Dynamics and variability of the coupled atmosphere ocean system

Transcription

1 Dynamics and variability of the coupled atmosphere ocean system Johan Nilsson Department of Meteorology Bert Bolin Centre for Climate Research Stockholm University, Sweden 1

2 What is coupled dynamics/variability? One definition: the dynamics under (partly) fixed surface fluxes; i.e. a change of the fluid state does not change the fluxes. An ocean model with fixed surface fluxes of momentum, heat and freshwater give some flavor of uncoupled ocean dynamics. However, these fluxes implicitly assumes the presence of an atmosphere. Venus and Mars (or a model with zero surface heat flux) are prototypes for uncoupled atmospheric dynamics. Is a hypothetical liquid ocean beneath Mars feeble atmosphere a prototype for uncoupled dynamics? What would the energy-transport partitioning be on this planet? 2

3 Outline: Part 1 1. Radiation balance and energy transport; re-iterate the arguments of one (1978). 2. The time-mean partitioning of the energy transport between the atmosphere and the ocean; simulations and conceptual models. 3. Hurricanes and other speculative ideas. 4. Time variability of the energy transport; Bjerknes compensation. 3

4 Meridional energy transport: i) The ocean dominates the low latitudes; the atmosphere the high ones. ii) Latent heat comparable to dry static energy transport. 4

5 Why are the ocean and atmosphere transports comparable? 1. Why does not the ocean carry all energy? After all, the bulk of the solar energy is absorbed by the ocean and its mass and heat capacity are huge. 2. Why does not the atmosphere carry all energy? The ocean absorbs the solar energy very near the surface. Thus the ocean is heated from above, whereas the atmosphere is heated from below. Moreover, the weak compressibility of water makes the ocean a poor heat engine. 5

6 Energy versus freshwater transport 1. There is no simple constraint determining the atmosphere ocean partitioning of the meridional energy transport. 2. Conservation of mass requires that the ocean, the rivers and the sea ice exactly compensate the meridional freshwater transport in the atmosphere. 3. In the present climate, the ocean essentially compensates the atmospheric freshwater transport, i.e. the river- and sea-ice-transport are negligible. 6

7 Steady-state energy balance; 1 Following Stone (1978) we consider the total meridional energy transport H T = H A + H O dh T dφ = 2πR2 cos φ[s(φ)(1 α(φ)) I(φ)], (1) where S is the solar radiation, the α the albedo, I the outgoing longwave radiation, φ and R the Earth s radius. Stone noted that H T is controlled primarily by the solar constant, the planetary albedo, and the orbital parameters (e.g. the axial tilt). However, I and α are not independet of H T. 7

8 Steady-state energy balance; 2 Further, Stone considered the limit of uniform albedo (say α 0 ) and OLR (I 0 ), for which S 0 (1 α 0 )/4 = I 0. For no-axial tilt, implying that S(φ) = (S 0 /π) cos φ, the transports is H T = S 0 (1 α 0 )R 2 [φ + sin φ cos φ (π/2) sin φ]. (2) Note that H T decreases with increasing α 0 ; it also decreases with the axis tilt, which reduces the latitudinal gradient in the annuallyaveraged insolation. For α 0 0.3, the simplified model of H T peaks at about 6 PW. The considerations of Stone suggest that H T is essentially independent of the details of the ocean atmosphere circulation. 8

9 where So is the solar constant. In all our calculations in this paper we will adopt for So the value of 1.95 cal/cm2/min, or equivalently, 1360 W/m 2. Upon substituting eq. 2 into eq. 1, integrating, and applying the boundary conditions that F(+~/2) = 0, we obtain: I o = S (1 - - C~o) ( 3 ) F= SoR2(1--C~o)( + sin cos ~--2 sin ~) (4) If we let ~bo be the latitude where F peaks, then in this model: Meridional energy transport (Stone, 1978)?T ~bo = arccos-~ = (5) \ 6 /,,, / Flux / (10 '~ watts) / \ r / / \ \ l, \ / 1 \ \ o Fig. 1. Total flux of energy across a latitude circle in the Northern Hemisphere vs. latitude: (1) for an earth with no latitudinal structure and no axial tilt (dashed curve), (2) for an earth with no latitudinal structure, but with an axial tilt (solid curve), (3) for the actual earth with axial tilt and latitudinal structure included (circles), and (4) for the approximation given by eq. 14 (x's). 9

10 Meridional energy transports Conceptually, the energy transports can be written as H A = E A M A ; H O = E O M O, (3) where M denote mass transport and E the flow-weigthed energy difference. Atmosphere: E A = c A T A + gz + L v q (moist static energy). Ocean: E O = c O T O. H O H A = E O E A MO M A Here follows an illustration of the atmosphere ocean overturning in the energy-latitude plane (Czaja and Marshall, 2006): 10

11 Annual-mean meridional overturning (Eulerian) Atmosphere (ERA40) Tellus A Page 30 of Ocean 4 (model 5 simulation) 6 7 STC=Subtropical 8 cells 9 D=the Deacon Cell 10 NADW=North Atlantic Deep 11 Water cell 12 AABW=Antarctic Bottom 13 Water Cell STC NADW STC D 4. AABW The atmospheric meridional 11

12 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 63 FIG. 9. Annual mean atmospheric (black) and oceanic (gray) mass streamfunction within constant energy layers. The contour interval is 10 Sv, dashed when circulating anticlockwise. The y axis is an energy coordinate (C ) in units of 10 4 J kg 1. The oceanic cells are the same as shown in Fig. 7 (annual mean) while the 12

13 MAY 2006 C Z A J A A N D M A R S H A L L 1499 FIG. 2. Schematic of the distribution of atmospheric moist potential temperature ( A, i.e., moist static energy) and oceanic potential temperature ( O ) as a function of latitude and height (black contours). The equator is indicated as a vertical dashed line. FIG. 1. (a) Estimates of oceanic (H O, gray) and atmospheric (H A, black) heat transport in PW (1 PW W). (b) Relative contribution of ocean (gray) and atmosphere (black) to the total energy transport H H O H A using (a). Continuous curves correspond to NCEP-based estimates, while dashed curves correspond to ECMWF-based estimates. The ratios in (b) were not plotted in the deep Tropics (2 S 2 N) where H A H O vanishes. mosphere and potential temperature referenced to the surface for the ocean). Such a decomposition is commonly carried out in oceanography (e.g., Talley 2003). tor forms a pronounced thermocline. In the atmosphere, by contrast, tropical deep convection acts to return the fluid to marginal stability to moist processes in which A, the moist static energy, has weak vertical gradients. The state of affairs is schematized in Fig. 2. Hence, as Held (2001) emphasized, dominance of ocean heat transport over atmospheric is expected in the deep Tropics. It is not straightforward to carry this argument to mid-to-high latitudes where it is well established that atmospheric transient eddies cannot be ignored when estimating meridional mass transports. Thus we might expect A and O to decouple moving away from the 13

14 (a) (b) (c) (d) Fig. 2. Configurations of the ocean basins on the aqua-planet: grey denotes Ocean-planets of Enderton and Marshall. Thelight model has ocean, a resolu in both fluids. The simplified atmospheric tion of black about physics land. 2.8 The land, when present, comprises a thin strip running in a 180 arc from pole includesto radiation, boundary layer, and convection. There is a therpole and does not protrude into the atmosphere. Meridional gaps are introduced in the modynamic ice model and the GM scheme is applied in the ocean. thin strip of land in EqPas and Drake. Where there is ocean, its depth is a constant 5.2 km. 14

15 The partitioning in idealized experiments Enderton and Marshall (in press) report simulations with a coupled model on an ocean-covered planet. Their atmospheric model has 5 vertical levels and simplified physics. They consider 4 versions of single-basin geometries: Ridge has a one-grid cell land barrier connecting the poles, i.e. a single basin with meridional boundaries. A warm climate without sea ice. Drake is similar but has a circumpolar channel in the south, where there is sea ice. EqPas is similar but has a periodic channel in the tropics. A warm climate without sea ice. Aqua has an ocean without meridional boundaries. Polar sea-ice caps. 15

16 C !10 Aqua Surface Air Temperature Aqua Ice Extent Aqua Ice Extent!20!60! Latitude EqPas Surface Air Temperature C Ridge Surface Air Temperature !10!20!60! Latitude Drake Surface Air Temperature Drake Ice Extent C 10 C !10!10!20!60! Latitude!20!60! Latitude 16 Fig. 4. Zonal mean surface air temperature ( C) for the coupled calculations; the black

17 Fig. 5. Total (top), oceanic (bottom left), and atmospheric (bottom right) heat transport 17

18 Summary of results In the simulations of Enderton and Marshall H T remains nearly constant, despite drastic changes in H O and H A. Note also the compensating changes in α(φ) and I(φ)! Qualitative similar compensating transport changes have been reported by Seager et al. (2002) [GCM results] and Vallis and Farneti (2009) [idealized ocean-planet model]. Although that H T varies little in these simulations, there can be profound changes of the high-latitude near surface climate: Regimes with strong atmosphere and weak ocean transports generally have larger sea-ice extents. 18

19 Aqua,! and " res Ridge,! and " res Pressure [hpa] Pressure [hpa] Ice Ice No Ice No Ice 30 Depth [m] Depth [m] !60! Latitude 2000!60! Latitude 0 EqPas,! and " res Drake,! and " res Pressure [hpa] Pressure [hpa] No Ice No Ice Ice No Ice 30 Depth [m] Depth [m] !60! Latitude 2000!60! Latitude 0 19 Fig year time and zonal mean potential temperature (shading) and overturning (black contour lines). Atmosphere and ocean potential temperature contour intervals are

20 A conceptual atmosphere ocean Hadley cell S(y) The Ekman-layer transports M A and M O set the meridional overturning cell strengths. The energy transport induced by eddies and horizontal gyre circulation is neglected. (cf. Held, 2001) 20

21 Ekman Transports and Overturning (775 mb); NCEP annual-mean data !M A M O! A Zonally!integrated Ekman transport Transport (Sv) 25 0!25!50!75!100!30!20! Latitude M A (y) = τ/f dx, and M O (y) = C O τ/f dx; ξ M A /M O. 21

22 Model assumptions 1. The strength of the meridional overturning cells set by the surface Ekman transport. 2. The energy transport induced by eddies and horizontal gyre circulation is neglected. 3. The upwelling is concentrated to the equator; no interactions with the extratropics and the deep ocean 4. The model has singular features at the equator and the poleward cell boundary. 22

23 Hadley Cell transports; the atmosphere In the surface branch, E A = c A T (y) + L v q s (y), where T (y) is the SST and q s the surface specific humidity. In the upper branch (assuming adiabatic ascent from the equator), E A = c A T (0) + L v q(0). Accordingly. E A (y) = c A [T (0) T (y)] + L v [q s (0) q s (y)] For saturated conditions E A c A (Γ d /Γ m ) T A ; where T A T (0) T (y) and Γ d /Γ m = 1 + L v /c A dq /dt. 23

24 Hadley Cell transports; the ocean In the surface branch, E O = c O T (y). in the thermocline branch, E O is set by the flow-weigthed surface temperature distribution of the downwelling waters. Calculations (Klinger and Marotzke, 2000) show that E O (y) = c O M O yp y M O dt dy dy C O T O (y). (4) A constant surface temperature gradient and M O (1 y/y P ) b, yields T O (y) = (1 y/y P ) 1+b y dt P dy. For b = 1, T O (0) = 0.5 y dt P dy ; i.e. the maximum T O is half of the surface temperature range. 24

25 Hadley Cell transports; the partitioning H O H A c O T O c A (Γ d /Γ m ) T A MO M A. (5) Note that M O /M A 0.8 averaged over the Tropics and c O /[c A (Γ d /Γ m )] 1.3. Thus, H O /H A T O (y)/t A (y). Note that T A increases poleward whereas T O decreases. We now present result from calculations based on zonal-mean values of surface temperature, specific humidity, and zonal wind stress; data from the World Ocean Atlas 2005 and NCEP. 25

26 6 5 Eneregy diff.:!t,!h/c O Energy Transports ATM OCE NET Kelvin Peta Watt 0.2 0!0.2!0.4!0.6 0!30!20! Latitude!0.8!1!30!20! Latitude 26

27 The Model Energy Transport; summary 1. The conceptual model gives a plausible explanation for why the ocean transport exceeds the atmospheric one near the equator in the Hadley cell. 2. However, the model under estimates the energy transports. From observations H A + H O 3 PW at 15, whereas the model yields 1 PW. 3. Energy transport induced by eddies and gyres are important, particularly near the poleward cell boundary (cf. Hazeleger et al., 2004). 27

28 SST ( C ) 24 o N 12 o N 0 o 12 o S 24 o S 120 o E 140 o E 160 o E 180 o W 160 o W 140 o W 120 o W 100 o W 80 o W 60 o W

29 Mid latitude transports; the atmosphere 1 Here the eddies do the transport. We assume diffusive energy transport (Vallis and Farneti, 2009): v h = k h y, (6) where k is the eddy diffusivity; it depends on the basic state in some complicated fashion. The energy transport scales roughly as H A c A (Γ d /Γ m ) T A ρ A k H d, (7) where H d is the density scale height and T A the temperature difference across the baroclinic zone. The eddy-induced mass transport is M A ρ A kh d and E A c A (Γ d /Γ m ) T A. 29

30 Mid latitude transports; the atmosphere 2 The surface winds stress is approximately related to the verticallyintegrated PV flux: τ s ρ A v Q dz, (8) where Q is the potential vorticity. Assuming diffusive PV transport (accomplished by the same eddies that transport energy): v Q = k Q y kβ. (9) Thus the surface wind stress scale as τ s ρ A kh d β, which implies that M A τ s β 1. (10) 30

31 Mid latitude transports; atmosphere/gyres From the Sverdrup relation, the mass transport in wind-driven ocean gyres scale as Thus, the partitioning is given by H O H A M O τ s β 1. (11) c O T O c A (Γ d /Γ m ) T A, (12) where T O is the flow-weigthed temperature difference in the gyre. The partitioning between the oceanic gyres and atmospheric eddies should depend primary on the thermal contrast in the two fluids. If τ s increases, both H A and H O should increase. 31

32 Thermohaline circulation (THC); 1 The classical thermocline scaling predicts that M O b 1/3 κ 2/3 A 2/3, where b is the buoyancy difference, κ the turbulent vertical diffusivity, and A the basin area. The rate of work performed by the turbulent mixing: E = ρ 0 κn 2 dz κ b. Thus, κ E/ b which yields (Nilsson and Walin, 2001) M O b 1/3 (E A) 2/3. (13) For fixed E, the THC decreases with increasing b! Note that b = b T + b S ; frequently b S < 0. 32

33 Thermohaline circulation (THC); 2 Main factors that control the mixing energy E: 1) Large-scale surface winds E τ. 2) Hurricanes E H ; depends on SST, atmospheric shear, etc. 3) Tides E T, depends on basin topography and N. H O c O T b 1/3 (E A) 2/3 ; E = E τ + E H + E T. (14) The THC induced heat transport is partly decoupled from the largescale atmosphere circulation. Assume (incorrectly) that b T, then H O ( T E A) 2/3. 33

34 THC, hurricanes, and equable climates A conceptual model of equable climates with warm poles and strong ocean transport (Emanuel, 2002). Key elements: 1) E H q (SST ) 3 ; the mixing increases rapidly with SST 2) Also the ocean transport increases H O T 2/3 q (SST ) 2. 3) The atmospheric circulation slows down; below a threshold deep convection emerges in the subtropics. This moistens the clear skies and reduces the OLR. 4) To compensate, the high latitudes warms to elevate the OLR. Compared to the present state, the equable climate has slightly warmer Tropics but much warmer poles. 34

35 Potential hurricane intensity (Korty et al., 2008) 648 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 8. The annually averaged PI of tropical cyclones in (a) a simulation with interactive mixing and 338-ppm CO 2 and (b) a simulation with interactive mixing and 3380-ppm CO 2. are considerably warmer (not shown), and the potential intensity increases (Fig. 8), which leads to stronger mixing through (8). Throughout the tropics, PI values are 10% (near the equator) to 40% (at the subtropical edge) higher in Fig. 8b than in Fig. 8a; note the rapid transition to small PI values in the subtropics of both simulations. The increases in PI force the values of, via (8), to be substantially higher in the warm climate than in the present one. Figures 9a,c,e show the total value of in both the present climate and Figs. 9b,d,f Note that P I 2 q (SST ) and E H P I 6. The role of hurricanes for the THC remains an open question. 35

36 Stommel and Csanady (1980) A relation between the T -S curve and the global heat and atmospheric water transport. The idea: H O c O T M O. The oceanic freshwater transport is F O ( S/S 0 )M O. Since F O = F A, one obtains H O L v F A = c O T L v ( S/S 0 ) 0.5. (15) A caveat is that the M O carrying heat is different from the one carrying salt. Suppose that sea-ice transports (F I ) balances F A. (L I F I )/(L v F A ) = L I /L v

37 Salinity, Atlantic 20W (LGM simulation) 38!0.5!1!1.5! Depth (km)!2.5!3 36!3.5!4!4.5! !60!40! Latitude 34 Sea-ice freshwater transport important in this coupled-model simulation (with the CCSM3)! 37

38 Bjeknes compensation Bjeknes (1964) proposed that on decadal timescales anomalies in the meridional energy transport in the ocean and the atmosphere should be of the opposite sign, acting keep the total transport nearly preserved. If the storage in the ocean does not vary significantly, Bjerknes compensation is expected from Stone s steady-state argument that H T should be fairly constant. Let s look at Bjerknes compensation in the idealized ocean-planet model of Vallis and Farneti (2009): 38

39 [PW] 0 OHT AHT PHT R[OHT!AHT] =!0.71! [years] Low-passed filtered variability of H averaged between 30N and 60N [PW] 0

40 6026 J O U R N A L O F C L I M A T E Low-passed filtered correlation between H T and H A from Hadley Centre model (van der Swallow et al., 2007). Note the positive correlations in the tropics. 40

41 Bjeknes compensation in the simulations In the simulations, Bjerknes compensation occurs partly on decadal timescales. It is the overturning ocean circulation that drives anomalies in H T, to which the atmosphere compensate. In the Hadley Centre model, changes in salinity and sea-ice cover are important dynamical elements. In the idealized model of Vallis and Farneti (2009), Bjerknes compensation is essentially absent in the (southern) hemisphere with the circumpolar channel. 41

42 Correlation of H_A and H_O with H_T 1 AHT!PHT Atoms.!0.5! !0.5 60S 40S 20S 0 20N 40N 60N Latitude OHT!PHT Decadal data Annual data Ocean!1 60S 40S 20S 0 20N 40N 60N Latitude Figure 10. Top: correlation between atmospheric energy transport and planetary (total) energy transport. Bottom: correlation between oceanic energy transport and planetary (total energy transport. Thick solid lines is the correlation from low-passed time series (a decade and longer) and the dotted lines allow successively shorter time scales to pass. The thick dashed lines use annual averaged time series. Vallis and Farneti (2009) 42