estimation of the pacific ocean meridional heat flux at 35°n

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This article was downloaded by: [The University of Manchester Library] On: 06 November 2014, At: 06:30 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Atmosphere-Ocean Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tato20 Estimation of the Pacific Ocean meridional heat flux at 35°N G.A. McBean a a Atmospheric Science Programme, Department of Geography , University of British Columbia , Vancouver, B.C. Published online: 19 Nov 2010. To cite this article: G.A. McBean (1991) Estimation of the Pacific Ocean meridional heat flux at 35°N, Atmosphere-Ocean, 29:3, 576-595, DOI: 10.1080/07055900.1991.9649418 To link to this article: http://dx.doi.org/10.1080/07055900.1991.9649418 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is

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Page 1: Estimation of the Pacific Ocean meridional heat flux at 35°N

This article was downloaded by: [The University of Manchester Library]On: 06 November 2014, At: 06:30Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK

Atmosphere-OceanPublication details, including instructions for authorsand subscription information:http://www.tandfonline.com/loi/tato20

Estimation of the Pacific Oceanmeridional heat flux at 35°NG.A. McBean aa Atmospheric Science Programme, Departmentof Geography , University of British Columbia ,Vancouver, B.C.Published online: 19 Nov 2010.

To cite this article: G.A. McBean (1991) Estimation of the Pacific Oceanmeridional heat flux at 35°N, Atmosphere-Ocean, 29:3, 576-595, DOI:10.1080/07055900.1991.9649418

To link to this article: http://dx.doi.org/10.1080/07055900.1991.9649418

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all theinformation (the “Content”) contained in the publications on our platform.However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness,or suitability for any purpose of the Content. Any opinions and viewsexpressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of theContent should not be relied upon and should be independently verified withprimary sources of information. Taylor and Francis shall not be liable for anylosses, actions, claims, proceedings, demands, costs, expenses, damages,and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of theContent.

This article may be used for research, teaching, and private study purposes.Any substantial or systematic reproduction, redistribution, reselling, loan,sub-licensing, systematic supply, or distribution in any form to anyone is

Page 2: Estimation of the Pacific Ocean meridional heat flux at 35°N

expressly forbidden. Terms & Conditions of access and use can be found athttp://www.tandfonline.com/page/terms-and-conditions

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Page 3: Estimation of the Pacific Ocean meridional heat flux at 35°N

Estimation of the PacificOcean Meridional Heat Flux

at 35°N

G.A. McBean

Atmospheric Science Programme

Department of Geography

University of British Columbia, Vancouver, B.C.

[Original manuscript received 29 November 1990; in final form 2 April 1991]

ABSTRACT The meridional heat flux in the North Pacific Ocean at 35°N is estimated pri-marily using hydrographic section data, following the method of Bryan (1962) and Bennett(1978). The meridional heat flux in the Kuroshio, computed using the Worthington andKawai section across the current, was 1.76 PW (positive northward), with over 80% of theflux occurring in the upper 400 m. The large-scale baroclinic heat flux across the rest ofthe section (145°Ε to North America) was —1.0 PW for the INDOPAC (1976) section and—0.5 PW for the IOS-72 section. The fluxes across the sections were also concentratedin the upper ocean with the upper 300 m accounting for over 75% of the flux. The meanhorizontal barotropic gyre circulation results in little (0.1 PW) net heat flux because thenorthward-moving water is only about 0.5°C warmer than the southward-moving water. Thecontributions due to Ekman heat flux (—0.16 PW) and flow through the Japan Sea (0.13 PW)are also relatively small. The eddy heat flux is quite uncertain, but estimated to be about0.3 PW. The total meridional heat flux, for the 1976 section, is calculated to be about 1.0PW. The total is very dependent on the baroclinic heat flux in the highly variable Kuroshioregion. The northward heat flux found in this study is more consistent with large-scaleatmospheric estimates and with Bryden et al. 's (1990) estimate for 24°Ν in the Pacific.

RÉSUMÉ On estime principalement le flux thermique méridional du Pacifique Nord à 35°Nen utilisant des données hydrographiques sectionnelles, selon la méthode de Bryan (1962)et Bennett (1978). Dans le Kuroshio, ce flux calculé à l'aide de la section Worthington etKawai à travers le courant est de 1,76 PW (positif vers le pôle), avec plus de 80% du fluxdans les 400 m supérieurs. Le flux barocline de grande échelle à travers le reste de la section(145"E à l'Amérique du Nord) était de —1,0 PW pour la section INDOPAC (1976) et de -0,5PW pour la section 1OS-72. Les flux à travers les sections étaient aussi concentrés dans lacouche supérieure de l'océan, les 300 premiers mètres comptant pour plus de 75% du flux-La circulation gyratoire moyenne barotropique horizontale donne un petit flux thermique netde 0,1 PW parce que l'eau qui se déplace vers le nord est seulement d'environ 0,5°C pluschaude que celle allant vers le sud. Les contributions provenant du flux d'Ekman (—0,16PW) et du flux dans la mer du Japon (0,13 PW) sont relativement petites. Le flux thermiquetourbillonaire est bien incertain mais, on l'estime, à environ 0,3 PW. On calcule le fluxthermique méridional total, pour la section de 1976, à environ 1,0 PW. Le total est fort

ATMOSPHERE-OCEAN 29 (3) 1991, 576-595 0705-5900/91/0OOO-O576$01.25/0© Canadian Meteorological and Oceanographic Society

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 577

dépendant du flux thermique barocline dans la région très variable du Kuroshio. Le fluxthermique vers le nord que l'on a trouvé est plus consistent avec les estimés atmosphériquesà grande échelle et celui de Bryden et al. (1990) pour 24°N dans le Pacifique.

1 IntroductionThe atmosphere and the oceans must transfer heat meridionally in order to maintaina quasi-steady-state climate. The mechanisms by which the meridional transferoccurs in the ocean are of fundamental importance to understanding and modellingthe climate system. There are several possible approaches (Dobson et al., 1982;McBean et al., 1983) to determining the meridional oceanic heat flux. In thispaper, heat flux will refer to the total amount of heat moved across an area, withunits of J s"1 or watts. One approach is based entirely on atmospheric budgets;gains or losses in an atmospheric volume must be compensated by exchanges ofheat between the ocean and the atmosphere. A second approach is to estimate thesurface fluxes directly. In both approaches, oceanic heat flux is determined as aresidual. A third approach, the one to be used in this paper, primarily involvesuse of océanographie data to deduce the flux. The North Pacific Ocean is a majorcomponent of the climate system and it is necessary to understand its circulationand fluxes.

Carissimo et al. (1985) used an atmospheric budget approach to show that theocean heat flux must be comparable with that of the atmosphere. At 35°N, theocean heat flux was about 3 PW (1 PW = 1015 W) and the atmosphere, 2.5 PW.Hsiung (1985), using the surface flux method, found the North Atlantic heat fluxwas northward and in reasonable agreement with estimates based on océanographiesection data (Hall and Bryden, 1982) and other surface flux estimates (Bunker,1976). For 35°N, Hsiung computed the heat flux in the North Atlantic to be 0.8 PWand in the North Pacific, 0.3 PW; a total much less than Carissimo et al.'s. Hsiungnotes, "The Pacific Ocean is also where there are large differences among the resultsfrom various estimates." Talley (1984), also using estimates of surface fluxes, foundthe North Pacific heat flux to be negative (equatorward), but concluded that theaccuracy of such estimates was not sufficient to deduce the direction confidently,let alone the magnitude.

Bryan (1962) was the first to use the océanographie method and computed theheat flux across several océanographie sections, including 32°N in the Pacific (—1.0PW). Bennett (1978) used a similar method to estimate the heat and salt fluxes inthe Southern Hemisphere. As noted above, several authors have analysed sectionsin the North Atlantic. Roemmich and Wunsch (1985) showed that ocean heat fluxesat 24.5°N (1.2 PW) and 36.25°N (0.8 PW) in the Atlantic, based on 1981 data,were "indistinguishable from those obtained from the IGY (1957-59) data and fromcomputations of air-sea heat exchange." Rago and Rossby (1987) found that theheat flux at 32°N in the Atlantic Ocean was 1.38 PW with an annual cycle of about0.4 PW from a minimum in the first half of the year to a maximum in the secondhalf.

Roemmich and McCallister (1989) have recently examined data from seven sec-

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578 / G.A. McBean

tions of hydrographie data in the North Pacific Ocean, including the INDOPAC sectionat 35°N, which is used in this paper. They used a least squares inversion procedureto estimate the large-scale circulation and patterns of heat and freshwater transport.Roemmich and McCallister found there is a large heat loss in the western NorthPacific and modest heat gains elsewhere. The heat fluxes were found to be 0.75 PWacross 24°N, -0.16 PW at 35°N and -0.09 PW at 47°N. From the 24°N sectionalone, Bryden et al. (1991) calculated the heat flux to be 0.76 ± 0.3 PW.

The Kuroshio Current system shows large temporal variations in the vicinityof 35°N. Masuzawa (1972) describes the Kuroshio's path south of Japan as:" . . . northeastward close to the continental slope, though it occasionally makes adetour south of Honshu. Crossing the Izu-Ogasawara Ridge approximately 140Έ,roughly 500 to 1500 m deep, the Kuroshio leaves the Japanese coast at CapeInubozaki (36°N), and flows generally east in a remarkable meandering path."Mizuno and White (1983) found quasi-stationary meanders at 144Έ, 150°E and160°E, which frequently intersect 35°N. For these reasons (Kuroshio moving al-most eastward and high level of eddy activity), it is recognized that 35°N is not anideal latitude to attempt this type of analysis. However, two trans-Pacific sections(INDOPAC: Kenyon, 1983; IOS-72: Wong et al., 1974) exist for 35°N, and supple-mentary océanographie and atmospheric data are also available. In view of theuncertainties discussed above, it is appropriate to examine these data to determine,to the extent possible, the meridional heat flux. In Section 2, the océanographie dataare described and in Section 3 the method for heat flux calculations is outlined.Sections 4 to 10 present the results that are summarized in Section 11.

2 Océanographie section dataIn March-April 1976, the Scripps Institution of Oceanography conducted a deepsection, called INDOPAC, across 35°N (Kenyon, 1983). The first INDOPAC station was at122°W (on 25 March 1976) and the last was at 14ΓΕ (station 98 on 29 April 1976)(Fig. 1). Generally, deep stations were completed every two degrees of longitude,with measurements to 1200 m halfway between. The deep stations from 130 to160°W were completed in July 1977 and have been used to extend the 1976 datato the bottom, when appropriate. A section of 98 stations at 1° intervals across thebasin was created by linearly interpolating between the 2° interval deep stations.Because most of the variability is in the upper levels, the interpolation below 1200m does not affect the results.

In October 1972, the CSS Parizeau of the Institute of Ocean Sciences, Sidney,Canada (Wong, unpublished cruise report and Wong et al., 1974), made deep (gen-erally to deeper than 4000 m) hydrographie measurements at 5° intervals across thePacific, and also at 35°N. The first station was at 145°E and there were 19 stations(Fig. 1). These data will be referred to as IOS-72.

Roemmich and McCallister (1989) note that the INDOPAC section does not wellsample the bottom waters or the boundary flows and, in this respect, the IOS-72section is more deficient. As will be shown (and as reported in Bryden et al. 1991),the deep waters do not contribute much to the total flux. To address the Kuroshioheat flux, additional data have been used. In August-September 1965, Atlantis

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 579

50°;

30»· ·•

20°··

INDOPAC-76/77

140° 150° 160° I7O°E 180° I7O°W 160° 150° 140" 130° 120° no"

Fig. 1 Locations of stations for the trans-Pacific sections. The long ticks above the line at 35°N indicatethe locations of the IOS-72 stations; the long ticks below, the deep stations; and the short ticksthe 1200-m stations, both for INDOPAC. The line from the Japanese coast, labelled I, is theInubozaki section.

/ / occupied three deep océanographie sections across the Kuroshio (Worthingtonand Kawai, 1972); one extended southeastward from the Inubozaki Peninsula andcrossed the Kuroshio near 35°N. These data, referred to as the Inubozaki section,will be used to investigate the fluxes in the western boundary current.

3 Oceanic heat flux calculationsWe start by considering the total volume flux into a volume of the ocean, the NorthPacific Ocean between 35°N and the Bering Strait. The volume fluxes are across thesection (United States to Japan) at 35°N (Vo); through the Japan Sea (VJS); throughthe Bering Strait (VBS); and the net freshwater flux from precipitation, evaporationand river inflow (P — Ε + R). The oceanic fluxes are considered positive in thenorthward direction. When averaged over a suitable time, the net volume flux mustbe zero. Therefore

Vo = VBS-VJS-(P-E + R) 0)

The Bering Strait has an estimated volume flux of 1.5 Sv northward (1 Sv = 106

m3 s~') (Aagaard and Greisman, 1975). Warm water flows northward through theTsushima Straits between Japan and Korea into the Sea of Japan with an estimatedannual volume of 2.2 Sv (Yoon, 1982). Net freshwater input from precipitationminus evaporation plus runoff is quite uncertain. McBean (1989) compared theresults from several sources and obtained a range from 0.09 to 0.42 Sv. Roemmichand McCallister (1989) computed a net freshwater flux of 0.56 Sv. These resultslead to an estimate of between —0.8 and —1.3 Sv volume flux (i.e. about 1 Svsouthward) across the section at 35°N. In view of the volume fluxes discussedbelow, this volume flux is negligible.

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58ο / G.A. McBean

The total heat flux across 35°N, F 3 5 , is

^35= / / pev dzdx + pVjse (2)Jo J-z

where the first term is Fos, the heat flux across the ocean section, ν is the meridionalvelocity (positive northward), χ is the coordinate in the east-west direction, L is thewidth of the basin, e is the total energy, ρ is the density, ζ is the vertical coordinate,and Ζ is the depth at location x.

The total energy can be approximated by (Bryan, 1962) as:

e = e0 + C9 (3)

where eo is the total energy at an arbitrary reference state, C is the mean heatcapacity at atmospheric pressure, and θ is the potential temperature.

Following the technique of Bennett (1978), which is based on Bryan (1962), themeridional flux of heat, across an ocean section, can be divided into a barotropicflux, FBT> and a shear flux, F S H .

Fos = FBT + FSH (4)

The barotropic flux contains the products of vertically averaged velocity and verti-cally averaged heat content. The shear term contains the vertical average of productsof the anomalies from vertical averages. Since these anomalies are due to both baro-clinic and Ekman velocities, it is useful to split the shear flux into baroclinic andEkman fluxes:

FSH = F B C + F E (5)

The baroclinic flux is determined by the geostrophically balanced baroclinic merid-ional velocity. The Ekman mass flux is determined by the wind-stress-driven merid-ional velocity in the near-surface or Ekman boundary layer and must be balancedby a return flow that will be assumed to be distributed uniformly across the sec-tion. The Ekman heat flux, F E , is the difference between the heat transported bythe Ekman mass flux and the compensating return flow.

Each term can be considered in terms of depth and longitudinal averages anddeviations from them. The depth average is defined as:

ν dz (6)-ζ

where Z is the depth at the position x. Deviations from the depth average are

The longitudinal average is defined as:

vdx (8)

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 581

where Xw and Xe = Xw +L are the positions of the west and east coasts, respectively,and L is the width of the sections, at depth z. The longitudinal anomalies are

ν* = υ - [v] (9)

Each of the barotropic, baroclinic and Ekman fluxes can be separated into fluxesdepending on longitudinal averages and those depending on longitudinal anomalies,using the above definitions. Then,

(10)= Lo[Z{v}][{e}) M}

where the first term on the right-hand side is equal to pVo«o and LQ = L(z = 0).

FBC=F2+F3

(ID= CZM{L[vg

+][Q+]}

FE=F4+F5

(12)= CLÇ>{Z[VE}][%] { } S

where vg and zfc are the geostrophic and Ekman velocities, respectively, and ZM

is the maximum depth of the section; even-numbered fluxes contain the productsof longitudinal averages, whereas odd-numbered fluxes contain longitudinal aver-ages of the products of longitudinal anomalies. F\ is the depth-averaged horizontalmotion (gyre plus eddies), F2 is the longitudinally averaged overturning or thermo-haline circulation and F3 is the baroclinic horizontal gyre circulation. F4 and F5are the Ekman fluxes.

The mean heat flux requires knowledge about the reference state, CQ, if the meanvolume flux across the section is non-zero. As shown above, the mean volume fluxthrough the section at 35°N (Vo) is very small (PÖ 1 Sv) and the mean volumeflux across 35°N is also very small (Vo + VJS ^ 1 Sv) and can be neglected. Wecan assign an arbitrary reference state (we chose θ = 2.84°C, the average potentialtemperature across the section, based on the INDOPAC data) and compute heat fluxeswith respect to that.

4 Heat fluxes through the Japan Sea

Relative to 2.84°C, the heat flux through the Japan Sea can be computed, based onYoon's (1984) data for 4 layers of flow into the Japan Sea, each with a differenttransport and mean temperature, as:

FJS = 0.13 PW

The Japan Sea heat flux is within the uncertainty of larger terms, to be discussedbelow. Bryan (1962) estimated the Japan Sea heat flux as 0.18 PW.

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5 Heat flux by the Kuroshio

As noted by Roemmich and McCallister (1989), the INDOPAC section may nothave extended close enough to the Japanese coast to include the transports bythe Kuroshio. Hence, before we present the results for the oceanic section, weneed to consider the details of the flow in the Kuroshio. The Inubozaki section wasconducted in September 1965 by Worthington and Kawai (1972) and consisted of18 stations in a line from the coast about 320 km to the southeast (221°) acrossthe Kuroshio. Neutrally buoyant floats were used to establish the reference levelfor velocity calculations. They computed the volume transport to be 88 Sv. For asection upstream off Shikoku, they found a volume transport of 84 Sv. Hall (1989a)analysed current-meter mooring data (for two years) in a north-south line acrossthe Kuroshio Extension at 35°N, 152Έ and obtained a transport of 87 ± 21 Sv.Hall notes that this may be an underestimate due to missing edges of the Kuroshioand suggests a value of 93.5 Sv may be appropriate.

The temperature and velocity data published by Worthington and Kawai (1972)were used to compute the heat flux across the section as:

FK = pC f [ Μ(Θ - 2. %A)dzdx = 3.26 PW (13)

where the integral is over the section and u is the velocity perpendicular to thesection (approximately northeastward). For the Inubozaki section, the average po-tential temperature, [{Θ}], was 3.27°C. This heat flux through the section is toward041°. However, the true direction of the vector heat flux is likely more toward theeast since the Kuroshio is turning eastward at this latitude. Note that Hall (1989a)found a similar volume transport, but directed eastward, in her measurements at152°E. The float data of Worthington and Kawai (1972) indicate that the meanflow direction was 059°. Using this angle, the northward or meridional componentof the heat and volume fluxes is computed to be

Most of this heat flux is carried by the warmer upper layer. Over 80% of the fluxis in the top 400 m and the contributions below 1000 m are negligible.

The interpretation of F% requires some clarification. First, it should be stressedthat the flux is based on one section through a highly variable part of the Kuroshio.Kawabe (1986) shows how variable the Kuroshio path is, with marked variationsoccurring over a few months. The northeastward flow across the Inubozaki sectionwill also cross the INDOPAC section, although the part nearest the coast will not beobserved. The projection of the Inubozaki section to the northeast on the INDOPACsection overlaps from the coast to about 145°W. Hence, when using the INDOPACdata, only the section from 145°W eastward will be used. It is possible that sometransport is missed, but this is considered to be small. In the calculation, we haveassumed that only half of the heat flux and volume transport across the Inubozakisection goes north of 35°N. It should also be noted that the computation of themeridional flux is quite sensitive to uncertain knowledge of the true direction oftotal flux. If the angle were towards 064° (instead of 059°), then F% = 1.4 PW.

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 583

6 The large-scale barotropic flux

Now consider the heat flux across the ocean section, assuming the mean heat

flux (FQ) is negligible because the mean volume flux is very small. F\ is deter-

mined by correlation between longitudinal anomalies of depth-averaged velocity

and depth-averaged potential temperature. There are two components to this term.

The large-scale flux, F\is is due to the basin-scale horizontal gyre. The barotropic

eddy flux, Fu,e will be discussed in Section 9. Depth-averaged velocities are diffi-

cult to determine from direct measurements. For Fi!s, Hall and Bryden (1982) used

the measured volume flux of the Florida Straits to specify the average barotropic

velocity across the Atlantic on the assumption that the water volume moving north

through the Florida Straits must return southward over the rest of the basin at the

same latitude. Temperature measurements across the Florida Straits were used with

velocity data to compute the heat flux. Bryan (1962) and Bennett (1978) used the

Sverdrup transport, due to the longitudinally averaged curl of the wind stress, as a

reasonable measure of the barotropic volume flux in the western boundary current.

Both approaches make the assumption that boundary current and return total vol-

ume flux over the rest of the section must have the same net volume fluxes (but in

opposite directions). Since there is no information on the longitudinal distribution

of the return flux, it must be assumed that the depth-averaged temperature is inde-

pendent of longitude. The large-scale barotropic heat flux is proportional then to

the volume flux times the difference between the mean temperatures of the bound-

ary current and the rest of the section. For the North Pacific Ocean, the large-scale

barotropic flux results from northward flux in the Kuroshio and southward flux in

the interior return flow. The term can be written as:

' Λ ' Λ, J (14)

where L\ is the width of the boundary current.Depth-averaged potential temperatures were computed by linearly extrapolating

potential temperature to the bottom. Since INDOPAC data measurements generallyextended to near the bottom, the uncertainty due to the method of extrapolation isinsignificant. For IOS-72, the uncertainty is larger but still unimportant. For INDOPACand IOS-72 cruises (Fig. 2), temperatures over the eastern half of the ocean arevery uniform. For stations between 175°W and 175°E, depths are relatively shallowand depth-averaged temperatures are about 1°C warmer. For the western part ofthe sections, temperatures show considerable variation. Differences between thesections reflect seasonal differences between INDOPAC data, mainly from April 1976,and IOS-72 data from October 1972. Levitus (1987) published a map of verticallyaveraged annual mean potential temperatures. At 35°N in the Pacific Ocean, thevalue is close to constant across the basin and near 3°C. These results indicatethat the assumption that {Θ} is independent of longitude is valid, except near thedate-line and the coasts.

The depth-averaged potential temperature for the INDOPAC section is 2.84°C (or if

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584 / G.A. McBean

3-

2-

0-

Z(m)

7000140° 150» 160° I7O°E 180° I7O°W 160° 150° 140° 130° 120°

LONGITUDE

Fig. 2 Top: The depth-averaged potential temperatures from INDOPAC (crosses) and IOS-72 (circles)

as a function of longitude. Bottom: The ocean depth (based on the INDOPAC stations) and the

depth of the deepest data point for each station (squares).

we exclude some shallow stations near ridges or the California coast, 2.76°C). Forthe Inubozaki section, the depth-averaged potential temperature across the Kuroshiois 3.27°C. The average for the four westernmost stations of the INDOPAC section (atlatitudes 141-144°W) is 3.34°C. Thus, δθ is between 0.4 and 0.6°C.

The meridional volume flux of the Kuroshio was estimated from the Inubozakidata to be 48 Sv. Roemmich and McCallister (1989) computed a volume flux of45.9 Sv northward across 35°N between the coast and 150°E. They suspect thatthis is an underestimate since they did not have stations across the Kuroshio to thecoast. Further, since there is recirculation (water moving southward) on the eastside of the Kuroshio, which is included in the zone from the coast to 150°E, theRoemmich and McCallister value should be less than the Kuroshio transport. Taft(1972) estimated the volume flux of the Kuroshio (relative to 800 db) to be nearly50 Sv at 139°E, 33°N. Hall (1989a), as noted above, found an eastward volume

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flux of 87 Sv (with a possible value as large as 94 Sv). Meridional volume fluxesfor 35°N, assuming the Sverdrup balance, have been calculated by Evenson andVeronis (1975) and by Katsuwada (1982). Both studies find annual variations withmaxima in fall and spring. Katsuwada computed the fall (September-November)volume flux to be 47 Sv, in good agreement with the result from the Inubozakidata. His spring value is 46 Sv and his annual average 37 Sv (omitting a singledubious large negative value). These results suggest that about 40 Sv may be agood estimate of the annual value. A maximum possible value would be about90 Sv, allowing for the full volume flux to be directed northward. However, thissituation is unlikely to last since Shoji (1972) reports that the longest mean life ofa pattern is about 2 months.

For V = 40 Sv and δθ = 0.6°C, the heat flux is 0.1 PW. A maximum valuewould be 0.2 PW, for V = 90 Sv and δθ = 0.6°C. Bryan (1962) computed thebarotropic flux to be 0.04 PW. Since the actual ship track crossed the Kuroshionorth of 32°N (on its way to Tokyo), this value is comparable to the value for35°N.

These data lead to the conclusion that differences between the depth-averagedtemperatures of northward- and southward-moving barotropic components of thecirculation are not large enough to transfer large amounts of heat. The flux is about0.1 PW which is within the uncertainty of calculations to be discussed later.

7 The baroclinic heat fluxes

The term F2 can be associated with the longitudinally averaged overturning orthermohaline circulation (mean meridional circulation); F3 is the small-scale (oreddy) baroclinic flux. Geostrophic velocities were calculated from hydrographiedata, using

Vg = -f~ldDßx (15)

where D is the anomaly of the dynamic height difference that is computed relativeto 1500 m. The heat flux results are actually independent of the reference level.

The geostrophic velocity was calculated for each station pair. For the regionsbetween the coast and the nearest station, it was assumed that the potential tem-peratures and velocities were the same as the closest interior data. The differencebetween this assumption and the assumption of no flow in the regions adjacent tothe coast was less than 15%.

8 The large-scale baroclinic heat fluxThe longitudinal average of the INDOPAC geostrophic velocities (Fig. 3) (relative tothe depth-averaged geostrophic velocity) is negative (equatorward) from a maxi-mum (—0.008 m s"1) at the surface to zero at 1500 m, positive but small down to5000 m and then negative again. The results in the deep water are not very reliablebecause of poor sampling and interactions with topography. The IOS-72 verticalprofile of geostrophic velocity anomaly has a slower southward flow near the sur-face that extends only to 400 m. The northward flow was also weaker. Hall andBryden (1982), for 24°N in the Atlantic Ocean, found a meridional velocity profile

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Ο τ "Γ Ο

ΙΟΟΟ- • -1000

2000-• - 2 0 0 0

3000-•

Z(m)

4 0 0 0 -

-•3000

Z(m)

-•4000

5000-- -5000

6000-- --6000

7000- -+- •+--15 -10 -5

[Vgrt+](m !

- 4Η 1-

4 8ΙΘ*1(°Ο

12 16 -10 -8 -6 -4 -2 Ο

LIV/1 [θ*] (m2°C$-1)(xl05)

-7000

Fig. 3 Longitudinally averaged deviations from depth-averaged variables. From left to right: geostrophic velocity; potential temperature; and their product weighted

by the width of the section at that depth.

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that was negative (—0.015 m s"1) at the surface, and a northward core with itsmaximum (0.001 m s"1) at 800 m; below about 1000 m, the velocity was negativeto a depth of over 4500 m.

The longitudinal average of the INDOPAC vertical potential temperature anomaliesshows a maximum of +12.6°C at the surface decreasing to zero at 1200 m becoming-1.56°C at 5000-m depth. The [θ+] profiles indicate that the IOS-72 data werewarmer in the upper levels and correspondingly colder below.

For the INDOPAC data, the [ι^+][θ+] product is largest negative near the surfaceand small elsewhere. It is positive between 1300-1500 m and below 5000 m andnegative elsewhere. The result is a net equatorward heat flux by the mean meridionalcirculation. Over 40% of the total flux occurs in the upper 100 m and 75%, inthe upper 300 m. Although the deep waters are interesting for their water masscharacteristics, the flows below 1000 m contribute only about 12% of the totallarge-scale baroclinic heat flux. The IOS-72 results are similar near the surface(higher temperatures are compensated by smaller velocities) but different below600 m. Because the IOS-72 fluxes are either positive or less negative at depth,the net heat flux is smaller in magnitude. In the IOS-72 results, 54% of the fluxoccurs in the upper 100 m, and 91% in the upper 300 m. Less than 5% of thetotal large-scale baroclinic heat flux is due to flows below 1000-m depth. Thus,although the deep waters were poorly sampled in both sections, their impact on thebaroclinic heat flux is likely quite small, and better sampling is unlikely to changethese results. Because of the importance of the upper ocean in these calculations,the time of the year for each section may be important.

The large-scale baroclinic flux, Ft, was computed to be —0.75 PW for theINDOPAC section and —0.51 PW for the IOS-72 section. Since the station spacingfor the IOS-72 section certainly undersamples the western part of the section, itsvalue is less reliable. Bryan (1962) found the large-scale baroclinic flux was 1.41PW. Since the INDOPAC section overlaps the Inubozaki section, F2 was calculatedfor the INDOPAC section from 145°E to the California coast to give Fi = —1.02PW. The value is more negative because the westernmost stations provide positivecontributions to the integral. Hence, F2 = — 1.02 PW will be used for the purposeof tabulating the total heat flux for the océanographie section.

9 Eddy heat fluxes

The barotropic eddy flux, F\be, is not directly measurable and is difficult to es-timate. Bennett (1978) noted that the term can be written as the covariance ofeddy anomalies of surface geostrophic velocity and depth-averaged eddy tempera-ture anomaly or as the product of the standard deviation of eddy anomalies and acorrelation. He concluded that the term could be as large as 20 PW, but is morelikely of order 1 PW or smaller. A different approach, due to Holloway (1986; seebelow) estimates the total eddy heat flux.

The small-scale or eddy baroclinic flux, F3, can, in principle, be calculated fromhydrographie data. F$ results from deviations from the longitudinally averaged,depth-averaged velocities and temperatures. The observations need to be closelyspaced to resolve the eddy field (see Bennett and White, 1986) and the 1° obser-

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588 / G.A. McBean

800 η

-I20C +140 150 160 I70E 180 I70W 160 150 140 130 120

Fig. 4 The longitudinal variation of the vertical integral of the product of small-scale velocities and

potential temperatures.

vations available here undoubtably miss the finer structure. The vertical integral ofthe product of these deviations is largest near the western boundary (Fig. 4), smallthrough most of the central region, and larger again near the California coast. TheKuroshio meanders that are near the western boundary add and subtract heat fluxwith the net result that about 80% of the total flux is contributed in the first 3000km out from the Japanese coast, with about 10% coming from the region adjacentto the California coast. Very little contribution is made from the central part of theocean. Bennett and White (1986) have a similar finding.

The small-scale baroclinic heat flux can be written in terms of the temperatureand velocity standard deviations and their correlation; i.e.

= pCZML (16)

where

σν — rms {Vgfσθ = rms (θ+)*rV(, correlation coefficient of (ζ>+)*(θ+)*

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 589

In Fig. 5, each of these terms is shown. σν is a maximum of 0.18 m s"1 atthe surface and decreases to a minimum of 0.02 m s"1 at 2000 m. The standarddeviation of potential temperature has its maximum of 2.0°C at 250 m, a rapiddecrease to 0.7°C at 800 m and a more gradual decrease below. The covariancehas a maximum value at 30 m (0.017) and a minimum at 250 m. A secondarypositive maximum of the covariance occurs at 900 m where the correlation is 0.34(for 20 degrees of freedom this is significant at the 10% level). The correlationitself has a maximum at 1100 m (0.39). Using current meters at 35°N, 152Έ,Hall (1989b) measured the correlations of meridional velocity and temperature. At250 and 625 db, the correlation coefficients were about —0.6. These are values forone location in an eddy-active zone, over a period of 390 days. The correlationspresented in Fig. 5 are averages across the section.

Using (16), limits can be put on the small-scale baroclinic heat flux, assumingthat the variances of the velocity and temperature anomalies are better sampled thantheir covariance. If the correlation between the two were 1.0 at all depths, then theheat flux would have been 5 PW. If the correlation were 0.5 in the upper 1000 mand zero below, the heat flux would have been 2 PW. Bennett (1978) commentsthat indirect estimates indicate that the correlation is about 0.1 and his dynamicalestimate is that it is about 0.005. The former would give a baroclinic eddy heatflux of 0.5 PW; the latter, 0.03 PW. For the variances and the eddy heat fluxcomputed here, the depth-averaged correlation is 0.04. Freeland (pers. commun.)has computed velocity-temperature correlations from mooring data in the NortheastPacific (near Station P). He finds values up to 0.01 at 200 m and less than 0.002 forall other levels (600, 1500 and 3000 m). Until there is more complete informationabout the correlation of baroclinic eddy velocities and temperatures, including theKuroshio region, it is not possible to pursue this analysis further.

The cross-section, length-weighted covariances integrate to F 3 . About 78% ofthe contributions to the integral are from the upper 1000 m. There is a northwardflux near the surface resulting from poorly correlated but large variations of veloc-ity and temperature. There is a southward flux at 200-300 m where temperaturefluctuations are a maximum. This maximum results from variations in the depthof the thermocline across the section. Below this region is a broad depth range ofnorthward flux, mainly from 600 to 2000 m, where the velocity and temperaturefluctuations, although much smaller than those nearer the surface, are more highlycorrelated.

Bennett and White (1986) examined the eddy heat flux in the latitude range3O-5O°N, using TRANSPAC XBT data on a one-half degree latitude-longitude grid, atstandard océanographie levels to 400 m. They computed a standing eddy heat flux(time-averge of the correlation of longitudinal anomalies) to be 0.07 PW at 35°N.By modelling the velocity profile as an exponential function of depth, they deduceda correction factor (of 3.3) for the assumption of 400 m as the velocity referencelevel. The resulting standing eddy heat flux was 0.23 PW. The transient eddy heatflux was very small (less than 0.02 PW). The standing eddy heat flux, as definedby Bennett and White, is not directly comparable with any of F\ to F3. However,for comparison, the INDOPAC data were used to calculate the instantaneous eddy heat

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Ζ (m)

0-

1000-

2000-

3000-

4000-

5000-

6000-

7000-

r?—

\

κ1 1 1 1

0 5 10 15

σ ν (m s" )(xlO) σ-gCc)

h20 -002 -001 0 0 1

-H h-002 -0-4 -&2 0-2 0-4

Fig. 5 From left: the standard deviations of small-scale velocity (solid line) and temperature (dashed line) deviations; the product of small-scale deviations; and thecorrelation coefficient for the small-scale deviations; all as a function of depth.

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 591

flux for the time of the INDOPAC section (April 1976). Use of a reference velocitylevel of 400 m resulted in an instantaneous eddy heat flux of 0.10 PW in the upper400 m, in general agreement with the Bennett and White result. The INDOPAC datacan be used to investigate the effect of different reference levels. The computedinstantaneous eddy heat flux integrated over all depths was within 10% of 0.35 PWfor Zref between 700 and 2000 m and decreased somewhat for deeper levels, thussupporting the approach of Bennett and White.

Holloway (1986) coupled theoretical considerations of two-dimensional turbu-lence and statistics of fluctuations of sea-surface elevation, as determined fromSeasat altimetry, to deduce a meridional eddy diffusivity. Applying these diffusiv-ities to meridional gradients of depth-averaged temperatures, Holloway estimatedthe meridional eddy heat flux to be between 0.1 and 0.2 PW from 18 to 32°N, 0.35PW at 34°N and 0.33 PW at 36°N. Farther north, the eddy heat flux decreased toabout 0.1 PW at 46°N and then dropped to much smaller values poleward. Themaximum eddy heat flux at latitudes 34-36°N is consistent with information on thedistribution of oceanic eddies. Freeland (1987) confirmed these general conceptsbut suggested that the estimated heat flux may be a factor of 2 to 3 too high .

10 Ekman heat fluxHeat flux by the Ekman current has been evaluated using the temperatures fromthe trans-Pacific sections and the Katsuwada (1982) wind stress data. It is assumedthat the Ekman flux results in surface layer water moving in direct response tothe wind, with water returning over the rest of the section at the section-averagedtemperature. Bryan and Bennett both used the surface temperatures for the Ekmanlayer temperature, and Hall and Bryden used a weighted average of the surface and50-m values. The difference between the methods is only 0.1 °C for the INDOPAC

data. The surface temperature is 12.6°C warmer than the section average.The Ekman flux (based on Katsuwada, 1982) varies from —13.8 Sv (southward)

in February to 0.9 Sv (northward) in August and September. The annual averageis —4.5 Sv. Evenson and Veronis (1975) computed values that are more positive(winter fluxes of —6.4 Sv; summer values of 2.1 Sv). Assuming that the Ekmanlayer responds more quickly to the stress than the Sverdrup flux, it is appropriateto use a weighted March and April value for the INDOPAC data, which is —3.4 Sv.The resulting heat flux is -0.16 PW. The Katsuwada Ekman flux for October,when the IOS-72 data were collected, is 0 Sv. Bryan (1962) computed a value of0.08 PW. Levitus (1987) calculated meridional Ekman heat fluxes for 35°N in thePacific Ocean to have an annual mean of —0.25 PW with an annual range fromabout +0.2 PW in July-August to —0.6 PW in December-February. The Marchvalue was about —0.4 PW and the October value near zero. Based on these results,we can only conclude that the Ekman heat flux is about —0.2 to —0.4 PW for theINDOPAC section and near zero for the IOS-72 section.

There is also a contribution to the Ekman heat flux, F5, due to the longitudinalaverage of the correlations of the deviations of Ekman velocities and Ekman layertemperatures from their longitudinal averages. This can be represented in terms ofstandard deviations of Ekman velocities and Ekman layer temperatures and their

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592 / G.A. McBean

correlation coefficient. The standard deviation of the Ekman layer temperatures isabout 1.5°C (Fig. 5). Based on Katsuwada's maps of wind stress for January itwould seem unlikely that the standard deviation of the Ekman flux is much largerthan its mean, 5 Sv. Since the standard deviation of the Ekman temperature isabout Vio of its mean and the correlation between the two deviations is less thanunity, the term F5 must be '/io or less of F4; i.e. negligible. Bennett (1978) alsofound that F5 was negligible.

11 Summary and conclusionsHydrographie and other data have been used to estimate the meridional heat fluxesat 35°N in the Pacific Ocean and the results are summarized in Table 1, whichalso includes the results of Bryan (1962) for a section at 32CN. The dominatingterms are the heat flux in the Kuroshio (about 1.8 PW northward) and the large-scale baroclinic flux across the rest of the section (about 1 PW southward). TheKuroshio term, based on the Inubozaki section, has a major uncertainty due tosampling in a region that shows a large amount of temporal and spatial variation.The Inubozaki section was interrupted by a storm that results in dubious velocitiesin the middle of the section. There is also difficulty in determining the directionof the vector flux so that an uncertainty of up to 0.5 PW in the Kuroshio fluxis possible. However, it is clear that for at least some instances, there is a largebaroclinic heat flux in the Kuroshio. Rago and Rossby (1987) found a similarlylarge positive baroclinic heat flux across the Gulf Stream at about the same latitude.

The other major term, the large-scale baroclinic flux, would have a smaller un-certainty, about 0.25 PW. The Japan Sea flux (northward) almost cancels the Ekmanflux (southward). The eddy heat flux is quite uncertain, with the best estimate beingabout 0.3 PW, based on Holloway's computations. The result is a net northwardheat flux of about 1 PW, but with an uncertainty of greater than 0.5 PW. Thisvalue, 1 PW, is equal but opposite in direction to that found by Bryan (1962).It is also much larger than the —0.16 PW found by Roemmich and McCallister(1989). The major difference is the contribution due to the Kuroshio as sampledby the Inubozaki section of Worthington and Kawai (1972). The value reportedhere is more consistent with the recent computation for 24°N by Bryden et al.(1990), which was 0.76 PW northward. In the region of the North Pacific Oceanbetween 24 and 35°N, the net annual heating of the ocean is small, but the sign isindeterminate (Talley, 1984). If the value of 0.76 PW is assumed correct at 24°N,and we assume the net annual heating is between +20 and —20 W m~2, then theflux at 35°N must be between 0.5 and 1.0 PW. In view of the uncertainties in bothcalculations, the results are consistent. It is interesting to note that for the NorthAtlantic Ocean, Hall and Bryden (1982) and others obtained a value of 1.2 PW at24°N, whereas Roemmich and Wunsch (1985) obtained 0.8 PW at 36.25°N, andRago and Rossby obtained 1.38 PW at 32°N. Collectively, these results indicatethat the poleward oceanic heat fluxes in both the Atlantic and the Pacific are about1 PW (with a 50% uncertainty) between 24 and 36°N.

The heat fluxes are dominated by the fluxes in the upper ocean. Over 80%of both the Kuroshio and the large-scale baroclinic heat fluxes are in the upper

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Estimation of the Pacific Ocean Meridional Heat Flux at 35°N / 593

TABLE 1. Summary of heat transports (see text for discussion) and theresults presented by Bryan (1962) (in PW)

Term

F,sF"kFusF2

FiF*

Total

Bryan

0.18

0.04-1.41

0.110.08

-1 .0

This Study

0.131.760.1*

-1 .00.3

-0.16

1.0

Data Source

Yoon (1982)Inubozaki sectionINDOPAC sectionINDOPAC section (145°-coast)HollowayKatsuwada, INDOPAC section

*Not included in total since it is effectively included in F"jç.

400 m. For both the INDOPAC and IOS-72 sections, the baroclinic flux results pri-marily from warm water moving equatorward in the upper ocean. Flows in theupper 300 m of water accounted for 75% of the total large-scale baroclinic heatflux for the INDOPAC section and over 90% for the IOS-72 section. Bryden et al.(1991) also found that the upper ocean fluxes dominated. They note "This north-ward heat transport is due half to a zonally averaged vertical-meridional circulationcell and half to a horizontal circulation cell." Both cells were effectively in the up-per 700 m. Although the methods of computation are different, which makes exactcomparison difficult, the results are consistent.

Because of the importance of the upper ocean for the heat fluxes, sampling andtemporal differences may be important. For the INDOPAC section, the large-scalebaroclinic heat flux is -1 .0 PW; for the IOS-72 section, it is -0.51 PW. If theINDOPAC data are sub-sampled to give the same station locations as the IOS-72 sec-tion, the result is still about —1.0 PW. This implies large temporal differences orother impacts of sampling. It is very important that the section sample well thewestern boundary current. Further investigation of these differences seems war-ranted. Hall and Bryden (1982) computed the large-scale baroclinic flux at 25°Nin the Atlantic to be -0.91 PW.

For sections across the Atlantic (Hall and Bryden, 1982), the barotropic heatflux was a major term due to the large differences in depth-averaged tempera-ture between the northward-moving barotropic flow in the Gulf Stream and thesouthward-moving return flow across the section. Hall and Bryden had 29.5 Sv ofvolume flux northward at 15.6°C in the Gulf Stream (at 25°N) and returning at5.4°C; the resulting heat flux was 1.23 PW. For Rago and Rossby's (1987) anal-ysis of data at 32°N in the Atlantic, the results are quite different. They compute97.7 Sv of volume flux northward in the Gulf Stream at 6.23°C with the mainreturn flow of 59.6 Sv being across the section at 6.19°C. There is also returnflow in the Gulf Stream inflow at 6.53°C and smaller amounts through the slopewater, the recirculation gyre and the Bering Strait. Because the depth-averagedtemperatures are almost equal, the net barotropic heat flux is only 0.02 PW. At35°N in the Pacific Ocean, the differences in depth-averaged temperature betweenthe northward-moving Kuroshio and the return flow across the section are alsovery small. The depth-averaged potential temperature of the section is 2.84°C. The

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594 / G.A. McBean

equivalent value across the Kuroshio is about 3.3°C (3.34°C for the 4 westernmoststations of the section; 3.27°C for the Inubozaki section across the Kuroshio). Avolume flux of 40 Sv and the small temperature difference indicated above gave0.1 PW barotropic heat flux due to the large-scale horizontal barotropic gyre cir-culation. Doubling the volume flux still gives only 0.2 PW. Although larger thanthat estimated by Rago and Rossby for a similar latitude in the Atlantic, the fluxis still relatively small.

The small-scale or eddy baroclinic heat flux, due to the correlations of verticalanomalies of velocity and temperature, was computed using geostrophic velocitiesrelative to an arbitrary reference level and is estimated from the INDOPAC data to be0.23 PW northward. About 78% of the flux occurred because of flows above 1000m. Hence, the flux is primarily based on the 1° (91 km) spacing of the 1200-m-deep stations. Since there is considerable smaller scale motion in the ocean, thisnumber can only be considered representative of eddies of larger than a few hundredkilometres. Holloway (1986) has provided an alternative estimate for the PacificOcean, based on a theory of oceanic eddies, satellite altimetry measurements andthe mean meridional temperature gradient: 0.34 PW at 35°N. In view of Freeland'scomments (1987) and the result for the baroclinic eddy flux, it is assumed that theeddy heat flux is about 0.3 PW.

It is clear that there continues to be considerable uncertainty in the North Pacificheat flux at 35°N, where the Kuroshio is full of meanders and the transport isnear zonal. This makes 35°N a very difficult place to compute heat fluxes for. Theresults, as best as they can be determined, indicate that the upper ocean flux in theKuroshio dominates the flux across the section to give a poleward heat flux thatis more consistent with general heat budget studies. Further research is needed onthe role of ocean eddies and on the possibility of temporal variations.

Acknowledgements

The INDOPAC data were provided to the author by Dr W. White of Scripps Institutionof Oceanography. The initial part of this work was conducted while the author waslocated at the Institute of Ocean Sciences, Sidney, British Columbia. The author isgrateful to Drs A. Bennett, H. Freeland and G. Holloway for helpful discussionsregarding this project.

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