Using eddy geopotential height to measure the western North Pacific subtropical high in a warming climate
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The western North Pacific subtropical high (WNPSH) is crucial to the East Asian summer climate, and geopotential height (H) is widely used to measure the WPNSH. However, a rapidly rising trend of H in the future is projected by the models from the Coupled Model Intercomparison Project Phase 5 (CMIP5). Diagnoses based on the hypsometric equation suggest that more than 80% of the rise in H are attributable to zonal uniform warming. Because circulation is determined by the gradient of H rather than its absolute magnitude, the spatially uniform rising trend of H gives rise to difficulties when measuring the WNPSH with H. These difficulties include an invalid western boundary of WNPSH in the future and spurious information regarding long-term trends and interannual variability of WNPSH. Using CMIP5 model simulations and reanalysis data, the applicability of a metric based on eddy geopotential height (H e ) to the warming climate is investigated. The results show that the H e metric outperforms the H metric under warming climate conditions. First, the mean state rainfall-H e relationship is more robust than the rainfall-H relationship. Second, the area, intensity, and western boundary indices of WNPSH can be effectively defined by the H e = 0-m contour in future warming climate scenarios without spurious trends. Third, the interannual variability of East Asian summer rainfall is more closely related to the H e -based WNPSH indices. We recommend that the H e metric be adopted as an operational metric on the WNPSH under the current warming climate.
The western North Pacific subtropical high (WNPSH) is the western extension of the North Pacific subtropical high (Yun et al. 2015). In summer, the WNPSH anchors the subtropical rain belt on its northwestern flank, where the moist southerly wind encounters mid-latitude air masses. The variability of the rain belt over East Asia is modulated by the variability of the WNPSH on intraseasonal (Zhu et al. 2003; Ren et al. 2013), interannual (Zhou and Yu 2005; Wen et al. 2015; Chen et al. 2016), and interdecadal (Gong and Ho 2002; Zhou et al. 2009; Matsumura et al. 2015) timescales. Wu et al. (2005) and Kim et al. (2012) showed that the WNPSH also regulates the genesis locations and paths of tropical cyclones over the western North Pacific (WNP). Anomalously strong or weak WNPSH causes widespread floods (Zhou and Yu 2005; Sampe and Xie 2010; Jiang et al. 2015), droughts (Park and Schubert 1997; Lin et al. 2012), and heat waves (Zhang et al. 2004; Wang et al. 2016) in East Asia.
Given the profound influence of the WNPSH on East Asian climate, great efforts have been devoted to monitoring and predicting abnormalities of the WNPSH. The WNPSH is usually measured by 500-hPa geopotential height (abbreviated as H hereafter). For example, a positive H anomaly over the WNP is interpreted as an anomalously strong WNPSH and vice versa (e.g., Gong and Ho 2002; Wu and Zhou 2008; Seo et al. 2013). China Meteorological Administration (CMA) defined the area, intensity, and western boundary indices of WNPSH based on H in its operational strategy. These real-time WNPSH indices are monitored (http://cmdp.ncc-cma.net/Monitoring/en_bulletin.php), and they are used as essential information for operational prediction of East Asian climate (Chen 1999; Liu et al. 2012).
However, it was reported that the H metric of the WNPSH may be misleading under the warming climate. Changes in circulation suggest that the WNPSH weakened and retreated eastward after the late 1970s (Huang et al. 2015; Huang and Li 2015; Wu and Wang 2015), although some previous studies showed intensification and westward extension of the WNPSH after the late 1970s based on the increase of H over the WNP (Gong and Ho 2002). Since the late 1970s, the zonal mean H (H m ) over the entire subtropical northern hemisphere has risen substantially due to global warming (Yang and Sun 2003; Wu and Wang 2015). This rise does not seem related to changes in circulation, since circulation is controlled by the horizontal gradient of H instead of the absolute magnitude of H. However, it remains unknown how fast H will rise in future and whether it is related to changes in circulation.
Recent studies have proposed a new metric of the WPNSH, i.e., eddy geopotential height (H e ), which is calculated by subtracting the simultaneous H m (0°N–40°N, 180°W–180°E averaged H) from the original H (Zhou et al. 2009; Huang et al. 2015; Huang and Li 2015; Wu and Wang 2015). The H e metric effectively captures the decadal change of the WNPSH seen in the late 1970s (Huang et al. 2015; Huang and Li 2015; Wu and Wang 2015), but it is not clear whether the H e metric is a good operational metric that well captures the mean state and interannual variability of the WNPSH in the warming climate. Based on the model projections of future climate from the Coupled Model Intercomparison Project Phase 5 (CMIP5) (Taylor et al. 2012) and on the reanalysis data, the current study aims to address the following questions: can we still use the H metric in the warming climate? Is the H e metric a good substitute for the H metric?
The remainder of the manuscript is organized as follows: the data, models, and methods are introduced in Sect. 2. The major difficulties in monitoring the WNPSH under the warming climate are documented in Sect. 3. A comparison between the H e metric and H metric is documented in Sect. 4. Finally, a summary is presented in Sect. 5.
2 Data, models, and methods
The observational datasets used in this study include (1) monthly geopotential height, temperature, surface pressure, and wind supplied by the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) (Kalnay et al. 1996) and (2) monthly precipitation from the Global Precipitation Climatology Project (GPCP) (Adler et al. 2003) and CPC Merged Analysis of Precipitation (CMAP) (Xie and Arkin 1997). Since the WNPSH has the greatest impact on East Asian climate during summer, we focus on the seasonal mean of June-July-August (JJA) for all the five variables.
The outputs of 31 CMIP5 models (Taylor et al. 2012) are adopted in this study. The names for these 31 models can be found in the supplementary information of He et al. (2015). The historical experiments are adopted as a baseline for the current climate, and the Representative Concentration Pathway 4.5 (RCP4.5) and RCP8.5 experiments are selected as the possible evolution pathways of future climate. The RCP4.5 (RCP8.5) is a median (high) pathway with a radiative forcing of 4.5 Wm−2 (8.5 Wm−2) by 2100 (Vuuren et al. 2011). For brevity, we only show figures based on RCP8.5 if they show similar spatial patterns to RCP4.5. Following the recommendation by Gleckler et al. (2008), we extract the forced response by using the multi-model median (MMM), which effectively suppresses the bias and internal variability of individual models. Although some models contain more than one ensemble member, we only use the first ensemble member (named “r1i1p1” in CMIP5 convention) of each model.
According to the four terms on the right-hand side of Eq. (3), the response of H to global warming is determined by the following four factors: uniform warming, temperature pattern, surface pressure, and the cross term of the nonlinear effect.
3 Difficulties with the H metric under the warming climate
To examine which terms in Eq. (3) dominate the rise of H, Fig. 1b–e shows the contributions of the four terms in Eq. (3) to changes in H, overlaid with the geostrophic wind derived from the corresponding H field. A uniform increase of H by 70 m is induced by zonal uniform warming (Fig. 1b), which contributes to more than 80% of the total increase of H over the WNP. Because wind is determined by the gradient of H but uniform warming makes little change to H gradient, the change in wind due to uniform warming is negligible over the WNP. The change in H attributable to the temperature pattern is characterized by a weakened meridional H gradient on the northern flank of the WNPSH, associated with strong easterly wind anomalies (Fig. 1c). Change in surface pressure contributes to a slight increase in the meridional H gradient and a slightly enhanced westerly wind on the northern flank of the WNPSH (Fig. 1d), which partially offsets the effect of temperature pattern. Changes in H and wind attributable to the cross term are negligible (Fig. 1e). The sum of the four aforementioned terms effectively reconstructs the total changes in H and off-equatorial winds (Fig. 1f). Overall, the rise in H is mostly caused by spatial uniform warming, which has negligible effects on circulation.
Although the rising trend of H is usually removed in scientific researches focusing on the interannual variability, however, the anomaly in operational practice is obtained by subtracting the climatology of a 30-year reference period. Following the recommendation of the World Meteorological Organization (WMO), the climatology is updated every 10 years (Livezey et al. 2007; Arguez and Vose 2011). For example, when discussing whether the WNPSH during 2011–2020 (2001–2010) are anomalously strong or weak, the corresponding climatology for the 1981–2010 (1971–2000) period should be adopted as a reference. The anomaly always lags the center of the reference period for 15–25 years, and on average, the anomaly lags the climatology for 20 years. As noted by Livezey et al. (2007), there is an extra lag of 2–3 years during which a new climatology is constructed and released. For example, the 1981–2010 climatology is likely to be released to substitute the 1971–2000 climatology in 2013 but not in January 1, 2011. However, as we will show later, a lag of only 20 years is enough to cause problems in characterizing the interannual variability of WNPSH.
As noted by both the MMM simulation (Fig. 3a) and reanalysis data (Fig. 3b), the amplitude of interannual variability (defined by the standard deviation of 8-year high-pass-filtered H) is smaller than 8 m at almost all grid points within the WNPSH. However, the MMM-projected rise of H m in 20 years is 22.2 m under RCP8.5 and 8.8 m under RCP4.5 (see Fig. 2a), which are greater than the interannual variability of H. Compared with an out-of-date climatology with much lower H m , positive anomalies of H would be obtained at almost all grid points in almost every year. Based on the positive anomalies of H, the WNPSH would be interpreted as anomalously wide, strong, and westward extended in almost every year, and the interannual variability of the WNPSH cannot be objectively monitored.
Under the warming climate, we encounter two major difficulties when measuring the WNPSH with the traditional H metric. First, the western boundary of the WNPSH as defined by the widely used H = 5880-m contour would become invalid in the near future, as a result of the increasing H m . Second, the rapidly rising H m , which has a negligible effect on circulation, would give rise to spurious information regarding the interannual variability and long-term change of the WNPSH. Although the widely used H metric performs well in an unchanged climate, it may not be suitable in a warming climate. It is necessary to look for a new operational metric that applies to the warming climate. This new metric should be convenient to use, and it should be a useful tool for diagnosing the climate phenomena associated with the WNPSH.
4 A comparison between the H metric and the H e metric under the warming climate
Area index, the area of the region enclosed by the boundary of the WNPSH. This was calculated as the number of grid points with H ≥ 5880 m over 110°E–180°E, 10°N–85°N. We suggest that the area index be calculated as the number of grid points with H e ≥ 0 m. A higher (lower) area index means that the area of WNPSH is larger (smaller).
Intensity index, the volume of the WNPSH in three-dimensional space. This was calculated as the sum of H minus 5870 m for all the grid points with H ≥ 5880 m over 110°E–180°E, 10°N–85°N. We suggest that the intensity index be calculated as the sum of H e for the grid points with H e ≥ 0 m over the same region. A higher (lower)-intensity index indicates a stronger (weaker) WNPSH.
Western boundary index, the location of the western boundary of the WNPSH. This was defined as the longitude of the westernmost grid point with H ≥ 5880 m over 90°E–180°E. We suggest that the western boundary index be defined as the longitude of the westernmost grid point with H e ≥ 0 m over 90°E–180°E. A higher (lower) western boundary index indicates an anomalous eastward retreat (westward extension) of the WNPSH.
Using the CMIP5 model outputs, the applicability of the H e metric in the future warming climate is assessed in Sect. 4.1, in comparison with the widely used H metric. Using observational data, a comparison between these two metrics is presented in Sect. 4.2 to investigate the applicability of the H e metric to observations.
4.1 A comparison between the H metric and the H e metric in model simulations
In contrast to the changing rainfall-H relationship, the relationship between rainfall and H e is consistent across different climate backgrounds (Fig. 4b). The least squares regression lines for the historical, RCP4.5, and RCP8.5 simulations almost overlap each other. For these three simulations, the linear relationships between rainfall and H e are all statistically significant at the 99% confidence level, according to the Student’s t test. This evidence suggests that it is more reasonable to relate the abundance of rainfall to a fixed H e contour rather than a fixed H contour under warming climate conditions.
As consistently shown by previous climate projection studies, the impact of global warming on East Asian climate is moderate, characterized by a generally unchanged location of the Meiyu (also called Baiu in Japanese or Changma in Korean) belt (Seo et al. 2013) and modest changes in the East Asian monsoon region (Kitoh et al. 2013). The WNPSH at 500 hPa is expected to weaken and retreat eastward in response to global warming, and the magnitudes of the changes will also be modest (He et al. 2015). Therefore, the strong trends of expansion, intensification, and westward extension shown by the H metric (lines in Fig. 5) are inconsistent with the projected future changes in circulation and rainfall.
Contrary to the H metric, the indices based on the H e metric show a moderate trend toward a contracted area, weakened intensity, and eastward retreat of the western boundary (bars in Fig. 5). The area index decreases from approximately 143 at the beginning (2006–2015) to approximately 105 at the end (2090–2099) of the twenty-first century. The intensity index decreases from about 90 m at the beginning to about 65 m at the end of the twenty-first century. The western boundary retreats from about 129°E at the beginning to about 136°E at the end of the twenty-first century, consistent with He et al. (2015). Unlike the invalid western boundary index based on H metric, all three indices can be well defined throughout the twenty-first century using H e metric.
The evidence presented above based on CMIP5 models suggests that the rainfall-H e relationship is more robust than the rainfall-H relationship. The area, intensity, and western boundary indices could be defined well using H e metric if the warming trend continues. The projected long-term trends of the area, intensity, and western boundary indices based on H e are consistent with the projected changes in circulation and rainfall. Given the inevitable bias of the models, it still must be addressed whether the H e metric is applicable to observation data for recent decades.
4.2 A comparison between the H metric and the H e metric with respect to observation data
The WMO recommended that an “anomaly” in operational practice be defined by subtracting the climatology of a 30-year reference period. In a warming climate with rising H m , an out-of-date climatology may lead to a spurious anomaly under the H metric. An example is shown in Fig. 7c for the western boundary index measured by H. Compared to the 1951–1980 climatology (blue horizontal line in Fig. 7c), anomalous westward extension of the WNPSH is seen in 8 of the 10 years during 1981–1990. Compared to the 1961–1990 climatology (green horizontal line in Fig. 7c), anomalous westward extension of the WNPSH is seen in all the 10 years during 1991–2000. Compared to the 1971–2000 climatology (red horizontal line in Fig. 7c), anomalous westward extension of WNPSH is seen in 9 of the 10 years during 2001–2010.
Despite the fact that there may have been real decadal trends of the WNPSH in past decades, a strong rising trend of H m without accompanying changes in circulation could also result in spurious anomalies based on the H metric. In such circumstances, the WNPSH would be taken as anomalously wide, strong, and westward extended in almost every year. This spurious information regarding the interannual variability of the WNPSH may further obstruct the prediction of climate phenomena related to the WNPSH. As already shown in Fig. 3, the rising trend of H m is strong enough to overwhelm the interannual variability of H over the WNP under both RCP4.5 and RCP8.5. Therefore, cautions should be taken when measuring the WNPSH with the H metric. However, we would not encounter such problems if we used H e metric, since the rising trend of H m is automatically removed when calculating H e .
Compared to the regression field based on the H metric (Fig. 8a), more areas with rainfall anomalies exceeding the 95% confidence level are seen based on the H e metric (Fig. 8b). In particular, the well-known meridional triple pattern of interannual rainfall variability in eastern China (e.g., Sun and Wang 2015) is captured by the H e metric. When the WNPSH is abnormally westward extended, both GPCP and CMAP data show positive rainfall anomalies along the Yangtze-Huai River, accompanied by negative rainfall anomalies over south China and north China (Fig. 8b). Consistent with the regressed rainfall anomalies, the regressed anomalies of vertical motion and horizontal water vapor transport are also stronger and more statistically significant if the western boundary index is defined by the H e metric (Fig. 8c, d). This evidence suggests that the H e metric better captures the relation of the WNPSH with the interannual variability of East Asia summer rainfall. Similarly, the H e metric also outperforms the H metric in terms of the area and the intensity indices of WNPSH under the warming climate (figure not shown).
Based on CMIP5 model simulations and NCEP/NCAR reanalysis data, the evidence presented here suggests that the H e metric is applicable to characterize the WNPSH under a changing climate. Previous studies have adopted other variables to overcome the difficulties caused by a rising H m , such as relative vorticity (Yang and Sun 2003; Qian and Shi 2016) and stream function (Li et al. 2012). However, relative vorticity is not good at characterizing the shape of the WNPSH (Huang et al. 2015). Although stream function captures the shape of the WNPSH as well as H e (Li et al. 2012; He et al. 2015), it is hard to calculate the stream function by solving Poisson equation using global wind field. However, it is much easier to calculate H e using the H data within the 0°N–40°N region, for both grid data and station observations. Therefore, the H e metric can be widely used as the operational metric of the WNPSH under the warming climate.
As determined by both theoretical formulation of the hypsometric equation and CMIP5 model projections, the zonal mean H (H m ) over the subtropical northern hemisphere is rising because of global warming. The MMM-projected linear trend of H m for the twenty-first century is 0.44 m/year under RCP4.5 and 1.11 m/year under RCP8.5. Decomposition according to the hypsometric equation suggests that more than 80% of the increase in H are attributable to spatial uniform warming, which has a negligible impact on circulation. The response of WNPSH circulation to global warming is determined by the change in H gradient, especially the meridional H gradient, which is mostly attributable to the change in temperature pattern, independent of the systematic rise in H m .
The rising trend of H m due to global warming gives rise to difficulties when measuring the WNPSH with the traditional H metric. Due to the rising H m , any fixed contour of H expands rapidly. Spurious expanding, enhancing, and westward extending trends may be interpreted from the rising H m . The western boundary of WNPSH may become invalid in a few decades if the current warming trend continues. Under both RCP4.5 and RCP8.5 scenarios, the rising trends of H are strong enough to overwhelm the interannual variability of H over the WNP. In operational practice, spurious anomalies on interannual timescales would result from comparing the current H value to the out-of-date climatology of the past 30-year period.
The H e metric effectively captures the variation of the WPNSH under the warming climate. Compared to H, H e is a better indicator of the abundance of rainfall, and the rainfall-H e relationship remains generally unchanged under different climate backgrounds. The area, intensity, and western boundary indices of the WNPSH can be effectively defined using the H e metric, and the long-term trends of these three indices are consistent with the projected changes in circulation. Finally, the indices defined by the H e metric effectively capture the relationship of the WNPSH to the interannual rainfall variability of East Asia.
Despite similar performance of the H metric and the H e metric under an unchanged climate, the H e metric is more suitable under a changing climate, especially in the current warming climate characterized by a rapidly rising H m . We recommend that the WNPSH be measured with H e by removing the simultaneous H m from the original H field. We also recommend the WNPSH indices be defined by the H e = 0-m contour instead of the H = 5880-m contour. Besides WNPSH, the H e metric may also be suitable for measuring other high/low-pressure systems, ridges, and troughs under the warming climate, such as the Indian-Burma trough (Wang et al. 2011) and the South Asia High (Wei et al. 2014; Xue et al. 2015; Qu et al. 2015).
We wish to thank the NOAA and PCMDI who provided the observational data and model data. The observational data were obtained via the NOAA website (http://www.esrl.noaa.gov/psd/data/), and the model data were obtained via the PCMDI website (http://pcmdi.llnl.gov). This work was supported by National Basic Research Program of China (2014CB953901), National Natural Science Foundation of China (41505067, 41330423, 41575043, 41375095, 41675096), and Science and Technology Program of Guangzhou (201607010153).
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