The role of semiannual cycle in modulating seasonality changes of surface air temperature over China and its mechanism

Taking the semiannual cycle of surface air temperature (SAT) into account in fitting the finer structure of the seasonal cycle, this study reveals the specific role of the semiannual cycle in modulating variations of the season onsets and lengths for the first time. The time-varying amplitudes and phases of the annual and semiannual SAT cycle for the period 1964 to 2017 in China are extracted from daily observations based on harmonic analysis. The results show that the phase differences between the two harmonics remain essentially unchanged, while the amplitude ratio of the semiannual to annual harmonics tends to increase after 1988. This enhanced semiannual cycle together with the global warming and annual cycle changes jointly led to a much longer summer with an average speed of 7.45 days/10 years and shorter spring, autumn, and winter with speeds of − 2.43, − 1.63, and − 4.26 days/10 years, respectively. Such obvious asymmetry cannot be found in fitting seasonal cycles by only annual harmonics. The average absolute percentages of the linear trends of season onsets and lengths caused by the intensification of the semiannual cycle are 52.63% and 78.66%. It indicates that season onsets and length not only depend on the phase of annual and semiannual harmonic, but also highly related to the strength of semiannual cycle. The time evolutions of semiannual cycle strength in China are found to be significantly correlated to the meridional temperature advection. The anomalous stronger southward wind in December can result in colder temperature and hence intensify the semiannual component.


Introduction
Seasonal cycle (SC) is the leading natural change that the atmosphere experiences every year. The changes in seasonality directly affect people's crop production (Park et al. 2016;Matiu et al. 2017) and health risks (Ryan et al. 2019); rhythms of living things and ecosystem (Cleland et al. 2007;Horton et al. 2020); atmosphere eddy activities (i.e., storm tracks) and heat wave occurrences (García-Herrera et al. 2010). Previous studies have reported different levels of the early spring and summer (Sparks and Menzel 2002;Paluš et al. 2005;Stine et al. 2009;Qian et al. 2011a;Peña-Ortiz et al. 2015) and delayed autumn and winter in different locations (Menzel 2000;Sparks and Menzel 2002;Christidis et al. 2007), which is usually attributed to the global mean temperature warming trend (Wang et al. 2021a, b;Lin and Wang 2022a, b), but the change of seasonal cycle is also an important factor. Qian et al. (2011a) found that in the east of northern China, the change in the spring phase of modulated seasonal cycle explains 40-60% of spring onset trend; this work proved the crucial role of seasonal cycle in season changes. However, even inside the seasonal cycle, the changes in annual cycle and semiannual cycle may not the same, and previous works seldom separated their effects. The attribution analysis for the finer structures in changing seasonality is lacking, and we still do not know the specific role of the semiannual cycle in the season changes.
Although observations show that the annual harmonic is by far the largest component of seasonal cycle in most areas of Earth (e.g., Qian et al. 2011b), higher order harmonics are 1 3 widely detected, especially the semiannual cycle. Recently, a growing number of research have used two harmonics to simulate seasonal cycle (Donohoe et al. 2020;Song et al. 2021;North et al. 2021;Yang and Wu 2022) and noticed the importance of semiannual cycle in modulating seasonality such as its asymmetry (Elissev and Mokhov 2003;Yang and Wu 2022). Unlike annual harmonic, which is dominated by direct shortwave absorption within the atmosphere and highly related to the variation in solar insolation (Donohoe and Battisti 2013;Lembo et al. 2017;Mckinnon et al. 2013;Pezzulli et al. 2005), the semiannual heating is attributable to more complicated sources. In the tropical atmosphere, the absorption of solar radiation must have a considerable semiannual component because of twice passage of the Sun over the equator. However, the larger contribution is from the wave-zonal flow interaction with accelerations of the westerly flow by Kelvin waves and the easterly flow by planetary Rossby waves (Hirota 1980). In the midlatitude and polar regions, the semiannual cycle is mainly associated with the activity of the transient eddy (Lembo et al. 2017). Besides, there are observed differences in the semiannual cycle between the Northern and Southern Hemisphere due to their different portion of land surface and the semiannual cycle is a coupled ocean-atmosphere phenomenon in mid to high latitudes (van Loon 1967;Meehl 1991).
We take China as an example to investigate how the semiannual cycle modulates the SAT seasonality changes. Here we first show three typical seasonal cycles extracted by Nonlinear Mode Decomposition (NMD) method (Iatsenko et al. 2015) in three different stations in China (Fig. 1). Comparing the climatological mean seasonal cycle (red dots) and the mean seasonal cycle with the semiannual cycle added (black lines), they fit very well. However, using only the annual harmonic (blue lines) can only partially fit the actual observations.
Since the shape of the seasonal cycle is influenced by both the annual cycle and semiannual cycle, the timings of seasons are not only related to the phase of annual harmonic, but also the amplitude and phase of semiannual cycle. Thus, we should consider the combination way of these two oscillations. In these three stations, the intensities of semiannual cycle (or the amplitude ratios of semiannual cycle to annual cycle) and phase shifts of semiannual cycle are different, so that the peak temperature of seasonal cycle appears on different dates and the season onsets and lengths are different (see their definition in the method section). The peak temperature in summer comes earlier in Haikou, then Beijing, and last in Yushu. Those key season timings actually depend on the phase of the first harmonic, as well as the amplitude ratio and phase difference between the two harmonics. Their amplitude ratios and phase differences are given in Fig. 1. In this work, we analyze the impacts of changing semiannual cycle on the observed changes in season onsets and lengths, and the mechanism behind it will be analyzed simultaneously.
The paper is organized as follows. Section 2 briefly describes the dataset and methods used in the study. Section 3 provides the main results and mechanism analysis. Discussions and summaries are given in Sects. 4 and 5.   ,station No. 54,511,39.48 N,116.28E. b for Yushu,station No. 56,029,33 N,96.58E. c for Haikou,station No. 59,758,20 N,110.15E was well investigated (Qian et al. 2011b) and the relatively larger semiannual component was found in China than other mid-to-high land areas (Yang and Wu 2022); the climate impacts of this semiannual component is exactly what we are interested in.
The dataset used to extract SC is the observed daily mean SAT of China National Surface Weather Station (V3.0) published by the National Meteorological Information Centre (2019, http:// www. nmic. cn/). The dataset covers 699 stations and is of high quality and relatively complete. The time period is from Jan 1, 1962 to Dec 31, 2019. Due to some consecutive missing data at some stations, 620 stations were finally selected for analysis. The individual single missing data are linearly interpolated, and it has been checked that they would hardly affect the results.
Aiming to find the dynamic causes for semi-annual cycle changes, the gridded geopotential height, u-velocity of wind, v-velocity of wind, and temperature at 1000 hPa, from the ERA5 monthly averaged dataset on pressure levels from 1962 to 2019 (Bell et al. 2021) have been used to calculate horizontal temperature advection in the region covering China.

Extraction of the seasonal cycle
To extract the amplitudes and phases of the SAT annual and semi-annual cycles, a new statistical method named Nonlinear Mode Decomposition (NMD) (Iatsenko et al. 2015) was used. This method can extract a set of harmonics whose frequencies are multiple of the basic frequency based on the wavelet analysis and Windowed Fourier Transform and was proved to be effective and robust for analyzing the changes in amplitude and phase of extracted harmonics (Deng and Fu 2019). In this work, we focus on the first two harmonics -the annual and semiannual cycle. Then a given temperature time series is decomposed into: where f = 1/365.25, A 1 (t) and 1 (t) are time-varying amplitude and phase of the annual cycle, A 2 (t) and 2 (t) are time-varying amplitude and phase of the semiannual cycle, (t) is the remained high frequency synoptic variability. It should be noted that NMD method initially removes the cubic polynomial of the signal so that the decomposition results do not contain the long-term trend. And because of the end effect of NMD method, the results of the first and end two years are excluded in the following further studies. (1) The seasonal cycle (SC) of temperature is specifically regarded as a superposition of annual and semi-annual harmonics. To better investigate the role of the semiannual cycle playing in the seasonality changes, the ratio of the absolute values of A 2 to A 1 (hereafter, amplitude ratio) and the remaining phase shift 1 − 2 after division by π [written as mod( 1 − 2 , ) ; hereafter, phase difference] are calculated. The variation of amplitude ratio can show the proportion changes of the semiannual component. And phase difference is to see whether the position of the superimposed state of the semiannual and annual harmonics is near the crest or trough of the wave. As the phase difference approaches 0, the peaks superimpose and the crest of the SAT annual cycle becomes sharper, indicating a possible shorter summer duration. As the phase difference approaches π/2, the peaks are weakened, the top of the SAT annual cycle pattern is flattened, and the summer duration may tend to become longer.

Definitions of season onsets and lengths
Although the time-varying phase of the annual and semiannual cycle can be directly obtained, the threshold method should be used to check the season timing for better understanding. There is a range of thresholds which can be used to classify the seasons. For example, 5 °C is widely adopted for determining spring onset at mid-tohigh latitudes (Menzel et al. 2003;Qian et al. 2011a;Deng et al. 2020) and different thresholds like 25 °C, 14 and 22 °C are set in Europe, Britain and China (Chang 1934;Tank and Können 2003;Kirbyshire and Bigg 2010). Since the season onsets depend on the geographical location of the region, it is not reasonable to use a fixed threshold for determining the seasons when studying on a large scale (Hekmatzadeh et al. 2020). In China, 5 and 22 °C might be suitable in most places, but in Southern China, the temperatures are generally higher than 5 °C for the whole year; and in the northeast, the temperatures are generally low and did not exceed 22 °C throughout the year; which makes it hard to define seasons in those places. Therefore, we applied the local temperature threshold based on percentile following the previous literature (Christidis et al. 2007;Park et al. 2016;Wang et al. 2021a, b;Lin and Wang, 2022a, b) so that the four seasons' onsets and lengths can be calculated in all places. In each location, the season timing is defined through its climatological mean temperature variation. The 75th quantile of the climatological mean is set as the threshold for the onset and end of summer. The end of summer is also set for the start of autumn. For the spring and winter onset, the 25th quantile is taken. For instance, Fig. 2 shows the SAT annual harmonic in 1988 and 2017 and the seasonal cycle calculated from the summation of annual and semiannual harmonic in 1988 and 2017 at the Beijing station. The dashed lines are the 25th and 75th quantile of the climatological mean, which is a constant for each station. The intersections of the dashed line and annual cycle (AC) or seasonal cycle (AC + SemiAC) are determined as four seasons.
The differences between the seasonal cycle in these two years come from three aspects: global warming trend, annual cycle changes, and semiannual cycle changes. Since the seasonal cycles we extracted do not contain any mean value and trend, we will add a three-order polynomial temperature trend which is calculated from the original data to model the observed daily temperature and calculate the season changes. The changes of annual harmonics and the whole seasonal cycles with the warming trend added are calculated respectively, in this case, they are 8 days and 12 days; hence the change caused by semiannual cycle is their difference − 4 days. When the season changes have long term trends, the shift trends caused by global warming and annual harmonic are denoted as t 1 ; while the trends caused by global warming and finer seasonal cycle are called t 2 . In the following analysis, we will present the more precise trend t 2 and the contribution of semiannual cycle t 2 − t 1 .

Thermodynamic energy equation
To better understand the process that contributes to SAT semiannual cycle changes, we analyze the wind and temperature data on 1000 hPa over China with terms in the thermodynamic energy equation, which can be written as (ECMWF, 2014, Clark andFeldstein, 2020). This equation states that the temperature may change in response to horizontal advection −u T∕ x − v T∕ y , vertical temperature advection −̇T∕ , adiabatic warming kT ∕p , and diabatic heating P T , the Res is a residual accounting for the analysis increment and for any inconsistencies between (2) and the precise equation implemented by ECMWF. According to previous studies, the changes in semiannual cycle can be attributed to eddy activities in midlatitudes (van Loon 1967;Wikle and Chen 1996), so we mainly examine the horizontal advection term.

Seasonal cycle characteristics and their time evolutions
Through NMD extraction, the temporal mean amplitude of annual ( Fig. 3a) and semiannual (Fig. 3b) cycles; the temporal mean phase of annual (Fig. 3d) and semiannual cycles (Fig. 3e); their amplitude ratio (Fig. 3c) and phase difference ( Fig. 3f) of the SAT semiannual to annual cycle are given at each of the 620 stations in China. The amplitude of the annual cycle is nearly 10 times of the semiannual cycle, and the higher the latitude, the larger the amplitude is. The amplitude of the semiannual cycle in central and eastern China is weak and thereby the amplitude ratio there is very small. The smaller the amplitude ratio, the closer to a standard trigonometric function the seasonal cycle is. In southern and western China, the amplitude ratio is relatively high, which caused the shape of the seasonal cycle less sinusoidal. In the south coast, the amplitude of semiannual harmonic is the largest, and then the southwest. As for phase, the phase of annual cycle is quite consistent, while the phase of semiannual cycle exhibits a tripole distribution, so as to the tripole distribution of phase difference. As shown in Fig. 1, phase difference is the major factor to shape the seasonal cycle. The phase differences in China are within the range of π/4 to π/2 in most areas (Fig. 3f). In central and eastern China, the average phase difference is closer to π/4, with posterior superimposed wave crests and a delayed summer onset and shortened summer duration compared with a standard symmetric trigonometric function. In other regions, the phase differences are close to π/2, which means the wave crests (summer) are weakened and the summer is extended with a longer time.
The time evolution of spatial averaged amplitude ratio and spatial averaged phase differences are calculated and shown in Fig. 4. The amplitude ratio in each station is subtracted its mean value to see its mean variation and standard deviation. A significant (p < 0.05 in F-test) increasing trends can be found in amplitude ratios after the year 1988. The increasing speed is 0.012/10 years. It means that the proportions of semiannual cycle become larger and the seasonal cycles turned to deviate from a standard trigonometric function after 1988. Another finding is that the decadal fluctuation of amplitude ratio is stronger before 1988. During that time, an 8-year cycle can be found in the amplitude ratio in all regions, which may be related to the atmospheric circulations (Paluš and Novotná 2009;Paluš et al. 2014Paluš et al. ). 1988 is an important turning point for the changes of semiannual cycle, even earlier than the turning point 1993 found in the annual cycle (Qian et al. 2011b;Deng and Fu 2022). In the case of phase difference, they are generally stable from 1964 to 2017, with no significant long-term trends. This does not mean the phases of seasonal cycle are steady, but the relative position of the two harmonics is stable. The phase difference controls the superposition states of the two harmonics, so the steady phase difference indicates that the dates of peak temperature occurrence have remained constant.

Long term trends in season onset and length
The above results show that the amplitude ratio of the semiannual to annual SAT cycle increases remarkably after the year 1988, while the phase difference remains largely unchanged. Phase shift is usually regarded as the reason for season onset shift and season length change. Here, we give a schematic diagram (Fig. 5) to show that only amplitude ratio changes can also cause season shift and their changing directions are different under different constant phase differences. In Fig. 5, the blue curves are annual components and the amplitude is set to be 10 degrees Celsius; the red curves are the summations of annual components and semiannual components whose amplitude is set to be 1 °C, and the yellow curves are the same as the red curves but with a stronger semiannual cycle amplitude (1.6 °C). Under variant phase differences, the intensification of semiannual cycle can result in different season shifts. In China, phase differences in most areas are close to π/2 (Fig. 3f), so Fig. 5c will be the main reference.
Based on the above results, we calculate two kinds of linear trends t 1 and t 2 of season onsets and lengths from 1988 to 2017 according to methodology mentioned in Sect. 2.2.2. In Fig. 6, the mean season onset in each station is given in the first column. For the spring onset and summer onset, they begin earlier in southern China and Northwest China and begin latest in the eastern coast. For the autumn and winter onset, the dates are relatively consistent except for southern China. In four seasons, summer onset has the largest differences in different regions. The linear trend t 2 of season onset caused by global warming and seasonal cycle changes are presented in the second column. We found they shift towards earlier spring and summer onsets (Fig. 6b and e) and delayed autumn and winter onsets ( Fig. 6h and k). For summer and autumn, the advancing and delaying trends are larger than those for spring and winter. The last column gives the contribution of semiannual cycle, t 2 − t 1 . For summer and autumn onsets, the contributions of semiannual cycle are in the same direction of linear trends, whereas for the spring and winter, semiannual cycle plays a contrary role. That does not mean the changes of semiannual cycle tend to delay the spring and advance the winter, but means the changing speed t 2 is smaller than the trends t 1 which caused by only the annual cycle and global warming. Figure 2 gives a clear example.
As for season lengths, which are calculated based on season onsets, linear trends are more remarkable. Same as Fig. 6, the first column of Fig. 7 shows the mean season length distribution. The spring length is longer in the latitude of 30-40 and the shortest in southern China. The summer length is the longest among the four seasons in all areas, which is above 120 days in most regions and even reaches 160 days in southern China. The autumn length is relatively short, around two months in most regions and the winter length is the longest in the eastern coast, and the shortest in southern China. For the season length trends, the summer lengths are universally lengthened with a spatial mean trend of 7.45days/10 years (Fig. 7e), while the other three seasons are shortened, especially winter length. The shortening trend is slowest for autumn length, only − 1.63 days/10 years. In the linear trends of season length, the contributions of the semiannual cycle are shown in the last column of Fig. 7. For spring, summer, and autumn, the semiannual cycle gives the same direction of contribution as the linear trends. Notably, Fig. 6 Spatial distributions of season onset (first column), the linear trends t 2 in season onsets (second column) and contribution of semiannual cycle (last column) during 1988-2017. The sequence is spring (a-c), summer (d-f), autumn (g-i), and winter (j-l). Hollow circles indicate the trend is not significant at the 0.05 level based on F-test the semiannual cycle contributes to the entire linear trends for spring and autumn, and the shortening of spring is faster than the shortening of autumn. The different shortening speeds of spring and autumn indicated that the seasonal cycle is becoming more asymmetric. Another finding is that the contribution of the semiannual cycle in winter length is contrary to the linear trend of winter length. It means that the winter length tends to be shorter mainly because of global warming, but semiannual cycle intensification instead tends to lengthen the winter.
The details related to spatial averaged trends t 1 , t 2 , and (t 2 − t 1 )∕t 2 are presented in Table 1. The most contribution of semiannual cycle changes is on the spring onset changes and length changes of spring and autumn. They are − 102.61%, 106.58%, and 116.56% respectively.

Semiannual cycle and horizontal temperature advection
Through thermodynamic energy Eq.
(2) and preliminary mechanism analysis of the semiannual cycle in midlatitude, horizontal temperature advection is assumed to contribute to the generation of semiannual cycle. Since the phase differences of semiannual and annual cycles are more likely in π/2 at the target region, an extra negative heat transport can happen in December and June. Therefore, we calculate the temperature advection in December, which is easier to distinguish from the annual component than June, to investigate the distinctive dynamical processes. In the items in Eq. (2) Fig. 6, but for season length 0.34. Therefore, we combine these three items and find the meridional temperature advection −v T∕ y is most significantly (p < 0.05) correlated to semiannual amplitude, and the mean correlation coefficient is 0.41 (Fig. 8a). Their fluctuations matched well before 1988 and the increasing trend after 1988 can be roughly caught. Therefore, it can be assumed that the changes of semiannual cycle mainly rely on the temperature field advection driven by the meridional wind. The climatological mean meridional wind field (Fig. 8b) in December is southward in most areas, so the southward winds can bring cold air and the winds over the ocean are much stronger than the land. In the years when the semiannual cycle is relatively weak (average amplitude < 1.2 ℃), the composition wind field (Fig. 8c) shows positive anomaly over eastern China and the ocean, which means that the southward winds are weakened. At the same time, an anomalous warm state appears in most of China. In contrast, the wind velocity shows a negative anomaly in the whole field over China when the mean amplitude of the semiannual cycle is stronger than 1.2℃ (Fig. 8d), especially over the eastern ocean. This anomaly strengthens the southward transport of the cold air and hence leads to a colder winter (Fig. 8g).

Discussion
The above results demonstrate that from 1988 to 2017, spring and summer start generally earlier while the onset of autumn and winter is delayed, which is consistent with the results of previous studies (Wang et al. 2021a, b). Here we are more concerned about the playing role of semiannual cycle in the season changes since the semiannual cycle is getting stronger since 1988. We find and confirm that under the enhancement of the semiannual harmonics, the advance of summer is faster and the lengthening of summer is more pronounced; the winter tends to be colder and the spring and autumn lengths are shortened. Although the phase differences are relatively unchanged, they also played an important role in the season modulation (Fig. 5). As presented in Fig. 5, the phase difference in China is around π/4 to π/2 so the schematics of Fig. 5b and c serve the main references. However, the mean value of SAT seasonal cycle is unchanged in Fig. 5, while in the real data, the mean value will persistently increase so that the joint impacts of global warming, annual cycle changes, and semiannual cycle changes lead to the final trend. Figure 2 gives a clear example for summer onset. There is an intersection around 75% quantile of the climatological mean. In 1988, the intersection is below this 75% quantile so the existence of semiannual cycle delayed the summer onset. However, in 2017, the intersection is above this 75% quantile so the intensification of the semiannual cycle advanced the summer onset. Hence the lengthening of summer is amplified under the modulation of semiannual cycle. It is necessary to point out that the shift of season can be attributed to complex factors including global warming, annual cycle and semiannual cycle and even higher order harmonics. Any of the factors can be set as a constant and one can only change one factor to do the control experiments. In this paper, we mainly show the differences between the conditions with semiannual cycle added or not, and the main objectives is to confirm the contribution from the semiannual cycle. So, the global warming trend and annual component changes are maintained, and t 2 is supposed to be the true trend of observations. Since many previous works used the annual component to explain the season shift, e.g., Stine et al. (2009) used one sinusoidal function to fit the seasonal cycle changes and find the advance of season onset, here we denote these trends as t 1 . Our results reveal the importance of considering the semiannual cycle in seasonal cycle analysis by calculating the relative linear trend changes t 2 − t 1 and contribution percentages (t 2 − t 1 )∕t 2 . If the superimposed positions of the semiannual cycle in other regions are much different from Fig. 5b and c, the season changes may be totally different even when also under the intensification of the semiannual cycle.
To investigate the mechanism of semiannual cycle changes, we calculated the horizontal heat budgets in near surfaces and found the semiannual cycle amplitudes are significantly correlated to temperature field advection driven by meridional wind −v T∕ y . Previous studies of the Southern Hemisphere Seasonal Oscillation (SAO) in high latitudes concluded that the semiannual cycle is associated with wave fluctuations at high latitudes (van Loon 1967) and here we found it is also attributed to meridional wind-temperature interaction in midlatitude. The direction of anomalous meridional wind field and anomalous temperature field both control the strength of the semiannual cycle. It is well known that temperature gradient can generate transient eddies through baroclinic instability and baroclinic activity also has a semiannual cycle (Lembo et al. 2017). Therefore, the baroclinic semiannual activity can preferentially enhance the eddy activities in winter and in turn intensify the temperature semiannual cycle as feedback. Only in Tibet Plateau, the state is opposite. In addition to horizontal temperature advection, the vertical heat advection is also worth studying since there is also a semiannual cycle in the high level of the troposphere atmosphere. The present results identified general changing patterns for seasons in China, but in some places such as northwest and southwest China, the results are less consistent and representative owing to the fewer meteorological stations located in the western portion (Shen et al. 2014;Liu et al. 2022), and due to the unique topographic features in Tibetan Plateau which have strong effects on monsoon movement, so our results emphasize more on the influences of winter wind in the central and eastern China.
Except for the studies which only focused on the annual harmonic (Paluš et al. 2005;Stine et al. 2009;Dwyer et al. 2012), a growing number of recent studies have already considered the residual features of the seasonal cycle beyond the fundamental annual sine wave (Donohoe et al. 2020;Song et al. 2021;Yang and Wu 2022). For instance, using pentad average temperature (Lin and Wang 2022a, b) or 31-day running mean filtering or Ensemble Empirical Mode Decomposition method (Qian et al. 2011a, b) to define the season onsets and lengths has already included the finer features of meridional v′ in the December of the last years when mean amplitude of semiannual cycle in these four regions are below 1.2 ℃. d same as c but for the years when mean amplitude of semiannual cycle are above 1.2 ℃. e-g same as b-d but for temperature field the seasonal cycle. And many previous works have shown asymmetric changes in spring onset and autumn onset (Sparks and Menzel 2002;Donohoe et al. 2020), namely the different changing speeds of spring advancing spring and autumn delaying, which also confirms the influence of semiannual cycle. Our results on the changing direction of four seasons are consistent with them, but we further quantified the specific impacts of semiannual cycle and show that not only the phase of annual cycle can affect the seasonality, but also the amplitude of semiannual cycle can.
Analyzing the influences of annual and semiannual cycle separately can aid us in better understanding their different mechanisms and conducting seasonal predictions. Recent works have pointed out that the primary insolation (annual) cycle combined with the induced annual variation in some other quantity, such as heat capacity, ocean mixed layer depth, and the coalbedo, can plausibly account for the observed semiannual cycle in temperature (Song et al. 2021;Yang and Wu 2022). The enhancement of semiannual cycle after 1998 in China may relate to the turning from "global dimming" to "brightening" around 1990 (Wild 2009(Wild , 2012, which is attributable to the decrease in atmospheric shortwave absorption by aerosols and the increase in the SAT seasonal cycle (Qian et al. 2011b;Deng and Fu 2022). Meanwhile, the changes in semiannual cycle also correspond with the turning point in East Asian climate from dry to wet. Moisture soil can reserve more heat in the daytime and also lead to stronger SAT SC. Through the interactions between the insolation cycle and coalbedo cycle and soil heat capacity cycle, the semiannual cycle is accordingly produced and varying. Therefore, a detailed study is in progress to find out which factors dominate the origin and changes of semiannual component and the surface maximum and minimum temperatures will be investigated respectively to see the differences and examine whether urbanization and heat island effect also affected the seasonality changes.

Summary
This paper quantified the characteristics of SAT seasonal cycle mean states and their time evolution in China, thereby revealing the important role of semiannual cycle playing in the season timing shifts and length changes. The main findings can be summarized as follows: 1 The changes in the amplitude ratios in China all show a pronounced increasing trend after 1988. This is mainly caused by a significant semiannual harmonic enhancement after 1988, which is earlier than the annual harmonic intensification found in 1993. The changes in phase differences in China are relatively small and constant.
2 Under the combined effect of annual and semiannual cycles, the season onsets and lengths changed significantly. During 1988-2017, two kinds of linear trends of season onsets and lengths are calculated, they are (a) trends t 1 caused by global warming and annual cycle and (b) trends t 2 caused by global warming, annual cycle, and the semiannual cycle. The results showed that when considering the impacts of amplitude growth in the semiannual cycle, the advance speed of spring and delay speed of winter is reduced; the advance of summer and delay of autumn is strengthened. The mean absolute contribution percentage of the semiannual cycle in season onsets trends measurement is 52.63%, while for summer lengths, the contribution is even more remarkable, with the mean absolute percentage of 78.66%. That mainly comes from the shortening trends of spring and autumn. The different shortening speed of spring and autumn also shows the asymmetry in seasonality caused by semiannual cycle intensification. 3 Through thermodynamic equations we find that the strength of the semiannual cycle is evidently correlated to meridional temperature advection in the near surface, rather than zonal advection. The negative anomaly of meridional wind velocity and temperature field can facilitate the northward transport of cold air in winter and therefore intensify the semiannual cycle in SAT and alter the season characteristics.
In conclusion, we find that semiannual component has a nonnegligible effect on the season onsets and lengths, while prior works focused more on the greenhouse effect. The intensified semiannual cycle makes the seasonality more and more asymmetric, especially reminding us even under global warming, the extreme cold events might not decline too much due to the semiannual component enhancement in winter. While this study mainly considered the connection of semiannual cycle with the atmospheric circulation in winter, further research is needed to examine how atmosphere and surface albedo and soil heat capacity interact with temperature seasonal cycle to alter the semiannual cycle. The findings in this study should help improve our understanding of the effects of changing SAT semiannual cycle and be beneficial to the seasonal predictions.
Funding The work was supported by the Fundamental Research Funds for Central Universities, China University of Geosciences (Wuhan) (Grant CUG2106108).
Data Availability All data that support the findings of this study are included within the article.

Conflict of interest The authors declare no competing interests.
Ethical approval and consent to participate We confirm that this work is original and has not been published elsewhere, nor is it currently submitted to any other journal. We have read the Springer journal policies on ethical responsibilities of authors and submit this manuscript in accordance with those policies.
Consent for publication Not applicable.