Impacts of Shortwave Penetration Depth on Large-Scale Ocean Circulation and Heat Transport

a. The circulation model

Both optical models were tested using the most recent version of the National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model (MOM4: Griffies et al. 2003), which solves the hydrostatic, z-coordinate primitive equations. The model resolution is 2° in the east–west direction. The north–south resolution varies from 2° in midlatitudes, to ⅔° in the Tropics. Enhanced resolution is also used in the Arctic, where the tripolar grid of Murray (1996) is used, with an average resolution of 2° × 1°. The model has 50 vertical levels. In the top 230 m the resolution is uniform with a grid spacing of 10 m. Below 230 m vertical grid spacing increases linearly to 366 m at the bottom-most tracer cell.

The model is initialized using temperatures and salinities from the NOAA World Ocean Atlas (see online at http://www.nodc.noaa.gov) and run for a 10-yr period. In the model experiments, both temperature and salinity are restored to seasonally varying observations over a 10-day period. Additional fluxes of heat and freshwater are taken from the output of the GFDL atmospheric model run according to the Atmospheric Model Intercomparison Project (AMIP) protocol. Wind stress is given from a reanalysis dataset created for the Ocean Model Intercomparison Project (OMIP) (Roeske 2001), which includes realistic levels of synoptic variability. For the mixed layer the K-profile parameterization (KPP) scheme of Large et al. (1994) is employed. For the vertical and horizontal advection the “quicker” scheme of (Holland et al. 1998; Pacanowski and Griffies 1999) is employed. The neutral diffusion (Redi 1982) and thickness diffusion (Gent et al. 1995) according to Griffies (1998) and Griffies et al. (1998) is used with an along-isopycnal diffusivity of 1000 m² s⁻¹ for both tracers and layer thickness. Lateral friction is parameterized using a Laplacian viscosity. This consists of two components: one given by a background value that is constant in time and equivalent to the grid spacing times a velocity scale and an additional Smagorinsky-type viscosity that depends on the local horizontal shears (Griffies and Hallberg 2000; Smagorinsky 1963). Away from the equator a dimensionless constant of 2 is used to define the value of Smagorinsky component and a velocity scale of 0.5 m s⁻¹ is used to set the constant term. At the equator the velocity scale used to set the viscosity was much lower (0.05 m s⁻¹) and the Smagorinsky term was set to zero. This allows for a realistically narrow equatorial undercurrent and the presence of tropical instability waves. Vertical diffusivity was made a function of depth using the vertical profile of Bryan and Lewis (1979) with values of 0.05 cm² s⁻¹ in the surface ocean and 1.05 cm² s⁻¹ in the deep ocean.

b. Formulation of shortwave penetration

Solar penetration shifts the location of solar shortwave heating downward in the ocean column, resulting in heating at depth. The profile of downward radiative heat flux I(x, y, z) is represented as

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where I_o- (W m⁻²) is the total shortwave downwelling radiative flux per unit area incident just below the sea surface and J(z) is a dimensionless attenuation function that ranges from 1 at the surface to an exponentially small value at depth. Note that the total downwelling radiation I_o- is to be distinguished from the total shortwave flux I_o, where I_o-= (1 − α)I_o, with α ≈ 0.06 being the sea surface albedo (Morel and Antoine 1994).

Shortwave heating affects the local temperature (T)_t in a Boussineq fluid according to

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In this equation, F^z accounts for vertical processes such as advection and diffusion and C_p is the heat capacity of seawater. Shortwave heating leads to the following net heating rate (K m s⁻¹) over a column of ocean fluid

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with I(η) as the solar radiation at the free surface (z = η).

To compare the effect of solar irradiance parameterization on the ocean general circulation, two parameterizations have been picked that have been explicitly developed for large-scale ocean models with low resolution in depth space (Δz > 5 m).

1) Morel and Antoine solar irradiance parameterization

Morel and Antoine (1994, hereinafter MA94) expand the exponential function used by Denman (1973) into three exponentials to describe solar penetration into the water column. The first exponential is for wavelengths > 750 nm (i.e., I_IR) and assumes a single attenuation of 0.267 cosθ m, where θ is the solar zenith angle. For simplicity, we assume that the solar zenith is zero throughout the daily integration of the model. Thus, the resulting equation for the infrared portion of the downwelling radiation is

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where z is the depth in meters and I_IR−(x, y) is a fraction, of the total downwelling radiation I_o- such that

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where J_IR is the fraction solar radiation in the infrared (750–2500 nm) band. Although MA94 note that water vapor, zenith angle, and aerosol content can each affect the fraction of incoming radiation that is represented by infrared and visible light, in the present implementation, we have chosen to keep these fractions constant so that J_IR = 0.43. For the models used in this paper, the top level is 10 m thick so that essentially all infrared energy is absorbed in the top layer.

The second and third exponentials represent a parameterization of the attenuation function for downwelling radiation in the visible range (300–750 nm) in the following form:

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This form further partitions the visible radiation into long (V₁) and short (V₂) wavelengths, assuming

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and

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V₁, V₂, ζ₁, and ζ₂ are calculated from an empirical relationship as a function of chlorophyll a concentration using methods from MA94 (our appendix A). Throughout most of the ocean, V₁ < 0.5 and V₂ > 0.5. The e-folding length scales ζ₁ and ζ₂ are the e-folding depths of the long (ζ₁) and short visible and ultraviolet (ζ₂) wavelengths. Based on the chlorophyll a climatology used in the GFDL model, ζ₁ should not exceed 3 m while ζ₂ will vary between 30 m in oligotrophic waters and 4 m in coastal regions. All of these constants are based on satellite estimates of chlorophyll a plus pheaophytin-a, as well as parameterizations that have “nonuniform pigment profiles” (MA94). The nonuniform pigment profiles have been proposed to account for deep chlorophyll maxima that are often observed in highly stratified oligotrophic waters (Morel and Berthon 1989).

2) The Ohlmann (2003) shortwave penetration model

The second light transmission parameterization that we use to compare with that of MA94 is based on work done by Ohlmann (2003, hereinafter O03). Instead of three exponentials this parameterization uses two exponential functions, which broadly describe the attenuation of downwelling solar radiation in the visible and infrared wavebands. The HYDROLIGHT in-water radiative transfer model that resolves wavelengths from 250 to 2500 nm (Ohlmann and Siegel 2000) was used to produce synthetic data that could be used to fit a two exponential function and a term that takes into account the incident angle (θ) of the sun and the cloud index (ci):

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The first exponential parameters (V₁ and ζ₁) are used to describe the UV–visible spectrum (300–750 nm). It is this exponential that describes light transmission below 8 m. The second exponential parameters (V₂ and ζ₂) represent the fraction of light in the infrared spectrum (750–2500 nm) and attenuation depth of light between 2 and 8 m. Above 2 m a more rigorous model is needed to look at skin temperature and boundary layer dynamics (Ohlmann and Siegel 2000). All of the parameters in Eq. (9) have been fit as a logarithmic or exponential functions of chlorophyll using a full spectrum (300–2500 nm) light model called HYDROLIGHT (our appendix B). From the HYDROLIGHT model it can be observed that the solar angle of incidence significantly effects the solar transmission when the angle of incidence is >60°. Below that value the angle of incidence is not considered to significantly affect the transmission of light (O03). For consistency we have kept the angle incidence and cloud index equal to 0 in our implementation of this parameterization.

a. Shortwave penetration depths differences between MA94 and O03

As expected, the same spatial patterns exist for both light transmission parameterizations because both parameterizations use the same satellite observations of ocean color (Fig. 1). The main difference between the O03 and MA94 light transmission parameterizations is the penetration depth. Throughout most of the world oceans, the O03 parameterization predicts that the 1% light level is about 10% deeper than that of MA94 (Fig. 2). The difference in penetration depth between the two parameterizations also increases as chlorophyll a decreases (the largest differences are found in clear water). This difference is highlighted in the low chlorophyll a (0.045 mg m⁻³) area in the subtropical gyre of the South Pacific where there is more than an 18% difference in the depth of the 1% light levels. By contrast, in the high chlorophyll a (0.24 mg m⁻³) eastern equatorial Pacific region the difference between penetration depths is less than 10%.

The potential impact of the differences in penetration depth in O03 and MA94 can be further illustrated by looking at the fraction of downwelling shortwave radiation that is absorbed over a 10-m slab centered at the average depth of the annual mixed layer (Table 1). For the eastern equatorial Pacific the O03 parameterization increases shortwave heating at the top of the mean annual thermocline by ∼48% relative to MA94. In the southern subtropical gyre region the increase in shortwave heating at the top of the mean annual thermocline is ∼58%.

b. Model derived differences

While the differences in the penetration depth between O03 and MA94 are intriguing, the purpose of this study is not to analyze these differences in parameterizations but to understand the effects that these differences in shortwave penetration will have on the ocean circulation. From this perspective we focus on model diagnostics in the low latitude regions of the Pacific where the apparent differences between O03 and MA94 shortwave penetration profiles, and the resulting changes in circulation, are most pronounced.

a. Changes in mixed layer depth

From the results described above, the increase in shortwave irradiance at depth associated with the O03 parameterization over most of the low-latitude oceans, caused an increase in mixed layer depth. It is also clear that the difference between the O03 and MA94 parameterizations increases with decreases in the chlorophll a concentrations. It is not clear, however, that there is a direct relationship between the increase in penetration depth and the increase in mixed layer depth. Instead, there is a combination of likely causes for changes in mixed layer depths between parameterizations. These include density gradient below the mixed layer, wind speeds, and relative depth of the mixed layer.

In a one-dimensional analysis Strutton and Chavez (2004) point out that the relatively shallow mixed layer depths of the eastern equatorial Pacific make the mixed layer heat budget of this region particularly susceptible to changes in chlorophyll a concentrations. They point out that for mixed layer depths of 10 m the monthly heating rate would more than double as a result of a change in chlorophyll a concentrations from 0.1 to 0.4 mg m⁻³. One would also expect the same sensitivity from a model with a change in parameterization of shortwave penetration.

Results from the eastern equatorial region show quite the opposite. The change in penetration depth has significantly less effect on the mixed layer depths in the eastern equatorial Pacific than it does in areas to the west or at higher latitudes. There are three possible reasons for this behavior. First, most of the heat is absorbed in the top layer of the model with high concentrations of chlorophyll a. Thus, small changes in penetration of solar irradiance make little difference in such regions. Second, it is likely that large density gradients below the mixed layer (Fig. 4) and the overwhelming effect of the high zonal winds are the main factors that determine variability of the mixed layer depth in the eastern equatorial Pacific. Third, Table 1 indicates that the net change in heating at the base of the mixed layer is less in the equatorial region than areas with lower chlorophyll a concentrations.

In contrast, the biologically unproductive area of the subtropical gyre regions show large changes in mixed layer depths. There are three compounding factors driving these large changes in mixed layer depth: 1) low wind speeds over these regions, 2) small density gradient at the top of the thermocline, and 3) significantly more light penetration at depth in an area of low chlorophyll a concentrations. While regions just off the equator have much lower concentrations of chlorophyll a, a high wind regime (Fig. 9a) maintains deep mixed layer depths. Thus, small changes in the parameterization of chlorophyll a have little effect on the mixed layer depth in regions with strong winds. These observed relationships have been shown in one-dimensional models (Denman, 1973; Simpson and Dickey 1981), which have tested the effect of different parameterizations of solar irradiance on the mixed layer depth. While parameterizations of solar irradiance can have significant effects on mixed layer depths at low wind speeds, little difference in the mixed layer depth is seen at high winds (>8 m s⁻¹). In most studies, 1D models have shown that at higher wind speeds the mixed layer depends equally on the turbulent energy produced by the wind stress and the density gradient below the mixed layer (a measure of the buoyancy force encountered by the wind-driven turbulent mixing). Lewis et al. (1983) also uses similar one-dimensional models to argue that the mixed layer depths in optically clear waters of the subtropical gyres are likely to respond to changes in chlorophyll a concentrations. They argue that subsurface maximum in chlorophyll a are the primary driver for “nonuniform” changes in the local heating rates down through the water column. While there is no doubt that this may be a factor in the real ocean, neither the O03 nor MA94 parameterization simulate the nonuniformities in subsurface irradiance absorption to the degree needed to provide deeper mixed layers suggested by Lewis et al. (1983).

From the preceding discussion it is easy to understand why we see little change in the mixed layer at high latitudes. Essentially there are three basic reasons for this result. The first is high winds, which leads to the second—deeper mixed layer depths at high latitudes. The final reason is that the absolute value of downwelling shortwave irradiance at the sea surface is low. In summary, very little shortwave radiation makes it below the existing mixed layer depths no matter what the chlorophyll a concentration is at high latitudes.

b. Changes in circulation and restoring heat fluxes

While the one-dimensional effects of different parameterizations of solar irradiance in the water column are primarily manifested in changes in predicted mixed layer depth (Denman 1973; Simpson and Dickey 1981; Dickey and Simpson 1983; Woods and Onken 1982; Siegel et al. 1995; Ohlmann et al. 1996), this three-dimensional (GCM) study illustrates secondary responses to changes in the mixed layer depth. The changes in mixed layer depth appear to significantly affect surface restoring heat fluxes and, to a lesser degree, meridional heat transport in the Tropics. The large-scale meridional transport of water from the equatorial Pacific to the midlatitudes is primarily driven by easterly winds (τ_x/ρ). In addition to forcing surface waters away from the equator, easterly winds also drive warm, less dense waters to the west. The resulting pressure gradient forces an opposing meridional transport pushing waters to the low latitudes. The resulting meridional transport (M_y) can be quantified as

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where (1/ρ_o)∂p/∂x is the zonal pressure gradient, f is Coriolis force, η is the sea surface height, and D_ML is the mixed layer depth. The magnitude of the two components driving meridional transport in Eq. (10) are illustrated in Fig. 9. The first is the Ekman component, τ_x/ρ, which is considered to be constant in both model runs. The second is the geostrophic component, ∫^η_DML −(1/ρ)(∂p/∂x)dz, which is calculated to be significantly different for each experiment at 5°S in the equatorial Pacific. Figure 10 suggests that there is very little difference between the zonal pressure gradient, indicating that mixed layer depths are the primary cause of the differences in the total mixed layer meridional transport (fM_y) between these two models. The difference between the fM_y using the O03 and MA94 parameterizations is compared directly with the model diagnostics at 5°S in the equatorial Pacific (Fig. 11). Although small-scale differences exist because of lateral viscosity and other small-scale processes, the large-scale similarity between model simulated meridional transport and that computed [Eq. (10)] suggest that mixed layer depths are a dominant source of the variability in meridional mass flux at 5°S.

While it is clear from Eq. (10) that changes in either the zonal pressure gradient or the mixed layer depth, changing the shortwave penetration apparently results in a change in the mixed layer depth, without major changes in the baroclinic structure and thus in the surface pressure gradient. Deepening mixed layers throughout the tropical oceans results in an ∼10% decrease in poleward transport of water in the surface oceans using the O03 parameterization (relative to the MA94 parameterization).

Interestingly, the slowdown in poleward transport of surface waters results in a much smaller (4%) change for the net meridional heat transport (Fig. 7). We attribute the small decrease in heat transport despite the larger changes in mass transport to changes in the temperature gradients in mixed layer off the equator. A moderate (10%) decrease in the surface restoring heat flux (Fig. 5) at the equator indicates a warming of surface waters at the equator. At the same time, a more pronounced (>20%) increase in restoring heat flux off the equator in the subtropical gyre areas indicates a cooling of surface waters. The combination of these results is a significant increase in the meridional heat gradients that significantly impacts the total poleward heat transport.

To further test the effect of changing mixed layer depths on the overturning circulation and heat transport, a third model run was performed that combined both the O03 and MA94 shortwave parameterizations. The MA94 solar irradiance parameterization was used out to 10° latitude and then tapered to the O03 parameterization poleward of 15° latitude. In this case the change in overturning circulation clearly shows the predicted response: a slowdown in overturning circulation due to deeper mixed layers from ∼10° poleward to 30° latitude (Fig. 12). While there is only an overturning response from ∼10° to 30° latitude, small increases in temperature (0.1°C) in the thermocline at latitudes below 10° are evident (Fig. 13) indicating an increase in transport of heat below the mixed layer toward the equatorial region. The increase in transport of heat from the extratropics to the equator due to deeper solar irradiance penetration beyond latitudes of 10° is further exhibited by the reduction in restoring heat flux needed at the equator (Fig. 14).

While it clear that changing the parameterization of shortwave penetration depth using chlorophyll a concentrations makes a difference to the ocean circulation and heat transport, it is important to point out how changes in chlorophyll a concentration might change ocean circulation and heat transport. In particular, this study does not address how interseasonal or interannual variability in chlorophyll a concentration might affect ocean circulation or heat transport. In each model scenario the seasonal variability remains constant with no interannual variability. In addition, the differences shown between models are the result of 10-yr runs—the time necessary to reach a mechanical steady state in the tropical ocean. The results of this study illustrates how the meridional circulation and heat transport may change as a result of long term (> 1 yr), secular changes in chlorophyll a concentration both on and off the equator. On the equator, satellite observations of chlorophyll a suggest increases of almost 25% in surface chlorophyll a based on a comparison CZCS (1979–86) and SeaWiFS (1997–2000) records (Gregg and Conkright 2002). While these changes may be significant, it is difficult to assess how the observed trends in chlorophyll a have been biased by interannual variability on the equator. In particular, the SeaWiFS record does not include an El Niño event. Off the equator, at midlatitudes, satellite observations do not indicate that large changes in chlorophyll a have occurred in the long term. However, a time series of field measurements made in the North Pacific subtropical gyre (Karl et al. 2001; Venrick 1992, 1999; Venrick et al. 1987) show that chlorophyll a concentrations have more than doubled in the last three decades. A doubling of chlorophyll a concentrations from an average value of 0.04 mg (Chl a) m⁻³ to the present values 0.08 mg (Chl a) m⁻³ in the North Pacific subtopical gyre region would result in a 20% decrease in the penetration depth of solar irradiance in that region. This decrease in penetration depth is almost twice the difference between the O03 and MA94 parameterization in that region. From this perspective, the relevance of comparing the O03 and MA94 parameterizations is highly justified.

Since the days of Sverdrup (1953), there has been a strong belief that the inventory of light-adsorbing biomass in the water column is strongly controlled by mixed layer depth. It is therefore hard to assert that the observations of increased chlorophyll a concentrations in the North Pacific subtropical gyre will drive significant changes in the mixed layer depth since both mixed layer depth and chlorophyll a concentration are coupled and feed back on one another. By comparing the O03 and MA94 parameterizations, we are able to explore the relative role that light penetration plays in the feedback between ocean primary productivity and ocean circulation. Based on the results of this study, we expect that increases in chlorophyll a concentration would result in a decreased heat transport to the Tropics below the thermocline because of a decrease in penetration depth. Concurrently, we would also expect an increase in the meridional overturning circulation in the areas where mixed layer depth decreased. Further work is needed using an OGCM with interactive biogeochemistry to understand the full extent of the coupling between chlorophyll a concentration and ocean circulation.

c. Relevance of simulation to other studies

The effect of changing mixed layer depth through the parameterization of solar irradiance in water on the GCM provides significant insight into the mechanisms driving other modeling results. It also provides insight into how changes in biological production may affect circulation and the air–sea exchange of heat.

As with this study, previous studies by Murtugudde et al. (2002) and Nakamoto (2001) show that while a decrease in the attenuation depth of solar irradiance in the eastern equatorial Pacific causes mixed layer depths to decrease, there is no associated increase in SST as one might conclude when using a simple one-dimensional model. Nakamoto et al. (2001) use an isopycnal ocean GCM to show that 20-m decreases in mixed layer depths in the eastern equatorial Pacific due to higher chlorophyll a concentrations are concurrent with 2°C decreases in SST. In a similar study, Murtugudde et al. (2002) show that mixed layer depths decrease with increases in the attenuation of solar irradiance in the water column and that the change in SST is negative. However, Murtugudde et al. (2002) also suggest that both the response of the mixed layer depth and SSTs are variable depending on the degree to which the attenuation of solar irradiance is changed. While a change from a 25-m to 19-m shortwave attenuation e-folding depth in the eastern equatorial region made little difference to SSTs, a further decrease in attenuation depth to 17 m made a large difference in SST (∼1°C).

Although Murtugudde et al. (2002) argue that the difference in response to changes in e-folding depth of solar irradiance at the equator is merely the result of absolute changes in radiant energy below the thermocline, it is also likely that changes in mixed layer depths off the equator have an impact. As noted above, Murtugudde et al. (2002) run three different scenarios: one with a constant attenuation depth of 25 m, one with a constant depth of 17 m, and one with a variable depth attenuation based on the chlorophyll a concentration. In the scenario with variable attenuation depths, the mean attenuation depth is 19 m in the eastern equatorial Pacific and ∼25 m in the subtropical gyres. Thus, there is little difference between the penetration depths in the subtropical gyre regions when comparing the Murtugudde et al. (2002) experiment with a constant attenuation depth of 25 m to the experiment using spatially varying attenuation depths. Considering the observation made in our study, it is likely that the larger difference in equatorial SST observed by Murtugudde et al. (2002) between a spatially constant attenuation depth of 17 m and a spatially variable attenuation depth experiment is, in part, due to large differences in penetration depths off the equator.

d. Impact of off-equatorial processes on the equator

The off-equatorial impact can be demonstrated from two perspectives in this study. The first is the correlation between changes in meridional overturning circulation and off-equatorial changes in mixed layer depth demonstrated above [Eq. (10)]. With increases in mixed layer depth through deeper penetration of shortwave irradiance, there is a decrease in meridional divergence resulting in less upwelling of cold sub-mixed-layer waters. The result is a decrease in restoring heat flux, which is likely to translate into an increase in SSTs in a coupled ocean–atmospheric model. The second perspective is the longer term (>1 yr) transport of heat stored below the mixed layer with deeper penetration of solar irradiance in tropical and subtropical regions off the equator. This is demonstrated by the decrease in restoring heat flux at the equator resulting from moving to the deeper O03 parameterization in waters beyond 10° latitude (Fig. 14). The temperature changes in the thermocline at the equator appear to be the result of transport along isopycnals below the mixed layer from the extratropics (Fig. 13). Thus, the increase in temperatures below the mixed layer on the equator resulted in a decrease in the restoring heat flux needed to maintain SSTs at the equator (Fig. 14) despite the fact that no changes were made to the solar irradiance penetration depth at the equator. This result would imply that the deeply penetrating irradiance parameterization of O03 outside the equatorial region may be adding significant amounts of heat into the equatorial region. By inference, a decrease in chlorophyll a concentrations off the equatorial regions may act to increase SSTs at the equator. In summary, both deeper mixed layers off the equator and the transport of excess heat from the extratropics are mechanisms that are likely to affect SST at the equator.

This study has two important implications for our understanding of the overturning circulation and heat transport. The first is that when looking at near-equatorial dynamics, it is a mistake to think of the mixed layer as dynamically thin. In theoretical studies such as Luyten et al. (1983) the mixed layer is considered to be thin in comparison with the layers carrying the geostrophic, wind-driven flow. With such a limit, the Ekman pumping into the ventilated thermocline is essentially due to the wind stress alone. However, near the equator, the poleward flow in the mixed layer is balanced by an equatorward flow over a few hundred meters depth. A 50-m-deep mixed layer overlaps a substantial fraction of this flow. Changing the mixed layer depth induces a significant change in the Ekman pumping felt by the main thermocline.

The model results also have implications for understanding the relationship between mechanical forcing of the ocean and thermal heat transport by the ocean. The meridional overturning circulation is mechanically driven (Munk and Wunsch 1998; Toggweiler and Samuels 1998; Huang 1999; Gnanadesikan et al. 2005). For many years it has been thought that increasing mechanical mixing within the pycnocline would result in an increase in watermass conversion and poleward heat transport. An increasing flux of mechanical energy leads to an increased storage of available potential energy and thus more heat transport. However, this study demonstrates that such a relationship is not true for all energy inputs. While increasing the penetration of shortwave radiation does result in an increase in available potential energy, as heat is stirred deeper into the water column, it is also associated with a decrease in heat transport and watermass conversion. Gnanadesikan et al. (2002) found a similar result when they increased mixing within the surface layer in a 4° GCM. In conclusion, one cannot extrapolate simply from mechanical energy input to heat transport.