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 × PAL (Preindustrial Atmospheric Level, 1 PAL = 280 ppmv) are needed to produce the observed high-latitude continental winter warmth (e.g., Bice et al. 2006; Poulsen et al. 2007; Hunter et al. 2008), but these levels significantly exceed those of recent proxy estimates for the Cretaceous and early Cenozoic: ≈4–8 × PAL (Bice et al. 2006); 4 × PAL (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 vegetation–climate 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 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 also trigger high-latitude warming through the excitation of poleward-propagating planetary-scale Rossby waves, which transport heat poleward and induce sinking motions. Our proposed mechanism is based on the premise that under the high CO₂ loading conditions, tropical convection was more intense and localized during the Cretaceous and early Cenozoic than it is for the present-day climate. The rationale for this premise is that as the tropical sea surface temperature (SST) increases, due to the higher CO₂ loading, tropical convection over the western part of the largest ocean basin (the 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 minus 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. While increased CO₂ radiatively warms all latitudes, the proposed mechanism leads to a further warming at high latitudes and a cooling of the tropics through the heat transport and overturning circulation associated with the poleward-propagating waves.

Lee et al. (2011) examined the tropical precipitation trend for the months of December–February (DJF) over the time period of 1979–2002, using the Global Precipitation Climatology Project (GPCP), Climate Prediction Center Merged Analysis of Precipitation (CMAP), and the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data (ERA-40) datasets. Their Fig. 1 shows that the most pronounced positive trend occurred over the Indo–western Pacific warm-pool region. Although other processes may be involved in the changes shown in that figure, since the surface air temperature has increased during this time period, the Indo–western Pacific warm pool intensification of the convective precipitation is at least consistent with the theoretical expectation based on the Clausius–Clapeyron relation. Because the core of our proposed mechanism hinges on a warmer tropical SST during the Cretaceous and early Cenozoic, this mechanism may also be applicable for climates under other conditions, such as that characterized by stronger solar radiation, as long as it causes the tropical SSTs to increase.

To the best of our knowledge, there are no paleotemperature estimates available for the Indian and western Pacific Oceans. 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 32° and 43°C, with a typical value of 36°–37°C. 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 6°C and perhaps as much as 13°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–western Pacific Ocean.

One advantage of the proposed 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 advance the theoretical and empirical basis for this mechanism. The GCM employed for this study will be described in section 3, and the experimental design is discussed in section 4. The results are presented in sections 5–7, and the conclusions follow in section 8.

2. Mechanism: Planetary wave dynamics as the warming mechanism

The mechanism that we propose is that enhanced and localized tropical convection is capable of generating planetary-scale Rossby waves that, through the attendant poleward heat flux and overturning circulation (refer to Fig. 1), can trigger high latitude warming. This overturning circulation associated with poleward Rossby wave propagation needs further explanation. For Rossby waves, the poleward propagation out of the tropics must be accompanied by a transport of eastward angular momentum toward the tropics (for external Rossby waves, the angular momentum transport is always in a direction opposite to that of the wave propagation (Held 1975). This angular momentum transport results in a force imbalance, and as a response, an overturning circulation develops with sinking motion at higher latitudes and rising motion at lower latitudes. 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. 1b).

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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. (b) The east–west accelerations drive overturning circulations are shown. In our hypothesis, the associated adiabatic warming in high latitudes contributes toward polar amplification. The thick horizontal dashed line in (b) indicates the tropopause.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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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 internally consistent SST and convective precipitation fields. However, for our purpose, there are two reasons why a mixed layer ocean model with an idealized heat source is a better choice than a dynamic ocean model with internally generated warm-pool heating. First, there is the question of model fidelity in simulating the distribution and intensity of tropical convective precipitation. As was shown by Lin et al. (2006), even among the latest versions of the coupled models that participated in the Intergovernmental Panel on Climate Change (IPCC) Assessment Report 4 (AR4), there is large intermodel scatter in the intensity (a factor-of-2 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 the extratropical ocean circulation, which can also warm the Arctic. According to the calculations by Trenberth and Caron (2001), the poleward heat transport across 60°N in the Atlantic Ocean is on the order of 0.5 PW (petawatts = 10¹⁵ W). As Wunsch (2005) pointed out, while this is a small amount compared with the 4 PW of atmospheric heat transport across the same latitude, removing or adding 0.5 PW would correspond to an atmospheric radiative forcing change greater than that from a doubling of atmospheric CO₂. Therefore, if the increase in CO₂ can cause the extratropical ocean circulation to change, and if the coupled model can precisely simulate this process, then it would be difficult to isolate the effect of the proposed mechanism on the Arctic warming.

Given the above considerations, it is desirable to use a static ocean model for this study. One viable choice is a mixed layer ocean model 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 convective heating perturbations is estimated empirically and imposed in the model. An additional advantage of using a mixed layer ocean GCM is that many paleoclimate studies in the past have used the same type of model. If the proposed mechanism turns out to contribute to the polar warming, it indicates that mixed layer ocean GCMs may have been underestimating the polar temperature amplification. Thus, such a finding can ultimately contribute toward an improvement of paleoclimate models.

The experiments presented in this study use Global Environmental and Ecological Simulation of Interactive Systems (GENESIS) version 2.3, a GCM that 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 (≈3.75°) with 18 vertical levels, and the grid for all surface components is 2° × 2°. The GENESIS GCM has been used extensively in paleoclimatic 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 (1354.4 W m⁻²), and a circular orbit with obliquity (23.5°), 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 first perform two types of model runs: a run with no specified localized tropical heating and a series of runs with prescribed localized tropical heatings of varying strength. These runs will be referred to as EXP runs. By comparing these model runs, we are isolating the impact of localized tropical heating upon the Arctic surface air temperature for a range of plausible tropical heating values. 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.

We used the present-day tropical precipitation and heating distribution as a guide for determining the amplitude and horizontal structure of the heating in the model. Because our primary focus is on the warming mechanism in the Northern Hemisphere (NH) high latitudes during the winter, data from DJF are used. For the present-day climate, over the warm pool, the estimated latent heating from the convective precipitation 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 early Cenozoic, as discussed in the introduction, it would be expected that the warm-pool convection during that time period was 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 early Cenozoic was 4 × PAL. If the lower-tropospheric air temperature increases by 3°C for every doubling of CO₂ (according to the IPCC AR4, most GCMs predict temperature increases between 2° and 4.5°C), for an increase of CO₂ to 4 × PAL, the temperature would increase by about 6°C. If the precipitation rate increases by 2% for every 1°C increase (Held and Soden 2006), then for a CO₂ concentration of 4 × PAL, 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 (320–160 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. This amounts to 25% increase in the zonal heating contrast compared with the present value of ≈160 W m⁻².

Both SST and tropical precipitation changes associated with present-day climate change suggest that the above estimate of the increase in the zonal heating contrast is on the conservative side. Kumar et al. (2010) showed that between 1950 and 2008 the largest SST increase in the tropics occurred in the Indian and western Pacific Oceans. Thus, our assumption of a uniform tropical SST increase underestimates this rate. According to the 1979–2002 tropical precipitation trend of Lee et al. (2011), both the GPCP and CMAP data indicate that over a period of 50 years, the trend would result in an increase of about 22.5 W m⁻² in the warm-pool region and a decrease of 7.5 W m⁻² outside of this region. Thus, in 50 years, the zonal heating contrast would increase by 30 W m⁻². Relative to the current-day climatological 160 W m⁻² heating contrast, this amounts to an increase of 19%. Between 1958 and 2010, the CO₂ concentration measured at Mauna Loa Observatory (http://www.esrl.noaa.gov/gmd/ccgg/trends/#mlofull) shows an increase of about 25%. Therefore, our estimate of a 25% increase in the zonal heating contrast under a 4 × PAL CO₂ concentration is apparently a very conservative estimate.

Given the uncertainty in the zonal heating contrast that would have existed, and keeping in mind that the goal of this study is to perform a proof-of-concept test of our proposed hypothesis, rather than examining the climate response to a single value of the heating contrast, it would be more reasonable to consider a range of plausible values to examine the sensitivity of the surface air temperature to the tropical heating. Thus, the values of the tropical heating, Q_o, that we will consider for our EXP runs are 75, 120, 150, 180, and 225 W m⁻². The corresponding warm-pool/outside-warm-pool heating contrast is 100, 160, 200, 240, and 300 W m⁻². These values can be obtained by noting that our “warm pool” occupies 90 degrees longitude, with the remainder of the tropics spanning 270 degrees of longitude. For example, for the present-day case, the zonal mean heating equals (1 × 320 W m⁻² + 3 × 160 W m⁻²)/4 = 200 W m⁻² (see the above discussion). Therefore, the warm-pool additional heating above the zonal mean is 320–200 W m⁻² = 120 W m⁻². While the 120 W m⁻² value is used to simulate the present-day warm pool, the three higher values are regarded as plausible values for a 4 × PAL atmosphere. The 75 W m⁻² case is considered as an additional data point in our effort to examine the extent to which the surface air temperature response to the heating is linear.

Atmospheric CO₂ levels in these experiments were set to 4 × PAL value. For the EXP runs discussed above, a constant heating term was applied to the GCM atmosphere, with a vertically integrated column total of Q_o. The heating was distributed vertically with a parabolic dependence on σ (≡pressure/surface pressure), with nonzero values ranging between σ = 0.15 and 0.75, and a maximum heating at σ = 0.5. This was applied uniformly between latitudes 10°S and 10°N and from longitudes 10°–100°E (see the red-boxed area in Fig. 2), 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 a 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. 2), so that the net zonal and global mean heating are zero. For instance, if Q_o = 150 W m⁻², the heating difference between the heated and cooled region is 200 W m⁻². The values of Q_o considered in this study and the corresponding zonal heating contrast are summarized in Table 1, along with the symbol for each experiment. The symbols are written as EXPm-n, where m is the CO₂ factor relative to PAL and n = Q_o (W m⁻²). Hereafter, each experiment will be referred to by its symbol.

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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.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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Table 1.

Atmospheric CO₂ concentration, the imposed warm-pool heating (Q_o), and the resulting heating contrast in the zonal direction.

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The sensitivity of the high-latitude surface air temperature to the tropical heating contrast will also be examined for 1 × PAL atmosphere. There are reasons why the sensitivity may be dependent on CO₂ concentration. For instance, as model calculations of the present-day climate change indicate, the background atmospheric state changes as the CO₂ concentration increases. This change in the background flow would influence the Rossby wave propagation characteristics, on which our proposed hypothesis is dependent. Different CO₂ concentrations can also influence the base extent of snow and ice, and hence the degree of albedo feedback, as mentioned later.

Because the goal of this study is to perform a proof-of-concept test of our proposed hypothesis, we first examine the proposed mechanism by comparing the EXP4–150 (Q_o = 150 W m⁻²) run against the EXP4–0 run (see Table 1), which has no imposed heating and cooling, that is, Q_o = 0 W m⁻². This comparison can succinctly illustrate the mechanism by which localized tropical convection can warm the Arctic. 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 in the EXP4–0 run. In both of the model runs, the atmospheric CO₂ loading is 4 × PAL.

After examining the workings of the proposed mechanism in sections 5 and 6, the results from the various EXP runs will be presented in section 7. By intercomparing the EXP runs, we will be able to address the extent to which the proposed mechanism can contribute to the winter Arctic warming.

5. Surface warming and stationary wave

The difference in the January surface air temperature at the lowest model level (σ = 0.933), δT (Fig. 2), shows warming at high latitudes and an overall cooling in the tropics. [The notation refers to (EXP4−0), where is a given model variable. Note that is not an estimate of the actual Cretaceous changes relative to the modern world; the latter is addressed in section 7 and Figs. 8 and 9.] The warming in the Arctic is as high as 16°C, when compared to a model climate without the heating. This result demonstrates that the zonal localization of the tropical heating, without a net increase in tropical heating, is capable of substantially warming the Arctic surface air temperature. Figure 2 also shows that the midtropospheric 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, dynamical 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. 3b) shows a poleward-propagating wave train (see the arching solid arrow), which emanates from a subtropical high centered at 40°to 30°N. Being to the northwest of the imposed heating, the location of the subtropical high conforms to the Rossby wave response to a localized tropical heat source, as was shown by Gill (1980). If the tropical heating is lowered to 75 W m⁻² (EXP4–75), the stationary wave amplitude weakens (Fig. 3a), but the NH wave structure is similar to that of the EXP4–150 case. If the heating is increased to 225 W m⁻² (EXP4–225), the wave amplifies and takes on a structure that indicates that a poleward-propagating wave from the subtropical high is quickly refracted back toward the equator. This wave route is indicated by the arrow in Fig. 3c. It can be seen that the high in the equatorward-propagating wave is as strong as the high in the poleward-propagating wave. There is still evidence of poleward propagation farther into the Arctic (dashed arrow), but it appears that most of the wave energy is refracted toward the equator. As will be discussed later, these results suggest that increased equatorward refraction for large values of Q_o limit the extent to which the localized tropical heating can warm the Arctic.

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The January 250-hPa geopotential height δZ for (a) EXP4–75, (b) EXP4–150, and (c) EXP4–225.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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6. Attributes of surface air warming

To quantitatively assess the proposed mechanism, we consider a time and zonal mean of the thermodynamic energy equation. Because there is a large zonal mean contribution to the surface temperature and 250-hPa geopotential height fields poleward of 60°N (see Figs. 2 and 3), which is the region of our primary interest, we believe that zonal mean diagnostics provide a useful approach for examining the impact of the localized tropical heating. In fact, as is shown in Fig. 8, the Arctic warming is significant even for the zonal mean.

The thermodynamic energy equation in pressure coordinates can be written as

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where the notation follows Lorenz (1955), with the overbar denoting the time mean, and the square bracket denoting the zonal mean. Other notations are standard: T is temperature; υ is the meridional velocity; and 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 accounts for adiabatic warming (downward motion) or cooling (upward motion); S_p ≡ −(T/θ)(∂θ/∂p) is a static stability parameter, where θ is potential temperature. The third term represents radiative cooling, where γ⁻¹ is the radiative relaxation time scale. Finally, corresponds to the remaining diabatic heating contribution.

For the Arctic winter, the thermodynamic energy equation can be further simplified. First, the diabatic heating may be neglected because the Arctic winter receives virtually no sunlight and latent heat release is negligible. To evaluate the effect of the eddies 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 (Peixoto and Oort 1992), and thus the zonal mean component can be neglected. After making these assumptions, (1) can be rewritten as

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where the asterisk denotes a deviation from the zonal mean, and the prime denotes a deviation from the time mean. The first term on the right-hand side represents the meridional heat flux convergence by the stationary eddies and the second term the meridional heat flux convergence by the 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 4a 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 extending from 17° to 62°N. An exception is the narrow latitudinal range centered at 40°N. This warming is compensated by cooling in the tropics and to a lesser extent by cooling poleward of 62°N. Between 48° and 60°N, the warming occurs at values ranging between ≈2 × 10⁻⁶ K s⁻¹ and ≈6 × 10⁻⁶ K s⁻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 and 15 K. The temperature changes caused by these eddy heat fluxes are comparable to the lowest model level δT (Fig. 1b).

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The January (a) stationary eddy heat flux convergence, ; (b) transient eddy heat flux convergence, −δ(∂[υ′*T′*]/∂y); and (c) the sum of (a) and (b). The contour interval is 10⁻⁶ K s⁻¹.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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The response of the transient eddies to the tropical heating (Fig. 4b) 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 sum of the stationary and transient eddy heat flux convergences (Fig. 4c) shows that the strongest warming occurs between 50° and 80°N.

Poleward of 70°N, adiabatic warming plays a greater role in warming the surface. Figure 5a shows that between 70° and 82°N, the anomalous adiabatic warming accounts for a surface warming of up to ≈5 × 10⁻⁶ K s⁻¹. Once again assuming γ = 30⁻¹ day⁻¹, the resulting warming would be about 5–13 K. This anomalous adiabatic warming can be explained mostly by changes in the contribution, as can be inferred from (Fig. 5b).

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The January (a) adiabatic warming, and (b) vertical velocity, δ[ω]. The contour interval in (a) is 10⁻⁶ K s⁻¹ and (b) 10⁻² Pa s⁻¹.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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As was discussed in section 2, 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 (Fig. 5b) and the stationary eddy momentum flux convergence, (Fig. 6a), indicates that changes in contribute to the excitation of the adiabatic warming in the Arctic. To help facilitate the comparison, the middle- and high-latitude vertical motion that would be driven by is shown schematically in Fig. 6a. (The vertical motion in Fig. 6 is inferred by assuming that the secondary circulation induced by opposes the impact of the eddy driving. This results in a poleward flow in the upper troposphere where is negative, and vice versa. Mass conservation then implies the vertical motion shown by the arrows in Fig. 6.) This vertical motion field is in qualitative agreement with that shown in Fig. 5b. It is also worthwhile to note that the pattern of for the simulated stationary wave (Fig. 6a) agrees with the west–east acceleration pattern (Fig. 1b) associated with the idealized stationary wave (Fig. 1a). The above findings support 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 impact of the transient eddy momentum flux convergence (Fig. 6b) is weaker than that of the stationary eddy momentum flux convergence (Fig. 6a), and thus the sum of these two convergences (Fig. 6c) would still drive downward motion.

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The January (a) stationary eddy momentum flux convergence, ; (b) transient eddy momentum flux convergence, ; and (c) the sum of (a) and (b). The contour interval is 10⁻⁵ m s⁻². The arrows in (a) and (c) indicate 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.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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The eddy heat flux also drives an overturning circulation, but because this portion of the overturning circulation has a spatial structure that opposes the effect of the heat flux, the eddy heat flux cannot indirectly contribute to adiabatic warming in the region between 70°N and 82°N. Therefore, we are led to conclude that the adiabatic warming over the region ranging between 70° and 82°N can be ascribed primarily to the stationary eddy momentum flux convergence.

Over the Arctic Ocean (poleward of 80°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. 7). The CCRF mechanism (Sewall and Sloan 2004; Abbot and Tziperman 2008a,b) could be responsible for this increase in Arctic Ocean 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 EXP4–0 to the EXP4–150 state. Initially, dynamical processes may at 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.

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The January total cloud cover fraction difference.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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In the tropics, there is strong anomalous sinking motion (Fig. 5b) between the equator and 10°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. 1. Although the sinking motion warms the lower troposphere (Fig. 5a), the corresponding eddy heat flux divergence (Fig. 4a) cools the region. The cooling in the tropics therefore can be interpreted as being a result of the poleward eddy heat flux (Fig. 2a).

7. Sensitivity tests

The analysis presented in the previous section shows that the response to localized tropical heating can warm the surface air in the Arctic. With this picture in mind, we next examine the range of Arctic warmings caused by the tropical heating values listed in Table 1. Figures 8a and 8b show the zonal mean surface air temperature for the 4 × PAL cases for latitudes equatorward and poleward of 45°N, respectively. It can be seen that as the heating intensifies, the Arctic surface air temperature exhibits a marked increase (Fig. 8b). The warming is relatively rapid between EXP4–75 and EXP4–150, with a rate of ≈0.8°C per (10 W m⁻²) increase in Q_o.

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The January zonal mean surface air temperature for 4 × PAL CO₂ cases; the temperature in the interval between the (a) equator and 45°N, and (b) 45°N and 90°N is shown. In a similar manner, January zonal mean surface air temperature for (c),(d) 4 × PAL CO₂ cases is shown.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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For Q_o > 150 W m⁻², the rate of warming slows down. The maximum zonal mean warming between the EXP4–150 and EXP4–180 runs is a meager 1°C. A further increase in Q_o to 225 W m⁻² (EXP4–225) results in a slight cooling in the Arctic. It is evident then that there is a certain value of Q_o, between 180 and 225 W m⁻², beyond which the Arctic warming saturates. Insight into this behavior can be gained by examining the 250-hPa geopotential height field for the EXP4–225 run, which is shown in Fig. 3c. Compared with the EXP4–75 and EXP4–150 runs (Figs. 3a and 3b), the stationary wave in the EXP4–225 run shows a more pronounced equatorward refraction in the NH midlatitudes, as highlighted by the solid arrow. Presumably this refraction is caused by nonlinear wave dynamics because the wave amplitude can be seen to increase with larger Q_o. As the wave strengthens, nonlinear wave–wave interactions are expected to become increasingly important. This is indeed supported by the prominence of zonal wavenumber 3 and 4 features in Fig. 3c relative to Figs. 3a and 3b; The ratio of the zonal to the meridional component of the stationary wave group velocity vector is equal to k/l (James 1994), where k and l are the zonal and meridional wavenumbers, respectively. Therefore, as k increases, as is the case in Fig. 3, the propagation to higher latitudes is expected to be suppressed, and instead the trajectory would acquire a more zonal orientation.

Compared with the 4 × PAL EXP runs examined above, for 1 × PAL, intensifying the tropical heating results in a weaker Arctic warming (Fig. 8d), with an average rate of ≈0.3°C per (10 W m⁻²) increase in Q_o. This indicates that the impact of the localized tropical heating on polar warming is dependent on the CO₂ content of the atmosphere. This sensitivity to the CO₂ concentration could be caused by the difference in the background state, which can influence Rossby wave propagation characteristics (Grose and Hoskins 1979). In addition, the CCRF and ice–albedo feedback mechanisms could also contribute to this difference. By fixing the ice, snow, and clouds at their climatological values, the impact of dynamical processes can be isolated from the CCRF and ice–albedo feedback mechanisms. Similarly, by fixing the clouds, while allowing ice/snow to vary, the ice/snow–albedo feedback can be isolated from the CCRF mechanism. However, as was discussed in section 6, these processes can be nonlinearly dependent on each other. For example, the ice–albedo effect, which takes place during the warm season, may manifest itself during the following winter via the CCRF feedback mechanism. This relationship between the summer ice–albedo feedback and the winter CCRF can be tested with the second experiment mentioned above. However, performing these experiments is beyond the scope of this study.

Saturation of the Arctic warming with respect to Q_o also occurs for the 1 × PAL EXP runs, but compared with the 4 × PAL EXP runs, the 1 × PAL EXP runs show additional complexity in that the EXP1–120 case exhibits a lower Arctic temperature than the EXP1–75 case (Fig. 8d). However, this is just one exception to the general relationship between the Arctic surface warming and Q_o.

With the results from the set of 1 × PAL and 4 × PAL experiments, we can ask: What are the relative impacts of quadrupling the CO₂ content and strengthening the warm-pool heating on the Arctic surface air temperature? To address this question, using the results from both the 1 × PAL and 4 × PAL runs, we subtract the surface air temperature from the model runs with Q_o = 120 W m⁻², a value that corresponds to the warm-pool heating of the present-day climate, from model runs with Q_o = 150 W m⁻² and Q_o = 180 W m⁻², plausible values of warm pool heating from the Cretaceous and early Cenozoic. We begin by focusing on the impact of increasing Q₀ while fixing the CO₂ content at either 1 × PAL or 4 × PAL. As can be seen (Figs. 9d–g) the local temperature increases due to these changes in Q_o can be as large as 6°–8°C. For the 4 × PAL cases (Figs. 9d and 9e), the most significant warming occurs over northern Siberia and the adjacent Arctic Ocean. For the 1 × PAL cases (Figs. 9f and 9g), the strongest warming occurs near the present-day Greenwich meridian, and the surface air temperature shows stronger zonal asymmetry than the 4 × PAL cases. The differences between Figs. 9d and 9f and also Figs. 9e and 9g also indicate that not only the zonal mean response but also the local response to increased tropical heating is strongly influenced by the CO₂ content of the model atmosphere.

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The January surface temperature difference among various experiment runs. (a)–(g) The experiment runs used to produce the difference field are indicated.

Citation: Journal of Climate 24, 9; 10.1175/2011JCLI3825.1

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The impact of quadrupling the CO₂ content while fixing Q_o is shown in Fig. 9c. As can be seen, the Arctic warming is much greater in Fig. 9c than in Figs. 9d–g especially over the Arctic Ocean. This difference between the impact of the CO₂ quadrupling and that of the tropical heating is less marked over the northern Siberia where the localized tropical heating accounts for a temperature increase of 4°–8°C, which corresponds to about 30% of the warming associated with the CO₂ quadrupling. The combined impact of quadrupling the CO₂ content and increasing Q_o is shown in Figs. 9a and 9b. The similarity in the two temperature fields is consistent with Fig. 8b, which shows for this range of Q_o values that the Arctic surface air temperature increase is close to saturation. Also, the larger temperatures over northern Siberia in Figs. 9a and 9b, compared to Fig. 9c, further indicate that tropical heating has an important influence in that region even in the presence of CO₂ quadrupling.

Figures 8a and 8c show that the tropical surface air temperature slightly declines as Q_o is increased. The analysis of the thermodynamic energy budget presented in section 6 indicates that the localized tropical heating enhances the poleward heat transport, which results in a cooling of the tropics. Figures 9d–e all show that the strongest cooling occurs in the vicinity of the imposed heating. This seems counterintuitive, but it is important to recall that in our experiment the heating is prescribed to mimic convective heating rather than heating at the surface. If our model had a warm pool, the tropical cooling would be diminished because there would be a larger sensible heat flux from the ocean surface.

8. Concluding remarks and discussion

This study explores the hypothesis that localized tropical heating associated with a warm pool can excite poleward-propagating Rossby waves, which can enhance 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 localized diabatic heating over the deep tropics, along with compensating cooling at other longitudes. To illustrate the workings of the hypothesized mechanism, we first contrasted two model runs, one with this heating field and the other without, both with a 4 × PAL CO₂ content. We find that the run with the heating produces substantially larger high-latitude surface air temperatures.

Thermodynamic energy budget analysis was performed on the above two model runs. This analysis shows that the high-latitude warming (excluding the region poleward of 82°N) due to the localized tropical heating 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 over high latitudes, which results in adiabatic warming. Farther poleward, over the Arctic Ocean, the warming driven by the tropical heating coincides with an increase in cloud cover. Because solar radiation does not reach the Arctic Ocean during the winter, we interpret this warming to have arisen from radiative forcing that is enhanced by the increase in cloud cover. Our interpretation is that the dynamical processes—meridional heat flux and adiabatic warming—first warm the Arctic Ocean, hence increasing the cloud cover. As the cloud cover increases, radiative forcing by the clouds can take over the warming.

Setting aside for the moment the question of possible driving mechanisms for paleo–equable climates, from the perspective of improving our understanding the present-day climate, the role of warm-pool convective heating on reducing the north–south temperature gradient merits further discussion. Figure 8d shows that for a CO₂ level of 1 × PAL, the present-day warm-pool heating of 120 W m⁻² causes the zonal mean winter Arctic surface air temperature to rise by 3°C from that of a no-warm-pool climate. Therefore, our model calculations suggest that without the tropical warm-pool heating, the pole-to-equator difference in surface temperature would be greater than is currently observed. A comparison with the corresponding 4 × PAL cases (Fig. 8b) suggests that as the atmospheric CO₂ loading increases, localized tropical heating becomes more effective in generating Arctic warming. It is also worth noting that for the 4 × PAL runs, the north–south temperature gradient reverses between 75°N and the North Pole, if the tropical heating is greater than 120 W m⁻² (Fig. 8b). This reversal in the temperature gradient is reminiscent of the “warm arctic–cold continent” teleconnection pattern of the 200/2010 winter (http://www.arctic.noaa.gov/reportcard/atmosphere.html). Therefore, the warm arctic–cold continent teleconnection pattern may strengthen as atmospheric CO₂ loading increases and warm-pool convective heating intensifies.

The effect of the localized tropical heating is limited though. For warm-pool heating greater than 120 W m⁻², there is a decline in the rate of Arctic warming with respect to the heating intensity, and for heating greater than 180 W m⁻² the Arctic warming halts altogether. This saturation coincides with evidence of nonlinear processes whereby large amplitude waves with higher zonal wavenumbers refract equatorward. Thus, we interpret the high-latitude temperature saturation as arising from the suppression of wave propagation into high latitudes.

To evaluate the extent to which an intensification of the warm-pool convective heating can contribute to the Arctic warming during the Cretaceous and early Cenozoic, we compared the Arctic warming associated with 150 and 180 W m⁻² heating, possible values for that time period, to that for a heating of 120 W m⁻², a value that corresponds to the present-day warm-pool convective heating. Our model calculation finds an additional Arctic warming of 4°–8°C over northern Siberia and the adjacent Arctic Ocean. Relative to the warming due to a quadrupling of CO₂ alone, this temperature increase accounts for about 30% of the warming over this region. As such, this finding suggests that local tropical heating is not the major contributor to the winter Arctic warming. Nonetheless, warming of this amount suggests that strengthened warm-pool tropical convection may be an important contributor to equable climate.

Although the above results suggest that the influence of localized tropical heating can contribute to 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 proxy 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 indeed a warm pool present during the Cretaceous and early Cenozoic. Furthermore, the value of the 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 increased high-latitude warming, with the model temperatures representing possible range of values for high-latitude warming due to enhanced warm-pool convective heating.

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 30°–90°E. In their study, the increase of the model precipitation in this region was found to be about 25% greater than that outside of the model warm pool.

Under the 4 × PAL conditions, while the Arctic surface air temperature of the EXPm-n (n ≠ 0) runs is substantially higher than that of the corresponding EXPm-0 (m = 1 or 4) run, the differences in the overall tropospheric circulation pattern between the EXPm-0 and EXPm-n runs are rather subtle. Perhaps the most notable feature is that as the localized tropical heating intensifies, the upper-tropospheric equatorial wind becomes less easterly and eventually turns westerly. This eastward acceleration is to be expected because the imposed localized tropical heating generates Rossby waves, and as these waves emanate from the tropics they transport eastward momentum into the equatorial region where the wave source is located. Although this mechanism was not discussed by Bush and Philander (1997), their Cretaceous run shows an upper-tropospheric equatorial wind that is more westerly than those for the present-day run. This feature is consistent with increased poleward Rossby wave propagation out of the tropics.

Finally, it is worthwhile to note that the localization of the midtropospheric tropical heating is compensated by dynamical cooling caused by the poleward eddy heat flux associated with the poleward-propagating Rossby waves. 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 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.