Estimating the zonal wavenumber dependence of the meridional energy transport

Transcription

1 MO91 egree Project in Atmospheric Sciences, Oceanography and Climate, 3hp Estimating the zonal wavenumber dependence of the meridional energy transport Mattias Burtu Supervisor: Rune Grand Graversen epartment of Meteorology Stockholm University May 31, 212

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3 Abstract The zonal wavenumber dependence of the meridional atmospheric energy transport is investigated in the present day climate as well as in a future scenario of a warmer climate. This is done from model simulations made with the global coupled climate model EC-Earth, version 2.3. The transport is apart from wavenumber also divided into dry static and latent energy as well as in stationary and transient components. The total poleward transport is in the warmer climate found to increase at midlatitudes and to suffer a minor decrease closer to the poles. A clear majority of this change, of which much is seen in the latent energy, is done by the first 5 waves of which wave 4 and 5 are the main contributors. This shifts the transport from an about equal distribution between wavenumbers 1-5 and wavenumbers 6 in the present day climate to a stronger transport among wavenumbers 1-5 in the future scenario. The transport done by wavenumbers 6 do not increase but is shifted poleward in the southern hemisphere (SH). This is most evident in waves 6 and 7. No clear change is seen among these waves in the northern hemisphere (NH). Generally the transport done by waves 6 decreases with higher wavenumbers and the contribution from wavenumbers >1 is relatively small. The stationary component is only of importance among the 3 first waves. The higher wavenumbers are to a clear majority of a transient nature. No clear difference in the response to a warmer climate is however seen between the stationary and transient components.

4 1 INTROUCTION 1 Introduction The sun-earth orbital geometry creates an uneven heating of the planet done by the incoming shortwave solar radiation. The tropics are heated more than the poles. The outgoing longwave radiation on the other hand is much more evenly distributed over the latitudes. These factors imply a poleward transport of heat done by the atmosphere and ocean. Other influences, as cloud effects and surface albedo are in this case of secondary importance. Thus, the atmospheric and oceanic currents have a moderating influence in the formation of Earth s climate (Fasullo and Trenberth (27); Trenberth and Stepaniak (23b); Peixóto and Oort (1992)). Apart from heat different forms of energy e.g. latent and potential energy is transported poleward. Oort and Rasmusson (197) divided the atmospheric part of the meridional energy transport into a mean meridional (e.g. the Hadley and Ferrel cells), a stationary eddy (waves formed by contrasts in surface elevation and heating contrasts between continents and oceans) and a transient eddy (e.g. weather systems) part. Usually when the atmospheric meridional energy transport is computed it is divided into these parts mentioned above. This study is in that sense no exception. However, here this will be taken one step further by investigating the contribution to the meridional atmospheric energy transport from individual wavenumbers. The dominant waves, regarding the energy transport, in e.g. the transient part can in this way be determined. And what waves stands for the largest contribution to the transport, longer (e.g. Rossby waves) or shorter waves? This is also interesting as it in the future is believed that a Arctic temperature amplification will decrease the meridional temperature gradient (e.g. Koenigk et al. (212)), which is believed to make the baroclinic instability weaker affecting the shorter waves. In this study an estimate of the change of the energy transport done by the leading transient waves, using new climate simulations made with EC-Earth, is made. The change of the energy transport by the longer Rossby waves is also studied. The meridional energy transport has been the subject of a large number of studies before. A good summary of the transport; its variations and fundamental energetics can be found in Peixóto and Oort (1992). More recent examples are Trenberth and Caron (21), Trenberth and Stepaniak (23a), Trenberth and Stepaniak (23b) and Fasullo and Trenberth (27) whom 1

5 1 INTROUCTION all studied the transport in different sets of reanalysis data. Both Trenberth and Caron (21) and Fasullo and Trenberth (27) found the poleward atmospheric energy transport to peak at approximately 5.PW at about 4 S and 4 N (1PW = 1 15 W). Trenberth and Stepaniak (23b) studied the relationship between transient and stationary eddies and the Hadley cell. The cooling done by transient eddies in the subtropics was here found to be a fundamental driver of the Hadley cell. Trenberth and Stepaniak (23a) looked at the total atmospheric transport in parts of latent and dry static energy as well as in transient and stationary components. The interannual variability of the total transport was here seen to be substantially less than that of its components. There are a few studies on the contribution of the individual wavenumbers to the energy transport. These studies are, however, older then the previously mentioned and are often confined to a smaller area or shorter time period. Blackmon and White (1982) who studied the zonal wavenumber characteristics of transient eddies in the extratropical northern hemisphere (NH) is one example. Another is van Loon (1979) who partly looked at the transport of sensible heat done by the 6 first stationary waves in winter. The main carriers were here identified as the three first waves. The climate change and the effect it has on the meridional energy transport have also been studied before, however to my knowledge, not looking at individual wavenumbers. Model experiments on this subject, as summarized by Hwang and Frierson (21), have shown an increased poleward meridional energy transport at midlatitudes and in some models a minor decrease closer to the poles. A warmer climate has also been seen to cause a poleward displacement of the storm tracks, which is an important part of the meridional energy transport. This displacement has been seen to be accompanied by a poleward shift of the midlatitudes baroclinic regions (Yin, 25). Bengtsson et al. (26) could by modeling a climate with doubled CO 2, looking at wavenumbers >5, also see a poleward shift of the storm track. This was especially evident in the southern hemisphere (SH). A theory of the meridional energy transport and its components as well as the transport described with Fourier series is given in section 2. Section 3 presents the model, scenarios and methods that are used. The results are presented in section 4 and section 5 contains a discussion of the results. Finally the conclusions are presented in section 6. 2

6 2 THEORY 2 Theory 2.1 Meridional energy transport The total energy of the atmosphere is commonly divided into internal, potential, kinetic and latent energy. In clear majority are the internal and potential energy which, according to Peixóto and Oort (1992), stands for 7.4% and 27.1%, respectively, of the total. Almost all of the remaining 2.5% is latent energy of which much is associated with rain. The kinetic energy is thus a very small part of the total energy. However, if also the available energy for conversion into kinetic is considered the kinetic energy becomes a larger part of the total. These forms of energy; internal, potential, latent and kinetic energy are in the same order per unit mass of air written as IE = c v T P E = gz LE = Lq KE = 1 2 (u2 + v 2 ), (1) where c v is the specific heat capacity at constant volume, T is temperature, g is gravity, z is height, q is specific humidity, L is the latent heat of condensation or sublimation and u and v are the zonal and meridional velocities, respectivly. The total energy (TE) is simply the sum of the fundamental forms of energies presented in equation 1. T E = c v T + gz + Lq (u2 + v 2 ) (2) In terms of transport the dry static energy (SE) is often used. The SE is defined as c p T +gz, where c p is the specific heat capacity at constant pressure and c p T is known as sensible heat. Further, the moist static energy is often used, defined as SE + LE (Peixóto and Oort (1992); Hartmann (1994); Trenberth and Stepaniak (23a)). As mentioned above the sun-earth orbital geometry creates uneven heating of the Earth. This difference is evened out by a poleward transport of energy. To 3

7 2.1 Meridional energy transport 2 THEORY better see what processes are carrying out the transport at certain latitudes the atmospheric part is often, as e.g. done by Oort and Rasmusson (197), divided into a mean meridional, a stationary eddy and a transient eddy part Mean meridional circulation One implication of the uneven heating is the meridional cell closest to the equator, called the Hadley cell. This cell has an upward branch of warm air in the heated tropics and a downward branch in the subtropics of the winter hemisphere. Of this follows a poleward transport in the upper part of the cell and equatorward transport in the lower part. The upper transports potential energy and the lower internal and latent energy. However, the magnitude of the upper part exceeds the lower part. Hence, the net energy transport of the Hadley cell is poleward and of potential energy (Hartmann, 1994). In the subtropics, poleward of the Hadley cell, we find the Ferrel cell. This cell circulates in the opposite direction of Hadley cell, with rising motions in cold air and sinking in warm air. This results in a transport of energy from a cold area to a warm area, i.e. it is thermodynamically indirect (Hartmann, 1994). This part of the mean meridional circulation (MMC) is driven by the transient eddy transports of heat and momentum (Trenberth and Stepaniak, 23b). At high latitudes, poleward of the Ferrel cell, we find the Polar cell. This cell is thermodynamically direct but is far from as strong, regarding the energy transport, as the Hadley cell (Peixóto and Oort, 1992). The mean meridional cells are visible in zonal averages. The zonally averaged meridional energy transport done by these cells are therefore simply written as [v][e], where [...] denotes the zonal average and denotes the temporal average. The Ferrel cell is net equatorward and the Polar cell at higher latitudes is relatively weak. Hence, the poleward energy transport done by the MMC is only of primary importance in the tropics where we have the Hadley cell (Hartmann (1994); Peixóto and Oort (1992)) Stationary eddies The westerly flow exhibits variations around latitude circles associated with contrasts between land and ocean. These variations appear clearly in time averages and can along with contrasts in surface elevation, i.e. mountain 4

8 2.1 Meridional energy transport 2 THEORY ranges such as the Rocky Mountains create stationary waves. The stationary planetary waves are plainly visible in monthly mean tropospheric pressure patterns (Hartmann (1994); Peixóto and Oort (1992)). The structure of mountain ranges only change on a geological timescale. Hence, the seasonal change of stationary eddies is largely governed by the change in thermal contrast between the cold interiors of continents and e.g. the Gulf stream currents or the waters of Kuroshio (analogue to the Gulf stream situated in the north-western Pacific ocean) (Hartmann (1994); Trenberth and Stepaniak (23a)). As mentioned these waves can be seen as variations around a latitude circle that are stationary on a monthly time scale, and thus clearly visible in monthly means. However, they disappear in zonal means. Thus, when calculating the meridional transport, e.g. of energy, done by these waves it is the deviations from the zonal averages of v and E that are used. The zonally averaged energy transport is commonly written as [v E ], where denotes the deviation from the zonal average (i.e. v = v [v]) (Peixóto and Oort (1992); Hartmann (1994)) Transient eddies Transient eddies are, in contrast to stationary eddies, the part of the eddy field that varies with time. A large part of the transient eddies are synopticscale baroclinic waves at midlatitudes. These regions with migratory cyclones and anticyclones are generally called storm tracks and are associated with much of the precipitation and severe weather at these latitudes (Hartmann (1994); Yin (25)). Through baroclinic instability these waves can grow rapidly, creating a phase shift between the pressure and temperature fields of the wave. This produces an efficient poleward transport of momentum, heat and moisture, which in terms of weather systems are carried out by warm and cold fronts seen on daily weather maps. The strength of the meridional temperature gradient determines the intensity of these waves, which also can change the strength of the poleward transports (Holton (24); van Loon (1979); Hartmann (1994)). With respect to wavenumbers the storm track at midlatitudes have been defined to constitute of waves with a zonal wavenumber 6 (Bengtsson et al. (26); Blackmon and White (1982)). Blackmon and White (1982) identified, through observation and modeling studies of the extratropical NH, the 5

9 2.1 Meridional energy transport 2 THEORY strongest baroclinic waves to be of wavenumbers 6-8. Transient eddies are, hence the name, not as stationary eddies, visible in monthly temporal means. They do also show large variations in wind and temperature, which do not appear in a zonal average. Thus, when calculating the meridional transport, e.g. of energy, done by these waves it is the deviations from the monthly temporal averages of v and E that are used. The zonal mean transport is then commonly written as [v E ], where denotes the deviation from the temporal average (i.e. v = v v) (Peixóto and Oort (1992); Hartmann (1994)) Observed seasonal variation Summing up these parts mentioned above, the total atmospheric meridional energy transport can be written as [ve] = [v][e] + [v E ] + [v E ]. The seasonal variation of the total transport is of course dependent on the seasonal variation of its parts, e.g. the Hadley cell and low pressure systems. Observations have shown that the total transport is continuous with latitude. Yet the mentioned mechanisms carrying out the transport vary greatly much due to the latitudinal variation in the horizontal temperature gradients, which governs a large part of the transport. The seasonality in the horizontal temperature gradients therefore also largely determines the seasonality in atmospheric energy transports (Hartmann (1994); Trenberth and Stepaniak (23a)). The largest seasonal variation of the meridional temperature gradient is found in the NH, with maximum in NH winter. Hence, the poleward energy transport done by transient eddies in the NH is, as e.g. observed by Peixóto and Oort (1992), largest in NH winter. The transient eddies in the SH are more even in strength throughout all seasons. The horizontal temperature gradients between warm waters, of e.g. the Gulf Stream, and the interiors of continents are also strongest in NH winter. These conditions are, as mentioned above, favorable for stationary eddies which therefore peaks in poleward energy transport in this hemisphere and during this time of year. As a result of this and the fact that there are fewer large mountain ranges in the SH, the stationary eddies in the SH are also much weaker. Thus, the stationary eddies are primarily a factor in NH winter (Trenberth and Stepaniak (23a); Peixóto and Oort (1992)). 6

10 2.2 Meridional energy transport with Fourier series 2 THEORY The seasonal variation in the contribution to the poleward energy transport done by the MMC is clearest in Hadley cell, which zonally averaged has a clear poleward maxima in the winter hemisphere (Peixóto and Oort, 1992). These variations reflects in the variation of the total atmospheric transport. Trenberth and Caron (21) noted, studying NCEP-NCAR reanalysis data, that maximum transport occur in winter in both hemispheres, exceeding 8PW in the NH. The peak and annual cycle was smaller in the SH. The peak of the annually averaged total atmospheric poleward energy transport was estimated by Fasullo and Trenberth (27) to 5.1PW at 41 N and 4.9PW at 39 S. 2.2 Meridional energy transport with Fourier series Any reasonably well-behaved function of longitude, e.g. the atmospheric meridional energy transport, can be represented in terms of a zonal mean plus a Fourier series of sinusoidal components (Holton, 24). To compute the zonally averaged meridional energy transport as a function of wavenumber we first need the meridional velocity v and the the energy E. These components can be written with Fourier series as N E(x) ae 2 + [a E k cos( 2kπx ) + be k sin( 2kπx )] (3) k=1 N v(x) av 2 + [a v k cos( 2kπx ) + bv k sin( 2kπx )], (4) k=1 where x is the zonal coordinate, k is the zonal wavenumber, is the distance around a latitude circle and a E, a E k, be k, av, a v k and bv k are Fourier coefficients. How accurate these Fourier series are, is of course dependent on how many waves that are included. Equation 3 multiplied with equation 4 integrated zonally around the Earth and divided with the distance around respective latitude circle yields the zonally averaged meridional energy transport, [ve]. This product gives several terms with different products of sine and cosine. However, as result of the orthogonal relationship between cosine and sine functions, seen in Appendix A, only the quadratic terms (cos 2 and sin 2 ) will survive the zonal 7

11 3 ATA AN METHOS average, yielding [ve] = ae a v 4 + N k=1 [ ae k av k cos 2 ( 2kπx )dx + be k bv k sin 2 ( 2kπx )dx]. (5) The integrals in equation 5 both gives /2, which yields the following meridional energy transport where [ve] = ae a v 4 a E k = 2 a v k = 2 b E k = 2 b v k = 2 + a = 2 a = 2 N k=1 [ ae k av k 2 E(x) cos( 2kπx )dx v(x) cos( 2kπx )dx E(x) sin( 2kπx )dx v(x) sin( 2kπx )dx E(x)dx + be k bv k ], (6) 2 v(x)dx. (7) As follows from equation 7, the first term in equation 6 is simply [v][e], i.e. the MMC. The two terms in the sum are the contribution to the transport from the waves, in this case both from the transient and stationary parts. E.g. if a geopotential field is described with Fourier series the largest amplitude Fourier components will be those for which k is closest to the number of ridges or troughs around a latitude circle (Holton, 24). 3 ata and methods 3.1 Model description The data in this study is taken from model runs made with the global coupled climate model EC-Earth, version

12 3.2 Scenarios and computations 3 ATA AN METHOS The atmosphere component of the model is the Integrated Forecasting System (IFS) based on cycle31r1, of the European Center of Medium ranged Weather Forecasts (ECMWF). A T159 resolution and 62 vertical hybrid levels are used (Hazeleger et al. (212); Koenigk et al. (212)). Hybrid levels combine constant pressure levels with sigma levels. At upper levels the hybrid levels are like constant pressure levels while closer to the surface the hybrid levels more resembles pure sigma levels which tend to follow the terrain. The ocean component is based on the Nucleus for European Modeling of the Ocean (NEMO), version 2 and includes the Louvain la Neuve sea-ice model, also version 2. It uses a C-grid, a resolution of about 1 degree and 42 vertical levels. The grid has three poles; two near the North Pole in Canada and in Siberia and one on the South Pole. As a result the horizontal resolution is increased close to the North Pole (Hazeleger et al. (212); Koenigk et al. (212)). The present and pre-industrial climate of EC-Earth version 2.2 is presented by Hazeleger et al. (212). 3.2 Scenarios and computations Two different model runs with EC-Earth is used in this study, one covering the present time and climate together with a simulation of a future with further increased emissions of greenhouse gases. These model runs were all readymade and provided by the Swedish Meteorological and Hydrological Institute (SMHI) and the Meteorological Institute at Stockholm University (MISU). The future scenario (SS81) and hindcast (SHC1) are presented in Table 1. Scenarios Pathway Forcing at 21 [W m 2 ] Period SHC SS81 Rising > Table 1: Scenarios, given with the time period used in this study. For the future scenario also the radiative forcing in the year 21 and the pathway to this forcing. As written in Table 1 scenario SS81 reaches a radiative forcing of >8.5 Wm 2 in the year 21. This is equivalent to a CO 2 concentration of >137ppm. The pathway to this forcing in this scenario is called rising. A rising pathway means that the CO 2 concentration is rising throughout the scenario and that 9

13 3.2 Scenarios and computations 3 ATA AN METHOS the system has not yet stabilized in the year 21. There are different ways to reach a certain forcing. These are called Representative Concentration Pathways or RCP. For more information on new climate change scenarios and different RCPs see Moss et al. (21). The energy in SHC1 and SS81 is calculated from model data with a 6 hour time interval (the time step in EC-Earth is 1 hour) at each model level. I.e. variability within 6 hours is not included. As most of the release of latent heat is associated with rain and only to a minor extent snow the condensation value of L (25 J kg 1 ) is, as also done by Peixóto and Oort (1992), used to compute the latent part of the total energy. In model hybrid coordinates levels the total zonally averaged meridional energy transport integrated over the whole depth of the atmosphere can be written as [ve] = 1 1 g 1 v[c p T + gz + Lq (u2 + v 2 )] dp dηdx, (8) dη where η is the hybrid coordinate. Here the total atmospheric energy transport is calculated with equation 8, where v is multiplied with dp at each model level. The contribution from the MMC together with the 1 first waves are calculated at each model level with equations 6 and 7 and integrated over the whole depth of the atmosphere as done for the total energy transport, multiplying v with dp at each model level. Also note that the total energy here, in terms of transport, is written with sensible heat c p T instead of internal energy. To get the contribution from the stationary waves the same procedure is done, but for monthly averages of v and E. The transient contribution is calculated as the residual between the part of the total energy transport done by waves and the stationary waves. This is done both for the total energy as well as for only the latent energy. A dry static component is also computed by taking the residual between the total and latent energies. As can be seen above this way to compute the SE also includes the kinetic energy. However, as also mentioned above, the kinetic energy is a very small part of the total energy. Climatologies for the meridional energy transport are made for each scenario over the respective time period given in Table 1. These climatologies are 1

14 4 RESULTS then compared in order to study the changes in the energy transport over the 21 st century. Note that SS81 is the most extreme future scenario out of three made by SMHI and MISU. However, the differences between these three runs, regarding the meridional energy transport, have been shown to be of magnitude and not in structure (Koenigk et al., 212). The most extreme scenario is used in this study in order to investigate the structural changes in the energy transport. A so called Student s t-test is used to determine whether the changes in the meridional energy transport over the 21 st century are significant or not. 4 Results 4.1 Meridional energy transport The meridional energy transport can, as mentioned above, be split in many different ways. Here we first divide the total atmospheric energy transport into transport of latent and dry static energy. This, which is shown in Figure 1a, is both done for the total and for the MMC added to the 1 first waves. The meridional transport of total atmospheric energy is also divided into the MMC, waves 1-5 and, following the definition of the storm track at midlatitudes by Blackmon and White (1982) and Bengtsson et al. (26), waves 6. This is shown in Figure 1b. Both Figure 1a and 1b show the annual mean for the period (Here, and in all other figures, northward transport is defined positive.) The total transport (solid blue lines in Figure 1) reaches its maximum at midlatitudes; 5PW at about 4 S and 4.75PW at about 42 N. The equatorward transport of LE and poleward transport of SE (Figure 1a) done by the Hadley cell is also clearly visible. The poleward transport of SE is larger than that of LE at all latitudes. The differences between the solid and dashed lines of the same color in Figure 1a can be seen as the transport done by wavenumbers >1. As seen in the same Figure, this difference is relatively small and only visible in midlatitudes. Hence, a clear majority of the meridional energy transport is done by the MMC together with the 1 first waves. About equal peak values in transport is seen in Figure 1b between the groups of wavenumbers 1-5 and 6. Waves 6 are of main importance at midlat- 11

15 4.1 Meridional energy transport RESULTS (a) Transport divided into TE, LE and SE. (b) Transport divided into MMC, waves 1-5 and waves 6. Figure 1: Meridional atmospheric total energy transport annual mean divided in to latent and dry static components (1a) and into MMC, wavenumbers 1-5 and 6 (1b). The solid blue line is the same (the total atmospheric meridional energy transport) in both subfigures. itudes and waves 1-5 are important poleward of the higher wavenumbers in both hemispheres. Waves 1-5 also contribute to the transport at midlatitudes, however, not as much as the higher wavenumbers. The poleward transport of the MMC, also shown in Figure 1b, is only of primary importance in the tropics where we find the Hadley cell. The Ferrel cell is equatorward and a poleward transport from the Polar cell is only barely seen in the SH. The groups of wavenumbers 1-5 and 6 are further divided into transport of latent energy in Figure 2. The dry static component is calculated as a residual and is here simply taken as the difference between the solid and dashed lines of the same color. The latent transport is, as seen in Figure 2, strongest among wavenumbers 6 where this group has its maximum around 4 N and 4 S. Further poleward this transport decreases and shifts to the lower wavenumbers 1-5. If the latent transport is compared with the total it is seen that a clear majority of the poleward transport done by waves are of SE. 12

16 4.1 Meridional energy transport RESULTS Figure 2: Meridional atmospheric transport of total and latent energy done by waves 1-5 and waves 6, annually averaged The solid lines are the same as the lines of the same color in Figure 1b Wavenumbers 1-5 The above used group of wavenumbers 1-5 is further divided into individual wavenumbers, annually averaged , in Figure 3. The smooth almost sinusoidal variation in the transport seen e.g. in Figure 2 is here no longer as evident. A clear shift towards lower wavenumbers closer to the poles, as also seen in Figure 2, is however visible. This is especially evident in the NH. Figure 3: Annual mean of the meridional atmospheric energy transport done by waves 1, 2, 3, 4 and 5. In the SH, as seen in Figure 3, the transport done by waves 4 and 5 are of main importance at midlatitudes. Waves 1, 2 and 3 on the other hand are active further poleward, closer to the Antarctic continent. 13

17 4.1 Meridional energy transport RESULTS In the NH the most prominent wave is wave 2, with two clear peaks at 3 N and 6 N. A breakdown of this wave into the seasons of maximum transport which is, following the strength of the horizontal temperature gradients, winter and summer together with the stationary and transient components is presented in Figure 4. (Here (NH) winter and summer follows the standard definitions; ecember, January, February (JF) and June, July, August (JJA), respectively) (a) NH winter average (JF). (b) SH winter average (JJA). Figure 4: Seasonal means of the meridional atmospheric energy transport done by wave 2 in SH and NH winter, divided into transient and stationary components. As can be seen in Figure 4 the main component of wave 2 is stationary. Most prominent is the large stationary peak of about 1.1PW around 6 N in NH winter. The transport in the summer hemisphere is much weaker as a result of the weakened temperature gradients between the oceans and the interior of continents during this time of year (see section 2.1.4). The clear stationary peak in NH summer around 3 N do not follow this seasonal variation and have probably been created by mountain ranges in this area. The contribution from wave 2 to the energy transport in the SH is much less and more of a transient nature than in the NH. The transient feature in the SH reaches its maximum in SH winter (JJA) as a result of the stronger temperature gradients during this season. Waves 3 and 4 leaves, as seen in Figure 3, a larger contribution to the meridional energy transport in the SH compared with wave 2. A breakdown of these waves into seasonal averages for winter and summer together with the stationary and transient components are presented in Figures 5 and 6. 14

18 4.1 Meridional energy transport RESULTS (a) NH winter average (JF). (b) SH winter average (JJA). Figure 5: Seasonal means of the meridional atmospheric energy transport done by wave 3 in SH and NH winter, divided into transient and stationary components. If Figure 4a is compared with Figure 5a it becomes clear that the stationary component is smaller in wave 3 than in wave 2. The contribution to the energy transport done by wave 3 in NH winter is of about equal of transient and stationary nature, though the total is less compared with wave 2. In SH winter on the other hand the contribution from wave 3 in the SH is larger but with a peak a bit equatorward of the corresponding in wave 2. The general structure of the transport follows the typical seasonal variation with maximum in winter. In wave 4 the stationary component is further decreased (Figure 6). The transient on the other hand is increased, especially in SH winter of the SH where the total transport is about twice the size compared with wave 2. Another interesting part is about the only stationary feature, which is found in NH winter at 25 S. A stationary component of the meridional energy transport in the SH and as well in SH summer is not common and do not follow the general variation and appearance of stationary waves (see sections and 2.1.4). This peak have probably been generated by mountains at this latitude. A division into stationary and transient components of waves 1 and 5 are not shown here as wave 1 is practically all stationary in both hemispheres and wave 5 is almost all transient. The seasonal variation in transport done by these waves follows the same pattern as waves 2, 3 and 4 shown above with maximum transport in winter. 15

19 4.1 Meridional energy transport RESULTS (a) NH winter average (JF). (b) SH winter average (JJA). Figure 6: Seasonal means of the meridional atmospheric energy transport done by wave 4 in SH and NH winter, divided into transient and stationary components Wavenumbers 6-1 As can be seen in Figure 1a, which is also mentioned above, the contribution to the total transport from waves >1 is relatively small. Thus, the main contribution to the meridional energy transport from the midlatitude storm track and meso-scale waves such as shorter baroclinic waves comes from wavenumbers 6-1. This group of waves is divided into individual wavenumbers, annually averaged , in Figure 7. Figure 7: Annual mean of the meridional atmospheric energy transport done by waves 6, 7, 8, 9 and 1. One interesting feature in Figure 7, which is not at all seen among wavenumbers 1-5, is the clear decrease in transport with higher wavenumbers. How- 16

20 4.1 Meridional energy transport RESULTS ever, the shift towards lower wavenumbers closer to the poles is here, as for waves 1-5, still evident. As also can be seen in the same Figure the transport done by wave 6 and 7 is larger in the SH than in the NH. The transport done by waves 8, 9 and 1 is about equal in both hemispheres. Two of the most prominent waves regarding the meridional energy transport in midlatitudes are, as seen in Figure 7, waves 6 and 7. A breakdown of these waves into seasonal averages for winter and summer together with the stationary and transient components are presented in Figure 8. (a) Wave 6 - NH winter average (JF). (b) Wave 6 - SH winter average (JJA). (c) Wave 7 - NH winter average (JF). (d) Wave 7 - SH winter average (JJA). Figure 8: Seasonal means of the meridional atmospheric energy transport done by waves 6 and 7 in SH and NH winter, divided into transient and stationary components. Waves 6 and 7 follow the trend of a decreasing stationary component with higher wavenumbers (Figure 8). Almost all of the transport is here of tran- 17

21 4.2 Changes in meridional energy transport... 4 RESULTS sient nature, except a minor stationary contribution from wave 6 at 3 N in NH winter and from wave 7 at 35 N in SH winter. The seasonal variation is clear in the NH with maximum transport in winter. The seasonal variation in the SH is much weaker. This agrees with the observed seasonal variation of transient eddies which follows the variations in the meridional temperature gradient (see section 2.1.4). The transport done by wave 6 is larger than the transport done by wave 7 in both hemispheres and seasons, following the trend with decreasing transport by higher wavenumbers in the annual averages seen in Figure Changes in meridional energy transport over the 21 st century To show the change in the meridional energy transport over the 21 st century the difference (SS81-SHC1) between the future scenario and hindcast is computed. I.e. a positive change in the NH and negative change in the SH means an increased poleward transport. The change of the transport split into components as in Figures 1a and 1b is shown in Figures 9a and 9b. Here, the solid blue line (the same in both Figure 9a and 9b) shows an increased total transport at midlatitudes in both hemispheres and a minor decreased transport poleward of about 6 N and 6 S. The poleward meridional energy transport of LE increases at nearly all latitudes poleward of the tropics. As the transport of latent energy in the tropics done by the Hadley cell is equatorward the transport actually increases here as well. The maximum change in latent energy transport is also found here, around 1 S. The poleward transport of SE decreases poleward of the tropics and increases around the equator. I.e. it increases where the transport of LE decreases and vice versa. The difference between the solid and dashed lines in Figure 9a is small. Thus, the change in the transport done by wavenumbers >1 also is relatively small. Among the waves in Figure 9b it is the group of longer waves, wavenumbers 1-5, which stands out. In the NH this group of waves more or less stands for all of the change seen in the total meridional energy transport. The observed increase in the total poleward transport in the midlatitudes of the SH is also mainly due to the increase in the transport done by waves 1-5. However, here also changes in the shorter waves, wavenumbers 6, and in the MMC play a role. The transport done by the group of wavenumbers 6, at midlatitudes 18

22 4.2 Changes in meridional energy transport... 4 RESULTS (a) Change in transport divided into TE, LE and SE. (b) Change in transport divided into MMC, waves 1-5 and waves 6. Figure 9: Change in the meridional atmospheric total energy transport annual mean (SS81-SHC1) divided into latent and dry static components for the total transport as well as the MMC together with the 1 first waves (9a) and into MMC, wavenumbers 1-5 and 6 (9b). The solid blue line is the same (change of the total atmospheric meridional energy transport) in both subfigures. The change showed by this solid blue line is of a 95% significance from 75 S to 85 N except around 6 S, 12 S and 58 N, i.e. where there is no change. defining the storm track, is decreased with a peak of near.3pw around 3 S and increased with peak of approximately.13pw around 5 S. Thus, the main area of transport done by this group of waves is shifted poleward in the SH. The poleward transport done by the Hadley, and Ferrel cells decreases in the SH (i.e. equatorward transport done by the Ferrel cell increases). The change over the 21 st century of the meridional energy transport done by all waves is also shown and magnified in Figure 1. As in the corresponding Figure 2 the total transport done by the waves is here also divided into LE. Not surprisingly the largest increase in transport of LE is found among waves 1-5, since it is in this group of waves where the transport of total energy increases the most. However, in the Polar regions, where the total poleward transport by these waves decreases, the transport of LE increases into the Arctic and Antarctic. Thus the transport of the dry static component must decrease in these areas. The poleward transport of the dry static component (difference between solid and dashed lines of same color) decreases at nearly all latitudes among waves 19

23 4.2 Changes in meridional energy transport... 4 RESULTS Figure 1: Change in the meridional atmospheric total energy transport annual mean (SS81-SHC1) as divided in Figure 2. The solid lines are the same as the lines of the same color in Figure 9b. The significance of the change seen in the solid red line (waves 1-5) is 95% from 6 S to 9 N except around 6 S, and 6 N. The significance of the change seen in the solid green line (waves 6) is 95% at 82 S, between 6 S-5 S, 42 S-2 S, 14 S-, 2 N-3 N and 6 N-8 N. 6 but increases among waves 1-5. In the NH a clear majority of the change among the waves 1-5 is of LE. In the SH it is more even between the dry static and latent components Wavenumbers 1-5 As can be seen in Figure 3 the extension and structure of the meridional energy transport done by waves 1, 2, 3, 4 and 5 differs from wave to wave. The change of the transport done by these waves over the 21 st century (Figure 11) is, especially in the NH, also very different from wave to wave. Though, a general change (as the solid red line in Figure 1) with increase in midlatitudes and decrease closer to the poles can be seen in most waves. In the SH a more evident increase at midlatitudes is seen. This increase of the poleward transport is relatively large, especially in waves 4 and 5. An increase is also seen in waves 2 and 3 but not in wave 1. The transport done by wave 1 instead decreases largely around 55 S. As the poleward transport does not decrease in any of the other here seen waves in the SH, the decrease poleward of 6 S seen in the total transport (Figure 9) thus solely comes from wave 1. However, note that this change is not as significant (about 75%) as at other latitudes. (This change of wave 1 is seen in the stationary component (not shown here) and most evident in SH winter (JJA).) 2

24 4.2 Changes in meridional energy transport... 4 RESULTS Figure 11: Change (SS81-SHC1) over the 21 st in the annual average of the meridional atmospheric energy transport done by waves 1, 2, 3, 4 and 5. Most of the change in transport by these waves are of 95% significance. Exceptions are wave 1 at 6 S and between 35 N-58 N and 6 N-8 N and wave 3 between 3 N-7 N. The response of the meridional energy transport to a warmer climate is, as for wavenumber 1, of course also different depending on season. A breakdown of wave 2 in seasons and stationary and transient components, as done in Figure 4, is computed for the difference SS81-SHC1 and shown in Figure 12. (a) Change in NH winter average (JF). (b) Change in SH winter average (JJA). Figure 12: Change (SS81-SHC1) in the seasonal means of the meridional atmospheric energy transport done by wave 2 in SH and NH winter, divided into transient and stationary components. The large stationary peak in the meridional energy transport done by wave 2 in NH winter (Figure 4) increases in the warmer climate of scenario SS81 21

25 4.2 Changes in meridional energy transport... 4 RESULTS (Figure 12a). The transient component, however, suffers a small decrease at the same latitudes. Poleward of these changes both the stationary and the transient components decreases, following the change in the total transport. The stationary peak in SH winter also increases. As the mountains do not change much over a 1 years this increase is most likely a result of an increased horizontal temperature gradient or an increased phase shift between the v and E fields. Wave 2 is not as prominent, regarding the meridional energy transport, in the SH as in the NH. This is also true for the change seen in Figure 12. A minor decrease of the transient component is however seen around 45 S in SH winter. The same breakdown of wave 3, into NH and SH winter and transient and stationary components (Figure 5) shows a smaller meridional energy transport in the NH winter compared with wave 2. The change over 21 st century however, seen in Figure 13, is somewhat larger in wave 3 than in wave 2. (a) Change in NH winter average (JF). (b) Change in SH winter average (JJA). Figure 13: Change (SS81-SHC1) in the seasonal means of the meridional atmospheric energy transport done by wave 3 in SH and NH winter, divided into transient and stationary components. The change of the meridional energy transport done by wave 3 in NH winter is to the largest extent seen in the stationary component. The transient component in the same season and hemisphere is, compared with wave 2, not decreasing but also increasing. Poleward of 6 N in NH winter the total transport done by wave 3 is as wave 2 decreasing. But here this decrease is only visible in the transient component. 22

26 4.2 Changes in meridional energy transport... 4 RESULTS The largest change in wave 3 is seen in SH winter around 5 S. Both the stationary and transient component contributes to this change. This is interesting as the present day climate (see Figure 5) did hardly show no contribution from the stationary component at all in this season and hemisphere. And this combined with the decrease in wave 1 at these latitudes implies a minor shift of the meridional energy transport done by the stationary wave around the Antarctic continent in SH winter from wavenumber 1 to wavenumber 3. As mentioned above the transient component stands for a larger part of the meridional energy transport in higher wavenumbers. Wave 4 show a transport for the present day climate which is mostly of a transient nature (see Figure 6) and less stationary compared with waves 2, 3. The change of the meridional energy transport done by wave 4 is shown in Figure 14, divided as above. (a) Change in NH winter average (JF). (b) Change in SH winter average (JJA). Figure 14: Change (SS81-SHC1) in the seasonal means of the meridional atmospheric energy transport done by wave 4 in SH and NH winter, divided into transient and stationary components. Wave 4 have one stationary peak in the present day climate at 25 S in NH winter. This peak does not change much in the scenario of a warmer climate. Instead it is the transient component that stands for much of the seen increase in poleward transport in the SH of the NH winter (Figure 14a). In the NH of the same season an increase of the total poleward transport is seen around 35 N and a decrease is seen around 6 N. While both the stationary and transient components contribute to the decrease it is near only the transient component that increases at 3 N-45 N. 23

27 4.2 Changes in meridional energy transport... 4 RESULTS In SH winter, seen in Figure 14b, an interesting feature is the increase of the poleward transport done by the stationary component at 2 S, i.e. roughly at the same latitude as the stationary peak seen in the present day climate of NH winter. Otherwise it is an increase of the transient component, poleward of the just mentioned stationary peak, which stands out. This could imply a strengthening of the horizontal temperature gradient at these latitudes in the SH winter. Further poleward of this change the poleward transport decreases, following the change seen in the meridional transport of total energy (see Figure 9). The change in the poleward transport done by wave 4 is actually larger in fall and spring (not shown) and not as for the other waves in winter and summer when the transport reaches its maximum. Why the response to a warmer climate by wave 4 differs in such a manner from the other waves is not clear. (This is also implied by the magnitude of the change in the annual average of wave 4 seen in Figure 11 which is larger than the change of the NH and SH winter averages seen in Figure 14.) Wavenumbers 6-1 The meridional energy transport done by waves 6, 7, 8, 9 and 1 is, as seen in Figure 7, important at midlatitudes. The change of the transport by these waves in a warmer climate is shown in Figure 15. Figure 15: Change (SS81-SHC1) over the 21 st in the annual average of the meridional atmospheric energy transport done by waves 6, 7, 8, 9 and 1. Most of the change in transport by these waves are of 95% significance with an exception in wave 7 between 45 S-35 S. As mentioned above the group of wavenumbers 6 is shifted poleward in the scenario of a warmer future (Figures 9b and 1). This change reflects 24

28 4.2 Changes in meridional energy transport... 4 RESULTS primarily in the two most prominent waves in this group, waves 6 and 7, seen in Figure 15. The poleward shift is in waves 6 and 7 visible in both hemispheres, though it is more evident in the SH. The poleward transport done by waves 8, 9 and 1 decreases in the SH and is more or less unchanged in the NH. No poleward shift is seen among these waves. The changes in the transport done by waves 6 and 7 in NH and SH winter are presented in Figure 16, divided into stationary and transient components. (a) Wave 6 - Change in NH winter average (JF). (b) Wave 6 - Change in SH winter average (JJA). (c) Wave 7 - Change in NH winter average (JF). (d) Wave 7 - Change in SH winter average (JJA). Figure 16: Change (SS81-SHC1) in the seasonal means of the meridional atmospheric energy transport done by waves 6 and 7 in SH and NH winter, divided into transient and stationary components. As can be seen in Figure 16 the poleward shift of the transport done by 25

29 5 ISCUSSION waves 6 and 7 are for both strongest in the SH of the NH winter. No clear change is seen for wave 6 in SH winter while a minor poleward shift can be seen for wave 7 in the SH of the same season. As mentioned, the here seen change is mainly of transient nature. However, there is decrease of the poleward transport done by the stationary component of wave 6 at 35 N in NH winter. This is the same stationary peak observed in Figure 8a. 5 iscussion All the data used in this study comes from the model EC-Earth. The general structure and peak values of the annual total, latent and dry static meridional atmospheric energy transport produced by this model and presented in Figure 1a are also comparable with estimates from the NCEP-NCAR reanalyses for the period done by Trenberth and Stepaniak (23a). Koenigk et al. (212), who used the same hindcast (SHC1) and time period, also showed that the energy transport is in fairly good agreement with ERA-Interim at most high northern latitudes. Thus, EC-Earth produces a meridional atmospheric energy transport which is comparable with what have been observed. The stationary component of the transport is clearly seen to decrease with higher wavenumbers. E.g. the transport done by wave 2 (Figure 4) is to a clear majority done by the stationary component, wave 3 (Figure 5) is about equal of transient and stationary nature and wave 4 (Figure 6) is almost all transient. This agrees with van Loon (1979) who identified waves 1, 2 and 3 of the six first stationary waves to be the main stationary contributors to the transport of sensible heat. Most of the stationary components follow the general seasonal variation for stationary waves with maximum transport in winter in the NH. However, minor exceptions can be found in waves 2, 4 and 7. Wave 2 and wave 7 have a stationary peak at about 3 N in SH winter (Figures 4b and 8d) and wave 4 have a stationary peak at about 25 S in NH winter (Figure 6a). All these features appear in respective hemisphere summer when the thermal contrast between ocean and interiors of continents are relatively weak. The stationary waves producing this transport have therefore most likely been created by mountain ranges in these areas, probably the Himalayas in the NH and the Andes in the SH. The fact that the poleward transport done by the MMC, as seen in Figure 1b, 26

30 5 ISCUSSION only is of significant importance in the Tropics have been stated by others, e.g. Hartmann (1994) and Trenberth and Stepaniak (23b). This again also points to that the general structure of the transport produced by EC-Earth is reasonable. The other two groups showed in Figure 1b waves 1-5 and waves 6 are shown to be of about equal importance for the meridional energy transport produced by EC-Earth in the present day climate. The structure of the individual waves within each group is however different. The transport done by waves 6, 7, 8, 9 and 1 is decreasing with higher wavenumbers, implying that wavenumbers >1 do not contribute much to the poleward transport. This tendency is also visible in Figure 1a. One possible reason behind this could be that wavenumbers 1 simply are more common in the westerly flow than the higher wavenumbers and thus transporting more energy. Another reason could be a larger phase difference between the v and E fields among wavenumbers 1. A large phase difference between these fields are of main importance if waves will transport a significant amount of energy. The more varying latitudinal structure of the transport done by waves 1, 2, 3, 4 and 5 (Figure 3) suggests no such decreasing frequency among these waves. One feature that is visible in both groups of waves is the shift towards lower wavenumbers closer to the poles. This can probably be explained by the fact that the westerly flow with e.g. different storm tracks can appear as lower wavenumbers at higher latitudes. Because the same wavelength can appear as different wavenumbers at different latitudes, e.g. wavenumber 2 at 7 N has roughly the same wavelength as wavenumber 5 at 3 N. The change of the meridional energy transport in the future scenario is large, e.g. the transport done by wavenumbers 1-5 increases with roughly 24% at 4 S. Though, as the future scenario used here is only one of many possible scenarios the absolute values of the change is not to be focused on. According to Koenigk et al. (212), as also mentioned above, the difference regarding the energy transport between the future scenario used here (SS81) and other scenarios with a smaller radiative forcing was only of magnitude and not in structure. In the total poleward energy transport a significant increase is seen at midlatitudes and a minor decrease further poleward (Figure 9). The general structure of this change is also seen by Hwang and Frierson (21) and poleward of 3 N also by Koenigk et al. (212) who, as mentioned, used the same model and scenarios. The increase seen at midlatitudes is almost only 27