Variations in the Mechanical Energy Cycle of the Atmosphere

Transcription

1 Variations in the echanical nergy Cycle of the Atmosphere Liming Li * Andrew P. Ingersoll Xun Jiang Yuk L. Yung Division of Geological and Planetary Sciences, California Institute of Technology, 1200 ast California Boulevard, Pasadena, CA 91125, USA. * To whom all correspondence should be addressed. -mail: liming@gps.caltech.edu To be submitted to GRL, August 9,

2 Abstract The global atmospheric energy cycle and its variability are examined using the NCP-2 reanalysis - the most complete and physically consistent meteorological dataset of the modern satellite era ). A significant positive trend in eddy kinetic energy is concentrated in the Southern Hemisphere SH), which is consistent with a reported increase in the depth and radius of the SH storms. Trends are also found in the conversion rates between different energies and the corresponding generation and dissipation terms. These changes in the conversion rates integrated over the 27-year period are much larger than the observed changes in the atmospheric energies, suggesting that the climate system remains close to dynamical balance. The positive trends in all conversion rates and the increasing dissipation of kinetic energy further suggests that the efficiency of the atmosphere has increased during the modern satellite era. 2

3 1. Introduction The Lorenz atmospheric energy cycle describes the general circulation from a specific perspective that emphasizes energy transformation how the incoming solar radiation generates potential energy that is transferred to kinetic energy and is finally lost to frictional dissipation. Trends in the rates of energy transformation are a climate change indicator that focuses on the dynamics of the atmosphere. These statistical characteristics of the global atmospheric energy cycle are useful for the validation of general circulation models since they constitute the constraints that must be fulfilled. ost of the earlier computations of the energy components of the atmosphere are based on data sets that do not cover the area south of 20 N [Krueger et al., 1965; Wiin-Nielsen 1967; Peixoto and Oort, 1974; Oort and Peixoto, 1974, 1976; Hu et al., 2004]. The only early study that covered the globe [Oort, 1983] was based on a 10-year ) rawinsonde dataset with observational limitations due to the sparseness of stations in the Southern Hemisphere SH) and large data gaps at some stations due to adverse meteorological conditions. The advent of "data assimilation" techniques and new sources of data, particularly a wide range of observations coming from satellites, make it possible to construct homogeneous global meteorological data sets in a quality not available heretofore. The National Centers for nvironmental Prediction NCP) and National Center for Atmospheric Research NCAR) have cooperated to produce a retroactive record of more than 50 years of global atmospheric fields [Kalnay et al., 1996; Kistler et al., 2001; Kanamitsu, et al., 2002; Simmonds, 2003]. The so-called reanalysis datasets 3

4 have been utilized in numerous research papers. The NCP reanalysis 2 NCP-2) is an update of the NCP/NCAR reanalysis project that corresponds to the modern satellite era 1979-current), that has improvements in many aspects [Kistler et al., 2001; Kanamitsu, et al., 2002; Simmonds, 2003]. In this paper, the 27-year ) NCP-2 globally homogeneous daily dataset with horizontal resolution 2.5 degrees in the latitudinal and longitudinal directions and 17 levels in the vertical direction is utilized to address the global atmospheric energetics. The NCP-2 is obtained by assimilating past data into a frozen state-of-the-art analysis/forecast model system, which makes the database one of the most complete, physically consistent meteorological datasets [Kistler et al., 2001; Simmonds, 2003]. In addition, the zonal mean number of all types of observations in the modern satellite era 1979-current) roughly keeps constant on a global scale [Kistler et al., 2001]. Therefore, the physically consistent NCP-2 dataset, which has a longer time range compared to the 10-yr rawinsonde data used by Oort [1983], makes it possible to study the variations of the global atmospheric energy cycle. 2. ethods Following the formulation by Lorenz [1955] and the notation used by Peixoto and Oort [1974], we calculate the following terms in the energy cycle in the mixed space-time domain: the mean available potential energy P, the eddy available potential energy P, the mean kinetic energy K, the eddy kinetic energy K, the conversion rate between 4

5 the mean kinetic energy and available potential energy C K, P ), the conversion rate between the mean and eddy available potential energies C P, P ), the conversion rate between the eddy available potential energy and kinetic energy C P, K ), and the conversion rate between the eddy and mean kinetic energies C K, K ). ost of the computations are based on type A variables [Kalney et al., 1996], which are geopotential height, zonal wind, meridional wind, and temperature. These variables have the highest data quality rating in the NCP-2 reanalysis data set. The only type B variable pressure vertical velocity ω is used in some terms of the conversion rates C P, P ) and C K, K ). Our calculation indicates that these terms involving ω are roughly one order of magnitude smaller than the other terms in C P, P ) and C K, K ). The terms involving the vertical velocity in the other two conversion rates C P, K ) and C P, K ) were changed into terms including horizontal velocity by the continuity equation [Peixoto and Oort, 1974] because the horizontal velocity has higher data quality than the vertical velocity in datasets. The synoptic eddies cyclones and anticyclones), with length-scale around a thousand kilometers and time-scale of several days, play an important role in the atmospheric energy cycle. In this paper, the eddies with sizes and lifetimes smaller than the spatial and temporal resolutions of the daily NCP-2 ~ 250 km and 1 day) respectively are treated in the same category as molecular motions [Lorenz, 1955]. ost of the synoptic eddies have lifetime less than one month, so we present the monthly evaluation of the parameters that characterize the energy cycle based on the NCP-2 global daily data, in which the transient eddy component contains only eddies with time scales less than a 5

6 month. However, the yearly evaluation of the energy cycle, in which the transient eddy component is defined as eddies with all time scales less than 12 months, is given in the supporting online material in order to compare our results with the previous results based on the yearly evaluation of 10-year rawinsonde observations [Oort, 1983]. 3. Results Figure 1 shows the time series of monthly evaluation of the mean and eddy energies of the global atmosphere between 1979 and The energy cycle has a direction from the mean available potential energy to eddy potential energy, then to eddy kinetic energy, finally to mean kinetic energy [Lorenz, 1955]. The classical picture of the energy cycle depicted by Lorenz bears little resemblance to any previous theories that attribute the conversion of potential into kinetic energy to a general rising motion in low latitudes and sinking in high latitudes. A positive correlation between the mean potential energy and mean kinetic energy with correlation coefficient ~ 0.84 panel A and B of Fig. 1) is discovered. The correlation arises because geostrophic balance, in which the large-scale zonal flow is determined by the large-scale meridional temperature gradient, plays an important role in the global general circulation. In addition, Fig. 1 shows a positive linear trend J / m / year in the global eddy kinetic energy K panel D of Fig. 1). The student t-statistics see the auxiliary material) shows that the confidence level corresponding to the positive trend in K is around 99%. The global eddy potential energy P panel C of Fig.1) also shows a positive trend 6

7 2 712J / m / year ) with a confidence level ~ 98%. The mean potential energy, kinetic energy, and the total mechanic energy potential energy + kinetic energy) do not have significant trends. The yearly evaluation of the global atmospheric energetics Fig. A3 in the auxiliary material) also shows a clear trend in the eddy kinetic energy 2 890J / m / year with a confidence level 99%). However, the yearly evaluation of eddy potential energy does not show any trend. The different results on P between the monthly evaluation and the yearly evaluation indicates that the components with time scales less than a month do increase with time but those with longer time scales do not. The spatial distribution of the global eddy kinetic energy and trends are plotted in Fig 2. The top two panels of Fig. 2 A and B) show that the distribution of the eddy kinetic energy is mainly concentrated in mid-latitude oceans. The strongest centers of K in the Northern Hemisphere NH) are associated with the two storm tracks over the Pacific oceans and Atlantic oceans [Harnik and Chang, 2003]. The strong zonal belt of K in the middle latitudes of the SH is related to the storm tracks over the Southern Ocean SO) [Trenberth, 1991; Simmonds, 2003]. The middle two panels of Fig. 2 C and D) show that K has a positive trend in most areas of the SH with a confidence level larger than 95% panel ). Our calculations in the two hemispheres and different seasons Fig. A1 and A2 in the auxiliary material) reveal that the positive trend of K appears in all seasons of the SH. 7

8 The increase of K in the SH is supported by the positive trend in the mean radius and depth of cyclones over the SO during the modern satellite era [Simmonds, 2003]. The largest center of positive trend of K around W) and 55 S is roughly consistent with the strongest center of positive trend in the mean radius and depth of cyclones over the SO [Simmonds, 2003]. However, recent climate changes in the SH including the variations in cyclone behaviors, which probably cause the trend in the eddy kinetic energy, could not be explained in a simple way [Karoly, 2003; Simmonds, 2003; Turner et al., 2006]. The conversion rates between different energies are displayed in Fig. 3. The conversion term C K, P ) displays a positive trend W / m 2 / year ) with a confidence level ~98% panel A of Fig. 3). The term C P, K ) has a positive trend W / m / year ) with significance level ~99%. The other two terms C P, P ) and C K, K ) shows less significant positive trends W / m 2 / year for C P, P ) and W / m / year for C K, K ) ) with confidence levels ~ 91% and 96% respectively. The smallest change in conversion rates is that between the eddy kinetic energy and mean kinetic energy C K, K ). Nevertheless, the time integral of the excess of C K, K ) relative to 1979 over the 27 years ) generates a large increase in energy J / m ), which is much larger than the observed changes in energies, 0.1 m J / to 1 m J / over the same time period Fig. 1). Therefore, the 8

9 generation and dissipation terms in the energy cycle have to make corresponding changes to balance the large changes due to changing conversion rates. The fact that the changes in the atmospheric energies are small while the changes in conversion rates are large, suggests that the climate system remains close to dynamical balance. The increasing conversion rate C P, K ) will lead to an increasing eddy kinetic energy K. Therefore, the increasing K is probably attributed to the change in the C P, K ). In addition, the dissipation term D K ) must have increased in order to cancel the surplus in K generated by the increasing C P, K ), which can not be balanced by the observed increase value of K and the change in K generated by the small changing C K, K ). An increasing D K ) during a positive trend of K is reasonable because stronger eddy activity will inevitably result in friction increase. Likewise, the generation term G P ) have to increase during the modern satellite era in order to balance the great subtraction of P by the conversion term C P, K ). The increasing C P, K ) also makes a possible explanation why the cyclone system over the SO has become larger and deeper during the modern satellite era [Simmonds, 2003]. The mean energies P and K basically remain constant despite the large positive trend of C K, P ), which is much larger than the trends in the conversion terms C P, P ) and C K, K ). Therefore, the generation term G P ) and the dissipation term D K ) have to decrease to cancel the effect of the large increasing C K P ). The conversion, term C K, P ) is determined by the strength of the direct Hadley cell 9

10 C K, P ) < 0 ) and the indirect Ferrel cell C K, P ) > 0 ). The increasing C K, P ) suggests that the Hadley cell is weakening or the Ferrel cell is strengthening or both. A previous diagnostic study based on the same dataset NCP-2) shows that the strength of the Hadley cell basically keeps constant during the modern satellite era [itas and Clement, 2005]. Combining these factors, it suggests that the Ferrel cell becomes stronger during the time period of The Ferrel cell is associated with the eddy activity in the middle latitudes. Therefore, the result is consistent with the observations that the mean radius and depth of cyclones in the middle latitudes of the SH increase during the modern satellite era [Simmonds, 2003]. The positive trends in all conversion terms Fig. 3 and Fig. A5 in the auxiliary material) suggest that the global atmosphere is in a more efficient state. We compute the changes in dissipation of kinetic energies DK ) and DK ) from the changes in K, K, C P, K ), C K, K ), and C K, P ) Fig. 3). We find that DK ) increased by 0.3W / m 2, and DK ) decreased by 0.15 m 2 W / during the modern satellite era. Thus the total dissipation of kinetic energy increased by 0.15W / m 2, which is ~7% of the total dissipation 2.23W / m 2. This is much greater than the percentage change in the incoming solar radiation. Therefore, the efficiency of the atmosphere, defined as the ratio of the dissipation of kinetic energy and the incoming solar radiation [Peixoto and Oort, 1992], has increased during the modern satellite era. The time series of the energy terms Fig. 1) and conversion rates Fig. 3) shows obvious inter-annual variability besides trends. The power spectra of these time series show some 10

11 l Nino/Southern Oscillation NSO) and Quasi-Biennial Cycle QBC) signals in the time series Figs. A7 and A8 in the auxiliary material), which suggests that the interannual variability of the global atmospheric energy cycle is related with other climate variables. The 27-year mean global atmospheric energy cycle during the modern satellite era is depicted in Fig. 4 based on the monthly evaluations of the NCP-2. The monthly evaluation has larger mean energies and smaller eddy energies than the results based on the yearly evaluation Fig. A6 in the auxiliary material) because fluctuations in the monthly means are treated as eddies in the yearly evaluation. The yearly evaluation based on the NCP-2 Fig. A6 in the auxiliary material) shows the mean energies P and K have values of 37.1 m J / and 6.5 m J / respectively, which are larger than the results from 10-year rawinsonde dataset S 4 with values of J / and 33.3 m J / respectively. The differences between the two estimates based on 4.5 m different datasets are probably because the new NCP-2 dataset extends to polar regions including the coldest 10 latitudes ) and higher altitudes including the region of strong jets in the middle stratosphere, which do not exist in the previous rawinsonde observations. The energetics based on the monthly and yearly evaluation of the NCP-2 supports the classical process of globally atmospheric energy cycle suggested by Lorenz [1995] and Oort [1983]: P P K K. All important calculations from the monthly evaluation are repeated for the yearly evaluation of the NCP-2 data set Figs. A3, A4, A5, and A6 in the auxiliary material). 11

12 In general, the experiment based on the yearly evaluation confirms almost all results from the monthly evaluation in this paper. 4. Conclusions On a whole, the global atmospheric energies remain constant during the modern satellite era even though a linear trend is discovered in the eddy kinetic energy. At the same time, the conversion rates between the different energies display great changes during the modern satellite era, which suggests that the great changes exist in the generation and dissipation terms too. These changes in the generation and dissipation terms suggested by the conversion terms offer important hints to the distribution and variability on the global and local heating cooling), and friction and turbulence associated with mean and eddy circulations, which can not be measured easily. The fact that the observed changes in the atmospheric energies are much smaller than the integral of the excess of conversion rates over the modern satellite era suggests that the global atmospheric energy system remains close to dynamical balance. The positive trends in all conversion terms and the increasing dissipation further suggest that the global atmosphere is in a more efficient state even though it remains close to dynamical balance. These new results of the global atmospheric energy cycle will help to understand the climate changes in a broader perspective. 12

13 References 1. Harnik, N. and Chang,. K ), Storm track variations as seen in radiosonde observations and reanalysis data. Journal of Climate 16, Hu, Q., Tawaye, Y., and Feng, S. 2004), Variations of the northern hemisphere atmospheric energetics: Journal of Climate 17, Kalnay,. et al. 1996), The NCP/NCAR 40-year reanalysis project. Bulletin of the American eteorological Society 77, Kanamitsu,. et al. 2002), NCP-DO AIP-II reanalysis R-2). Bulletin of the American eteorological Society 83, Karoly, D. J. 2003), Ozone and climate change. Science 302, Kistler, R. et al. 2001), The NCP-NCAR 50-year reanalysis: onthly means CD-RO and documentation. Bulletin of the American eteorological Society 82, Krueger, A.F., Winston, J. S. and Haines, D. A. 1965), Computation of atmospheric energy and its transformation for the northern hemisphere for a recent five-year period. onthly Weather Review 93, Lorenz,. N. 1955), Available potential energy and the maintenance of the general circulation. Tellus 7, itas, C.. and Clement, A. 2005), Has the Hadley cell been strengthening in recent decades? Geophysical Research Letters 32, / 2004GL Oort, A. H. 1983), Global atmospheric circulation statistics, NOAA Professional Paper No 14, U. S. Government Printing Office, Washington, D. C

14 11. Oort, A. H. and Peixoto, J. P. 1974), The annual cycle of the energetics of the atmosphere on a planetary scale. Journal of Geophysical Research 79, Oort, A. H. and Peixoto, J. P. 1976), On the variability of the atmospheric energy cycle within a 5-year period. Journal of Geophysical Research 81, Oort, A. H. and Peixoto, P. 1983), Theory of climate. p edited by Saltzman, B., Academic press. 14. Peixoto, J. P., Oort, A. H. 1974), The annual distribution of atmospheric energy on a planetary scale. Journal of Geophysical Research 79, Peixoto, P. and Oort, A. H. 1993), Physics of climate. American Institute of Physics. pp American institute of physics. 16. Simmonds, I. 2003), odes of atmospheric variability over the Southern Ocean. Journal of Geophysical Research 108, / 2000JC Trenberth, K ), Storm tracks in the southern hemisphere. Journal of the Atmospheric Sciences 48, Turner, J. et al. 2006), Significant warming of the Antarctic winter troposphere. Science 311, Wiin-Nielsen, A. 1967), On the annual variation and spectral distribution of atmospheric energy. Tellus 19,

15 Figure captions Figure 1 Time series of the global mean atmospheric energies based on the monthly evaluation of the NCP-2 data set. Global mean energies are calculated by weighting the zonal-mean energies in the meridional direction by cosine of latitude and in the vertical direction by the different intervals of pressurek. A multiplication factor [Sltzman, 1983], which takes into account the mean mass distribution over the globe i.e., less mass over the mountains), is used. In addition, a 12-point moving average is used for the removal of the seasonal cycle. A) The mean available potential energy P. B) The mean kinetic energy K. C) The eddy available potential energy P. D) The eddy kinetic energy. ) The sum of P, K, P and K. The eddies with sizes and lifetimes smaller than the spatial and temporal resolutions of the daily NCP-2 ~ 250 km and 1 day) respectively are treated in the same category as molecular motions by following the idea from Lorenz 12, which is not included in the computation of eddy energies. Figure 2 Global distribution of the eddy kinetic energy and its trend. The eddy kinetic energy is integrated in the vertical direction for each grid-point in the global map 73 x 144). A linear trend is calculated for the monthly time series of the column eddy kinetic energy for each grid-point. A) The zonal-mean eddy kinetic energy. B) The global distribution of the column eddy kinetic energy. C) The zonal-mean linear trend of the column eddy kinetic energy. D) The global distribution of the linear trend of the column eddy kinetic energy. ) Areas in which linear trends having confidence levels larger than 95%. The confidence level of the linear trend at each grid-point of panel D) is 15

16 calculated by the student t-statistics Box et al., 2005). Green in panel ) denotes the areas that have linear trends with confidence levels larger than 95%. Figure 3 Time series of the global mean conversion rates based on the monthly evaluation of the NCP-2. Same weighting, multiplication factor, and 12-point moving average in Fig. 1 are used. A) The conversion rate between the mean available potential energy and the eddy available potential energy C P, P ). B) The conversion rate between the mean kinetic energy and mean potential energy C K, P ). Notice: the conversion term C K, P ) = C P, K ). ost of previous researchers used C P, K ). Here, we use C K, P ) based on the fact that energy is actually transferred from mean kinetic energy K to mean potential energy P. C) The conversion rate between the eddy available potential energy and the eddy kinetic energy C P, K ). D) The conversion rate between the eddy kinetic energy and the mean kinetic energy C K, K ). Figure 4 The 27-year mean global energy cycle based on the monthly evaluation of the NCP-2. The generation and dissipation terms G P ), G P ), D K ), and D K ) are evaluated by balancing the corresponding conversion terms, which are put in parentheses. The 27-year mean C K, P ) is positive, which indicates that energy is transferred from the mean kinetic energy K to the mean potential energy P. 16

17 Figures 1 17

18 Figure 2 18

19 Figure 3 19

20 Figure 4 20

21 Auxiliary aterial for Variations in the echanical nergy Cycle of the Atmosphere Liming Li * Andrew P. Ingersoll Xun Jiang Yuk L. Yung * To whom all correspondence should be addressed. -mail: liming@gps.caltech.edu Calculation of confidence levels on linear trends The confidence levels on the linear trends of the time series of the energies and conversion rates are estimated by the t-statistics. For the linear trend b calculated from the least-squares fitting, the t-statistics is defined by t = b / S b) [Box, Hunter, and Hunter, 2005]. S b) is the standard error of the linear trend b, which is estimated by 2 S b) = σ / N1 ) 1/ N 2 ) xi [Bevington, 1969], where σ is the standard deviation of the data, N 1 is the number of freedom of the data, N 2 is the length of the data, and x i i is the time series corresponding to a number of measurements with x = 0. The number of freedom N 1 is estimated by a formula suggested by Bretherton et al. [1999]: N 2 2 [ 1 r Δx) ] [ 1+ r Δx ] =, where r Δx) is the autocorrelation corresponding to a 1 N 2 ) lag of the time interval Δ x. The linear trend is statistically significant when t is larger than certain value t 0, which can be found from the t-distribution table [Box, Hunter, and Hunter, 2005]. nergies in the two hemispheres and different seasons Figure A1 shows that eddy kinetic energy K does not have a significant trend in the NH, but it displays a clear positive trend in the SH. The eddy kinetic energy K in all 21

22 seasons of the SH shows positive trend panel, F, G, and H of Fig. A2). The seasonal changes of the eddy kinetic energy K in the NH are a little complicated. In summer June, July, and August) and autumn September, October, and November) of the NH, the eddy kinetic energy has a positive trend. In spring arch, April, and ay) of the NH, the eddy kinetic energy has a negative trend. The eddy kinetic energy does not have a significant trend in winter December, January, and February) of the NH, which has largest eddy kinetic energy K. xperiment of the global atmospheric energy cycle based on the yearly evaluation of the NCP-2 As a second experiment, we check global atmospheric energy cycle based on the yearly 2 evaluation of the NCP-2. Figure A3 displays a positive trend 889J / m / year ) with a confidence level ~ 99% in the global eddy kinetic energy K, which is a little smaller 2 than the positive trend based on the monthly evaluation 1046J / m / year ). All other global energies do not have a significant trend. Figure A4 shows the global distributions of the eddy kinetic energy and its trend based on the yearly evaluation, that are almost same with the corresponding results based on the monthly evaluation. Figure A5 shows that the four conversion terms based on the yearly evaluation, that have the same trends with the corresponding results based on the monthly evaluation. Small differences are displayed in the values of trends and confidence levels with the yearly evaluation as following: 22

23 C K, P ) having a positive trend W / m 2 / year C P, P ) having a positive trend W / m 2 / year C P, K ) having a positive trend W / m 2 / year C P, K ) having a positive trend W / m 2 / year with a confidence level ~ 99%, with a confidence level ~ 97%, with a confidence level ~ 99%, with a confidence level ~ 98%. Figure A6 shows the 27-year mean global energy cycle based on the yearly evaluation of the dataset NCP-2. On a whole, the 27-year mean global atmospheric energy cycle based on the yearly evaluation of the NCP-2 agrees with the one based on the 10-year rawinsonde observations [Oort, 1983]. Power spectra of the time series in the Fig. 1 and Fig. 3 The l Nino/Southern Oscillation NSO) and Quasi-Biennial Cycle QBC) signals are revealed in the time series of the global energies and conversion rates. Notice, the NSO has broad time spectrum 2-7 year) so that the peaks around the average time period of NSO 4.7 years) can be regarded as the signals of NSO. At the same time, some lowfrequency signals ~ 10 years) are revealed in the power spectra of the time series. A1. Box, G.. P., Hunter, J. S., and Hunter, W. G. 2005), Statistical for experiments. 2 nd edition. pp , John Wiley & Sons, Inc. A2. Bevington, P. R. 1969), Data reduction and error analysis for the physical sciences. P. 117, cgraw-hill BOOK, Inc. 23

24 A3. Bretherton, C. S. et al. 199), The effective number of spatial degrees of a time varying field. Journal of Climate 12, A4. Oort, A. H. 1983), Global atmospheric circulation statistics, NOAA Professional Paper No 14, U. S. Government Printing Office, Washington, D. C

25 Figure captions Figure A1 Time series of the monthly eddy kinetic energy K in the two hemispheres. Same weighting, multiplication factor, and 12-point moving average in Fig. 1 are used. Figure A2 Time series of the monthly eddy kinetic energy in the different seasons of the two hemispheres. The left column is for the NH with A) winter December, January, and February), B) spring arch, April, and ay), C) summer June, July, and August), and D) autumn September, October, and November) from top to bottom. The right column is for the SH with A) winter June, July, and August), B) spring September, October, and November), C) summer December, January, and February), and D) autumn arch, April, and ay). Figure A3 Same with Fig. 1 except for the yearly evaluation on the global energies. Figure A4 Same with Fig. 2 except for yearly evaluation on the global eddy kinetic energy. Figure A5 Same with Fig. 3 except for yearly evaluation on the global conversion rates. Figure A6 Same with Fig. 4 except for yearly evaluation on the global atmospheric energy cycle. 25

26 Figure A7 Power spectra of the time series of different energies. A) mean available potential energy P. B) mean kinetic energy P. D) eddy kinetic energy K. C) eddy available potential energy K. ) Total potential and kinetic energy. The vertical dashed lines in C) donate NSO 48 months), QBC 28 months), QBC-AB 20 months), and annual cycle 12 months) from right to left. The red curves donate mean red noise spectrum, 90% confidence level, and 95% confidence level from bottom to top. Figure A8 Power spectra of the time series of conversion rates. A) conversion rate between the mean kinetic energy and mean available potential energy and C K, P ). B) conversion rate between the mean and eddy available potential energies C P, P ). C) conversion rate between the eddy available potential energy and kinetic energy C P, K ). D) conversion rate between the eddy and mean kinetic energies C K, K ). The vertical dashed lines and red curves are same with these in Fig A7.. 26

27 Figure A1 27

28 Figure A2 28

29 Figure A3 29

30 Figure A4 30

31 Figure A5 31

32 Figure A6 32

33 Figure A7 33

34 Figure A8 34