Impacts of ocean gateway and basin width on Tertiary tropical climate variability in a prototype model

Abstract

Using a simple tropical climate model, we investigated possible impacts of changes in oceanic seaways (Panama and Tethys) and ocean basin sizes (great Pacific and narrow Atlantic) on tropical climate variability during Tertiary. Our model showed that the opening of seaways had little influence on climate variability in the tropical Pacific because the climate variability in the Pacific Ocean’s large basins were internally generated, regardless of the variation in the tropical Atlantic Ocean. Conversely, the climate variability in the tropical Atlantic Ocean was highly dependent on the tropical Pacific Ocean; thus, an opening seaway, particularly the Panama seaway, was crucial in generating the interannual variability in the tropical Atlantic Ocean. We also found that in the Pacific Ocean, basin size strongly modified the period and amplitude of the interannual variability of both the Pacific and Atlantic Oceans due to ocean wave dynamics.

1 Introduction

The transition point from the Mesozoic to Cenozoic eras around 65 Ma ago, called the Cretaceous–Tertiary (KT) boundary, marks a period of mass extinction. The Earth’s average temperature gradually decreased after the Mesozoic, along with decrease in the amount of atmospheric carbon dioxide (Ruddiman 2008). The Cenozoic era is divided into the early Tertiary and later Quaternary periods. The Tertiary spanned from the KT boundary to 2.6 Ma ago, which was the beginning of a period of glaciation (e.g., Ruddiman 2008). The Tertiary climate was milder than the modern climate. Continental distributions during the Tertiary were significantly different than they are today. In particular, the sea gateway across Central America that is now in the Isthmus of Panama was open at that time (Fig. 1); thus, seawater was freely exchanged between the Atlantic and Pacific through this passage. Klocker et al. (2005) estimated that approximately 14 Sv seawater passed through this channel but concluded that closing the gateway did not significantly contribute to climate change in high latitudes. Another study suggested that the blocking of the gateway strengthened the Atlantic meridional circulation and contributed to the formation of the tropical Pacific cold tongue (Step et al. 2007). The Panama seaway was gradually diminished as the Central American continent uplifted and, around 4 Ma ago, became completely blocked (Cannariato and Ravelo 1997; Chaisson and Ravelo 2000; Jian et al. 2006; Li et al. 2006; Steph et al. 2006; Sato et al. 2008). The blocking of the channel stopped the influx of warm, high saline water from the Atlantic to the Pacific, and the mass of warm tropical Atlantic water was probably transported into the Northern Atlantic Ocean, which is thought to have resulted in the strengthening of the meridional overturning circulation (e.g., Maier-Reimerm et al. 1990; Haug et al. 2001). Conversely, as the influx of warm water into the tropical Pacific Ocean was reduced, the cold tongue (i.e., the SST over the equatorial eastern Pacific) developed, and consequently, the thermal contrast between the western and eastern Pacific was be intensified. The intensified thermal contrast over the tropical Pacific affected air–sea coupled instability known as “Bjerknes Feedback” (Bjerkens 1966, 1969); thus, it is naturally expected that the El Niño effect is amplified. The eastern Atlantic and western Pacific, on the other hand, were connected by the Tethys passage, which included the current Red Sea, Black Sea, and Mediterranean Sea, during the Tertiary. This channel closed sometime at the end of the Oligocene (i.e., 34–24 Ma ago) and is believed to have played an important role in the interactions between the two oceans.

Fig. 1

SST distribution of the GFDL Ocean Model (MOM4p1) simulating climatic conditions 55 Ma ago (Paleocene–Eocene boundary). Atmospheric forcing that was needed to run the ocean model was obtained from ECHAM5/MPIOM coupled model simulation of climatic conditions 55 Ma ago (Heinemann et al. 2009; Bice and Marotzke 2001)

The huge Mesozoic continent of Pangaea gradually began to break up 175 Ma ago and Africa, Asia, and North America started to take forms similar to their current shapes (Ruddiman 2008). The Atlantic Ocean gradually increased in width. The Indian subcontinent separated from Antarctica and slowly collided with the Asian continent, and Oceania also moved slowly to the north of the Indian Ocean. In the early Cenozoic era, the boundary between the Indian Ocean and the Pacific was not well defined; therefore, the two oceans could be considered a huge Pacific Ocean, while the Atlantic Ocean was very narrow in comparison with its current form (Fig. 1). The natural frequency of the ocean basin mode became lower (i.e., longer period) as the width increased (Jin 1997). Therefore, changes in the width of the ocean basin influenced the local climate. This is the reason why the current El Nino shows the strongest interannual variation in the tropical Pacific but is relatively weak in the Indian and Atlantic Oceans. Thus, changes in the ocean-width and open-closure of the seaways influence the natural basin mode of the oceans and consequently lead to a modification in local climate variability. However, the continents move very slowly on a time scale of approximately tenths of million-year; thus, it is almost impossible to perform a “transient run” (i.e., the external climate condition such as earth orbital forcing, geometry, greenhouse concentration etc, changes in time) to simulate long-term climate variation spanning the entire Cenozoic using current climate models due to limitations of computing resources. For this reason, the so-called slice run (i.e., the external climate condition is fixed) of the climate system model, which targets a fixed time point, is widely used. The slice run is useful for determining climate phenomena at a particular point in time, but gives a discontinuous or discrete picture of long-term climate change. Furthermore, in the slice run, the impact associated with a slow response component with respect to the forcing time scale tends to be overestimated (e.g., Ruddiman 2008). Rather than performing an actual transient experiment using a climate system model (such experiments were previously performed for limited time periods by a coupled general circulation model with intermediate complexes; e.g., Timm and Timmermann 2007); here, we depict a global picture showing the sensitivity of tropical climate variability to changes in continental configuration, particularly for changes in the seaways in Central America and Central Asia and for Atlantic and Pacific basin sizes. This approach is neither the transient run nor the slice run. Nevertheless, it may be close to the transient run because the change in the parameter can be considered as the time progression.

In Section 2, we introduce the model equations utilized in this study. In Section 3, we examine the role of seaway closure or opening in terms of climate variability. In Section 4, we describe our examination of the sensitivity of the size of the ocean basin. Our conclusions and remarks appear in Section 5.

2 Model equations

A prototype atmosphere–ocean coupled model was developed in order to quantify the tropical variations in two seaways, the Central American (Panama) Seaway and the Central Asian (Tethys) Seaway, the latter of which was open during most of the Tertiary. The model was developed based on a two-box approximation formula of the tropical Pacific atmosphere–ocean coupled model, originally proposed by Jin (1997). It has been extended to include two tropical oceans. Therefore, the model we used includes a total of four boxes (two boxes for each ocean) and seaways, through which the heat and mass are exchanged between oceans.

As seen in Fig. 2, the model used a very simple representation of the tropical oceans, such that the Indian and Pacific Oceans are not distinct; rather, they are merged into a huge Pacific Ocean. Moreover, the basin of the Atlantic Ocean at that time was narrower than it currently is. As seen in Fig. 2, which represents the model domain for Fig. 1, each ocean was divided into east and west boxes, with the Pacific and Atlantic Oceans connected through two seaways. In each box, the sea surface temperature and thermocline depth (T, h) are defined. The corresponding equations for the Pacific are as follows:

$$ \frac{{\partial {T_{\text{WP}}}}}{{\partial t}} = - \alpha \left( {{T_{\text{WP}}} - {T_r}} \right) - {u_{\text{P}}}\frac{{\left( {{T_{\text{EP}}} - {T_{\text{WP}}}} \right)}}{{\left( {{L_{\text{P}}}/2} \right)}} + {V_2}\frac{{\left( {{T_{\text{WP}}} - {T_{\text{EA}}}} \right)}}{{\left( {\left( {{L_{\text{P}}} + {L_{\text{A}}}} \right)/2} \right)}}\frac{{{W_2}}}{W} $$

(1a)

$$ \frac{{\partial {T_{\text{EP}}}}}{{\partial t}} = - \alpha \left( {{T_{\text{EP}}} - {T_r}} \right) - H\left( {{w_{\text{P}}}} \right)\frac{{\left( {{T_{\text{EP}}} - T_{\text{EP}}^{\text{sub}}} \right)}}{{{H_{\text{m}}}}} - {V_1}\frac{{\left( {{T_{\text{WA}}} - {T_{\text{EP}}}} \right)}}{{\left( {\left( {{L_{\text{P}}} + {L_{\text{A}}}} \right)/2} \right)}}\frac{{{W_1}}}{W} $$

(1b)

$$ {h_{\text{EP}}} = {h_{\text{WP}}} + b{L_{\text{P}}}{\tau_{\text{P}}} $$

(1c)

$$ \frac{{\partial {h_{\text{WP}}}}}{{\partial t}} = - {r_{\text{P}}}{h_{\text{WP}}} - \frac{{{r_{\text{P}}}b{L_{\text{P}}}{\tau_{\text{P}}}}}{2} - 2\delta {V_1}\frac{{{W_1}{D_1}}}{{W{L_{\text{P}}}}} + 2\delta {V_2}\frac{{{W_2}{D_2}}}{{W{L_{\text{P}}}}} $$

(1d)

where L _P and L _A indicate the basin lengths of the Pacific and Atlantic oceans, respectively. The subscripts “WP” and “EP” indicate western and eastern Pacific, respectively, and “WA” and “EA” are the western and eastern Atlantic oceans, respectively. H(${w_{\text{P}}}$) = ${w_{\text{P}}}$, only when ${w_{\text{P}}}$ is greater than zero; otherwise, H(${w_{\text{P}}}$) is zero.

Fig. 2

Schematic structure of the model used in this study

Equation 1a is the sea surface temperature (SST) tendency of the western Pacific (the temperature in the ocean’s mixed layer), where the first term is a comprehensive representation of the heat exchange at the ocean surface, including the longwave, shortwave, sensible heat, and latent heat that are simply represented as relaxation toward a radiative–convective equilibrium temperature, T _r . When there is no thermal advection, SST becomes a value of T _r (Jin 1997). Therefore, α is a relaxation time scale. The second term is the thermal advection by zonal current; thus, it is proportional to the temperature difference between the eastern and the western Pacific and surface zonal current. The zonal current is given as ${u_{\text{p}}}/\left( {{L_{\text{P}}}/{2}} \right) = {\varepsilon_{\text{P}}}\beta {\tau_{\text{p}}}\left( {{u_{\text{A}}}/\left( {{L_{\text{A}}}/{2}} \right) = {\varepsilon_{\text{A}}}\beta {\tau_{\text{A}}}\,{\text{for the Atlantic Ocean}}} \right)$, where τ _p (also τ _A) is pseudo wind stress defined at the center of the basin as in Eqs. 3a, 3b, of which unit is m, ε _P is a fraction parameter given by ε/(L _P/L), and β is the variation of the Coriolis parameter with latitude; therefore, the surface zonal current was mainly driven by surface wind. Note that the actual role of τ _P in this study just connects the ocean dynamic variables and SST gradient. The third term refers a thermal advection passing through Tethys Seaway, where V ₂ is the speed of the ocean currents through the channel and W is the meridional width of the ocean basin (although the northern and southern boundaries are not exactly defined, the meridional width is assumed to have a similar spatial scale to the equatorial waves or to be slightly wider than them), and W ₁, W ₂ indicate the width of the Panama and Tethys seaways, respectively. W ₁/W and W ₂/W are necessary to account for the difference between mass passing the seaway and that being redistributed over the half of the ocean basin.

Equation 1b is the sea surface temperature tendency equation in the equatorial eastern Pacific. The first term is the Newtonian cooling, as in Eq. 1a, and the second term represents the upwelling of the subsurface water in the eastern Pacific with a temperature, $T_{\text{EP}}^{\text{sub}}$. The subsurface temperature is determined by the depth of thermocline (details are found in Jin (1997)) as follows:

$$ T_{\text{EP}}^{\text{sub}} = {T_r} - \left( {\frac{{{T_r} - {T_c}}}{2}} \right)\left[ {1 - \tanh \left( {\left( {H - {h_{\text{EP}}} - {z_0}} \right)/h*} \right)} \right] $$

and for the eastern Atlantic,

$$ T_{\text{EA}}^{\text{sub}} = {T_r} - \left( {\frac{{{T_r} - {T_c}}}{2}} \right)\left[ {1 - \tanh \left( {\left( {H - {h_{\text{EA}}} - {z_0}} \right)/h*} \right)} \right] $$

Where H is a reference depth from which the model’s dynamic height (i.e., thermocline depth) is measured as a departure, z ₀ is the depth where the upwelling velocity is defined, T _c is the temperature beneath the thermocline, and h* measures the sharpness of the thermocline. The upwelling velocity is defined as ${w_{\text{P}}}/{H_{\text{m}}} = - \xi \beta {\tau_{\text{P}}}\left( {{w_{\text{A}}}/{H_{\text{m}}} = - \xi \beta {\tau_A}\,{\text{for}}\,{\text{the}}\,{\text{Atlantic}}\,{\text{Ocean}}} \right)$, where H _m is the mean mixed layer depth and ξ is a fraction parameter.

The third term in Eq. 1b is the thermal advection passing through the Panama Seaway, where V ₁ is the speed of ocean currents through the channel; thus, it is proportional to the temperature difference between the western Atlantic Ocean and the eastern Pacific Ocean.

Equation 1c indicates that the water pressure gradient between the eastern and western Pacific is maintained by the drag forcing of the wind stress at the central region, which operates under the assumption that the equatorial east–west contrast in the thermocline (or sea level pressure) rapidly adjusts to a given wind stress forcing, which is mainly attributed to a rapid adjustment through the equatorial Kelvin wave.

The thermocline tendency equation in the western Pacific (Eq. 1d) includes a slow-adjustment process applied by a linear damping term, representing the comprehensive slow-ocean adjustment process mainly through the equatorial Rossby waves; a thermocline generation term directly driven by wind stress; and mass exchange terms from the Panama and Tethys Seaways. The mass import or export from one basin to another cannot directly change thermocline depth, but the sea level, and thus change in thermocline depth (i.e., h in the model), must be estimated based on sea level change. The conversion factor δ is used to estimate thermocline depth from changes in sea level, which are based on the simple dynamical relationship between sea level and thermocline depth (e.g., ∆(sea level) ∼ g′∆(thermocline)). D ₁ and D ₂ are the mean depths of the Panama and Tethys Seaways, respectively.

The equations for the Atlantic Ocean were formulated in the same manner as were as those for the Pacific, except that the parameters appropriated to Atlantic Ocean were as follows:

$$ \frac{{\partial {T_{\text{WA}}}}}{{\partial t}} = - \alpha \left( {{T_{\text{WA}}} - {T_r}} \right) - {u_{\text{A}}}\frac{{\left( {{T_{\text{EA}}} - {T_{\text{WA}}}} \right)}}{{\left( {{L_{\text{A}}}/2} \right)}} + {V_1}\frac{{\left( {{T_{\text{WA}}} - {T_{\text{EP}}}} \right)}}{{\left( {\left( {{L_{\text{P}}} + {L_{\text{A}}}} \right)/2} \right)}}\frac{{{W_1}}}{W} $$

(2a)

$$ \frac{{\partial {T_{\text{EA}}}}}{{\partial t}} = - \alpha \left( {{T_{\text{EA}}} - {T_r}} \right) - H\left( {{w_{\text{A}}}} \right)\frac{{\left( {{T_{\text{EA}}} - T_{\text{EA}}^{\text{sub}}} \right)}}{{{H_{\text{m}}}}} - {V_2}\frac{{\left( {{T_{\text{WP}}} - {T_{\text{EA}}}} \right)}}{{\left( {\left( {{L_{\text{P}}} + {L_{\text{A}}}} \right)/2} \right)}}\frac{{{W_2}}}{W} $$

(2b)

$$ {h_{\text{EA}}} = {h_{\text{WA}}} + b{L_{\text{A}}}{\tau_{\text{A}}} $$

(2c)

$$ \frac{{\partial {h_{\text{WA}}}}}{{\partial t}} = - {r_{\text{A}}}{h_{\text{WA}}} - \frac{{{r_{\text{A}}}b{L_{\text{A}}}{\tau_{\text{A}}}}}{2} + 2\delta {V_1}\frac{{{W_1}{D_1}}}{{W{L_{\text{A}}}}} - 2\delta {V_2}\frac{{{W_2}{D_2}}}{{W{L_{\text{A}}}}} $$

(2d)

For the middles of the Pacific and Atlantic oceans, the pseudo wind stresses were defined using the following equations, respectively.

$$ {\tau_{\text{P}}} = {\tau_{{0{\text{P}}}}} - \mu \left( {{T_{\text{WP}}} - {T_{\text{EP}}}} \right)/\beta + \kappa \left( {{\tau_{\text{P}}} - {\tau_{\text{A}}}} \right) $$

(3a)

$$ {\tau_{\text{A}}} = {\tau_{\text{0A}}} - \mu \left( {{T_{\text{WA}}} - {T_{\text{EA}}}} \right)/\beta - \kappa \left( {{\tau_{\text{P}}} - {\tau_{\text{A}}}} \right) $$

(3b)

The first term of each equation is the mean trade wind related to the Hadley circulation, the second term is the zonal wind associated with the zonal SST contrast where μ is the coupling factor (e.g., Jin 1998; Timmermann and Jin 2003), which is a simplified form of Lindzen Nigam’s (1987) formula (see also An 2011), and the third term is the convergence feedback that couples two basins (Watanabe 2008). The first and third terms were not considered in this study.

The speed of the current at the channel is proportional to the water pressure between adjacent oceans, based on Bernoulli’s theorem:

$$ {V_{1}} = - {\theta _{1}}\frac{{\left( {{h_{{{\text{WA}}}}} - {h_{{{\text{EP}}}}}} \right)}}{{\left| {{h_{{{\text{WA}}}}} - {h_{{{\text{EP}}}}}} \right|}}\sqrt {{2g\prime \left| {{h_{{{\text{WA}}}}} - {h_{{{\text{EP}}}}}} \right|}} $$

(4a)

$$ {V_{2}} = - {\theta _{2}}\frac{{\left( {{h_{{{\text{WP}}}}} - {h_{{{\text{EA}}}}}} \right)}}{{\left| {{h_{{{\text{WP}}}}} - {h_{{{\text{EA}}}}}} \right|}}\sqrt {{2g\prime \left| {{h_{{{\text{WP}}}}} - {h_{{{\text{EA}}}}}} \right|}} $$

(4b)

Where g′ is the reduced gravity, and θ ₁ and θ ₂ are the control parameters for the impacts of the seaways. Again, subscript 1 and 2 indicate the Panama and Tethys seaways, respectively.

Finally, the four-box system, including the equations of (1)–(4), was solved using the Runge–Kutta 4th-order scheme. The values of the parameters used in this study are shown in Table 1. The radiative–convective temperature was set to 33°C, which was estimated from the maximum temperature of the tropical western Pacific, so-called the warm pool region (as in Fig. 1). For the control experiment, in which two seaways are open, the mean western and eastern equatorial Pacific SSTs were 30.9°C and 26.1°C, respectively, and the western and eastern equatorial Atlantic SSTs were 30.8°C and 28.0°C, respectively.

Table 1 Basic model parameters

3 Impacts of ocean gateways

The Atlantic and Pacific Oceans were connected through pathways during the Tertiary, unlike the current period. Furthermore, the width of the Atlantic Ocean was narrower and that of the Pacific Ocean was wider than at present. To investigate the impact of ocean gateways, we integrated the simple tropical system introduced in the previous chapter, in which we control two pathways. The effect of the pathways is controlled by tuning the level of the current at the channels. In our four-box model, the control parameters, θ ₁ = 0, θ ₂ = 0 (θ ₁ = 1, θ ₂ = 1) can be interpreted as the closed (open) ocean gateways.

First, we controlled the Panama gateway by setting θ ₁ = 0 (closed) or θ ₁ = 1 (open). Figure 3 shows the SST variation obtained from the aforementioned simple model when the Panama Seaway was open or closed. The model in this study simulated the total SST quantity, representing the interannual variability, such as El Niño, but does not include seasonal variation. When the Panama Seaway was open, the simulated SST in the equatorial eastern Pacific showed a regular oscillation with a period of approximately 4 years. Interestingly, the largest SST in the eastern Pacific almost reached the maximum value of the western Pacific sea surface temperature but did not exceed it. This is because the radiative–convective equilibrium temperature, T _r , at which SST can theoretically reach the highest, was given as an upper bound. Furthermore, if the eastern Pacific SST became higher than the western Pacific SST, then the warm advection by the zonal current would increase the western Pacific SST (this cannot occur because of the strong relaxation toward T _r , as described by a Newtonian cooling term). The western Pacific SST also showed an oscillating feature with the same period, but its amplitude was smaller. The tropical Atlantic Ocean also showed an interannual variation. The SST amplitudes of both the eastern and western Atlantic Oceans were similar to that of the western Pacific Ocean. The mean SST of the western Atlantic Ocean was larger than that of the eastern Atlantic Ocean. The similarity between the two oceans implies that the interannual fluctuation was driven by the interaction between two oceans, the associated mechanism of which can be determined from the results of the closed Panama Seaway.

Fig. 3

a Time series of SST in the equatorial Eastern Pacific (thick solid line), the equatorial western Pacific (thick dotted line), the equatorial Eastern Atlantic (thin solid line), and the equatorial western Atlantic (thin dotted line) obtained from a four-box model for the open Panama Seaway. b The same as in (a) but for the closed Panama Seaway. A coupling coefficient of μ = 0.0035 is used throughout

When the Panama Seaway was closed (Fig. 3b), significant differences between the open and closed cases were observed. The interannual fluctuation in the Atlantic Ocean disappeared. The narrow basin of the Atlantic Ocean might be the main cause of the lack of interannual oscillation. In other words, the oscillation period of the natural mode is related to the adjustment time scale of the ocean basin, generally determined by the equatorial wave dynamics, which are shorter than the annual time scale in the Atlantic Ocean. Closed seaways lead to longer oscillation periods in the Pacific Ocean SST of approximately 6 years. However, the amplitude of the SST in the tropical Pacific remained similar to that of the open Panama Seaway. The longer period for the closed gateway is related to the ocean dynamical adjustment. The ocean dynamical adjustment process proceeds through equatorial wave dynamics such that the equatorial adjustment is mainly accomplished by relatively fast eastward Kelvin waves, with the off-equatorial adjustment occurring due to slower westward Rossby waves. However, when there are boundaries, two equatorial waves interact through boundary reflections. For example, any perturbed signal in the ocean propagates to the east in the form of a Kelvin wave and to the west in the form of a Rossby wave. The eastward propagating equatorial Kelvin wave (the westward propagating Rossby wave) will be reflected as a long Rossby wave (equatorial Kelvin wave) when it hits the eastern boundary (western boundary). Therefore, the opening of a seaway influences the total duration of equatorial waves crossing the ocean basin. We can roughly measure how long a perturbed wave signal at the equator takes to come back to the same position after the propagation and reflection. In case of open seaways, reflection barely occurred, so the returning time is determined by only using the propagation of the equatorial Kelvin wave, thus becoming (L _P + L _A)/C _K, where C _K is the speed of the equatorial Kelvin wave. Conversely, when the seaways are closed, the return time becomes $0.{5}\left( {{L_{\text{P}}}/{C_{\text{K}}} + {3}{L_{\text{P}}}/{C_{\text{K}}}} \right) = {2}{L_{\text{P}}}/{C_{\text{K}}}$(when the perturbation starts at the center of the basin), where the first term indicates the duration of the equatorial Kelvin wave and the second term is the duration of the reflected Rossby wave. The speed of the fastest Rossby wave is approximately one third that of the equatorial Kelvin wave. Since the basin length of the Pacific is significantly longer than that of the Atlantic, the adjustment time for the closed seaway will be longer. Although the reflection at the boundaries cannot be completely ignored, even if the gateways open, the energy and mass exchanges through the gateways shorten the adjustment time.

The sensitivity of the model to the gradual opening of the two gateways, which was controlled by values of W ₁ and W ₂, is depicted in Fig. 4. To determine this, we integrated more than 1,000 years of given values of W ₁ and W ₂, computing the amplitude and period for each case. In Fig. 4, the amplitude indicates a half of the difference between the maximum SST and the minimum SST, and the period indicates the most dominant period of the SST obtained from the spectral analysis. The scale 0 and 1 in each axis stands for the completely closed and completely opened seaways, respectively. W ₁ = 1 and W ₂ = 1 refer to both gateways being open, while W ₁ = 0 and W ₂ = 0 refer to both gateways being closed. As seen in Fig. 4a, the amplitude over the eastern Pacific SST was not sensitive to changes in the seaway, which may indicate that the mechanism for controlling the amplitude of the eastern Pacific SST has nothing to do with changes in the seaway. Conversely, the period (Fig. 4b) of the eastern Pacific SST was sensitive to the seaway, as previously mentioned. In particular, the closed Panama Seaway and the opened Tethys Seaway provided the longest period, of approximately 9 years, while the opposite case produced the shortest period, of approximately 4 years. A period of interannual variation (i.e., ENSO) is usually related to a delayed negative feedback process. When the Tethys Seaway opened, the negative feedback weakens because of a leaking of the Rossby wave energy, which delays the negative feedback (Battisti and Hirst 1989) and results in a slow damping of ENSO and thus a longer period. When the Panama Seaway opened, the heat that escaped from the eastern Pacific into the Atlantic Ocean reduced the positive feedback and easily destroyed the cycle so that the demise of the ENSO seemed to be faster.

Fig. 4

Dependence of a amplitude (°C) and b period (months) of the equatorial eastern Pacific SST on the width of Panama Seaway (W ₁) and Tethys Seaway (W ₂). The unit scale of each axis indicates the maximum width of each gateway. c, d as in (a) and (b), respectively, but for the equatorial eastern Atlantic SST

Both the amplitude and period over the eastern Atlantic SST were significantly modified by seaway changes. The amplitude did not respond to changes of the Tethys Seaway but significantly changed as the Panama Seaway changed (Fig. 4c). The main source of the oscillation took place at the Pacific; thus, the method of transporting energy from the Pacific to Atlantic is a trigger for fluctuation in the Atlantic. When the Tethys Seaway opened, the Rossby wave signal in the Pacific first came into the eastern Atlantic Ocean, and then propagated westward without significantly influencing the eastern Atlantic. After a reflection of this signal as the Kelvin wave at the western boundary, the Rossby wave signal influenced the eastern Atlantic Ocean SST; however, it must have been weakened by damping during the longer propagation. The sensitivity of the oscillation period of the eastern Atlantic SST looks similar to that of the eastern Pacific SST. This may be because the fluctuation over the Atlantic was largely relayed on the fluctuation of the Pacific. As shown previously, when the two oceans were completely disconnected, the oscillation over the Atlantic Ocean disappeared.

4 Impacts of ocean basin size

The supercontinent of Pangaea was gradually separated into several continents during the Cenozoic. In particular, after the early Cenozoic, the width of the Atlantic Ocean grew wider and the width of the Pacific Ocean became narrower, that took place over several tenths of million years. We investigated the impact of the changes in ocean basin width on tropical variability using the model described in the previous section. The ocean basin width in the model was controlled by changing L _P and L _A. The model integrated the different values of L _P (Pacific basin width) and L _A (Atlantic basin width), where L _P was decreased to 70% of its standard value and L _A was increased to 120% of its standard value, which are close to the current sizes of both basins. Figure 4 shows the amplitude and period of the eastern tropical Pacific and Atlantic SSTs with respect to the different basin sizes. As seen in this figure, change in the Atlantic basin size had little impact on the SST fluctuations in both the Pacific and Atlantic. A 20% increase in the width of the Atlantic Ocean may not have been enough to generate a self-sustained interannual oscillation. Conversely, the Pacific basin during the early Tertiary was wide enough to generate a self-sustained interannual oscillation, and even after the Pacific basin was reduced to 70% of its size, the interannual oscillation survived. Since ocean width is related to the period of the natural (or basin) mode of the ocean, a narrower width contributes to a decrease in the period of interannual variation (Fig. 5).

Fig. 5

Dependence of a amplitude (°C) and b period (months) of the equatorial eastern Pacific SST on basin length of the Pacific (B ₁) and Atlatnic (B ₂). The unit scale for each axis indicates the maximum basin length. c, d as in (a) and (b), respectively, except for the equatorial eastern Atlantic SST

5 Concluding remarks

This study determined the possible impacts of changes in two ocean seaways (Panama and Tethys) and two basin sizes (great Pacific and narrow Atlantic) on the tropical oceans during the Tertiary using a prototype model. The model was used in previous modern ENSO studies (Jin 1997; An and Jin 2000) but was modified for this research. The results of our numerical experiments indicate that the opening of seaways did not significantly influence climate variability in the tropical Pacific because the Pacific Ocean was large enough in terms of basin size to generate its own self-sustained interannual oscillation, regardless of the variation in the tropical Atlantic Ocean. Conversely, the climate variability over the tropical Atlantic Ocean, which had a basin that was too small to generate a self-sustained interannual oscillation, was highly dependent on the climate over the tropical Pacific Ocean, and thus the opening of seaways, particularly the Panama Seaway, were critical to the generation of interannual variability in the tropical Atlantic Ocean. For the same reason, the basin size of the Pacific Ocean strongly modified the periods and amplitudes of interannual variability for both the Pacific and Atlantic Oceans.

The prototype model used in this study contains first order physical properties of the tropical atmosphere-ocean coupled system, including a slow ocean adjustment process (e.g., Jin 1997), the simplest possible surface wind response to the SST zonal gradient (e.g., Lindzen and Nigam 1987), zonal and vertical temperature advections in the ocean mixed layer, and Newtonian cooling. Therefore, the climate variability simulated by this model may not be realistic. However, the main purpose of this study was not to simulate realistic climate variability but to provide an insight on the possible impacts of ocean seaway and basin widths on tropical climate variability during the Tertiary, especially interannual variability. Therefore, the dynamic processes depicted in this study remain valid for understanding how tropical climate variability may have been modified by the opening of seaways and by changing basin sizes.