Ekman currents from Earth and Space Research (ESR); and airsea heat uxes from Comprehensive Ocean-

2005 Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: +1 858 534 4826; fax: +1 858 534 7452.

E-mail address: wbwhite@ucsd.edu (W.B. White).

Progress in Oceanography 64 (2005) 129

Progress inOceanography

www.elsevier.com/locate/pocean0079-6611/$ - see front matter 2005 Elsevier Ltd. All rights reserved.Atmosphere Data Set (COADS), National Centers for Environmental Prediction (NCEP), and European Center for

Mid-Range Weather Forecasts (ECMWF). With these products, we compute residual heat budget components by

dierencing long-term monthly means from the long-term annual mean. This allows the seasonal cycle of the DHS ten-

dency to be modeled. Everywhere latent heat ux residuals dominate sensible heat ux residuals, shortwave heat ux

residuals dominate longwave heat ux residuals, and residual Ekman heat advection dominates residual geostrophic

heat advection, with residual dissipation signicant only in the KuroshioOyashio current extension. The root-

mean-square (RMS) of the dierences between observed and model residual DHS tendencies (averaged over 10 lati-tude-by-20 longitude boxes) is

ual adiabatic heat storage (AHS) tendency arising from vertical displacements in the main pycnocline. This

latter component depends on such adiabatic processes as Ekman pumping and Rossby wave propagation(e.g., White, 1977), both of which alter the depth of the main pycnocline. Thus, the residual heat storage

tendency in the upper layer (i.e., above the top of the main pycnocline) is composed of DHS and AHS com-Keywords: Seasonal cycle; Pacic Ocean; Heat storage budget

1. Introduction

During planning for the World Ocean Circulation Experiment (WOCE) in 1985, an objective was pro-

posed to measure the global circulation of the upper ocean well enough to close residual diabatic heat stor-

age (DHS) budgets on annual and interannual period scales to within 10 W m2 (World Climate ResearchProgramme, 1986). This proposed objective was received with general skepticism because the various indi-vidual DHS budget components were believed to contain errors from random noise and systematic biases

>10 W m2 (e.g., Weare & Strub, 1981). Even larger errors were expected in the DHS tendency, since theerrors in individual DHS budget components combine (Young, 1962). The combined errors were expected

to overwhelm the amplitude of the observed DHS signal, be it seasonal or interannual. On the other hand,

others argued that the random noise in residual DHS budget components could be suppressed to

ments (Zhang, Rossow, Lacis, Oinas, & Mishchenko, 2003), and the KM sensible-plus-latent heat uxreanalysis based on satellite surface winds (Kubota & Mitsumori, 1997). We compute residual horizontal

heat advection from the estimation of geostrophic and Ekman current velocities in the Earth and Space

Research (ESR) reanalysis (Bonjean & Lagerloef, 2002). In the latter, geostrophic currents are computedfrom gradients in the sea surface height (SSH) measured by TOPEX-Poseidon satellite altimetry, referenced

to the annual mean dynamic height from Levitus, Burgett, and Boyer (1994a), Levitus and Boyer (1994b),

while Ekman currents are computed from surface winds measured by the satellite Special Sensor Micro-

wave Imager (SSM/I) (Atlas, Homan, Bloom, Jusem, & Ardizzone, 1996). Earlier, a scale analysis con-

ducted by Gill and Niiler (1973) had indicated that residual horizontal heat advection has little inuence

on the seasonal cycle of upper ocean heat storage over the interior ocean. Here we nd its magnitude com-

parable to that of the turbulent and radiative heat ux residuals nearly everywhere over the Pacic Ocean.

Our objective is to estimate the RMS of the dierences between observed and model residual DHS ten-dencies in the seasonal cycle of the Pacic Ocean from 20S to 60N. If theses RMS dierences are found tobe signicantly less than the RMS of the observed residual DHS tendency, then we can determine the dom-

inant heat balance. Initially, we minimize RMS dierences to estimate the cross-isopycnal heat ux at the

top of the main pycnocline (i.e., the dissipation) in the residual DHS budget. Subsequently, we suppress

random noise by conducting a 10 latitude-by-20 longitude box-average on all the elds. We focus discus-sion on the RMS of the dierences between observed and model DHS tendencies averaged over eight re-

gional 10 latitude-by-20 longitude boxes (a, Fig. 1). Boxes A, B, and C focus on the residual DHSbudget underneath the Westerly Winds in the mid-latitude North Pacic Ocean (Tanimoto, Iwasaka, Ha-nawa, & Tobe, 1993), contrasting the KuroshioOyashio current extension (Box A), the Subarctic Frontal

Zone in the central ocean (Box B), and the mid-latitude eastern ocean (Box C). Boxes D, E, and F focus

on the residual DHS budget underneath the northeast and southeast Trade Winds. Boxes G and H focus on

the residual DHS budget on the equator under the southeast Trade Winds, contrasting the Warm Pool in

the western ocean (Box G) with the Cold Tongue in the eastern ocean (Box H). Finally, we minimize RMS

dierences to correct for biases in the residual airsea turbulent heat ux and Ekman heat advection in the

COADS, NCEP, ECMWF, and ESR reanalysis products.

2. Dening budgets for diabatic and adiabatic heat storage residuals

We start by formulating the budget equation for residual DHS tendency in the upper ocean. Resid-

ual DHS is dened as the component of heat storage in the layer above the top of the main pycnocline

arising from the vertical-average temperature residual in that layer (Moisan & Niiler, 1998). The algo-

rithm for nding the top of the main pycnocline begins with the denition of the near-surface mixed

layer depth; i.e., the depth where temperature changes 0.1 C from that at the sea surface. This criteriondiers from the 0.3 to 0.8 C temperature change used by Kara, Rochford, and Hurlburt (2003) andmay have underestimated the residual DHS. Regardless, we have applied this denition whether tem-DHS component responds to residual horizontal heat advection and airsea heat ux, independent of mass

(volume) conservation, and can be expected to play the principal role in coupling ocean and atmosphere

over the seasonal cycle (e.g., White, Cayan, Dettinger, & Auad, 2001; White, Cayan, & Dettinger, 2003).

We utilize residual airsea heat uxes from ve sources; the Scripps Institution of Oceanography (SIO)

and Comprehensive Ocean-Atmosphere Data Set (SIO-COADS) reanalysis (Slutz et al., 1985; Cayan, 1992;Woodru, Lubker, Wolter, Worley, & Elms, 1993), the National Centers for Environmental Prediction and

National Center for Atmospheric Research (NCEP/NCAR) reanalysis (Kalnay et al., 1996; Kistler et al.,

2001), the European Center for Mid-range Weather Forecasts (ECMWF) reanalysis (Uppala et al., 1999;

Beljaars & Kallberg, 2001), the ISCCP reanalysis of shortwave heat ux based on satellite cloud measure-

W.B. White et al. / Progress in Oceanography 64 (2005) 129 3peratures decrease or increase with depth, the former (latter) indicative of a near- surface mixed layer

4 W.B. White et al. / Progress in Oceanography 64 (2005) 129dominated by a seasonal thermocline (seasonal temperature inversion). We have also applied it whethera barrier layer exists within the near-surface mixed layer due to shallow vertical salinity gradients

resulting from rainfall (Maes, Picaut, & Belamari, 2002; Sato, Suga, & Hanawa, 2004). This may have

over-estimated the residual DHS in parts of the western tropical and subtropical Pacic Ocean. The

DHS algorithm denes the top of the main pycnocline to be the depth of an isotherm (at each grid

point) dened by the deepest penetration of the near-surface mixed layer over the 7-year record (Moi-

san & Niiler, 1998). This choice of isotherm assures that no near-surface mixed layer penetrated deeper

than this isotherm over the 7-year record. It assumes negligible cross-isopycnal mixing at the top of the

main pycnocline across this isotherm. However, in realistic ocean general circulation model (OGCM)simulations of observed interannual variability in the Pacic Ocean (Auad, Miller, & White, 1998), real-

istic DHS anomalies were achieved only by simulating signicant cross-isopycnal mixing at the top of

the main pycnocline via dissipation. Thus, we relax this assumption by allowing dissipation in the resid-

ual DHS budget.

With the DHS dened in this manner, its residual budget can be derived from the conservation of the

residual heat storage in the near-surface layer above the top of the main pycnocline, displayed in ux form;

i.e.,

Fig. 1. (a) Location of eight boxes, designated A through H, within which residual DHS budgets of the Pacic Ocean are examinedfor the seasonal cycle averaged over the 7 years from 1993 to 1999. Each box has dimension of 10 latitude-by-20 longitude, which isconsistent with the 10 latitude-by-20 longitude box-average applied to all of the elds in this study. (b) Distribution of the RMS ofthe observed residual DHS tendency over the seasonal cycle in units of W m2. These data were originally interpolated onto 2latitude-by-5 longitude grid (White, 1995), but then averaged over a 10 latitude-by-20 longitude box in the present study. Contourintervals are 10 W m2 and hatching is for eect.

3. WOCE reanalysis products

near-one a

satell

Lager

and qThe

chumuality-controlled according to WOCE standards at the University of Hawaii (Mitchum, 1990).latter were used to provide ground truth for TOPEX-Poseidon altimetric SSH estimates (Mit-ature proles collected along high-resolution XBT-XCTD sections (Sprintall et al., 1996), along a den-

ser array of low-resolution XBT sections (White, 1995), and along the TAO thermister-array straddling

the equator (McPhaden et al., 1998). This temperature prole dataset is compiled by the National

Oceanographic Data Center (NODC) and quality-controlled according to WOCE standards at SIO

(Diggs, Hall, & White, 1996). The WOCE observing system for surface currents includes in situ mea-surements from near-surface drifting buoys, with data collated and quality-controlled according to

WOCE standards at the Atlantic Oceanographic and Meteorological Laboratory (AOML) (Niiler, Sy-

brandy, Bi, Poullain, & Bitterman, 1995). The WOCE observing system also includes surface wind vec-

tor (VA) data from the satellite SSM/I (Atlas et al., 1996), and SSH from the satellite TOPEX-

Poseidon altimeter, the latter collated at the Jet Propulsion Laboratory (JPL) (Fu et al., 1994). The

latter have been quality control according to WOCE standards (Tai & Kuhn, 1995). The WOCE

observing system also includes in situ SSH estimates from Pacic coastal and island stations, collatedsurface Ekman velocity (VE), and total airsea heat ux (QT). These products overlap withnother over the 7 years from 1993 to 1999, coinciding with operation of the TOPEX-Poseidon

ite altimeter (Fu et al., 1994) upon which geostrophic and Ekman velocities depend (Bonjean &

loef, 2002). The WOCE observing system for upper ocean temperature includes in situ temper-To examine the residual DHS budget in Eq. (2.2) over the Pacic Ocean, we utilize individual

monthly mean WOCE reanalysis products of the basic variables on a common grid, chosen to be

2 latitude-by-5 longitude. The basic variables are DHS, near-surface geostrophic velocity (VG),oqOCPOTH0=ot rH qOCPOTHV 0 Q0T KqOCPOTH0; 2:1

where T is the vertical-average temperature in the upper layer; (qOCPOTH) is the total heat storage inthe upper layer above the depth (H) at the top of the main pycnocline; V is vertical-average horizon-

tal current vector in that layer; QT is total airsea heat ux; qO is average density of sea water (i.e.,103 kg m3); CPO is average specic heat of sea water (i.e., 4.2 103 W s kg1 C1); and K1 is the e-folding time scale for dissipation resulting from cross-isopycnal mixing at the top of the main pycno-

cline. Primed quantities represent long-term monthly mean residuals about the long-term annual

mean.

This denition for the upper ocean residual heat storage allows it to be divided into two parts [i.e.qOCPOTH0 qOCPOT 0 H qOCPOTH 0]. The diabatic portion is associated with vertical-average tem-perature conservation (i.e., DHS0 qOCPOT 0 H ) and the adiabatic portion is associated with upper-layervolume conservation (i.e., AHS0 qOCPOTH 0), where the over-bar represents the mean and prime representthe residual. Thus, Eq. (2.1) is separated into two parts:

oDHS0=ot H 0 V HV 0 rHqOCPOT HV rHqOCPOT 0 Q0T KDHS0; 2:2

oAHS0=ot qOCPOTrH HV 0 H 0 V ; 2:3where Eq. (2.2) gives the residual DHS budget and Eq. (2.3) gives the residual AHS budget, the latter equiv-

alent to the continuity equation for the upper layer. Closing the budget for total heat storage residual in Eq.

(2.1) requires estimation of residual heat transport divergence, while closing the residual DHS budget in Eq.

(2.2) requires estimation of the residual horizontal heat advection.

W.B. White et al. / Progress in Oceanography 64 (2005) 129 5, 1994).

3.1. SIO upper ocean temperature and heat storage reanalysis

The upper ocean temperature proles from NODC have been reanalyzed at standard levels at SIO

(White, 1995; White et al., 2001). At each level, they have been optimally interpolated onto a 2 lati-tude-by-5 longitude grid. Earlier, White and Tai (1995) found signicant statistical regression betweenpatterns of TOPEX-Poseidon SSH anomalies and in situ upper-ocean heat storage (0/400 m) anomalies

from 30S to 60N in the Pacic Ocean. This was due to the physical dependence of SSH anomalies uponsteric height anomalies, the latter an alias of the total upper ocean heat storage anomalies. However, in

the present context the upper ocean heat storage (0/400 m) residuals are observed to derive mostly from

the AHS residuals (that is, from vertical pycnocline displacements), with much less contribution stem-

ming from DHS residuals (that is, from temperature changes in the upper ocean above the top of the

main pycnocline). Thus, TOPEX-Poseidon SSH residuals cannot be used to improve the estimation of

DHS residuals. On the other hand, White et al. (2001) recently conducted a comparison of the SIOmonthly sea surface temperature (SST) anomalies (White, 1995) with mixed in situ and satellite NCEP

monthly SST anomalies (Reynolds & Marisco, 1993). They found similar spatial patterns of anomalous

SST over the Pacic Ocean, but the magnitudes of the former were underestimated by 1/3 when com-pared to those of the latter. White et al. (2001) undertook to correct this underestimation by increasing

the decorrelation scales in the objective analysis used to interpolate the individual vertical temperature

prole data onto the 2 latitude-by-5 longitude grid. This step generated an SIO SST product with ba-sin-scale spatial patterns similar to those of the NCEP SST product, but with 10% smaller magnitudes.In the present study, we utilize the updated SIO upper ocean temperature reanalysis of White et al.(2001) to compute DHS residuals.

3.2. ESR geostrophic and Ekman surface current reanalysis

Surface currents are calculated from TOPEX-Poseidon sea surface height (SSH), SSM/I wind vector

(VA), and NCEP SST. The diagnostic model, constructed by Bonjean and Lagerloef (2002), derives from

linear quasi-stationary physics of the near-surface circulation and allows direct estimate of the upper layer

velocity averaged from the sea surface to 30 m depth. The model was tuned and veried in a study of thetropical Pacic circulation, improving the model developed earlier by Lagerloef, Mitchum, Lukas, and Nii-

ler (1999), particularly in the Cold Tongue in the eastern equatorial Pacic Ocean. The ow velocity is the

sum of geostrophic (VG), wind diusion (VE) and buoyancy gradient (VB) components computed from

SSH, VA, and SST, respectively. A turbulent viscosity A and a scaling depth H are required to close the

diagnostic model. The coecient A is parameterized as a nearly quadratic function of surface wind speed

|VA|, in agreement with prior studies (Santiago-Mandujano & Firing, 1990). The depth scale H = 30 m is

deduced from optimization of an equatorial balance between the pressure gradient force and surface wind

stress, yielding an a posteriori best-estimate of upper layer current velocity when compared with velocityobservations from drifting buoys between 20S and 20N and from TAO moorings straddling the equator.Because of the simplied physics in the model and the random noise in the data, the optimized equatorial

balance yields a nearly continuous solution of the model currents across the equator. The velocity from 8Nto 8N is approximated by a truncated expansion series of orthogonal polynomials. Poleward of 8N and8S, surface currents are obtained from the direct solution of the diagnostic model. The model here spansthe Pacic basin from 20S to 60N, extending the standard data set (i.e., 35S to 35N) north to 60N.

The TOPEX/Poseidon altimeter (Fu et al., 1994) provides SSH estimates for computation of VG. First,

the along-track SSH observations are interpolated by objective analysis to a 1 latitudelongitude grid inthe domain 20S to 60N, centered on the half-degree, repeated every 10 days from November 1992 toJune 2002 (Lagerloef et al., 1999). The 7-year mean 19931999 is subtracted to remove small geoid errors,

6 W.B. White et al. / Progress in Oceanography 64 (2005) 129and replaced with the annual mean surface dynamic height (0/1000 db) derived from the annual mean tem-

3.3. S

Th

bulent ux (QS + QL) and the incoming shortwave minus outgoing longwave radiative ux (QSWQLW). It

is computed as follows: QT = QSW QLW QS QL, so that QT is positive when directed into the ocean,with the same sign as QSW anomalies but of opposite sign as QLW, QS, and QL which are positive directed

out of the ocean.

Latent and sensible uxes are calculated from bulk formulae using COADS marine surface weather

observations from volunteer observing ships (Slutz et al., 1985; Woodru et al., 1993). The COADS set

does not provide the full heat ux computation, but does furnish monthly averages of the products

(wDq) and (wDT) using simultaneous pairs of individual synoptic observations, where w is the wind speed;Dq is the surface saturation specic humidity minus the surface specic humidity at the height of the obser-vation (10 m); and DT is the sea surface temperature minus the surface air temperature at the nominal10 m height (Cayan, 1992).

The bulk formulae used in computing the COADS sensible and latent heat uxes are

QS qACPACShwDT i;QL qALCLhwDqi:

3:1

In these equations, denotes the average over an individual month; qA is the density of the air at obser-vation level, calculated from the monthly mean surface temperature and sea-level pressure using the ideal

gas law, with a correction for the virtual temperature to compensate for the behavior of moist air; L is the

latent heat of evaporation of water, which is taken to be a constant (2.5 106 J kg1); CPA is the specicheat of air at constant pressure, taken as constant (1.0 103 J kg1 K1). CL and CS are the airsea ex-change coecients for latent heat (i.e., water vapor) and sensible heat, respectively.

The latent and sensible heat exchange coecients used here are taken from Isemer and Hasse (1985,Table 4, p. 14) who used experimental evidence (e.g., Smith & Dobson, 1984) to revise downwards those

of Bunker (1976). Under this formulation, CS is proportional to CL (i.e., CS = 0.94CL). The transfer coef-

cients increase with wind speed and decrease with vertical stability, as given by DT. In the monthlyCOADS dataset, the airsea exchange coecients are by necessity calculated from monthly mean wind

speed and DT. As such, the exchange coecients range between 0.0012 and 0.0016, being smallest at lowlatitudes and largest at high latitudes during winter, when wind speeds and DT are larger. Typical month-to-month variations of the exchange coecients are about 5% of their mean values at a particular gridpointIO/COADS airsea heat ux reanalysis

e net airsea heat ux (QT) is divided into its four constituents; the outgoing sensible-plus-latent tur-perature and salinity elds of Levitus et al. (1994a) and Levitus and Boyer (1994b). Subsequently, estimates

of VG are computed every 10 days over the 7-year record.The SSM/I wind vector (VA) data between November 1992 and July 1999 (Atlas et al., 1996) allows for

the computation of A and VE. The VA is converted to wind stress (s) utilizing the Large and Pond (1981)bulk formula, and s is interpolated to the same 1 latitudelongitude grid as the SSH analysis. The wind-diusion velocity VE over the upper 30 m is computed as a function of the two parameters A and H. For

latitudes adjacent to the equator (|y| < 2.6), VE reduces to the Stommel wind-driven velocity (Stommel,1960). For higher latitudes (|y| > 2.6), VE quickly becomes equivalent to the classic Ekman velocity, whereit is nearly indistinguishable from that computed by Lagerloef et al. (1999).

In addition, the SST product of Reynolds and Marisco (1993) provides rst-order estimates of the sur-

face buoyancy gradient (neglecting surface salinity gradient) for calculating VB. This term is signicant

within the Cold Tongue where it accounts for the eastward deection of the current near the sea surface.

However, when averaged over the 30 m layer, this component was found to be negligible compared to VE.

W.B. White et al. / Progress in Oceanography 64 (2005) 129 7.

Individual monthly mean reanalysis products of DHS, VE, VG, QT, and their associated interpolation

DHS

into t

gitud

by aspace and time averages is not precise, it allows us to understand how random noise in the heat budget com-

ponents on both sides of Eq. (2.2) can be suppressed. Moreover, it compels us to examine systematic biases

in these products, which are not suppressed by either temporal or spatial averaging.

Already White (1995) found the interpolation error of monthly upper ocean temperature on the 2 lat-itude-by-5 longitude grid to be 0.4 C. Propagating this through to the computation for DHS [i.e.

(0.4 e box-averages further reduces the random noise in DHS, VG, VE, and QT residuals conservatively

factor of 2 (Young, 1962). While this exercise of random noise propagation through the variousage) reduces the random noise of VG and VE, and QT conservatively by factors of 3 and 2, respectively. Thislatter estimation assumes that each gridded estimate is independent of its neighbor, with random noise as-

sumed to be sub-grid. Then, we formed long-term monthly and annual means at each grid point over the

Pacic Ocean for the 7-year record, allowing the formation of the mean seasonal cycle about the long-term

annual mean. This temporal averaging reduced the random noise in all four variables conservatively by a

factor of 2.5. Again, this assumes that estimates in each year are independent from one another. On theother hand, forming the dierence of long-term monthly and annual means increases random error by 1.4.

Subsequently, we formed box-averages over 10 latitude-by-20 longitude to reduce random error further.Again, assuming the remaining random noise to be sub-grid, the computation of 10 latitude-by-20 lon-. Since random noise reduces as the inverse square root of the number of independent estimates going

he average (e.g., Young, 1962), this linear interpolation (which is eectively a weighted spatial aver-errors, were initially available over the 7-year record on a variety of dierent grids: i.e., 1 latitude-by-1longitude for VG and VE; 2 latitude-by-2 longitude for QT; and 2 latitude-by-5 longitude for DHS.So, we linearly interpolated the VG, VE, and QT onto the same 2 latitude-by-5 longitude grid of theCayan (1992) estimated the net shortwave heat ux (QSW) and net terrestrial longwave heat ux (QLW) at

the sea surface from bulk formulae (Reed, 1977), expressing radiative uxes in terms of volunteer observing

ship (VOS) surface marine weather observations. Here we consider both the bulk formula estimate for QSWand a remotely sensed estimate from satellite-derived clouds (Bishop & Rossow, 1991). The bulk formula

estimate for QSW is

QSW 0:94IO1 0:62C 0:0019H; 3:2where IO is estimated incoming shortwave radiation at the sea surface under cloudless conditions, adjusted

for transmissivity of the atmosphere and varying with astronomical parameters; C is total cloud cover in

tenths; and H is noon solar altitude. The remotely sensed estimate of QSW is produced from the Interna-tional Satellite Cloud Climatology Project (ISCCP) data set, which is a blend of satellite-derived clouds

measured several times per day. The ISCCP dataset is collated from multiple geostationary and polar orbit-ing satellites beginning in July 1983 and continuing through the present. The remotely sensed estimate of

QSW derives from a state-of-the-art radiation transfer model (Zhang et al., 2003). Its spatial resolution

(2.5) is comparable to COADS surface marine weather observations data.The bulk formula estimate for QLW is that employed by Bunker (1976); i.e.,

QLW 0:022eSrBT 4a11:7 0:23ea1 c 4eSrBT 3aSST T a; 3:3where Ta is air temperature at the nominal 10 m height, eS is surface emissivity; rB is Boltzmann constant; eais surface vapor pressure; and c is a latitude-dependent constant. QSW and QLW are estimated on a 2 lat-itudelongitude grid.

4. Estimation and propagation of error

8 W.B. White et al. / Progress in Oceanography 64 (2005) 129C)(70 m)(qOCPO)] according to Young (1962) yields a standard error of 5.0 107 W s m2, where a

scale depth of 70 m has been assumed. Subsequently, multiplying this error estimate by the frequency of the

annual cycle yields a standard error for the residual DHS tendency of 10 W m2. This monthly grid-pointerror reduces conservatively to 4 W m2 when formed into long-term monthly mean residuals about thelong-term annual mean. It reduces again to 2 W m2 when averaged over the 10 latitude-by-20 longi-tude boxes. Yet, it is the sampling bias determined by White et al. (2001, 2003) that is of most concern,indicating that the amplitude of the seasonal cycle in DHS is underestimated by 10%. Furthermore, sys-tematic biases may arise from two additional sources: (1) using the 0.1 C temperature dierence criterionto determine the depth of the near-surface mixed layer above the top of the main pycnocline; and (2) the

inability to take into account the presence of the barrier layer (Maes et al., 2002), which may conne the

residual DHS tendency to a layer shallower than the top of the main pycnocline dened by the 0.1 C tem-perature-change criterion.

We nd the residual horizontal heat advection in Eq. (2.2) dominated by the residual Ekman advection

of mean heat (see below). Bonjean and Lagerloef (2002) have estimated the interpolation errors associatedwith residual VE to be 0.02 m s1 on a 1 latitude-by-1 longitude grid. Propagating this through the com-putation for residual Ekman advection of mean heat [i.e. (30 m)(qOCPO) (0.02 ms

1)(1.0 105 C m1)]according to Young (1962) yields a standard error of 12 W m2. In this computation, the Ekman scaledepth of 30 m from Bonjean and Lagerloef (2002) is used and the scale horizontal temperature gradient

of 1.0 105 C m1 is assumed. These random errors, initially on a 1 latitudelongitude grid, reduceto 4 W m2 when interpolated onto the 2 latitude-by-5 longitude grid. They reduce again to2 W m2 when formed into long-term monthly mean residuals about the long-term annual mean. Finally,they reduce to 1 W m2 when averaged over the larger 10 latitude-by-20 longitude boxes. Yet, again, itis the bias that is of most concern. The estimation of Ekman ow depends on imperfect knowledge of the

airsea exchange coecient for the turbulent transfer of momentum, which is a function of wind speed and

stability of the atmospheric planetary boundary layer (e.g., Greenhut, 1982; Smith, 1988; Friehe et al., 1991;

Xie, Ishiwatari, Hashizume, & Takeuchi, 1998; White & Annis, 2003). Moreover, Ekman currents may be

overestimated since the wind-driven ow averaged over the upper layer (i.e., from the sea surface to the top

of the main pycnocline) generally extends deeper than 30 m depth (Bonjean & Lagerloef, 2002). Here, we

estimate the overall bias in the residual Ekman heat advection by conducting least-squares minimization of

the RMS of the dierences between observed and model residual DHS tendencies (see below).The seasonal cycle of sensible and latent heat uxes, and shortwave and longwave radiative uxes, dis-

play similar patterns regardless of the source or the bulk formulae used (Esbensen & Kushnir, 1981;

Hsiung, 1986; Isemer & Hasse, 1985). However, Weare and Strub (1981), Taylor (1984), Hanawa and Toba

(1987), Weare (1989), Kent and Taylor (1991), Kent, Truscott, Taylor, and Hopkins (1991), Cayan (1992),

Moisan and Niiler (1998), and White (2001) found signicant dierences in magnitude, deriving from both

random noise and bias. All of the airsea ux products utilize the same surface marine weather observa-

tions from the volunteer observing ship (VOS) network. But signicant sampling biases exist in this

VOS network. Most important is the under-sampling of synoptic storms, which leads to underestimationin the transfer of heat, moisture, and momentum across the airsea interface. Sampling bias also derives

from seasonal changes in the geographical coverage by the VOS network. Whilst absolute total airsea heat

ux can have uncertainties ranging from 30 to 60 W m2 from random noise and bias (Cayan, 1992), theresiduals about the annual mean are more accurate, since some of the systematic bias is retained in the an-

nual mean. Thus, the random noise and bias in the residual total heat ux range from 15 to 30 W m2 onthe 2 latitudelongitude grid. When the residual total airsea heat ux is interpolated onto the standard 2-by-5 latitudelongitude grid and formed into long-term monthly mean residuals, the random noise isreduced to 5-to-10 W m2. And reduced again to 3-to-5 W m2 when averaged onto the 10 by 20 lati-tudelongitude grid. Yet, again, it is the bias that is of most concern. Here, we estimate the overall bias

in the residual airsea turbulent uxes by conducting least-squares minimization of the RMS of the dier-

W.B. White et al. / Progress in Oceanography 64 (2005) 129 9ences between observed and model residual DHS tendencies (see below).

5. Relative magnitudes of the residual DHS budget components

Closing the residual DHS budget requires the observed residual DHS tendency on the left-hand-side of

Eq. (2.2) to be balanced by the model residual DHS tendency on the right-hand-side due to the sum of

residual horizontal heat advection, airsea heat ux, and dissipation. We begin by examining the distribu-tion of the root-mean-square (RMS) of the observed residual DHS tendency determined from upper ocean

temperature measurements (b, Fig. 1), where the 10 latitude-by-20 longitude box-average has been ap-plied. This nds largest values (170 W m2) in the KuroshioOyashio extension current o the east coastof Japan, decreasing eastward and equatorward to smaller magnitudes o the west coast of North America

(3090 W m2), decreasing to minimum values along the Intertropical Convergence Zone (

tropical Pacic Ocean. This ratio increases in the equatorial wave guide to 60% to 160%, maximum in the

vicinity of the Cold Tongue where ratios are >160% for COADS, NCEP, and ECMWF airsea heat ux

residuals (c, Fig. 2a).

The residual horizontal heat advection on the right-hand-side of Eq. (2.2) derives from mean and resid-

ual geostrophic and Ekman currents from ESR (Bonjean & Lagerloef, 2002). The distribution of the RMSof residual geostrophic heat advection (a, Fig. 2b) is largest in the KuroshioOyashio current extension

(15 W m2) and in the central equatorial Pacic (>5 W m2), smaller over most of the remainder of

W.B. White et al. / Progress in Oceanography 64 (2005) 129 11Fig. 2b. (a) Distribution of the RMS of the residual geostrophic heat advection over the seasonal cycle in units of W m2. (b)Distribution of the RMS of the residual Ekman heat advection over the seasonal cycle in W m2. (c) Distribution of the ratio of theRMS of the residual geostrophic heat advection to that of the residual Ekman heat advection in units of percentage. (d) Distribution of

the RMS of the mean advection of residual heat over the seasonal cycle in W m2. (e) Distribution of the RMS of the residualadvection of mean heat over the seasonal cycle in W m2. (f) Distribution of the ratio of the RMS of the mean advection of residualheat to that of the residual advection of mean heat in units of percentage. Here, the 10 latitude by 20 longitude box-average has been

applied to all the elds. Contour intervals are 5 W m2 in (a), (b), (d) and (e), whilst 10% in (c) and 20% in (f); hatching is for eect.

the Pacic Ocean. The distribution of the RMS of residual Ekman heat advection (b, Fig. 2b) is largest in

the KuroshioOyashio current extension (>60 W m2) and in the vicinity of the Cold Tongue (>20 W m2),smaller over the remainder of the Pacic Ocean. When the ratios of the RMS of the residual geostrophic

heat advection to the RMS of residual Ekman heat advection are computed (c, Fig. 2b), the former are

found to be 2070% of the latter over the Pacic Ocean.The residual horizontal heat advection can also be partitioned into the mean advection of residual heat

and the residual advection of mean heat (d and e, Fig. 2b). The distribution of the RMS of the mean advec-

tion of residual heat (d, Fig. 2b) is largest near the KuroshioOyashio current extension (10 W m2) andon the equator (5 W m2), but

South Pacic Ocean to peak values of 20 W m2. The distribution of the RMS of shortwave-minus-long-wave heat ux residuals from the three products (b, Fig. 2c) has them increasing poleward from minimum

value along the ITCZ (10 W m2) to maximum value in the high-latitude North Pacic Ocean (6080 W m2), larger in ECMWF estimates than in COADS and NCEP-1 estimates. When the ratios of theRMS of sensible-plus-latent heat ux residuals to the RMS of shortwave-minus-longwave heat ux resid-uals are computed (c, Fig. 2c), the former are found to be 100300% of the latter in the western Pacic

Ocean (particularly along the KuroshioOyashio current extension and along the ITCZ), but 20% to

100% in the eastern Pacic Ocean. The ratios from the three products are similar in the mid-latitude North

Pacic Ocean, but those from NCEP and ECMWF are smaller than those from COADS throughout the

tropics.

The residual radiative heat ux on the right-hand-side of Eq. (2.2) depends on the dierence between

residual shortwave and longwave heat ux from COADS, NCEP, and ECMWF (Fig. 2d). The distribution

of the RMS of longwave heat ux residuals from the three products (a, Fig. 2d) has minimum value nearthe equator (

14 W.B. White et al. / Progress in Oceanography 64 (2005) 129sensible heat ux residuals from the three products (a, Fig. 2e) has minimum value in the tropics

(

W.B. White et al. / Progress in Oceanography 64 (2005) 129 15and to the RMS of the observed residual DHS tendencies (b, Fig. 1), where in both distributions the

10 latitude-by-20 longitude box-average has been applied. The RMS of the dierences between ob-served and modeled residual DHS tendencies over the seasonal cycle (b, Fig. 3) shows them to be

16 W.B. White et al. / Progress in Oceanography 64 (2005) 129satellite-derived winds, the RMS dierences between observed and model residual DHS tendencies per-

form better in the KuroshioOyashio current extension but marginally worse everywhere else (d, Fig.

3). This indicates that internal consistency among the set of radiation and turbulent heat ux residuals

from COADS, NCEP, and ECMWF is at least as important as improving individual ux estimates byincorporating satellite data into their computation.

Fig. 3. (a) Distribution of the RMS of the model residual DHS tendencies on the left-hand-side of Eq. (2.2) in units of W m2 fromCOADS (left), NCEP (middle), and ECMWF (right). (b) Distribution of the RMS of the dierences between the observed residual

DHS tendencies (b, Fig. 1) and model residual DHS tendencies in (a) from COADS (left), NCEP (middle), and ECMWF (right). (c)

Same as in (b), but where the residual shortwave heat ux has been replaced by that of Zhang et al. (2003). (d) Same as in (b), but where

the residual turbulent heat ux has been replaced by that of Kubota and Mitsumori (1997). Here, the 10 latitude-by-20 longitudebox-average has been applied to all the elds prior to computation of the RMS of the residuals and their dierences. Contour intervals

are 10 W m2 in (a), and 5 W m2 in (b), (c), and (d); hatching is for eect.

7. Analysis of the residual DHS budget in regional boxes over the Pacic Ocean

Now we identify the dominant terms in the residual DHS budget in Eq. (2.2) in the 10 latitude-by-20longitude boxes labeled A through H (a, Fig. 1). In each box, we overlay time sequences of the observedresidual DHS tendency and the model residual DHS tendency computed from the sum of terms on theright-hand-side of Eq. (2.2) extending over one seasonal cycle (a, Figs. 4a, 4b, and 4c). We also display

the residual airsea turbulent heat ux, airsea radiation heat ux, horizontal heat advection, and dissipa-

tion on the right-hand-side of Eq. (2.2). from COADS, NCEP, and ECMWF.

We begin with residual DHS budgets in boxes A, B, and C (Fig. 4a) located in the mid-latitude NorthPacic Ocean under the inuence of the Westerly Winds (Fig. 1). The RMS of the dierences between ob-

served and modeled residual DHS tendencies in the KuroshioOyashio current extension (Box A) is 33, 43,

and 51 W m2 for the COADS, NCEP, and ECMWF airsea heat ux residuals, respectively (Fig. 4a). Thisis reduced in the central mid-latitude North Pacic Ocean (Box B) to 16, 21, and 28 W m2 for the threeproducts, respectively, and reduced even more in the eastern mid-latitude North Pacic Ocean (Box C) to 8,

4, and 15 W m2, respectively (Fig. 4a). In the three mid-latitude sub-regions, the residual shortwave heatux dominates the residual longwave heat ux, and the residual latent heat ux dominates the residual

W.B. White et al. / Progress in Oceanography 64 (2005) 129 17Fig. 4a. The seasonal cycle of the DHS tendency for 10 latitude-by-20 longitude boxes A, B, and C in the Pacic Ocean, thelocations of which are displayed in Fig. 1. (a) The seasonal cycle of observed DHS tendency (heavy-line) and the model DHS tendency

(light-line) from COADS (left), NCEP (middle), and ECMWF (right) for each box. (b) Seasonal cycle of shortwave heat ux (QSW)

and longwave heat ux (QLW). (c) Seasonal cycle of latent heat ux (QL) and sensible heat ux (QS). (d) Seasonal cycle ofhorizontal heat advection over one cycle. (e) Seasonal cycle of dissipation due to cross-isopycnal mixing at the top of the mainpycnocline over one cycle. The RMS of the dierences between observed and modeled residual DHS tendencies is at lower left in (a).

18 W.B. White et al. / Progress in Oceanography 64 (2005) 129sensible heat ux, consistent with Figs. 2d and 2e. Moreover, in all three sub-regions, residual horizontal

heat advection is comparable with residual latent heat ux and shortwave heat ux.

In the KuroshioOyashio current extension (Box A), the observed residual DHS tendency uctuates inphase with the model estimate in all three products (Fig. 4a). In this sub-domain, the amplitudes of residual

latent heat ux, shortwave heat ux, horizontal heat advection, and dissipation are comparable. In the cen-

tral mid-latitude North Pacic Ocean (Box B), the observed residual DHS tendency lags the model estimate

by 0.5 month in all three products (Fig. 4a), with the amplitudes of residual latent heat ux, shortwaveheat ux, and horizontal heat advection comparable, with dissipation much less. In the eastern midlatitude

North Pacic Ocean (Box C) the observed residual DHS tendency uctuates in phase with the model esti-

mate from COADS, but lags by 0.5 months for NCEP and ECMWF products, with residual shortwave

heat ux dominating the other terms (Fig. 3). In all three mid-latitude sub-regions, residual latent heat uxtends to uctuate in phase with the residual horizontal heat advection because both terms are proportional

to zonal wind speed residuals in the Westerly Winds. That is, an increase in Westerly Winds produces larger

latent heat ux out of the ocean, whilst increasing the Ekman advection of cool water equatorward.

Next, we examine the residual DHS budgets in boxes D, E, and F (Fig. 4b) of the tropical PacicOcean under the inuence of the Trade Winds (Fig. 1). The RMS of the dierences between observed

and model residual DHS tendencies in the eastern tropical North Pacic Ocean (Box D) is 6, 6, and

11 W m2from COADS, NCEP, and ECMWF, respectively (Fig. 4b). This is similar to those in the westerntropical North Pacic Ocean (Box E) of 12, 7, and 11 W m2 (Fig. 4b), and again in the western tropicalSouth Pacic Ocean (Box F) of 9, 11, and 5 W m2, respectively (Fig. 4b). In all three sub-regions, residual

Fig. 4b. Same as Fig. 4a, but for boxes D, E, and F in the Pacic Ocean, the locations of which are displayed in Fig. 1.

W.B. White et al. / Progress in Oceanography 64 (2005) 129 19shortwave heat ux dominates residual longwave heat ux and residual latent heat ux dominates residual

sensible heat ux, consistent with Figs. 2d and 2e. In the two western sub-regions, the residual latent heat

ux and shortwave heat ux are comparable to the residual horizontal heat advection, with residual dissi-

pation negligible.In the eastern tropical North Pacic Ocean (Box D), the observed residual DHS tendency is misaligned

with the model estimate by 0.5 months or so (Fig. 4b). On the other hand, in the western tropical Northand South Pacic oceans (Box E and Box F), the observed residual DHS tendency leads the model estimate

by 1 month in all three products (Fig. 3). In these three sub-regions, residual latent heat ux uctuates outof phase with the residual horizontal heat advection because both terms are proportional to residual zonal

wind speed in the Trade Winds. That is, an increase in Trade Winds produces larger latent heat ux out of

the ocean, whilst increasing the Ekman advection of warm water poleward.

Finally, we examine residual DHS budgets in boxes G and H (Fig. 4c) straddling the equatorin the Warm Pool and Cold Tongue, respectively (Fig. 1). The RMS of the dierences between

Fig. 4c. Same as Fig. 4a, but for boxes G and H in the Pacic Ocean, the location of which are displayed in Fig. 1.

Paci

Ocea

ECM

both comparable to residual horizontal heat advection. Yet, the observed residual DHS tendency leads themodel estimate by 1 month in the three products in response to overestimation of the semi-annual cycle in

the residual shortwave heat ux and/or horizontal heat advection. The seasonal cycle of residual shortwave

heat ux from COADS is out phase with that from NCEP and ECWMF.

8. Suppressing bias errors in residual airsea turbulent heat uxes and Ekman currents by minimizing RMS

dierences

Bias errors in residual airsea turbulent heat uxes arise from sampling and measurement biases in wind

speed and in airsea temperature and specic humidity dierences (e.g., Smith, Legler, & Verzone, 2001),

and from systematic biases in the airsea exchange coecients (e.g., Smith, 1988). Bias errors in residual

horizontal Ekman heat advection arise from systematic biases in the exchange coecients and in the xeddepth (30 m) over which wind-driven Ekman currents are estimated (Bonjean & Lagerloef, 2002). The sam-

pling bias in satellite winds used to compute mean and residual Ekman currents (Atlas et al., 1996) is dif-

ferent from that for in situ winds (Slutz et al., 1985; Woodru et al., 1993) used to compute residual airsea

turbulent heat uxes at SIO.

We suppress these biases by minimizing the RMS of the dierences between observed and model esti-

mates at each grid point. Minimization in the least-squares sense allows estimation of coecients a andb that modify the residual sensible-plus-latent heat ux and residual Ekman heat advection, respectively.This alters Eq. (2.2) as follows; i.e.,

oDHS0=ot Q0SW Q0LW aQ0S Q0L bqOCPOH 0 V E HV 0E rHT HV E rHT 0 qOCPOH 0 V G HV 0G rHT HV G rHT 0 KqOCPOT 0 H; 8:1

where VE and VG are Ekman and geostrophic current vectors, respectively. Least-squares estimation of the

coecient a and b on the right-hand-side of Eq. (8.1) yields new estimates for the model residual DHSIn the Warm Pool (Box G), the observed residual DHS tendency is inuenced by a semi-annual compo-

nent, but is still dominated by the annual cycle (Fig. 4c). On the other hand, the residual airsea heat ux

and horizontal heat advection are largely governed by the semi-annual cycle. As over most of the Pacic

Ocean, residual shortwave heat ux dominates residual longwave heat ux and residual latent heat ux

dominates residual sensible heat ux, consistent with Figs. 2d and 2e. Again, residual shortwave and latent

heat ux are comparable with residual horizontal heat advection, with dissipation mostly negligible. Even

so, the residual shortwave heat ux in each of the three products accounts for the incorrect dominance of

the semi-annual component in the model residual DHS tendencies. Here, residual latent heat ux uctuatesapproximately in phase with residual horizontal heat advection. This occurs because an increase in south-

east Trade Winds over the equator produces larger latent heat ux out of the ocean, while increasing Ek-

man heat advection poleward.

In the Cold Tongue (Box G), the observed residual DHS tendency is governed by the annual cycle,

whereas residual shortwave heat ux and horizontal heat advection are dominated by a semi-annual cycle

(Fig. 4c). As over most of the Pacic Ocean, residual shortwave heat ux dominates residual longwave heat

ux and residual latent heat ux dominates residual sensible heat ux, consistent with Figs. 2d and 2e, withtendec Ocean (Box H) it is 15, 8, and 6 W m2respectively. In the eastern equatorial Pacicn, COADS airsea heat ux residuals perform signicantly worse than those of NCEP and

WF.observed and modeled residual DHS tendencies in the western equatorial Pacic Ocean (Box G) is

6, 6, and 4 W m2from COADS, NCEP, and ECMWF, respectively, whilst in the eastern equatorial

20 W.B. White et al. / Progress in Oceanography 64 (2005) 129ncy on the left-hand-side. The resulting minimized RMS dierences decrease to

W.B. White et al. / Progress in Oceanography 64 (2005) 129 21KuroshioOyashio current extension and to

decrease in residual airsea turbulent heat ux (Ekman heat advection) by 0.2 (0.4) in the ECMWFproduct.

In the eastern tropical North Pacic Ocean (Box D), bias suppression decreases the RMS of the dier-

ences to 6, 4, and 9 W m2 in the COADS, NCEP, and ECMWF products, respectively (Fig. 6). To achievethis requires an increase in the residual airsea turbulent heat ux (Ekman heat advection) by 1.6 (1.6) inthe COADS product, a decrease by 0.6 (0.2) and 0.4 (0.4) in the NCEP and ECMWF products, respec-

tively. In the western tropical North Pacic Ocean (Box E), bias suppression decreases the RMS of the

dierences to 6, 2, and 2 W m2 for the three products, respectively, requiring an increase in the residualairsea turbulent heat ux (Ekman heat advection) by 2.0 (1.4) in the COADS product and changes by

1.2 (0.6) and 1.2 (0.2) in the NCEP and ECMWF products, respectively. In the western tropical South

Pacic Ocean (Box F), bias suppression decreases the RMS of the dierences to 7, 3, and 2 W m2 inthe three products, respectively, requiring an increase in the residual airsea turbulent heat ux (Ekman

thermal advection) in the COADS product by 1.6 (1.6), and decreases by 0.4 (0.4) and 0.6 (0.8) in the NCEPand ECMWF products, respectively.

On the equator in the Warm Pool (Box G), bias suppression decreases the RMS of the dierences to 6, 6,too large by a similar amount. On the other hand, along the ITCZ near 10 N the COADS and NCEPresidual sensible-plus-latent heat uxes are too weak by factors ranging from 1.2 to 1.6, whilst the ECMWF

residual sensible-plus-latent heat uxes are too weak in the Warm Pool of the western equatorial Pacic

Ocean. In the eastern tropical South Pacic Ocean, residual sensible-plus-latent heat uxes in all three prod-

ucts are too small by factors ranging from 1.0 to 1.8.The distributions of the best-t coecient b (modifying residual Ekman heat advection) display simi-

larities and dierences among the COADS, NCEP, and ECMWF products (c, Fig. 5). In the western and

central mid-latitude North Pacic Ocean, Ekman currents in all three products are determined to be too

large by factors ranging from 0.4 to 0.8. Similarly along the equator and/or along the ITCZ, Ekman cur-

rents in all three products are too large by a similar amount. On the other hand, in the Northeast Trade

Winds and Southeast Trade Winds in the eastern ocean, the COADS Ekman currents are too weak by fac-

tors ranging from 1.2 to 1.8. In the western tropical South Pacic Ocean, Ekman currents in all three prod-

ucts are determined to be too large by factors ranging from 0.4 to 0.8.

9. Analysis of the optimized residual DHS budget in regional boxes in the Pacic Ocean

We now revisit the analysis of observed and model residual DHS tendencies (Fig. 6) in boxes A throughH, initially conducted in Figs. 4a, 4b, and 4c after suppressing suspected biases in the residual airsea tur-bulent heat ux and Ekman heat advection via minimization of the RMS dierences. This procedure deter-

mines the best-t coecients a and b in Eq. (8.1), which indicate how the biases lead to overestimation orunderestimation of the residual airsea turbulent heat uxes and Ekman heat advection in the COADS,

NCEP, and ECMWF products.

In the KuroshioOyashio current extension (Box A), bias suppression decreases the RMS of the dier-

ences to 18, 17, and 15 W m2 in the COADS, NCEP, and ECMWF products, respectively (Fig. 6). Toachieve this requires a decrease in the residual airsea turbulent heat ux by 0.4 to 0.6 and no change in

Ekman heat advection. In the central mid-latitude North Pacic Ocean (Box B), bias suppression decreases

the RMS of the dierences to 11, 10, and 11 W m2 for the three products, respectively, requiring a decreasein the residual airsea turbulent heat ux (Ekman heat advection) in the three products by 0.40.6 (0.41.0).In the eastern mid-latitude North Pacic Ocean (Box C), bias suppression decreases the RMS of the dier-

ences to 5, 4, and 6 W m2 in the three products, respectively, requiring in increase in residual airsea tur-bulent heat ux (Ekman heat advection) by 1.21.0 (1.81.4) in the COADS and NCEP products, and a

22 W.B. White et al. / Progress in Oceanography 64 (2005) 129and 5 W m2 in the COADS, NCEP, and ECMWF products, respectively (Fig. 6). To achieve this requires

W.B. White et al. / Progress in Oceanography 64 (2005) 129 23a decrease in the residual airsea turbulent heat ux (Ekman heat advection) in the COADS and NCEPproducts by 0.4 (0.8) and 0.8 (0.6), respectively, with no change in the ECMWF product. On the equator

in the Cold Tongue (Box H), bias suppression decreases the RMS of the dierences to 2, 2, and 5 W m2 for

Fig. 6. The seasonal cycle of the observed DHS tendencies (heavy line) and of the optimized model DHS tendencies (light line) in Eq.

(8.1) for rectangular boxes A through H, the locations of which are displayed in Fig. 1 from COADS (left), NCEP (middle), andECMWF (right). The coecients a and b that modify the box-average residual airsea turbulent heat ux and Ekman heatadvection, respectively, are quantied in each panel, together with the minimized RMS of the dierences.

in the KuroshioOyashio current extension (b, Fig. 3). Second, we suppressed biases in residual airsea tur-bulent heat ux and Ekman heat advection by minimizing the RMS of the dierences between observed and

model residual DHS tendencies. This produced best-t coecients a and b that tell us whether the resid-ual airsea turbulent heat ux and Ekman heat advection are underestimated or overestimated in the appli-

cation of COADS, NCEP, ECMWF, and ESR reanalysis products to residual DHS budget closure. This

bias suppression decreased the RMS dierences to

wave guide. When residual airsea shortwave heat ux components in COADS, NCEP, and ECMWF

products were replaced by those from ISCCP satellite cloud measurements (Zhang et al., 2003), the

RMS of the dierences was reduced (increased) marginally in the tropics for COADS (NCEP and

ECMWF) products, with little or no change in the mid-latitudes. When residual airsea turbulent heat ux

components in COADS, NCEP, and ECMWF products were replaced by satellite-derived airsea turbulentheat uxes (Kubota & Mitsumori, 1997), the RMS of the dierences was reduced in the KuroshioOyashio

current extension by 20% but increased marginally everywhere else.The level of accuracy achieved with noise and bias suppression (i.e.,

mation in the upper layer reduces the accuracy of the DHS algorithm in the presence of inversions and bar-rier layers brought on by shallow vertical salinity gradients (Maes et al., 2002; Sato et al., 2004). Thus, some

portion of bias suppression of the residual airsea turbulent heat ux and Ekman heat advection in the

model residual DHS tendency really belongs to bias suppression in the observed residual DHS tendency.

Smith et al. (2001) compared the NCEP surface wind product against an accurate set of WOCE shipobservations taken over the globe, nding NCEP sensible and latent heat uxes over-estimated in the

northern hemisphere from 10 to 50N and underestimated near the ITCZ. This was traced to the mis-mea-sure of airsea temperature and specic humidity dierences by the NCEP reanalysis. In the present study,

we nd similar results with the NCEP sensible-plus-latent heat ux residuals. However, a similar result oc-

curs with the COADS and ECMWF sensible-plus-latent heat ux residuals. This indicates that assimilation

into the NCEP and ECMWF reanalysis models of incorrect airsea temperature and specic humidity dif-

ferences from the surface marine weather observations collected by the VOS network is a principal source

of bias error.The remaining question is whether, with random noise and bias suppression, we have achieved our goal

of understanding of the thermodynamics dominating the seasonal cycle of the diabatic heat storage ten-

dency in the Pacic Ocean (Fig. 6). In each of the sub-regions (a, Fig. 1), the RMS of the dierences be-

tween model and observed diabatic heat storage tendencies is signicantly less than the RMS of the

seasonal cycle, except in the Warm Pool (Box G, Fig. 6) where both RMS estimates are comparable.

So, clearly we do not understand the thermodynamics of the seasonal cycle in the Warm Pool. However,

we probably do understand the thermodynamics in the other sub-regions. This is a true statement even

prior to bias suppression (i.e., Figs. 4a, 4b, and 4c). Furthermore, these results do not depend on whetherCOADS, NCEP, or ECMWF reanalysis products were utilized, though NCEP and ECMWF products

yielded signicantly smaller RMS dierences than COADS products in the Cold Tongue (Box H, Fig.

4c). This level of understanding has been made possible by the utilization of Ekman currents from the

ESR reanalysis, since the residual Ekman heat advection plays a signicant role in the seasonal cycle of

the DHS tendency just about everywhere. In the future, we need to rene these results principally by sup-

pressing biases, not through least-squares estimation, but by realizing adequate sampling and more accu-

rate measurements of winds and airsea temperature and specic humidity dierences from both in situ and

satellite sources.

Acknowledgments

Appreciation is extended to programmer Arthur (Ted) Walker, who computed the heat budget analysis

conducted in this study. We extend our thanks to Andrea Fincham who is responsible for drafting the g-

ures displayed in this study. White is supported by the National Aeronautics and Space Administration

(NASA) under Contract JPL-1205106. Warren White is also supported by the Scripps Institution of Ocean-ography of the University of California, San Diego. Gridded TOPEX/Poseidon sea level height elds were

provided by G. Mitchum (USF) and the SSM/I-based surface wind analyses were furnished by J. ArdizzoneWe nd closure of the residual DHS heat budget most dicult to achieve in the KuroshioOyashio cur-

rent extension, the Warm Pool, and in the Cold Tongue. This arises principally from biases in residual air

sea turbulent heat uxes and Ekman heat advection discussed in Section 3; i.e., biases in sampling density,

in measurements of wind speed, airsea temperature and specic humidity dierences, and in the turbulent

exchange coecients and in the depth of the Ekman currents. Sampling and systematic biases also occur inthe residual DHS tendency as well. An under-estimation of the residual DHS residual of at least 10% de-

rives from inadequate sampling density (White et al., 2003) and, perhaps additionally, from the denition of

the depth of the near-surface mixed layer (Kara et al., 2003). The lack of broad-scale salinity-depth infor-

26 W.B. White et al. / Progress in Oceanography 64 (2005) 129and R. Atlas at GSFC. Fabrice Bonjean and Gary Lagerloef are supported under NASA Grant NAG5-

and drifter data. Journal of Geophysical Research, 104, 23,31323,326.

Large, W. G., & Pond, S. (1981). Open ocean momentum ux measurements in moderate to strong winds. Journal of Physical

W.B. White et al. / Progress in Oceanography 64 (2005) 129 27Oceanography, 11, 324336.

Levitus, S., Burgett, R., & Boyer, T. (1994). World Ocean Atlas 1994, Vol. 3: Salinity (p. 99). NOAA Atlas NESDIS 3, NOAA,

Washington, DC.

Levitus, S., & Boyer, T. (1994). World Ocean Atlas 1994, Vol. 4: Temperature (p. 117). NOAA Atlas NESDIS 4, NOAA, Washington,7255. John Moisans research was supported by the National Aeronautics and Space Agency (NASA) un-der Project Number NAGW-3128. Support for David M. Legler was provided by NASA oceanography

as well as by NOAA Oce of Global Programs and the National Science Foundation.

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The seasonal cycle of diabatic heat storage in the Pacific OceanIntroductionDefining budgets for diabatic and adiabatic heat storage residualsWOCE reanalysis productsSIO upper ocean temperature and heat storage reanalysisESR geostrophic and Ekman surface current reanalysisSIO/COADS air ndash sea heat flux reanalysis

Estimation and propagation of errorRelative magnitudes of the residual DHS budget componentsRMS differences between observed and model residual DHS tendenciesAnalysis of the residual DHS budget in regional boxes over the Pacific OceanSuppressing bias errors in residual air ndash sea turbulent heat fluxes and Ekman currents by minimizing RMS differencesAnalysis of the optimized residual DHS budget in regional boxes in the Pacific OceanDiscussion and conclusionsAcknowledgmentsReferences