Selection of representative GCM scenarios preserving uncertainties

Since climate change studies are the process of forecasting an uncertain future, ‘uncertainty’ is most definitely a keyword of all climate change assessments. According to the four assessment reports published by the Intergovernmental Panel on Climate Change (IPCC), of which the first report was published in 1990 (IPCC 1990), projected temperatures are on a continuous increasing trend on average in East Asia (including the Korean Peninsula), and uncertainties in accordance with climate change have also increased, due to the large range of temperature rise year after year. The greater the level of uncertainty, the more difficult it has become to project what may happen in the future. Furthermore, since climate change studies are conducted in various steps, using Global Climate Models (GCMs), Regional Climate Models, downscaling techniques, and rainfall-runoff models, the uncertainty is all the more amplified. Although previous studies recognized such uncertainties, studies have only quantified and shown the uncertainties in each step of the climate change assessments using a form of sensitivity analysis (Katz 2001; Kay et al. 2009; Prudhomme & Davies 2009; Chen et al. 2011; Poulin et al. 2011; Zhang et al. 2011).

According to existing studies, of all the uncertainties that are generated from climate change assessments, uncertainties from GCM scenarios are known to be the greatest (Wolock & McCabe 1999; Wilby & Harris 2006; Kay et al. 2009; Prudhomme & Davies 2009; Chen et al. 2011). Therefore, it is inevitable that future water resource projections will be much impacted by which GCM scenario is used. In the review of existing studies, using only one with a few different initial conditions or a small number of multiple GCM scenarios was recommended, to project and assess the impact of climate change. It is not convincing that a single GCM scenario selected at present would occur some decades in the future. On the other hand, one may employ all the GCM scenarios provided by IPCC to cover more possibilities in the future, but this would be an impractical alternative to decision-making in practice, even if it were possible for research purposes. Therefore, it is necessary to select several scenarios, to show the possible number of cases, to the maximum extent possible.

Until now, standard criteria for selecting climate change scenarios have not been obvious. GCM scenarios were selected depending on arbitrary means, or the subjective judgment of the researcher. For example, climate impact assessments have been mainly conducted using a GCM scenario developed by their own country, or using high-resolution GCM scenarios. The most objective method of selecting a GCM scenario is to compare performances of various GCM scenarios during a certain past period (i.e. baseline simulation), and to select the GCM scenario with the best accuracy, which implies the assumption that the best projection occurs 100% of the time, but the others never occur. One may assign a different weight to each scenario, to create a combined scenario, but it is considered that all GCM scenarios in the 4th Assessment Report of IPCC (2007) have equal possibilities of occurrence, due to lacking information to make reliable estimates of which are more or less likely to occur. Moreover, the nonstationarity concept in climate change implies that the future would not be a repetition of the past, and thus some best-performed GCM scenarios could not explain the uncertainties of all GCM scenarios in the future.

The purpose of this study is to propose a new approach for selecting some representative GCM scenarios (called the ‘principal’ scenarios). Here we underline preserving the uncertainty the IPCC GCM scenarios show. Using the maximum entropy (ME) theory, this study also quantifies the uncertainty of the selected GCM scenarios, to prove the principal scenarios that attempt to preserve the whole range of uncertainty of all GCM scenarios are more effective than the ‘best’ individual scenarios. Finally, based on the proposed approach, this study proposes some GCM scenarios that are more appropriate for future water resources management in the Korean Peninsula.

As mentioned in the introduction, this study proposes selecting the ‘principal’ scenarios which best represent the uncertainty range of all IPCC GCM scenarios, rather than the ‘best’ scenarios which performed best in the past, with respect to a certain accuracy measure. The best scenario approach would be unconvincing, because the best scenarios selected based on a historical period may not perform well in the future (Raisanen 2007), due to the ‘nonstationary’ climate, where the key statistics of hydro-climate variables are a function of time, and thus the future would not be a repetition of the past. Furthermore, the uncertainty in climate change assessment is generally huge, and thus characterized as ‘deep uncertainty’ (United Kingdom Climate Impacts Programme (UKCIP) 2003), where even likelihoods of future scenarios are generally unknown. Therefore, in such a nonstationary world, preserving future uncertainty should be more focused on deep uncertainty. In this study, the principal scenario approach consists of two steps: first, ‘clustering’ scenarios; and then, ‘selecting’ a representative scenario from each cluster.

The scenario clustering step groups the entire set of GCM scenarios used into several clusters, according to only the statistical properties of each GCM scenario not a GCM structure, because even GCMs have different scenarios under identical research. Among many cluster analysis methods, the characteristic-based K-means cluster analysis method is able to cluster the data, after reducing the dimensionality (e.g. the number of data) of higher-order time series, such as GCM scenarios, using only statistical characteristics (Wang & Smith 2006). In this study, the uncertainties are assumed to all be captured with six statistical characteristics (i.e. average for the total period, average for each month, standard deviation for the total period, standard deviation for each month, trend for each month, and lag-1 autocorrelation). In other words, it is assumed that the GCM scenarios in the same cluster classified by the characteristic-based K-means cluster method, are statistically the most similar.

The second step of the principal scenario approach selects a representative scenario from each cluster, by evaluating the performance of GCM scenarios belonging to each cluster. In this step, the choice of a selection measure should first be determined. Previous studies utilized various measures, such as bias (Wilks 2005; Gleckler et al. 2008), root mean square error (Murphy 1996; Wilks 2005; Gleckler et al. 2008; Pitman & Perkins 2008; Reichler & Kim 2008; Winter & Nychka 2009; Chiew et al. 2009), correlation (Epstein & Murphy 1989; Murphy 1989), brier score (Raisanen & Palmer 2001), relative entropy (Kleeman 2002; Shukla et al. 2006), potential predictability (Ma & Cao 1999; Boer 2004; Boer & Lambert 2008), and Taylor diagram (Taylor 2001).

The above ME theory implies that the distribution with the largest entropy should be chosen if nothing is known about a distribution except the given information. For example, when values of a maximum and a minimum are given, the uniform distribution has the ME. In this study, the ME theory was applied to quantify the uncertainty of the selected projections. More specifically, the selected scenarios provide the maximum and minimum values and Equation (3) calculates the entropy of the selected scenarios as the uncertainty measure.

In this study, GCM scenarios were selected to study the climate change impact on water resources for the South Korean Peninsula. The South Korean Peninsula is located in a temperate climate region at 33–43 degrees north latitude and 124–132 degrees east longitude, and its total area is 99,646 km² (Korea Institute for National Unification 2009). The annual average precipitation in the regime is 1,314.21 mm/year over the past 40 years (1970–2009), and its standard deviation is 247.26 mm/year. Its annual average temperature is 12.36 °C, maximum monthly average temperature is 27.71 °C, and minimum monthly average temperature is −4.80 °C.

To enhance the understanding of climate phenomenon, and improve the simulation technique with computers, several advanced countries developed GCMs to project the future climate, and suggested the results from GCMs to the international society. For a typical example, the IPCC 4th Report (AR4 hereafter) offers 148 GCM scenarios, based on a total of six emission scenarios (1PTO2X, 1PTO4X, COMMIT, SRES A1B, SRES A2, and SRES B1) and two baseline simulations (20CM3 and P1_cntrl) from 25 GCMs of 15 countries that were used in the AR4. The centers (and the corresponding scenarios) providing GCM scenarios are BBC and LAGS (China), BCCR (Norway), GISS, NCAR and GFDL (USA), INGV (Italy), INM (Russia), IPSL and CNRM (France), CSIRO (Australia), MPI-M (Germany), MIUB, METRI and M&D (Germany and Korea), CCCma (Canada), MRI and NIES (Japan), and UKMO (UK).

This study tested 71 AR4 GCM scenarios for the South Korean Peninsula. These consist of scenarios based on the 20C3M emission scenario before 2000 (from January 1970 to December 1999), and scenarios based on the SRES A2 (economic growth oriented) and B1 (environment oriented) emission scenarios after 2000 (from January 2001 to December 2009). Selected GCM scenarios were directly downloaded from the IPCC Data Distribution Centre (www.ipcc-dds.org), and in each GCM scenario, monthly average precipitation and temperature for Korea were calculated as a simple average of the GCMs grid values that include the South Korean Peninsula. This study dealt with monthly average precipitation and temperature time series instead of the annual time series because the hydrological characteristic in the summer season (two-thirds of total precipitation occurs) of the Korean Peninsula is very distinct from that of the winter season. As shown in Figure 2(a) and 2(b), the simulated monthly average precipitation of the AR4 GCMs based on 20C3M and A2 & B1 emission scenarios, are very heterogeneous. As a result, none of those scenarios capture the summer monsoon pattern during the three-month flood season from mid-June to mid-September, when two-thirds of the annual precipitation falls. Therefore, it was concluded that the use of the AR4 GCM was still inadequate for flood mitigation purposes. On the other hand, some GCM scenarios performed well in precipitation during the nine-month dry season, which suggested that these GCM scenarios can be utilized for water supply purposes (refer to Table 1). Simulated monthly average temperature of the AR4 GCMş however, follows the general pattern of observations well (Figure 3(a) and 3(b)), underestimating the observations consistently, by about 3 °C, on average.

Like the majority of the climate change assessment studies (Taylor 2001; Shukla et al. 2006; Perkins et al. 2007; Gleckler et al. 2008; Climate Impacts Group 2009), the selection procedure was carried out based on the 20C3M emission scenario, because the projection period (i.e. 10 years) of the SRES A2 & B1 emission scenarios is too short for testing GCMs. Therefore, this study mainly utilizes 17 GCMs of the 20C3M emission scenario. It is interesting to examine how the best GCMs are based on the PDF method from 20C3M or the other emission scenarios. As shown in Figure 4, for example, the selection of the best GCMs varies significantly between the emission scenarios: the third-ranking GCM, UKMO-HadCM3 in 20C3M, is ranked the 16th and the 12th in A1B and A2, respectively, while the best GCM in A1B is ranked the sixth in 20C3M. This fact would be a symbol of nonstationarity, although a short length in A1B and A2 would also cause the sampling uncertainty. In other words, Figure 4 warns the best selection based on a certain period may be meaningless, in different periods in the climate change era.

The above equations were applied to the precipitation scenarios of each GCM, month by month. Table 2 reports averages and standard deviations over all the GCM scenarios, before and after the bias correction, compared with the observation. Note that Equations (4) and (5) were calibrated using the period from January 1960 to December 1979, while the verifications shown in Table 3 were based on the period from January 1980 to December 1999.

This section illustrates how to select five representative GCM scenarios for the South Korean Peninsula. One can select the five best, or the five principal scenarios, as described in the following two subsections.

• (1)

  Five best GCM scenarios

The five best-performed GCM scenarios were selected using the PDF selection method. The selection was carried out with the 20C3M emission scenario from January 1980 to December 1999, and applied to the GCM precipitation scenarios only when their skill scores in temperature exceeded 80%. The resulting five best scenarios (and their skill scores) include MRI-CGCM232 (Germany), UKMO-HadCM3 (UK), UKMO-HadGEM1 (UK), CNRM-CM3 (France), and BCCR-BCM (China).

• (2)

  Five principal GCM scenarios

The characteristic-based K-mean method was applied to the 17 IPCC GCM scenarios, based on the 20C3M emission scenario. Table 4 presents the resulting five clusters, their member GCMs, and their overall averages and standard deviations, among the six statistical characteristics used in the cluster analysis. It is obvious in Table 4 that the averages and standard deviations are very heterogeneous over the clusters. A single scenario was then selected from each cluster, in the same way as the PDF method for the selection of five best scenarios. The above two-step selection procedure finally resulted in the five principal scenarios, namely MIUB-ECHO-G (Germany/Korea), MPI-ECHAM5 (Australia), GISS-AOM (USA), MRI-CGCM232 (Germany), and CSIRO-Mk30 (Australia). Table 5 compares the best and principal GCM scenarios for the South Korean Peninsula. The two approaches share MRI-CGCM232, while four out of the five GCMs in each approach are different.

The issue of how to select representative GCM scenario is dealt with, when many scenarios are available. This study warns that selecting the best-performing scenarios based on a historical period should be avoided in nonstationary cases like climate change, and then proposes a new approach that can preserve the uncertainty that all scenarios contain. The new approach groups all GCM scenarios into several clusters, and then selects a single representative scenario among member scenarios of each cluster, based on their skill scores. The proposed approach is termed ‘selecting the principal GCM scenarios’, and is applied to select five principal GCM scenarios for the South Korean Peninsula, among 17 GCM scenarios of the 20C3M emission scenario. The uncertainty preservation is measured with the ME theory. It is learnt from our case study that:

1. GCMs that perform well for the 20C3M historical period often do not perform well for other emission scenarios in the future, which confirms that selection of the best GCMs based on a historical period should be avoided;

2. the principal GCM scenarios preserve 100% of the total uncertainty, while the best GCM scenarios preserve less than 65%; and

3. five GCMs, namely MIUB-ECHO-G, MPI-M-ECHAM5, GISS-AOM, MRI-CGCM232, and CSIRO-Mk30, are proposed as the representative GCMs for climate change impact assessments in the South Korean Peninsula. In future, therefore, national water resources plans coping with climate change should be established on the basis of these five GCM scenarios.

   Selecting an essential number of scenarios among the many scenarios available is very important, because using all the scenarios is impossible in practice. The proposed approach can be applied to any GCM scenario selection that is dominated by nonstationarity with large uncertainty.

This research was supported by the Daejin University Research Grants and also supported by a grant from the Advanced Water Management Research Program funded by the Ministry of Land, Infrastructure and Transport of Korea (14AWMP-B082564-01).