Eddy-induced meridional heat transport in the ocean

Authors


Abstract

[1] A global ocean data synthesis product at eddy-permitting resolution from Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) project are used to estimate the oceanic eddy heat transport. We show that in a number of locations the time-mean eddy heat transport constitutes a considerable portion of the total time-mean heat transport, in particular, in the tropics, in the Southern Ocean and in the Kuroshio Current. This research demonstrates that the variability of the eddy heat transport is a significant contributor to the variability of the total heat transport and globally it explains about 1/3 of its variance. Eddies are also found to explain a significant portion of the seasonal-interannual heat transport variance.

1. Motivation

[2] The ocean's role in climate is primarily determined by its ability to transport heat from the tropics towards the poles. The time-mean oceanic heat transport is of the same order of magnitude as the atmospheric heat transport [e.g., Trenberth and Caron, 2001]. The oceanic temperature flux across any given latitude y at time t is well approximated by:

equation image

where the integration is carried out over depth and zonally, V = V(x, y, z, t) is the meridional component of the absolute velocity across the latitude, θ = θ(x, y, z, t) is potential temperature, ρ is the density of seawater, and Cp is the specific heat capacity of seawater at constant pressure [Hall and Bryden, 1982] (hereinafter referred to as HB1982). In general, the value of Q depends on the definition of zero temperature (e.g., degree K or C). In the absence of the net mass flux across zonal sections Q represents a meaningful heat transport [Montgomery, 1974]. The time-mean of the oceanic heat transport has been reasonably well addressed by combining hydrographic observations using inverse models. For the World Ocean the estimates of the northward heat transport across 24°N range from 1.5 ± 0.3 PW [Macdonald and Wunsch, 1996] to 1.8 ± 0.3 PW [Ganachaud and Wunsch, 2000, 2003] (1 PW = 1015 W). The remaining uncertainties are mainly attributed to the temporal variability unresolved by the one-time hydrographic measurements. The temporal variability of the oceanic heat transport is not well known. Usually, neither the seasonal cycle nor the eddy-induced variability is resolved by full-depth hydrographic surveys. Most of the ocean circulation models, used to compute the heat flux do not adequately reproduce the mesoscale eddy field. HB1982 showed that the eddy heat flux at 24°N could be as much as 25% of the total and it was the largest error in their estimate.

[3] The oceanic meridional eddy heat transport can be estimated by calculating the deviations from the time-mean heat transport:

equation image

where the angle brackets indicate averaging over a certain time interval. It has been perceived that globally eddies play only a minor role in the time-dependent heat transport, but in a number of locations they contribute to the time-mean heat transport [Jayne and Marotzke, 2001, 2002] (hereinafter referred to as JM2001 and JM2002). It has been shown that in some locations the meridional eddy heat transport may be compensated by the mean flow, which transports heat in the opposite direction [Bryan, 1996]. JM2002 estimated the time-mean eddy heat transport using the output of the Parallel Ocean Climate Model (POCM). They found that the zonally integrated eddy heat transport makes a significant contribution to the total time-mean heat transport in the tropics and in the Antarctic Circumpolar Current. In the northern mid-latitudes they estimated a small eddy heat transport with a peak amplitude of 0.2 PW. JM2002 acknowledged, however, that POCM with an average horizontal resolution of 1/4° and 20 vertical levels does not adequately resolve the eddy field. The eddy kinetic energy, simulated by the model, was too weak by a factor of 4 compared to the altimetry observations. Therefore, there is a need to revisit the subject of the eddy heat transport using a higher-resolution and more realistic model. Moreover, the calculations of the eddy heat transport by JM2002 included variability on all time scales, i.e. everything that is time varying, because they used the mean values of θ and V in the equation (2) for the entire 9-year period of their study, which includes temporal variability that is not due to the mesoscale eddies (e.g., semiannual, seasonal and interannual). In addition to the issue of defining the eddy heat transport in terms of time scales, we want to discuss the effects of eddies not only on the time-mean, as has been done earlier [JM2002; Bryan, 1996], but also on the temporal variability of the heat transport.

[4] In this paper we revisit the findings of JM2002 and present results obtained using high-resolution global-ocean data syntheses from the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) project (www.ecco2.org).

2. The ECCO2 Model Simulations

[5] The ECCO2 project aims to synthesize available global-ocean and sea-ice data with a state-of-the-art ocean general circulation model at eddy-permitting resolution. An ECCO2 data synthesis is obtained by least-squares fit of a global full-depth-ocean and sea-ice configuration of the Massachusetts Institute of Technology general circulation model [Marshall et al., 1997] to the available satellite and in-situ data using the Green's function method [Menemenlis et al., 2005]. The model employs a cube-sphere grid projection. Each face of the cube comprises 510 by 510 grid cells for a mean horizontal grid spacing of 18 km. The model has 50 vertical layers and the vertical resolution ranges from 10 m at the surface to 456 m near the bottom. In contrast to the POCM and many other models that have been used to study the Meridional Overturning Circulation and heat transport, ECCO2 includes the Arctic ocean.

[6] The maps of the surface eddy kinetic energy (EKE), computed from satellite altimetry (Figure 1a) and from an ECCO2 simulation (Figure 2b) as half the sum of the squared surface geostrophic velocity anomalies averaged over 10 years, compare reasonably well. As the zonally integrated altimetry- and ECCO2-derived EKE show (Figure 1c), the model still underestimates the variability, but by a factor of 1.5 on average. The removal of the EKE seasonal signal, which is present in some regions [Qiu, 1999], does not significantly change this ratio. This comparison illustrates that using ECCO2 we may expect more robust estimates of the oceanic eddy heat transport than those obtained by JM2002. Because most of the eddy energy is contained in periods less than 100 days, in order to compute the eddy heat transport in the equation (2) we use averages of θ and V computed over 3-month intervals. Therefore, our estimates will include most of the eddy variability as well as shorter period Ekman layer variability and the tropical instability waves in the equatorial regions, but exclude periods longer than 3 months (mainly seasonal cycle, semi-annual and inter-annual variability).

Figure 1.

(a) Altimetry-derived and (b) ECCO2-derived eddy kinetic energy (cm2/s2), and (c) altimetry (blue) and ECCO2 (red) zonally integrated eddy kinetic energy.

Figure 2.

(a) Time-mean zonally integrated total heat transport (PW), (b) time-mean zonally integrated eddy heat transport (PW), (c) standard deviation of the zonally integrated eddy heat transport (PW), and (d) portion of the total heat transport variance explained by the zonally integrated eddy heat transport.

3. Total and Eddy Heat Transport

[7] The time-mean total heat transports for the World Ocean and for individual ocean basins estimated from ECCO2 are displayed in Figure 2a. Individual ocean basins are defined from 37°S to 65°N for the Atlantic and the Pacific Oceans and to 26°N for the Indian Ocean. For the total heat transport the Pacific and the Indian Oceans are treated as one Indo-Pacific ocean basin because of the difficulty to separate them due to the net mass flux associated with the Indonesian Through Flow (ITF). For the eddy heat transport these oceans can be treated separately, because eddies represent deviations from a mean value. The time-mean eddy heat transport for the World Ocean and for the individual ocean basins, defined as the record-mean difference between the total heat transport calculated using total θ and V and that calculated using 3-month averages of θ and V in the equation (2), is presented in Figure 2b. It should be noted, however, that part of the net mass transport of the ITF may still be present in the eddy heat transport estimates for the Pacific and the Indian Oceans because the ITF has intra-seasonal fluctuations of the net mass transport with periods less than 3 months. But we believe that because the time-mean eddy heat transports in the Pacific and in the Indian Oceans do not cancel out (Figure 2b), they are mostly due to eddies and other high-frequency variability rather than to the net mass flux in both oceans.

[8] At 20°N the northward heat transport for the global ocean is almost 1.5 PW (Figure 2a). Nearly 2/3 of this transport (1 PW) is supplied by the Atlantic Ocean and the remaining 1/3 (0.5 PW) is supplied by the Pacific Ocean. These estimates agree well with earlier hydrography-based [e.g., Ganachaud and Wunsch, 2000, 2003] and model-based (JM2002) studies. At many latitudes the eddy heat transport significantly contributes to the time-mean total heat transport, particularly in the tropics (but away from the equator) and in the Southern Ocean (Figure 2b). Near the equator there is a strong convergence with a southward eddy heat transport of about −0.55 PW at 5°N and a northward eddy heat transport of about 0.2 PW at 2°S. In both locations the eddy heat transport has a comparable magnitude as the total heat transport, but with a different sign. This strong convergence is basically associated with tropical instability waves with periods from 20 to 50 days, which have been found to account for most of the eddy heat transport in the equatorial regions [e.g., Jochum et al., 2004]. The equatorial Pacific has the largest contribution to the southward eddy heat transport at 5°N (−0.3 PW). South of the equator the largest contribution to the northward eddy heat transport at 2°S comes equally from the Pacific and Indian Oceans, while in the South Atlantic the eddy heat transport is small.

[9] Further north and south from the equator there are secondary peaks of the eddy heat transport, which are especially notable in the Pacific at about 12°N, in the Atlantic at about 14°N, and in the Indian Ocean at around 12°S. These peaks are mainly concentrated in the western parts of the basins (JM2002). In the western Indian Ocean the peak at 12°S is associated with eddies propagating along the South Equatorial Current as well as with other intra-seasonal variability. Peaks of the eddy heat transport near 12°N in the Pacific and 14°N in the Atlantic are associated with the North Equatorial Currents in both oceans. Elsewhere, the eddy heat transport is large in the Southern Ocean. There, we estimate three peaks of the southward eddy heat transport of about −0.3 PW at 40°S, −0.2 PW at 48°S and 55°S. Thus, in the Southern Ocean the magnitudes of the eddy and the total heat transports are comparable. In the southern Indian Ocean the eddy heat transport, mainly associated with the Agulhas Current, almost reaches −0.1 PW. This constitutes about 15% of the total southward Indo-Pacific heat transport. In the South Atlantic between 37°S and 20°S the eddy heat transport is northward because of the transport caused by Agulhas rings and it constitutes almost 10% of the total heat transport. In the Northern Hemisphere, a significant peak of the northward eddy heat transport of 0.15 PW is located at 36°N and mainly associated with the Kuroshio Current. At this latitude the eddy heat transport equals the total heat transport, which means that eddies play a dominant role in transporting heat northward. Further north starting from 42°N the global northward eddy heat transport is primarily due to the North Atlantic Current eddies, although their contribution to the total heat transport in the North Atlantic at 42°N is about 15%.

[10] The spatial patterns of our estimates of the eddy heat transport are similar to those obtained by JM2002, but different in magnitude. Despite the higher spatial resolution, the ECCO2 eddy heat transports near the equator and in the Southern Ocean are lower than those of JM2002. For example, our estimate of the southern part of the equatorial convergence is 0.21 PW compared to 0.55 PW from the POCM estimate of JM2002. Our estimate of the northern part of the equatorial convergence is −0.55 compared to about −0.9 PW of JM2002. The southward eddy heat transport in the Southern Ocean at 40°S is −0.3 PW compared to −0.6 PW. We attribute this discrepancy to the difference in the definition of the eddy heat transport between our study (variations shorter than 3 months) and JM2002 (all temporal variations). To verify this we computed “eddy” heat transport that includes the variability on all time scales (as by JM2002) and found a much better agreement between our estimates and the estimates of JM2002. The northward and the southward eddy heat transports in the equatorial convergence increased to 0.4 PW and −0.85 PW, respectively. The southward eddy heat transport at 40°S in the Southern Ocean increased to −0.6 PW as shown by JM2002. Another source of difference between our and the POCM estimates is the horizontal resolution. For example, when we compute the “eddy” heat transport similar to JM2002 including variability on all time scales, our estimates at mid-latitudes in the Northern Hemisphere are larger than those obtained by JM2002 by approximately a factor of 1.5 for the World Ocean and a factor of 2 for the Atlantic Ocean at 42°N. This comparison demonstrates (1) the importance of separating the eddy signal from lower frequency temporal variability in future estimates of the eddy heat transport and (2) the need to increase the spatial resolution towards eddy-resolving models (ECCO2 is only eddy-permitting).

4. Temporal Variability

[11] The temporal variations in the eddy contribution to the heat transport variability are believed to be rather small (JM2001), which is essential to our ability to estimate the time-mean oceanic heat transport from compilations of one-time hydrographic sections. JM2001 estimated the root-mean-square variability of the eddy contribution of the order of 0.1 PW over the mid-latitude oceans. This estimate follows the notation of HB1982 and is obtained from the decomposition of the baroclinic heat transport associated with the shear flow into the transport by the zonal mean of the shear flow and deviations from it. The barotropic eddies are, therefore, not included in their computations. By calculating the time-dependent eddy heat transport from (2) only for the periods less than 3 months instead of performing a dynamic decomposition, as done by HB1982, we capture the barotropic eddy contribution in addition to that by baroclinic eddies. As the ECCO2 simulation shows, in most parts of the World Ocean the barotropic eddy heat transport is comparable in magnitude to the baroclinic eddy heat transport; in the Southern Ocean the eddy heat transport is mostly barotropic.

[12] The standard deviation of the eddy heat transport (Figure 2c) shows that its temporal fluctuations are large in the tropics and near the equator with amplitudes of 0.2–0.8 PW. Over the mid-latitude oceans the amplitude decreases to 0.1–0.3 PW, which is not always a small value compared to the time-mean heat transport (Figure 2a). For example, in the Southern Ocean and in the North Pacific the amplitude of the eddy heat transport fluctuations is well comparable to the time-mean heat transport. In the South Atlantic the amplitude of the eddy heat transport fluctuation is around 0.1 PW, which is 20% of the time-mean heat transport. In the North Atlantic the amplitude of the eddy heat transport fluctuation constitutes from 10 to 20% of the time-mean heat transport. At 25°N in the North Atlantic the amplitude of the eddy heat transport fluctuation is 0.15 PW, which is 3 times higher than the value obtained by JM2001, and it constitutes about 15% of the total heat transport. This value, however, is small enough to allow adequate estimates of the time-mean heat transport from hydrographic measurements at this latitude. In many other regions of the World Ocean the eddy noise is larger and it is more difficult to infer the time-mean heat transport using measurements from synoptic hydrographic sections.

[13] The amplitude of the eddy heat transport does not provide any information on its contribution to the variability of the total heat transport. The variability of the heat transport is not a well addressed research topic, because of the inadequate resolution of observations and models. This is especially true regarding the variability of the eddy heat transport. The time-mean eddy heat transport across a particular latitude can be zero, but its fluctuations may contribute to the time-dependent heat transport. Here we address this issue by computing the portion of the variance of the total heat transport explained by the eddy heat transport (Figure 2d). Globally, on average, the eddy heat transport accounts for about 1/3 of the variance. The largest contribution occurs in the North Atlantic Ocean, where in most parts the eddy heat transport explains over 40% of the variance. In the South Atlantic the explained variance reaches 30–42%. In the subpolar gyres of the North Atlantic and North Pacific the explained variance reaches 55% and 40%, respectively. Over most of the Indian Ocean the eddy heat transport explains about 20–40% of the variance. The eddy variability is responsible for the large explained variance in the tropical North and South Pacific (∼60% and ∼40%, respectively) and in the tropical North Atlantic (∼60%), but the time-mean eddy heat transport at this zonal bands is close to zero. In the Southern Ocean the eddy heat transport explains up to 50% of the heat transport variance. These estimates demonstrate that signals with periods less than 3 months, mainly associated with the eddy-induced variability, have an important contribution to the variability of the total heat transport. The rest of the variability is dominated mainly by the seasonal signal, which is well analyzed by JM2001.

[14] In order to understand how much of the seasonal-interannual heat transport variance is due to eddies, we low-pass filtered the time series of the total and eddy heat transport with a 7-month running average (Figures 3a and 3b) and then computed the variance explained by the low-pass filtered eddy heat transport. (Figure 3c). Eddies appear to account for up to 40% of the seasonal-interannual heat transport variance in the Southern Ocean, 20% near the equator and at mid-latitudes in the Northern Hemisphere. At the same time the seasonal-interannual eddy heat transport explains about 10% of the total heat transport variance near the equator and from 5–10% to about 20% of the total heat transport variance at mid-latitudes (Figure 3c).

Figure 3.

(a) The time series of the total (solid curve) and eddy (dashed curve) heat transport at 40°S. (b) The same as Figure 3a, but low-pass filtered with a 7-month running mean. (c) The portion of the seasonal-interannual (solid curve) and the total (dashed curve) heat transport variance explained by the seasonal-interannual eddy heat transport.

5. Summary

[15] We used the ECCO2 high-resolution eddy-permitting global ocean data syntheses to estimate the oceanic eddy heat transport. In contrast to previous studies the eddy heat transport was estimated as the deviation of the zonally integrated heat transport from its 3-month averages. The estimated heat transport, thus, contains signals only with periods shorter than 3 months, which are mainly associated with the eddy variability. Our results show that the eddy heat transport has a significant contribution to the time mean heat transport in the tropics, in the Southern Ocean, and in the Kuroshio Current. Comparing our findings to the earlier study of JM2002 we show the importance of increasing the spatial resolution of models and a proper separation of the eddy signal from lower frequency variability for obtaining robust estimates of the eddy heat transport. This research demonstrates that the variability of the eddy heat transport is a significant contributor to the variability of the total heat transport and globally it explains about 1/3 of its variance. Eddies are also found to influence the seasonal-interannual variability of the heat transport. They explain up to 20% of the seasonal-interannual heat transport variance near the equator and at mid-latitudes in the Northern Hemisphere and up to 40% in the Southern Ocean. In light of these findings synoptic hydrographic measurements can be used to infer the time-mean heat transport, but only at latitudes where the variability of the eddy heat transport is small compared to the total heat transport value. For example, in the subtropical North Atlantic where the Atlantic Meridional Overturning Circulation has been monitored. In other regions, like the North Pacific and the Southern Ocean, eddy noise poses a difficulty to the analysis of heat transport using synoptic observations.

Acknowledgments

[16] This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, within the framework of the ECCO2 project, sponsored by the National Aeronautics and Space Administration. The efforts of all members of the ECCO2 group involved in running model-simulations are appreciated.

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