The seasonal cycle of meridional heat transport at 24°N in the North Pacific and in the global ocean



[1] An improved estimate of the Kuroshio transport and its seasonal variation derived from the World Ocean Circulation Experiment (WOCE) moored current meter array east of Taiwan (referred to as PCM-1) is combined with various wind products and available hydrographic data in the ocean interior to determine the meridional heat transport at 24°N in the North Pacific. The resulting seasonal cycle of meridional heat transport has a minimum heat flux of ∼0 PW in January and February and a broad maximum in the second half of the year, with a peak of 1.1 PW in July and a secondary maximum of 1.0 PW in November. The annual mean heat transport is 0.62 PW, with an uncertainty of 0.2 PW. Of the total heat transport, 0.37 PW is associated with the “overturning” circulation, and 0.25 PW is contributed by the horizontal “gyre” circulation. The Parallel Ocean Program (POP) model simulation of the meridional heat flux at 24°N compares favorably with the observations with regard to both the seasonal variation and the annual mean value. The vertical and horizontal cells are found to contribute about 3/5 and 2/5 of the total heat transport, respectively, and they are confined in the upper ocean on the annual mean and longer timescales. However, for the seasonal variation the vertical cell dominates the variation and involves circulation changes through the entire water column, while the horizontal cell heat flux remains nearly constant year-round. The new estimate of meridional ocean heat flux across 24°N in the Pacific is combined with an updated estimate in the Atlantic at this latitude to yield a total oceanic heat flux across the latitude circle of 24°N of 2.1 ± 0.4 PW, with an annual cycle that ranges from 1.1 PW in February to 2.8 PW in August. This is the first such estimate of the seasonal cycle of the world ocean heat flux across 24°N from direct oceanographic observations.

1. Introduction

[2] Heat transport by ocean currents plays an important role in determining the rate of global climate change and regional climate patterns [U.S. World Ocean Circulation Experiment, 1991]. Observations and model experiments show that 24°N is close to the latitude of maximum poleward ocean heat transport [Vonder Haar and Oort, 1973; Carissimo et al., 1985; Semtner and Chervin, 1992]. At this latitude the oceanic northward heat flux takes place in two basins, the Atlantic and the Pacific. With well-established Florida Current transport estimates, the transatlantic heat flux across this latitude has been extensively investigated, and its annual mean value and seasonal cycle have been quantified [Hall and Bryden, 1982; Roemmich and Wunsch, 1985; Gordon, 1986; Molinari et al., 1990; Fillenbaum et al., 1997]. A thorough study of the heat transport in the Pacific sector is thus necessary to supplement these values and to understand the world ocean heat transport across this latitude circle.

[3] Both indirect and direct methods have been used to estimate the oceanic heat flux through zonal sections using observational data. There are two indirect methods, the “air-sea exchange” method and the “radiation budget” method, the details of which are reviewed by Bryden and Imawaki [2001]. The sparsity of observations in the oceanic and atmospheric boundary layer and errors in the bulk formulae used to calculate the sea surface heat fluxes can result in large uncertainties in the estimates of meridional oceanic heat transport using the “air-sea exchange” method [e.g., Talley, 1984]. Until recently, results from the radiation method were substantially different from those derived from direct ocean observations [Bryden, 1993]. Trenberth and his colleagues [e.g., Trenberth and Solomon, 1994] presented more reasonable results using compatible top-of-atmosphere radiation from the Earth Radiation Budget Experiment combined with European Centre for Medium Range Weather Forecasts (ECMWF) reanalysis, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis, and Comprehensive Ocean Atmosphere Data Set (COADS). They showed that earlier residual calculations suffered from biases in the satellite measurements and poor estimates of the atmospheric heat transport over the oceans, where there were few observations.

[4] Direct methods for determining the meridional ocean heat transport involve calculation of the meridional heat flux integral from transoceanic zonal hydrographic data coupled with current measurements near the boundaries. Hall and Bryden [1982] used annual mean volume and temperature transport of the well-defined Florida Current in addition to hydrographic data along 24°N to estimate the transatlantic heat flux and to conduct an error analysis. Their work established the direct method as the most reliable one for estimating the oceanic heat transport. Bryden et al. [1991] estimated the transpacific heat flux across 24°N to be 0.76 ± 0.3 PW northward from the one-time transpacific hydrographic survey (P03) along this latitude. A similar estimate of 0.75 PW was obtained by Roemmich and McCallister [1989] using an inverse model of the North Pacific constrained by sections at 24°N, 35°N, and 47°N, and additional meridional hydrographic sections made in different years (and different seasons), under an assumption that the ocean was in steady state. However, more recent global inverse models by Macdonald and Wunsch [1996] and Ganachaud and Wunsch [2000], using the same 24°N section data and other available transbasin hydrographic sections, suggest a lower northward heat flux of 0.5 ± 0.3 PW across 24°N in the Pacific. The available mean transpacific heat flux estimates using either direct or indirect methods at 24°N are summarized in Table 1, which shows a rather large range of values.

Table 1. Previous Estimates of Oceanic Heat Flux Across 24°–25°N in the Pacific Oceana
ReferenceHeat Flux, PWMethod
  • a

    Error bars that are available in these studies are also listed.

Talley [1984]∼0 ± 0.3surface heat flux
Moisan and Niiler [1998]0.3 ± 0.15and heat storage
Esbensen and Kushnir [1981]0.74 
Oberhuber [1988]0.79 ± 0.3 
Hsiung et al. [1989]0.83 ± 0.6 
Hastenrath [1980]1.10radiation, atmospheric heat transport
Keith [1995]1.2 ± 0.5 
Trenberth and Solomon [1994]0.96 ± 0.18 
Trenberth [1997]0.7 ± 0.3 
Trenberth et al. [2001]
Wilkin et al. [1995]0.37Semtner and Chervin [1992]
Roemmich and McCallister [1989]0.75hydrographic
Bryden et al. [1991]0.76 ± 0.3 
Macdonald and Wunsch [1996]0.5 ± 0.3 

[5] The error analysis performed by Hall and Bryden [1982] suggests that errors in estimating the transport of western boundary currents on continental slopes and over shallow regions can introduce large errors into meridional oceanic heat flux estimates. The oceanic state measured by a single hydrographic section can be aliased by eddies and seasonal and interannual variability, especially near the western boundary where the variability is most energetic. The uncertainty of the Kuroshio volume and temperature transport may thus lead to significant errors in presently available transpacific heat flux estimates.

[6] Here we make a new estimate of the annual mean meridional ocean heat transport across 24°N in the Pacific and its seasonal variation using the WOCE PCM-1 array data [Johns et al., 2001], various wind data sets, and an improved interior hydrographic climatology. The main purpose of this paper is to use the new PCM-1 Kuroshio transport measurements to constrain the 24°N Pacific meridional heat transport estimate. By incorporating the PCM-1 transport time series measurements, errors introduced into snapshot surveys by eddies and seasonal variations can be largely reduced or removed. A second purpose of this paper is to compare the observed heat flux estimate with model simulations by the Parallel Ocean Program (POP) in the Los Alamos National Laboratory. These model-data comparisons not only provide the necessary validation for model simulations to be used for climate studies but also test the methods used to calculate meridional heat flux from limited observational data and to help understand the associated heat flux mechanisms.

[7] After this introduction the paper is organized as follows: Section 2 briefly introduces the heat flux calculation method and procedures used to prepare the hydrographic data fields in the interior ocean, as well as the POP model configuration. In section 3 we present the time series of heat transport in terms of three principal (mass-balanced) components: the Kuroshio heat transport, the interior ocean baroclinic (geostrophic) heat transport, and the Ekman heat transport. In section 4 we compare the mean heat transport and its seasonal cycle with that of the POP simulation, followed by an investigation of the heat transport mechanisms. The heat transport estimates from this study are then combined with the climatological estimates in the Atlantic near 24°N [Fillenbaum et al., 1997] to form an estimate of the seasonal cycle of the heat transport across the world ocean at 24°N. Section 5 presents a summary and conclusions.

2. Methodology and Data

2.1. Method

[8] Jung [1952], Bryan [1962], and Warren [1999] have demonstrated that meridional oceanic heat flux Qnet, through a zonal cross section, can be adequately approximated by

equation image

where Cp is the specific heat capacity at constant pressure, ρ is the density of the sea water, v is the north-south component of absolute velocity, θ is the potential temperature, L is the width of the basin at the particular latitude being considered, and H(x) is the depth of the ocean. A meaningful estimate of the meridional ocean heat flux requires the above integration over a full oceanic section with a zero net mass transport; otherwise, the calculated heat transport depends on an arbitrary temperature reference [Montgomery, 1974]. In the following analysis we will refer to the integration over a zero net mass transport as the heat transport or heat flux and to the integration over a nonzero transport section (say the PCM-1 section across the Kuroshio) as the temperature transport (referenced to 0°C). The mass transport across the 24°N Pacific section is indeed nearly zero because there is only a small transport occurring through the Bering Strait with negligible effects on the poleward heat flux calculation at midlatitudes [Hall and Bryden, 1982; Bryden et al., 1991].

[9] Following the general methodology of Hall and Bryden [1982], we break down the total meridional heat flux into components which represent the western boundary current (Kuroshio) contribution QK, the interior baroclinic contribution due to geostrophic flow QI, and the Ekman contribution QEK,

equation image

These contributions are given by

equation image

QK can also be broken down into barotropic and baroclinic contribution terms as

equation image

where VK = ∫ ∫Kvdxdz is volume transport; VEK is Ekman transport, equation image; equation image is vertically averaged θ, v; θ′(x, z), v′(x, z) is deviation from vertical average; 〈θ〉 is vertically and zonally averaged θ; and equation image is flow-weighted average θ. Subscripts K, EK, and I represent the region of the Kuroshio, the cross-basin Ekman layer, and the interior ocean, respectively, over which the integrals or averages are calculated. For the detailed derivation of these breakdowns the reader is referred to Bryden and Hall [1980], Hall and Bryden [1982], and Molinari et al. [1990]. The above quantities represent long-term mean or climatological (monthly mean) values and do not include eddy transport terms that can arise due to temporal correlations of the velocity and temperature fluctuations, which are later shown to be small at this latitude. For each of the terms above we calculate climatological annual cycles and the annual mean values, which then are combined to yield the total 24°N transpacific heat flux and its seasonal variation.

2.2. Kuroshio Measurements by the PCM-1 Moored Array

[10] The estimate of heat transport contribution by the Kuroshio is primarily based on the current and temperature observations collected by a current meter array moored in the East Taiwan Channel (ETC). This array (Figure 1) is referred to as the PCM-1 array, deployed between September 1994 and May 1996 as part of the WOCE. Figure 1 displays the mooring locations of this array that survived the harsh sea conditions and heavy fishing activities in this region. Formed by the Ilan Ridge between the east coast of Taiwan and the southern Ryukyu island of Iriomote, the ETC serves as a choke point for the Kuroshio flowing across the 24°N section into the East China Sea (ECS) and provides a natural location for monitoring the Kuroshio. A detailed description of mooring deployments and data recovery is given by Johns et al. [2001].

Figure 1.

(top) Schematic of the western boundary currents with estimated mean transports in the vicinity of the East China Sea [Nitani, 1972]. The striped area east of Taiwan marks the East Taiwan Channel, where the WOCE PCM-1 moored current meter array was deployed. (bottom) Moorings and tide gauge locations on the topography of the Ilan Ridge. Shaded area indicates depth <200 m.

[11] Prior to the deployment of the PCM-1 array, estimates of the mean transport of the Kuroshio near 24°N ranged from 20 to 33 Sv, mainly determined from hydrographic sections across the East China Sea [Guan, 1981; Nitani, 1972; Ichikawa and Beardsley, 1993; Roemmich and McCallister, 1989; Bingham and Talley, 1991]. From the PCM-1 observations [Johns et al., 2001; Zhang et al., 2001; Lee et al., 2001] the Kuroshio transport is found to have large fluctuations of O (±10 Sv), which can occur on timescales of days when the crests of 100-day period Kuroshio meanders collide with the southern Ryukyu Islands and cause large amounts of Kuroshio water to bypass the entrance to the East China Sea. This short-term transport variation reaches 50% of the mean Kuroshio transport and makes transport estimates from limited number of hydrographic sections less suitable for representing the annual mean. Nevertheless, among the historical transport estimates the mean transports of Guan [1981] and Ichikawa and Beardsley [1993], 21.3 and 23.7 Sv, respectively, are very close to the mean transport, 21.5 ± 2.5 Sv, derived from the 600-day continuous PCM-1 moored current records [Johns et al., 2001]. The above two historical estimates both used a large number of hydrographic sections to estimate the mean transport in the ECS. Recently, Liu et al. [1998] estimated the mean Kuroshio transport to be 22.6 Sv using 11 shipboard acoustic Doppler current profile (ADCP) sections across the ETC to average out the tidal signals.

[12] In this study, we used cross-sectional fields of downstream velocity v and potential temperature θ derived from the PCM-1 array on a 5-km horizontal and 25-m vertical grid to estimate the temperature transport of the Kuroshio. In the following, horizontal currents are rotated by 30° so that v is downstream and perpendicular to the alignment of the array. All quantities were low-pass filtered with a 40-hour Lanczos filter to remove tidal and inertial oscillations and were subsampled at 12-hour intervals. The methods used to generate the gridded θ and v fields are described and validated by Johns et al. [2001]. The extrapolation of θ into the surface layer considers the vertical shear measured by the mooring and seasonal variation of SST from cross-channel conductivity-temperature-depth (CTD) surveys during 1990–1996 [Johns et al., 1995; Liu et al., 1998].

[13] The results from the PCM-1 array are shown in Figure 2. The time series shown include the total volume and temperature transport (referenced to 0°C), and the barotropic and baroclinic components as defined in equation (1). All time series show the influence of the dominant 100-day period Kuroshio variation in the ETC [Zhang et al., 2001; Johns et al., 2001], though the effect is particularly obvious in the barotropic and total temperature transport, both of which closely resemble the volume transport time series. The barotropic component of the temperature transport is much larger than the baroclinic component, similar to that found for the Florida Current [Molinari et al., 1990]. The mean barotropic and baroclinic temperature transports of the Kuroshio in the ETC are 1.47 and 0.32 PW, compared with 2.15 and 0.33 PW, respectively, in the Florida Current from Molinari et al. [1990]. The total temperature transport varies from approximately 0.8 to 2.8 PW, a range of 2.0 PW, and it can fluctuate up to 0.8 PW in days. This huge variability of the total temperature transport in the ETC is caused by Kuroshio offshore meandering. It suggests that any estimates of the annual mean or seasonal cycle of the Kuroshio heat transport based on the limited number of synoptic hydrographic surveys could be largely aliased by these strong mesoscale variations.

Figure 2.

(a) Temperature transport (thick curve) and volume transport (thin curve, right-side axis) of the Kuroshio and (b) barotropic (thick curve) and baroclinic (thin curve) Kuroshio temperature transports in the East Taiwan Channel, derived from the PCM-1 moored current meter array.

[14] The spatial structures of mean temperature transport and eddy heat flux of the Kuroshio in the ETC during the PCM-1 period are shown in Figure 3. Here the mean eddy heat flux is defined as

equation image

where asterisk represents deviations of the variables from their long-term time averages, denoted by〈 〉t. This quantifies the meridional heat flux due to temporal correlation between the velocity and temperature fluctuations. Both the mean temperature transport and eddy heat flux are concentrated near the mean Kuroshio core. However, the eddy heat flux of the Kuroshio over the PCM-1 period is only 0.007 PW, which is <1% of the total temperature transport. The remarkably small eddy heat flux shown here in the western boundary region, where mesoscale eddy is expected to be strongest, and in the interior ocean at this latitude shown by Stammer [1998] based on altimetry data suggests that the eddy contribution to the oceanic meridional heat flux is probably negligible at this latitude. A similar conclusion was reached by Fillenbaum et al. [1997] using the current meter data collected to the east of Bahamas in their study of the Atlantic ocean meridional heat flux at 24°N.

Figure 3.

(a) Temperature transport, average 〈vt〈θ〉t cross section of PCM-1 array. (b) Eddy heat flux average 〈v*θ*〉t cross section of PCM-1 array. Units are cm s−1 × °C. Superimposed are the instrument positions, circles for temperature measurements and crosses for velocity measurements.

2.3. High-Resolution Hydrographic Climatology

[15] For the interior baroclinic heat flux, QI, we use the Levitus [1994] climatology across the 24°N section combined with an enhanced “Hydrobase” [Curry, 1996] analysis of the available historical hydrographic station data in the western boundary layer off the Ryukyu Islands. The Fillenbaum et al. [1997] study in the Atlantic showed that the large-scale smoothing and 1° resolution of the Levitus data set is not sufficient for capturing the detailed shear structure and baroclinic heat flux in the equivalent Atlantic regime off the Bahamas. We will show in the following that the large-scale Levitus smoothing spreads the Kuroshio signature into the interior of the western Pacific off the Ryukyus. Considering these limitations, we use the Hydrobase analysis package to generate a higher resolution (0.25° × 0.25°) bimonthly climatology across the Pacific basin from 20°N to 30°N. Another advantage of this approach is that Hydrobase analysis averages the scattered station data onto isopycnal surfaces rather than depth or pressure levels. This isopycnal average has been shown to avoid the creation of unrealistic water properties, which occurs when averaging on depth or pressure levels in strong frontal regions [Lozier et al., 1994].

[16] The original quality-controlled station data in the North Pacific were obtained from Macdonald et al. [2001]. Their base data sets are the same as the World Ocean Atlas 1994 [Boyer and Levitus, 1994] plus the available 579 WOCE and pre-WOCE CTD stations. We conduct similar quality control procedures to include the new data published in the National Oceanographic Data Center (NODC) World Ocean Database (1998) and the CTD data from 20 recent cruises in the ETC and the western Philippine basin in the 1990s. The final quality-controlled T and S data are grouped bimonthly. Figure 4 shows the data distribution of January–February and July–August, which corresponds to the minimum and maximum data coverage, respectively. To resolve the seasonal variation in the interior ocean, a large radius of influence must be applied to interpolate station data onto grids as by Levitus [1994], whereas in this study, there is enough data in the western and eastern boundary regions to generate a higher resolution climatology with a smaller smoothing distance.

Figure 4.

Station locations of all available temperature and salinity measurements (both T and S are measured) in January–February and July–August, representing the worst and best data coverage seasons, respectively, in the year. The data includes the National Oceanographic Data Center (NODC) World Ocean Database 1998 (WOD98), available World Ocean Circulation Experiment (WOCE) and pre-WOCE conductivity-temperature-depth (CTD) sections, and the CTD surveys conducted in the western Philippine basin in the 1990s.

[17] In addition to the above hydrographic station data, a large number of temperature-only (expendable bathythermograph (XBT) and mechanical bathythermograph (MBT)) profiles are incorporated into the analysis to better represent the climatological states, especially in the upper several hundred meters near the western boundary where mesoscale features are prominent [Zhang et al., 2001]. By combining these temperature profiles with climatological salinity values derived from locally tight TS relations, more than 10,000 additional profiles are recovered in the region from the Ryukyu Islands to 145°E. To generate the 0.25° by 0.25° bimonthly climatology, we first average the station data into 0.25° bins while attempting to maintain at least 10 observations per bin, allowing a search radius of up to 2° if necessary. This technique results in less smoothing in the well-sampled regions and greater smoothing in the more poorly sampled regions. Instead of making a new climatology in the interior from 145°E to 130°W, where data is still sparse, we retain the Levitus [1994] monthly climatological T and S profiles on their original 1° grid for this region. A final 2° Parzen filter is performed to damp small-scale variations. All of the above procedures are performed on the isopycnal surfaces, and the data are then projected back to depth levels of Levitus [1994]. We do not expect any large differences between averages on the isopycnal and level surfaces in the interior ocean where the isopycnal surfaces are relatively flat and energy levels are relatively low [Macdonald et al., 2001].

[18] Figure 5 illustrates the difference between the annual mean potential temperature of the high-resolution climatology and Levitus [1994] along 24.5°N. The only obvious difference is in the western boundary region, both within the ETC and to the east of Ryukyu Islands. The shear signature of the Kuroshio in the ETC is almost nonexistent in Levitus's [1994] climatology because of the coarse resolution and the greater smoothing distance. East of the Ryukyus the Levitus [1994] climatology is warmer due to the artificial spreading of the Kuroshio shear to 130°E. In the following sections we will calculate the geostrophic baroclinic heat flux from both Levitus [1994] and this new blended climatology.

Figure 5.

Annual mean potential temperature in the high-resolution climatology (solid curve) and Levitus [1994] (dashed curve) along the 24°N section of Pacific. The longitude scale is amplified in the western boundary region (west of 150°E), where the differences in the two climatologies are the greatest.

2.4. Wind Climatology

[19] For the Ekman contribution to the heat transport, QEK, we use a suite of available marine boundary layer wind products [Hellerman and Rosenstein, 1983] (COADS, ECMWF, and Florida State University (FSU)) to determine the range of the annual mean QEK and climatological annual cycles. The COADS monthly climatology is calculated from the pseudo wind stress over the period of 1959–1995 using the Large and Pond [1981] drag coefficient formula. The ECMWF climatology is generated over the period of 1985–1995 and is the same wind forcing used to drive the POP model. We use an average of these wind products in the final calculations of QEK, with error bars accounting for the rms differences between them.

2.5. POP Model

[20] The POP model is an updated version of the Bryan-Cox-Semtner global ocean model that has been improved by replacing the rigid-lid approximation with a free sea surface and coded to run efficiently on parallel computers [McClean et al., 1997]. The model equations are integrated on a Mercator grid with an average resolution of 1/6° and 20 nonuniformly spaced depth levels. Surface momentum fluxes were obtained from 3-day averaged ECMWF winds for the period 1985–1995. While the surface salinity is restored to the Levitus salinity, the heat flux from ECMWF is imposed at the ocean surface. Deep thermohaline forcing is allowed at high latitudes (70°N–78°N and 70°S–78°S) by restoring to Levitus climatology in the upper 2000 m with a 3-year timescale. The POP simulations have been shown to compare well with Topex/Poseidon altimetry observations and surface drifter data [McClean et al., 1997] in the ocean interior and with observations of the transport and variability of the Kuroshio in the ETC [Lee et al., 2001].

3. Heat Flux Components

3.1. The Kuroshio Heat Transport QK

[21] The western boundary currents in the subtropical gyre of the North Pacific have three branches flowing northward: the major branch enters the East China Sea through the ETC with a maximum depth of 1000 m; the second branch, the East Ryukyu Current (ERC), separates from the major branch to the south of the ETC due to the topographic blocking of the Ilan ridge and flows northward off the Ryukyus; and the third small branch is through the Taiwan Strait between mainland China and Taiwan with mean depth of only 60 m. According to the breakdown of equation (1), the total contribution of the branches through the ETC and the Taiwan Strait to the meridional heat flux is called the Kuroshio component, QK. The contribution of the ERC is included in the interior baroclinic heat flux component, QI, similar to the treatment of currents east of the Bahamas in the North Atlantic [e.g., Hall and Bryden, 1982]. Analogous to the currents east of the Bahamas [e.g., Fillenbaum et al., 1997], the ERC's barotropic contribution to the mean meridional heat flux is small because its vertical mean potential temperature is close to the cross-section mean potential temperature, and this part will be included as a correction to the total heat flux.

3.1.1. Kuroshio temperature transport in the ETC

[22] The PCM-1 data establishes a close relationship between the volume and temperature transport (Figure 6a) with a correlation coefficient of 0.99. The highly linear relation between the volume and temperature transport is illustrated in Figure 6b. For comparison, the temperature and volume transports of the Florida Current based on Molinari et al. [1990] are also shown in Figure 6b. There are striking similarities between the Kuroshio in the ETC and Florida Current in the straits of Florida. Both currents have similar flow weighted temperature with small variations, 19.79 ± 0.65°C for the Kuroshio and 19.82 ± 0.69°C for the Florida Current. The mean Florida Current temperature transport is 2.48 PW, 0.69 PW higher than that of Kuroshio (1.79 PW). This difference is caused by the larger Florida Current volume transport, 31 Sv, in comparison with the Kuroshio transport in the ETC, 22 Sv.

Figure 6.

(a) Temperature transport measured by PCM-1 moored current meter array (solid curve) and that from linear regression of the temperature and volume transports (dashed curve). The correlation is 0.99. (b) Linear regression of the temperature and volume transport of the Kuroshio, measured by the PCM-1 array, and that of the Florida Current, derived from monthly climatology of Molinari et al. [1990].

[23] The energetic 100-day temperature transport variability (Figure 2) makes it impossible to derive a robust seasonal cycle from the 21-month PCM-1 current meter measurement. However, the study by Johns et al. [2001] showed a strong relationship between sea level difference (SLD) across the ETC and Kuroshio volume transport (Figure 7a). The SLD between Ishigaki Island in the southern Ryukyus and Keelung on the east coast of Taiwan was found to be related to the volume transport according to linear regression V = 0.41 × SLD + 22.0 Sv, with a correlation coefficient of 0.78 for 10-day averaged transports. Using this relationship, and the above relationship between Kuroshio volume and temperature transport determined from the PCM-1 observations, we use a 7-year (1989–1996) SLD time series between Ishigaki and Keelung to estimate the climatological annual cycle of the Kuroshio temperature transport. By doing so, we obtain a more representative annual cycle and remove or reduce the aliasing introduced by mesoscale variations. A detailed comparison of the derived seasonal variation with three high-resolution numerical model results and local and remote wind forcings is given by Lee et al. [2001].

Figure 7.

(a) Kuroshio volume transport in the ETC measured by the PCM-1 array and sea level difference across Kuroshio between Keelung and Ishigaki. (b) Kuroshio volume transport climatology (thick dashed curve) derived from the SLD of 1989–1996 with the calibration from the PCM-1 measurements; the seasonal cycle of the temperature transport derived from the volume transport climatology is based on the linear regression of Figure 6, with its standard deviation shown by dashed curves.

[24] Figure 7b shows the seasonal cycle of the Kuroshio volume transport inferred from the 7-year SLD and its standard deviation envelope, as well as its conversion to the Kuroshio temperature transport. It is assumed in these calculations that the relationships between SLD and Kuroshio volume transport and between volume and temperature transport derived during the PCM-1 period are representative of the full 7-year period. The mean Kuroshio transport derived from the 7-year SLD record is 21.8 Sv, which is very close to the mean transport of 22.0 Sv observed during the PCM-1 period. The standard deviation envelope in Figure 7b illustrates the degree of interannual variation that may occur about the average annual cycle, which can be relatively large in the ETC, as also found for the Kuroshio in Tokara Strait [Kawabe, 1988]. A robust feature is the summer maximum and fall minimum, which occurs in all but 2 of the 7 years analyzed [Lee et al., 2001]. The seasonal amplitude of the Kuroshio temperature transport is ∼0.35 PW around an annual mean of 1.79 ± 0.11 PW.

3.1.2. Temperature transport in the Taiwan Strait

[25] A part of the Kuroshio water has long been believed to flow through the Taiwan Strait all year long [Guan, 1994; Fang and Zhao, 1988; Chuang, 1985] even though the currents in the strait are strongly influenced by the monsoon. Although the available current measurements are not sufficient to resolve the climatological seasonal cycle, Zhao and Fang [1991] estimated the northward volume transport in the Taiwan Strait to vary from 1.05 Sv during the winter monsoon to 3.16 Sv during the summer monsoon on the basis of segments of current meter data. The authors further proposed that the current can be separated into two components: a seasonally independent northward mean flow forced by a northward pressure gradient and a wind-induced component that varies seasonally. They also showed that there is a good linear relationship between the 15-day low-pass filtered wind stress and current fluctuations in the eastern part of the strait, with a correlation coefficient as high as 0.84.

[26] To estimate the monthly mean volume transport in the Taiwan Strait, we first make an estimate of the transport using only the monthly mean surface current values across the strait obtained from the Mariano ship drift climatology [Mariano et al., 1995]. On the basis of observed current profiles in the Taiwan Strait, the vertical mean currents in this shallow channel are assumed to be about half the size of the surface currents. The resulting annual volume transport cycle is closely related to the seasonal wind changes but has an annual range somewhat larger than that suggested by Zhao and Fang [1991], ranging from −0.5 Sv in November to 3 Sv in August. Assuming that these results catch the phase of seasonal variation, we linearly scale them to the maximum and minimum seasonal volume transports suggested by Zhao and Fang [1991] by the following relationship,

equation image

where Tr′(i) is the adjusted volume transport in the Taiwan Strait for month i, and Tr(i) is our transport estimate from the ship drift climatology (with minimum Trmin = −0.5 Sv in November and maximum Trmax = 3 Sv in August). The resulting seasonal variation is shown in Figure 8a and is in excellent agreement with the POP model simulation. Such a good agreement implies that the simple linear dynamics of seasonal wind in controlling the transport cycle in the Taiwan Strait is robust.

Figure 8.

(a) Seasonal variation of northward volume transport in the Taiwan Strait derived from Mariano ship drift climatology and Zhao and Fang [1991] estimates in comparison with the POP simulation and the longshore wind-forced transport anomalies (right axis). (b) Seasonal cycle of the temperature transport and cross-section mean temperature in the Taiwan Strait.

[27] Lee and Williams [1988] have applied and tested a simple analytical wind-forced model to the straits of Florida in simulating the transport variation of the Florida Current. The total wind-driven volume transport forced by along-channel wind anomalies, τys, can be expressed by

equation image

where L is the width of the strait, equation image is the barotropic radius of deformation, and t is the frictional adjustment time (the time necessary for the alongshore current to response to the alongshore wind anomalies and determined by the bottom resistence). To apply this model to the Taiwan Strait, we chose appropriate parameters L = 180 km, H = 60 m, and t = 11 hours. This frictional adjustment timescale is the same as that estimated by Lee et al. [1989] using the current meter array measurements and the alongshore winds on the South Carolina continental shelf, which is in the same depth range as the Taiwan Strait. The resulting volume transport variation (Figure 8a) in Taiwan Strait forced by COADS monthly climatology [da Silva et al., 1994] is also in good agreement with the other two estimates. In summary, although there is not much data available to directly derive the seasonal transport variation, the combination of the available direct current measurements and ship drift data seems to do a good job in estimating the transport seasonal cycle in the Taiwan Strait in response to the seasonal winds.

[28] To estimate the temperature transport, we simply multiply the volume transport by the climatological cross-strait mean temperature derived from the NODC World Ocean Database 1998 (WOD98) data. This should be close to the flow-averaged temperature in this shallow and well-mixed region, as confirmed by the small vertical gradients in profiles of climatological mean temperature in the NODC WOD98 data set and the POP model results [Zhang, 2000]. Figure 8b shows the seasonal cycle of the temperature transport and cross-section mean temperature in the Taiwan Strait.

3.1.3. Kuroshio heat flux component

[29] According to equation (1), the total Kuroshio heat flux (Figure 9a) is the sum of the temperature transports by the Kuroshio and by currents in the shallow Taiwan Strait, subtracting the temperature transports of the balancing southward mass fluxes in the interior ocean at the cross-section mean temperature. Assuming that the variability of the interior mean temperature, 〈θI〉, is negligible compared with that in the Kuroshio, the error of Kuroshio heat flux by equation (1) in the ETC is taken as the standard error of the mean temperature transport derived from the 7-year SLD time series calibrated by the PCM-1 moored array data. This standard error is 0.04 PW, which shows that the direct results provided by PCM-1 combined with the long-term sea level measurements provide a robust estimate of the heat transport in the ETC. To estimate the heat transport error in the Taiwan Strait, we first estimate the standard deviation of the volume transport, equation image, which is integrated from the standard deviation of ship drift velocity in the Mariano climatology [Mariano et al., 1995] and the standard deviation of temperature, σT, from NODC WOD98. The heat flux error in the strait is obtained as the square root of VTS × σT2 + T × σVTS2, where VTS is the volume transport and T is the cross-section mean temperature. This gives a value of 0.05 PW for the standard error of the Taiwan Strait temperature transport.

Figure 9.

Final estimate of transpacific heat flux at 24°N with error bar. (a)–(c) Kuroshio, interior geostrophic baroclinic, and Ekman components with annual means 1.58 ± 0.07 PW, –1.81 ± 0.15 PW, and 0.78 ± 0.07 PW. (d) The total heat flux, whose annual mean is 0.62 ± 0.21 PW. The error bar includes the upper bound of possible barotropic correction term (0.11 PW) related to the East Ryukyu Current.

[30] Finally, the total Kuroshio heat flux error (Figure 9a) is calculated from the two error sources in the ETC and in the Taiwan Strait by the standard propagation of uncertainty method, which involves taking the square root of the sum of squares of errors, resulting in a mean error of 0.07 PW for QK. A large part of the error source here is from the poorly observed Taiwan Strait, although it is shallow and only transports 1–3 Sv of water.

3.2. Geostrophic Baroclinic Component in the Interior, QI

[31] We derived QI from both the Levitus [1994] and high-resolution hydrographic climatologies. The advantages of the high-resolution climatology over that of Levitus [1994] are: (1) it includes all of the newly available hydrographic data in the eastern and western boundary regions; (2) the station data used in deriving it are averaged onto grids along isopycnal surfaces, which helps to correctly resolve fronts and prevents the generation of artificial water masses [Lozier et al., 1994]; (3) the increased resolution helps to avoid artificial smearing or broadening of high-gradient regions near the boundaries; and (4) Levitus's [1994] study has an obvious shortcoming regarding the Kuroshio misplacement (Figure 5). Because of these issues, the final QI is based on the high-resolution climatology, whose annual mean is 0.07 PW higher than that derived from Levitus [1994] (Figure 9b).

[32] The error estimate of QI is not straightforward, with difficulties arising from the scattered data sampling in both space and time in the interior. For example, Figure 10 shows the east-west cumulative QI derived from the high-resolution climatology for January–February. The “wiggles” in this curve are most likely due to aliasing from geostrophic eddies that are not completely averaged out in the sparse hydrographic data set, which are more common and energetic in the western half of the basin. As pointed out by Wacongne and Crosnier [1997], as long as these wiggles on the cumulative QI are in the interior ocean, like a realistic eddy-induced anomaly, they would not have a large effect on the net integration since one side of the integration largely cancels that on the other side as one integrates through. The residual effect of eddy heat transport seems to be small at this latitudinal section (∼24°N) according to Stammer [1998]. However, when such wiggles occur near the boundary, they can alter the final QI value dramatically and can cause spurious seasonal variation and a biased annual mean estimate. Thus we quantify the errors by the following steps: (1) derive a smoothed cumulative QI curve by a cubic spline smoothing of the original QI distribution for each bimonthly period (e.g., Figure 10); (2) calculate the differences between the original and smoothed QI distributions and determine the maximum value of this difference for each bimonthly period; and (3) use the average of these maximum differences as an estimate of the error in the bimonthly and annual mean QI. This value, 0.15 PW, is plotted as an error bar (dotted lines) in Figure 9b together with the bimonthly QI values.

Figure 10.

Cumulative QI of January–February from the high-resolution hydrographic climatology and its smoothed zonal structure by cubic spline smoothing. The smoothed curve is expected to exclude the significant aliases from the incompletely resolved eddies by irregular sampling of hydrographic stations.

[33] Since the eddy heat flux is negligible even in the energetic western boundary (only 0.007 PW in the ETC) and in the interior at this section [Stammer, 1998], we assume that the uncertainties associated with the eddy heat flux in the interior are included in the errors of QI, as derived above and in Figure 10. Note the eddy contribution to the wiggles can be caused by both sampling problems (e.g., aliasing of eddies in both space and time) and real ocean processes (e.g., the asymmetry of eddies). Our error estimate for the interior ocean baroclinic component QI (0.15 PW) is similar to that (0.16 PW) for the Atlantic at 27°N by Molinari et al. [1990] and Fillenbaum et al. [1997], who used the standard deviation of the 12-month values of QI derived from Levitus [1982] as the error bar. However, in addition to QI, they introduced the uncertainty of eddy heat flux, ±0.24 PW, to the interior ocean contribution. This value was adopted from Hall and Bryden [1982] and was chosen to represent the uncertainty of the eddy contribution in their noneddy-resolving (a typical spacing of 150–200 km between stations) one-time transatlantic hydrographic data. The different treatment of the eddy heat flux is one factor leading to the larger error bar for the seasonal transatlantic heat flux by Molinari et al. [1990] and Fillenbaum et al. [1997] compared with our estimate for the Pacific at 24°N (section 3.4).

3.3. Ekman Heat Flux QEK

[34] Using the same transpacific survey along 24°N conducted in April and May 1985, Bryden et al. [1991] and Macdonald and Wunsch [1996] estimated the net meridional heat flux to be 0.76 and 0.50 PW, respectively. Even though Macdonald and Wunsch's [1996] estimate is also influenced by the other two transects at 47°N and 11°N occupied in August–September and February–April, respectively, the authors attribute the different estimates in the two studies to the wind products used (the ECMWF wind climatology for Macdonald and Wunsch [1996] and Hellerman and Rosenstein's [1983] wind (HR) for Bryden et al. [1991]). Böning and Herrmann [1994] also demonstrated that the annual cycle of meridional heat flux in their North Atlantic Ocean model is sensitive to the choice of wind products between HR and Isemer and Hasse [1987]; it increases from 0.5 PW in the case of HR forcing to almost 0.8 PW with Isemer and Hasse [1987] forcing. To assess the range of estimates for the Pacific 24°N section, four wind products (HR, ECMWF, FSU, and COADS) are used here to derive the Ekman heat flux seasonal cycle according to equation (1). Assuming the Ekman flow is decreased linearly from its surface to zero at 50 m depth as by Bryden et al. [1991], the vertically averaged θE in the Ekman layer is calculated as an average of the temperatures at 0, 20, and 40 m depths,

equation image

The product of zonal wind stress times θEK integrated along 24°N yields the average temperature equation imageEK for the Ekman layer temperature,

equation image

[35] The annual mean values of QEK from the four wind products (HR, COADS, ECMWF, and FSU) range from 0.64 to 0.91 PW, and the mean climatological cycle formed from the average of these wind products is shown in Figure 11. All wind products show a similar annual variation even though they differ in their annual mean values. The standard error of QEK (Figure 9c) is derived as the standard deviation from the ensemble mean calculated from the four wind products. The noticeable difference between the ensemble mean and that derived from the ECMWF winds is the decrease of the annual range from 1.05 (ECMWF) to 0.95 PW (four wind products mean) and an increase of the annual mean by 0.03 PW. A remarkable feature of the seasonal cycle is a precipitous decrease from 1.21 PW in November to 0.28 PW in January, which is mainly controlled by the Ekman volume transport variation. This precipitous fall is found to be real and not due to low observation density in winter since it is also a feature of the seasonal cycle derived from the ERS satellite wind products in the 1990s.

Figure 11.

Ekman heat fluxes calculated from four wind products and Levitus [1994] climatology. The mean of all four wind estimates is also shown, which is used as the best estimate for the heat flux.

3.4. Transpacific Heat Flux at 24°N Qnet

[36] The sum of the three components of QK, QE, and QI yields the net meridional heat flux across 24°N. To complete the error analysis, we must consider the error due to unresolved structure of the barotropic flows in the interior, which is often referred to as the “barotropic correction” term in the traditional observational heat flux breakdown [e.g., Hall and Bryden, 1982; Fillenbaum et al., 1997]. The heat flux formulation in equation (1) assumes that the barotropic return flow in the interior ocean occurs at an uniform temperature 〈equation image〉 so that the barotropic temperature transport can be approximated as VK × 〈equation image〉. However, if strong barotropic flows occur in regions where the vertically averaged temperature is significantly different than the transect mean (e.g., near islands and ridges), then an error is introduced. The barotropic correction term is defined as the difference between the barotropic temperature transport, and the value that would be obtained if the constant temperature 〈$\bar{\theta}$〉 is used instead of the actual instantaneous local vertical mean temperature $\bar{\theta}$. It can be written as

equation image

where the overbars indicate the vertical averages.

[37] The most important contribution to this error probably comes from the northward East Ryukyu Current to the east of the Ryukyus, which is expected to have an annual mean volume transport of ∼12 Sv [Hautala et al., 1994; Lee et al., 2001]. This value is consistent with the POP model results, which show a similar amount of northward transport confined in the western boundary (126°E–128°E) to the east of the Ryukyus (the heat transports in this region from the model will be discussed in section 4). Lee et al. [2001] further suggested that its seasonal variation should be of the order of ±8 Sv, consistent with the large range of transport estimates, 4–26 Sv, reported by Bryden et al. [1991], Worthington and Kawai [1972], and Yuan et al. [1998]. In the high–resolution climatology the difference between the vertically averaged θ over 126°E–128°E and the transect mean is between 1.42°C and 1.49°C for different seasons, similar to that reported by Bryden et al. [1991] in the P03 transpacific hydrographic section, 1.37°C. The barotropic correction term for the ERC can thus be approximated as

equation image

[38] The net meridional heat transport is therefore the sum of three components, QK, QE, and QI, adjusted by +0.07 PW to account for the barotropic correction (Figure 9d). It has a minimum of ∼0 PW in January and February and becomes stronger in the second half of the year, with the maximum of 1.1 PW in July and a secondary maximum of 1.0 PW in November. The annual mean value is 0.62 PW.

[39] Given the large expected seasonal variation of ERC volume transport (±8 Sv), the barotropic correction term could be as large as 0.11 PW in the seasonal cycle. Since no information about the phase of the seasonal variation can be obtained, we simply assume 0.11 PW as the largest possible error from the ERC in our following seasonal cycle estimation of the total heat transport. Combining the errors from the three heat flux components (Kuroshio, interior geostrophic baroclinic, and Ekman) and the maximum uncertainty (0.11 PW) associated with the barotropic correction term gives rise to the total uncertainty shown by the dashed curves enveloping the mean net heat flux (Figure 9d). The annual average of the total uncertainty is 0.21 PW.

4. Discussion

4.1. Comparison With the POP Model Simulation

[40] A surprising result from this analysis is the large amplitude of the inferred seasonal cycle of oceanic heat flux across 24°N in the Pacific, including the nonintuitive finding of a zero heat transport in winter. The annual heat flux cycle is dominated by the Ekman heat flux variation, with a secondary influence from the Kuroshio annual cycle. As shown below, the same basic results are also found in the POP numerical model simulation. In what follows, we first break down the model heat flux into the same components as used for the observations so that the two can be directly compared. This breakdown is then compared against the full heat flux calculated from the v and θ fields in the model to validate the assumptions used in the observational breakdown.

[41] As shown in Figure 12a, the QK in the ETC from both the model simulations and the observations resemble their respective volume transport cycles [Lee et al., 2001]. They both have distinct summer maximum, but the observed QK seasonal amplitude is about twice that simulated by the model. The biggest difference occurs in winter, when the observed QK has a secondary maximum, while the model simulation shows a minimum. The main difference between the POP simulation and the observation in terms of the total Kuroshio heat flux is not in the Taiwan Strait but in the ETC. Although the mean transport of Kuroshio in the ETC simulated by the model is slightly larger (23 Sv) than the one (21.8 Sv) derived from the 7-year SLD across the ETC calibrated by the PCM-1 measurements, the simulated Kuroshio heat flux is smaller than the observation because of a cooler flow-averaged Kuroshio temperature (18.35°C in POP versus 19.72°C by PCM-1) and a warmer cross-section averaged θ of the interior in the model (4.45°C in POP versus 3.78°C by Levitus [1994] and high-resolution climatologies). The smaller amplitude of the Kuroshio seasonal heat flux cycle in the model is due to the smaller amplitude of the modeled transport in the ETC (1 Sv) compared with the observed seasonal amplitude (∼2 Sv, Figure 7b). Thus the model has both a smaller annual mean QK than the observations (1.5 versus 1.6 PW) and a smaller annual cycle of QK (±0.1 versus ±0.2 PW).

Figure 12.

(a) QK from observation (thick solid curve) and POP simulation (thin solid curve). K and T (K + T) are Kuroshio in the ETC and currents in the Taiwan Strait. K is in the ETC only. (b) QI, from Levitus [1994], the high-resolution climatology, and POP model results. (c) QEK, from observation and POP. Both use ECMWF wind. (d) Total Qnet using Levitus [1994] and high-resolution climatology for the interior ocean and from POP simulation (POP modes, dashed thin curve) as the sum of the three components in Figures 12a, 12b, and 12c. The net heat transports from observation are adjusted by 0.07 PW to account for the ERC barotropic contribution. The heat transport directly integrated from the modeled absolute v and θ fields across the whole section is plotted as the thin solid curve.

[42] The seasonal cycle of the interior baroclinic heat flux QI derived from Levitus [1994], from the POP simulation, and from the bimonthly high-resolution climatology, are shown in Figure 12b. Of the three estimates the POP simulation has the highest annual average, −1.60 PW (weakest southward heat transport), and the high-resolution climatology has the smallest seasonal amplitude. The higher values of QI in the POP simulation are caused by the differences of the mean θ at 24°N between the simulation and the climatology: The POP simulation is colder in the upper 200 m across the whole section but warmer in the deeper ocean, a discrepancy that was also reported by Wilkin et al. [1995] in Semtner and Chervin's [1992] model. The annual mean QI obtained from the high-resolution climatology is −1.81 PW, 0.07 PW higher than that calculated by Levitus [1994]. This is caused by the difference in the θ field between the two data sets in the western boundary, where the Kuroshio signal leaks eastward to 130°E (Figure 5), as found by Levitus [1994].

[43] In terms of the seasonal amplitude of QI, the estimate based on the study by Levitus [1994] is a bit larger than the high-resolution climatology, but the difference is not significant considering the error bar (∼0.15 PW) associated with the QI (Figure 9b). Detailed analysis suggests that the much larger seasonal cycle of QI in POP is confined mostly to the western boundary off the Ryukyus with little interior seasonal variation. Interestingly, while the modeled seasonal signal of the Kuroshio heat flux (QK) in the ETC is smaller than in the observations (Figure 12a), the modeled seasonal signal of QI to the east of the Ryukyus is larger. The deficiency of the model in simulating the seasonal signal of the heat transport in the ETC and to the east of the Ryukyus may thus be related to the local dynamics in the western boundary region and could be caused by the poorly resolved complex topography or coarse resolution of the atmospheric forcing fields in this region.

[44] The Ekman heat fluxes, QEK, in Figure 12c are calculated according to equation (1) using the climatological monthly mean ECMWF reanalysis from 1985 to 1995, which is also the forcing for the POP simulation. The Ekman heat flux in the POP simulation and that derived from ECMWF wind and Levitus [1994] are almost identical. (The Ekman heat flux using the high-resolution climatology is the same as that using Levitus's [1994] climatology and is not plotted here.) The similarity between the model results and the observation is not surprising because, again, the Ekman volume transport is the dominant factor in influencing the Ekman heat flux (QEK) variability.

[45] The total meridional heat transport across 24°N is shown in Figure 12d for the POP simulation and for the observations using both the Levitus [1994] and the high-resolution climatologies. The two curves plotted for the model results show both the directly calculated heat transport (thin solid curve) using its monthly mean fields of (v,θ) and from the breakdown into model components (thin dashed curve) analagous to those used for the observations. All of the curves in Figure 12d have similar seasonal variation, with a minimum in February and a maximum in the second half of the year, controlled largely by the annual cycle of the Ekman heat flux. The summer maximum of the Kuroshio heat flux enhances the summer values of the total heat flux in July, making it comparable to the November maximum. The seasonal amplitudes of geotrophic baroclinic heat flux of Levitus [1994] and in the high-resolution climatology are small. Much of the difference between the modeled and observed seasonal cycle of Kuroshio heat flux (Figure 12a) is compensated by the larger amplitude of the interior geotrophic baroclinic heat flux in POP so that the total heat flux from the model compares favorably to the observation. The comparison of the total heat fluxes calculated from the direct integration of the model v and θ fields across the section and from the sum of the three heat flux components (Figure 12d) shows that in the model the breakdown into the terms in equation (1) can provide a reasonable estimate of the transpacific heat flux through 24°N without knowing the barotropic flow structure in the interior ocean. The annual means of the two calculations in the model are only different by 0.04 PW (0.54 PW from direct integration, 0.58 PW from the breakdown of the heat fluxes according to equation (1)). A larger uncertainty of 0.11 PW due to the barotropic correction term was taken into account in the observations because of the potentially large seasonal transport variation of the ERC.

[46] Finally, the error of seasonal heat transport estimation due to interannual variabilities can be estimated from the 11-year POP model simulation using the fields of absolute v and θ. The standard errors of the seasonal heat transport components due to interannual variabilities are comparable to the error bars shown in Figure 9, with the annual mean of 0.07, 0.11, 0.09, and 0.14 PW for the interannual variability induced errors in QK, QI, QEK, and Qnet, respectively. The maximum standard errors are all in winter with 0.12 PW for QK, 0.16 PW for QI, 0.18 PW for QEK, and 0.25 PW for Qnet.

4.2. Meridional Heat Flux Mechanisms: Horizontal and Vertical Cells

[47] On the basis of P03 transpacific section data at 24°N, Bryden et al. [1991] demonstrated that the northward meridional heat flux is half due to the zonally averaged vertical meridional circulation cell and half due to a horizontal circulation cell. They further showed that the heat flux carried by the horizontal circulation occurs in the upper 800 m of the water column, and all but 0.02 PW of the heat flux in the vertical meridional circulation is due to the zonally averaged circulation above 800 m depth. Conversely, in the Atlantic the northward heat flux is due mostly to the zonally averaged vertical meridional circulation associated with the thermohaline circulation, and the horizontal circulation actually contributes a small southward heat transport across 24°N [Hall and Bryden, 1982; Bryden, 1993]. Since the POP model simulation is shown to give promising results in comparison with the observations in the western boundary and the transpacific heat flux at 24°N, we can use the model results here to study the heat flux mechanisms in relation to the seasonal variation.

[48] The northward ocean heat transport due to the vertical circulation cell, Hv, is defined as

equation image

while the heat transport per unit depth due to the horizontal circulation cell, HH(z), is defined as

equation image

where 〈 〉 represents the zonal average across the entire 24°N section at each depth (z); L(z) is the distance across the section at depth z. The vertical cell Hv is commonly referred to as the “overturning” component of the heat transport, and the horizontal cell HH is referred to as the “gyre” component of the heat transport.

[49] Figure 13 shows the seasonal variation of the heat flux from Hv and HH. A striking feature is the dominance of Hv in the total heat flux variation, while HH contributes an almost constant value of about 0.22 PW throughout the year. The resemblance of the Hv and QEK seasonal variation indicates that they are closely related. The annual mean Hv is 0.33 PW or about 3/5 of the total annual heat flux, while HH accounts for about 2/5 of the annual mean heat flux. It is only in 3 months of the year, April, May, and June, that the vertical and horizontal circulation cells contribute equally to the total heat flux, while in November, Hv is 4 times HH. Interestingly, the April–June period is when P03 was conducted, and the modeled heat flux during this period, ∼0.5 PW, is fairly close to the annual mean of 0.54 PW.

Figure 13.

POP simulations at 24°N. (a) Total meridional heat transport (solid curve) and heat transports by vertical (dashed curve) and horizontal (dotted curve) cells. (b) Total heat transport (thick curve), temperature transports of upper 800 m (thin solid), and deeper ocean (dashed curve). (c) Seasonal variation of volume transport anomaly (thick curve) in upper 800 m, Ekman transport (dotted curve), and the sum of Ekman and western boundary current transport (dashed curve, including the ETC and Taiwan Strait).

[50] From the observations we can obtain values for the annual mean vertical and horizontal cells by adding a uniform barotropic flow to the interior geostrophic velocity that balances the mean Kuroshio and Ekman transports. The resulting heat transport by the vertical cell is 0.37 PW, and 0.25 PW by the horizontal cell, which is very similar to the partitioning found in the model.

[51] The temperature transport in the upper 800 m and deeper ocean are plotted in Figure 13b. It seems that all of the total meridional heat flux occurs in the upper 800 m, which is in agreement with previous studies [e.g., Bryden et al., 1991; Wilkin et al., 1995]. However, we find that the total volume transport in the upper 800 m is nonzero except in the months of April–June, and this transport variation closely resembles the seasonal variations of the Ekman transport alone or the variation of the Ekman plus the western boundary transport (Figure 13c). The large seasonal variation of the volume transport in the upper 800 m must be balanced by the variation of deep ocean flows, indicating the importance of the deep ocean circulation in the heat flux mechanism.

[52] To understand the mechanism of meridional heat flux across 24°N, it is better to look at the volume transports in temperature classes (Figure 14). A clear impression from Figure 14 is the similarity between the annual and April–May mean, which explains why the heat flux in April and May is so close to the annual average. The modeled transport distribution in the temperature classes compares remarkably well with the P03 transect data from Bryden et al. [1991; Figures 5 and 6], except that the largest northward transport occurs in a temperature class 2°C colder in the model (22°C instead of 24°C), and the surface return flow starts above 21°C in the model but above 19°C in the P03 section. The southward flow between 1.5 and 2.5°C in Figure 14 can be related to the North Pacific deep water at 1.05–1.9°C in the P03 section, and the northward flows between 2.5 and 6.5°C and between 0.5 and 1.5°C are the Antarctic intermediate water and Antarctic bottom water, which in the P03 data are 1.9–4.5°C and <1.05°C, respectively. Bryden et al. [1991] suggests the North Pacific deep water as a return flow formed by the mixing of the Antarctic intermediate and bottom waters flowing northward across 24°N. The curve in Figure 15a shows the seasonal variation of the volume transport in the 1.5–2.5°C temperature class. Its large range, ∼9 Sv, suggests that not all of the southward flow at about 2°C in the model can be viewed as a mean southward flow of the North Pacific deep water to compensate for the northward flow of the Antarctic intermediate and bottom waters within the thermohaline circulation. Such a large seasonal signal must be related to higher frequency forcing rather than the slow variation of thermohaline circulation. The almost identical transport variations shown by the solid curves in Figure 15b for different temperature classes ranging from <6°C up to <20°C, and the similar transport variation of the deep ocean currents at temperature colder than 2°C indicate that the ocean adjusts to the large-scale forcing barotropically on the seasonal timescale, consistent with theoretical and model studies [Gill and Niiler, 1973; Anderson et al., 1979]. The transport variation of all waters <6°C, whose variability is largely determined by the <2°C southward flow, suggests an approximate balance between the deep ocean currents and the Ekman transport fluctuations (Figure 15b). Furthermore, Figure 15c shows the similarity between seasonal variations of the Kuroshio transport and the residual of the transport colder than 6°C and Ekman flow, demonstrating that the deep ocean flows closely balance the sum of the Ekman and Kuroshio transport variations. In summary, on seasonal timescales the deep currents are strongly perturbed by the subtropical gyre and Ekman flows in the surface layer and fluctuate considerably about their yearly mean values.

Figure 14.

Modeled net northward transport (Sv) across 24°N in the Pacific as a function of temperature. Transports are determined over temperature intervals of 1.0°C. (top) Annual mean. (bottom) April–May mean.

Figure 15.

POP simulation at 24°N. (a) Volume transport of waters of 1.5°–2.5°C. (b) Ekman transport and transports of various temperature classes in the interior ocean east of the Ryukyus. Dashed curves show transport colder than 2°C. Bold curves (transports colder than 6°C and 16°C) mark the range which most close to the reverse of Ekman transport. (c) Seasonal transport anomalies of the Kuroshio (solid curve, ETC and Taiwan Strait) and the balance of Ekaman transport and transport colder than 6°C.

4.3. Comparison With Existing Direct Meridional Heat Transport Estimates at 24° N in the Pacific

[53] Table 2 compares our estimate of the annual mean heat flux from this study with those from Roemmich and McCallister [1989], Bryden et al. [1991], and Macdonald and Wunsch [1996], all of which are mainly based on the P03 one-time transpacific hydrographic survey along 24°N. The estimate from this study, 0.62 PW, is 0.12 PW higher than the one from Macdonald and Wunsch [1996], 0.50 PW, although the new Kuroshio transport of 23.8 Sv from this study (including the Kuroshio in the ETC and the flow through the Taiwan Strait) is 2.8 Sv smaller than their estimate of 26.6 ± 3.3 Sv. The difference between our estimate and that of Bryden et al. [1991], 0.76 PW, is reflected in all three heat flux components. The 28.3 Sv of Kuroshio transport estimated by Bryden [1993] is 4.5 Sv higher than our estimate, 23.8 Sv, and higher than other indirect calculations using multiple-section data [Guan, 1981; Ichikawa and Beardsley, 1993; Liu et al., 1998]. This leads to a Kuroshio heat transport that is 0.15 PW higher in Bryden's [1993] treatment than in ours (1.73 PW versus 1.58 PW). The Ekman heat flux from Bryden et al. [1991], 0.93 PW, is calculated from the annual mean HR wind and is 0.15 PW higher than our ensemble mean of the four wind products. Finally, the QI of Bryden et al. [1991] is 0.1 PW more southward than our −1.81 PW, and 0.07 PW associated with the ERC barotropic contribution is included in our final estimate. These partially offset the above differences and lead to a net difference of 0.14 PW between the two heat flux estimates.

Table 2. Comparison of Direct Heat Flux Estimates of This Study With Those of Bryden et al. [1991] and Macdonald and Wunsch [1996]
 Bryden et al. [1991]Roemmich and McCallister [1989]Macdonald and Wunsch [1996]This Study
  • a

    Adjusted by a 0.07 PW barotropic correction from the ERC.

  • b

    Abbreviations are as follows: PW, petawatt; NA, not available; CTD, conductivity-temperature-depth; ADCP, acoustic Doppler current profiler; PCM, profiling current meter; and SLD, sea level difference.

  • c

    Includes estimate of 2.0 ± 0.5 Sv for transport through the Taiwan Strait.

  • d

    From Hellerman and Rosenstein, [1983].

  • e

    Winds from and the European Centre for Medium-Range Weather Forecasts [Trenberth, 1989].

Qnet0.76 ± 0.3 PWb0.75 PW0.50 ± 0.3 PW0.62 ± 0.21 PWa
QK1.73 PW, CTD/ADCPbNAbNA1.58 ± 0.07 PW, PCM-1b array with 7-year SLDb
VK28.3 Sv32 Sv26.6 ± 3.3 Sv23.8 ± 3.0 Svc
QEK0.93 PWdNAdNAe0.78 ± 0.07 PW, average of wind products
QI−1.91 PW, one-time sectionNA, inverse modelNA, inverse model−1.81 ± 0.15 PW, moored measurements and high-resolution climatology

[54] Both of the Kuroshio volume transports (32 and 26.6 Sv) by Roemmich and McCallister [1989] and Macdonald and Wunsch [1996] are higher than our calculation from the PCM-1 current meter data. For their inverse model study a comparative breakdown into simple components is unavailable. However, the main differences between Macdonald and Wunsch [1996] and this study can be understood as follows. For the Kuroshio heat flux component our results show that the sensitivity of QK to the Kuroshio volume transport is ∼0.03 PW/Sv; that is, QK increases by ∼0.03 PW for each 1-Sv increase in Kuroshio volume transport. Thus the higher value of the Kuroshio volume transport found by Macdonald and Wunsch [1996] (by 2.8 Sv) should lead to about a 0.1 PW larger heat flux than ours for their QK. Their use of ECMWF winds for the Ekman heat flux should offset this increase slightly since it is about 0.03 PW smaller than our average value from the various wind products. The including of 12 Sv ERC adds 0.07 PW northward barotropic heat transport in our analysis. A remaining difference of ∼0.1 PW is then implied in the interior baroclinic heat flux (QI), theirs being larger southward, which is consistent with Bryden et al.'s [1991] value from the same (P03) hydrographic section in comparison to ours obtained from the annual climatology.

4.4. World Ocean Meridional Heat Flux Across 24°N

[55] Since the Indian Ocean is confined to latitudes south of 24°N, the sum of the heat flux in the Pacific and the Atlantic gives the meridional heat flux in the world ocean across the 24°N latitude circle. A new estimate of the global ocean heat flux across 24°N and its seasonal variation can be obtained by combining the results of this study with a similar analysis in the Atlantic [Fillenbaum et al., 1997]. Table 3 compares the annual mean heat flux obtained by these combined studies with previous direct and indirect estimates at this latitude. The mean value obtained from this study is 2.06 ± 0.39 PW, which falls about midway in the range of the reported values of 1.6–2.5 PW.

Table 3. Estimates of Oceanic Heat Flux Across 24°–27°N in the World Oceansa
ReferenceHeat Flux, PWMethod
PacificAtlanticPacific and Atlantic
  • a

    The transatlantic heat transport estimate in this study is taken from Fillenbaum et al. [1997]. Error bars that are available in these studies are also listed.

Hsuing et al. [1989]0.83 ± 0.60.98 ± 0.51.81 ± 0.9Surface heat flux heat storage
Trenberth and Solomon [1994]1.0 ± 0.21.1 ± 0.22.1 ± 0.3Radiation, atmospheric heat transport
Keith [1995]1.2 ± 0.51.3 ± 0.52.5 ± 0.7 
Trenberth [1997] ± 0.3 
Trenberth et al. [2001]
Bryden et al. [1991]0.76 ± 0.31.22 ± 0.31.98 ± 0.42hydrographic one-time section
Macdonald and Wunsch [1996]0.5 ± 0.31.1 ± 0.31.6 ± 0.42(inverse)
Ganachaud and Wunsch [2000]0.5 ± 0.31.3 ± 0.31.8 ± 0.42(inverse)
This study0.62 ± 0.211.44 ± 0.332.06 ± 0.39climatology

[56] Historically, oceanic heat flux estimates that were obtained indirectly by subtracting the atmospheric heat flux from the total ocean and atmosphere heat transport required by the radiation budget at the top of the atmosphere were much larger than direct estimates from oceanographic data [e.g., Carissimo et al., 1985]. However, the more recent estimates using these methods are quite close to the direct estimates, especially when one considers the error bars in both methods (Table 3). Trenberth and Solomon [1994] pointed out that the smaller heat transport in the atmosphere obtained in previous studies can be attributed to the inadequate rawinsonde measurements over the oceans, which failed to capture the vigor of the atmospheric heat transport. Our estimate of the global 24°N ocean heat flux is in agreement with the value proposed by Bryden et al. [1991], although the relative contributions in the Atlantic and Pacific basins are different. Our estimate in the Pacific is 0.14 PW smaller than Bryden et al.'s [1991] 0.76 PW, while the Fillenbaum et al. [1997] estimate in the Atlantic of 1.44 PW is ∼0.2 PW larger than the 1.2 PW estimate by Hall and Bryden [1982] that Bryden et al. [1991] used in their global estimate. The values obtained by Macdonald and Wunsch [1996] in the Atlantic (1.1 PW) and the Pacific (0.5 PW) are the lowest of the direct estimates in both basins and lead to their smaller global estimate of 1.6 PW. A recent update of their inverse model suggests a higher heat transport in the Atlantic (1.3 PW) and hence a higher total heat transport (1.8 PW) across 24°N [Ganachaud and Wunsch, 2000]. Using the sea surface heat flux and upper ocean heat storage, Hsiung et al. [1989] obtained the meridional heat transport in both the Pacific and Atlantic. Although their estimate of the annual mean Pacific heat flux at 24°N is 0.21 PW higher than ours, their Atlantic estimate is 0.46 PW lower than that of Fillenbaum et al. [1997], and their resulting total oceanic heat flux at this latitude (1.81 PW) is thus comparable to the sum of the direct estimates in the two basins. Note that the error bar of Hsiung et al.'s [1989] estimate is as large as 0.7 PW in the Pacific and 0.5 PW in the Atlantic.

[57] Perhaps the most important contribution from this study is that it provides a first direct estimate of the global seasonal cycle of oceanic heat transport across 24°N. Figure 16a shows the seasonal variation of the meridional heat flux across the Pacific 24°N from this study and that in the Atlantic (actually at 26.5°N) from Fillenbaum et al. [1997]. All seasonal variations are smoothed by a 3-month running mean filter to remove the month to month variability. The smoothed seasonal cycle in the Pacific ranges from 0.08 PW in February to 0.93 PW in August, while the Atlantic heat flux ranges from 0.96 PW in February to 1.86 PW in August. The range of the annual cycle in the Atlantic and Pacific is thus comparable (0.8–0.9 PW). The phase of the two cycles appears to be somewhat different, however, with the summer maximum heat flux in the Pacific tending to extend farther into the fall season than in the Atlantic. Combining these two estimates, we find that the world ocean heat flux across 24°N is lowest in February, 1.10 PW, the highest in August, 2.79 PW, with a total annual range of 1.7 PW.

Figure 16.

(a) Three-month smoothed seasonal variation of meridional heat flux across 24°–27°N in the Pacific (this study), Atlantic [from Fillenbaum et al., 1997], and the World Ocean. (b) Meridional heat flux across 24°–27°N in the Pacific and Pacific and Atlantic, in comparison with Hsiung et al. [1989], using sea surface heat flux and upper ocean heat storage change.

[58] Figure 16b plots the seasonal variation of our estimate in the Pacific and the world ocean across the latitudes of 24–26.5°N against Hsiung et al.'s [1989] results. Though both the mean and seasonal range of the heat flux from Hsiung at al. [1989] in the Pacific are larger than our estimates, their seasonal variation of the heat flux across the world ocean is quite similar to our seasonal cycle of the Pacific and Atlantic together.

5. Summary

[59] The current velocity and temperature of the Kuroshio measured by the long-term WOCE PCM-1 current meter moored array in the East Taiwan Channel are used to estimate the Kuroshio heat transport. This measurement is important because the heat transported by the energetic western boundary current on the relatively shallow shelf and slope region is critical in determining the transbasin meridional heat flux.

[60] Volume and temperature transport fluctuations of the Kuroshio in the ETC are concentrated on 100-day timescales. These large 100-day variations can change the temperature transport by up to 0.8 PW within 10 days, and the range can be as large as 2.0 PW. The 100-day variations can therefore badly alias the temperature transport derivation from single nonsynchronous section surveys. A strong linear relationship between the Kuroshio volume and temperature transport and the cross-stream SLD is found in the 21-month PCM-1 record. The climatological seasonal cycle of the Kuroshio temperature transport is thus derived from a 7-year SLD time series across the ETC. It is noted that the large year-to-year variation in the SLD time series still results in significant uncertainties in determining the temperature transport seasonal cycle. The associated uncertainty is accounted for by choosing the standard deviation of the 7-year climatological seasonal cycle to represent the error bar.

[61] The seasonal cycle of the Kuroshio volume and temperature transport is then incorporated with an estimate of the temperature transport in the shallow Taiwan Strait, a high-resolution bimonthly interior ocean hydrographic climatology, and various wind products to yield the seasonal cycle of transpacific heat flux across 24°N. It is shown to have a minimum heat flux of ∼0 PW, in January and February, and becomes stronger in the second half of the year with a maximum of 1.1 PW in July and a secondary maximum of 1.0 PW in November (Figure 9). The large amplitude of the seasonal variation comes mainly from the Ekman component. The annual mean is 0.62 PW, and the associated error bar is ∼0.21 PW. Of the total mean heat transport, 0.37 PW is contributed by the “overturning” circulation, 0.25 PW is by the horizontal “gyre” circulation.

[62] The POP numerical simulation of the meridional heat flux at 24°N compares favorably with the observations in terms of both its seasonal variability and annual mean. On the annual mean the vertical and horizontal cells are found to contribute about equally to the heat flux, and the deep ocean (>800 m) contribution is negligible, in agreement with Bryden et al. [1991]. However, on seasonal timescales the vertical cell of the heat flux extends much deeper than 800 m, which is consistent with the expectation that the ocean adjustment to the large-scale seasonal wind forcing is barotropic. The seasonal heat flux variation is dominated by the vertical cell, while the contribution of the horizontal cell to the heat flux remains nearly constant.

[63] The heat flux in the Pacific derived from this study, together with recently updated estimates in the Atlantic from Fillenbaum et al. [1997], yields the first direct estimate of the seasonal cycle of oceanic heat flux across the latitude circle of 24°N. The combined annual mean heat flux is 2.06 ± 0.39 PW, in good agreement with that from Bryden et al. [1991], 1.98 ± 0.42 PW, although the latter is obtained from a larger value in the Pacific (0.76 PW) and a smaller value in the Atlantic (1.22 PW). The annual range of the total oceanic heat flux at this latitude is 1.7 PW, with a maximum in August (2.79 PW) and a minimum in February (1.10 PW). The seasonal cycle of the world ocean heat transport across 25°N from Hsiung et al.'s [1989] “air-sea exchange” method is close to ours, and it ranges from 0.7 PW in January to 2.4 PW in August but with uncertainties as large as 0.9 PW. Their estimate in the Atlantic is smaller than the accepted values with a mean magnitude of only 0.98 PW, while the annual mean in Pacific is 0.83 PW. Recent estimates of annual mean oceanic heat flux from the residual of top-of-atmosphere net radiation and atmospheric heat transports in reanalysis products are encouragingly close to the ocean heat flux derived directly from the observational data. An important next step in comparing these methods will be to calculate the seasonal variation of the global ocean heat flux with this indirect method and compare it with the seasonal cycle reported here.

[64] For long-term monitoring of meridional heat transport variations it will be important to (1) monitor the Kuroshio transport, (2) resolve the heat transport contribution of the East Ryukyu Current, and (3) obtain better measurements of surface winds and hydrographic variations in the ocean interior. Currently, there are intensified sea level measurements being obtained in the Kuroshio region, advanced scatterometry measuring the wind fields, and continuing high-resolution XBT/expandable conductivity, temperature, and depth profiling system (XCTD) sections and proposed float programs monitoring the interior. A comprehensive current meter study similar to the PCM-1 is much needed to investigate the structure and heat transport contribution by the East Ryukyu Current in more detail and to develop a long-term monitoring strategy by combining the detailed knowledge gained from such an array with the altimetry and long-term hydrography measurements in the nearby regions.


[65] This work was supported by the National Science Foundation through grants OCE9302187 and OCE9818672. D. Zhang greatly appreciates the University of Miami's support through its generous award of the Koczy Fellowship. We thank Bob Malone of Los Alamos National Laboratory for providing the POP modeling results for comparison and Alison Macdonald for her initial hydrobase data in the North Pacific. The comments from the reviewers helped to improve the manuscript. This publication is partially supported by the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) under NOAA Cooperative Agreement NA67RJ0155, contribution 860.