the assumption of bias stationarity. Additionally, the conclusion of this study differs from that of many others [e.g., Piani et al., 2010; Terink et al., 2010; Maurer et al., 2013] which considered biases of climate model outputs as being generally stationary. This may be because those previous studies were mostly concerned with evaluating improvements provided by bias correction methods. On the other hand, this paper is directly concerned with the impact of natural variability on bias stationarity. Bias correction remains nonetheless needed as most impact models are unable to provide an adequate real-world response when using raw outputs from climate models. In comparison to the magnitude of the climate change signal, temperature biases were found to be relatively stationary over most of Canada and the contiguous U.S. As such, bias-correcting temperature is a reasonable solution to deal with temperature biases when using climate model outputs for impact studies. In comparison to GCMs, the advanced Earth system model and middle- to high-resolution RCMs have potential advantages in terms of reducing output biases but have shown little advantages in overcoming the nonstationarity problem. In other words, bias magnitude over the reference period appears not to be related to bias stationarity over time. In this respect, bias nonstationarity appears to be mostly related to climate natural variability and climate sensitivity, although the former appears to dominate considering the time scale of this study. Furthermore, this study shows that using the multimodel ensemble mean has little impact on the bias nonstationarity of modeled precipitation. While the ensemble mean would normally be expected to be more stationary than for any individual model, this was not the case in this study as it appears that climate models all underestimated the natural variability of precipitation. In other words, precipitation changes over the two chosen historical periods were smaller for all modeled data compared to the observed record. The opposite was found for temperature, indicating that natural variability is much better simulated. While there is no perfect relationship between the magnitude of bias and bias nonstationarity, results apparently indicate that regions where climate models display large biases are more likely to experience nonstationarity issues. However, this behavior is more notable over mountainous areas and in regions where the observational network is less dense. In other words, a combination of deficiencies in the data record and modeling problems over hilly terrain may explain this result. This partly explains why temperature biases are more stationary than for precipitation, since precipitation is generally considered to be more poorly simulated by climate models [Sun et al., 2006; Dai, 2006]. In addition, temperature usually changes CHEN ET AL American Geophysical Union. All Rights Reserved. 1135

14 much more gradually than precipitation in both time and space. Since bias nonstationarity is much more important for precipitation than temperature, water resources impact studies in particular should take steps to represent this additional source of uncertainty and its impact on the overall climate change signal. The incorporation of natural climate variability by systematically using a number of ensemble members for each climate model should be emphasized in all future impact studies. Acknowledgments This work was partially supported by the Natural Science and Engineering Research Council of Canada (NSERC), Hydro-Quebec, and the Ouranos Consortium on Regional Climatology and Adaption to Climate Change. The authors would like to acknowledge the Canadian Centre for Climate Modelling and Analysis, Environment Canada for providing CGCM3, CanESM2, and CanRCM4 data. 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