Can Planetary Wave Dynamics Explain Equable Climates?

Can Planetary Wave Dynamics Explain
Equable Climates?
Sukyoung Leea , Steven Feldsteina , David Pollardb , and Tim Whiteb
a
Department of Meteorology, The Pennsylvania State University, University Park,
Pennsylvania
b
Earth and Environment Systems Institute, The Pennsylvania State University,
University Park, Pennsylvania
May 3, 2010
Corresponding author address: Dr. Sukyoung Lee, Department of Meteorology, The
Pennsylvania State University, University Park, Pennsylvania 16802, USA. E-mail:
[email protected]
Abstract
Viable explanations for equable climates of the Cretaceous and early Cenozoic (about
145 to 50 million years ago), especially for the above-freezing temperatures detected for highlatitude continental winters, have been a long-standing challenge. In this study, we suggest
that enhanced and localized tropical convection may be capable of triggering a high-latitude
warming through the excitation of poleward propagating Rossby waves. This warming takes
place through the poleward heat flux and overturning circulation that accompany the Rossby
waves. This mechanism is tested with an atmosphere-mixed layer ocean general circulation
model (GCM). By comparing results from two GCM runs, one with localized tropical heating
and the other without, we find that the run with the heating produces substantially warmer
high-latitudes. Given a contrast of 200 W m−2 between the localized tropical heating and
compensating cooling elsewhere in the tropics, the high-latitude temperature increase is as
large as 16o C in the Northern Hemisphere (NH) winter. This result suggests that through
Rossby wave dynamics an enhanced and localized tropical heating may be able to significantly
reduce the pole-to-equator temperature difference.
1
1
Introduction
Proxy data indicate that climates during the Cretaceous and early Cenozoic (from about
145 to 50 million years ago) were more equable than the present-day climate, with smaller
latitudinal variations in surface air temperature (Huber 2008; Spicer et al. 2008). The
primary suspect is higher levels of greenhouse gases. General circulation model (GCM)
experiments show that CO2 levels of at least 10 × P AL (Preindustrial Atmospheric Level,
1 P AL = 280 ppmv) are needed to produce the observed high-latitude continental winter
warmth (e.g., Bice et al. 2006; Poulsen et al. 2008; Hunter et al. 2008), but these levels
significantly exceed those of recent proxy estimates for the Cretaceous and early Cenozoic:
≈ 4 − 8 × P AL (Bice et al. 2006); 4 × P AL (Fletcher et al. 2008).
Mechanisms proposed to date include an enhanced poleward oceanic heat transport (e.g.,
Barron et al. 1993; Sloan et al. 1995), a warming caused by substantially greater polar
stratospheric cloud cover (Sloan and Pollard 1998; Sloan et al. 1999, Kirk-Davidoff et al.
2002), a greatly expanded Hadley cell (Farrell 1990), a convection-cloud radiative forcing
(CCRF) feedback (Sewall and Sloan 2004; Abbot and Tziperman 2008a,b), a vegetationclimate feedback (Otto-Bliesner and Upchurch 1997; DeConto et al. 2000), an intensification
of the thermohaline circulation due to driving by tropical cyclones (Sriver and Huber 2007;
Korty et al. 2008), and a decreased cloud reflectivity due to a reduction in the number of
cloud condensation nuclei (Kump and Pollard 2008).
In this study, we propose and then test the mechanism that enhanced and localized
tropical convection can trigger the high-latitude warming through the excitation of poleward propagating planetary-scale Rossby waves. Our proposed mechanism is based on the
2
premise that under the high CO2 loading conditions, tropical convection was more intense
and localized than during the present-day climate. The rationale for this premise is that
as the tropical sea surface temperature (SST) increases everywhere, due to the higher CO2
loading, tropical convection over the western part of the largest ocean basin (warm pool,
hereafter) will intensify more rapidly than elsewhere because saturation vapor pressure is
an exponential function of temperature (the Clausius-Clapeyron equation). Based on the
Clausius-Clapeyron relation, Held and Soden (2006) formulated a scaling for the sensitivity of precipitation−evaporation (P−E) to surface temperature change. In response to a
surface temperature increase, their theoretical prediction shows that the largest increase in
P-E occurs over the Indian and western Pacific Oceans. As shown in Fig. 1, the change
in the convective precipitation over the latter half of 20th century also exhibits maximum
increase over the tropical western Pacific and eastern Indian Oceans. Although other processes may be involved in the change shown in Fig. 1, since the surface air temperature has
increased during this time period, the western-Pacific/eastern-Indian Ocean intensification
of the convective precipitation is at least consistent with the theoretical expectation based
on the Clausius-Clapeyron relation. Because the core of the proposed mechanism hinges on
a warmer tropical SST, the proposed mechanism may also be applicable for climates under
other conditions, such as those characterized by stronger solar radiation, as long as they
cause the tropical SSTs to increase.
To the best of our knowledge, there are no paleotemperature estimates available for the
western Pacific warm pool region. However, paleotemperature estimates from the western
Atlantic at the Demerara Rise during the Cenomanian-Turonian period (Forster et al. 2007)
indicate values that range between 32o C and 43o C, with a typical value of 36o C − 37o C.
3
Therefore, if we assume that a similar SST increase relative to the present-day climate
occurred in other tropical oceans, and that a warm pool existed in the western part of the
paleo Pacific ocean, as in the present-day climate, these paleotemperature estimates suggest
that the SSTs in the western Pacific warm pool region were higher than the present-day
values by at least 6o C. While the precise SST values differ between Cretaceous simulations,
Bush and Philander (1997) and Otto-Bliesner et al. (2002) support the assumption that the
warmest SSTs would have occurred over the paleo Indian and western Pacific Oceans.
One advantage of this mechanism is that it is at best only weakly dependent upon
the equator-to-pole temperature gradient. As a result, if enhanced and localized tropical
convection takes place, it can readily generate a high-latitude warming in the presence of a
wide range of background equator-to-pole temperature gradients.
In section 2, we present a theoretical and empirical basis for this mechanism. The GCM
employed for this study will be described in section 3 and the experimental design is presented
in section 4. The results are presented in sections 5-7, and the conclusions will follow in
section 8.
2
Mechanism: planetary wave dynamics as the warming mechanism
The mechanism that we propose is that enhanced tropical convection is capable of generating planetary-scale Rossby waves which, through the attendant poleward heat flux and
overturning circulation (refer to Fig. 2), can trigger high latitude warming. Although these
tropical Rossby waves are not generated by baroclinic instability, as these waves propagate
4
poleward where the zonal wind is westerly, they can also propagate upward (Charney and
Drazin, 1961). Because upward propagating waves transport heat poleward, the tropically
forced Rossby waves, in principle, can generate a poleward heat flux.
This overturning circulation associated with poleward Rossby wave propagation needs
further explanation. For Rossby waves, the poleward propagation into high latitudes must
accompany a transport of eastward angular momentum out of high latitudes (for external
Rossby waves, the angular momentum transport is always in a direction opposite to that of
the wave propagation (Held 1975). This momentum transport results in a force imbalance,
and as a response, an overturning circulation develops with sinking motion at even higher
latitudes and rising motion in midlatitudes. This process of inducing vertical motions, which
is ubiquitous throughout the atmosphere, is known as thermal wind adjustment (e.g., Holton
2004). The impact of these vertical motions is to adiabatically warm high latitudes and
adiabatically cool midlatitudes (see Fig. 2b).
3
Model Description
This mechanism is tested using a coupled atmosphere-mixed layer ocean GCM that has
a local heat source which is designed to mimic warm pool convective heating. One may
question whether a coupled atmosphere-dynamic ocean GCM is more suitable because such
a model can generate an internally consistent SST and convective precipitation. However,
for our purpose, there are two reasons why a mixed layer ocean model is a better choice
than a dynamic ocean model. First, there is the question of model fidelity in simulating
the distribution and intensity of tropical convective precipitation. As was shown by Lin et
5
al. (2006), even amongst the latest versions of the coupled models which participated in
the IPCC AR4, there is large inter-model scatter in the intensity (a factor of two difference
between some models) of the Indo-Pacific warm pool tropical precipitation.
More importantly, even if we are given a perfect coupled model, with such a model it
is difficult to tease apart the impact of tropically forced atmospheric waves from influences
caused by other processes. For example, changes in the greenhouse gas composition may
influence extratropical ocean circulations which can also warm the Arctic. If such a process
does indeed occur in the real world, and if the perfect coupled model can precisely simulate
this process, the presence of this process would makes it difficult to isolate the effect of the
proposed mechanism on the Arctic warmth.
Given the above consideration, it is desirable to use a static ocean model for this study.
One viable choice is a mixed-layer ocean with no ocean currents but with diffusive heat
transport. The lack of an explicit ocean circulation means that the model poorly simulates
zonally asymmetric oceanic features such as the western warm pool, and the east-west distribution of tropical convective heating (see Figs. 3a and 3c in Thompson and Pollard (1997)).
For this reason, the intensity of tropical heating perturbations was estimated empirically
and imposed in the model.
The experiments presented in this study use GENESIS version 2.3, a GCM which is
composed of an atmospheric model coupled to multilayer models of vegetation, soil, land,
ice, and snow (Thompson and Pollard, 1997). Sea-surface temperatures and sea ice are
computed using a 50-m slab oceanic mixed layer with diffusive heat fluxes. The atmospheric
GCM has a T31 spectral resolution (≈ 3.75o ) with 18 vertical levels, and the grid for all
surface components is 2o ×2o . The GENESIS GCM has been used extensively in paleoclimatic
6
applications; previous Cretaceous studies include DeConto et al. (2000), Bice et al. (2006),
Poulsen et al. (2007), Zhou et al. (2008), and Kump and Pollard (2008).
For the Cretaceous simulations in this study, the boundary conditions were those used
in Poulsen et al. (2007) for the middle Cretaceous, including Cenomanian paleography
and topography with high sea-level stand, a reduced solar luminosity (1354.4W m−2 ), and
a circular orbit with obliquity (23.5o ), similar to modern values. A uniform land-surface
corresponding to a savanna biome was specified. The ocean diffusive heat-flux coefficient
was set to a value that provides the best simulation of the modern climate.
4
Experimental Design
In light of our aim to test the hypothesis that enhanced and localized tropical heating can
excite Rossby waves which can in turn warm the Arctic, we perform two model runs. One
model run is with a specified local heating profile, to be described below, and the other run
lacks this imposed heating. By comparing these model runs, we are isolating the impact of
localized tropical heating upon the Arctic surface air temperature. It is important to keep in
mind that this approach has limitations, since it does not take into account various processes
such as the impact of the heating on the ocean circulation. As such, one should regard the
findings of this study as a qualitative assessment of Arctic warming due to localized tropical
heating.
The horizontal structure of the tropical heating in the model is based on the present-day
tropical precipitation distribution. Because our primary focus is on the warming mechanism in the Northern Hemisphere (NH) high latitudes during the winter, the present-day
7
precipitation field during the months of December, January, and February (DJF) is used to
determine the model heating. For the present-day climate, over the warm pool, the estimated
latent heating is approximately 320 W m−2 . Over the rest of the tropics, the average latent
heating is approximately 160 W m−2 . Thus, for the present-day climate, the warmest part
of the tropical ocean is associated with an additional 160 W m−2 of heating compared with
other tropical locations. Because of the larger amount of CO2 in the atmosphere during
the Cretaceous and Cenozoic, it is to be expected that the warm pool convection during
that time period would have been stronger and more localized than that of the modern-day
climate (Bush and Philander 1997).
For our estimation of the tropical heating, we first assume that the CO2 level for the
Cretaceous and Cenozoic was 4×P AL. If the lower tropospheric air temperature increases by
3o C for every doubling of CO2 (according to the IPCC AR4, most GCMs predict temperature
increases between 2o C and 4.5o C), for an increase of CO2 to 4 × P AL, the temperature
would increase by about 6o C. If the precipitation rate increases by 2 % for every 1o C
increase (Held and Soden 2006), then for a CO2 concentration of 4 × P AL, the precipitation
rate would increase by 12 %. If one assumes that this increase occurs uniformly over the
entire tropics, the difference in latent heating between the warm pool and the rest of the
tropical ocean would be about (320 W m−2 − 160 W m−2 ) × 1.12 ≈ 180 W m−2 . Because
most precipitation occurs over the warm pool, if this increase occurs primarily in that region,
then the difference in latent heating between the warm pool and elsewhere would instead be
320 W m−2 × 1.12 − 160 W m−2 ≈ 200 W m−2 . To this end, we emphasize again that the goal
of this study is to perform a proof-of-concept test of our proposed hypothesis, rather than
to present the hypothesis as the mechanism for the Cretacous equable climate. It is from
8
this perspective that we justify using the above estimated heating rate for our calculation.
Atmospheric CO2 levels in these experiments were set to either 4× or 8× its pre-industrial
value (1120 or 2240 ppmv, respectively). For experiments with imposed diabatic heating,
as discussed above, a constant heating term was applied to the GCM atmosphere, with
a vertically integrated column total, Qo , of 150W m−2 (or 75W m−2 for some experiments).
The heating was distributed vertically with a parabolic dependence on σ (≡ pressure/surface
pressure), with non-zero values ranging between σ = 0.15 and 0.75, and a maximum heating
at σ = 0.5. This was applied uniformly between latitudes 10o S and 10o N , and from longitudes
10o E to 100o E ((see the red-boxed area in Fig. 3), a region approximately akin to the
present-day warm pool. For this reason, although there is no warm pool in the slab ocean,
this region will be referred to as paleo warm pool. A corresponding cooling with the same
vertical profile was applied uniformly between the same latitudes and throughout all other
longitudes (see the blue-boxed area in Fig. 3), so that the net zonal and global mean heating
is zero. For Qo = 150W m−2 , the heating difference between the heated and cooled region is
200W m−2 , the estimated value discussed above. Similarly, for Qo = 75W m−2 , the heating
difference is 100W m−2 .
The primary model runs that are analyzed in this study are the experiment run (EXP),
where Qo = 150W m−2 , and the control run (CTL) with Qo = 0 W m−2 (no imposed heating
and cooling). In both runs, the atmospheric CO2 loading is 4 × P AL. As discussed earlier,
because of the absence of ocean currents in this model, without the added heating, there
is essentially no zonal variation in tropical heating. Therefore, by comparing the model
responses between the EXP and CTL runs, we can test whether the zonal variation in
the tropical heating can warm the high latitudes. Accordingly, most model results will be
9
presented as the difference between the time mean states for these two model runs. For a
given model variable, F, the difference, F(EXP )−F(CT L), will be denoted as δF. Because
the NH high-latitude warmth is the primary feature of equable climates, this paper will focus
on January for the NH.
5
Surface warming and stationary wave
The difference in the January surface air temperature at the lowest model level (σ = .933),
δT (Fig. 3), shows warming at high latitudes and an overall cooling in the tropics. The
warming in the Arctic reaches as high as 16o C. This δT field demonstrates that the zonal
localization of the tropical heating, without a net increase in the tropical heating, is capable
of substantially warming the Arctic surface air temperature. Figure 3 also shows that the
mid-tropospheric heating cools the surface at the location where the heating is imposed. In
fact, this surface cooling also extends to the subtropics. As we will discuss below, dynamic
processes associated with Rossby waves forced by the heating can account for this cooling.
The high latitude surface warming is accompanied by stationary waves. The January
250-hPa geopotential height (δZ) field (Fig. 4a) shows a poleward propagating wave train
(see the arching arrow in Fig. 4a) which emanates from a subtropical high centered at (40o ,
30o N ). Being to the northwest of the imposed heating, the location of the subtropical high
conforms to the Rossby wave response to a local tropical heating, as was shown by Gill
(1980). The wave signatures are more evident if the zonal mean field is subtracted from the
total field. The resulting flow field, which will be referred to as the eddy field, is shown in
Fig. 4b.
10
Originating from the heating region, the waves are seen to first propagate poleward and
then to turn equatorward. The equatorward turning can be inferred from the northeastsouthwest tilt of the eddies poleward of 30o N between −180o and −120o . The first wavetrain
(indicated by the solid arrow in Fig. 4b) is reminiscent of the present-day Pacific North
American (PNA) teleconnection pattern (Horel and Wallace 1981; Wallace and Gutzler
1981; Barnston and Livezey 1987) for which tropical heating is shown to play an important
role (Schubert and Park, 1991; Mori and Watanabe 2008; Johnson and Feldstein 2010). The
stationary wave response is weaker in July (not shown) in both NH and SH, indicating that
the January NH flow is conducive to generating a large-amplitude stationary wave response
to the tropical heating. Again, this finding is consistent with the present-day PNA growth
mechanisms (Simmons et al. 1983; Feldstein 2002).
6
Surface warming attributes
To quantitatively assess the proposed mechanism, we consider an appropriate thermodynamic equation. Taking a time and zonal average, the thermodynamic energy equation in
pressure coordinates can be written as
0=
∂[vT ]
∂[T ]
=−
+ [Sp ω] − γ[T ] + [Qr ],
∂t
∂y
(1)
where the notation follows Lorenz (1968), with the overbar denoting the time mean, and
the square bracket the zonal mean. Other notations are standard; T is temperature, v the
meridional velocity, ω ≡ dP/dt, where P is pressure. The first term on the right-hand-side
is the meridional convergence of the heat flux. The second term on the right hand side
∂θ
accounts for adiabatic warming (downward motion) or cooling (upward motion); Sp ≡ − Tθ ∂z
11
is a static stability parameter, where θ is potential temperature. The third term, γ[T ],
represents radiative cooling, where γ −1 is the radiative relaxation time scale. Finally, [Qr ]
represents the remaining diabatic heating contribution.
For the Arctic winter, the thermodynamic energy equation can be further simplified.
First, the diabatic heating [Qr ] may be neglected because the Arctic winter receives virtually
no sunlight and latent heat release is negligible. In order to evaluate the effect of the
stationary eddies (Fig. 4b) on the Arctic warming, it is useful to decompose the heat flux
term into a contribution from the eddies and from the zonal mean meridional flow. In
the extratropics, the eddy contribution is much greater (Pexioto and Oort 1992), and thus
the zonal mean component can be neglected. After making these assumptions, (1) can be
rewritten as
!
δ[T ] ≈ γ −1
∂
∂
∗
δ[v 0∗ T 0∗ ] + δ[ωSp ] ,
− δ[v ∗ T ] −
∂y
∂y
(2)
where the asterisk denotes a deviation from the zonal mean, and the prime a deviation from
the time mean. The first term on the right hand side represents the meridional convergence
of heat by stationary eddies and the second term by transient eddies. This equation states
that Arctic warming will occur if the sum of the heat flux convergence and adiabatic warming
is positive in that region.
As was hypothesized, the eddy heat flux convergence is found to contribute to the NH
winter high latitude warming. Figure 5a shows that the change in the stationary eddy heat
flux convergence, caused by the localized tropical heating, warms the lowest model level
(σ = 0.993) across a broad zone encompassing between 17o N and 62o N . An exception is
the narrow latitudinal range centered at 40o N . This warming is compensated by cooling in
12
the tropics, and to a lesser extent by cooling poleward of 62o N . Between 48o N and 60o N ,
the warming occurs at values ranging between ≈ 2 × 10−6 Ks−1 and ≈ 6 × 10−6 Ks−1 . If
γ = 30−1 day −1 , (2) indicates that the warming caused by the stationary eddy heat flux at
these latitudes is between 5 K and 15 K.
The response of the transient eddies to the tropical heating (Fig. 5b) results in a low
level warming that is comparable to that by the stationary eddies, except that the transient
eddy warming is confined to a smaller range of latitudes and occurs farther poleward. Again
if we assume that γ = 30−1 day −1 , the warming caused by the transient eddy heat flux
convergence at these latitudes can reach 15 K. The temperature changes caused by these
eddy heat fluxes are comparable to the lowest model level δT (Fig. 2b). The sum of the
stationary and transient eddy heat flux convergences (Fig. 5c) shows that the strongest
warming occurs between 50o N and 80o N .
Poleward of 70o N , adiabatic warming plays a greater role in warming the surface. Figure
6a shows that between 70o N and 82o N , the anomalous adiabatic warming, δ[ωSp ], accounts
for a surface warming of up to ≈ 5 × 10−6 Ks−1 . Once again assuming γ = 30−1 day −1 , the
resulting warming would be about 5K − 13K. This anomalous adiabatic warming (δ[ωSp ])
can be explained mostly by changes in the (Sp [δω]) contribution, as can be inferred from δω
(Fig. 6b).
As was discussed in Section 2, δ[ω] arises from an adjustment to changes in the heat and
momentum fluxes. First, considering the stationary eddy momentum flux convergence, a
comparison between the sign and location of δ[ω] and the stationary eddy momentum flux
∂
∂
convergence, −δ ∂y
[u∗ v ∗ ] (Fig. 7a), indicates that changes in − ∂y
[u∗ v ∗ ] contribute to the
excitation of the adiabatic warming in the Arctic. To help facilitate the comparison, the
13
∂
vertical motion that would be driven by −δ ∂y
[u∗ v ∗ ] is shown schematically in Fig. 7a. [The
vertical motion in Fig. 7 is inferred by assuming that the secondary circulation induced by
∂
−δ ∂y
[u∗ v ∗ ] opposes the impact of the eddy driving. This results in a poleward flow in the
∂
upper troposphere where corresponding −δ ∂y
[u∗ v ∗ ] is negative, and vice versa. Mass conser-
vation then implies the vertical motion shown by the arrows in Fig. 7.] This vertical motion
field indicates a qualitative agreement with that shown in Fig. 6b. It is also worthwhile to
∂
[u∗ v ∗ ] for the simulated stationary wave (Fig. 7a) agrees with
note that the pattern of −δ ∂y
the west-east acceleration pattern (Fig. 2b) associated with the idealized stationary wave
(Fig. 2a). This finding supports the hypothesized mechanism that the vertical motion driven
by the stationary wave may contribute significantly to the high latitude winter warming. In
the Arctic where the adiabatic warming is taking place, the transient eddy momentum flux
convergence (Fig. 7b) is weaker than the stationary eddy momentum flux convergence (Fig.
7a), and the sum of these two convergences (Fig. 7c) would still drive a downward motion.
The eddy heat flux also drives overturning circulations, but because this portion of the
overturning circulations should oppose the effect of the heat flux, the eddy heat flux cannot
indirectly contribute to adiabatic warming in the region (between 50o N and 80o N ) where
the heat flux converges. Therefore, we are led to conclude that the adiabatic warming over
the region ranging between 70o N and 82o N can be ascribed primarily to the stationary eddy
momentum flux convergence.
Over the Arctic Ocean (poleward of 80o N ), the above dynamical process cannot directly
explain the warming, as the eddy heat fluxes and vertical motions all contribute toward high
Arctic cooling. Instead, the warming over the Arctic Ocean can be ascribed in part to an
increase in positive radiative forcing, as indicated by the increase in cloud cover (Fig. 8).
14
The CCRF mechanism (Sewall and Sloan, 2004; Abbot and Tziperman, 2008a,b) could be
responsible for this increase in Arctic Ocean’s cloudiness. However, at least in this model, the
ultimate source of this enhanced cloudiness is the dynamical response to localized tropical
heating. This can be understood if we consider the transient evolution of the flow from the
CTL to the EXP state. Initially, dynamical processes may first warm the Arctic Ocean.
Then, as the cloud cover increases, radiative forcing by the clouds could take over the
warming, and the influence of the dynamical processes would wane.
In the tropics, there is strong anomalous sinking motion (Fig. 6b) between the equator and 10o N , flanked by anomalous rising motion. These anomalous vertical motions are
consistent with the thermal wind adjustment that would arise from the stationary Rossby
waves shown in Fig. 2. Although the sinking motion warms the lower troposphere (Fig.
6a), the corresponding eddy heat flux divergence (Fig. 5a) is larger. As a result, the tropics
undergoes a cooling (Fig. 3a).
7
Ice/snow albedo feedback and sensitivity tests
The aforementioned dynamical processes, although the impetus behind the high latitude
warmth in our numerical model experiments, cannot explain all of the high latitude warming.
The dynamical warming is intense enough to melt snow and ice, as evidenced by the reduction
in the surface albedo (Fig. 9). Thus, the ice/snow-albedo feedback process may also play
a role in the high-latitude warming. Although the estimated dynamics-driven δT (see (2))
is comparable to the simulated value (Fig. 2), the presence of an ice/snow-albedo feedback
in the model raises the question as to whether the simulated warming depends in part
15
on this feedback process. If so, there may be a critical value in the dynamical warming
beyond which the ice/snow-albedo feedback starts to operate to bring about the required
high-latitude warming.
To test if the dynamical warming, produced by a prescribed tropical heating, is near the
critical value, additional model runs are preformed. Figure 10 shows the anomalous surface
temperature field, with Qo = 75 W m−2 , a value half that of the standard perturbation run
in this study. The CO2 loading level in this run is the quadrupled value as before. As can
be seen, the strength of the high-latitude warming is almost half of that shown in Fig. 3a,
suggesting that, at least in the parameter space spanned by 75W m−2 ≤ Qo ≤ 150W m−2 with
4 × CO2 , the relationship between the warming and the imposed tropical heat perturbation
is linear. Similarly, within a parameter region spanned between 2 × CO2 and 8 × CO2 , with
Qo fixed at 150 W m−2 , a nearly linear relationship is found between the CO2 loading and
the high latitude warming (not shown). It can be concluded therefore, at least for the CO2
loading and Qo values of interest, that the high-latitude warming is not sensitive to the
ice/snow-albedo feedback.
8
Concluding remarks and discussion
This study explores the hypothesis that localized tropical heating associated with a paleo
warm pool can excite poleward propagating Rossby waves which can generate the high
latitude warming associated with equable climates such as that of the Cretaceous and early
Cenozoic. For this purpose, we use an atmosphere-mixed layer ocean GCM with a localized
diabatic heating over the deep tropics, along with a compensating cooling at other longitudes.
16
By comparing results from two model runs, one with this heating field and the other without,
both with 4 × CO2 , we find that the run with the heating produces warmer high-latitude
surface air temperatures. For a tropical heating of 150W m−2 , an estimated value based
on the present-day warm pool convective heating, this increase in the high-latitude surface
air temperature can be as large as 16o C in the NH winter. Even though this study aims to
isolate impact of localized tropical heating, which implies that the result of this study should
be seen as no more than qualitative assessment, the above value suggests that this might be
a viable mechanism for generating warm high latitudes of equable climates.
Analysis of the thermodynamic energy equation shows that this high-latitude warming
during the NH winter can be ascribed to eddy heat and momentum fluxes associated with the
Rossby waves forced by the tropical heating. In addition to the warming by both stationary
and transient eddy heat flux convergence, the eddy momentum flux also contributes to the
warming through its induction of sinking motion which results in adiabatic warming over
high latitudes. Over the Arctic Ocean, the warming coincides with an increase in cloud
cover. Because solar radiation does not reach the Arctic Ocean in January, we interpret this
warming to have arisen from radiative forcing which is enhanced by the increase in cloud
cover. The increase in cloud cover, in turn, must be ultimately caused by the localized
tropical heating. Our interpretation is that the dynamical processes - meridional heat flux
and adiabatic warming - first warm the Arctic Ocean, hence increase the cloud cover. As
the cloud cover increases, radiative forcing by the clouds can take over the warming.
Although the above results suggest that the influence of localized tropical heating can
account for the high-latitude warming, it is important to keep in mind that there are limitations to the model used in this study. For example, as far as we are aware, there is no
17
evidence for a paleo warm pool in the Pacific, even though by analogy to the present-day
ocean circulation, it would not be surprising if there was a warm pool during the Cretaceous. Furthermore, the value of tropical heating is uncertain, especially because reasonably
accurate values of proxy SST in the hypothesized warm pool are not known. Given these
uncertainties, it is best to interpret our findings as representing a plausible mechanism for
the high-latitude warming, with the model temperatures representing possible values of the
high-latitude warming due to dynamical processes alone.
Notwithstanding these shortcomings, our assumption of a paleo warm pool along with
localized diabatic heating appears to be consistent with the findings of Bush and Philander
(1997), who used a coupled atmosphere-ocean GCM to examine Cretaceous climate. Their
model findings indicate the presence of a warm pool along with enhanced precipitation
that spanned the longitudes from approximately 30o E to 90o E. Furthermore, the increase
of the model precipitation in this region was found to be about 25% greater than that
outside of the model warm pool, a value which is twice that used in our GCM calculation.
Therefore, the dynamical high-latitude warming found in our study might be regarded as a
conservative estimate. Although they did not discuss the mechanism proposed in this study,
the atmospheric circulation shown by Bush and Philander (1997) indicates features that are
consistent with the workings of our mechanism. For example, their Cretaceous run shows
an upper tropospheric equatorial wind that is more westerly and a Hadley circulation that
is weaker than those for the present-day run. These features are consistent with increased
poleward Rossby wave propagation out of the tropics (cf. Fig. 2).
It is also important to indicate that the physical mechanism proposed in this study
represents a relatively minor adjustment from those processes that take place in present18
day climate. That is, besides the quadrupling of the CO2 , the heating added to the model
represents an increase in convective heating that would exist if there was a warm pool present
that was several degrees warmer than that observed today. The recent observed warming
during the Arctic winter may in part be due to the same physical mechanism, i.e., enhanced
precipitation in the tropics, and the ensuing high latitude warming due to the influence of
poleward propagating Rossby waves.
Finally, it is worthwhile to note that the localization of the mid-tropospheric tropical
heating is compensated by dynamical cooling caused by the Rossby waves that are excited
by the heating. If greenhouse gas warming causes tropical convective heating to be more
localized, as was discussed in Section 2, this mechanism implies that the cooling caused
by the eddy heat flux divergence may compensate for the greenhouse gas warming in the
tropics. Therefore, in the face of increased greenhouse gas loading, one may expect to find
a muted warming in the tropics.
Acknowledgments:
For this study, the first author was supported by National Science Foundation Grant
ATM-0647776, and the second author by National Science Foundation Grant ATM-0649512.
The authors acknowledge Dr. Dorian S. Abbot for his helpful comments on this manuscript,
and Mr. Changhyun Yoo for generating Figure 1.
19
References
[] Abbot, D.S. and E. Tziperman, 2008a: A high-latitude convective cloud feedback and
equable climates. Q. J. R. Meteorol. Soc. 134, 165-185.
[] Abbot, D.S. and E. Tziperman, 2008b: Sea ice, high-latitude convection, and equable
climates. Geophys. Res. Lett. 35, L03702, doi:10.1029/2007GL032286.
[] Allan, R. P., and B. J. Soden, 2008: Atmopsheric warming and the amplification of
precipitation extremes. Science, 321, 1481-1484. DOI: 10.1126/science.1160787
[] Barron, E.J., W.H. Peterson, D. Pollard and S.L. Thompson, 1993: Past climate and the
role of ocean heat transport: model simulations for the Cretaceous. Paleoceanography, 8,
785-798.
[] Barnston, A. G., and R. E. Livezey, 1987: Classification, seasonality, and persistence of
lowfrequency atmospheric circulation patterns. Mon. Wea. Rev., 115, 1083-1126.
[] Bice, K.L., D. Birgel, P./A. Meyers, K.A. Dahl, K.-U. Hinrichs and R.D. Norris, 2006: A
multiple proxy and model study of Cretaceous upper ocean temperatures and atmospheric
CO2 concentrations. Paleocean ogr., 21, PA2002, doi:10.1029/2005PA001203.
[] Bush, A. B., and S. G. H. Philander, 1997: The late Cretaceous: Simulations with a
coupled atmosphere-ocean general circulation model. Paleoceanography, 12, 495-516.
[] Charney, J. G., and P. G. Drazin, 1961: Propagation of planetary-scale disturbances from
the lower into the upper atmosphere. J. Geophys. Res., 66, 83-109.
20
[] DeConto, R.M., E.C. Brady, J.C. Bergengren and W.W. Hay, 2000: Late Cretaceous
climate, vegetation and ocean interactions in Warm Climates in Earth History, B. R.
Huber, K. G. MacLeod, S. L. Wing, Eds., Cambrige Univ. Press, pp. 275-296.
[] Emanuel, K., 2008: The hurricane-climate connection. Bull. Amer. Meteor. Soc., 89, 5,
ES10-ES20.
[] Farrell, B. F., 1990: Equable climate dynamics. J. Atmos. Sci. 47, 2986-2995.
[] Fletcher, B.J., S.J. Brentnall, C.W. Anderson, R.A. Berner and D. J. Beerling, 2008:
Atmospheric carbon dioxide linked with Mesozoic and early Cenozoic climate. Nature
Geoscience 1, 43-48.
[] Forster, A., Schouten, S., Baas, M., Sinninghe Damste, J., 2007: Mid-Cretaceous AlbianSantonian sea surface temperature record of the tropical Atlantic Ocean, Geology, 35(10),
919-922.
[] Gill, A. E., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J.
Roy. Meteor. Soc., 106, 447-462.
[] Held, I.M., 1975: Momentum transport by quasi-geostrophic eddies. J. Atmos. Sci. 32,
1494-1497.
[] Held, I.M. and Soden, B.J., 2006: Robust repsonses of the hydrological cycle to global
warming. J. Climate 19, 5686-5699.
[] Holton, J. R., 2004: An Introduction to Dynamic Meteorology. Academic Press, , 535 pp.
535 pp.
21
[] Horel, J. D. and J. M. Wallace, 1981: Planetary-Scale Atmospheric Phenomena Associated
with the Southern Oscillation. Mon. Wea. Rev., 109 , 813–829.
[] Huber, M., 2008: A hotter greenhouse? Science 321, 353-354.
[] Hunter, S. J., P. J. Valdes, A.M. Haywood and P. J. Markwick, 2008: Modelling Maastrichtian climate: investigating the role of geography, atmospheric CO2 and vegetation.
Clim. Past Discuss., 4, 981-1019.
[] Johnson, N. C. and S. B. Feldstein, 2009:
The continuum of North Pacific sea level
pressure patterns: Intraseasonal, interannual and interdecadal variability. J. Climate, , in
press.
[] Kirk-Davidoff, D.B., P. Schrag and J.G. Anderson, 2002: On the feedback of stratospheric
clouds on polar climate. Geophys. Res. Lett., 29, 11, 1556, doi: 10.1029/2002GL014659.
[] Korty, R.L., K.A. Emanuel and J.R. Scott, 2008: Tropical cyclone-induced upper-ocean
mixing and climate: Application to equable climates. J. Climate, 21, 638-654.
[] Kump, L.R. and D. Pollard, 2008: Amplification of Cretaceous warmth by biological cloud
feedbacks. Science, 320, 195.
[] Lin, J.-L., G. N. Kiladis, B. E. Mapes, K. M. Weickmann, K. R. Sperber, W. Lin, M.
C. Wheeler, S. D. Schubert, A. Del Genio, L. J. Donner, S. Emori, J.0F. Gueremy, F.
Hourdin, Ph. J. Rasch, E. Roeckner, and J. F. Scinocca, 2006: Tropical intraseasonal
variability in 14 IPCC AR4 climate models. Part I: convective signals. J. Climate, 19,
2665-2690.
22
[] Matthews, A. J., B. J. Hoskins and M. Mastuni, 2004: The Global Response to Tropical
Heating in the Madden-Julian Oscillation during Northern Winter. Q. J. R. Meteorol.
Soc., 130, 1991–2011.
[] Mori, M., and M. Watanabe, 2008: The growth and triggering mechanism of the PNA: a
MJO-PNA coherence. J. Meteor. Soc. Japan, 86, 213-236.
[] Otto-Bliesner, B.L. and G.R. Upchurch, 1997: Vegetation-induced warming of highlatitude regions during the late Cretaceous period. Nature, 385, 804-807.
[] Otto-Bliesner, B.L., E.C. Brady and C. Shields, 2002: Late Cretaceous ocean: Coupled
simulations with the National Center for Atmospheric Research Climate System Model.
J. Geophys. Res., 107, D2, 4019, doi: 10.1029/2001JD000821.
[] Peixoto, J. P. and A. H. Oort, 1992: Physics of Climate. American Institute of Physics, ,
520 pp.
[] Poulsen, C. J., Pollard, D. and White, T. S., 2007: General Circulation Model simulation
of the d18O content of continental precipitation in the middle Cretaceous: A model-proxy
comparison. Geology, 35, 199-202.
[] Schubert, S. D. and C.-K. Park, 1995:
Low-Frequency Intraseasonal Tropical-
Extratropical Interactions. J. Atmos. Sci., 48, 629-650.
[] Sewall, J.O. and L.C. Sloan, 2004: Arctic Ocean and reduced obliquity on early Paleogene
climate. Geology, 32, 477-480.
23
[] Sloan, L.C. and D. Pollard, 1998: Polar stratospheric clouds: a high latitude warming
mechanism in an ancient greenhouse world. Geophys. Res. Lett., 25, 3517-3520.
[] Sloan, L. C., J.C.G. Walker and T.C. Moore, 1995: The role of oceanic heat transport in
early Eocene climate. Paleoceanography, 10, 347-356.
[] Sloan, L.C., M. Huber and A. Ewing, 1999: Polar stratospheric cloud forcing in a greenhouse world. In: Reconstructing Ocean History: A Window into the Future, eds. Abrantes
and Mix, Kluwer Academic/Plenum Publ., 273-293.
[] Spicer, R.A., A. Ahlberg., A.B. Herman, C.-C. Hofmann, M. Raikevich, P.J. Valdes and
P.J. Markwick, 2008: The Late Cretaceous continental interior of Siberia: A challenge for
climate models. Earth Plan. Sci. Lett., 267, 228-235.
[] Sriver, R.L. and M. Huber, 2007: Observational evidence for an ocean heat pump induced
by tropical cyclones. Nature, 447, 577-580.
[] Thompson, S.L. and D. Pollard, 1997: Greenland and Antarctic mass balances for present
and doubled CO2 from the GENESIS version 2 global: climate model. J. Climate, 10,
871-900.
[] Wallace, J. M., and D. S. Gutzler, 1981: Teleconnections in the geopotential height field
during the Northern Hemisphere winter. Mon. Wea. Rev., 109, 784–804.
[] Zhou, J., C.J. Poulsen, D. Pollard and T.S. White, 2008: Simulation of modern and
middle Cretaceous marine d18O with an ocean-atmosphere general circulation model.
Paleoceanography, 23, PA3223, doi:10.1029/2008PA001596, 1-11.
24
Figure List
Figure 1: The 1982-2002 minus 1958-1978 ERA40 (European Center for Medium Range
Forecast Reanalysis) convective precipitation (mm day −1 ).
Figure 2: Schema of (a) Rossby waves excited by localized tropical convective heating. The
thick straight arrow indicates a subtropical jet. The letters, ‘E’ and ‘W’ denote eastward and
westward accelerations driven by the waves. These east-west accelerations drive overturning
circulations, as shown in (b). In our hypothesis, the associated adiabatic warming in high
latitudes contributes toward polar amplification. The thick horizontal dashed line in (b)
indicates the tropopause.
Figure 3: The January 0.993-sigma (the lowest model level) δT . The red-boxed area indicates the region of enhanced, localized heating, and the blue-boxed area is the region of
compensating cooling.
Figure 4: The January 250-hPa (a) geopotential height δZ and (b) eddy geopotential height,
δZ ∗ .
∗
Figure 5: The January (a) stationary eddy heat flux convergence, −δ ∂[v ∗ T ]/∂y , (b)
transient eddy heat flux convergence, −δ (∂[v 0∗ T 0∗ ]/∂y), and (c) the sum of (a) and (b). The
contour interval is 10−6 K s−1 .
25
Figure 6: The January (a) adiabatic warming, δ[ωSp ] and (b) ‘vertical velocity’, δ[ω]. The
contour interval is (a) 10−6 K s−1 and (b) 10−2 P a s−1 .
Figure 7: The January (a) stationary eddy momentum flux convergence, −δ (∂[u∗ v ∗ ]/∂y),
∗
∗
(b) transient eddy momentum flux convergence, −δ ∂[u0 v 0 ]/∂y , and (c) the sum of (a)
and (b). The contour interval is 10−5 m s−2 . The arrows in (a) and (c) indicates high-latitude
overturning circulations induced by the corresponding momentum flux convergence. No arrows are drawn in (b) because the momentum flux convergence structure is too complex to
readily infer the vertical motion.
Figure 8: The January total cloud cover fraction difference.
Figure 9: The difference in the January surface albedo. Because sunlight does not reach
north of 70o N , the values are undefined in that region.
Figure 10: January surface temperature difference between the Qo = 75W m−2 (half of
the EXP run’s Qo value) run and the CTL run.
26
Figure 1: The 1982-2002 minus 1958-1978 ERA40 (European Center for Medium Range Forecast
Reanalysis) convective precipitation (mm day −1 ).
27
pole
(a)
W
equator
E
east
W
west
E
east
(b)
height
Adiaba/c
warming
E
W
E
equator
W
pole
Figure 2: Schema of (a) Rossby waves excited by localized tropical convective heating. The thick
straight arrow indicates a subtropical jet. The letters, ‘E’ and ‘W’ denote eastward and westward
accelerations driven by the waves. These east-west accelerations drive overturning circulations, as
shown in (b). In our hypothesis, the associated adiabatic warming in high latitudes contributes
toward polar amplification. The thick horizontal dashed line in (b) indicates the tropopause.
28
Figure 3: The January 0.993-sigma (the lowest model level) δT . The red-boxed area indicates
the region of enhanced, localized heating, and the blue-boxed area is the region of compensating
cooling.
29
(a)
(b)
Figure 4: The January 250-hPa (a) geopotential height δZ and (b) eddy geopotential height, δZ ∗ .
30
∗
Figure 5: The January (a) stationary eddy heat flux convergence, −δ ∂[v ∗ T ]/∂y , (b) transient
eddy heat flux convergence, −δ (∂[v 0∗ T 0∗ ]/∂y), and (c) the sum of (a) and (b). The contour interval
is 10−6 K s−1 . Solid (dashed) lines are for positive (negative) values. Positive values are shaded.
31
Figure 6: The January (a) adiabatic warming, δ[ωSp ] and (b) ‘vertical velocity’, δ[ω]. The contour
interval is (a) 10−6 K s−1 and (b) 10−2 P a s−1 . Solid (dashed) lines are for positive (negative) values.
Positive values are shaded.
32
Figure 7: The January (a) stationary eddy momentum
flux convergence, −δ (∂[u∗ v ∗ ]/∂y), (b)
∗ ∗
transient eddy momentum flux convergence, −δ ∂[u0 v 0 ]/∂y , and (c) the sum of (a) and (b).
The contour interval is 10−5 m s−2 . The arrows in (a) and (c) indicates high-latitude overturning
circulations induced by the corresponding momentum flux convergence. No arrows are drawn in
(b) because the momentum flux convergence structure is too complex to readily infer the vertical
motion. Solid (dashed) lines are for positive (negative) values. Positive values are shaded.
33
Figure 8: The January total cloud cover fraction difference.
34
Figure 9: The difference in the January surface albedo. Because sunlight does not reach north of
70o N , the values are undefined in that region.
35
Figure 10: January surface temperature difference between the Qo = 75W m−2 (half of the EXP
run’s Qo value) run and the CTL run.
36