Propagating oscillations in summer air temperature over Eurasian
To investigate the propagation features of intraseasonal oscillations in air temperature at 850 hPa during boreal summer, the CEOF analysis is employed. The real and imaginary parts of CEOF-1 (Fig. 1a and b) reveals a zonal wavelike pattern over Eurasian continent, which explains 15.7% variability. Upper-level meridional wind changes with a zonally wave train over Eurasia during summer have been found (Muetzelfeldt et al., 2023; Zhu et al., 2023). Our results imply that lower-level temperature changes align with upper-level wind changes. The spatial amplitude and phase of CEOF-1 are exhibited in Fig. 1c. The CEOF-1 amplitudes characterize a zonal band with the large values between 40°N and 70°N extends from 30°E to 110°E. The peak amplitude region indicates the activity hotspot, where the intensity of air temperature intraseasonal oscillations is at its maximum. While the spatial phases of CEOF-1, undergoing almost one complete cycle across the peak amplitude region, suggests that the air temperature intraseasonal oscillation is propagating. All characteristics of the results in the 850hPa air temperature are consistent with those at 2-m air temperature in CEOF analysis (Supplementary Fig. S1), inferring robustness of our results. This also indicates that the air temperature intraseasonal propagating oscillations can occur at the surface, further influencing temperature changes and may potentially being associated with HWs.
Since the propagating signal of CEOF-1 for 850 hPa air temperature is identified, we further calculate its spatial and temporal phases to determine the direction of the propagation. It can be observed that the peak amplitude region of the propagating oscillation occurs between 40°N and 70°N (Fig. 1c). Therefore, we calculate the 10-degree latitudinal averaged spatial phases along 40°N to 70°N, as shown in Fig. 2a-c. The temporal phase is displayed in Fig. 2d. According to previous studies, the spatial derivative of spatial phases measures wavenumber \(\:k\) and the time derivative of the temporal phase represents the angular frequency \(\:\) (Susanto et al., 1998; Terradas et al., 2004; Hannachi et al., 2007; Majumder et al., 2019). The slope of the spatial phase represents the wavenumber and that of the temporal phase represents the angular frequency. We can see that CEOF-1 of summer air temperature over Eurasia has wavenumbers around 0.087 \(\:rad\bullet\:{\left(^\circ\:longitude\right)}^{-1}\), 0.077 \(\:rad\bullet\:{\left(^\circ\:longitude\right)}^{-1}\), and 0.069 \(\:rad\bullet\:{\left(^\circ\:longitude\right)}^{-1}\) within 40°-50°N (Fig. 2a), 50°-60°N (Fig. 2b), and 60°-70°N (Fig. 2c), respectively. The angular frequency of CEOF-1 is 0.343 \(\:rad\bullet\:{day}^{-1}\) (Fig. 2d). The phase speed can be obtained using the relation \(\:c=/k\) from the values of the wavenumber and angular frequency. The average phase speed along 40°N and 70°N is 5.6 \(\:m{s}^{-1}\), which is close to the speed of synoptic-scale Rossby travelling waves having phase speeds from 6 to 12 \(\:m{s}^{-1}\) with zonal wavenumbers 6 and higher (Fukutomi et al., 2012; Kornhuber et al., 2017). Positive value of phase speed suggest the summer air temperature intraseasonal oscillation propagates eastward over Eurasia.
Mechanisms of propagating oscillation in summer air temperature
To explore the possible mechanisms of the intraseasonal air temperature eastward propagating oscillation, the atmospheric temperature budget analysis is performed. This analysis can elucidate the contributions of the atmospheric heating processes, including advection and diabatic heating. The linear regressions for temperature changing rate, total heating rate, advection heating rate, and diabatic heating rate are regressed on the real and imaginary CPC-1 of air temperature at 850 hPa, respectively (Fig. 3). Spatial regression patterns of temperature changing rate exhibit statistically significant zonal wavelike patterns (Fig. 3a and e). These regression patterns, linearly explained by CPC-1, are in a good agreement with the air temperature CEOF-1 patterns shown in Fig. 1. While the results of the total heating rate exhibit similar structures with that for temperature changing rate, as evidenced by Fig. 3b and f. The alignment between the temperature changing rate and total heating rate indicates that the atmospheric total heating largely contributes to temperature changes associated with the summer air temperature intraseasonal propagating oscillations. We further investigate the relative roles of advection and diabatic heating processes in atmospheric heating. The regressed spatial patterns of the advection heating rate onto CPC-1 (Fig. 3c and g) show a resemblance to that of the total heating rate, particularly between 40°N and 70°N. Additionally, the diabatic heating rate displays nearly opposite responses to CPC-1 (Fig. 3d and h). It suggests that the Eurasian summer air temperature eastward propagating oscillation accompanied by temperature changes are mainly attributed to the advection heating processes, while the diabatic heating partially compensates.
The association between propagating oscillations and HWs
Here we aim to link the Eurasian summer intraseasonal air temperature eastward propagating oscillation to HWs. The relationship between HWs and the propagating oscillation might vary along with the variability of the propagating oscillation intensity in different years. To approach our objective, it is necessary to first establish a metric that can measure the interannual variability of the intensity of the propagating signals. The temporal amplitude based on CPC-1 of summer air temperature reflects the intensity of the eastward propagation oscillation across Eurasian continent over time. Therefore, the metric that represents the interannual variability of the propagating signals can be obtained as the time-averaged absolute amplitude of CPC-1 for each year as given by:
\(\:A\left(yr\right)=\frac{1}{J}\underset{j1}{\overset{j2}{\int\:}}\left|{\stackrel{\sim}{T}}_{1}(yr,j)\right|dj\) (3),
where \(\:{\stackrel{\sim}{T}}_{1}\) is the temporal amplitude calculated as the square root of real and imaginary CPC-1 of 850hPa air temperature, j is the Julian day with j1 and j2 corresponding June 1st and August 31st, and J is the number of days during the period (92 days).
The yearly averaged absolute amplitude metric constructed by CPC-1 of air temperature at 850 hPa is displayed in Fig. 4a. This metric exhibits interannual variability in the intensity of the propagation signals with a range between about 0.6 and 1.3. We then take the values which are greater than plus one standard deviation relative to the mean value as strong values of the yearly absolute amplitude metric. A total of nine years (1983, 1987, 1989, 1999, 2006, 2010, 2014, 2015, and 2021) with strong propagating signals are selected as strong events. Phase diagrams of real and imaginary CPC-1 of the nine strong events are shown in Fig. 4b-j. The strongest values are around 2 in all nine years. Among the nine years, 1983 (Fig. 4b), 1987 (Fig. 4c), and 1989 (Fig. 4d) have relatively weak values and fewer days with strong values than that in the other years. Minobe et al. (2022, preprint) have already identified that Eurasian HWs in 2021 exhibit eastward propagating signals. Besides, during the years in 2006, 2010, and 2015, HWs and the associated zonal wavenumber 6–8 circulation patterns are also observed over Eurasia but with focus on the quasi-stationary (standing) Rossby waves (Petoukhov et al. 2013; Duchez et al., 2016; Kornhuber et al., 2019). Moreover, the values in the nine strong events show magnitudes almost double the weakest values in nine years (Supplementary Fig. S2). These results provide evidences that the amplitude metric can well measure the intensity of the summer air temperature eastward propagating oscillation over Eurasia.
We have already identified the years with strong propagation signals based on the amplitude metric. Besides, we found the critical role of advection heating process in the propagating oscillation. Existing studies pointed out that warm air temperature advection contributes to the atmospheric HWs (Screen, 2014; Horton et al., 2016; Garfinkel and Harnik, 2017). We further investigate the relationship between the advection heating related air temperature intraseasonal eastward propagating oscillation and HWs during the years when the propagation signals are strong.
Figure 5 shows latitudinal averaged daily 2-m maximum air temperature anomalies that satisfy the HW condition overlayed with the positive values of the estimated air temperature anomalies using the integration of reconstructed advection heating rate at 850 hPa from CEOF-1 between 40°N and 70°N. A good relationship between air temperature anomalies estimated by advection heating rate and HWs over Eurasian can be observed in those nine years. For the years 1983, 1987, and 1989 with relative weak propagation signals, the HWs occur less than that in other years but still exhibit eastward propagating signals for mid-August in 1983 (Fig. 5a), early-August in 1987 (Fig. 5b), and early-July in 1989 (Fig. 5c). In the year 2010 with strongest value of the metric, a HW event lasted from June until mid-August is prominently exhibited in Fig. 5f. This long-lasting HW is also reported (Barriopedro et al., 2011; Dole et al., 2011; Matsueda, 2011). Here we find this long-lasting HW event also exhibits propagating signal. While for the other years, eastward propagating signals can also be found for early-July in 1999 (Fig. 5d) and 2006 (Fig. 5e), early-August in 2014 (Fig. 5g), early-June in 2015 (Fig. 5h), and mid-June in 2021(Fig. 5i) accompanied with estimated anomalous air temperature. The results show a good association between HWs and estimated air temperature anomalies during the years with strong propagation signals. Furthermore, our results are not sensitive to the definitions of HWs (Supplement Fig. S3 and S4), indicating a robust linkage between HWs and the intraseasonal air temperature eastward propagating oscillation.
Summary and discussion
In this research, we investigated the features and mechanisms of intraseasonal propagating oscillation in air temperature over Eurasian during boreal summer and its linkage with HWs. By applying CEOF method, we revealed its wavelike pattern and eastward propagating property. To understand its possible mechanisms, we performed atmospheric temperature budget analysis. By regressing each component onto CPC-1, it is found that the advection heating processes are crucial in driving this eastward propagating oscillations, while the diabatic heating partially compensates. To explore the linkage between propagation and summer HWs, we established a metric to measure the interannual variability of eastward propagating oscillations based on CPC-1. We selected nine years in total with strong propagating signals, where we also identified the heatwave events. It is found that a good relationship between air temperature anomalies estimated by advection heating rate and HWs over Eurasia can be observed in those nine years, suggesting a robust linkage.
However, several related points should be further considered. Firstly, although the advection processes are found to be the critical driver for this eastward propagation, a deeper understanding such as whether zonal or meridional component is more important still remains inadequate. This may need more advanced statistical analysis or model experiments in the future. Besides, it can be found from Fig. 4 that the occurrences of strong eastward propagating signals after 1990s is almost twice than before. Even among these nine strong events, the intensity after 1990s is considerably higher. Coincidently, the Atlantic Multidecadal Oscillation (AMO; Schlesinger and Ramankutty, 1994; Kerr, 2000) changes phase from negative to positive around this timepoint. As an internal variability over North Atlantic with muti-decadal time scale, AMO can influence the climate over Eurasian at upstream by changing atmospheric circulation (Zhang et al., 2018; Huang et al., 2019). A tentative question is, why the intensity of propagating oscillation is higher and heatwave events occur more frequently when the AMO turns to its positive phase? Maybe the current period (43 years) used in the current study is too short for discussing this question, and we would like to leave it for future research.