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Feb.  2023

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# A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming

• Based on the Complex Empirical Orthogonal Functions (CEOFs) of bandpass-filtered daily streamfunction fields, a quantitative method of detecting transient (synoptic) Rossby wave phase speed (RWPhS) is presented. The transient RWPhS can be objectively calculated by the distance between a high (or low) center in the real part of a CEOF mode and its counterpart in the imaginary part of the same CEOF mode divided by the time span between two adjacent peaks (or bottoms) of two principal component curves for the real and imaginary parts of that CEOF mode. The new detection method may partly reveal the spatiotemporal heterogeneity of Rossby wave prorogation. Although the mean westerly jet at 200 hPa doubles the speed of its counterpart at 500 hPa, the estimated RWPhS at both levels are around 1000 km d–1 and quantitatively consistent with the quasigeostrophic-theory-based RWPhS, confirming that the meridional potential vorticity gradient induced by the barotropic and baroclinic shears of mean flow, together with the β effect, play an essential role in Rossby wave propagation. Both observations over the past four decades and a 150-year historical simulation suggest no evidence for slowing wintertime transient Rossby waves in the Northern Hemisphere, but possible regional changes are not excluded. We emphasize that not only the mean flow speed, but also the barotropic and baroclinic shears of the mean flow, and their associated contributions to the meridional potential vorticity (PV) gradient, should be considered in investigating the possible change of Rossby waves with global warming.
• Figure 1.  The first mode of complex empirical orthogonal function (CEOF1) and corresponding principal component (PC1) of 2–9-day Lanczos-filtered streamfunction at 200 hPa (a–c) and 500 hPa (d–f) during December, January, and February (DJF) of 2008/09: (a) Real part and (b) imaginary part of CEOF1 (colored contours, m2 s–1), and mean zonal wind speed at 200 hPa in 2008/09 DJF (black contours, m s–1); (c) Real part (black line) and imaginary part (blue dashed line) of PC1, dots mark the data with |PC|≥0.5); (d)–(f): same as (a)–(c), but for 500 hPa. The criterion for the dotted centers in (a) and (b) is the absolute value being larger than 1.5×106 m2 s–1.

Figure 2.  (a) 200-hPa streamfunction anomaly (original streamfunction on 9 January 2009 minus 2008/09 DJF-averaged streamfunction), (b) 2–9-day Lanczos-filtered streamfunction at 200 hPa on 9 January 2009, (c) reconstructed streamfunction on 9 January 2009 from CEOF1 (i.e., real part of 2008/09 DJF 200-hPa CEOF1 multiplied by real part of PC1 on 9 January 2009 plus imaginary part of CEOF1 multiplied by imaginary part of PC1 on 9 January 2009); (d) reconstructed streamfunction on 9 January 2009 from the first four CEOFs; (f)–(i) are the same as (a)–(d), but for 11 January 2009. Black contours (m s–1) are mean zonal wind speed of 2008/09 DJF at 200 hPa. (e) and (j) are the real and imaginary parts of daily streamfunction at grid point C in Fig. 1 during 2008/09 winter. Black curves are from the original 2–9-day Lanczos-filtered time series [in (e)] and its Hilbert transform [in (j)], while the red curves are reconstructed from the truncated sum of the first 1–4 CEOF modes. Units: 107 m2 s–1. The two days are utilized to illustrate the propagation of Rossby waves during about one-fourth of a wave period.

Figure A1.  The intraseasonal variability of RWPhS over north Pacific (a) and north Atlantic (b) regions during DJF of 2008/09

Figure A2.  Box-and-whisker diagrams of zonal Rossby wave phase speed (RWPhS) at 200 hPa between 20°N and 60°N based on (a) annual and (b) decadal statistics separately obtained from the second CEOF modes for the winter of 1979/80 to 2018/2019. (c) and (d) : The same as (a) and (b), but for the third CEOF mode; (e) and (f): The same as (a) and (b), but for the fourth CEOF mode.

Figure 3.  Box-and-whisker diagrams of zonal Rossby wave phase speed (RWPhS) at 200 hPa between 20°N and 60°N based on (a) annual and (b) decadal statistics from the CEOF1 for the winters of 1979/80 to 2018/19. The short red line in (b) marks the median value. Medians in (a) are connected by a black curve, and the thick red curve is the 5-year Gaussian smoothing of medians. The bottom and top blue lines of the boxes are the 25th- and 75th- percentile values, respectively, while the whiskers extend to the minimum and maximum of the data, except for outliers, which fall outside of 99.3%; (c) and (d) are the same as (a) and (b) but for the zonal RWPhS at 500 hPa.

Figure 4.  The same as Figs. 3a and 3b, but for RWPhS at 250 hPa during boreal winters from 1850/51 to 1999/2000 in the CESM2 historical simulation.

Figure 5.  The zonal wind speed (m s−1) at 200 hPa (a) and 500 hPa (b) and the mean $\partial \overline{{\rm{PV}}}/\partial y$ (×10−11 m−1 s−1) at 200 hPa (c) and 500 hPa (d) during boreal winter (DJF) averaged over 1979/80–2018/19.

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## Manuscript History

Manuscript revised: 03 July 2022
Manuscript accepted: 06 July 2022
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming

###### Corresponding author: Jianhua LU, lvjianhua@mail.sysu.edu.cn
• 1. School of Atmospheric Sciences, Sun Yat-Sen University and Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519082, China
• 2. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing100029, China
• 3. Guangdong Province Key Laboratory for Climate Change and Natural Disaster Studies, Sun Yat-sen University, Guangzhou 510275, China

Abstract: Based on the Complex Empirical Orthogonal Functions (CEOFs) of bandpass-filtered daily streamfunction fields, a quantitative method of detecting transient (synoptic) Rossby wave phase speed (RWPhS) is presented. The transient RWPhS can be objectively calculated by the distance between a high (or low) center in the real part of a CEOF mode and its counterpart in the imaginary part of the same CEOF mode divided by the time span between two adjacent peaks (or bottoms) of two principal component curves for the real and imaginary parts of that CEOF mode. The new detection method may partly reveal the spatiotemporal heterogeneity of Rossby wave prorogation. Although the mean westerly jet at 200 hPa doubles the speed of its counterpart at 500 hPa, the estimated RWPhS at both levels are around 1000 km d–1 and quantitatively consistent with the quasigeostrophic-theory-based RWPhS, confirming that the meridional potential vorticity gradient induced by the barotropic and baroclinic shears of mean flow, together with the β effect, play an essential role in Rossby wave propagation. Both observations over the past four decades and a 150-year historical simulation suggest no evidence for slowing wintertime transient Rossby waves in the Northern Hemisphere, but possible regional changes are not excluded. We emphasize that not only the mean flow speed, but also the barotropic and baroclinic shears of the mean flow, and their associated contributions to the meridional potential vorticity (PV) gradient, should be considered in investigating the possible change of Rossby waves with global warming.

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