Atmospheric Local Energetics and Energy Interactions between Mean and Eddy Fields. Part II: An Example for the Last Glacial Maximum Climate

MARCH 2011 M U R A K A M I E T A L. 533 Atmospheric Local Energetics and Energy Interactions between Mean and Eddy Fields. Part II: An Example for the Last Glacial Maximum Climate SHIGENORI MURAKAMI Climate Research Department, Meteorological Research Institute, Tsukuba, Japan RUMI OHGAITO Research Institute for Global Change, JAMSTEC, Yokohama, Japan AYAKO ABE-OUCHI Atmosphere and Ocean Research Institute, University of Tokyo, Kashiwa, and RIGC, JAMSTEC, Yokohama, Japan (Manuscript received 15 June 2010, in final form 23 November 2010) ABSTRACT The atmospheric local energy cycle in the Last Glacial Maximum (LGM) climate simulated by an atmosphere ocean GCM (AOGCM) is investigated using a new diagnostic scheme. In contrast to existing ones, this scheme can represent the local features of the Lorenz energy cycle correctly, and it provides the complete information about the three-dimensional structure of the energy interactions between mean and eddy fields. The diagnosis reveals a significant enhancement of the energy interactions through the barotropic processes in the Atlantic sector at the LGM. Energy interactions through the baroclinic processes are also enhanced in the Atlantic sector, although those in the Pacific sector are rather weakened. These LGM responses, however, are not evident in the global energy cycle except for an enhancement of the energy flow through the stationary eddies. 1. Introduction The ultimate energy source of the atmospheric general circulation is the solar radiation reaching the earth. Spatial and temporal contrasts of the solar heating under the earth s gravitational field generate the free energy that is stored in the atmosphere as the available potential energy (APE). A part of the APE is converted to kinetic energy (KE) through the convection or baroclinic processes. These processes maintain the atmospheric general circulation, and the KE dissipates into internal energy of the atmosphere through the friction process. The internal energy is converted to radiative energy and finally is emitted out to space as longwave earth radiation. The atmospheric part of these processes is often described and quantified using a box diagram of the Lorenz energy cycle (Lorenz 1955), which reveals many properties of the atmospheric general circulation. Corresponding author address: Shigenori Murakami, Meteorological Research Institute, 1-1 Nagamine, Tsukuba 305-0052, Japan. E-mail: shimurak@mri-jma.go.jp For example, the tropospheric general circulation is mainly maintained by the baroclinic processes of the midlatitudes (e.g., Oort 1964), and the lower stratospheric circulation is characterized as an indirect circulation maintained by the kinetic energy flux from the troposphere (e.g., Dopplick 1971). However, the Lorenz energy diagram gives only a summary of global energy cycle and cannot describe its local features. If we try to draw a box diagram to describe local features of the Lorenz energy cycle, we are faced with some difficulties because the energy conversion term between mean and eddy fields has two different local expressions whose spatial distributions are different, although they give the same value when averaged over the entire atmosphere (e.g., Holopainen 1978; Plumb 1983). In Part I of this paper (Murakami 2011, hereafter Part I) one of the authors developed a new diagnostic scheme for the atmospheric local energetics analysis. The key concept of this analysis is the interaction energy flux. Using this concept, he shows it is possible to represent the local feature of the Lorenz energy cycle in a form of box diagram for the division of basic variables into timemean and transient-eddy components. Moreover, a set of DOI: 10.1175/2010JAS3583.1 Ó 2011 American Meteorological Society

534 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 the interaction energy flux and the two local expressions of energy conversion term mentioned above provides the complete information about the three-dimensional structure of the energy interactions between mean and eddy fields. Here, as a first example (and a test) of this type of analysis, we investigate the energy interactions between time-mean and transient-eddy fields for the Last Glacial Maximum (LGM; 21 000 yr before present) climate simulated by a coupled atmosphere ocean general circulation model (AOGCM). This is also a continuation of Murakami et al. (2008). In Murakami et al. (2008), the global-scale meridional energy transport in the LGM simulation was investigated. The target of this paper is to investigate the local feature of the energy transport related to the energy conversions between mean and eddy fields. Since GCMs were put to practical use, many LGM climate simulations have been conducted. In early stages of paleoclimate modeling studies, atmospheric GCMs were used with lower boundary conditions reconstructed from the paleoclimate proxy data (e.g., Williams et al. 1974; Gates 1976). In a second stage, atmospheric GCMs coupled with mixed layer ocean models were used for those studies (e.g., Manabe and Broccoli 1985; Dong and Valdes 1998). In recent studies, fully coupled AOGCMs are usual tools for such the studies (e.g., Hewitt et al. 2001; Kitoh et al. 2001; Kitoh and Murakami 2002; Otto- Bliesner et al. 2006). Particularly over the recent few decades, the Paleoclimate Modeling Intercomparison Project (PMIP) has been playing an important role in leading paleoclimate modeling studies (e.g., Joussaume and Taylor 2000; Braconnot et al. 2007). Many simulations and analyses have been performed for the LGM climate in the framework of this project or in relation to it. Several studies focused on the transient eddy activity or the storm tracks in the LGM climate (e.g., Hall et al. 1996; Kageyama et al. 1999; Laîné et al. 2009; Li and Battisti 2008). This paper also deals with the transient eddy activity in one of such the simulations. However, the main target of this paper is to investigate the local feature of energy interactions between mean and eddy fields and how they respond to the LGM boundary conditions, which conventional energetics analysis could not reveal. In section 2, we briefly describe the diagnostic scheme developed in Part I. A brief description of the LGM boundary conditions and some basic results are given in section 3. We also give a quick description of the energy density fields themselves in that section. In section 4, three-dimensional distributions of energy conversion terms between mean and eddy fields and interaction energy fluxes are plotted for the LGM and control (CTL) climate simulations. In section 5, box diagrams of the local energy cycle are shown for several typical locations in the Pacific and Atlantic sectors. Section 6 contains discussions and section 7 provides a summary. 2. Diagnostic scheme for local energetics The key point of Part I is that each energy equation for APE or KE is divided not into two but into three parts consisting of the (time) mean, (transient) eddy, and interaction energy equations, when basic variables are divided into time-mean and transient-eddy components. We denote corresponding energy components as A M, A T, and A I for APE and K M, K T, and K I for KE (see appendix A for details). Using this notation, the basic equations of local energetics analysis are given as A M 5 G(A t M ) C(A M, K M ) C(A M, A I ) B(A M ) 1 R(A M ), A T t A I t and K M t K T t K I t 5 G(A T ) C(A T, K T ) C(A T, A I ) B(A T ), (1a) (1b) 5 0 5 C(A M, A I ) 1 C(A T, A I ) F(A I ), (1c) 5 C(A M, K M ) C(K M, K I ) D(K M ) B(K M ), 5 C(A T, K T ) C(K T, K I ) D(K T ) B(K T ), (2a) (2b) 5 0 5 C(K M, K I ) 1 C(K T, K I ) F(K I ), (2c) where the term G(A * ) denotes the APE generation rate, C(A *, K * ) the energy conversion rate from APE to KE, C(* M,* I ) the conversion rate from mean energy to interaction energy, C(* T,* I ) the conversion rate from eddy energy to interaction energy, D(K * ) the dissipation rate of KE, R(A M ) the residual term, B(*) the boundary flux term, and F(* I ) the flux term of the interaction energy equation. It should be noted that the time derivative terms in the interaction energy equations (1c) and (2c) vanish since the time averages of A I and K I are always zero. Detailed mathematical expressions for the above terms are given in appendix B, and the derivation of the equations is given in Part I.

MARCH 2011 M U R A K A M I E T A L. 535 The main differences of the above equations from the usual ones are the two additional equations (1c) and (2c) and the presence of two types of energy conversion terms between mean and eddy fields. In place of conventional conversion terms such as C(K M, K T ), two conversion terms, C(K M, K I ) and C(K T, K I ), appear. The relationship among these two types of conversion terms and the flux term of interaction energy (hereafter referred to as the interaction energy flux) is given by (1c) or (2c) (see Part I for details). As shown after, these three quantities provide useful information about the energy interactions between mean and eddy fields. The balance among all the terms in the above equations is represented by a box diagram shown in Fig. 1. It should be noted that the residual term R(A M )in(1a) is, for simplicity, included in the term B(A M )inthe diagram. 3. Experiments and basic results First of all, we briefly summarize the LGM experiment analyzed in this paper. The model used here is the Center for Climate System Research (CCSR) National Institute for Environmental Studies (NIES) Frontier Research Center for Global Change (FRCGC) coupled GCM called the Model for Interdisciplinary Research on Climate 3.2.2 (MIROC3.2.2). This is basically the same model that was used in the Intergovernmental Panel on Climate Change s (IPCC s) Fourth Assessment Report (AR4) by the CCSR NIES FRCGC model group, but a bug fix about the treatment of momentum and heat fluxes over the ice sheets was made. A detailed description of the model is given in Hasumi and Emori (2004). Two simulation runs were conducted using LGM and preindustrial control (CTL) boundary conditions. Under the PMIP2 protocols, the LGM experimental conditions are summarized as follows: 1) reduced greenhouse gas (GHG) concentrations, 2) insolation change due to 21 000 yr before present orbital parameters, 3) surface albedo changes due to prescribed ice sheets, 4) orography changes due to prescribed ice sheets, and 5) changes in land sea distribution and altitude due to LGM sea level drop (about 120 m). Detailed descriptions of the experimental design can be found on the PMIP2 Web site (available online at http:/pmip2.lsce.ipsl.fr/). The above boundary conditions cause a large surface air temperature (SAT) cooling in the northern high latitudes in addition to the global mean SAT cooling (about 4.58C) compared to the CTL climate. This situation increases the north south SAT gradient in the midlatitudes and enhances the low-level baroclinicity (see, e.g., Fig. 1 of Murakami et al. 2008). Moreover, FIG. 1. Box diagram of the local energy cycle. The boxes indicated by A M, A T, K M, and K T represent the mean and transienteddy components of APE and KE. The arrows indicated by G(*), D(*), and B(*) represent generation, dissipation, and boundary flux terms in the energy balance equations. The arrows indicated by C(*, *) represent the energy conversion terms, and the wavy arrows indicated by F(A I ) and F(K I ) represent the interaction energy fluxes of APE and KE. large ice sheets on the North American continent enhance the stationary waves around that region (even for the annual mean) and enhance the poleward dry static energy transport (by stationary eddies) in the mid- and high latitudes (see Murakami et al. 2008 for details). These results are consistent with previous GCM simulations (e.g., Manabe and Broccoli 1985) or the linearized model calculations by Cook and Held (1988). In the upper troposphere, however, the relatively large cooling in the tropics rather acts to weaken the north south temperature gradient. The main interest of this paper is how the transient eddies respond to such situations and interact with mean fields. All calculations in this paper were performed on the 30-yr time series of 6-hourly snapshot output for eastward wind speed u,northward wind speed y, pressure velocity v, temperaturet, and diabatic heating Q. Before investigating energy interactions, we briefly examine the spatial distributions of each energy component for APE and KE, and their response to the LGM boundary conditions. In this section, the time-mean fields are further divided into zonal-mean and stationary-eddy components, indicated respectively by subscripts Z and S (e.g., A Z, A S ). Figure 2a shows vertically integrated APE density in both climates. Thick lines (solid and dotted) in Fig. 3a indicate the corresponding zonal mean profiles. Since APE is defined as square of temperature deviation from the global mean, the APE density is large in high latitudes and the response to the LGM conditions is also large in the northern high latitudes. This is consistent with the response of SAT mentioned above.

536 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 FIG. 2. Vertically integrated (a) APE density, (b) KE density, and (c) generation rate of APE for (left) CTL and (right) LGM simulations. Contour intervals are 30 3 10 5 Jm 22 for APE, 6 3 10 5 Jm 22 for KE, and 6 W m 22 for APE generation. Shading in right panels indicates deviation from the CTL. Figure 2b shows a similar map for KE, and the thick lines in Fig. 3d are the zonal-mean profiles of total KE. In contrast to the APE case, KE distribution has peaks in midlatitudes. Particularly in the NH, KE peaks are located over the two major oceans corresponding to the two jet stream maxima. At the LGM, the peak over the Atlantic increases more than 100%, but the peak over the Pacific decreases, except downstream of its maximum. Figure 2c shows the vertically integrated generation rate of APE for both climates. It shows that G(A) is larger at high latitudes, similar to the APE density case, and at the convective precipitation zones in the tropics. At the LGM, it increases over the NH polar region, tropical western Pacific, and the icecovered regions. The regions of increased G(A) in the tropics are also characterized by an increase of precipitation.

MARCH 2011 M U R A K A M I E T A L. 537 FIG. 3. Latitudinal profiles of vertically integrated and zonally averaged (a) total and zonal APE, (b) T-eddy APE, (c) S-eddy APE, (d) total and zonal KE, (e) T-eddy KE, and (f) S-eddy KE density. Solid and dotted lines indicate the values in LGM and CTL, respectively. Unit is 10 5 Jm 22. Next, we examine the each component of APE and KE. The A M and K M have similar spatial distribution to total APE and KE, respectively, and their responses to the LGM conditions are also similar to those of total energies (not shown; only the zonal mean profiles are shown in Figs. 3a and 3d). As shown in Fig. 4a, A T has two broad peaks over the eastern coast of the Eurasian continent and over the North American continent. On the other hand, K T has peaks over the North Pacific and the North Atlantic (Fig. 4b). The peaks of the energy conversion rate C(A T, K T ) shown in Fig. 4c are located between the peaks of A T and K T. At the LGM, they decrease over the Pacific and increase over the Atlantic. This is consistent with response of K T density itself shown on Fig. 4b. In addition, a significant increase of A S and K S is observed over the North American continent

538 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 FIG. 4. Vertically integrated (a) transient-eddy APE (A T ), (b) transient-eddy KE (K T ), and (c) energy conversion rate from A T to K T for (left) CTL and (right) LGM simulations. Contour intervals are 10, 3, and 3 3 10 5 Jm 22, respectively. Shading in right panels indicates deviation from the CTL. at the LGM (not shown; only the zonal profiles are given in Figs. 3c and 3f). 4. Energy interactions between mean and eddy fields, and interaction energy fluxes In this section, we investigate details of the energy interactions between mean and eddy fields using the interaction energy fluxes defined in Part I. Figure 5 just shows the relationship represented by (1c) for the CTL climate. Figures 5a and 5b show the vertically integrated energy conversion terms C(A M, A I ) and C(A I, A T ) 52C(A T, A I ). As mentioned in Part I, these two quantities have different spatial distributions. The former is larger in high latitudes and the latter has peaks in midlatitudes. These features are related to the fact that the generation and storage of APE are large in the high latitudes, and the conversion from APE to KE

MARCH 2011 M U R A K A M I E T A L. 539 FIG. 5. Vertically integrated (a) C(A M, A I ), (b) C(A I, A T ), and (c) interaction flux of APE and its convergence in the CTL simulation. Units for the conversion rate and flux are W m 22 and J m kg 21 s 21, respectively. and the KE density itself are large in the midlatitudes (see Figs. 2c and 4c). The difference between these two spatial distributions implies the existence of an energy flow from the high latitudes to midlatitudes. Figure 5c displays the vertical integration of the horizontal part of interaction energy flux p 2k A I u95c p (u hui)u9u9 (3) p 0 (arrows) and its convergence (color shades). The interaction energy flux A I u9 well captures the energy flow from the regions where the APE generation is active (in high latitudes) to the regions where the energy conversion from eddy APE to eddy KE is active (in midlatitudes). In addition, the convergence of interaction energy flux for APE just agrees with C(A I, A T ) 2 C(A M, A I ) 52fC(A M, A I ) 1 C(A T, A I )g. From these figures and relation (1c), we can confirm the following facts: 1) the local value of C(A M, A I ) is equal to the sum of in situ conversion C(A I, A T ) and the divergence of A I flux; 2) the local value of C(A I, A T ) is equal to the sum of in situ conversion C(A M, A I ) and the convergence of A I flux; and 3) the interaction energy flux A I u9 transports the

540 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 interaction energy from its divergence regions to its convergence regions. In contrast to the conventional energetics analysis dealing only with the conversion term C(A I, A T ), the diagnosis using these three quantities gives the complete information about the energy conversions (interactions) between mean and eddy fields. It should be noted that the divergence of interaction energy flux vanishes when averaged over the entire atmosphere, and the two conversion terms give the same value. Another important feature seen from Fig. 5 is that the quantities C(A M, A I ) and C(A I, A T ) are positive in most regions. This means that the energy conversion A M / A T is dominant in the real atmosphere. This is just the fact that the classical energetics analysis revealed. Therefore, we can generally recognize the following energy flow pattern (or energy path, in terms of Part I): G(A M )! AM! A A I u9 I A I! A T! K T. (4) The chain of these processes should be referred to as baroclinic conversion from the viewpoint of this paper. Figure 6 shows the three-dimensional structure of the energy interactions for APE in the CTL climate. Figures 6a and 6b display the zonal mean and vertical section along the 458N parallel of C(A I, A T ) and the corresponding interaction energy flux. Figure 6c is the same as Fig. 5c, but the vertical integration of C(A I, A T ) is displayed as color shading. Each panel also displays the transient eddy APE density A T by thin green lines. In the troposphere, the interaction energy flux for APE generally tends to go from upper to lower levels and from the high to low latitudes. This is related to the fact that the APE generation peaks appear in the upper troposphere in high latitudes (except in the tropics). Also, A I converges to the eastern coasts of two major continents in the NH midlatitudes where the generation and growth of baroclinic disturbances (baroclinic processes) are active. Figure 7 shows the same diagnosis for the difference between LGM and CTL. Under the LGM boundary conditions, the A I flux convergence and C(A I, A T ) are significantly enhanced in the North American region, but those on the Eurasian side are rather weakened. In addition, as shown in zonal mean profiles of Fig. 7a, the interaction energy fluxes of APE and C(A I, A T )are weakened in the upper troposphere and enhanced in the lower troposphere. These responses are consistent with the temperature response mentioned in section 3 (not shown). Similar responses are also seen in the SH (Fig. 7a). Figure 8 shows the relationship represented by (2c) for the CTL climate. In this case, C(K I, K M )andc(k I, K T ) are plotted in Figs. 8a and 8b, respectively. Similarly to the case of APE, the spatial distributions of the two quantities C(K I, K M )andc(k T, K I ) 52C(K I, K T ) are different. In addition, in contrast to the case of APE, the direction of energy conversion varies from place to place, and moreover, in many locations, the directions of C(K I, K M ) and C(K T, K I ) are opposite (this is evident from the same color shading in Figs. 8a and 8b for the same locations). This means that the energy interaction pattern K M Y [ K T ;;;;;. K M [ Y K T (5) is commonly seen for KE in the real (or simulated) atmosphere, which is never recognized from the conventional energetics analysis. The sum C(K I, K M ) 1 C(K I, K T ) 52fC(K M, K I ) 1 C(K T, K I )g just gives the convergence of the interaction energy flux for KE: K I u95uu9u91y y9u9. (6) Similarly to the case of APE, we can confirm the following facts: 1) the local value of C(K I, K M ) is equal to the sum of in situ conversion C(K T, K I ) and the convergence of K I flux; 2) the local value of C(K I, K T )is equal to the sum of in situ conversion C(K M, K I ) and the convergence of K I flux; and 3) the interaction energy flux K I u9 transports the interaction energy K I from its divergence regions to its convergence regions. Figure 9 shows the three-dimensional structure of the energy interactions for KE. Figures 9a and 9b display the zonal mean and vertical section along the 408N parallel of C(K I, K M ) and the corresponding interaction energy flux; Fig. 9c displays the vertical integration of C(K I, K M ) and interaction flux of KE. In addition, the mean KE density K M is indicated by thin green contours as an indicator of the climatological jet stream. The KE interaction flux stands out mainly in the upper troposphere along the jet stream. It diverges at the jet entrance regions and converges at the exit regions. In addition, some vertical transport of K I is also observed, which is associated with the growth and decay of the baroclinic turbulence. Figure 10 shows the same diagnosis for the difference between LGM and CTL. Under the LGM conditions, C(K I, K M ) and interaction energy flux are significantly enhanced in the Atlantic sector according to the enhancement of the jet stream, although those in the Pacific are generally weakened. This result may be related to the existence of the Laurentide Ice Sheet on the

MARCH 2011 M U R A K A M I E T A L. 541 FIG. 6. (a) Zonal mean, (b) vertical section along 458N, and (c) vertical integration of C(A I, A T ) and interaction flux of APE in the CTL simulation. Units for the conversion rate are (a),(b) 10 24 Wkg 21 and (c) W m 22. Units for the horizontal and vertical components of flux vector are J m kg 21 s 21 and J Pa kg 21 s 21, respectively. The vertical component of the flux vector is 100-fold in (a) and (b). Thin green contours indicate T-eddy APE density with contour intervals of 100 J kg 21, 180 J kg 21, and 5 3 10 5 Jm 22. North American continent, but a sensitivity study will be needed to separate the orographic effect. In addition, as seen from Fig. 10a, the zonal mean poleward K I flux is weakened in both hemispheres. 5. Box diagrams of local and global energy cycle a. Local energy cycle In this subsection, we draw box diagrams of the local energy cycle for several specific locations. Some features described in this section can be already seen from the figures and discussions in the previous sections. However, the utility of the local box diagram is that the diagram correctly represents the balance of all terms in the energy equations and makes it easy to quantify the differences between the different locations or between the different climate states. Figure 11 show such diagrams for both climates. The locations of the chosen areas are shown in Fig. 12 as rectangles denoted by capital letters B H, except for the

542 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 FIG. 7. As in Fig. 6, but for the difference between LGM and CTL simulations. Thin green contours indicate T-eddy APE density at LGM. area corresponding to Fig. 11a. The letters B H correspond to Figs. 12b h. Numerals in each diagram indicate the vertically integrated values of the variables defined in Fig. 1. Upper and lower numerals correspond to the values in LGM and CTL, respectively. A negative value means that the energy flows against the arrow. The values in parentheses (dissipation terms) are obtained as residuals of the balance equations. The values in curly brackets that is, values of C(A M, K M ) are not directly used for the calculation because those values are significantly different from the others. Instead, the values of (a hai)v and u grad h F are used, where grad h means the horizontal component of the gradient operator. As defined in Part I, we refer to an energy flow pattern recognized in the energy diagram as an energy path. Thick arrows in each diagram indicate the dominant energy paths at that place. We choose the first area A as the region north of 808N (i.e., Arctic region) because the generation and storage of APE is large there. As shown by the diagram displayed in Fig. 12a, the generated mean APE A M is converted to A I and flows out from this region as the A I flux. At the LGM, the generation and storage of APE increase, but the increment of G(A M ) mainly flows out as the boundary flux of B(A M ) and the interaction energy flux does not necessarily increase in this region. The main energy path in this area can be expressed by the following simplified energy diagram:

MARCH 2011 M U R A K A M I E T A L. 543 FIG. 8. Vertically integrated (a) C(K I, K M ), (b) C(K I, K T ), and (c) interaction flux of KE and its convergence in the CTL simulation. Units for the conversion rate and flux are W m 22 and m 3 s 23, respectively. G(A M ) F(A I )! AM! A I. (7) This type of energy path is typically seen at high latitudes. Area B (Fig. 12c) is chosen over Labrador, where the Laurentide Ice Sheet covered the ground at the LGM, and the APE generation might be enhanced (see Fig. 2c). The main energy path in this area at LGM is similar to area A. In this region, however, the increment of G(A M ) mainly flows out as the interaction energy flux of APE (Fig. 11b). We choose area C on the eastern coast of the Eurasian continent where the growth of the baroclinic disturbances is active (Fig. 12a). The characteristic of this area is shown in Fig. 12 as an overlap of a divergence peak of A I flux (green line) and a conversion peak of C(A I, A T ) (red line). The conversion peak of C(A T, K T ) shown in Fig. 4c also has a peak there. Therefore, as shown in Fig. 11c, the main energy path can be expressed as F(A I ) AI! A T! K T B(K T ). (8)

544 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 FIG. 9. (a) Zonal mean, (b) vertical section along 408N, and (c) vertical integration of C(K I, K M ) and interaction flux of KE in the CTL simulation. Units for the conversion rate are (a),(b) 10 24 Wkg 21 and (c) W m 22. Units for the horizontal and vertical components of flux vector are m 3 s 23 and Pa m 2 s 23, respectively. The vertical component of the flux vector is 100- fold in (a) and 1000-fold in (b). Thin green contours indicate mean KE density with contour intervals 100 J kg 21, 200 J kg 21, and 5 3 10 5 Jm 22. This energy path is a typical one of the baroclinic conversion. Under the LGM conditions, this energy path weakens by about 10%. We can recognize another energy path in the diagram described by B(K M ) KM! K I F(K I ). (9) Since area C is located at the entrance region of the Pacific jet, the convergence of K M [i.e., 2B(K M )] is very large (about 470 W m 22 ). Most of converging K M is converted to A M (about 450 W m 22 ), a part of the residual is dissipated (about 10 W m 22 ), and the rest is converted to K I and flow outs as the interaction energy flux of KE (K I flux; 4.9 W m 22 ). It should be noted that only the net effects are indicated for B(K M ) and B(A M ) in the energy diagrams of Fig. 11, and the effect of dissipation is omitted in the simplified diagram (9) for simplicity. The intensity of this energy path does not change so much at LGM. Another notable feature for

MARCH 2011 M U R A K A M I E T A L. 545 FIG. 10. As in Fig. 9, but for the difference between LGM and CTL simulation. Thin green contours indicate mean KE density at LGM. this area is that a part of converted energy K I [from K M as C(K M, K I )] further converted to K T as C(K I, K T ) even though the value is small (about 1 W m 22 ) compared to other energy paths. This point will be addressed again. Area D over the Atlantic is analogous to area C of the Pacific sector (Fig. 11c). In the CTL climate simulation, the intensity of the energy path described by diagram (8) in this place is less than half that at C. However, at the LGM this energy path intensifies corresponding to the enhancement of the baroclinicity at that region as expected from Fig. 7. In addition, a significant enhancement of the energy path described by diagram (9) is observed. This enhancement is related to the fact that the split jet streams by the Laurentide Ice Sheet join together near that place in the LGM simulation. This change is also clear from Fig. 10. We choose area E as the location to the southsoutheast of area C (Fig. 12a). This is also an area where the baroclinic process is active, but several differences can be seen. At this place, in contrast to area C, the converted K T from A T further converts to the interaction energy K I and diverges as K I flux. In addition, the energy conversions described by diagram (9) also occur. Therefore, this area is characterized by a strong divergence of K I. Figure 8 clearly shows this characteristic. The main energy path in this area is expressed as

546 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 FIG. 11. Box diagrams of the local energy cycle corresponding to several typical locations shown in Fig. 12. Numerals indicate the vertically integrated values of the variables corresponding to Fig. 1. Upper and lower numerals correspond to the values in LGM and CTL, respectively. The values of R(A M ) are included in the value of B(A M ). Units for the values in the boxes and beside arrays are 10 5 Jm 22 and W m 22, respectively. See the text for details.

MARCH 2011 M U R A K A M I E T A L. 547 FIG. 12. Maps of the conversion and convergence peaks of interaction energy over the (a) Pacific in CTL, (b) Pacific in LGM, (c) Atlantic in CTL, and (d) Atlantic in LGM. Color lines indicate the contour around the peaks of each quantity denoted in (a). Unit of the contours is W m 22. Rectangles denoted by the letters B H indicate the areas where the energy diagrams in Fig. 11 are calculated. See the text for details.

548 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 G(A M ) / B(K M ) ;;;;;. K M Y A M / A T /K T K I ;;;;;.F(K I ) [ : (10) The difference between Figs. 11c and 11e (or the diagrams of Figs. 8 and 9 and Fig. 10) represents the difference of climatological features for these two areas. We refer to the upper and lower branches in energy path (10) as the barotropic part and baroclinic part, respectively. At the LGM, the baroclinic part of this energy path is enhanced by about 10% and the barotropic part is weakened about 10%. Area F in the Atlantic sector is similar to area E of the Pacific sector (Fig. 12c). The main energy path at this place is similar to that of area E except that the main energy source at this point is the convergence of the mean APE flux B(A M ). At the LGM, changes from CTL are small, similar to place E except for the enhancement of barotropic part. We choose area G over the central Pacific, where a convergence peak of K I flux and a peak of C(K I, K M ) overlap (Fig. 12a). The main energy source at this place is convergence of interaction flux of KE, and the energy path is characterized by F(K I ) B(K M ) KI! K M. (11) Converging KE is mainly converted to K M and mainly flows out as the mean boundary flux B(K M ), and is partly converted to K T. Under the LGM conditions, the main peaks of K I flux convergence and C(K I, K M ) shift to the eastern Pacific (Fig. 12b). Therefore, the energy path is weakened at area G and enhanced over the eastern Pacific. It is also notable that there are typically two types of regions over the convergence area of K I flux, which can be determined from the sign of C(K T, K I ). The interaction patterns of KE in those regions are expressed as K M [, ;;;;; and Y K T K M [, ;;;;; [ K T. (12) From Fig. 8, we can see that the latter pattern of energy interaction is dominant in the eastern North Pacific. This FIG. 13. A six-box diagram of the global mean energy cycle. Upper and lower black numerals indicate the values in LGM and CTL, respectively. In addition, the percentages of increments at LGM to the CTL are denoted by colored numerals. Units for the values in the boxes and beside arrays are 10 5 Jm 22 and W m 22, respectively. See the text for details. interaction pattern may be associated with the decay process of baroclinic disturbances (also see Fig. 9b). Figure 11h shows the energy cycle at a region located over the eastern Atlantic indicated by rectangle H in Fig. 12c. This region is basically an energy converging region of K I similar to the eastern Pacific. The main energy path is same as diagram (11) and the intensity increases by more than 100% at the LGM. However, C(K T, K I ) is basically positive in this region. b. Global energy cycle Finally we show the globally averaged energy balance in both climates. By integrating over the entire atmosphere, the diagram of Fig. 1 turns into the conventional four-box diagram. Here, we divide the time-mean state further into zonal-mean and stationary-eddy components and draw a six-box diagram, following Lee and Chen (1986), to clearly see the role of stationary eddies. Figure 13 displays this diagram for both climates (for details, see Lee and Chen 1986). The values of boundary flux terms and residual terms basically vanish except the contributions from the lower boundary. Those are less than 0.3 W m 22 as a global mean and are omitted in this diagram. Similarly to Fig. 11, the upper and lower numerals in the boxes or beside the arrows respectively denote the values for the LGM and CTL. We also add the percentage of increment at LGM to the CTL as the colored numerals. The main energy path we can recognize from the diagram is expressed as G(A Z ) / AZ / A T / K D(K T T / ) or (13) G(A Z ) / AZ / A T / K T / K D(K Z Z / ) (14)

MARCH 2011 M U R A K A M I E T A L. 549 which implies the importance of baroclinic process in the atmosphere, consistent with previous classical studies. Figure 13 also shows the 100% enhancement of the energy path through the stationary eddies (colored arrows in Fig. 13). However, some local characteristics and those responses to the LGM conditions that we have seen in the previous sections are not evident in Fig. 13. 6. Discussion In this paper, in connection with the analysis in Murakami et al. (2008) and as the first test of the new scheme, we treated the data with annual mean basis and no filtering has been applied. It is difficult to compare our results directly with previous studies that mainly analyze the wintertime statistics of eddies, but we can find some similarities and some differences. Li and Battisti (2008), for example, report an intensification of the Atlantic jet and an enhancement of low-level baroclinicity for the National Center for Atmospheric Research (NCAR) Community Climate System Model version 3 (CCSM3) that are similar to the results in this paper, but they also report a weakening of wintertime transienteddy KE in contrast with our results. Laîné et al. (2009) also report a weakening of wintertime total-eddy energy (A T 1 K T ) for the MIROC3.2 model (the model version is slightly different from the model used here; see section 3). It is difficult to extract some robust results from those about the response of transient-eddy activity itself. However, as shown in the previous sections, the main target of this paper is a local feature of the energy interactions, which conventional energetics analysis cannot reveal. As mentioned in the introduction of Part I, there are some studies that deal with the local energetics analysis by dividing basic variables into time-mean and transienteddy fields. In those studies, only the terms C(A I, A T ) and C(K T, K I ) (in terms of this paper) are treated and referred to as baroclinic conversion and barotropic conversion, respectively. Therefore, the results related to those terms, particularly the results for baroclinic conversions, can be obtained from the methods used in those studies, although the interaction energy flux of this study provides more complete information. From the viewpoint of the present paper, as mentioned in section 5b, the classical concept of baroclinic conversion should be represented by a long chain of energy conversions described by diagram (14). The final part of this diagram (K T / K M )maybe accomplished by the decay process of baroclinic disturbances that is dominant over the eastern North Pacific or the North Atlantic. However, the local values of those processes are relatively small compared to other processes. From Fig. 8, we can recognize more intense interactions in the midlatitudes that are expressed as K M! K I K I! K M or (15) K T! K I K I! K T. (16) Only the interaction pattern (16) or the direct interaction patterns K M / K T and K T / K M are recognized from conventional local energetics analysis, and only the global average of those three interactions is recognized as barotropic conversion from the classical Lorenz diagram. As seen from Figs. 8a and 8b, the interaction pattern (15) is generally more intense than pattern (16), and the energy convergence pattern in Fig. 8c reflects mainly the former pattern. Figure 10 shows that this interaction pattern is significantly enhanced in the Atlantic sector at LGM. As mentioned in Part I, this type of energy interaction transports the mean KE from a place to another as the interaction energy K I and hardly affects the transient-eddy KE field as a time mean. We may have overlooked this process by treating only the term C(K T, K I ) as the energy conversion between mean and eddy fields. From the viewpoint of this paper, as mentioned also in Part I, it is rather C(K M, K I ) that represents the energy conversion from (or to) mean KE and that is appropriately referred to as barotropic conversion. A recent paper by Hernandez-Deckers and von Storch (2010), published after the submission of this paper, deals with the Lorenz energy cycle in a CO 2 doubling experiment. Although their diagnosis is typical of the classical energetics analysis based on the global Lorenz energy cycle, they reported an enhancement of the energy path A Z! A E! K E! K Z in the upper troposphere and lower stratosphere, and weakening in the middle and lower troposphere by dividing the whole atmosphere into upper and lower parts, where A E 5 A T 1 A S and K E 5 K T 1 K S. Those responses are generally opposite to the LGM case reported in this paper or in Li and Battisti (2008). It will be interesting to investigate global warming experiments in the manner of this paper in order to reveal the local features of energy interactions between mean and eddy fields. 7. Summary The local feature of the energy interactions between time-mean and transient-eddy fields in the LGM simulation was investigated, using the interaction energy fluxes and box diagrams for the local energy cycle. The response of energy interactions to the LGM boundary

550 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 68 conditions is quite different between in the Atlantic and Pacific sectors. The baroclinic conversion from mean APE to eddy APE is enhanced in the Atlantic sector corresponding to the increase of the baroclinicity in that region. On the other hand, in the Pacific sector the baroclinic conversion is rather weakened except in the lower troposphere. The energy interactions between mean KE and interaction KE (barotropic conversion; in terms of this paper) is significantly enhanced in the Atlantic sector simultaneously with an intensification of the Atlantic jet stream, but slightly weakened in the Pacific sector. These responses, however, are not evident in the classical Lorenz energy cycle. Acknowledgments. The author thanks three anonymous reviewers. Their constructive comments greatly improved the paper. The computation of LGM and CTL simulations that gave a basis of the analysis in this paper was performed on the Earth Simulator of the JAMSTEC. A part of this work was performed when author Shigenori Murakami was at the Frontier Research Center for Global Change of JAMSTEC. APPENDIX A Definitions of APE and KE Densities and Those Divisions In the pressure coordinate system, APE and KE densities per unit mass are expressed as A 5 C p 2 g(t hti)2 5 C p p 2k g(u hui) 2, (A1a) 2 p 0 K 5 u2 1 y 2, (A1b) 2 where u is the eastward wind speed, y the northward wind speed, p the pressure, p 0 the reference pressure (51000 hpa), T the temperature, C p the atmospheric specific heat at constant pressure, k the ratio of gas constant and specific heat (5R/C p ), u the potential temperature [5(p 0 /p) k T ], and g is an index for static stability of the dry atmosphere defined by g 5 k p k 1 0 dhui. (A2) p p dp In these expressions, angle brackets denote the global average operator over the constant pressure surface and the overbar denotes the time mean operator. Corresponding to the division of basic variables into the time mean and transient eddy, APE and KE densities are divided into three components as where A 5 A M 1 A T 1 A I and (A3a) K 5 K M 1 K T 1 K I, (A3b) A M 5 C p 2 g(t hti)2, (A4a) A T 5 C p 2 gt92, (A4b) A I 5 C p g(t hti)t9, and (A4c) K M 5 u2 1 y 2, (A5a) 2 K T 5 u92 1 y9 2, 2 (A5b) K I 5 uu91yy9. (A5c) It follows directly from above definitions that the time mean of A I and K I vanish, and A 5 A M 1 A T and K 5 K M 1 K T hold. Of course, relations A M 5 A M and K M 5 K M also hold. In the main text, we denote A M, A T, K M, and K T simply as A M, A T, K M, and K T, respectively. APPENDIX B Detailed Expressions of the Terms in Energy Balance Equations Detailed mathematical expression of the terms of energy balance equations in the spherical pressure coordinate system appearing in section 2 are given asgeneration terms: G(A M ) 5 g(t hti)(q hqi) and (B1a) G(A T ) 5 gt9q9; dissipation terms: (B1b) D(K M ) 5 u F and (B2a) D(K T ) 5 u9 F9; conversion terms from APE to KE: (B2b)

MARCH 2011 M U R A K A M I E T A L. 551 C(A M, K M ) 5 va and (B3a) C(A T, K T ) 5 v9a9; (B3b) conversion terms between eddies and mean fields (APE): divx 5 1 a cosu X l 1 Y cosu u 1 Z p, (B8b) where C and X 5 (X, Y, Z) are arbitrary scalar and vector fields. p 2k C(A M, A I ) 5 C p g(u hui)divu9u9 and (B4a) p 0 p 2k C(A T, A I ) 5 C p gu9u9 grad(u hui); (B4b) p 0 conversion terms between eddies and mean fields (KE): C(K M, K I ) 5 u divu9u91ydivy9u9 tanu (uu9y9 yu9u9) a and (B5a) C(K T, K I ) 5 u9u9 gradu 1 y9u9 grady 1 tanu (uu9y9 yu9u9); (B5b) a boundary flux terms: p 2k B(A M ) 5 C p g div (u hui)2 hui 2 u, (B6a) 2 p 0! p 2k B(A T ) 5 C p g div u92 2 u 1 u92 2 u9, (B6b) p 0 u 2 1 y 2 B(K M ) 5 div 1 F u, and (B6c) 2! ( ) B(K T )5div u92 1 y9 2 u9 2 1y9 2 u 1div 1F9 u9 ; 2 2 (B6d) and residual terms: p R(A M ) 5 C p p 0 2k g(u hui) divhuui 1 divhu9u9i. (B7a) Here, Q, F, v, a, and a are diabatic heating, horizontal friction force [i.e., F ¼ (F l, F u, 0)], pressure velocity, specific volume, and the earth s radius, respectively. The gradient and divergence operators in the spherical pressure coordinate system are given as follows: 1 C gradc5 a cosu l, 1 C a u, C p and (B8a) REFERENCES Braconnot, P., and Coauthors, 2007: Results of PMIP2 coupled simulations of the mid-holocene and Last Glacial Maximum Part 1: Experiments and large-scale features. Climate Past, 3, 261 277. Cook, K. H., and I. M. Held, 1988: Stationary waves of the ice age climate. J. Climate, 1, 807 819. Dong, B., and P. J. Valdes, 1998: Simulations of the Last Glacial Maximum climate using a general circulation model: Prescribed versus computed sea surface temperatures. Climate Dyn., 14, 571 591. Dopplick, T. G., 1971: The energetics of the lower stratosphere including radiative effects. Quart. J. Roy. Meteor. Soc., 97, 209 237. Gates, W. L., 1976: The numerical simulation of Ice Age climate with a global circulation model. J. Atmos. Sci., 33, 1844 1873. Hall, N. M., B. Dong, and P. J. Valdes, 1996: Atmospheric equilibrium, instability and energy transport at the Last Glacial Maximum. Climate Dyn., 12, 497 511. Hasumi, H., and S. Emori, 2004: K-1 coupled model (MIROC) description. K-1 Tech. Rep. 1, Center for Climate System Research, University of Tokyo, 34 pp. [Available online at http://www.ccsr.u-tokyo.ac.jp/kyosei/hasumi/miroc/tech-repo. pdf.] Hernandez-Deckers, D., and J.-S. von Storch, 2010: Energetics responses to increases in greenhouse gas concentration. J. Climate, 23, 3874 3887. Hewitt, C. D., A. J. Broccoli, J. F. B. Mitchell, and R. J. Stouffer, 2001: A coupled model study of the Last Glacial Maximum: Was part of the North Atlantic relatively warm? Geophys. Res. Lett., 28, 1571 1574. Holopainen, E. O., 1978: A diagnostic study on the kinetic energy balance of the long-term mean flow and the associated transient fluctuation in the atmosphere. Geophysica, 15, 125 145. Joussaume, S., and K. E. Taylor, 2000: The paleoclimate modeling intercomparison project. Proc. Third PMIP Workshop, Geneva, Switzerland, WMO, 9 24. [Available online at http://pmip.lsce. ipsl.fr/publications/local/wcrp111_009.html.] Kageyama, M., P. Valdes, G. Ramstein, C. Hewitt, and U. Wyputta, 1999: Northern Hemisphere storm tracks in present day and Last Glacial Maximum climate simulations: A comparison of the European PMIP models. J. Climate, 12, 742 760. Kitoh, A., and S. Murakami, 2002: Tropical Pacific climate at the mid-holocene and the Last Glacial Maximum simulated by a coupled ocean atmosphere general circulation model. Paleoceanography, 17, 1047, doi:10.1029/2001pa000724.,, and H. Koide, 2001: A simulation of the Last Glacial Maximum with a coupled atmosphere ocean GCM. Geophys. Res. Lett., 28, 2221 2224. Laîné, A., and Coauthors, 2009: Northern Hemisphere storm tracks during the last glacial maximum in the PMIP2 ocean atmosphere coupled models: Energetic study, seasonal cycle, precipitation. Climate Dyn., 32, 593 614, doi:10.1007/s00382-008-0391-9.

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