Intraseasonal Variability of Summertime Surface Air Temperature over Mid–High-Latitude Eurasia and Its Prediction Skill in S2S Models

中高纬欧亚大陆夏季地表气温季节内变率及其在S2S模式中的预报技巧

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  • Corresponding author: Shuangyan YANG, yangsy@nuist.edu.cn
  • Funds:

    Supported by the National Key Research and Development Program of China (2018YFC1505803 and 2018YFC1505905), Natural Science Foundation of Jiangsu Province (BK20210660 and BK20191404), and National Natural Science Foundation of China (42088101)

  • doi: 10.1007/s13351-021-1131-x

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  • Features of the dominant modes of surface air temperature (SAT) on the intraseasonal timescale over the mid–high-latitude Eurasia (MHE) during boreal summer (June–September) are investigated based on the ERA5 reanalysis data from 1979 to 2016. The intraseasonal variability (ISV) of SAT over MHE is primarily characterized by an eastward propagation along 60°N, which is found to impact the regional weather in China, including summertime extreme hot and cool events. The forecast skill and potential predictability of the ISV of SAT over MHE are assessed for 5 dynamical models that have participated in the subseasonal-to-seasonal (S2S) prediction project, by analyzing 12 years’ (1999–2010) model reforecast/hindcast data. By using the principal component (PC) index of the leading intraseasonal SAT modes as a predictand, we found that the forecast skill for ISV of SAT can reach out to 11–17 days, and the ECMWF model exhibits the best score. All the S2S models tend to show 1) a relatively higher skill for strong intraseasonal oscillation (ISO) cases, 2) a systematic underestimate of the amplitude of the SAT ISV signal, and 3) different skills during different phases of ISO cases. Analysis of potential predictability based on the perfect-model assumption reveals a 4–6-day skill gap for most models, and the skill gap also varies among different phases of ISO events. The results imply the need for continued development of operational forecasting systems to improve the actual prediction skills for the ISV of SAT over MHE.
    基于1979–2016年ERA5再分析资料地表气温数据,本文揭示了欧亚大陆夏季地表气温季节内变率的主要模态。该气温模态主要表现为沿60°N向东传播的特征,并且会对我国的区域天气(比如极端温度事件)产生一定的影响。使用5家参与次季节–季节(S2S)预报计划的模式回报资料,分析了动力模式对该时间尺度气温模态的预报能力。使用气温主模态对应的主成分序列(PC)作为预报因子,研究发现5家动力模式对该季节内气温模态的预报水平可以达到11–17天,其中ECMWF数值预报模式表现最优。所有的模式都表现为对强振幅事件更高的预报技巧,并且都对观测中的季节内信号振幅有系统性的低估。同时,所有模式都表现为明显的预报技巧的位相依赖性特征。基于完美模式假设的潜在可预报性分析表明,对于大多数S2S模式,目前的预报技巧仍有4–6天的提升空间。这些结果表明了持续发展改进动力模式预报系统、提高中高纬欧亚大陆地表气温季节内信号预报技巧的可能性和重要性。
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  • Fig. 1.  Distributions of the variance (shading; K2) of (a) daily SAT (namely T2m) anomaly and (c) 10–50-day filtered SAT anomaly during boreal summer (June–September; JJAS) of 1979–2016. (b) The power spectra of the areal-averaged SAT anomaly (K2) over the box area in (a), including the Markov red noise spectrum (dashed curve) and the 95% confidence level (dash-and-dot curve).

    Fig. 2.  The (a) first and (b) second EOF modes of the intraseasonal SAT field during summer (JJAS) of 1979–2016. Hatching indicates the statistical significance at the 95% confidence level for shaded anomalies. (c) The lead–lag correlation between the first two PCs. The red dashed lines represent the 95% confidence level. (d) Schematic phase–space diagram formed by PC1 and PC2. The location of the positive SAT anomaly for the corresponding phase space is labeled in the diagram.

    Fig. 3.  Composites of the intraseasonal SAT (shading; K) and 850-hPa horizontal wind (vector; m s−1) anomalies for (a–h) eight SAT phases during boreal summer for the period of 1979–2016. Refer to Section 3 for the definition of eight SAT phases. Shaded areas indicate the SAT anomalies exceeding the 95% confidence level (Student’s t-test).

    Fig. 4.  Composites of intraseasonal SAT anomalies for (a–h) eight SAT phases during boreal summer for the period of 1979–2016. The black dots denote the areas exceeding the 95% confidence level (Student’s t-test).

    Fig. 5.  Distributions of the occurrence frequency of (a) extreme hot days and (b) extreme cool days for eight SAT phases in boreal summer of 1979–2016. See Section 3 for definitions of extreme hot/cool days.

    Fig. 6.  Bivariate (a) anomaly correlation (ACC), (b) root-mean-square error (RMSE), and (c) ensemble mean RMSE (dashed lines) and ensemble spread (solid lines), as a function of lead time for S2S reforecasts during summer of 1999–2010. ECCC—Environment and Climate Change Canada, JMA—Japan Meteorological Agency, UKMO—the UK Met Office, CMA—China Meteorological Administration.

    Fig. 7.  Bivariate ACC as a function of lead time (day) for S2S reforecasts for initial (denoted by dash-and-dot lines) and target (denoted by dashed lines) strong ISO cases over MHE during boreal summer of 1999–2010. Solid curves are the ACCs estimated for all ISO cases as in Fig. 6a.

    Fig. 8.  (a) Bivariate ACC (shading) as a function of lead time (x axis; day) and initial phases (y axis) for S2S reforecasts for initial strong ISO cases (amplitude larger than 1.0). (b) As in (a), but for prediction skill as a function of lead time (x axis; day) and target phases (y axis) during summer of 1999–2010. Solid curves highlight the ACCs of 0.5.

    Fig. 9.  (a) Amplitude error of the first two PCs for S2S reforecasts. (b) Amplitude bias of the first two PCs averaged over the first 15 days in individual target ISO phase for S2S reforecasts. (c) Phase angle error (°) for the target strong ISO cases for S2S reforecasts. (d) Phase angle error (°) averaged over the first 15 days in individual target ISO phases for S2S reforecasts during boreal summer of 1999–2010.

    Fig. 10.  (a) The actual skill (solid curve) and an estimation of potential predictability (dashed curves) as functions of lead time (day) for S2S reforecasts for all ISO cases. (b) The potential predictability (contours) and skill gap (predictability minus actual prediction skill; shadings) as functions of lead day and target ISO phases for five S2S model reforecasts during summer of 1999–2010.

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Intraseasonal Variability of Summertime Surface Air Temperature over Mid–High-Latitude Eurasia and Its Prediction Skill in S2S Models

    Corresponding author: Shuangyan YANG, yangsy@nuist.edu.cn
  • 1. Key Laboratory of Meteorological Disaster, Ministry of Education (KLME)/Joint International Research Laboratory of Climate and Environmental Change (ILCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing 210044, China
  • 2. International Pacific Research Center and Department of Atmospheric Sciences, School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, USA
Funds: Supported by the National Key Research and Development Program of China (2018YFC1505803 and 2018YFC1505905), Natural Science Foundation of Jiangsu Province (BK20210660 and BK20191404), and National Natural Science Foundation of China (42088101)

Abstract: Features of the dominant modes of surface air temperature (SAT) on the intraseasonal timescale over the mid–high-latitude Eurasia (MHE) during boreal summer (June–September) are investigated based on the ERA5 reanalysis data from 1979 to 2016. The intraseasonal variability (ISV) of SAT over MHE is primarily characterized by an eastward propagation along 60°N, which is found to impact the regional weather in China, including summertime extreme hot and cool events. The forecast skill and potential predictability of the ISV of SAT over MHE are assessed for 5 dynamical models that have participated in the subseasonal-to-seasonal (S2S) prediction project, by analyzing 12 years’ (1999–2010) model reforecast/hindcast data. By using the principal component (PC) index of the leading intraseasonal SAT modes as a predictand, we found that the forecast skill for ISV of SAT can reach out to 11–17 days, and the ECMWF model exhibits the best score. All the S2S models tend to show 1) a relatively higher skill for strong intraseasonal oscillation (ISO) cases, 2) a systematic underestimate of the amplitude of the SAT ISV signal, and 3) different skills during different phases of ISO cases. Analysis of potential predictability based on the perfect-model assumption reveals a 4–6-day skill gap for most models, and the skill gap also varies among different phases of ISO events. The results imply the need for continued development of operational forecasting systems to improve the actual prediction skills for the ISV of SAT over MHE.

中高纬欧亚大陆夏季地表气温季节内变率及其在S2S模式中的预报技巧

基于1979–2016年ERA5再分析资料地表气温数据,本文揭示了欧亚大陆夏季地表气温季节内变率的主要模态。该气温模态主要表现为沿60°N向东传播的特征,并且会对我国的区域天气(比如极端温度事件)产生一定的影响。使用5家参与次季节–季节(S2S)预报计划的模式回报资料,分析了动力模式对该时间尺度气温模态的预报能力。使用气温主模态对应的主成分序列(PC)作为预报因子,研究发现5家动力模式对该季节内气温模态的预报水平可以达到11–17天,其中ECMWF数值预报模式表现最优。所有的模式都表现为对强振幅事件更高的预报技巧,并且都对观测中的季节内信号振幅有系统性的低估。同时,所有模式都表现为明显的预报技巧的位相依赖性特征。基于完美模式假设的潜在可预报性分析表明,对于大多数S2S模式,目前的预报技巧仍有4–6天的提升空间。这些结果表明了持续发展改进动力模式预报系统、提高中高纬欧亚大陆地表气温季节内信号预报技巧的可能性和重要性。
    • In the climate research community, the prediction in the subseasonal range, which usually refers to the forecast timescale between 2 weeks and 3 months, has been an increasingly hot topic in the last 10 years (Brunet et al., 2010; Robertson et al., 2015; Mariotti et al., 2018, 2020), and it plays a vital role in improving the weather service and associated social economy (Lemos et al., 2012). It is recognized that the short-range weather forecast (less than 10 days) depends primarily on the atmospheric initial conditions, while the skill and predictability of climate prediction (monthly to seasonal) usually stem from the boundary forcing (i.e., land, ocean, snow cover, and sea ice). However, the subseasonal prediction, which lies between the timescale of weather forecast and that of climate prediction, is both an initial value problem and a boundary value problem, and it has long been considered as a “desert of predictability.” The grand challenge for the subseasonal prediction lies in that the information included in the initial condition of the atmosphere is almost lost (Lorenz, 1969) and it only marginally benefits from the underlying boundary forcing (White et al., 2017), calling for substantial efforts to develop a rationale for subseasonal prediction (NASEM, 2016). In spite of the great challenge, the subseasonal prediction has achieved remarkable and inspiring progress in the past decades with the aid of some multi-agency and international projects. For example, in Novem-ber 2013, the World Weather Research Programme (WWRP) and World Climate Research Programme (WCRP) jointly created an international subseasonal-to-seasonal (S2S) prediction project (Vitart et al., 2017), with the aim of addressing this challenge and bridging the gap between the weather forecast and climate prediction communities (Hudson et al., 2011).

      As the most prominent mode of subseasonal variability in the tropical atmosphere, the Madden–Julian oscillation (MJO) has been recognized as one of the primary predictability sources for subseasonal predictions in the global climate system. Predictions of the MJO signal in various state-of-the-art dynamical models have been discussed in a number of studies (e.g., Liu et al., 2017; Kim et al., 2018; Jiang et al., 2020). Many studies also demon-strated that the impact of the teleconnection associated with MJO can extend into the middle and high latitudes, taking the form of Rossby wave trains induced by anoma-lous diabatic heating (Sardeshmukh and Hoskins, 1988; Ferranti et al., 1990; Kiladis and Weickmann, 1992; Jin and Hoskins, 1995; Stan et al., 2017). It is widely accepted that MJO has an important influence on the extratro-pical climate and weather on the subseasonal timescale. For example, it is reported that MJO can act as a critical player in modulating the subseasonal variability of surface air temperature (SAT) over the Northern Hemisphere continents (Seo et al., 2016), including Canada (Lin and Brunet, 2009), the Contiguous United States (Hu et al., 2019), the Arctic region (Yoo et al., 2012; Cui et al., 2020), and East Asia (Jeong et al., 2005). However, the impact of MJO on predictions of the mid- and high-latitude SAT variability is still a vague problem. Xiang et al. (2019, 2020) pointed out that the role of MJO in subseasonal predictions of extratropical wintertime SAT anomalies over the Northern Hemisphere is not that significant.

      Additionally, in recent decades, a growing number of studies have been devoted to unraveling the characteris-tics and dynamics of the intraseasonal oscillation (ISO) over middle and high latitudes (Ghil and Mo, 1991; Plaut and Vautard, 1994; Yang and Li, 2016; Xu et al., 2020; Zhu et al., 2020; Zhu and Yang, 2021). The mid–high-latitude ISO is usually characterized by a quasi-barotropic vertical structure, which is significantly distinct from the baroclinic vertical structure of the tropical intraseasonal oscillation. It is noteworthy that the mid–high-latitude ISO signals also have significant impacts on the weather and climate over the extratropics. For example, it can modulate rainfall variability (Lau and Weng, 2002), heat waves (Teng et al., 2013), and blockings (Yang and Li, 2017) in the mid–high latitudes. Wang et al. (2013) investigated the initiation and development of the midlati-tude ISO over North Pacific in boreal summer and found that the ISO signal is mainly caused by local processes. In contrast, only about 20% of the total subseasonal variability can be explained by the tropical forcing. Stan and Krishnamurthy (2019) pointed out three significant propagating oscillations over the extratropics and found that in a linear regression model, the potential predicta-bility of SAT anomalies can be extended to approxi-mately 20 days when the midlatitude oscillations are added into the predictors.

      Furthermore, the prediction of the ISO over mid–high latitudes has also been investigated with the aid of the state-of-the-art dynamical models in recent years. On the basis of the hindcast data from three dynamical prediction models, Lin (2018) assessed the model skill in predicting the leading modes of intraseasonal SAT ano-malies in boreal winter over extratropics (the Eurasian mode and North American mode). The Eurasian mode in their study is found to have better skills and can benefit from the initial MJO signal. With a Geophysical Fluid Dynamics Laboratory (GFDL) coupled model, the subseasonal prediction of SAT during boreal winter is investigated in Xiang et al. (2019). The Eurasian meridio-nal dipole mode, which is one of the most predictable modes in their study, can be skillfully predicted four weeks in advance. However, there is still little research on systematic assessment of the prediction skill for the mid–high-latitude ISO in dynamical models during boreal summer. Thus, in this study, we will examine the dominant intraseasonal SAT modes over mid–high-latitude Eurasia (MHE) in boreal summer (June–September), in conjunction with a systematic estimation of the prediction skill and potential predictability of the intraseasonal SAT variability based on the S2S model hindcasts.

      The remainder of the paper is structured as follows. In Section 2, the data (observations and S2S hindcasts) and methodologies utilized to assess the prediction skill are introduced. Section 3 illustrates the structure and evolution characteristics of the observational SAT signals on the intraseasonal timescale over MHE during boreal summer, along with the impacts of the ISO signals on extreme temperature events over China. The prediction skill for the intraseasonal variability (ISV) of SAT over MHE in the S2S models is assessed in Section 4. Section 5 documents the potential predictability estimated for the SAT ISV over MHE in five S2S models. Section 6 is the summary and discussion.

    2.   Data and methodology
    • Our analysis is based on the reforecast (sometimes known as hindcast) data from five operational centers in Europe, China, Japan, Canada, and the United Kingdom, which participated in the S2S prediction project. The hindcast data used in this study cover 12 extended summers (June–September) from 1999 to 2010. The common lead time from Day 0 to 30 are used and the data on varied horizontal resolutions from different S2S models are interpolated onto a 1.5° × 1.5° grid. More details about the S2S hindcast data used in this study can be found in Vitart et al. (2017).

      The daily zonal and meridional winds, geopotential height, and surface air temperature at 2 m (T2m) on a 1.5° grid from the fifth generation ECMWF atmospheric reanalysis (ERA5; Hersbach et al., 2018) are utilized as the observational data to verify the prediction skill of the ISV of SAT over MHE. Daily T2m and precipitation data on a 0.25° grid for 1961–2017 from the CN05.1 dataset produced by the China Meteorological Administration (CMA) are also used in the present study (Wu and Gao, 2013).

      Considering that the length of the reforecast dataset is too short for employing traditional temporal band-pass (BP) filter to compute the intraseasonal fields, we define forecast intraseasonal (10–50-day) fields by using a non-BP-filtering method following Hsu et al. (2015). Detailed steps of the non-BP-filtering method in extracting the intraseasonal signals in observations and S2S model reforecasts can be found in the “Method” section in our previous work (Cui et al., 2021).

      To obtain the dominant patterns of the MHE SAT anomalies on intraseasonal timescale in the observation, an empirical orthogonal function (EOF) analysis is applied to the observational SAT anomalies. The amplitude of an ISO event is defined as $ {\rm{IS}}{{\rm{O}}_{{\rm{amp}}}}{\rm{ = }}\sqrt {{\rm{PC}}{{\rm{1}}^{\rm{2}}}{\rm{ + PC}}{{\rm{2}}^{\rm{2}}}}$, in which the PC1 and PC2 are the normalized principal components (PCs) of the leading two EOFs. Forecast PCs are derived by means of projecting the forecast anomalous SAT field onto the observational EOF1 and EOF2 patterns.

      To measure the prediction skill of the ISV of SAT over MHE in S2S reforecasts, the anomaly correlation (ACC) and root-mean-square error (RMSE) in the forms applicable to a bivariate index are used to evaluate the model forecasts at individual lead time (Lin et al., 2008). The bivariate ACC and RMSE computed between the observational and predicted PCs are commonly used when estimating the forecast skill of intraseasonal oscillations (Jie et al., 2017; Liu et al., 2017; Cui et al., 2021). It is elucidated in Lin et al. (2008) that the bivariate ACC can measure the skill of models in predicting the phase of an ISO event, and it is insensitive to amplitude errors. In contrast, the bivariate RMSE is associated with both the phase and amplitude errors. Furthermore, the bivariate ACC and RMSE are respectively equivalent to a pattern correlation and the areal-averaged RMSE between the observation and model reforecast when expressed by the first two EOFs. The propagation speed of ISO signals in predictions is also evaluated in this study by using the phase angle error. Further details on the measures of prediction skills can be found in Rashid et al. (2011) and Lin et al. (2008).

    3.   Dominant intraseasonal SAT modes over MHE
    • Variance of the anomalous SAT field over the Eurasia continent in boreal summer is illustrated in Fig. 1a. It is found that mid-to-high-latitude land regions (51°–75°N, 60°–141°E; denoted by the box in Fig. 1a) show pronounced SAT variability. As suggested by the power spectra of the areal-averaged SAT time series over the box area (Fig. 1b), the SAT anomalies over this domain exhibit a significant intraseasonal period of about 10–50 days based on the red noise spectrum at the 95% confidence level. Shown in Fig. 1c is the variance of 10–50-day SAT anomalies filtered by the Lanczos BP filter (Duchon, 1979). It is noted that relatively larger intraseasonal SAT variability is found over MHE as depicted in Fig. 1a as well. Accordingly, in the analysis below, we will focus on the 10–50-day intraseasonal SAT variability over MHE during boreal summer.

      Figure 1.  Distributions of the variance (shading; K2) of (a) daily SAT (namely T2m) anomaly and (c) 10–50-day filtered SAT anomaly during boreal summer (June–September; JJAS) of 1979–2016. (b) The power spectra of the areal-averaged SAT anomaly (K2) over the box area in (a), including the Markov red noise spectrum (dashed curve) and the 95% confidence level (dash-and-dot curve).

      An EOF analysis is utilized to derive the prominent modes of MHE SAT on intraseasonal timescale, and it is conducted for the anomalous SAT fields in the region of 36°–81°N, 21°–141°E during boreal summer (June–September) from 1979 to 2016. Illustrated in Figs. 2a, b are the first two spatial patterns of the EOF analysis (i.e., EOF1 and EOF2), which are not separable and are independent from higher EOF patterns in accordance with the criteria of North et al. (1982). The percentage of variance explained by the first two modes is 15.4% and 13.3%, respectively. EOF1 captures the west–east dipole mode of the intraseasonal SAT anomalies over the MHE domain and EOF2 exhibits a triple mode of the SAT perturbation centers over this domain, representing the propagating features of the ISV of SAT over MHE. The correlation between the two PCs reaches the maximum with PC1 leading (lagging) PC2 by about four days (Fig. 2c). It is noteworthy that the same EOF analysis has been applied to the intraseasonal SAT obtained by using the abovementioned non-BP-filtering method. The result demonstrates that the spatial distribution of the two leading EOF patterns and the lead–lag relationship between the corresponding PCs show common characteristics with that derived from traditional BP-filtering method (figures omitted).

      Figure 2.  The (a) first and (b) second EOF modes of the intraseasonal SAT field during summer (JJAS) of 1979–2016. Hatching indicates the statistical significance at the 95% confidence level for shaded anomalies. (c) The lead–lag correlation between the first two PCs. The red dashed lines represent the 95% confidence level. (d) Schematic phase–space diagram formed by PC1 and PC2. The location of the positive SAT anomaly for the corresponding phase space is labeled in the diagram.

      As illustrated in Fig. 2d, based on PC1 and PC2, eight phases of the intraseasonal SAT anomalies over MHE are then defined by using the same method developed in Wheeler and Hendon (2004). The ISO at a certain time can be denoted as a two-dimensional spatial vector T.

      $$\hspace{-6pt} {\boldsymbol{T}}\left( t \right)=\left[ {{\rm{PC1}}\left( t \right),{\rm{PC2}}\left( t \right)} \right], $$ (1)
      $$\hspace{-6pt} {{A}}\left( t \right) = {\rm{PC}}1^{2}{{\left(t \right)}}+ {\rm{PC}}2^2{{\left( t \right)}}, $$ (2)
      $$\hspace{-18pt} {{a}}\left(t \right){\rm{ = ta}}{{\rm{n}}^{{\rm{ - 1}}}}\left[ {\dfrac{{{\rm{PC2}}\left( t \right)}}{{{\rm{PC1}}\left( t \right)}}} \right], $$ (3)

      where A(t) represents the amplitude of an ISO event, and a(t) is the phase angle between PC1 and PC2 in the range from −$ –\pi $ to $ \pi $. It is assumed that a(t) equals ${{a}}\left( t \right) +{\rm{ 2}}{\pi}$ when a(t) is negative in this study. Taking the 16-day life cycle as an example, the duration of each phase is about 2 days. As depicted in Fig. 2c, when PC1 leads PC2 by four days, their positive correlation coefficient reaches a peak. As shown in Fig. 2d, when PC1 and PC2 are both positive and PC1 is greater than PC2, which means that the value of a(t) is between 0 and π/4, the ISO case is in Phase 1. The eight phase angle range is from 0 to 2π and the angle interval is π/4.

      According to the SAT phases defined by PC1 and PC2, composites of 10–50-day filtered SAT and 850-hPa horizontal wind anomalies for the eight phases are illustrated in Fig. 3, clearly depicting the eastward-propagating characteristic of the ISV of SAT over MHE. The positive SAT perturbation center is located over western Russia at about 60°N, 70°E, which is approximately to the north of the Ural Mountains in Phase 2. The subsequent phases witness the continuous eastward propagation of the anomalous positive SAT center and it is situated to the north of Lake Baikal at about 60°N, 110°E in Phase 5. From Phase 6 to 1, southward shifting of the positive SAT center from about 60° to 40°N is detected, which indicates that the anomalous SAT filed over East China can be affected by the ISO signal, albeit with the relatively small amplitude of positive SAT signals in these phases. The same analysis using the anomalous SAT field derived from the non-BP-filtering method for the composites exhibits similar propagating and evolutionary features, as shown in Fig. 3.

      Figure 3.  Composites of the intraseasonal SAT (shading; K) and 850-hPa horizontal wind (vector; m s−1) anomalies for (a–h) eight SAT phases during boreal summer for the period of 1979–2016. Refer to Section 3 for the definition of eight SAT phases. Shaded areas indicate the SAT anomalies exceeding the 95% confidence level (Student’s t-test).

      Considering the significant ISO signals of SAT anomalies over MHE, we further investigate the possible impacts of the leading intraseasonal SAT mode on the occurrence frequency of extreme events over China, which can exert considerable impacts on the society and economy. Composite maps of SAT anomalies for different phases over China are illustrated in Fig. 4. Taking the positive anomalous SAT signals for example, significant positive SAT anomalies are located over Northwest China in Phases 5 and 6, which strengthen and move southeastward, and reside over central China and Northeast China in Phases 7 and 8. In Phases 1 and 2, the positive SAT anomalies are mainly observed over South China with a relatively small amplitude. In Phases 3 and 4, the impact of the positive anomalous SAT signals is mainly detected over Northwest China. Daily mean SAT from the CN05.1 dataset is utilized to identify extreme weather events in summer (June–September) following Hsu et al. (2017). The extreme hot (cool) day is defined as the date when daily mean SAT goes over (falls below) the climatological 95th-percentile (5th-percentile) thre-shold. Being largely in accord with spatial patterns of the intraseasonal SAT mode, the relatively frequent occurrence of extreme hot (cool) days is observed over Northwest China in Phases 5–6 (1–2), and over South China in Phases 7–8 (5–6) (Figs. 5a, b). For North China, one of the most populated regions in China, it tends to have the relatively more frequent extreme hot (cool) days in Phases 7–8 (3–4).

      Figure 4.  Composites of intraseasonal SAT anomalies for (a–h) eight SAT phases during boreal summer for the period of 1979–2016. The black dots denote the areas exceeding the 95% confidence level (Student’s t-test).

      Figure 5.  Distributions of the occurrence frequency of (a) extreme hot days and (b) extreme cool days for eight SAT phases in boreal summer of 1979–2016. See Section 3 for definitions of extreme hot/cool days.

      In a nutshell, the ISO signals of SAT over MHE can modulate the occurrence of extreme temperature events over China during boreal summer, which may be favorable to the prediction of these extreme events over China. Since we mainly focus on the observational ISO signals in the analysis above, next we will further investigate how well the state-of-the-art operational models predict the ISO signals of SAT over MHE.

    4.   Forecast skill of the ISV of SAT
    • The prediction skill of the MHE SAT signals on intraseasonal timescale in S2S model reforecasts is evaluated with the PCs derived by projecting the reforecast SAT anomalies onto the observed two leading EOF modes, as mentioned in Section 2. Many previous studies have utilized this method for the estimation of the forecast skill (e.g., Vitart et al., 2007; Lin et al., 2008; Seo et al., 2009).

      Figure 6 displays the forecast skill of the PC index computed between the observations and S2S model reforecasts in boreal summer for the common reforecast period of 1999–2010. As depicted in Fig. 6a, taking bivariate ACC = 0.5 as the upper bound of useful skill, these S2S models exhibit maximum prediction skills of 11–17 days, with ECMWF model exhibiting the highest skill (17 days). As illustrated in Fig. 6b, the variation of RMSE also indicates that the prediction of ISV of SAT over MHE turns out to be unskillful beyond the lead time of about 11–17 days for these models, when the bivariate RMSE goes beyond the value of $ \sqrt {\rm{2}} $. Note that due to the fact that the forecast skill estimated for ensemble mean reforecasts for these operational models is superior to that from individual member (figures omitted), only the ensemble mean results for S2S model reforecast data are presented in this study.

      Figure 6.  Bivariate (a) anomaly correlation (ACC), (b) root-mean-square error (RMSE), and (c) ensemble mean RMSE (dashed lines) and ensemble spread (solid lines), as a function of lead time for S2S reforecasts during summer of 1999–2010. ECCC—Environment and Climate Change Canada, JMA—Japan Meteorological Agency, UKMO—the UK Met Office, CMA—China Meteorological Administration.

      It is obvious that the prediction skill for the ISV of SAT over MHE varies among different S2S models. As demonstrated in many previous studies, some factors may account for the limits of prediction skills in dynamical models, such as the impact of the mean state, ensemble generation, ocean–atmosphere coupling, and so on (Kim et al., 2018).

      For example, Yang and Li (2016) demonstrated that the mean flow plays a vital role in the evolution of the ISO of SAT over MHE. It is further conjectured that the difference of the prediction skill of the mean flow among these S2S models may also affect the prediction skill of the intraseasonal variability of SAT to some extent.

      Ensemble generation can act as another possible cause for the difference in prediction skills. A bivariate form of the ensemble spread is measured as the combined standard deviations of the first two PCs in the ensemble members about their respective ensemble mean. In a statistically consistent ensemble, for each forecast lead time, the RMSE of the ensemble mean is supposed to equal the ensemble spread (ensemble standard deviation; Whitaker and Loughe, 1998). However, as discussed in Neena et al. (2014), ensemble predictions in most of the dynami-cal models for MJO tend to be under-dispersive and models possessing better-dispersed ensembles usually show a relatively higher skill for the ensemble mean results. The similar result is found in this study. Figure 6c illustrates the ensemble mean RMSE (dashed curves) and ensemble spread (solid curves) for S2S reforecasts. It is found that the ensemble mean RMSE is larger than the ensemble spread at each lead time in all the five S2S models, indicating that the under-dispersive ensembles for the ISO of SAT over MHE commonly exist in these S2S models. The dispersive level can be estimated on the basis of the closeness of the ensemble spread curve and the ensemble mean RMSE curve, which is obviously distinct among different S2S models as shown in Fig. 6c. Among the five S2S models, the two curves are the closest to each other for the ECMWF model (denoted by filled dots), especially at longer lead days, suggesting that the ECMWF model have better-dispersed ensembles, which corresponds to its higher prediction skill for the ISO of SAT over MHE.

      Additionally, different model physics and initial conditions may also play a certain role in the distinct performance in predicting the ISO signal. For example, the MJO prediction skill is shown to be sensitive to the quality of initial conditions, especially the atmospheric initial conditions (Vitart et al., 2007; Dee et al., 2011). Liu et al. (2019) and Bo et al. (2020) pointed out the significant skill improvement in predicting MJO and BSISO (boreal summer intraseasonal oscillation) due to optimization of initial conditions and improved model physics in the updated version of the CMA S2S model.

      The choice of dataset for validation can act as another possible impact factor. Taking the ECMWF model for example, the model reforecasts with the ERA5 reanalysis data for verification exhibit a slightly higher skill than with the NCEP reanalysis data for the validation (figure omitted). This may be attributed to the fact that the ECMWF reforecasts have been initialized with the ECMWF Interim (ERA-Interim) reanalysis data.

    • Skill dependence on the initial/target amplitude of the MHE ISV for these S2S models is further examined in this subsection. An ISO event is defined as an initial/target strong case if its amplitude is larger than 1.0 in the observations at the corresponding initial/target lead days of model reforecasts. More specifically, for a model reforecast with a start date on 1 July 1999 and a 10-day forecast length, the date of 1 July 1999 is defined as the model initial day and the date of 11 July 1999 is the reforecast target day. The solid lines in Fig. 7 represent the bivariate ACCs for S2S reforecasts when taking all the ISO cases into account, while the dash–dotted and dashed lines denote those of the initial and target strong cases, respectively. Our results show that, for JMA, ECCC, UKMO, and CMA models, compared with the initial strong cases, target strong cases tend to exhibit higher prediction skills, with the enhancement of skills by at least three days. However, for the ECMWF model, both the initial and target strong cases show the enhancement of forecast skills by about 6–7 days, which is an appreciable enhancement for the subseasonal forecast of the summertime ISV of SAT over MHE.

      Figure 7.  Bivariate ACC as a function of lead time (day) for S2S reforecasts for initial (denoted by dash-and-dot lines) and target (denoted by dashed lines) strong ISO cases over MHE during boreal summer of 1999–2010. Solid curves are the ACCs estimated for all ISO cases as in Fig. 6a.

      The analysis above implies that these S2S models tend to possess better skills in the case of predicting target strong ISO events. Conversely, the strong ISO signals in the initial condition appear to have the relatively slight impact on the forecast skills for most of the models.

    • Considering the propagating feature of the intraseasonal SAT anomaly over MHE, the prediction skill of model reforecasts may also rely on the initial and target phases. For example, for a model reforecast with a start date on 1 July 1999 and a 10-day forecast length, the corresponding observational ISO phase on 1 July 1999 is defined as the initial phase and the observational ISO phase on 11 July 1999 is the target phase. Then the prediction skills (ACCs) are calculated for S2S model reforecasts at different initial/target phases. It is noted that only initial/target strong ISO cases are considered here, as have been stated in Section 4.2. As shown in Fig. 8a, the relatively larger skill variations with the initial phase are detected as the lead time increases. Characteristics of skill dependence on the initial phase vary from model to model. For example, the ECMWF model exhibits better skills in initial Phases 5, 7, and 8, while lower skills are found in initial Phases 2, 3, and 6. The dependence of the forecast skills on the lead time and target phase are shown in Fig. 8b. Generally, for these S2S models, the gap of prediction skills among different target phases become appreciable after about five lead days, with the relatively lower skills for target Phase 5, indicating that the models tend to have difficulty in predicting the ISO signal when its positive anomalous SAT center is located to the north of Lake Baikal at about 60°N, 110°E. For the ECCC model, skills are also lower for Phase 2 after 10-day lead time; for the ECMWF model, poor skills are found for Phases 7 and 8 between 15- and 20-day lead times; and for the JMA model, relatively lower ACC skills are also seen in Phases 3 and 4 between 15- and 20-day lead times. For most of the S2S models, better skills are detected in target Phases 3 and 6 (or Phase 7).

      Figure 8.  (a) Bivariate ACC (shading) as a function of lead time (x axis; day) and initial phases (y axis) for S2S reforecasts for initial strong ISO cases (amplitude larger than 1.0). (b) As in (a), but for prediction skill as a function of lead time (x axis; day) and target phases (y axis) during summer of 1999–2010. Solid curves highlight the ACCs of 0.5.

      The feature of the skill dependence on target phases may be in part due to the varied amplitude of the ISO events in different propagating phases. We have calculated the averaged amplitude of the observed ISO cases during the summertime of 1999–2010. The result shows that the smallest ISO amplitude tends to appear in Phase 5. As mentioned in the analysis in Section 4.2, models show better scores when predicting target strong ISO cases. It is conjectured that weaker ISO signals may lead to the lower prediction skill in target Phase 5 in most of the S2S models. Conversely, the relatively larger ISO amplitude is detected in Phase 6, which may account for the higher skill for Phase 6 in some S2S models. However, it is noted that the ISO amplitude in Phases 3 and 7 is just around the average, indicating that other possible factors may contribute to the high skill in these target phases, which remains to be further investigated.

      In addition, it is expected that the MHE SAT signal on intraseasonal timescale can be modulated by tropical forcing such as summer MJO, primarily in the form of Rossby wave trains. However, currently, the role of tropical forcing in predicting the SAT anomalies over extratropics is uncertain (Xiang et al., 2019, 2020). Lin (2018) pointed out the modulation of MJO of different phases on the prediction skills of Eurasian mode of SAT during boreal winter in three S2S models. It is conjectured that the tropical convection may also act as a possible cause of the distinct skill features in different ISO phases in these S2S models. Accordingly, it is necessary to thoroughly understand the role of tropical forcing in predicting the ISO over MHE with further investigations in the future.

    • Illustrated in Fig. 9a is the amplitude error estimated between the observed and model predicted ISO events. The amplitude error is expressed as $ \dfrac{{{{\it{A}}_{{\rm{model}}}} - {{\it{A}}_{{\rm{obs}}}}}}{{{{\it{A}}_{{\rm{model}}}}}}$ and A represents the amplitude of an ISO event as defined above. The negative value of the error means an underestimation of the observed ISO amplitude. As a common feature for these S2S models, the predicted ISO amplitude is underestimated and the error grows with the lead time. We further examine the phase-dependent feature of the model amplitude bias, which is defined as the difference of ISO amplitude between the observation and S2S model reforecast on each target phase. Shown in Fig. 9b are the bivariate ACCs on individual target phase averaged over the first 15 lead days for the five S2S models. Only target strong ISO cases (amplitude larger than 1.0) are considered here. For most of the S2S models, the underestimated amplitude during the first 15 days is the most evident in Phases 4 and 5, while the minimum amplitude bias is found in Phase 1.

      Figure 9.  (a) Amplitude error of the first two PCs for S2S reforecasts. (b) Amplitude bias of the first two PCs averaged over the first 15 days in individual target ISO phase for S2S reforecasts. (c) Phase angle error (°) for the target strong ISO cases for S2S reforecasts. (d) Phase angle error (°) averaged over the first 15 days in individual target ISO phases for S2S reforecasts during boreal summer of 1999–2010.

      Additionally, the propagation speed bias of the ISO events is evaluated with the phase angle error. A positive value indicates that the predicted propagation speed is faster than the observation. Shown in Fig. 9c is the phase angle error for target strong ISO cases in S2S reforecasts. The JMA, UKMO, and CMA models tend to predict the ISO events with a faster propagation speed than observation during the first 15 days. Conversely, for the ECMWF and ECCC models, the predicted propagation speed of the ISO events appears to be slower than the observation during the first 10 and 13 days, respectively. As for the average phase angle error during the first 15 days, it varies among different target phases and different models as shown in Fig. 9d. For most of these S2S models, it appears that overestimate of the propagation speed is more evident for Phases 1 and 2, while underestimate of the propagation speed is more appreciable in Phases 4 and 8. However, for the ECMWF model, the maximum negative phase angle error appears in Phase 3 instead.

    5.   Potential predictability of the ISV of SAT
    • A model’s potential predictability can be utilized to quantify the gap between the actual forecast skill and the predictability of the model for intraseasonal SAT signals. The potential predictability is computed following a perfect-model assumption introduced in Rashid et al. (2011). In their approach, one of the reforecast ensemble members is firstly picked out, in turn, as the “observation.” Next, the prediction skill of the ensemble mean of the remaining members is scored against the “observation.” Lastly, the averaged skills of all the ensemble subsamples are considered as the potential predictability for the model. Note that all the ISO cases are taken into consideration in the analysis below.

      Figure 10a illustrates the forecast skill, together with the potential predictability of the ISV of SAT over MHE estimated for S2S model reforecasts. The distinction between the potential skill and actual skill is regarded as the skill gap for each S2S model. As mentioned above, these models possess useful forecast skills of the SAT signal on intraseasonal timescale out to 11–17 days. As for the potential predictability, take the ECMWF model for example, the upper bound of the skillful predictions is around 23 days according to a perfect-model assumption, which indicates that this model has the scope for further improvement of its forecast skill of the SAT signal on intraseasonal timescale over MHE by up to 6 days before reaching the upper bound of the potential skill. The UKMO and JMA models show a 4–6-day gap between the actual skill and potential predictability. The skill gap for ECCC model is relatively small, which is about one day. The difference between the potential predictability and actual prediction skill commonly exists in most of the S2S models, which can be assumed as the extent to which the forecast skill will possibly achieve with improvement in model initial conditions, reduction of mo-del systematic error, and so on, in the current prediction scheme.

      Figure 10.  (a) The actual skill (solid curve) and an estimation of potential predictability (dashed curves) as functions of lead time (day) for S2S reforecasts for all ISO cases. (b) The potential predictability (contours) and skill gap (predictability minus actual prediction skill; shadings) as functions of lead day and target ISO phases for five S2S model reforecasts during summer of 1999–2010.

      The potential predictability and skill gap for individual target phase are also studied for the five S2S models (Fig. 10b). For the ECMWF model, the predictability of ISO over MHE is about 20–25 days for eight target phases. Evident skill gaps can be found in Phase 2 at 20–25 lead days and in Phases 7 and 8 beyond 15 lead days. For the JMA model, the skill gap in Phases 3 and 4 at about 15–20 lead days is rather evident. These may be attributed to the low forecast skills at the same range of lead days in these target phases for these two S2S models. UKMO and CMA also exhibit relatively larger skill gaps at certain phases especially at 10–15 lead days. Analysis of the skill gaps indicates that the forecast skill of the ISV of SAT over MHE at longer lead days in certain phases is expected to be improved for most of the S2S models, and more efforts in reduction of systematic error and improvement of initial conditions in numerical models are needed.

    6.   Summary and discussion
    • Features of the dominant SAT modes on intraseasonal timescale over the MHE during boreal summer are investigated in this study. The leading ISV modes of SAT over MHE are obtained by an EOF analysis of the 10–50-day intraseasonal SAT field over the region of 36°–81°N, 21°–141°E during boreal summer (June–September) of 1979–2016. EOF1 exhibits a west–east dipole mode of the intraseasonal SAT anomalies, and EOF2 represents a triple mode of the SAT perturbations with centers over the MHE domain. The eastward propagation of the ISV of the anomalous SAT field over MHE is clearly displayed in the eight phases defined by the first two leading PCs. The position of the positive SAT perturbation center propagates from the north of the Ural Mountains in Phase 1 to the north of Lake Baikal in Phase 5. Southward shifting of the positive SAT center is detected from Phase 6 to 8, indicating the possible influence of the ISV of SAT on the temperature anomalies over East China. Additionally, the ISV of SAT can modulate the occurrence frequency of extreme hot and cool days in certain regions of China in boreal summer.

      The forecast skill of the ISV of SAT modes on intraseasonal timescale is assessed with the reforecast data for 1999–2010 from five dynamical models participating in the S2S prediction project. The prediction skill is measured by bivariate ACC and RMSE, which are computed between the observation and model reforecast PCs.

      The results show that these five S2S models possess useful prediction skill for ISV of SAT over MHE of up to 11–17 days, and the ECMWF model exhibits the best skill. The models tend to show higher prediction skill for strong ISO cases than for all ISO cases, with the enhancement of the skill by at least three days. The prediction skills with respective to individual initial and target ISO phases are further assessed. Characteristics of the skill dependence on the initial phase vary from model to model, especially at the longer lead time. Most of the models show relatively higher skills for target Phases 3 and 7 when the positive and negative SAT perturbation centers reside over central Russia, and lower skills for target Phase 5 when the positive anomalous SAT center is located to the north of Lake Baikal. Additionally, underestimate of the observed ISO amplitude commonly exists in all the five S2S models, and the error grows over the lead time. The amplitude bias also varies among different target phases, and it is the most evident in Phases 4 and 5 during the first 15 days of the prediction. Prediction skill of the propagation speed is measured by the phase angle error. The JMA, UKMO, and CMA models tend to show a faster phase propagation speed than observation when predicting the ISO events over the first 15 days. Conversely, the ECMWF and ECCC models are found to have a slower propagation speed compared with the observation during the first 10 and 13 days, respectively. The predicted propagation speed shows a relatively large variation among different models. For most of the S2S models, overestimate of the propagation speed is more evident for Phases 1 and 2, while underestimate of the propagation speed tends to be more appreciable in Phases 4 and 8.

      The potential predictability for the leading ISV mode of SAT over MHE for the five S2S models is further explored under a perfect-model assumption. The result reveals a skill gap of 4–6 days between the actual forecast skill and potential predictability in most of the S2S models. The skill gap for individual target phase varies among different models, and it is possible for the enhancement of forecast skills at longer lead days in certain phases for most of the S2S models; thus, more work along this line can be done to improve current operatio-nal forecasting systems.

      Although characteristics of the SAT modes on intraseasonal timescale are revealed and the associated prediction skill of five S2S models are assessed in this study, some other relevant questions remain open, such as the role of tropical forcing on the forecast skill of the 10–50-day SAT modes and their possible predictability sources, and so on. Further investigations are needed.

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