In this study, the equidistant cumulative distribution function (EDCDF) quantile-based mapping method was used to develop bias-corrected and downscaled monthly precipitation and temperature for China at 0.5° × 0.5° spatial resolution for the period 1961–2099 for eight CMIP5 GCM simulations. The downscaled dataset was constructed by combining observations from 756 meteorological stations across China with the monthly GCM outputs for the historical (1961–2005) and future (2006–99) periods for the lower (RCP2.6), medium (RCP4.5), and high (RCP8.5) representative concentration pathway emission scenarios. The jackknife method was used to cross validate the performance of the EDCDF method and was compared with the traditional quantile-based matching method (CDF method). This indicated that the performance of the two methods was generally comparable over the historic period, but the EDCDF was more efficient at reducing biases than the CDF method across China. The two methods had similar mean absolute error (MAE) for temperature in January and July. The EDCDF method had a slight advantage over the CDF method for precipitation, reducing the MAE by about 0.83% and 1.2% at a significance level of 95% in January and July, respectively. For future projections, both methods exhibited similar spatial patterns for longer periods (2061–90) under the RCP8.5 scenario. However, the EDCDF was more sensitive to a reduction in variability.
Global climate change leads to a rise in temperature along with changes in precipitation patterns, which are highly variable at the regional or local scale (Santidrián Tomillo et al. 2015). Under the impacts of climate change, precipitation in China has increased by 2%, and the frequency of precipitation events has decreased by 10% from 1960 to 2000 (Liu et al. 2005). Meanwhile, near-surface air temperature has increased by 0.5°–0.8°C during the twentieth century, with an accelerated warming of 1.1°C during the second half of the century, which is slightly higher than the global temperature trend for the same period (Ding et al. 2007; Chen and Frauenfeld 2016). The warming trend and variability of changing precipitation patterns have likely led to more flood and drought hazards (Wang et al. 2011; IPCC 2012). The changes of precipitation patterns will directly affect regional water resources and the availability of the food supply (Dore 2005). In particular, China may become more vulnerable to climate change in the future, because agriculture plays a central role in ensuring the food security for about 1.3 billion people (Piao et al. 2010). The China National Committee for Disaster Reduction (CNCDR) reported that 748 flooding events occurred from 2000 to 2008 in China, which led to 3.6 million houses damaged, over 50 million hectares of crops destroyed, and over US$43 billion incurred as an economic cost (Li et al. 2012). The floods of 1996 and 1998 caused material losses of about US$26 billion and US$30 billion, respectively, and are considered the top two costliest flood events globally (Jiang et al. 2008). Wang and Zhai (2003) found that the severe droughts in 1997 and 1999–2002 over many areas of northern China and the devastating drought over Yunnan in 2010 caused large economic and societal losses. Therefore, better understanding of climate change in the future is essential for ensuring the water and food security of China in the twenty-first century.
The CMIP5 multimodel datasets used for the IPCC Fifth Assessment Report (AR5) are widely used in climate studies, in particular to evaluate potential future changes. The CMIP5 models have higher horizontal and vertical resolution than models from the previous CMIP phases and include more comprehensive treatments of physical processes, which offer unprecedented opportunities to analyze the attribution of climate change and generate regional and continental projections for the twenty-first century (Taylor et al. 2012). However, the outputs of global circulation models (GCMs) remain relatively coarse in terms of their spatial and temporal resolutions, on the order of tens of kilometers at daily or monthly resolutions, which is very coarse compared to that of hydrologic processes and would be unable to resolve significant subgrid-scale features (Grotch and MacCracken 1991; Cloke et al. 2013). Moreover, GCM simulations are biased in both the spatial and temporal scales because of the uncertainty in the parameterization of unresolved processes, which prevents their direct use in climate change impact and adaptation studies (Xu and Singh 2004; Wood et al. 2004; Randall et al. 2007; Ojha et al. 2013). Therefore, it is necessary to downscale and bias correct long-term GCM simulations to obtain fine spatial-scale information (Wood et al. 2004; Fowler et al. 2007; Cavazos and Arriaga-Ramirez 2012; Wang and Chen 2014a).
Both dynamical downscaling and statistical downscaling approaches can be used to remove systematic biases in models and transform simulated climate fields from coarse resolution to a finer spatial resolution (Castro et al. 2005; Maurer and Hidalgo 2008; Rockel et al. 2008; Maraun et al. 2010). The statistical downscaling approach offers a relatively fast and efficient way to formulate the statistical relationship between coarse-resolution climate variables (from climate model outputs) and fine-resolution observations (Fowler and Wilby 2007; Cavazos and Arriaga-Ramirez 2012; He et al. 2016). Several bias-correction methods have been developed to downscale climate variables from climate models, such as the linear-scaling approach (Lenderink et al. 2007), variance scaling (Chen et al. 2011), distribution mapping (Teutschbein and Seibert 2012), and delta-change correction (Graham et al. 2007). In general, bias-correction methods assume the statistical relationship between the historic model simulation and observations will remain stable in the future period, while it has been shown that the distribution is expected to change in the future, especially for the higher-order moments (Wood et al. 2004; IPCC 2007). Compared to conventional bias-correction methods, the equidistant cumulative distribution function (EDCDF) method, developed by Li et al. (2010), uses the distribution of the model output to match all statistical moments with respect to the observations and explicitly incorporates changes in the distribution of the future climate data. This method can incorporate both the GCM climatological mean and variance by taking into account the changes of climate fields in the future period (Watanabe et al. 2012; Aloysius et al. 2016).
We apply the EDCDF method for CMIP5-simulated precipitation and temperature based on the observational data in China. The aim is to evaluate the performance of this bias-correction method in capturing the temporal and spatial pattern of climate fields in China. Another aim is to increase the confidence in predicting the future changes of precipitation and temperature, which has direct effects on socioeconomic development in China. In this study, section 2 describes the datasets used, the statistical downscaling approach, and the methods used to assess the model performance. The performances of the CDF method, EDCDF method, and raw CMIP5 models for seven subregions as well as the whole of China are shown in section 3, while features of the climate change projections in the future during the near and long term under three RCP scenarios are also discussed in section 3. Section 4 summarizes the main findings.
2. Materials and methods
Daily precipitation and temperature data covering the period from 1961 to 2005 from 756 stations over China are used in this study, which are obtained from the National Climate Center of the China Meteorological Administration. The locations of these stations and the digital elevation model (DEM) are shown in Fig. 1. Because the data for most stations are available from 1960, our analysis is conducted from 1961 to 2005, during which all of the stations are in operation and have the same record periods for both variables. The observed data are interpolated to 0.5° × 0.5° grid cells using bilinear interpolation but with adjustments for differences in elevation between the two grids, taking into account the lapse rate of −0.65°C for every 100-m increase in elevation.
In this study, the whole territory of China is divided into seven climatic regions according to Wang et al. (2011): northeast China (NE), northern China (N), southeast China (SE), eastern northwest China (ENW), southwest China (SW), western northwest China (WNW), and the Tibetan Plateau (Tibet). (Note that Taiwan and Hainan both belong to SE.)
We focused on the application of the EDCDF method for CMIP5 models in China and for future projections under the RCP2.6, RCP4.5, and RCP8.5 scenarios. Limited by data availability, we only obtained monthly precipitation and surface air temperature for eight climate models for the climate change projections under the three RCP scenarios (Table 1). Because of the different spatial resolutions adopted by different GCMs, all model outputs were first bilinearly interpolated onto a common 0.5° × 0.5° grid and matched to the spatial resolution of the gridded observations. Meanwhile, we categorized the eight CMIP5 model simulations at the monthly time scale for the training period (1961–90) for calibrating the model parameters, and the validation period is from 1991 to 2005. For future projections, we analyzed the near-term (2031–60) and long-term (2061–90) changes compared with the reference period (1961–90) for the three RCPs.
b. The equidistant quantile-based mapping method
The traditional quantile-based matching method (CDF method hereafter), based on the statistical moments of cumulative distribution functions of observations and GCM simulations, maps the projected climate variables to the observed CDFs with Eq. (1) (Panofsky and Brier 1958; Gudmundsson et al. 2012):
where is the quantile function corresponding to observations o for a historic training period c, is the CDF of model simulated fields m for a historic training period, and p is the future projection climate fields.
This method assumes that the relationship between the model simulated and observed values during the training (historic) period also applies to the future period. However, IPCC (2007) found that this assumption may not be true because of the nonstationarity of the climate change process, which has a profound influence on climate impact studies. Considering the difference between the CDFs for the future and reference periods, the EDCDF method applies a quantile-based mapping of the CDFs between both the historic and projection period and matches the climatic fields in the future projection period.
For temperature, the projection period is bias corrected using
This method uses a four-parameter beta function [see Eq. (3)] to fit the temperature fields:
where B is the beta function, a and b are the range parameters as the extreme values from the data, extended by a certain percentage of the standard deviation, and p and q are the shape parameters determined by the maximum likelihood estimation method.
Based on the quantile-based mapping of the CDFs between both the historic and projection periods, precipitation of the future projection period can be corrected by Eq. (4):
A two-parameter gamma distribution is used for the portion of a given time series with precipitation:
In addition, taking into account the intermittent nature of precipitation, a mixed gamma distribution is used to model the distribution of precipitation:
where P is the percentage of months with precipitation, and H is a step function having a value of zero when there is no precipitation and a value of 1 when there is precipitation. Parameter Gm−p is the two-parameter gamma distribution of the precipitation fields in the future projection period.
In this method, the parametric distributions fit to both the temperature and precipitation fields at each grid point and the distribution range parameters were taken as the extreme values from the data extended by half of one standard deviation of each grid point. Figure 2 illustrates how the two bias-corrected methods work. The CDFs for the observations (OBS; gray solid line) and model are constructed from the temperature field for a point near 24°N, 98°E. For the CDF method (Fig. 2a), a value of 15°C in a future projection time series corresponds to the model simulation for the current climate (MODc; cyan dotted–dashed line) value of 0.15 under the current climate, which can be transferred to the observed value according to the quantile function of the observations (black circle). However, in the EDCDF method (Fig. 2b), the value of 15°C corresponds to 0.05 in the CDFs of the future model projection (MODp), which is different from that estimated by the CDF method. In the EDCDF method, the difference between MODc and OBS under the current climate is subtracted from the MODp to get the bias-corrected value. The future projection time series can then be used to construct the CDFs for the bias-corrected future projection time series of temperature (EDCDF; pink dashed line). Figure 2 is solely for the purpose of illustration, and more details can be found in Li et al. (2010).
c. Statistical assessment method
We compare the results of the CDF and EDCDF methods against the observations by cross validating with the jackknife method (Lafon et al. 2013; Wang and Chen 2014b). First, we take the period 1961–90 as the training period to calibrate the parameters, and then we bias correct the temperature and precipitation for the remaining 15 years as one experiment. Then, the training period is repeatedly moved 1 year forward and the bias correction and validation are carried out for the remaining years. This procedure is repeated 15 times. Therefore, 16 continuous 30-yr periods are chosen as training periods and the corresponding remaining years as validation periods. The following analyses of the performance of the two bias-corrected methods all are based on the mean of the 16 jackknife experiments to minimize the effects of the choice of training period and to guarantee the robustness of the assessment. Furthermore, based on the baseline period (1961–90), we bias correct the near term (2031–60) and long term (2061–90) for the future period.
In this study, the multimodel ensemble (MME) average is calculated with equal weight, a method that is commonly used for reducing noise in the predictions (Aloysius et al. 2016). We first analyze the bias and MAE of the two bias-corrected methods compared to the raw models for cross validation. Subsequently, we evaluate the performance of EDCDF using the root-mean-square error (RMSE), quantile–quantile (Q–Q) plots, and normal distribution of the extreme values. The RMSE is defined as
where Pi and Oi are the simulation and observed fields, respectively, and n is the number of spatial points or temporal fields.
3. Discussion and results
a. Cross validation of the EDCDF method
We compare the spatial patterns of bias from the raw models and the mean of 16 jackknife experiments using the CDF and EDCDF methods against the observations in Figs. 3 and 4. Compared to the observations, the raw CMIP5 model ensemble underestimates the temperature around the Tibet subregion and overpredicts the temperature along the coastal regions and in some northeastern and northwestern regions, while overestimating the precipitation by more than 90% in most of the western parts of China. This is due to the lower precipitation in these regions, which leads to a larger percentage bias compared with other wetter subregions (Fig. 3). The spatial patterns for bias using the CDF and EDCDF methods show a dramatic reduction in the mean and range of the biases. The spatial biases of precipitation and temperature for the CDF and EDCDF methods are very similar. This indicates that the CDF and EDCDF methods exhibit comparable skill in terms of reducing the biases of the raw models, which is similar to the results of Li et al. (2010). However, there are still some differences in the spatial distribution of biases between the two bias-corrected methods relative to the observations (Fig. 4). The EDCDF method has a lower bias of about 1 mm month−1 in the northwest part of the NE and the southeast part of the N subregions for precipitation than that of the CDF method. For temperature, lower temperature biases of the EDCDF method are mostly found in parts of the WNW, ENW, N, and NE subregions, while higher biases are located in parts of the SW subregion.
Furthermore, we compare the 5th (95th) percentiles of MAE for the CDF and EDCDF methods in January and July. In general, both methods show a significant reduction and very similar MAE, especially for temperature. Thus, we only present the results for precipitation in Table 2. Overall, both methods show considerably smaller MAE, but less skill in January compared to July. In particular, they show very similar skill for the 5th percentile in July. However, the EDCDF method has a slight advantage over the CDF method for the 95th percentile of January and July. The former shows a further reduction in MAE, varying from 0.01 to 0.37 less than that of the CDF method in January. Thus, the EDCDF applied for China seems more skillful in bias correction than the CDF method. These results are consistent with Li et al. (2010) and Aloysius et al. (2016).
b. Performance of EDCDF method
To further evaluate the performance of the EDCDF method in China, we analyze the RMSE and Q–Q plots of the EDCDF simulations against the observations. Figure 5 shows the RMSE for monthly precipitation and temperature in seven subregions of China. The EDCDF method outputs exhibit closer similarity for all climate fields to the actual observed data than to the raw model simulations. The bias-corrected mean RMSE is improved dramatically with a mean value of 38.82 mm, while that of the raw model is about 56 mm for all models over seven subregions. The performance of bias-corrected precipitation in winter is better than that in summer, which is generally better in wetter regions than that in drier regions. The best performance of EDCDF-simulated precipitation occurred in WNW and ENW with mean values of 10.72 and 17.92 mm, respectively. The highest RMSE value is found in SE (92.44 mm) after downscaling, especially in the months of June–August. This probably because of the difficulty in resolving small-scale processes in the driest regions, which is similar to the findings of Goodess et al. (2012) and Wetterhall et al. (2006).
The temperatures of all eight models are well matched with observations with lower RMSEs than those of the raw models across the seven subregions. The RMSEs of the bias-corrected models vary from 0.9° to 4.5°C, while those of the raw models vary from 1.52° to 16.3°C. The lowest RMSEs of temperature occurred in June–August for all models, whereas the highest values are in January, February, and December. Meanwhile, the SW (1.68°C) and SE (1.93°C) subregions have the lowest RMSE for all seasons, but the WNW (2.68°C) and NE (2.53°C) subregions have the highest RMSEs. In general, the eight CMIP5 models bias corrected by the EDCDF method are able to capture the seasonal pattern of climate fields in China.
Figure 6 compares the monthly precipitation in terms of the full distribution over the whole study domain using Q–Q plots in January and July. The Q–Q plots of precipitation show reasonable bias-corrected performance compared with observations over the whole study domain area, yielding data points very close to the reference line in January. However, the EDCDF method underestimates the precipitation by less than 105 mm in July. For temperature, the Q–Q plots indicate that all bias-corrected models have satisfactory skill in downscaling temperature in January, whereas all downscaled models overestimate the temperature in July.
Additionally, we use the ensemble spread of interannual value and the normal distribution of the extreme monthly values to analyze the uncertainty of EDCDF bias-corrected precipitation and temperature. Figure 7 shows the domain-averaged bias-corrected annual precipitation and temperature of individual bias-corrected models and the multimodel ensemble compared to the observations. Results demonstrate that the individual model simulations deviate more from the observations, whose spread varies from 28.68 to 187.67 mm. For temperature, the deviation of individual model simulations from the observations varies from 0.44° to 0.90°C, which is smaller than that of precipitation. This indicates that the bias-corrected precipitation shows large interannual variations and larger uncertainties compared to those of temperature.
Figure 8 presents the normal distribution of the extreme values for the seven subregions during wet and dry years, according to the climatology for all seven subregions. During the wet years, the bias-corrected MME results in greater extreme values than the observations in all subregions above the 0.9 probability level. In contrast, the bias-corrected MME results in smaller values of extreme precipitation during the dry years in NE and N, but greater values in the other five subregions. Notably, the EDCDF method has more precipitation for wet/dry years under the 0.2 probability level in SE. This indicates that the gamma distribution for the precipitation in SE does not match the extreme low value of the observations as well. Meanwhile, the normal distributions of temperature during the wet and dry years show good agreement with the observation for all subregions, which illustrates that the EDCDF method has better skill in simulating the temperature than precipitation.
c. Future projections
For the future projection, we compare the mean and standard deviation of the raw model simulation and outputs after bias correction using the CDF and EDCDF methods under the RCP8.5 scenario (Figs. 9, 10). In general, the CDF and EDCDF methods give similar spatial patterns for the mean and standard deviation of the temperature as compared to the raw model outputs (Fig. 9). For the mean value of temperature, the EDCDF method shows a different range (higher than 25°C) compared to that of the CDF method (lower than 25°C). The CDF method has a colder mean temperature for most parts of China in January than the other two results. Both methods show higher temperatures in July, which is consistent with the correction of the model cold bias in the observational period. In July, the mean temperature of the CDF method shows a colder value in the SE, N, and NE subregions than that of the EDCDF method. A colder northern region and warmer southeast region are expected in January at the end of the twenty-first century under the RCP8.5 scenario. On the other hand, the two methods show a clear reduction in the variability of temperature for most parts of China in January and July. However, there are some subtle differences in the variability of the two methods: the EDCDF method shows a smaller variability for the southeast and southwest regions compared to that of the CDF method.
In terms of the precipitation, the spatial patterns for the mean and standard deviation from 2061 to 2090 are very similar for the two methods in January and July (Fig. 10). The variability of precipitation is substantially reduced by both methods. Notably, there are some differences between the two bias-correction methods. In January, the EDCDF method has a higher value of mean precipitation for the WNW and SE subregions and lower variability for the WNW and NE subregions than that of CDF and the raw model. In July, the CDF method shows higher variability for the WNW and ENW subregions and lower mean precipitation for the Tibet and NE subregions than that of the EDCDF method.
Furthermore, we analyze the relative changes in precipitation and temperature during the near term (2031–60) and long term (2061–90) compared to the reference period (1961–90) under the RCP2.6, RCP4.5, and RCP8.5 scenarios in China. The spatial patterns of the MME changes are illustrated in Figs. 11 and 12 and Table 3. The changes in precipitation and temperature exhibit similar increasing changes under the three different RCP scenarios in the future. However, both precipitation and temperature in the MME display different spatial patterns of change under the three RCPs. Relative to the reference period (1961–90), the regionally averaged precipitation in China and the seven subregions will continue to increase from 2031 to 2090 with increasing spatial variation (Fig. 11), especially for the difference between the northwest and southeastern regions. In general, changes in China vary from 4.1% to 4.6% in the near term and from 5.0% to 10.2% in the long term under the three RCP scenarios. In the near term, the MME projects a clear increase in precipitation in the WNW, ENW, and Tibet subregions and a slight decrease in the SE, SW, and NE subregions. The precipitation in the WNW subregion was found to increase by 10.7%, 13%, and 14% in the near term relative to the reference period under RCP2.6, RCP4.5, and RCP8.5, respectively. Meanwhile, these increases will be more obvious in the WNW subregion over the long term, with values of 16.7%, 14%, and 21.5% under the three RCP scenarios, respectively. Over the long term, RCP8.5 projections exhibit a larger spatial variability in precipitation than the RCP2.6 and RCP4.5 projections. The precipitation in the NE, N, and SE subregions and Tibet will increase under RCP8.5 but will slightly decrease in some parts of China under RCP2.6 and RCP4.5.
For temperature, the MME projects similar and significant changing patterns for the area-averaged annual mean values under the three RCP scenarios for the future period (Fig. 12, Table 3). The projected annual temperature is similar across the emission pathways over China and most of the subregions except Tibet. RCP8.5 projects the highest rise in temperature and RCP4.5 projects a lower increase, while RCP2.6 projects the lowest increase. In the near term, RCP8.5 drives temperature increases across China in excess of 0.8° and 1.1°C, significantly warmer than the increases projected under RCP2.6 and RCP4.5. RCP2.6 and RCP4.5 project similar spatial patterns, but RCP4.5 projects a greater change in temperature than RCP2.6 in the SE subregion. Meanwhile, differences in the simulated temperature changes are clearly observed in the Tibet and SW subregions of the three RCPs. In Tibet, the temperature change in the near term is projected to be −0.6° and −0.1°C for RCP2.6 and RCP4.5, respectively, but has a 1.3°C increase under RCP8.5.
For the long term, the temperatures under RCP2.6 and RCP4.5 follow patterns of change similar to those of the near term. RCP2.6 projects decreasing temperatures varying from −5° to −1°C in the northern part of China, while it projects a slightly increasing change in the NE, N, SE, and WNW subregions. One interesting result is that RCP8.5 projects a remarkable increase, while RCP2.6 and RCP4.5 project a nearly equivalent decrease in the Tibet and SW subregions. Particularly in the Tibet subregion, the RCP2.6 projects a temperature decrease of about −0.7°C, while RCP4.5 and RCP8.5 project increases of approximately 0.4° and 3.2°C, respectively.
In this study, we apply the EDCDF method for eight CMIP5 models in China and present the climate change projections in the twenty-first century under the RCP2.6, RCP4.5, and RCP8.5 scenarios. The jackknife method is used for cross validating the performance of the EDCDF and CDF methods. For removing the effect of the training period choice, we repeat the jackknife experiment 15 times by moving the training period one year forward each time. The result of the average of the 16 experiments shows that the CDF and EDCDF methods are able to reduce biases in the eight CMIP5 models’ temperature and precipitation fields significantly. The EDCDF method has a slight advantage in reducing the bias of precipitation in NE and N. The EDCDF method has a lower bias of temperature in WNW, ENW, N, and NE than that of the CDF method. Meanwhile, the EDCDF method seems more skillful in reducing the MAE of precipitation in the 95th percentile for January and July. These results indicate that the CDF and EDCDF methods are successful in downscaling the climate fields of CMIP5 models, but the latter has a slight advantage in reducing the extreme values. It should be noted that the EDCDF method has smaller extreme values in precipitation during the wet years for all subregions and the southern parts of China during dry years, which indicates that the EDCDF method has lower skill in capturing extreme precipitation with higher seasonal variability. On the other hand, the EDCDF method shows superior skill in reducing the variability of temperature and precipitation from 2061 to 2090 under the RCP8.5 scenario than that of the CDF method.
Compared to the reference period (1961–90), precipitation will increase by about 4.1%–4.6% in the near term and 5.0%–10.2% in the long term under the three RCP scenarios. Meanwhile, temperature under the RCP8.5 scenario shows a dramatic increase for the near term (2031–60) and long term (2061–90) compared with the other two RCP scenarios. RCP8.5 drives temperature increases of about 2.0° and 3.8°C for the two future periods, respectively. The warming trend and variability of precipitation changes probably lead to more uncertainty in the changes of water resources in China. China’s responses to climate change, including the institutional and political structures and legal framework, should consider the potential implications for water resources, and associated sectors such as agriculture, when taking action on climate change mitigation and adaptation measures.
Because of the data limitation, we only bias corrected eight CMIP5 models for the historical period (1961–2005) and future projections under the RCP2.6, RCP4.5, and RCP8.5 scenarios. In the future, we will focus on downscaling a larger set of CMIP5 models to produce a more complete dataset over China, which can be used in hydrologic and ecosystem modeling and to develop diagnostic tools for analyzing threats of climate change to water and food security.
This research was financially supported by the National Key Research and Development Program under Grant 2016YFA0601504 approved by Ministry of Science and Technology, the People’s Republic of China. This research has been also funded by the National Natural Science Foundation of China (51579066) and the Fundamental Research Funds for the Central Universities (2015B14514). We thank Haibin Li (Department of Earth and Planetary Sciences, Rutgers University) for providing the help with the downscaling analysis and Xiaogang He (Department of Civil and Environmental Engineering, Princeton University) for helpful discussions.