How Much Net Surface Heat Flux Should Go into the Western

Pacific Warm Pool?

Xiangzhou Song** and Lisan Yu

Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods

Hole, Massachusetts, USA.

** Present Affiliation: Physical Oceanography Laboratory, Ocean University of China,

Qingdao, Shandong, China

Submission to Journal of Geophysical Research - Oceans

Submitted December 2012

Revised March 2013

______________________________________________________________

Corresponding author address: Xiangzhou Song, 5 Yushan Road, Physical

Oceanography Laboratory, Ocean University of China, Qingdao, China, 266100.

Email: oucsxz@ouc.edu.cn

Regular Article Journal of Geophysical Research: OceansDOI 10.1002/jgrc.20246

This article has been accepted for publication and undergone full peer review but has not beenthrough the copyediting, typesetting, pagination and proofreading process which may lead todifferences between this version and the Version of Record. Please cite this article asdoi: 10.1002/jgrc.20246

© 2013 American Geophysical UnionReceived: Dec 13, 2012; Revised: Apr 07, 2013; Accepted: May 20, 2013

2

Abstract

The western tropical Pacific warm pool, with the surface area bounded by the 28°C

isotherm, receives heat from the atmosphere through the year. However, the exact amount of

net surface heat flux into this area remains to be determined. A survey of nine heat flux

climatologies (including three latest atmospheric reanalyses, three early reanalyses, and three

analyzed products) shows that the estimates are clustered into two groups, with a mean of 18

Wm-2

for the five-member low net heat flux group (ERA-Interim, CORE.2, NCEP 1 and 2

and ERA-40) and of 49 Wm-2

for the four-member high net heat flux group (CFSR,

OAFlux+ISCCP, NOCSv2.0 and MERRA). This study used a pool-area based heat budget

analysis together with in situ air-sea and subsurface measurements to examine the physical

consistency of the nine flux climatologies and to ascribe the statistical uncertainty of each

product.

The heat budget analysis indicates that the annual mean net surface heat flux should be

28±10 Wm-2

. The observed eddy coefficient along the 28°C isotherm is 1.5 cm2s

-1 based on

the TAO/TRION buoys and the historical records. The ocean cannot dissipate the excessive

high heat fluxes, while the low fluxes cannot balance the estimated diffusive heat flux across

the isotherm. Both the one-point direct comparison and pool integrated eddy diffusive heat

flux analysis demonstrate that, the high net heat flux climatologies have high bias; on the

other hand, the low fluxes have low bias. These biases and uncertainties are given and

documented in this paper.

3

1. Introduction

The Western Pacific Warm Pool (WPWP) is one of the warmest regions in the World

Ocean, with mean sea surface temperature (SST) exceeding 28ºC all year round [Levitus,

1982]. The high mean SSTs in the WPWP are a major thermal driver for atmospheric deep

convection and atmospheric circulation in the tropics [Bjerknes, 1969; Graham and Barnett,

1987]. Many studies have shown that global weather and climate variability are sensitive to

the change of the warm pool's position and volume [Palmer and Mansfield, 1984; Trenberth

et al., 1998; Hoerling and Kumar, 2003]. A better understanding and quantification of the

WPWP's variability is of significance for improving climate prediction on seasonal-to-

interannual and even longer timescales.

The warm water volume (WWV) of the WPWP undergoes significant seasonal changes

characterized by variations in meridional extent and intensity. Ho et al. [1995] showed that

the WWV migrates seasonally in the meridional direction from 10ºS to 20ºN, while the

displacement of the WWV in the zonal direction is less affected by the seasonal cycle [Ho et

al., 1995; Picaut and Delcroix, 1995]. Schneider et al. [1996] suggested that the seasonal

north-south movement of WWV is governed by seasonal net air-sea heat flux. However, on

the interannual time scales, the change in the WWV is marked by significant east-west

migration in phase with El Niño - Southern Oscillation (ENSO) [Rasmussen and Carpenter,

1982; Wyrtki, 1985], resulting from basin-scale coupled atmosphere-ocean interactions [Cane

and Zebiak, 1985; Meinen and McPhaden, 2001]. Apparently, surface heat fluxes play a

comparably more important role in controlling the WWV variability on seasonal timescales

[Meyers et al., 1986; Godfrey and Lindstrom, 1989; Gent, 1991]. This indicates that the

simulation of the seasonally varying WWV would be sensitive to the upper-ocean heat budget,

particularly to the surface heat flux. In light of the large differences in presently available flux

products, the sensitivity can be used as a diagnostic tool to understand and quantify the

4

uncertainties in surface heat flux estimates. The present study is thus motivated to explore the

physical consistency of the current state of estimation of the surface heat flux using the

WPWP as a test-bed. Net heat flux (hereafter QNET) at the air-sea interface is the sum of

sensible heat flux (SHF), latent heat flux (LHF), shortwave radiation (SW), and longwave

radiation (LW). The amount of QNET over the WPWP is, however, still not accurately

determined, despite many progresses that have been made to improve quantification of air-sea

fluxes through better measurements and improved modeling. Estimates of QNET into the

western equatorial Pacific vary considerably, ranging from near zero, concluded from earlier

studies [Hoffert et al, 1983; Newell, 1986] to about 100 Wm-2

[Godfrey et al, 1991]. Godfrey

et al. [1998] proposed a near-zero flux through estimating the heat diffusivity at the base of

the mixed layer by the cruise data obtained in January 1986. Godfrey and Lindstrom [1991]

later updated the estimate to be 38 Wm-2

through direct in situ observations of shortwave and

longwave radiations, along with parameterized turbulent heat fluxes. Lukas et al. [1991]

examined coupled ocean-atmosphere model experiments and suggested that the annual-mean

net heat flux between the ocean and atmosphere should be small (< 20 Wm-2

) due to negative

feedbacks of deep convection on the net heat flux.

At present, there are several surface heat flux climatologies available. Some are

atmospheric reanalysis products, such as National Center for Environmental

Prediction/National Center for Atmospheric Research (NCEP/NCAR; aka NCEP 1)

reanalysis [Kalnay et al., 1996], NCEP/Department of Energy (NCEP/DOE; aka NCEP 2)

reanalysis [Kanamitsu et al., 2002], the European Center for Medium–Range Weather

Forecasting (ECMWF) 40-year Reanalysis (ERA-40) [Uppala et al., 2005], and the latest

ERA-Interim [Dee and Uppala, 2009], NCEP Climate Forecast System Reanalysis (CFSR)

[Saha et al., 2010], the NASA Modern Era Retrospective-analysis for Research and

Applications (MERRA) [Bosilovich et al., 2007; Rienecker et al., 2010]. Others are

5

constructed from surface meteorological variables using bulk flux parameterizations,

including the ship-based NOCSv2.0 [Berry and Kent, 2009, 2010], a satellite-reanalysis-

based hybrid CORE.2 [Large and Yeager, 2009], the satellite-based radiation analysis such as

the International Satellite Climatology Cloud Project (ISCCP) [Zhang et al., 2004] and

NASA Global Energy and Water Cycle Experiment (GEWEX) Surface Radiation Budget

(SRB) Project [Stackhouse et al., 2001, 2004], as well as the Objectively Analyzed Air-sea

Fluxes (OAFlux) [Yu and Weller, 2007; Yu et al., 2008]. In this study, the latter two products

are combined to produce a net heat flux (hereafter referred to OAFlux+ISCCP), while all

other products are full-flux products. Differences among these products indeed exist due to

uncertainties in surface meteorological variables and the empirical bulk flux

parameterizations in use. Figure 1(a) shows the climatological annual-mean QNET over the

WPWP averaged from the above-mentioned nine products, with the standard deviations (STD)

among the nine QNET means superimposed. It can be seen that, on an annual-mean basis, the

nine-product averaged QNET is about 32 Wm-2

but the STD among the nine products is about

16 Wm-2

, which accounts for half of the mean value. Godfrey and Lindstrom [1989]

suggested that the accuracy of QNET in the equatorial western Pacific should be 10 Wm-2

or

less for the products to be used for research purposes. Even without taking into account of the

systematic bias for all the flux products, the uncertainty in the presently available products is

too large to meet the requirement.

In situ flux measurements acquired from buoys and ships have long been used as a

reference base to quantify the accuracy of surface heat flux products. There have been many

studies on documenting the statistical properties (i.e., the mean, variance, STD, skewness, etc)

of the flux estimates relative to in situ observations [e.g., Smith et al., 2001; Josey, 2001; Yu

et al., 2004; Cronin et al., 2006; Pinker et al., 2009; Brunke et al., 2011]. This statistical

approach is effective in identifying errors, biases, and outliers. However, the approach has

6

three shortcomings. Firstly, in situ measurements are available only at limited locations, and

the evaluation results cannot be applied to the basin and global scales. Secondly, direct flux

measurements are difficult to make at open oceans and under all ranges of weather conditions.

Most often, in situ fluxes are computed from bulk flux algorithms, which are not completely

objective when used in evaluating global flux products that are constructed from the same or

similar flux algorithms. Thirdly, no measurement platform can provide direct QNET

observations, but this is the quantity that is needed in understanding the change of the tropical

warm pool and its interaction with the atmosphere. Improving heat flux estimates,

particularly QNET, through integrating in situ validation with other independent measures is

highly desired.

This study explores the use of a heat budget constraint to examine the quality of nine

available flux products in the WPWP. The time-varying heat budget equation that this study is

based upon was developed by Toole et al. [2004, hereafter TZC04] from extending the time-

mean framework of Niiler and Stevenson [1982] and Walin [1982]. Niiler and Stevenson

[1982] formulated time-mean heat budgets for the warm pool volumes bounded by an

isotherm, showing that the net surface heat flux into the water volume is primarily balanced

by the diffusive heat flux across the pool boundaries; mean advection in and out of such a

control volume does not contribute to the heat budget of the volume. This approach, which

considers the heat balance within a three-dimensional (3-D) ocean volume bounded by an

oceanic isothermal surface, is often called ‘the bubble analysis’ [Enfield and Lee, 2004].

Zhang and Talley [1998] applied the bubble formulation by Niiler and Stevenson [1982] to

the Indian Ocean to compute diapycnal diffusivity values for the upper oceans. The time-

dependent version of TZC04 allows the study of the temporal behavior of the heat balance by

including a time-variable heat storage term. TZC04 found that there is an approximate

balance between the annual variations of air-pool heat exchange and the time-varying heat

7

storage in the pool’s mean seasonal heat budgets [Gill and Niiler, 1973]; and that the diffusive

flux across the pool’s bounding isotherm, which is derived as a residual, is relatively steady

and downward through the year. In other words, for an enclosed WWV surrounded by colder

water, the diffusive flux must be negative (down the temperature gradient). TZC04 showed

that NCEP and ECMWF reanalyzed fluxes are too low in the warm pool regions, because

they lead to up-gradient diffusive flux and are incompatible with the pool’s heat budget. It is

thus proposed that, if temperature data are reasonably accurate, the sign of the diffusive flux

inferred from the heat budget is a powerful constraint for validating the physically-

consistency of surface heat flux estimates.

The formulation of TZC04 is conceptually simple and straightforward to implement.

However, there is a limitation. The inferred diffusive flux can tell the compatibility of an air-

sea flux climatology with the temperature data, but it cannot determine the error size in the

flux climatology. In analyzing the heat balance of the Western Hemisphere warm pool

(WHWP), Enfield and Lee [2004; hereafter EL04] coupled the TZC04 approach with a slab

layer of constant dimensions that includes the advective contributions. EL04 used the

diffusion inferred from the bubble approach as an input to the slab analysis, and considered

the advective heat flux divergence as a residual output in the slab model. The combined

bubble and slab methods enable some quantification of the range of air-sea heat fluxes

needed by the heat balance in the WHWP. In this study, a combination of the TZC04

approach with in situ air-sea measurements obtained from three TAO/TRITON buoys in the

western equatorial Pacific is taken into consideration.

In terms of structure, this paper has five sections besides the introductory part. The

paper is organized as follows: Section 2 describes the method of time-dependent heat budget

analysis of TZC04. Section 3 makes a brief description of nine flux climatologies used in this

study and an analysis of their differences. Diagnosis of physical-consistency of air-sea flux

8

climatologies based on the TZC04 approach is presented in Section 4, and the analysis with

in situ buoy measurements is included in Section 5. Summary and conclusion are given in

Section 6.

2. Methods

Considering a 3-D ocean volume bounded by the sea surface (As) and an oceanic

isothermal surface (Ab), TZC04 obtained the following time-dependent energy budget

equation:

[( ) ]p x NET s PEN s DIF b

B C DA

dV dc V Q dA Q dA Q dA

dt dt

(1)

where is the seawater density, cp is the specific heat, <> is the potential temperature

averaged over the pool volume V, and x is the bounding temperature which is set to be 28°C

in this paper (Fig. 1(b), black line), following the common practice [Wyrtki, 1989; Ho et al.,

1995; Weller and Anderson, 1996; Godfrey et al., 1998].

Term A in Equation (1) has two contributions, one is the change of the pool volume

and the other is the change of the mean temperature of the pool. TZC04 called term A the

“pseudo-heat content” because the control volume is not fixed but changes, while EL04

named this changing volume as a ‘bubble’. The three terms on the right-hand side (R.H.S.) of

Equation (1) represent the net air-sea heat flux (QNET) integrated over the surface (As) (term

B), the penetrative shortwave radiative (SW) flux (QPEN) across the isothermal base (term C),

and the total diffusive heat flux (QDIF) across the sides and the base of the pool whose surface

area is Ab (term D). The SW penetration QPEN is computed from an empirical relation,

assuming that the SW decays exponentially with a 25 m e-folding depth [Wang and

McPhaden, 1999]. As is seen from Equation (1), the ocean advective contributions to the heat

balance are eliminated, which is the greatest strength of the bubble approach. Except for the

diffusion term D, all the other terms on the R.H.S. in Equation (1) can be computed directly

9

using existing datasets. Therefore, the diffusion term is estimated as a residual. The

fundamental concept of TZC04 is that, for an enclosed pool volume surrounded by colder

waters, the diffusive flux must be out of the volume. This reflects the fact that, on the annual-

mean basis, the warm pool gains heat from the atmosphere and loses heat to the surrounding

colder waters by diffusive process [Niiler and Setvenson, 1982]. As demonstrated in TZC04

and EL04, whether the surface QNET is large enough to compensate the diffusive process and

give rise to the observed change in the pseudo-heat content (i.e., the terms on the left-hand

side of Eq. 1) is an important constraint for identifying the low bias in net downward heat

flux estimates. This constraint is a key measure in the following analysis of the uncertainties

for nine QNET products in the WPWP region.

Clearly, Equation (1) provides a physical way to examine the consistency of existing

heat flux estimates with the temperature fields. For this purpose, the climatological monthly-

mean temperature fields of the World Ocean Atlas 2009 [WOA09, Locarnini et al., 2010] is

chosen to compute the pseudo-heat content of the pool in term A. Since the pool’s volume has

an irregular shape and changes with time, the geophysical position of the volume bounded by

the 28°C isotherm was linearly interpolated from neighboring points if the isotherm is not on

the grid. The volume-averaged temperature ( 1V dV ) was computed by volume

weighting over the entire volume. The monthly increments of the pool’s volume and

temperature in term A are represented by the differences between the last 5-day-mean and the

first 5-day-mean of the month. The daily pool volume (V) and volume-averaged temperature

were obtained from linear interpolation of the monthly values.

The annual-mean SST field in the western Pacific is shown in Figure 1(b), and the

surface area of the warm pool bounded by the 28°C isotherm is highlighted. In this study, the

WPWP includes the main Western Pacific, the Indonesian Seas and small part of Indian

10

Ocean. The transport through the Malacca Strait is neglected, and the WPWP is regarded as

an enclosed volume.

3. Surface heat flux climatologies and uncertainty

The nine air-sea heat flux products to be examined in the study include three analyzed

global flux products, three first-generation atmospheric reanalyses from numerical

predication models (NWP), and three latest atmospheric reanalyses. Major characteristics of

these products are summarized in Table 1, and a brief description is given below.

3.1 Flux climatologies

3.1.1 Analyzed flux products

The analyzed flux products denote those products that are developed from flux

parameterizations using surface meteorological variables obtained from ship observations,

satellite retrievals, and/or NWP outputs with various levels of bias adjustments. Three global

QNET products are included (Tab. 1). The first product is the combined OAFlux+ISCCP [Yu

and Weller, 2007; Yu et al., 2008; Zhang et al., 2004]. OAFlux was developed from an

objective synthesis of surface meteorological variables from multi-satellite sensors and multi-

platforms with those from reanalyses. The synthesis with linear least squares estimator [Yu et

al., 2008] produces a solution with minimum variance. OAFlux does not have surface

radiation datasets yet, and so it is combined with ISCCP surface radiation to produce a QNET

climatology. The second one is the ship-based QNET climatology from the National

Oceanography Centre, Southampton version 2.0 (NOCS v2.0) [Berry and Kent, 2009, 2010],

an update from the NOCS v1.1 [Josey et al., 1998]. It was constructed on the basis of data

from observations by the Voluntary Observing Ships (VOS) from 1973 to present. In addition,

it is independent of buoys and satellites. The third dataset is the version 2 forcing for

Common Ocean-ice Reference Experiments (CORE.2) [Large and Yeager, 2009]. It was

developed from a hybrid combination of the reanalyzed near surface wind speed, air

11

temperature and humidity from NCEP 1, a SST analysis based on in situ and satellite

measurements, and ISCCP surface radiation. Major adjustments were applied, which

included a general increase in wind speed, decrease in humidity, and a uniform 5% reduction

in solar radiation from 50ºS to 30ºN to achieve a global heat budget balance.

3.1.2 The first-generation reanalyses

Three reanalysis products are grouped into this category (Tab. 1), namely, NCEP 1,

NCEP2, and ERA-40. These reanalysis have been around for many years, representing the

first efforts toward producing a comprehensive record of past atmospheric conditions using a

fixed, up-to-date data assimilating/forecasting system. NCEP 2 is regarded as an update of

NCEP1 but not a next-generation reanalysis, as it attempts to correct known errors in NCEP1

from 1979 to present and to improve parameterizations of some physical processes. The two

reanalysis systems use the same T62 L28 resolution, the same raw observed data, and the

same turbulent flux algorithm but differ largely in the parameterization of SW, cloud and soil

moisture. The NCEP surface fluxes are available every six hours, on Gaussian 19294 grid

(approximately 1.875° in longitude and latitude). ERA-40 is produced from the T159 L60

version of the Integrated Forecasting System, which includes a comprehensive assimilation of

satellite data from a variety of platforms. The surface fluxes are archived four times daily on

an N80 reduced Gaussian grid, with approximately uniform 125km (~1.125°) spacing.

3.1.3 The latest reanalyses

The three latest reanalyses (Tab. 1) are the NCEP CFSR, the NASA MERRA, and the

ERA-Interim. The recently completed CFSR is the third global reanalysis of NCEP. It boasts

a number of advantages in model functions and assimilation techniques over NCEP 1 and

NCEP 2. There are three main differences between two earlier NCEP efforts include higher

resolution (T382 L64), the use of a coupled atmosphere-ocean-land surface-sea ice system,

and the assimilation of radiance measurements from historical satellites in addition to all

12

conventional data [Saha et al., 2010]. The CFSR is casted as the successor of NCEP 2, and is

planned to extended back to 1948, which will then be the successor of NCEP 1. MERRA is a

NASA reanalysis for the satellite era (from 1979 onward) using a major new version of the

Goddard Earth Observing System Data Assimilation System Version 5 (GEOS-5). The

project’s objectives are to support NASA’s climate strategies by placing NASA EOS suite of

observations in a climate framework and to improve the representation of the water cycle on

a broad range of weather and climate time scales. ERA-Interim is a bridge between ERA40

and the next-generation extended reanalysis envisaged at ECMWF. The major advances in

ERA-Interim are many model improvements, the use of 4-dimensional variational analysis, a

revised humidity analysis, bias correction for satellite data, and a higher spatial (T255) and

temporal resolutions. The ERA-Interim surface variables are available at 3-hour intervals, on

an N128 reduced Gaussian grid of about 80km or 0.7° spacing.

3.2 Uncertainties in QNET climatologies

Differences in the nine flux climatologies are analyzed before applying these products to

Equation (1). Three aspects are examined, namely, the position of the zero line of QNET

related to the WPWP location, seasonal variations of QNET and the four components

integrated over the WPWP, as well as the relation of the regional WPWP fluxes to those over

the global ocean.

3.2.1. Position of the zero-line of QNET

Figure 2 shows the climatological monthly evolution of the zero-line of QNET from the

nine climatologies with the surface 28ºC isotherm of the WPWP added as a reference. To

provide a full spatial view of QNET variability, the entire Pacific is shown. Seasonal north-

south migration of the WPWP is evident. The northern edge of the WPWP is at the

southernmost location (10ºN) in March and the northernmost location (~30ºN) in September.

13

Zonal extension of the WPWP is not significant compared with the meridional migration, and

the easternmost edges of the warm pool stay between 130ºW–140ºW throughout the year.

The meridional migration of the WPWP shows a close association with the seasonal

movement of positive QNET over the warm pool regions [Ho et al., 1995; Schneider et al.,

1996]. The northward displacement of the WPWP in April-September occurs at the time

when QNET is positive in the northern hemisphere and negative in the southern hemisphere.

Similarly, the southward displacement of the WPWP in October-March is the time when QNET

is negative in the northern hemisphere and positive in the southern hemisphere. Throughout

the 12 months, the location of the WPWP tends to follow the positive territory of QNET,

although the entire pool may not be completely under the positive QNET forcing. This can be

seen from the location of the zero line of QNET. Despite the differences in the nine products,

all of them show that the entire pool receives net heat from the atmosphere from January to

March, with the zero line on the northern edge of the pool. As will be shown in the next

section (Fig. 4(a)), the volume and intensity (warmth) of the WPWP increase rapidly during

these months. A similar situation is also depicted by most flux climatologies in June-August,

during which the pool’s intensity shows a weak second peak (Fig. 4(a)).

The zero lines of QNET derived from the nine flux climatologies are different; however,

the degree of the spread is highly dependent of the season. The nine zero lines have

remarkably good agreement in boreal summer (June and July) and winter (November,

December, and January), but have major disagreement in spring (March, April, and May) and

fall (September and October). For the rest two months, February and August, the nine zero

lines have similar zonal orientation but differ in meridional position. In particular, the nine

products can be divided into two groups, high and low net heat flux products. This is due to

the fact that the meridional position is a good indicator of the magnitude of QNET. If net heat

flux is into the North (South) Pacific, the farther southward (northward) the zero line of QNET

14

is located, the larger positive QNET the ocean receives. It can be seen that the high net heat

flux products include two latest reanalyses (CFSR and MERRA) and two analyses

(NOCSv2.0 and OAFlux+ISCCP), and the low net heat flux products include the three first-

generation reanalyses (NCEP 1&2, and ERA40), the hybrid CORE.2, and the recent ERA-

Interim. The large spreads of the nine zero lines during the spring and fall transition months

are due largely to the spread in the low products.

3.2.2. Seasonal variations of surface heat fluxes over the WPWP

To characterize the cause of the differences between the nine products, seasonal

variations of QNET along with the four contributing heat flux components (SW, LW, LHF, and

SHF) are averaged over the WPWP bounded by the surface 28°C isotherm (Figs. 3(a)-(e)).

Positive sign denotes that the flux is downward into the ocean (i.e., the ocean receives heat

from the atmosphere), whilst negative sign denotes that the flux is upward into the

atmosphere (i.e. the ocean losses heat). The five plots in Figure 3 show that QNET is

downward through the year in all products except for ERA-40 that has a near-zero QNET in

June-July. Evidently, the WPWP is heat gain region on the annual-mean basis, although the

exact amount of QNET gained by the pool varies with products. Figure 3 also shows that the

primary term that balances the incoming shortwave radiation into the ocean is latent heat loss,

followed by longwave radiation; sensible heat loss is an order of magnitude smaller than

latent heat loss.

Although the magnitude differs, the semiannual cycle of QNET over the WPWP is well

depicted by all nine climatologies, with a primary maximum in March and a secondary

maximum in September (Fig. 3(a)). The nine QNET products are nicely grouped into two

categories, with the high net heat flux category including CSFR, MERRA, NOCSv2.0 and

OAFlux+ISCCP, and the low net heat flux category including ERA-40, ERA-Interim, NCEP

1&2, and CORE.2. This high-low separation is consistent with the analysis of Figure 2. The

15

mean difference between the two groups is roughly 20 Wm-2

, which is of the similar

magnitude to the annual mean of the low products.

The semiannual cycle in QNET is dictated by surface net SW (Fig. 3(b); positive sign

denotes net downward flux). There are significant discrepancies in the SW climatologies,

with the difference 100 Wm-2

between the largest (ERA-40) and smallest (NCEP 1). The peak

of SW in March and September reflects that the Sun passes the Equator twice a year.

However, the SW over the WPWP is controlled not only by solar zenith angle but also by

cloud radiative effects and surface properties [Webster and Stephens, 1984; Hartmann and

Doelling, 1991; Chen et al., 2000]. WPWP is the region of the strongest deep convection,

where the downward cloud-induced radiative flux changes can be as large as 118 Wm-2

[Chen

et al., 2000].

A weak semiannual cycle is observed in surface net long wave radiation (Fig. 3(c);

negative sign denotes net upward flux). All LW estimates show a similar weak cycle, except

for ISCCP that has a major peak in October and a secondary peak in April-May. ISCCP is the

only satellite product in this analysis. ERA-40 has the strongest net upward LW (~70Wm-2

)

and CSFR has the weakest LW (~40Wm-2

), while all others have a mean around 50-55 Wm-2

.

LHF in most products shows a seasonal cycle that has a clear minimum heat lossin April

but no clear maximum heat loss (Fig. 3(d)). CFSR, which features a semiannual cycle with a

second peak in November, deviates from other products. EAR-40 produces the strongest

latent heat loss from the ocean, and its mean magnitude is more than 60 Wm-2

larger than all

others. SHF is weak, about 10% of LHF (Fig. 3(e)). Nevertheless, one feature stands out:

ERA-40 SHF has the strongest magnitude among all products.

Net heat flux is the balance between downward net SW and upward net LW, LHF, and

SHF, and differences in the four flux components compensate. For instance, ERA-40 has the

larger magnitude in all the four flux components, but has a smallest QNET. Hence, the low

16

ERA-40 is not caused by a weaker SW but by an over compensation of an excessive

incoming SW. If putting ERA-40 aside, it is generally true that the low net heat flux products

(CORE.2, ERA-Interim, NCEP 1&2) are caused by weaker SW and stronger LHF while the

high net heat flux products (CFSR, MERRA, NOCSv2.0, and OAFlux+ISCCP) are by

stronger SW and likely weaker LHF (such as MERRA and OAFlux+ISCCP). To see this

more clearly, the annual means of QNET and the four contributing flux components for the

nine climatologies are listed in Table 2. In summary, differences in SW and LHF are the two

major error sources in QNET, followed by errors in LW.

3.2.3. Implication for the global heat budget balance

The WPWP is a major heat gain region over the global basins, and the representation of

the nine flux climatologies in this region has important implication for global energy budget

analysis. For instance, it would be interesting to know how sensitive the global energy budget

analysis is to the high/low net heat flux products. Here QNET averaged over the global oceans

using the nine products are contrasted to the QNET over the WPWP in Table 2. The products

are organized into the high and low net heat flux groups where they are listed in alphabetical

order.

Evidently, the products that are in the high net heat flux category (CFSR, MERRA,

NOCSv2.0, and OAFlux+ISCCP) over the WPWP have a large residual (>15 Wm-2

) over the

global ice-free oceans, and those that are in the low category (CORE.2, ERA-40, ERA-

Interim, NCEP 1&2) have a small residual (<11 Wm-2

) over the global oceans. Thus, the

WPWP QNET has a similar tendency to the global mean. For the high net heat flux group, the

globally averaged QNET is 15 Wm-2

by CSFR, 22 Wm-2

by MERRA, 25 Wm-2

by NOCSv2.0,

and 30 Wm-2

by OAFlux+ISCCP. It is apparent that the combined OAFlux LHF/SHF with

ISCCP SW/LW produces the largest global heat imbalance, although it is not the highest net

heat flux product over the WPWP. Unlike the other eight climatologies that have the radiative

17

and turbulent heat fluxes produced by using the same model/data source, OAFlux and ISCCP

are from two independent research groups. It seems that a direct combination of the two

unrelated products is not an optimal choice, because the combination can enhance the errors

in the flux components rather than compensating them. This is seen that, among the nine

products over the WPWP, ISCCP net radiation (SW-LW) is not the second largest downward

flux, nor is OAFlux turbulent heat component (LHF+SHF) the second weakest upward flux.

The resulting QNET being the second highest shows that these products are internally

inconsistent and the inconsistence amplifies the errors in each component, leading to an

imbalanced QNET.

For the low net heat flux group, the globally averaged QNET is 1 Wm-2

by NCEP 1, 4

Wm-2

by NCEP 2, 4 Wm-2

by CORE.2, 7 Wm-2

by ERA-40, and 11 Wm-2

by ERA-Interim.

The CORE.2 applied major adjustments, for example, general increase in wind speed,

decrease in humidity, and a uniform 5% reduction in solar radiation from 50ºS to 30ºN. In

addition, a near-zero QNET for CORE.2 is obtained over the global ice-free basins. Here the

calculation focuses only on the global ice-free oceans excluding the ice-covered Polar

Regions. Now that it is worth noting that, for the same ice-free ocean regions, the three latest

reanalyses have a much larger QNET residual than the previous reanalysis which shows a

global balance within 7 Wm-2

. This raises a question as to the importance of the air-sea

exchange at high latitudes in balancing the global energy budget. However, the research

along this direction is beyond the scope of this study. Nevertheless, the physically consistent

heat budget analysis over the WPWP contributes to an improved understanding of the bias in

QNET and helps to find solution to achieve a globally balanced budget.

4. Heat budget analysis results

Term A in Equation (1) represents the “pseudo-heat content” of the WPWP because the

control volume is not fixed but changes. The seasonal evolution of term A in the WPWP has a

18

semiannual cycle with maximum values in April and September, but minimum values in June

and December (Fig. 4(a)). Although semiannual periodicity is seen in both volume and mean

temperature of the pool, the change of the pseudo-heat content of the pool between

November and May is primarily dominated by the expansion and contraction of the pool,

while its change between June and October can be mostly attributed to the cooling and

warming of the pool’s water.

The monthly variations of the pseudo-heat content are in phase with the monthly

variations of QNET, as is shown in the time evolution of Term B ( NET sQ dA ) (Fig. 4(b)),

which is the net air-sea heat flux integrated over the sea surface. The whole surface area of

the WPWP bounded by the 28ºC isotherm is 30±2.9×106 km

2 on average, where the error bar

is the STD of the monthly means. Similar to Figure 3(a), there is a clear separation between

the high and low QNET climatologies. The mean difference of ~20 Wm-2

between the two

groups is equivalent to ~ 0.5 PW (1 PW = 1015

Watts) total surface energy. Computation of

the SW penetration in the WPWP is based on the model of Wang and McPhaden [1999],

assuming an exponential decay of surface SW with a constant 25-m e-folding depth. Figure

4(c) shows the time evolution of the energy loss due to the SW penetration (Term C) as

estimated from the nine climatologies. A semiannual periodicity is also displayed, with the

largest penetrative loss occurring in August and the second largest in March-April. The phase

of the semiannual cycle of the SW penetrative loss differs from that of net SW shown in

Figure 3(b). The cause of the difference is due to the nonlinear effect of the variances of the

28ºC isotherm depth on the computation of Term C. Unlike the estimates for Term B, the flux

climatologies have a small spread in estimates of Term C if ERA-40 and CFSR are excluded.

The latter two produce a large SW penetration because of the large net SW they have. The

other seven SW products indicate that the total SW penetrative loss varies in the range from -

0.4 PW to -0.6 PW.

19

Term D represents the total diffusive (horizontal+vertical) heat flux and is obtained as

the residual of Terms A, B, and C. Whether this term directs from the warm to the

surrounding colder water is used as a diagnostic tool in TZC04 and EL04 to validate the

physical compatibility of flux climatologies. This physical constraint is based on the fact that

on average the warm pool gains heat from the atmosphere and loses heat to the underlying

colder waters and hence, the diffusive flux must exit across the pool boundaries. The residual

diffusive flux (Term D) diagnosed from the nine flux climatologies using Equation (1) is

shown in Figure 4(d) with the annual mean numbers and STDs listed in Tab. 3. Obviously,

the flux products in the high net heat flux group (CFSR, MERRA, NOCv2.0, and

OAFlux+ISCCP) all lead to a down-gradient diffusive flux through the year, which satisfies

the imposed physical requirement. The magnitude of the annual mean diffusive heat flux

ranges from -36 Wm-2

to -29 Wm-2

(Tab. 3) for the high net heat flux climatologies. However,

for the low climatologies, the annual mean diffusive heat flux is smaller, about -5 Wm-2

.

Although the net annual mean diffusive heat flux is down-gradient for the low climatologies

except for ERA-40, an up-gradient diffusive heat flux is obtained with a varying degree in

different months. ERA-40 is the worst, as it depicts a large diffusive flux into the warm pool

through most of the year. NCEP 1 and NCEP 2 are also low, showing an incoming diffusive

flux for half of the year. ERA-Interim and CORE.2 fluxes are unphysical mostly during May-

June-July.

It should be noted that although Equation (1) is an effective diagnostic tool in identifying

the flux climatology that is not physically compatible with the chosen temperature fields, it

couldn’t serve as a quantitative measure to evaluate the error sizes in the flux climatologies.

Specifically, all the flux products in the high net heat flux category are consistent with the

warm pool thermal dynamics and produce a down-gradient diffusive heat flux. Whether the

amount of the diffusive heat flux is within a reasonable range is, however, not possible to

20

obtain from Equation (1). Therefore, additional tools and/or approaches are needed to

strengthen the heat budget analysis based on Equation (1).

5. Uncertainty analysis of QNET climatologies using in situ observations

5.1 Methodology and data

Conventionally, in situ buoy observations serve as benchmark time series to evaluate the

air-sea flux estimates at the buoy sites. Here a different approach is attempted by using

subsurface temperature and velocity measurements from the buoy together with the diffusive

heat flux (Term D) to first infer the eddy diffusivity coefficient and then diagnose the errors

in the flux products.

Three moored buoys in the WPWP from the TAO/TRITON array are chosen for the

study. They are located at equatorial 147°E, 156°E, and 165°E. Locations of these buoys

relative to the seasonal migration of the WPWP can be found in Figure 2. The buoy at 165°E

has daily temperature and velocity time series from 1990 to present, and complete air-sea flux

measurements (SW, LW, LHF and SHF) from August 2006 to August 2007. This buoy site

allows not only the computation of the mean Richardson-number-dependent eddy diffusive

coefficient but also a direct evaluation of the flux climatology. The other buoy sites have no

LW measurements but do provide temperature and velocity time series which can be used as

a supplement to the buoy site at 165°E. Within the upper 200 m, temperature observations are

available at the depth of 1, 10, 30, 50, 75, 100, 125, 150, 175, and 200m and the acoustic

current profile is available with a vertical resolution of 5 m. The depth of 200m was chosen

here because the depth of 28ºC isotherm does not extend beyond 200m.

5.2 Inferring vertical eddy diffusivity coefficient from Term D

Term D in Equation (1) represents the total (horizontal+vertical) diffusive heat flux

across the pool’s boundaries. To relate the 3-D ‘bubble’ analysis to the 1-D analysis at a fixed

buoy site, one needs to know the relative partition between the vertical (denoted as V ) and

21

horizontal (denoted as H ) components to the total integrated diffusive heat flux. The two

integrated components can be expressed in terms of the eddy coefficient and temperature

gradient along the isotherm as follows:

vV v p v

TV Q dA c k S

z

(2)

hH p h l

l

TH Q dA c k S

y

(3)

where VQ and HQ the respective vertical and horizontal diffusive flux, S and lS the whole

surface and lateral projection area of the WPWP, vk and hk the vertical and horizontal eddy

coefficients, and vT

z

and hT

y

the vertical and horizontal temperature gradient respectively.

The horizontal mixing in the meridional direction is considered, since the zonal temperature

gradient is smaller compared to the meridional.

If assuming the shape of the ‘bubble’ bounded by the 28°C isotherm as an idealized

bowl, the spatial scale of the bowl can be approximated by a radius ( R ) of 15° in the

meridional direction and a depth ( H ) of 75m. Given that vT and hT are the same within

the bowl if integrating along the isothermal boundaries, the ratio of the vertical diffusive heat

flux to the horizontal counterpart can be scaled as

2 2/

2 / 2

v

v v v v

hh l h h h

TV k S k R T H k Rz

Tk S k RH T R k HH

y

(4)

If the vertical eddy coefficient vk is set to 10-4

m2s

-1 and the horizontal eddy coefficient hk is

taken to be 2000 m2s

-1 based on the Gent–McWilliams [1990] parameterization, the ratio of

V

H is about 20. This estimation, though crude, demonstrates that the vertical turbulent heat

flux might have a dominant contribution to Term D of Equation (1). The scale analysis

22

provides a basis for the choice of the integration isotherms. For example, if the 28.5°C or

29°C is chosen, the ratio of V

His about 3 or 1, therefore, it will introduce other difficulties to

estimate total heat diffusivities.

For simplicity, we attribute the total diffusive heat flux to the vertical component in the

following analysis, bearing in mind that there is at least 5% error in such analysis. By doing

so, the diffusive heat flux can be represented as

DIF v

dTQ k k

dz (5)

where k is the vertical unit vector. By using the residual Term D and the mean temperature

gradient at the pool base, the vertical eddy coefficient vk for the high net heat flux group can

be inferred. The mean eddy coefficients (Tab. 3) for these high net heat fluxes thus obtained

are 4.3 cm2s

-1 for CFSR, 4.0cm

2s

-1 for OAFlux+ISCCP, 3.4cm

2s

-1 for NOCSv2.0 and

MERRA. Even if we deduct 5% from these estimates by taking into account of the neglected

horizontal eddy diffusivity, these numbers are still far larger than the ones in the literatures

(1.4 cm2s

-1 on average) of the past four decades [Gregg, 1976; Osborn and Bilodeau, 1980;

Kanari et al., 1992; Schneider and Bhatt, 2000; Sriver et al., 2010]. However, the annual

mean eddy coefficients derived from the low net heat flux category are 0.6 (0.8) cm2s

-1 for

CORE.2 and ERA-Interim, 0.5 (1.1, 0.8) cm2s

-1 for NCEP 1 and 2, but an unphysical up-

gradient diffusivity coefficient -0.8 (0.5) cm2s

-1 for ERA-40. These numbers are only about

1/3 of the existing literatures. The eddy coefficients in the parentheses for those months with

down-gradient fluxes only are also smaller than the ones in the references shown above.

Figure 5 shows all the inferred eddy diffusive coefficients for the nine climatologies and their

comparison with existing references and the in situ observations based on the TAO/TRITON

buoy (next subsection). There have been many efforts to estimate the mean along-isotherm

diffusion coefficient in terms of ocean observations and theoretical projections [Joyce, 1980;

23

Niiler and Stevenson, 1982; Speer, 1997; Zhang and Talley, 1998; TZC04; EL04]. However,

the estimates differ considerably in magnitude. For instance, Niiler and Stevenson [1982]

derived from microstructure observations that an eddy diffusivity of 0.1-0.4 cm2s

-1 is

adequate to balance a net heat flux of 7-22 Wm-2

for the warm water pool bounded by 26°C

isotherm. Schneider and Bhatt [2000] showed that the mean diffusivity of the western Pacific

bounded by the 28 ºC isotherm is of 1.3–1.5 cm2s

-1. All the estimates are based on the

assumption that the diffusive heat fluxes are only represented by downward gradient

diffusivities. In Figure 5, the diffusivity coefficients in the WPWP region found in the

literatures are listed. It can be seen that those estimates are within the range of 1.0-2.0 cm2s

-1

and 1.4 cm2s

-1 on average, while the diffusivity coefficients for the high net heat fluxes

derived from Term D are much greater than 2.0 cm2s

-1, but smaller than that for the low heat

flux climatologies. Clearly, the high/low net heat flux input from the air-sea interface is too

excessive/deficient to be balanced by the changes of the pool’s temperature and volume. All

the high (low) net heat flux climatologies have a higher (lower) bias over WPWP.

5.3 Estimating vertical eddy diffusivity coefficient from buoy subsurface measurements

Vertical eddy diffusivity is usually related to the Richardson number

2( )

g zRi

u z

(6)

where u is the mean velocity, the seawater density, and g the acceleration of gravity.

Based on Pacanowski and Philander [1981], the dependence of vk on iR can be simply

expressed as:

21 ( )z

v n

i z

uk

R T (7)

where zu represents the velocity shear, and zT is the buoyancy frequency in terms of

temperautre. By using buoy measurements of subsurface temperature and velocity, vk can be

24

estimated from Equation (7). The monthly mean eddy coefficients at the three buoy sites are

superimposed onto Figure 5 (the black lines in the lower part of the plot). Two features are

noteworthy. First, the mean eddy coefficient estimated from the three sites is 1.2±0.2 cm2s

-1,

which is consistent with the existing estimates in the literatures (see the assembly of symbols

at the left side of the monthly-mean time series). In particular, this estimate is in good

agreement with the study by Schneider and Bhatt [2000]; the latter is regarded as the mean

diffusivity over the entire isotherm surface. Second, the buoy-based vk values show moderate

seasonal variability, being relatively larger in the boreal fall and winter and weaker in the

boreal spring and summer. The monthly changes of vk derived from Term D display a similar

seasonal pattern (Fig. 5, the colored lined in the upper part of the plot). Although these values

represent the mean diffusivity of the 3-D bubble, the similarity to the buoy-based pattern

appears to justify the change of vk with seasonal.

To gain a better understanding of the buoy estimates of vk , Figures 6(a)-(e) show the

mean monthly evolution of temperature, zonal velocity, buoyancy frequency, velocity shear

and Richardson-number-dependent eddy coefficient computed from the buoy measurements

(1990-2007) in the upper 200m at 165ºE. The other two moorings (147ºE and 156ºE) have

similar structures, which are not shown here. For reference, the depth of the 28°C isotherm

averaged over the entire WPWP is displayed together with the isotherm of 28ºC at the buoy

location. Although the pool-averaged depth is about 20m shallower, the pattern of seasonal

variations is similar to that of the buoy, showing that the buoy has a reasonable representation

of the mean state of the pool.

Marked seasonal variations in zonal velocity are observed. A strong Equatorial

Undercurrent (EUC) is seen below 160 m, with a maximum eastward zonal current exceeding

50 cms-1

during March-August. Meanwhile, the surface zonal currents exhibit a semiannual

reversal of the current direction, featuring a westward jet in January-February/September-

25

October and an eastward jet during April-August/November-December. Strong velocity shear

is resulted when a westward surface jet is on top of EUC, which is clearly depicted in Figure

6(d). The eddy flux at the depth of the 28°C isotherm is dominated by the velocity shear, so

that the lager shear indicates a stronger mixing between the down-gradient heat flux and the

surrounding colder water and larger eddy diffusivity. This explains the enhancement of eddy

diffusive heat flux during the boreal fall and winter that is seen in diffusivity estimates

derived both from buoy observations and from Term D using flux climatologies. It appears

that, though Term D is too large, the pattern of monthly change in diffusive flux is well

depicted and hence, the flux climatologies have a good representation of seasonal variability

of net surface heat flux in the WPWP.

5.4 Uncertainty analysis of the QNET climatologies by in situ complete measurements

The buoy at equatorial 165ºE provides the full air-sea heat flux measurements (SW, LW,

LHF and SHF). The monthly mean QNET was obtained by averaging the daily buoy

observations from August 2006 to August 2007. The one-point monthly QNET from the nine

climatologies were compared directly with the in situ observed QNET (Fig.7). As there is no

overlap in temporal duration between the ERA-40 and buoy fluxes; therefore, ERA-40 is

excluded here. The CORE.2 only extends to December 2006 with the uncertainty analysis

absent since January 2007. Net heat fluxes at 165ºE from the eight climatologies show similar

seasonal evolution with direct TAO/TRITON observations but differ greatly in magnitude.

However, NOCSv2.0 tends to be an exception. The large seasonal discrepancy between the

NOCSv2.0 and buoy observations might be ascribed to the interpolation for the ship

measurements, which can cause unphysical processes and affect the accuracy of the flux

quantifications. Although the monthly surface heat fluxes in Figure 7(a) vary greatly in

magnitude, however, the current heat flux climatologies can capture the flux variations,

similar to the above pool-integrated results.

26

Figure 7(b) and Table 3 show and list the annual mean difference and the STDs between

the eight heat flux climatologies (ERA-40 excluded) and the in situ flux observations. As

shown in the above analysis, the high net heat fluxes also have high bias in the one-point

comparison, and low ones have low bias. However, the NOCSv2.0 tends to be an exception

with a low annual mean bias -30 Wm-2

. The high net heat flux group have the high bias 34

Wm-2

for CFSR, 6 Wm-2

for OAFlux+ISCCP and 8 Wm-2

for MERRA , whilst, the low group,

namely, ERA-Interim, CORE.2 and NCEP 1&2 have the low bias of -4 Wm-2

, -33 Wm-2

, -1

Wm-2

and -2 Wm-2

, respectively. The OAFlux+ISCCP, MERRA, ERA-Interim and NCEP

1&2 have the relative smaller differences. The low flux climatologies ERA-Interim and

NCEP 1&2 even have close to zero annual mean biases. The CFSR has the largest high bias,

while the NOCSv2.0 and CORE.2 have the equivalent low biases. The error bars in Figure

7(b) (also listed in Tab. 3) represent the STDs of the QNET difference between the monthly

flux observations and the heat flux climatologies. CORE.2, CFSR, OAFlux+ISCCP, MERRA,

ERA-Interim and NCEP 1 have the moderate magnitudes, while NCEP 1 and NOCSv2.0

have the largest STDs.

5.5 Uncertainty analysis of the pool-integrated QNET climatologies

The mean surface QNET is inversely obtained by Eq. (1). Term A and term D were

computed using the 3-D subsurface temperature data and the mean eddy diffusivity

coefficients. The climatological solar radiation penetration (term C) through the 28ºC

isotherm was obtained by averaging the nine QPEN estimates. The annual mean QPEN is -17±2

Wm-2

, and the mean diffusive heat flux (QDIF) at the pool base quantifies -11±1 Wm-2

. The

term A has a slight long-term residual heat -0±6 Wm-2

. Using Equation (1), the annual mean

QNET that should go into the WPWP can be inversely estimated 28±7 Wm-2

based on the heat

budget balance of the whole system. Physically, the mean QNET over the WPWP can be stored

and transported downward to the surrounding cold water by the radiation penetration (term C)

27

and diffusion (term D) processes on the annual mean state. The accumulated heat energy can

be taken away by the western boundary current systems to the high latitude to maintain the

global meridional heat transport. Seasonal changes of QNET are mainly balanced by the

seasonal pseudo-heat content changes (term A), while the changes of term C and D are

secondary. Figure 8(a) shows the inversely constructed QNET has a similar semiannual

variability with the nine climatologies as shown in Figure 3(a). However, there are still

statistical errors for the calculation. The potential uncertainties for the constructed QNET can

be ascribed to the physical assumption (e.g. ignoring the lateral mixing energy) and the errors

of the data input (e.g. deviations of WOA09 climatological temperature data and the

TAO/TRITON buoy observations). The shading areas in Figure 8(a) indicate that the

constructed QNET has an error of 38%±18%.

The above-mentioned estimate on the QNET can be used as a test-bed for the existing flux

climatologies. In terms of an annual mean bias, the analyzed climatologies of

OAFlux+ISCCP and NOCSv2.0 are about 22±4 Wm-2

and 18±5 Wm-2

higher than the

physical constructed QNET (Fig. 8b). In addition, the newly reanalysis of CFSR and MERRA

have high biases of 27±6 Wm-2

and 18±5 Wm-2

respectively. Moreover, the lower

climatologies have the bias of -6±4 Wm-2

for ERA-Interim, -6±4 Wm-2

for CORE.2, -8±6 for

NCEP 2, -9±7 Wm-2

for NCEP 1 and -12±7 Wm-2

for ERA-40. Considering the above

combination of OAFlux and ISCCP from two independent data sources can produce large

uncertainties. For OAFlux, other attempts are also diagnosed, for example, the combination

with Surface Radiation Budget (SRB) in the program of Global Energy and Water Cycle

Experiment (GEWEX) and NASA Clouds and Earth’s Radiant Energy System (CERES). The

uncertainty of OAFlux+SRB is 27±7 Wm-2

, close to that of the CFSR, but even worse than

uncertain elements in the OAFlux+ISCCP, however, the OAFlux+CERES show good

improvements over the other versions with the high bias 16±6 Wm-2

(Fig. 8b).

28

6. Summary and conclusions

On the annual mean state, the surface heat flux is primarily balanced by the diffusive

heat flux and the solar radiation penetration across the 28ºC isotherm; however, the seasonal

variations of the QNET are primarily balanced by the pseudo-heat content changes. The

seasonal variability of isothermal heat diffusion is closely associated with the ocean dynamics:

the velocity shear between the Pacific tropical surface jet and EUC can enhance the vertical

eddy coefficient ( vk ) and facilitate the downward heat flux diffusivity. The inversely

obtained net surface heat flux over the WPWP is 28 Wm-2

with the mean error 10 Wm-2

(35%)

by estimating the pseudo-heat content changes, solar radiation penetration and eddy diffusive

heat flux.

A survey of nine heat flux climatologies indicates that the WPWP should receive 18

Wm-2

for the five-member low net heat flux group and 49 Wm-2

for the four-member high net

heatflux group. For the high net heat fluxes, WPWP cannot dissipate the excessive heat

through the thermal dynamics. The required vertical eddy coefficient for the dissipation of the

excessive surface heat of the high fluxes ranges from 3.4 to 4.3 cm2s

-1, which is much larger

than the observations (1.5 cm2s

-1) and the historical estimates (1.4 cm

2s

-1). However, the eddy

coefficient is about 0.5 cm2s

-1 for the low net heat flux category, smaller than the observations.

The input surface heat flux cannot balance the warm pool heat budget. This indicates a low

bias for the low net heat flux climatologies.

The one-point direct comparison also indicates high bias for the high net heat flux

climatologies except for NOCSv2.0, and low bias for the low category. However, the bias of

the reanalysis of ERA-Interim, NCEP 1&2 ranges from -4 to -1 Wm-2

, close to zero.

OAFlux+ISCCP and MERRA also have smaller biases, 6 and 8 Wm-2

respectively. The

remaining products, CFSR, NOCSv2.0 and CORE.2 have greater bias over 30 Wm-2

(Tab. 3).

The inversely constructed QNET based on the pool integration shows that, the high

29

climatologies have the mean bias of ~20 Wm-2

, while that of the low ones is ~-9 Wm-2

. The

low net heat flux group have relative smaller biases, from -12 (ERA-40) to -6 (ERA-Interim

and CORE.2) Wm-2

, on the other hand, the high group's biases are from 18 (MERRA and

NOCSv2.0) to 27 (CFSR) Wm-2

. The reanalysis ERA-Interim, NCEP 1 & 2 have relatively

smaller bias for both the one-point and pool integrated heat budget comparisons, while the

other climatologies perform significantly less well. Although these diagnostics are still

strongly affected by the physical assumption and the data errors, they can provide a

straightforward and efficient way to validate the flux estimate in future.

Acknowledgements

This research was conducted while X. Song was a visiting graduate student at WHOI. X.

Song acknowledges the WHOI Academic Programs Office for hosting his two-year visit. He

is grateful to the support from China Scholarship Council (CSC), National Natural Science

Foundation of China (NSFC, Reference No. 40930844, 40976004, 40921004 and 41222037),

the Specialized Research Fund for the Doctoral Program of Higher Education

(2011013213001), the Ministry of Education of PRC's 111 Project (B07036) and the

Fundamental Research Funds for the Central Universities (0905-841313038). L. Yu

acknowledges the support from the NOAA Office of Climate Observations (OCO). X. Jin is

thanked for preparing the datasets used in this study and Shirley Cabral McDonald for the

editorial support. Two anonymous reviewers are acknowledged for their constructive and

valuable comments. Projects of OAFlux, ISCCP, NOCSv2.0, CORE.2, NCEP 1&2, ERA-40,

ERA-Interim, CFSR, MERRA, WOA09 and TAO/TRITON are acknowledged for making

the products/data available.

30

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37

FIGURE AND TABLE CAPTIONS

TAB. 1. Key features of the nine global gridded surface heat flux climatologies.

TAB. 2. Mean averages of SW, LW, LHF, SHF, QNET (Wm-2

) over the WPWP bounded by

the 28°C isotherm plus QNET over the global ice-free oceans. The global means are the area-

weighted means based on the same land-sea mask. The top four products are the high net heat

flux group and the bottom five products are the low net heat flux group.

TAB. 3. Numbers of the residual heat diffusivity (QDIF, term D) from Eq. (1) and its STDs

(the first and second column), inferred vertical eddy coefficients from the heat budget balance

(the third column), the QNET differences between the nine climatologies and the in situ

observation (the fifth and sixth column) and pool integrated method (the seventh and eighth

column). Numbers in the parentheses represent the mean values in those months when the

heat diffusivity is down-gradient.

FIG. 1(a). Annual mean net air-sea heat flux QNET (units: Wm-2

, colored) over the Western

Pacific by averaging the nine heat flux products OAFlux+ISCCP, NOCSv2.0, CORE.2,

NCEP 1, NCEP 2, ERA-40, CFSR, MERRA and ERA-Interim (introduced subsequently),

contour of 17 Wm-2

standard deviation is superimposed. (b). Climatological annual mean

(1958-2009) SST (ºC) from OAFlux with contour interval 1 ºC. Contours of 28ºC and 29ºC

are highlighted by solid black and white line respectively. The location of plotted region in

the global map is indicated in bottom left in (a).

38

FIG. 2. Seasonal evolution of the WPWP location by the 28°C isotherm boundary (black

contour) versus the zero-contour of the nine heat flux products (colored contours) with the

legends in the bottom. For clarity, a 35-point (zonal direction) running mean for the longitude

in the Pacific basin is applied for the zero-contours of the heat flux products.

FIG. 3. Seasonal variability of QNET (a), SW (b), LW (c), LHF (d) and SHF (e) over the

WPWP using the 28ºC isotherm boundary. The positive means downward flux, while the

negative represents the upward.

FIG. 4. Seasonal evolution of the heat budget terms in Equation (1). (a), pseudo-heat content

change (Term A) based on WOA09 temperature data: [( ) ]p x

dV dc V

dt dt

denoted as solid thick black line; left part ( )p x

dVc

dt and right part p

dc V

dt

are

presented by dashed and solid thin lines respectively; (b), QNET term B: NET sQ dA using

nine different heat flux products diagnostically; (c), SW penetration term QPEN (Term C)

PEN sQ dA using Wang and McPhaden’s [1999] model; and (d), diffusive heat flux term D

QDIF at the base: DIF bQ dA estimated by a residual, with the units 1 PW = 1×1015

W.

FIG. 5. Inferred eddy coefficient vk (cm2s

-1) for the nine climatologies (plotted in colors),

Richardson-number-dependent eddy coefficient using daily TAO/TRITON moorings’

observations (black lines with triples) and the referenced mean vk from literatures (black

labels).

39

FIG. 6. Long-term-mean observations of TAO/TRITON mooring at western equatorial

Pacific 165ºE. (a), Seasonal variability of temperature (ºC) from surface to the 200m depth.

Note that the dashed black line represents the pool-averaged 28ºC isotherm and solid black is

the 28ºC isotherm of the local mooring; (b), depth dependent zonal velocity u (cms-1

); (c),

buoyancy frequency calculated by temperature, 2 g TN

T z

(s

-2); (d), magnitude of the

velocity shear: 2 2( ) ( )u v

z z

(cm

2s

-2); (e) the seasonal eddy coefficient vk (cm

2s

-1) derived

from the Richardson number ( iR ).

FIG. 7. (a) Monthly evolution of the net surface heat flux at equatorial 165ºE, the direct

TAO/TRITON observations versus the eight climatologies from August 2006 to August 2007,

(b), Mean differences of QNET (Wm-2

) between the TAO/TRITON and the eight climatologies.

FIG. 8. (a), The constructed seasonal QNET (unit: Wm-2

) over the WPWP by the quantification

of pseudo-heat content changes (term A), solar radiation penetration (term C) and bottom

diffusive heat flux (term D). The shaded error bars show the calculation errors arise from

WOA09, TAO/TRITON errors and solar radiation penetration uncertainties from nine heat

flux data sets; (b), Annual mean difference between the QNET (Wm-2

) of the nine

climatologies and the constructed QNET, and the error bars represent the seasonal deviations.

40

TAB. 1. Key features of the nine global gridded surface heat flux climatologies.

Category Acronym Location Spatial resolution Temporal resolution

and duration

References

Analysis

OAFlux

+ISCCP

WHOI

NASA/GISS

1º×1º

2.5°×2.5º

Daily, 1958 to present

3-hourly, 1984 to 2009

Yu et al., 2007, 2008

Zhang et al., 2004

NOCSv2.0 NOC 1º×1º Monthly, 1973 to present Berry and Kent, 2009

CORE.2 NCAR 1º×1º Monthly, 1949 to 2006

Large and Yeager,

2008

First-

generation

Reanalysis

NCEP 1 NCEP 1.875º×1.875º 6-hourly, 1948 to present Kalnay et al., 1996

NCEP 2 NCEP 1.875º×1.875º 6-hourly, 1979 to present Kanamitsu et al., 2002

ERA-40 ECMWF 1.125º×1.125º 6-hourly, 1957 to 2002 Uppala et al., 2005

Latest

Reanalysis

CFSR NCEP 0.5 º×0.5º Hourly, 1979 – 2009 Saha et al., 2010

MERRA NASA/GMAO 0.5º (lat)

× 0.667º (long) 6-hourly, 1979 onward

Bosilovich et al., 2007

Rienecker et al., 2010

ERA-Interim ECMWF 0.7°×0.7º 3-hourly, 1989 onward Dee and Uppala, 2009

41

TAB. 2. Mean averages of SW, LW, LHF, SHF, QNET (Wm-2

) over the WPWP bounded by

the 28°C isotherm plus QNET over the global ice-free oceans. The global means are the area-

weighted means based on the same land-sea mask. The top four products are the high net heat

flux group and the bottom five products are the low net heat flux group.

Acronym SW

WPWP

LW

WPWP

LHF

WPWP

SHF

WPWP

QNET

WPWP

QNET

Global

CFSR 250 -56 -134 -6 54 15

MERRA 226 -58 -115 -8 45 22

NOCSv2.0 226 -41 -130 -10 45 25

OAFlux+ISCCP 229 -53 -118 -8 50 30

CORE.2 216 -51 -135 -11 19 4

ERA-40 292 -69 -195 -13 15 7

ERA-Interim 217 -51 -133 -12 21 11

NCEP 1 197 -50 -120 -9 18 1

NCEP 2 208 -48 -136 -5 19 4

42

TAB. 3. Numbers of the residual heat diffusivity (QDIF, term D) from Eq. (1) and its STDs

(the first and second column), inferred vertical eddy coefficients from the heat budget balance

(the third column), the QNET differences between the nine climatologies and the in situ

observation (the fifth and sixth column) and pool integrated method (the seventh and eighth

column). Numbers in the parentheses represent the mean values in those months when the

heat diffusivity is down-gradient.

Acronym QDIF (Wm-2) STD (Wm-2)

vk (cm2s-1)

One-

point

comparis

on QNET

Differenc

e (Wm-2)

STD

(Wm-2)

Pool-

Integrate

d QNET

Differenc

e (Wm-2)

STD

(Wm-2)

CFSR -36 6 4.3 34 15 27 6

MERRA -29 5 3.4 8 17 18 5

NOCSv2.0 -29 6 3.4 -30 41 18 5

OAFlux+ISCCP -33 5 4.0 6 13 22 4

CORE.2 -5 (-7) 5 0.6 (0.8) -33 6 -6 4

ERA-40 7 (-4) 7 -0.8 (0.5) -12 7

ERA-Interim -5 (-7) 4 0.6 (0.8) -4 13 -6 4

NCEP 1 -4 (-9) 7 0.5 (1.1) -1 16 -9 7

NCEP 2 -4 (-7) 5 0.5 (0.8) -2 32 -8 6

1717

17

17

17

17

1717

17 1

7

17

17

17

17

1717

90oE 120

oE 150

oE 180

oW 150

oW 120

oW

24oS

12oS

0o

12oN

24oN

(a) QNET

and STDWm

−2

−100

−50

0

50

100

28

2828

28

2828 2

8

28

2828

28

2929

2929

29

90oE 120

oE 150

oE 180

oW 150

oW 120

oW

24oS

12oS

0o

12oN

24oN

(b) SSToC

18

20

22

24

26

28

30

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

>0

(a) January

Qnet

<0

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

>0

(b) February

Qnet

<0

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

>0

Qnet

<0

(c) March

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

<0

Qnet

>0

(d) April

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

<0

Qnet

>0

(e) May

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

<0

(f) June

Qnet

>0

CFSR OAFlux+ISCCP NOCSv2.0 MERRA

ERA−Interim CORE.2 NCEP 2 NCEP 1

ERA−40 TAO Pool Boundary WOA09

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

(a) July

Qnet

<0

Qnet

>0

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

(b) August

Qnet

<0

Qnet

>0

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

<0

Qnet

>0

Qnet

<0

(c) September

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

>0

Qnet

<0

(d) October

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

>0

(e) November

Qnet

<0

120oE 160

oE 160

oW 120

oW 80

oW

50oS

25oS

0o

25oN

50oN

Qnet

>0

(f) December

Qnet

<0

CFSR OAFlux+ISCCP NOCSv2.0 MERRA

ERA−Interim CORE.2 NCEP 2 NCEP 1

ERA−40 TAO Pool Boundary WOA09

J F M A M J J A S O N D

0

20

40

60W

m2

Month

(a) QNET

J F M A M J J A S O N D

200

250

300

Wm

2

Month

(b) SW

J F M A M J J A S O N D

−70

−60

−50

−40

Wm

2

Month

(c) LW

J F M A M J J A S O N D

−200

−180

−160

−140

−120

−100

Wm

2

Month

(d) LHF

J F M A M J J A S O N D

−14

−12

−10

−8

−6

−4

Wm

2

Month

(e) SHF

0 2 4 6 8 10 120

0.2

0.4

0.6

CFSR OAFlux+ISCCP

NOCSv2.0 MERRA

ERA−Interim CORE.2

NCEP 2 NCEP 1

ERA−40

J F M A M J J A S O N D−0.3

−0.2

−0.1

0

0.1

0.2

0.3P

W

Month

(a)

Term A

Left Part of Term A

Right Part of Term A

J F M A M J J A S O N D

0

0.5

1

1.5

2

(b)

PW

Month

J F M A M J J A S O N D−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

(c)

PW

MonthJ F M A M J J A S O N D

−1

−0.5

0

0.5

(d)

PW

Month

CFSR OAFlux+ISCCP

NOCSv2.0 MERRA

ERA−Interim CORE.2

NCEP 2 NCEP 1

ERA−40

J F M A M J J A S O N D−2

−1

0

1

2

3

4

5

cm

2s−

1

Month

Eddy Coefficient Kv

CFSR

OAFlux+ISCCP

NOCSv2.0

MERRA

ERA−Interim

CORE.2

NCEP 2

NCEP 1

ERA−40

TAO165oE

TAO156oE

TAO147oE

Gregg (1976)

Osborn and Bilodeau (1980)

Kanari et al. (1992)

Schneider and Bhatt (2000)

Sriver et al. (2010)

Dep

th (

m)

(e) Eddy Diffusivity

J F M A M J J A S O N D

−150

−100

−50

0

1

2

3

4

5

Dep

th (

m)

(d) Velocity Shear

J F M A M J J A S O N D

−150

−100

−50

0

1

2

3

4

5

Dep

th (

m)

(c) Buoyancy Frequency

J F M A M J J A S O N D

−150

−100

−50

0

0.02

0.04

0.06

Dep

th (

m)

(a) Temperature

J F M A M J J A S O N D−200

−150

−100

−50

20

25

30

Dep

th (

m)

(b) Zonal Velocity

J F M A M J J A S O N D−200

−150

−100

−50

−50

−25

0

25

50

Aug−06 Oct−06 Dec−06 Feb−07 Apr−07 Jun−07 Aug−07−60

−40

−20

0

20

40

60

80

100

120

Month−Year

(a)

CFSR

OAFlux

NOCSv2.0

MERRA

TAO/TRITON

ERA−Interim

CORE.2

NCEP 2

NCEP 1

1 2 3 4 5 6 7 8−65

−55

−45

−35

−25

−15

−5

5

15

25

35

45

55

65

1 CFSR

2 OAFlux + ISCCP

3 NOCSv2.0

4 MERRA

5 ERA−Interim

6 CORE.2

7 NCEP 2

8 NCEP 1

Heat Flux Products

(b)

J F M A M J J A S O N D−10

0

10

20

30

40

50

60

(a)

1 2 3 4 5 6 7 8 9 10 11−20

−10

0

10

20

30

40

(b)

1 CFSR 2 OAFlux+SRB3 OAFlux+ISCCP4 NOCSv2.05 MERRA6 OAFlux+CERES7 ERA−Interim8 CORE.29 NCEP 210 NCEP 111 ERA−40