1 Introduction

The East Asian winter monsoon (EAWM) dominates the wintertime weather and climate over East Asia and exhibits apparent variations in both its intensity and pathway (e.g., Chang et al. 2011; Wang and Lu 2017). Its abnormal behaviors are often accompanied by strong winds, freezing temperature, snowstorms, among other hazards, and exert essential influences on human lives and society (e.g., Zhou et al. 2011). The EAWM is also a crucial link of the global energy cycle because it is a primary passage for the cold air in the high latitudes to penetrate southwards (Chang et al. 2005, 2006; Liu et al. 2021). Its variability is closely associated with internal atmospheric dynamics (e.g., Chen et al. 2005; Chen and Li 2007; Wang et al. 2009; Takaya and Nakamura 2013; Nakamura et al. 2016; Luo et al. 2016a, b; Yao et al. 2017; Ma and Zhu 2019) and external forcing (e.g., Zhang et al. 1996; Wang et al. 2000; Honda et al. 2009; Wu et al. 2011, 2019; Inoue et al. 2012; Mori et al. 2014; Wang and Chen 2014a, b) on multi timescales spanning from synoptic to interdecadal and beyond. Hence, it is not only scientifically essential but also practically crucial to understand and predict the variability of the EAWM well.

Climatologically, the EAWM prevails from November to March of the next year (e.g., Chen et al. 2000). Therefore, the 3-month or 5-month mean variables are frequently used in the climate research and predictions of the EAWM (e.g., Lee et al. 2013; Sun et al. 2016; Tian et al. 2018; Xiao et al. 2018; Fan et al. 2020). For example, most of the seasonal forecasts made by major operational centers in the world are for rolling 3-month periods. In many studies, the winter mean temperature anomalies of the EAWM are often considered and explained via the anomalous advection of winter mean temperature by winter mean wind anomalies, which may be further attributed to the seasonal mean sea surface temperature, snow cover, or Arctic sea ice. Recently, some scholars noticed the deficiency of this 3-month or 5-month mean approach and found distinct differences in the variability of the EAWM between early and later winter (e.g., Chang and Lu 2012; Wei et al. 2014, 2020), demonstrating the necessity to consider the sub-seasonal variability of the EAWM. Nevertheless, they still use the mean anomalies of the circulation or its lower boundaries in early or late winter to explain the observed EAWM anomalies. These facts indicate that it has been a conventional and popular approach to use the anomalies of atmospheric circulations and atmospheric external forcing averaged over specific months to explain the seasonal behaviors of the EAWM or to evaluate the skills or performance of seasonal prediction models. A similar situation also exists for climate studies in other seasons and in other regions of the world.

The abovementioned approach based on seasonal mean variables has been proved successful and enlightening to understand the variability of climate, including the EAWM, especially on the interannual to interdecadal timescales. This result seems natural because the climate is generally regarded as the composite of the bulk behavior of weather (e.g., Hartmann 2002), so it seems sufficient to explain the seasonal behavior of climate, including the EAWM, with its corresponding mean circulation. However, it has been long recognized that the short-term variability of the atmosphere can feedback onto the long-term variability, such as the feedback of synoptic eddies onto the seasonal mean fields (e.g., Lau and Holopainen, 1984; Žagar et al. 2020). This knowledge implies the plausible insufficiency of the abovementioned conventional approach in climate studies and suggests the importance of understanding intraseasonal (referring to timescales shorter than a season) variability in interpreting the seasonal behaviors of the climate. The EAWM has distinct and substantial intraseasonal variability, such as synoptic cold waves (e.g., Chang et al. 2006; Gong et al. 2014; Zuo et al. 2015; Oldenborgh et al. 2019) and quasi-periodic variability whose period is weeks (e.g., Song et al. 2016; Yang and Li 2016). However, it remains open how the intraseasonal variability contributes to the seasonal behavior of the EAWM to the best of the authors' knowledge, and this issue will be addressed by investigating the role of cold waves based on a case study of the 2018–2019 winter. Section 2 describes the data and methods used in this study. Section 3 interprets the seasonal mean behavior of the EAWM in 2018–2019 winter using the common approach, i.e., via the winter mean circulation. Section 4 discusses the insufficiency of the approach used in Sect. 3 and proposes a different angle to understand this winter. Section 5 summarizes the main findings and discusses some remaining issues.

2 Data and methods

Monthly mean and four-times daily atmospheric reanalysis data are from the Japanese 55-year Reanalysis (JRA-55) dataset (available at https://jra.kishou.go.jp/JRA-55/index_en.html) with 1.25° latitude by 1.25° longitude resolution (Kobayashi et al. 2015). The data have 37 pressure levels extending from 1000 to 1 hPa and spans the period from 1958 to the present. The four-times daily data are averaged into daily mean data, and monthly mean data are averaged into winter mean data, derived from the averaged over December, January, and February. The seasonal cycle is defined as the daily climatology derived from the 30-year (1981–2010) average, which is provided by the JRA-55 dataset. Daily anomalies are defined as departures from the seasonal cycle. Composite and linear regression analyses are used. The confidence level of regression analysis is estimated with the two-tailed Student's t-test, and that of composite analysis is estimated with the Monte Carlo bootstrapping technique (Efron and Tibshirani 1994) with 1000-times resampling. Analyses are also repeated with other reanalysis datasets, and the results remain almost identical (not shown). Hence, only results based on the JRA-55 dataset are shown. In this study, we focus on the 2018–2019 winter (denoted as 2018 winter hereafter) that caused widespread influences in East Asia and documented in several recent papers (Jian et al. 2020; Li et al. 2020; Shen et al. 2021).

3 Explaining the EAWM of 2018 from the seasonal mean perspective

Figure 1a is the anomalous pattern of the winter mean surface air temperature (SAT) 2 m above ground in the 2018 winter. It resembles the second mode of the wintertime SAT over Asia (Fig. 2a in Miyazaki and Yasunari 2008) and shows significant cold anomalies over the central Siberia, the northern part of the Indian subcontinent, and most of eastern China between 20° N and 40° N and strong warm anomalies over Indochina Peninsula, coastal areas of East Asia, and large portions to the east of 120° E. Meanwhile, above-normal precipitation is observed in broad land regions to the south of 40° N, especially over South China and Indochina Peninsula (Fig. 1b). Below-normal precipitation is observed in central Siberia and Northeast China (Fig. 1b). The combined effects of precipitation and temperature imply a severe winter over inland Asia, characterized by a cold and dry north and cold and wet south. According to the statistics from the National Climate Center (NCC) of China Meteorological Administration, historical low temperature is observed in more than 50 meteorological stations in northern China in December 2018, leading to a new record-high load on the electrical grid in Beijing (NCC 2018). The blizzard in southern China caused the closure of many highways due to roadway icing, the collapse of more than 100 houses, and damage of more than 1300 houses in late December, which led to direct economic losses exceeding 191 million US dollars in agriculture alone in 151 counties.

Fig. 1
figure 1

The winter mean anomalies of a SAT and b precipitation in 2018 winter. c The normalized SAT index for winters 1958–2018. Stippling in a, b indicates values exceeding the 99% or 1% percentile estimated from 1000 bootstrapped samples during 1958–2018 winters. Rectangles in a, b, and the rest of the Figures indicate the area (40° N–55° N, 80° E–110° E) to define the SAT index in c

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As mentioned in the introduction, the seasonal mean circulation is usually used to explain the seasonal mean temperature pattern, so the winter mean atmospheric circulation anomalies in the 2018 winter are shown in Fig. 2. There are two wave-like patterns in the upper troposphere at the middle and high latitudes of the Eurasia continent (Fig. 2a). The mid-latitude one stretches from the North Atlantic to East Asia along approximately 35° N with a barotropic structure (Fig. 2a, b), resembling the phase-locked wave train along the Asian jet (Hu et al. 2018). The high-latitude one stretches from the Ural Mountains region at approximately 60° N towards East Asia. In the lower troposphere, the sea level pressure is above normal from the Ural to Siberia (Fig. 2b). The vertical structure of the high-latitude wave train is barotropic over the Ural and baroclinic over the Siberia, consistent with the typical circulation pattern associated with amplified Siberian high (e.g., Takaya and Nakamura 2005; Song et al. 2016). The associated lower-tropospheric wind shows evident anticyclonic anomalies over inland Asia and western North Pacific (Fig. 2c). Climatologically, the lower-tropospheric temperature is the lowest over northeast Asia and increases westward and southward over inland Asia (Fig. 2c). Hence, the anticyclonic wind anomalies over inland Asia (Fig. 2a) may explain the observed cold anomalies over central Siberia (Fig. 1a) through temperature advection. An El Niño matured in the 2018 winter (Fig. 3), and it could excite an anomalous anticyclone over the western North Pacific in the lower troposphere (e.g., Zhang et al. 1996; Wang et al. 2000), consistent with the observation (Fig. 2c). This configuration facilitates the convergence of water vapor towards East Asia and leads to enhanced precipitation in South China (e.g., Zhang et al. 1999; Wu et al. 2003; Wang and Feng 2011).

Fig. 2
figure 2

The winter mean anomalies of a 300 hPa geopotential height, b sea level pressure, and c 850 hPa winds (vector) in 2018 winter overlaid with the climatology of the 850 hPa air temperature (shading with white contour). Stippling in a, b indicates values exceeding the 99% or 1% percentile estimated from 1000 bootstrapped samples during 1958–2018 winters. The thick black contour in c indicates zero values

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Fig. 3
figure 3

The winter mean sea surface temperature anomalies in 2018 winter

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In order to further confirm the above argument, especially regarding the mid- and high-latitude circulations that account for the cold anomalies, an SAT index is constructed by averaging the winter mean SAT anomalies over the central Siberia (40°–55° N, 80°–110° E) to delineate the interannual variations of the temperature pattern (Fig. 1c). The winter mean atmospheric circulations are further regressed onto the normalized SAT index. A barotropic wave-like pattern appears over the Eurasian continent (Fig. 4a, b), almost identical to that associated with the Scandinavian pattern (e.g., Figs. 6d, 4c of Liu et al. 2014). Although the regressed wave-like pattern does not resemble that observed in 2018 winter as a whole, it projects onto the observed pattern to some extent, especially surrounding Siberia. For example, the upper-tropospheric geopotential heights are both anticyclonic and cyclonic over the Ural and Siberian areas, respectively (Figs. 2a, 4a). The sea level pressures are both positive over central Siberia, indicating an amplified Siberian high (Figs. 2b, 4b). As a result, the regressed 850 hPa winds (Fig. 4c) show significant northeasterlies surrounding and in the target region (i.e., the box in Fig. 1a), facilitating below-normal SAT over the central Siberia via cold advection (Fig. 4d).

Fig. 4
figure 4

Regression of the winter mean a 300 hPa geopotential height, b sea level pressure, c 850 hPa winds (vector) overlaid with the climatology of the 850 hPa air temperature (shading with white contour), and d SAT onto the normalized SAT index during 1958–2018. Stipplings in a, b, and d and vectors in c indicate the 99% significance level based on the two-tailed Student's t-test. The thick black contour in c indicates zero values

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4 Importance of the intraseasonal variability

The approach shown in Sect. 3 seems well explain the seasonal mean behavior of the EAWM in 2018, but it has at least two apparent deficiencies. The first is the sharp contrast between the observed large-scale cold anomalies over central Siberia (Fig. 1a) and the weak down-temperature-gradient wind vectors (Fig. 2c), which implies weak cold advection by the seasonal mean wind anomalies. The second is the overall dissimilarity between the regressed and observed wave-like patterns (Figs. 2a, 2b, 4a, 4b), which implies that something is still missing in the explanation. For example, when the origin of the cold anomalies over central Siberia are explained, a crucial role is attributed to anomalous easterly in observation (Fig. 2c) and to anomalous northeasterly in regression analysis (Fig. 4c). These deficiencies motivate us to seek a better explanation of the origins of the EAWM’s seasonal behavior in 2018. The hypothesis is that the intraseasonal variability of the EAWM may be the key, as discussed in the introduction. Recall that intraseasonal variability refers to variability whose timescale is shorter than a season.

Cold waves are an essential component of the EAWM's intraseasonal variability that usually lasts for less than a week (e.g., Chang et al. 2006). The daily evolution of the SAT index in the 2018 winter shows clear intraseasonal variability (Fig. 5). Three SAT minimums are observed on 6 and 26 December 2018 and 8 February 2019, respectively, indicating the occurrence of three cold waves. In order to explore the role of the cold waves in the seasonal behavior of the EAWM, the 90 days in 2018 winter are classified into two groups. One is the cold wave (CW) group that consists of 15 days from the three cold waves, where each cold wave is defined as 5 days centered on their respective SAT minimum. The other is the non-cold wave (non-CW) group that consists of the remaining 75 days. The composites within the two groups are calculated, and their confidence levels are evaluated via the Monte Carlo bootstrapping resampling with respect to the 5490 winter days during 1958–2018 for SAT and 2070 winter days during 1996–2018 for precipitation. The composite and resampling are both performed using daily anomalies.

Fig. 5
figure 5

The time series of daily mean SAT index in 2018 winter (solid black line), the climatology of the daily mean SAT in winter (dashed black line), and the daily historical minimum SAT in winter (shading). The three vertical blue lines indicate the central date of the three cold waves

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Figure 6 shows the mean SAT anomalies and accumulated precipitation anomalies in the CW and non-CW groups. The SAT pattern during CW days (Fig. 6a) projects much better onto the observed (Fig. 1a) and regressed (Fig. 4d) winter mean SAT anomalies than that during the non-CW days (Fig. 6c). Moreover, when the CW days' contributions are removed, the cold anomalies over the northern part of central Siberia in the winter mean field become warm anomalies, and those over eastern China weaken and become less significant (Fig. 6c). The accumulated precipitation during CW days quite resembles that during non-CW days over East and Southeast Asia. Their amplitudes are similar over South China and the north part of the Indochina Peninsula (Fig. 6b, d), where above-normal seasonal mean precipitation is observed (Fig. 1b). It suggests that the frontal precipitation in this winter induced by the confluence of cold and warm air is comparable to the monsoonal precipitation induced by the large-scale background flow. The conclusion remains similar, especially regarding the SAT, if the duration of a cold wave is altered from the current 5 days to 3 or 7 days (not shown). These results suggest that the SAT pattern in 2018 winter is primarily shaped by the three cold waves that cover only one-sixth of the winter days and that the precipitation pattern in 2018 winter is also largely determined by the three cold waves.

Fig. 6
figure 6

The composite of a SAT anomalies and b accumulated precipitation during the 15 CW days in 2018 winter. c, d are the same as a, b, but for the 75 non-CW days in the 2018 winter. Black contours indicate zero values. Stippling indicates values exceeding the 99% or 1% percentile estimated from 1000 bootstrapped samples

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The above results are not entirely beyond expectation because the seasonal mean cold anomalies are anticipated to weaken when the coldest days are excluded. However, it is somewhat out of expectation that the cold anomalies turn to neutral and even warm anomalies. It means that the cold situation in a season may not be determined by the bulk behavior of all days in a season but by several extreme cold days. This fact is crucial to understand the formation mechanism of the seasonal mean SAT pattern and the discrepancies between Figs. 2a–c and 4a–c. Figure 7 compares the atmospheric circulation anomalies during CW and non-CW groups. During non-CW days, the wave-like patterns quite resemble their winter mean counterparts (Fig. 2a, b). However, the high latitude wave pattern is much weaker and statistically insignificant at the 99% confidence level in both the upper and lower troposphere (Fig. 7e, f). Hence, the associated 850 hPa wind anomalies do not show a clear down-temperature-gradient component (Fig. 7g) and only lead to cold anomalies over limited regions of central Siberia (Fig. 6c) via weak temperature advection (Fig. 7h). In contrast, the high latitude wave-like pattern is strong and statistically significant during CW days (Fig. 7a, b), resembling the regressed wave pattern from the Ural to Siberian area (Fig. 4a, b). The associated northeasterly wind anomalies (Fig. 7c) can induce significant cold anomalies over central Siberia (Fig. 6a) via strong cold advection (Fig. 7d).

Fig. 7
figure 7

The composite anomalies of a 300 hPa geopotential height, b sea level pressure, and c 850 hPa winds (vector) overlaid with the climatology of the 850 hPa air temperature (shading) during the 15 CW days in the 2018 winter. d The horizontal temperature advection at 850 hPa during the 15 CW days in 2018 winter. e–h are the same as a–d, but for the 75 non-CW days in the 2018 winter. Black contours indicate zero values. Values exceeding the 99% or 1% percentile estimated from 1000 bootstrapped samples are stippled in a, b, e, and f and shown in c, g

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Note that the high-latitude Scandinavian pattern-like structure is only evident during CW days (Fig. 7a). The high similarity between Figs. 4a–c and 7a–c suggests that the regression analysis on the seasonal mean variables successfully captures this key circulation pattern that leads to the winter mean cold anomalies over central Siberia. However, this key circulation pattern was not well reflected in the seasonal mean circulation field (Fig. 2), likely because of its short duration. Nevertheless, the SAT anomalies induced by this key circulation pattern is well accumulated and contribute substantially to the formation of the seasonal mean SAT pattern. In contrast, the low-latitude wave-like pattern is evident in both CW and non-CW days (Fig. 7a, e), indicating that it is a seasonal background signature in this winter. This low-latitude wave-like pattern contributes constructively to the cold anomalies over the southern portion of central Siberia, but it cannot explain the cold anomalies over the northern portion of central Siberia. The inefficiency of the non-CW days in inducing cold anomalies suggests that it is not this seasonal background that caused the cold condition over central Siberia. Hence, these results suggest that it may obscure the real reason for a cold winter by examining the seasonal mean circulation alone. In other words, the role of intraseasonal variabilities, such as cold waves, should be taken into account to explain a cold winter besides considering the role of the seasonal mean circulation.

5 Summary and discussion

It is a regular approach to explain the seasonal mean climate anomalies through the seasonal mean atmospheric circulation or atmospheric boundary forcing. Based on a case study of the EAWM, it is demonstrated that the above approach may miss some crucial aspects in explaining the underlying mechanism and that the intraseasonal variability needs to be taken into account to supplement these missing aspects. From the seasonal mean perspective, the EAWM in 2018 winter features below-normal SAT over central Siberia and eastern China and enhanced precipitation over South China and Indochina Peninsula. The winter mean atmospheric circulations can partly explain the observed SAT and precipitation patterns, but there remain some discrepancies between the observed atmospheric circulation pattern and the identified mechanism. By examining the intraseasonal variability of the SAT, three cold waves are identified in the 2018 winter. Although they only take up approximately one-sixth of days in this winter, they are able to shape the winter mean SAT pattern and to explain approximately 50% of the accumulated precipitation over East Asia. This result indicates that the primary climate condition in this winter is not determined by the bulk behavior of all days but by limited days during extreme phases of the intraseasonal variability. More importantly, the essential circulation pattern to explain the occurrence of these extreme phases is not well reflected in the seasonal mean circulation field. Hence, it is insufficient and somewhat misleading to explain the seasonal mean climate anomalies through the seasonal mean atmospheric circulation alone for this winter.

The result shown in this study indicates the importance of considering the intraseasonal variability to explain the seasonal mean behaviors of climate from the methodological point of view, at least for some particular cases. On the one hand, this information might motivate a reconsideration of the approach to investigate and interpret the seasonal mean climate. In this regard, more case studies or statistical studies are needed to confirm the role of intraseasonal variability. Meanwhile, studies on related governing equations are also needed to provide theoretical understandings of this issue, where nonlinear processes are likely to play some crucial role. It is essential to evaluate whether and to what extent a similar situation exists in other cases. The occurrence of three cold waves indicates an active intraseasonal variability in the 2018 winter. Hence, it is inferred that the conclusion depends on the activeness (e.g., frequency or magnitude) of the intraseasonal variability, and more work is needed to confirm this inference in the future. On the other hand, it should be kept in mind that there are interactions among variabilities of different timescales. The intraseasonal variability may contribute to the seasonal mean behaviors of the climate, and the seasonal mean climate may serve as a background and modulate the intraseasonal variability. Hence, it is also essential to consider this two-way interaction between different timescales when the role of the intraseasonal variability is investigated.