Summer rainfall variability over the Southeastern United States and its intensification in the 21st century as assessed by CMIP5 models
Earth and Ocean Sciences, Nicholas School of the Environment and Earth Sciences, Duke University, Durham, North Carolina, USA
Corresponding author: L. Li, Earth and Ocean Sciences, Nicholas School of the Environment and Earth Sciences, Duke University, 322 Old Chem. Bldg, PO Box 90227, Durham, NC 27708, USA. (email@example.com)
 The variability of Southeastern (SE) United States (U.S.) summer precipitation in the current and future climate is analyzed using Coupled Model Intercomparison Project-Phase 5 (CMIP5) models. By comparing simulated historical precipitation variability with observations, we categorize CMIP5 models into two groups: Group 1 (G1) models that simulate the summer precipitation variability reasonably well and Group 2 (G2) models that need further improvements. Our analysis suggests that the relatively higher skill of G1 models is attributable to their ability to accurately represent the dynamical linkage between SE U.S. summer precipitation variability and North Atlantic Subtropical High (NASH) western ridge position. In contrast, the inability of G2 models to represent such linkage leads to their biases in simulating SE U.S. summer precipitation variability. According to our analysis, the ensemble projection of CMIP5 models suggests that under the Representative Concentration Pathway (RCP) 4.5 scenario, SE U.S. summer precipitation variability will intensify and that this intensification is more pronounced among G1 models. Our analysis further suggests that this intensification is most likely due to the projected pattern shift of the NASH western ridge in a warming climate. Under the RCP4.5 scenario, the NASH western ridge will extend further westward leading to more frequent occurrences of the northwestward and southwestward ridge patterns that are respectively related to dry and wet summers in the SE U.S. Consequently, more frequent occurrence of summer precipitation extremes would be expected over the SE U.S. in the future.
 Summer precipitation is important for hydrology, ecology, and the local economy in the Southeastern United States (SE U.S.). In recent decades, SE U.S. summer precipitation has exhibited intensified variability on interannual scales [Wang et al., 2010], manifested by increased year-to-year fluctuations between extremely dry and extremely wet summers. For example, the lasting drought in 2007 followed by a historical flood in 2009 caused tremendous agricultural and economic losses over the region [e.g., Manuel, 2008; Martinez et al., 2009; Gotvald and McCallum, 2010].
 Previous studies identified possible contributors to observed summer precipitation anomalies in this region [Mearns et al., 2003], including convective systems [Baigorria et al., 2007] and hurricane land falling. The influence of these synoptic-scale systems, however, is mainly along the coastal regions [e.g., Konrad and Perry, 2010; Barlow, 2011] and over short periods [Kunkel et al., 2010]. Over a larger spatial area and at seasonal time scales, the summer rainfall in the SE U.S. is predominantly controlled by large-scale circulation, especially those associated with the North Atlantic Subtropical High (NASH) [e.g., Henderson and Vega, 1996; Davis et al., 1997; Katz et al., 2003; Li et al., 2011; Bowden et al., 2012; L Li et al., 2012a]. In particular, the position of the NASH western ridge has been found to regulate vertical motion over the SE U.S. and moisture transport from adjacent oceans, effectively impacting regional precipitation [L Li et al., 2012a]. NASH circulation, in turn, is impacted by a variety of factors, including the sea surface temperature anomalies (SSTAs) over the Pacific and Atlantic [e.g., Wang et al., 2008; Kushnir et al., 2010; Wang et al., 2010; L. Li et al., 2012a]. Thus, NASH circulation can provide a dynamical linkage between large-scale summer precipitation over the SE U.S. and a wide range of climate factors [e.g., Enfield, 1996; Anchukaitis et al., 2006; Mo and Schemm, 2008; Wang et al., 2010; L. Li et al., 2012a; Wu et al., 2007; Xue et al., 2012].
 Another factor that may impact SE U.S. summer precipitation is anthropogenic forcing associated with increased concentration of atmospheric greenhouse gases (GHGs) [e.g., Chen et al., 2003; Liang et al., 2006; Christensen et al., 2007; Li et al., 2011]. The increase in GHGs moistens the troposphere [e.g., Held and Soden, 2006] and alters the atmospheric circulation pattern [e.g., Vecchi et al., 2006; W. Li et al., 2012c], which potentially regulates moisture transport and thus SE U.S. summer precipitation. In the future, GHG concentrations are expected to rise; however, the future impact of this rise on SE U.S. summer precipitation and the role of NASH in this relationship, if any, remain uncertain.
 Previous studies have modeled future precipitation over the SE U.S. using both Global Climate Models (GCMs) and Regional Climate Models (RCMs) [e.g., Chen et al., 2003; Liang et al., 2006; Christensen et al., 2007]. Generally, these studies focus on the change in mean precipitation. However, future changes in precipitation variability have not been fully addressed and the controlling mechanism has not been studied. This study focuses on examining precipitation variability and its controlling mechanism, because many critical impacts of climate are controlled by rainfall variability rather than the mean [Katz and Brown, 1992].
 By analyzing SE U.S. summer precipitation as simulated by Coupled Model Intercomparison Project-Phase 5 (CMIP5) models, this study addresses the following specific questions: (1) How well can CMIP5 models simulate SE U.S. summer precipitation variability in the current climate, and what processes are responsible for a reasonable simulation of SE U.S. summer precipitation variability? (2) Will the enhanced summer precipitation variability in recent decades continue to intensify in a warming climate based on CMIP5 models? (3) What are the mechanisms controlling future rainfall changes in model-projected climate?
 The rest of the paper is organized as follows. In section 2, data and methods are described. In section 3, CMIP5 model simulations of SE U.S. summer precipitation are compared with observations. Factors and processes key to the precipitation variability are identified. This section also presents CMIP5 model projections of changes in SE U.S. summer precipitation variability in response to increasing GHG concentrations under the Representative Concentration Pathway 4.5 (RCP4.5) scenarios. Sections 4 and 5 present the discussion and conclusions.
2 Data and Methods
2.1 Observation Data and Model Output
 The observational precipitation data used in this study includes the National Oceanic and Atmospheric Administration (NOAA)'s PRECipitation REConstruction over Land (Prec/L) data sets [Chen et al., 2002], NOAA Climate Prediction Center (CPC) U.S. unified precipitation [Higgins et al., 2000], and the Global Precipitation Climatology Centre (GPCC) monthly precipitation data set [Rudolf et al., 2005], covering the 1950–1999 period. The SE U.S. is defined as the terrestrial domain over 91°W-76°W, 25°-36.5°N, namely seven states including North Carolina, South Carolina, Georgia, Florida, Alabama, Tennessee, and Mississippi. Despite their differences in data sources and data processing methods, these three observational precipitation data sets show high agreement in terms of the climatology and the interannual variation of SE U.S. summer precipitation (not shown). The consistency in the observational data ensures the reliability of the precipitation reference metric for model evaluation.
 Atmospheric circulation from reanalysis data sets is treated as proxy of observations in this study. This approximation is generally valid in this research domain, since the available reanalysis data sets show considerable consistency in describing the summertime hydroclimate over the SE U.S. [L Li et al., 2012b] and dominant large-scale circulation, i.e., the NASH [Li et al., 2011]. Both NCEP/NCAR [Kalnay et al., 1996] and ERA-40 [Uppala et al., 2005] are adopted in this study due to their relatively longer temporal coverage (1948 to present for NCEP/NCAR and 1958–2002 for ERA-40) than those more up-to-date reanalysis data sets such as the NCEP North American Regional Reanalysis (NARR) [Mesinger et al., 2006] and the Japanese 25 year Reanalysis Project (JRA-25) [Onogi et al., 2007].
 Previous studies suggest that NASH and its western ridge movement largely regulated SE U.S. summer precipitation and precipitation variability [e.g., Henderson and Vega, 1996; Davis et al., 1997; Katz et al., 2003; Li et al., 2011; L Li et al., 2012a, 2012b]. In this study, CMIP5 model simulations of NASH circulation and its impact on SE U.S. summer precipitation are analyzed.
 The 850 hPa geopotential height is chosen instead of sea level pressure to represent the NASH circulation to avoid the complication caused by topography and land-sea distribution along the western edge of the system [Li et al., 2011]. The ridge line of NASH is where tropical easterly wind reverses to midlatitude westerly. It can be identified mathematically by u = 0, [Liu and Wu, 2004]. The western boundary of NASH is determined by the western portion of the 1560 geopotential meter (gpm) isoline. The western ridge of NASH is thus defined as the intersecting point of the 1560 gpm isoline with the defined ridge line (Figure 1) [Li et al., 2011]. The identified western ridge in each summer is divided into four quadrants: Northwest (NW), Southwest (SW), Northeast (NE), and Southeast (SE) according to the ridge's location relative to the 60 year (45 years for ERA-40) climatology (Figure 1) [L Li et al., 2012a].
 In this study, summer precipitation and 850 hPa geopotential height simulated by 24 CMIP5 models (Table 1) are analyzed. Two experiments are considered: Historical run (1950–1999) and RCP 4.5 (2050–2099). Among CMIP5 long-term experiments, these two are the core and are given higher priority by each modeling center [Taylor et al., 2009; 2012]. Thus, larger output sample size will be available to ensure the statistical robustness of the analysis results.
Table 1. CMIP5 Models Used in This Study
Resolution (Lat. × Lon., Level)
 Historical experiments represent the current climate and are driven by observed atmospheric composition changes and other forcing agents. Time-evolving land cover changes are considered for the first time in CMIP5 models [Taylor et al., 2012]. The RCP4.5 is a midrange mitigation emission scenario, in which CO2 concentrations increase to 650 ppm in 2100 and are stabilized afterward. Meanwhile, radiative forcing steadily increases to 4.5 W m−2 till 2100 and is then stabilized [Moss et al., 2010; Taylor et al., 2012].
 To avoid the possible spread of the 850 hPa geopotential height along the western boundary of the NASH among CMIP5 models, we adjust the western boundary of NASH to the geopotential height isoline straddling 86°W, where the climatological 1560 gpm isoline is located in NCEP/NCAR and ERA-40 [Li et al., 2011]. The intersecting point of the modeled western boundary with the ridge line is identified to enable studying the movement of the NASH western ridge for each model.
 Global atmospheric temperature is projected to increase in the RCP4.5 scenario. The temperature rise in the lower troposphere increases the thickness of an atmospheric layer bounded by two isobaric surfaces and thus elevates the 850 hPa surface uniformly. This uniform increase in the 850 hPa geopotential height field, however, does not directly contribute to the dynamic (wind) fields of the NASH. In this study, the uniform increase in the 850 hPa geopotential height in response to the mean warming effect in the RCP4.5 has been removed according to pressure-height relationship (see Appendix A).
 In this study, the multi-model ensemble (MME) is applied to project future climate. The MME emphasizes precipitation changes due to climate forcing and deemphasizes differences in models' dynamic cores and parameterization schemes [Gleckler et al., 2008]. Of the 24 CMIP5 models, 21 provide multiple runs for Historical experiments (Table 1). For these models, a 50 year subsample is drawn to represent the multiple run sample sets. The subsampling avoids artificial weight added to any single model. The multiple run sample set is subdivided into 50 quantiles with cumulative probability monotonously increasing by 2% for each quantile from low to high quantiles. From this multiple run sample set, a 50 year sample was drawn and subdivided into the same quantiles as the original sample set. This subsampling process was repeated 1000 times. The subsample with smallest quantile distance from the original sample was chosen to represent this specific model's simulation of SE U.S. summer precipitation (The quantile distance is defined as the Eulerian distance between the precipitation quantile vectors from subsample and the original sample: , where qai is the ith quantile precipitation rate in subsample and qbi is the ith quantile precipitation rate from original sample.). Compared with the variance of the original sample, this subsampled precipitation shows high confidence in representing the model's precipitation variability.
 Future changes in SE U.S. summer precipitation were analyzed by comparing probability density function (PDF) curves which are constructed based on 24 CMIP5 models in Historical and RCP4.5 experiment. We used the Gamma kernel to construct PDFs for its better fit with SE U.S. summer precipitation than Gaussian kernel, especially for precipitation in the wet-tails, due to the skewness of precipitation distribution. In some regions, precipitation better fits the Log-Normal, Log-Pearson Type III, or Generalized Extreme Value type II distribution. “Goodness of fit” was also tested for these three distribution kernels. Our analysis indicates that these distribution kernels, although implying higher complexity, do not show obvious advantages over the Gamma kernel in representing SE U.S. summer precipitation in current climate. Further, projections of SE U.S. future precipitation are insensitive to the choice of distribution kernels. In this study, only the PDFs fitted using Gamma kernel are shown and discussed.
 Quantile-normalization method [Bolstad et al., 2003] is applied to SE U.S. summer precipitation simulated by CMIP5 models to avoid artificial precipitation variability caused by model spread in simulating regional climate. Let Prk = (Prk1, …,Prk50) denote a 50 year precipitation sample simulated by the kth model. The quantile normalization process is as follows: (a) precipitation time series from the kth model is sorted from low to high as qk = (qk1, …,qk50); (b) calculate the ensemble mean of the ith quantile precipitation simulated by each model , where bar is ensemble mean of model simulated ith quantile precipitation and qk,i is the ith quantile precipitation simulated by the kth model; and (c) construct PDFs using the .
3.1 CMIP5 Model Simulations of SE U.S. Summer Precipitation Variability in Current Climate (1950–1999).
 The SE U.S. summer precipitation as simulated by CMIP5 models in Historical runs is compared with observations (Figure 2). Generally, the spatial pattern of simulated summertime precipitation climatology shows considerable discrepancy from observations (Figure 2). Three observation data sets consistently show a higher precipitation along the coastal regions associated with localized land-sea diabatic heating contrast [Wu et al., 2009]. The precipitation rate decreases inland with a gradient in the northwest-southeast orientation (Figure 2a). Compared with observations, the MME of 24 CMIP5 models shows a higher precipitation rate in the interior domain rather than along the coastal regions (Figure 2b). In other words, CMIP5 models generally overestimate (underestimate) precipitation inland (over the coastal regions). Furthermore, such a bias pattern prevails among most CMIP5 models (Figures 2c–2z).
 The mismatch of the precipitation pattern between CMIP5 models and observations makes the representation of spatially heterogeneous features of SE U.S. summer precipitation using CMIP5 models problematic. However, compared to observations, the dominant rainfall pattern over the SE U.S. is reasonably simulated by almost all CMIP5 models, according to the Empirical Orthogonal Function (EOF) analysis. Figure 3 shows the first EOF mode of the summer precipitation derived from observations and model simulations. The observations show a spatially uniform mode over the SE U.S., which explains 38% of the precipitation variance (Figure 3a). This mode is well captured by CMIP5 models (Figures 3b–3z). The ensemble of the first EOF mode shows remarkable similarity with observations, in terms of both the magnitude of mode variability and the locations of local maxima (Figure 3b). Furthermore, each individual model is skillful in simulating this leading EOF mode (Figures 3c–3z), despite the differences in model resolution, configuration and complexity, etc.
 Corresponding to this homogenous spatial mode (Figure 3), the temporal variation of the first EOF mode (as represented by the first Principle Component (PC1)) covaries with the areal-averaged precipitation. The R2 between PC1 and areal-averaged precipitation reaches 0.95 (0.96) in observations (CMIP5 models on average), indicating that areal-averaged precipitation can reasonably characterize the interannual variation of SE U.S. summer precipitation in both observations and CMIP5 models (Figure 4). Most importantly, the areal average methods de-emphasize the spatial heterogeneity of SE U.S. summer precipitation which is not well simulated by CMIP5 models (Figure 2) and thus makes the simulated temporal variation of summer precipitation comparable with that observed.
 This study focuses on the variability of areal-averaged SE U.S. summer precipitation. The gauge data suggest that the maximum likelihood estimator (MLE) of the precipitation standard deviation is 0.65 mm d−1 for the period of 1950–1999, with the 95% confidence interval (CI) [0.55, 0.73]. These statistics provide an evaluation metric to assess the model simulation of SE U.S. summer precipitation variability.
 Figure 5 shows SE U.S. summer precipitation variability simulated by CMIP5 models (Historical run) and the comparison of model results with observations. Among 24 CMIP5 models, 50% of the models simulate the standard deviation of summer precipitation within the 95% CI, suggesting that half of the models (Group 1 (G1) models) reasonably capture the precipitation variability in the 1950–1999. On the other hand, 37.5% (12.5%) of the models underestimate (overestimate) the summer precipitation variability compared to observations; these models are categorized as Group 2 (G2) models which need certain improvement (Figure 5a).
 On average, the ensemble of CMIP5 model simulated SE U.S. summer precipitation variability is within the 95% CI of the observed variability, although the exact value is about 10% below the MLE of observations. In addition, we compared the precipitation variability in Earth System Models (ESMs) to that in coupled atmosphere-ocean GCMs (AOGCMs) [Meehl and Hibbard, 2007; Hibbard et al., 2007]. The ESM ensemble shows summer precipitation variability closer to observations than the AOGCM ensemble (Figure 5b). This improvement may be attributed to a more realistic representation of ecosystem and its interaction with atmosphere, indicating an important role of biosphere dynamics in SE U.S. regional hydrology [e.g., Peters et al., 2003; Stoy et al., 2006; Siqueira et al., 2009]. However, since the sample size of ESMs is relatively small and certain intermodel spread exists, it is still hard to ascertain that ESMs outperform AOGCMs in simulating SE U.S. summer precipitation variability at current stage.
3.2 Roles of NASH Western Ridge in the Simulation Skills of Summer Precipitation Variability over the SE U.S.
 The CMIP5 models diverge in their simulation skills of SE U.S. summer precipitation variability. Understanding factors critical to the simulation skills of SE U.S. summer precipitation variability is thus important to improve the model performance in representing SE U.S. summer climate.
 Previous studies have established a relationship between SE U.S. summer precipitation and the variation of NASH, especially its western ridge [e.g., Henderson and Vega, 1996; Katz et al., 2003; Li et al., 2011; L Li et al., 2012a]. The displacement of the western ridge regulates moisture transport and vertical motion over the SE U.S.; thus, regional precipitation is sensitive to the position of the NASH western ridge [L Li et al., 2012a]. Furthermore, the NASH western ridge position explains more SE U.S. summer precipitation variance than other climate factors, such as ENSO [L Li et al., 2012b]. In fact, previous research indicated that the impact of many climate factors upon SE U.S. summer precipitation is likely through modulating the NASH western ridge [e.g., Wang et al., 2008; Hu et al., 2011; L Li et al., 2012a]. It implies that a reasonable simulation of the relationship between the NASH western ridge and summer precipitation over the SE U.S. might be a key factor.
 Using observed precipitation, NCEP/NCAR, and ERA-40 reanalysis data sets, Figure 5 depicts the relationship between NASH western ridge and SE U.S. summer precipitation. Both reanalysis data consistently suggest a uniform increase (decrease) in summer precipitation over the SE U.S. during years when the NASH western ridge presents SW (NW) type. The increase (decrease) in precipitation exceeds 0.8 mm d−1, equivalent to 1.2 standard deviation of SE U.S. summer precipitation, and is statistically significant (0.05 level) according to Monte Carlo test (Figures 6a, 6b, 6e, and 6f). In contrast, precipitation anomalies are less apparent and show higher spatial heterogeneity over the SE U.S. during NE and SE years (Figures 6c, 6d, 6g, and 6h). Furthermore, SE U.S. summer precipitation anomalies in NE-year differ between the two reanalysis data sets. Specifically, the NCEP/NCAR (ERA-40) composite shows a slightly above (below) normal precipitation (Figures 6c and 6g). This discrepancy suggests a larger uncertainty in the response of SE U.S. summer precipitation to the western ridge position when the ridge is located relatively eastward.
 This “NASH western ridge position-SE U.S. summer precipitation” relationship is reasonably captured by G1 models, as shown in Figures 7a–7d. On average, G1 models simulate a drier (wetter) summer in the SE U.S. during NW (SW) years (Figures 7a and 7b); whereas summer precipitation shows no significant anomalies during NE and SE summers (Figures 7c and 7d). Although the decrease in summer precipitation during NW years is about 0.2 mm d−1 less than observations, the key features of the observed relationship (Figure 6) are well simulated by G1 models. The magnitude of deficit and excessive precipitation during NW and SW years far exceeds intermodel rainfall spread, indicating a high agreement of signal among G1 models (Figures 7a–7d).
 In contrast, G2 model simulation of the “NASH western ridge position-SE U.S. summer precipitation” relationship differs from observations (Figures 7e–7h). Generally, G2 models fail to simulate wetter summers when the ridge is in SW position (Figure 7f). During SW years, summer precipitation remains close to its climatology; the weak wet anomalies along the North and South Carolina border are not statistically significant (Figure 7f). In a SE year, however, G2 models tend to simulate wet summers over the SE U.S., especially in Florida, Southern Georgia, and Alabama (Figure 7h). Although G2 models generally suggest a below normal summer precipitation during NW years, the dry anomalies concentrate in the southern part of SE U.S., instead of the entire region as suggested by observations (Figures 6a and 6e); and the magnitude is weaker than that of observations.
 Overall, the “NASH western ridge position-SE U.S. summer precipitation” relationship is not well captured by G2 models (Figures 7e–7h). Specifically, in G2 models, the westward extension of the western ridge does not show enhanced impact on SE U.S. summer precipitation, especially in SW years. The inability of G2 models to simulate this circulation control on SE U.S. summer precipitation [Li et al., 2011; L. Li et al., 2012a] might cause their biases in the summer precipitation variability. However, why G2 models cannot simulate the “NASH western ridge position-SE U.S. summer precipitation” relationship needs further investigation.
 To ensure that the ensemble results in Figure 7 are not dominated by any single model, the consistency of precipitation signal among models in the two groups is assessed, respectively. Generally, G1 models show higher consistency in the simulated precipitation anomaly pattern than G2 models. Almost all G1 models simulate the increase (decrease) in SE U.S. summer precipitation with ridge in SW (NW) position, suggesting such simulation skills are common features among G1 models (Figures 7a–7d), although the magnitude of precipitation anomalies differ slightly among G1 models. In contrast, G2 models largely spread in simulating the “western ridge position-SE U.S. summer precipitation” relationship. For example, about 50% of G2 models indicate a decrease in SE U.S. summer precipitation when the western ridge is in SW position, while the other 50% suggest the opposite (not shown).
 We further compared the differences in the simulated SE U.S. summer precipitation variability between models that can capture the “NASH western ridge-SE U.S. summer precipitation” and models that cannot. Models capable of representing this ridge-rainfall relationship simulate SE U.S. summer precipitation variability within the 95% CI of the observed precipitation variability. The averaged precipitation standard deviation obtained from these models is 0.67 mm d−1 close to the MLE of observations (0.65 mm d−1). In contrast, models misrepresenting the ridge-rainfall relationship generally underestimate the summer precipitation variability, which results in the simulated precipitation variability outside the 95% CI of observations (not shown).
 Thus, the results suggest that the simulation skills of SE U.S. summer precipitation variability could be attributed to the representation of the “NASH western ridge position-SE U.S. summer precipitation” relationship. Such a relationship is well simulated by G1 models (Figures 7a–7d), but is not captured by G2 models (Figures 7e–7h). The lack of such a relationship in G2 models' simulation largely contributes to their bias in simulating SE U.S. summer precipitation variability. Our results thus suggest that improving the simulation of the “NASH western ridge position-SE U.S. summer precipitation” relationship in G2 models might help to correct their simulation bias.
3.3 Intensification of Future Precipitation Variability over the SE U.S.
 There is a broad consensus among observations and model simulations that the continuously increasing GHGs could moisten the troposphere [e.g., Ross and Elloitt, 2001; Dai, 2006; Sherwood et al., 2010], accelerate the global hydrological cycles [e.g., Ohmura and Wild, 2002; Yang et al., 2003; Stocker and Raibe, 2005; Held and Soden, 2006; Huntington, 2006], and result in the shift of global and regional precipitation patterns [e.g., Groisman et al., 2004; Huntington, 2006; Trenberth, 2011]. Over the U.S., the increase in GHG concentrations tends to cause drying over the Southwest [e.g., Seager et al., 2007; Cayan et al., 2010] and summertime Northeast [Hayhoe et al., 2007], wetting over the Midwest and Great Lakes during winter and spring [e.g., Cook et al., 2008; Karl et al., 2009; Patricola and Cook, 2012].
 Over the SE U.S., no significant trend of precipitation is observed in recent decades. However, summer precipitation variability has significantly intensified [Wang et al., 2010; Li et al., 2011]. Consistent with Li et al. , CMIP5 models suggest that the recently intensified summer precipitation variability would further intensify in a warming climate. Under the RCP4.5 scenario, the ensemble of CMIP5 models shows an increase in the standard deviation of summer precipitation over a large majority of the SE U.S. domains, especially the eastern coasts (Figure 8a). The further intensification of the summer precipitation variability can also be inferred from PDFs of SE U.S. precipitation constructed upon the ensemble of 24 CMIP5 models (Figure 8d). The future climatology of SE U.S. summer precipitation shows insignificant changes because no apparent shift in the modes of Historical (1950–1999) and RCP4.5 (2050–2099) PDFs is found (Figure 8d). In contrast, the scale parameter of RCP4.5 PDF increases significantly at α = 0.01 level (χ2 test) with both wet and dry tails of the PDF extend further (Figure 8d) (The value of scale parameter determines the “statistical dispersion” of a PDF and thus reflects the tail behavior of the PDF. The large value of scale parameter indicates the sample distribution tends to be more spread, whereas the small value indicates the distribution is more concentrated.). Overall, the ensemble of CMIP5 models suggest that the increase in GHG concentrations will likely enhance SE U.S. summer precipitation variability and result in more frequent occurrence of both dry and wet extremes in the future (Figure 8d).
 Beside the ensemble of all CMIP5 models, we analyzed SE U.S. summer precipitation simulated by G1 and G2 models separately. Increase in the summer precipitation variability shows a higher magnitude over the SE U.S. by G1 models (Figure 8b) than the ensemble of all CMIP5 models (Figure 8a). Over large areas of the SE U.S., the increase in the standard deviation of summer precipitation exceeds 0.1 mm d−1 (Figure 8b). Furthermore, G1 model ensemble suggests an increase in precipitation variability over the SE U.S. and the feature is highly consistent among G1 models (Figure 8b). In contrast, there is no apparent shift of SE U.S. summer precipitation variability as projected by G2 models. The scale parameters of the PDFs and thus the tail behavior of the summer precipitation remain almost unchanged from Historical to RCP4.5 scenarios (Figure 8f). G2 models show an east-west dipole pattern in the variability change, with the variability increase over the eastern coast but decrease in the west of the domain (Figure 8c).
 Our analysis suggests that the model quality in simulating current precipitation variability matters for future projection, consistent with previous work [e.g., Li et al., 2008]. Thus, a projection of future precipitation is made by applying weight function to CMIP5 models: models simulating precipitation variability closer to observations in the current climate are given higher weight in projecting future precipitation (Appendix B). The assumption is that “models simulating the current climate accurately will likely make a more reliable future projection.” Such an assumption is physically sound, because the models' good simulations of SE U.S. summer precipitation are related to their reasonable simulations of the underlying physical mechanism: the “NASH western ridge position-SE U.S. summer precipitation” relationship (Figures 6 and 7). In the discussion section, we will further show that the projection of future precipitation change by G1 models is also linked to this physical mechanism. The constructed RCP4.5 PDF (Figure A2) after applying the weight functions (Figure A1c) extends further than the equally weighted PDF (Figure 8a). The PDFs constructed using weighted ensemble method also resemble those constructed using G1 models, since G1 models are given a higher weight as they are less biased.
 Overall, CMIP5 models suggest that SE U.S. summer precipitation variability would further intensify as GHG concentrations increase. The enhancement in the summer precipitation variability will likely drive the SE U.S. toward a more “extreme” climate in the future. That is, as warming continues, more frequent occurrences of dry and wet summers are expected, leading to increased climate extremes over the SE U.S.
 The CMIP5 models collectively suggest that the variability in SE U.S. summer precipitation will further intensify in the future with the increase in atmospheric GHG concentrations (Figures 8a, 8d, and A2). Previous studies have attributed the intensified SE U.S. summer precipitation variability in recent decades to the westward extension of NASH western ridge (Figure 9a) and the increased occurrence of NW and SW-type ridge patterns [Li et al., 2011; L Li et al., 2012a; 2012b]. The role of NASH in the future intensification of SE U.S. summer precipitation variability is analyzed by comparing the 850 hPa geopotential height under Historical and RCP4.5 scenarios simulated by G1 models due to their capability to represent the “NASH western ridge position-SE U.S. summer precipitation relationship.”
 The 850 hPa geopotential height simulated by G1 models shows substantial changes along the NASH western ridge in the future. As the uniform thermal expansion component of the high system has been removed (Appendix A), the results have mainly dynamical implications for future climate. In a warming climate, G1 models suggest that the western ridge would extend westward into the U.S. continent, dynamically (Figure 9b). From Historical to RCP4.5 scenarios, the western ridge extends westward by about 5° (Figure 9b) and the westward extension is highly consistent among G1 models. The westward movement of the NASH western ridge could alter the prevailing wind and moisture transport over the SE U.S., indicating a more important influence of NASH on SE U.S. summer precipitation in the future [Li et al., 2011; L Li et al., 2012a].
 Accompanying the westward movement of the NASH western ridge, the frequencies of both NW and SW-type ridges would increase. From G1 model simulations, the NW-type ridges are projected to increase by 10% and the SW-type ridges triple under the RCP4.5 scenario compared to Historical scenario (Figure 10). The northwestward movement of the NASH western ridge could further suppress upward motion over the SE U.S. due to the prevailing descending motion south of the western ridge [Liu and Wu, 2004; L Li et al., 2012a]. In contrast, as the ridge extends further southwestward, the moisture flux would more likely converge into the SE U.S. and favor heavier summer precipitation [L Li et al., 2012a]. Thus, the intensity of abnormally dry and wet summers could increase over the SE U.S.
 Collectively, the NASH western ridge pattern changes could lead to the projected increase in SE U.S. summer precipitation variability. In the future, as the NASH western ridge moves westward (Figure 9b) and its occurrence in the NW and SW position increases more frequently (Figure 10), more summers with enhanced flood/drought intensity would likely occur over this region.
 The SE U.S. hydrology, ecology, and economy are strongly impacted by extremely dry and wet summers, indicating the importance of understanding summer precipitation variability in the region. In this study, CMIP5 model simulations of SE U.S. summer precipitation variability in the current and future climate are analyzed using the Historical run and the future projection under the RCP4.5 scenario.
 Compared with observations, most CMIP5 models have bias in simulating the spatially heterogeneous features of SE U.S. summer precipitation. However, the interannual variation of SE U.S. summer precipitation is dominated by the leading EOF pattern, which is reasonably captured by CMIP5 models. This pattern of summer precipitation and its variance can largely be explained by the areal averaged precipitation. Thus, the simulated regional mean precipitation and its interannual variation pattern are comparable to observations.
 Among 24 CMIP5 models analyzed in this study, 50% simulate a magnitude of SE U.S. summer precipitation variability comparable to observations. In contrast, the other 50% fail to simulate summer precipitation variability well. According to model performance in SE U.S. summer precipitation variability, CMIP5 models can be categorized into two groups: G1 models which reasonably simulate summer precipitation variability and G2 models which need certain improvement.
 The relatively high simulation skills of G1 models are largely attributable to their capability in representing the dynamical linkage between precipitation and NASH western ridge. When the western ridge is in NW (SW) position, the SE U.S. tends to undergo abnormally dry (wet) summers; conversely, when the ridge is located in NE or SE position, SE U.S. summer precipitation deviates little from its climatology. However, G2 models fail to capture this relationship and thus exhibit lower simulation skills. Our analysis suggests that accurate simulations of SE U.S. summer precipitation variability rely largely on the representation of this dynamical linkage.
 Ensemble projection using all 24 models and G1 models suggests that SE U.S. summer precipitation variability will intensify as GHG concentrations increase in the future. As MME generally provides a more statistically reliable projection of future climate than a single model, and G1 models' projections are more trustworthy given their better capture of the underlying mechanisms, the projected intensification in precipitation variability can be both statistically and dynamically robust. Thus, the SE U.S. will likely experience more frequent occurrences of abnormally dry and wet summers in the future.
 The projected precipitation changes are linked to the pattern shifts of the NASH western ridge in a warming climate. In the future, the western ridge is expected to extend further westward, when both the frequency and magnitude of NW and SW ridges are expected to increase. According to the “NASH western ridge position-SE U.S. summer precipitation” relationship, the SE U.S. will likely experience more floods and droughts during future summers.
 We thank the international modeling groups for providing their data for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modeling (WGCM), and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity. We thank M. Susan Lozier, Paul A. Baker, Ana P. Barros, and Gabriel Vecchi for their insightful discussion; Editor Steve Ghan and three anonymous reviewers for constructive comments; and Apurva Dave, Diane Bryson, Maria Parker, Hannah Aird, and Patrick T. Brown for editorial assistance. The Duke University authors (Li and Li) are supported by the NSF Grant AGS-1147608 and the Georgia Tech author (Deng) is supported by the NSF Grant AGS-1147601.
Appendix A: Removal of the Uniform Thermal Expansion of Geopotential Height
 Under the approximation of hydrostatic balance, the thickness of an atmospheric layer bounded by two isobaric surfaces is proportional to the mean temperature in the layer, i.e., , where Z is the geopotential height, T is atmospheric temperature in K, R = 287J kg− 1 K− 1 is the gas constant, and g = 9.8 m s− 2 is the gravitational acceleration.
 At a latitude-longitude location, setting P2 to 850 hPa and P1 to sea level pressure (SLP), Z2 corresponds to the geopotential height at 850 hPa and Z1 = 0. The pressure-height relationship can be applied to infer the 850 hPa geopotential height given the information of SLP and temperature distribution from the sea level to 850 hPa:
 The pressure-height relationship indicates that the increase of temperature from surface to 850 hPa would increase the geopotential height even though SLP remains unchanged. This relationship is applicable to the geopotential height field change in the RCP4.5 scenario where the increase in GHGs warms the lower troposphere, thermally expanding the atmospheric layer beneath 850 hPa and thus increases 850 hPa geopotential. The contribution of temperature increase to geopotential height change in RCP4.5 is analyzed as
where δ = RCP4.5 − Historical, and ((A2)) can be further partitioned into the thermal direct (temperature change) and thermal indirect (SLP change) components as
 The warming of the lower troposphere over the North Atlantic and its contribution to the increase in Z850 are estimated by calculating the areal-averaged (100°W-20°W, 15°N-45°N) thermal direct term in equation ((A3)). This uniform expansion component is subtracted from the RCP4.5 geopotential height field. From our calculation, this uniform expansion term substantially varies among CMIP5 models, ranging from 6 to 21 gpm.
Appendix B: Construction of Variability Weight Functions
 Considering the model spread in simulating SE U.S. summer rainfall in the current climate, a weight function based on model bias in precipitation variability is constructed using a Gaussian distribution kernel ∼ N(μ,σ2). Here, the model bias is defined as the difference in the standard deviation of the summer precipitation between a model's simulation and observations. We adjusted the model bias to relative bias as follows:
where stdi is the standard deviation of the summer precipitation simulated by the ith model and stdobs is the observed standard deviation of the summer precipitation. The denominator is the average of the absolute bias among 24 CMIP5 models.
 In our analysis, μ is set to 0, meaning that the models with the same standard deviation of observations are treated as “perfect models” and are thus assigned the highest weight. The σ determines the strength of the weight function; i.e., a small value of σ results in heavy weight, because the probability density is concentrated around 0. The weight function constructed with small σ assigns disproportionally high weight to one or two “best” models but low weight to the majority of CMIP5 models (Figure A1a). Thus, such a weight function tends to over-emphasize certain individual models thus are not representative of the ensemble set. In contrast, the large σ tends to disperse the probability density (Figure A1b). As σ increases to infinity, the Gaussian distribution approximates the Uniform distribution. Thus, the weighted ensemble converges to equal-weighted ensemble results.
 In our analysis, the determination of σ comes from a Monte Carlo simulation. We draw 10,000 σ samples evenly distributed between [0.1, 10]. The model weight is calculated with each of the 10,000 σ:
We select the optimal σ for our weight function using the following criteria: (1) the weight assigned to the “best” model should not exceeds 20 times that assigned to the “worst” model and (2) after applying the weight function, the standard deviation of the Historical samples is closest to observations.
 The weight function is converted to be the sample size of each individual model. We assign 50 model samples to the “worst” model. The number of samples from the ith model can then be calculated from
 We constructed a new precipitation sample set with ni samples drawn from the ith model. According to our analysis, the optimal σ used to determine the weight function and sample size is σ = 1.22. After applying the weight function (~ N(0,1.222)), the standard deviation from the weighted Historical sample becomes 0.61 mm d−1 compared to 0.65 mm d−1 in observations. This weight function is also applied to future precipitation projection under RCP 4.5 scenario (Figure A1c).
 The summer precipitation PDFs constructed while taking into account model quality weight are shown in Figure A2. Compared with equal-weighed ensemble PDFs (Figure 8d), the RCP4.5 PDF tails extend further as suggested by the weighed ensemble (Figure A2). As the G1 models are assigned higher weight in the ensemble, the PDFs resemble those from G1 models (Figure 8e).