JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL.
93, NO. Cll,
PAGES
14,005-14,012, NOVEMBER
15, 1988
A New Method for Estimating the Turbulent Heat Flux at the Bottom
of the Daily Mixed Layer
SHIROIMAWAKI,
1 PEARNP. NIILER,2 CATHERINE
H. GAUTIER,
2 DAVID HALPERN,
3 ROBERT
A. KNOX,2
WILLIAMG. LARGE,
4 DOUGLASS. LUTHER,
2 JAMESC. MCWILLIAMS,
4 JAMESN. MOUM,5
AND CLAYTON A. PAULSON5
A new method is presented for estimating the vertical turbulent heat flux at the bottom of the daily
mixed layer from the temperature data in the mixed layer and net solar irradiance data at the sea surface.
We assume that fluctuations in the divergence of advective heat flux have longer than daily time scales.
The method is applied to data from the eastern tropical Pacific, where the daily cycle in the temperature
field is confined to the upper 10-25 m. The night-to-day difference of the turbulent heat flux calculated
from the data obtained during nine daily cycles in November 1984 agrees well on average with the same
quantity estimated from microstructure observations. The night-to-day difference of the turbulent heat
flux, estimated at several mooring stations near the equator (an average over 100 to 300 daily cycles),
variesfrom 120 to 220 W/m 2 with larger valueson the equator. Equatorial turbulencemeasurements
show that the turbulent heat flux is much larger during nighttime than daytime. Therefore the present
estimatesgive approximately the nighttime average, which is the major part of the turbulent heat flux.
From the daytime heat budget we obtain divergence of the low-frequency horizontal heat advection at
1•30'S, 140-•W; it is governed by equatorial mesoscalefluctuations having a predominant period of 15-20
days.
Recent observations of the significant nighttime increase of
turbulent dissipation at 140:W longitude on the equator
[Gregg et al., 1985; Mourn and Caldwell, 1985] suggest that
the formation of the daily thermocline occurs during daytime
periods of weak turbulence and its erosion occurs during
nighttime periods of strong turbulence. Individual temperature
profiles should demonstrate this difference of the vertical
transport process. However, the time scale and amplitude of
these processesin the open ocean are comparable to the time
scales and amplitudes of random internal waves, and thus a
description of the daily heat budget or the night-to-day differencesin the temperature profiles requires a large data set. In
the Tropic Heat and Equatorial Pacific Ocean Climate Studies (EPOCS) programs [Eriksen, 1985; Hayes et al., 1986],
highly vertically resolved temperature time series of 6 months
and longer together with simultaneous surface heat flux estimatesmake sucha daily heat budgetstudy practicable.
During the sunlight hours, the upper 25-40 m of the ocean
is heated directly by solar radiation and cooled by latent and
sensibleheat fluxes and by longwave radiation. Near the equator a daily thermocline is established on most days because
heating is larger than cooling over a significant portion of the
afternoon. During nighttime the cooling persists,and so some
of the stored heat is given back to the atmosphere almost at
the same rate as during the daytime before. But because
strong turbulence is found at night, some of the stored heat
also mixes vertically. Therefore in a water column of fixed
thickness, the change in heat content from sunrise to sunset
less the change in heat content from sunset to sunrise should
•Geophysical
Institute,Kyoto University,Kyoto, Japan.
2Scripps
Institutionof Oceanography,
La Jolla,California.
3jet PropulsionLaboratory,Pasadena,California.
•National Centerfor AtmosphericResearch,Boulder,Colorado.
5Collegeof Oceanography,
OregonStateUniversity,Corvallis.
Copyright 1988 by the AmericanGeophysicalUnion.
Paper number 8C0334.
0148-0227/88/008 C-0334505.00
reflect, principally, the sum of the shortwave radiation absorbed in the column during daytime and the heat transported
out of the bottom of the column during nighttime. Such a
simple balance, of course, assumesthat persistent and significant night-to-day differencesin divergenceof advection or surface cooling do not occur (we show later that night-to-day
differencesin surfacecooling rates are not significant). It is the
purpose of this paper to demonstrate, from observations of
ensemble averages of daily heat content changes and surface
radiation budgets, that the upper 25 m of broad areas of the
equatorial Pacific loses significantly more heat during nighttime than during daytime. Becauseno significant night-to-day
bias is found in atmosphericcooling, the implication is that an
increase of nighttime mixing occurs over broad areas of the
equatorial Pacific in all seasons.This phenomenon was discovered by detailed turbulence measurements over a few days
at 140øW.
2.
METHOD
The equations governing the conservation of heat in the
daily mixed layer during daytime and nighttime are
i.•tD -- QSO1
-- D -- Qsurf
-- D -- (Jadv
D -- Qturb
o
(1)
i•t N -- -- Qsurf
- N - (Jadv
N -- (Jturb
N
(2)
respectively (see Figure 1). Here H is the heat content of a
water
column
with
a unit area and constant
thickness
h and is
calculated
fromH = •_høpcrdz,wherepc is thespecific
heat
capacity per unit volume, T is the temperature, and z is the
vertical coordinate. The subscript t denotes the local rate of
change in time. Qsolis the net solar irradiance (heating) at the
sea surface,and Qsurfis the surfacecooling term, which consists of the net outgoing longwave radiation, latent heat flux,
and sensibleheat flux. The principal component to Qadvis
expectedto be the vertically integrated divergenceof advective
heat flux in the horizontal direction' Qturbis the vertical turbulent heat flux at the bottom of the column. The divergence of
horizontal turbulent heat flux as well as the divergence of
vertical advective heat flux are both additional components of
14,005
14,006
IMAWAKIETAL.' NEW METHODFORTURBULENT
HEATFLUX ESTIMATION
DAYTIME
Osolar
NIGHTTIME
litI ¸surf
I Qsurf
dv
adv
I
I
Fig. 1.
depthit is 30 W/m2 at noon and 240 W/m2 at midnight.
Thereforewe anticipatethat the night-to-day differenceof the
turbulentheat flux is almostequalto the nighttimeaverage,or
Ht
Qturb
Direct measurementsof turbulent activity and estimatesof
turbulentflux near the equatorat 140øW[Gregget al., 1985]
show that the turbulent heat flux in the upper layer is much
larger during night than during the day. For example,at 25-m
Qturb
Schematicdiagram of heat balancein the daily mixed layer
during {left)daytime and (right) nighttime.
the major contribution to this flux.
With the assumptionthat the divergenceof advectiveheat
flux varieswith a time scalemuchlongerthan the daily cycle,
the daily meandivergence
of advectiveheat flux (Q•av)is estimated by
(Jadv
-- -- I-•tD-I-C)sol
D-- (Jsurf
D
(4)
Here we neglect the turbulent heat flux during daytime appearing in the right-hand side of (1) becauseit is much smaller
than other terms(or any sum terms).The divergenceof advec-
tive heat flux is related to the spatial mean velocity(u, v, w)
gradient(Tx, T.v,T•)as
the divergence
of advective
heatflux (Qaav).
Expressions andtemperature
and Q'• meanthe daytime(from0600 through1800local
Qadv--pC (urx + vTy+ wT0 dz + horizontaldiffusion
meantime) averageand the nighttime(from 1800through
h
0600thenextmorning)averageof Q, respectively.
In the presentpaper,we are interested
in the daily cycle,
(5)
andin thebeginning,
we assume
that the divergence
of advective heat flux varieswith a time scalemuchlongerthan the In the present case, the divergenceof vertical advective heat
to be smallbecause
the bottomof the layer
daily cycle; the average divergenceof advectiveheat flux flux is considered
is closeto the sea surface,vertical velocity is small, and the
((jaav
N)duringnighttime
is assumed
to beequalto that(Qadv)
-o
duringdaytime.Of course,internalwavesdo advectheat,but
their contributionto the day-to-nightdifferencesin the divergenceshouldaverageout over severaldaily cycles.There is a
daily accelerationof currentsin the upper oceanas stratificationbuildsup duringthe day in the surfacelayer and momentum flux from the wind becomes distributed over shallow-
vertical gradient of temperatureis also small in the layer.
Horizontal "diffusion"is due to those spaceand time scales
which are not resolved.Here we simply neglectthis contri-
bution. Therefore an approximation to (5) is
Q•av= Apch(uTx
+ vTy)
(6)
er mixedlayerdepths.We havetriedto computethe night-to- wherethe horizontalvelocitiesand temperaturegradientsare
day differencein the divergenceof north-south advection of
estimated at 10-m depth, h is 25 m, and A is a coefficientof
heat on 150-kmspatialscaleand find it to be a very noisy order unity (to be determinedusinga least squaresmethod).
Sincewe do not totally resolvev in z and T in y, A is a
of
later that this assumptionmakessense.As we shall seelater, coefficientwhichmodelsreplacing(5) by (6). The divergence
signal.In our paper we assumeit to be small ab initio and find
the contributionof motionswith a time scaleof severaldays advectiveheat flux estimatedfrom the heat budget on the
right-hand side of (4) will be compared with that estimated
kinematically
from (6). Strong vertical velocities have been
will estimateit also.We proceed,however,with the assumption that thereis no night-to-daybiasin the divergence
of the measuredon the equator [Bryden and Brady, 1985] with a
to the divergenceof advectiveheat flux is important,and we
horizontaladvection.With this assumption,the subtractionof
mean over a seasonof about v½= 1 x 10-5 m/s, at 25-m
(2) from (1) gives
depth. The variations about the mean are the same size. Be-
/•,• -- /•,• : {j,o,• -- (Qsurf
- • -Q,u,•
- • )+ (C)turb
N- IC)turb (3)
cause a vertical temperature gradient builds up during the
daytime, the daytime average of the divergenceof vertical
advectionis about pch½• ø (about 20 W/m2). Again, this
The day-to-night
difference
(/7tD-/7t N)of thelocalheatcon- term is much smallerthan thosekept in (3) or (4)
tentchangeis givenby the verticalintegralof theday-to-night
difference
of temperature
change
as'pcI_hø(A
TD-- AT•) dz/At,
where A T• is the temperature differencebetween 0600 and
1800, A T• is the temperature difference between 1800 and
3.
DATA
Three general data sets from the Tropic Heat and EPOCS
0600thenextmorning,andAt isthetimedifference
of 0.5day. programs are used in this study. The air-sea interaction data
Therefore,using (3), measurements
of the temperature come from R/V Wecoma shipboard hourly observations of
changesin the upper layer, the net solar irradiance,and the bulk meteorological parameters and measurements of net
night-to-daydifferenceof the seasurfacecooling,we can esti- shortwave and longwave fluxes at (0ø, 140ø10'W) from Nomate the night-to-day differenceof turbulent heat flux at the vember 19 to December1, 1984 (Figure 2). Also, 15-min
baseof thelayer.From thelimitedhourlymeteorological
time averagetime seriesof wind,air temperature,
humidity,and sea
serieswe have near the equator at 140øW,it is found that the surfacetemperature(SST) were recordedat mooringstation
term {Jsurf
D-Qs,rf
-- N in (3) is not only small in comparison TH10 (1ø30'S, 140ø30'W) from December 1984 to June 1985
withQ-•ol
t•(seesection
4),butis alsosmallin comparison
with [Payne, 1988]. Latent and sensibleheat fluxes were estimated
the sum of all other estimated terms. So we assume this to be from theseobservations
by bulk methods(for methodology,
thecaseoverotherareasof theeasterntropicalPacific.
see Large and Pond [1982] for Wecoma observationsand Ste-
IMAWAKI ET AL.' NEW METHOD FORTURBULENTHEAT FLUX ESTIMATION
IOøN
•
I
•
•
a period from November 19 to December 1, 1984, from R/V
Wecoma. From these data the vertical profile of the daytime
and nighttime averageturbulent heat fluxesis estimatedin the
upper layer (0- to 100-m depth) for 12 days' the techniqueis
describedby J. N. Moum et al. (Processesin the equatorial
mixed layer, submitted to Journal of GeophysicalResearch,
•
_
-
140, WECOMA
125
I10
ß TH I0
©TH
II
_
iOoS
150 øW
Fig. 2.
--
I
140 ø
I
I
I;50 ø
120 ø
I
I10ø
I
14,007
1988,hereinafter,Moum et al., 1988).Daily valuesof
/•t N are alsocalculatedfrom hourly averagedprofiledata obtained by the RSVP. The RSVP station, or Wecoma station,
was about 1 n. mi (1.9 km) east of mooring station 140.
I00'
Locations of ship observation (R/V Wecoma) and mooring
4.
stations.
RESULTS
The turbulent heat flux at 25-m depth estimated from mooring station 140 temperaturedata and Wecomaheat flux obseryenson[1982] for mooring station THI0). At mooring station vations is first compared with that estimated from the RSVP
TH10 the net longwave budget was considered to vary only measurementsduring the period of November 19 to December
becauseof the change in humidity and SST, and it was esti- 1, 1984. Figure 3 shows vertical profiles of a half of the daymated by the bulk method [Stevenson,1982]; at the Wecoma time minus nighttime temperature change [(ATD --ATN)/2]
station it was directly measured by radiometers. The net from mooring station 140. This is equivalent to the average
hourly shortwave budget was measured directly at the amplitude of daytime and nighttime temperature changesbeWecoma station. The net shortwave budget was also com- cause the nighttime temperature change is usually negative,
puted from GOES 6 satellite irradianceson a daily basis at while the daytime value is positive. The individual daily promooring stations 140, 125, and THI0 [Gautier et al., 1986]; file variability is quite large, especiallybelow 20-m depth. This
the shortwave data were sampled on 14 x 14 km pixels and is probably due to the advection associated with highaveragedover 42 x 42 km2 areasaroundeachlocation.Com- frequency internal waves or small-scale fronts which exists
parison of Wecomadata with the remotely sensedshortwave even in the daily thermocline.The ensembleaverageover the
irradiance data at station 140 over a 12-day average yields a observation of 10 daily cycles, however, yields a significant
-6 W/m2 biasand a 12 W/m2 rmsdifference.
amplitude only in the upper 20- to 30-m layer. (The profile on
The temperature and velocity data come from vector year day 328 is excludedfrom the averagebecauseof its extreme value but is shown in Figure 3.) Below, the error of the
averaging current meters, or VACMs (for technique see Halpern [1987]), and temperature recorderson surfacemoorings mean is as large as the ensemblemean. We note that the
from various periodsin 1984 and 1985. Table 1 lists the moor- average depth of the surface mixed layer during nighttime
ing locations and periods of data used. Typically, data were observedby the RSVP is about 25 m (Moum et al., 1988).
recorded every 15 min on moorings and arithmetically
Figure 4 displays an intercomparisonof the time seriesof
averagedhourly values are used here. The nominal depths of several terms appearing in (3) during the Wecoma observaupper ocean temperature data are 1, 10, 25, and 45 m; cur- tions,computedfrom the mooringstationdata (sparsevertical
rents were measured at 10, 25 and 45 m. Moorings T44, T46,
samplingand continuoustime sampling)and the RSVP data
and T50 have additional temperature sensorsat 35-m depth. (continuousvertical samplingand sparsetime sampling).The
The velocity and temperaturedata usedin estimationof daily day-to-nightdifference
(/7tD-/7t •) of the local heat content
mean advective heat flux divergence were further processed change is calculated by the integration of the day-to-night
through a Godin filter with bandwidth of 71 hours [Godin, differenceof temperaturechangeshownin Figure 3 from the
1972] to eliminate the high-frequencyfluctuations, and were sea surfaceto 25-m depth. These separateestimatesagree very
subsampledonce a day. The daily cycleof advectionwas thus well except on year days 328 and 329, when the upper layer
also filtered.
temperaturesat mooring station 140 were unusually low at
The third data set was obtained from the rapid sampling sunset(328) and those at the RSVP station were unusually
vertical profiler, or RSVP [Caldwell et al., 1985]. Vertical pro- low at the next sunrise (329). A small-scalefront must have
files of temperature and turbulent dissipation rates were mea- existedbetween 140 and the RSVP station. Comparison of the
sured on the equator at 140ø10'W, 5-10 times in an hour over continuous profile estimatesfrom the RSVP with the discrete
TABLE
1.
Location and Duration of Temperature and Velocity Data From Mooring Stations
Station
Mooring
Program
TH10
THll
140
125
TH10
THll
T44
T40
T46
T50
T38
T42
T47
T51
Tropic Heat
Tropic Heat
EPOCS
EPOCS
EPOCS
EPOCS
EPOCS
EPOCS
EPOCS
EPOCS
110
Location
- lø30'N,
-3ø10'N,
-0ø02'N,
-0ø02'N,
-0ø01'N,
-0ø01'N,
0ø00'N,
0ø03'N,
0ø04'N,
0ø06'N,
140ø30'W
140ø23'W
140ø09'W
124ø33'W
124ø34'W
124ø35'W
109ø13'W
109ø51'W
110ø04'W
110ø01'W
Data Period
Dec. 6, 1984, to June 13, 1985
Dec. 9, 1984, to April 30, 1985
Oct. 26, 1984, to April 28, 1985
April 22 to Sept. 26, 1984
Oct. 20, 1984, to May 5, 1985
May 5 to Oct. 5, 1985
Nov. 2, 1983, to April 17, 1984
April 18 to Oct. 16, 1984
Oct. 17 to Nov. 29, 1984
May 9 to Sept. 17, 1985
14,008
IMAWAKI ET AL.' NEW METHOD FORTURBULENTHEAT FLUX ESTIMATION
sured on board R/V I'Vecoma. It is fairly steady with an
averageof 535 _+10 W/me over 11 days of daylighthours.
Also shown is the day-to-night difference of the turbulent and
longwaveheatfluxcomponents
throughthe seasurface,
-Q,,a •. The l 1-dailycycleaveragevalueof Q•a is quite
-"-
significant,havinga daytimeaverageof 135 + 14 W/m e, and
nighttimeaverageof 160 + 13 W/m:. However,its day-tonightdifferenceis small,havingan averageof -25 + 6 W/m :.
2O
From thesequantitieswe can now estimatethe night-to-day
difference
of theturbulentheatflux(•t,•t,• - •t•t,/9)(triangles
in Figure 4) using (3). An estimate over a single day does not
make sense because both weak negative and large positive
values occur, mostly due to the high-frequency fluctuation of
the day-to-night difference of the local heat content change.
Apparently, internal waves or small-scaleadvective features
are presentin the daily thermocline.The averageof (Q-t•t,
•
-D
-- Qturt,) averageover nine daily cyclesfrom mooringstation
- 0.5
0
TEMPERATURE
0.5
DIFFERENCE (øC)
140 is 131 + 74 W/m2; the averagefrom WecornaRSVP temperatureprofilesis 87 + 77 W/m 2.
during the 11 daily cyclesof Wecornaobservation. Solid lines are for
Estimatesof vertical heat flux due to turbulent mixing were
also made from RSVP dissipation measurements.The nighttime mean of the turbulent heat flux at 25-m depth is 112
individual daily profiles,and the dotted line is for the 10 daily cycle
average.The dashedline is the extremevalue omitted(year day 328).
W/m: on an averageover 9 daily cycles(with year days 328
and 329, excluded,and the daytimeone is 47 W/m :, the latter
Fig. 3. Vertical profilesof a half of the daytime minus nighttime
temperaturechange[(ATo -- ATN)/2] observedat mooringstation140
occurs mostly from 0600 to 1000 local time (Moum et al.,
1988). Therefore the night-to-day difference of the turbulent
profile estimatesfrom the mooring data, showsthat the mooring data at discretedepthsare adequatefor the presentanaly-
heat flux is 65 W/m e. The aboveestimatesbasedon the heat
sis. The day-to-night difference of the local heat content
change averaged over nine daily cycles(with the 328 and 329
with this value within
budget from temperature and net solar irradiance data agree
estimated
errors.
A similar analysis is now done at the mooring stations in
year daysexcluded)is 691 _ 81 W/m 2 from the mooringdata the easterntropical Pacific, which have sufficientresolution of
and 644 -i- 87 W/m2 from the RSVP data.If all 11 dailycycles temperature in the upper ocean. Here the day-to-night differ-
are included,the mooring data yields 592 q- 137 W/m 2 and
the RSVP yields670 -i- 127W/m e.
Figure4 alsodisplaysthe net solarirradiance(•so•/9)
mea-
ence(Q•a
-Q•,•
) of the net surfaceheat flux is neglected
everywhere,becauseit is small where the data exist to estimate
this quantity. Figure 5 showsthe time seriesof daytime mean
--
D
(Qsua)andnighttimemean(Q,•a•) of thenetsurface
heatflux
1500
I
I
I
I
I
I
I
I
I
I
I
I
I
I
at mooring station TH10. Fluctuations of these two are
strongly correlated, having a correlation coefficient of 0.92.
The day-to-nightdifferenceis very small;it is --6 W/m: on
an averagewith the rmsfluctuationof 23 W/m :.
0
The monthly ensembleaveragesof a half of the daytime
I000
4OO
E
5OO
300
ß,
0
.
j
':'i
2OO
--
ß
I00
_
500'
5,?.5
330
YEAR
Fig. 4.
335
DAY OF 1984
Heat budget estimated during the I'Vecomaobservation.
Theday-to-night
difference
(/•tD-/•t N,dots)of thelocalheatcontent
change,
thenetsolarirradiance(•so•D,solidline),andtheday-to-night
difference
({]surf
a - {].•,aN,dashedline)of thenetsurface
heatfluxare
shown.The trianglesare the night-to-daydifference
(•tu•bs- •tu•ba)
50
I00
150
YEAR DAY OF 1985
of the turbulent heat flux calculatedfrom thesequantities (solid symbols are from meeting station data). Open circlesare the day-to-night
difference of the local heat content change calculated from the RSVP
-- D, top solid line), and
Fig. 5. Time seriesof daytimemean Qsua
nighttimemean (Q.•ua, dottedline) of the net surfaceheat flux at
mooringstationTH10, and also their difference(Q•ua
- a -- Q•ua
- s,
data.
bottom solid line).
--
N
IMAWAKIET AL.' NEW METHOD FORTURBULENTHEAT FLUX ESTIMATION
TH I0
140
included in the November 1984 value at mooring station 140
(Figure 6a). At 140øW (Figure 6a) the daily fluctuation of
temperature is restricted to the upper 25-m layer on average,
and the amplitude of sea surface(1-m depth) temperaturefluctuation is 0.2ø-0.4øC. (Resultsfrom mooring station TH11 are
not shown here becausethe sea surface temperature data are
missing,but amplitudes at 10-m and 25-m depths are similar
in amplitude to those at mooring stations 140 and TH10.)
Moving to the east, the situation becomes different. At 110øW
(Figure 6c) there seemsto be a seasonalchange of the upper
ocean temperature cycle. In January through April, the daily
fluctuation does not penetrates deeper than 10-m depth and
the amplitude of the sea surface temperature is as large as
0.7ø-0.8øCßthis is the period of warming sea surface temperature and weakening wind. In July through October, wind
strength increases,the daily cycle penetrate deeper than 10-m
depth, and the sea surface temperature change is reduced to
0.2ø-0.5øC. At 110øW the fluctuations at 25-m depth, which
are reflected in the estimated errors, are larger than these at
0.6
0.4
.,.-..,. 0.2
lorn
n,- 0.4
•
0.2
uJ
0
n
0.4
•-
0.2
25m
•
-O2
ii
12
i
2
1984
3
121
4
-
2545
1984
1985
1985
Fig. 6a
125
0.6
Jm
140øW because at 110øW
0.2
o
I I
0
I
• I
I
I
25m
0.2
--0.2
•
I
I
I
I
i
I
I
I
I
I
I
I
I
II
12
I
2
•
4
5
6
7
8
9
I
56789
1985
1984
Fig. 6b
II0
io
Jrn
0.8
0.6
0.4
0.2
o
10rn
0.4
I
o
0.4_
0.2-
defined
0
-0.2
-0.4
I
II
I I
12 I
1983
I
2
I
3
I
4
I
5
I
6
I
7
I
8
I
9
I
I0
I
II
I
I
56789
I
I
1985
1984
Fig. 6c
Fig. 6. The monthly mean of a half of the daytime minus nighttime temperaturechange[(,&To - ,&TN)/2
] observedat three depths(1,
10, and 25 m) at mooring stations (a) 140 and TH10, (b) 125, and (c)
110 (see Figure 2 for locations).The bars are the errors of the mean.
The abscissa is time in months
from
the main
thermocline
is closer to the
surface, and internal waves are larger at a shallower depth. It
is interesting to note that a warming of the deeper levels at
night occurs both at 125øW and 110øW (Figures 6b and 6c)
when maximum heating occurs during the day in the upper
layers. This could conceivably be explained by the coincidence
that the sensorswere in that part of the upper layers which
were warmed at night by vertical mixing.
The monthly mean day-to-night differenceof the local heat
content change is calculated from the temperature change difference to 25 m (Figure 6) and is shown in Figure 7. Results
are not shown for mooring station 110, partly because it is
apparent that vertical resolution of the temperature data
available is not sufficient to resolve the shallower daily cycle,
and partly becausethe net solar irradiance data are not available at that longitude. In Figure 7 the monthly mean net solar
irradiance, as estimated from satellite data, is also shown. It is
quite uniform in time and spaceover the moored array.
From these two quantities we calculate the monthly mean
night-to-day difference of the turbulent heat flux at the bottom
of the layer by use of (3), neglecting the net surface heat flux
terms. At mooring station 125, even monthly ensemble means
fluctuate, mostly owing to the large temperature fluctuation at
the sea surface (Figure 6b)' there a seasonal signal is not evident in the present data. The record length averages of the
terms in (3) are tabulated in Table 2. A 6-month mean is well
I I I
0.4
0.4
14,009
1983 to 1985.
minus nighttime temperature changes at the upper three
depths(1, 10,and 25 m) are shownin Figure6 (theva]ues
which lie outside 3 standard deviationsof the original data set
are excluded).The data during the Wecoma observationsare
at each station
because the error
of the mean is much
smaller than the mean. The night-to-day difference of the turbulent heat flux is smaller at mooring station TH10, which is
off the equator, than at equatorial stations. We resist the
temptation to infer a quantitative seasonalcycle, based on less
than 2 years of data. Nevertheless,it is suggestedqualitatively
and might be resolved with longer records especially at
110øW.
The daily mean divergenceof advective heat flux (Qadv)is
calculated at mooring station TH10 (at 1ø30'S)by use of the
heat budget equation (4), and its components are shown in
Figure8a neglecting
about50 W/m2 for Qt,rbD.The dailydata
are smoothed by a Gaussian three-point filter with weights
(0.25-0.5-0.25) to emphasize the lower-frequency fluctuations.
The largest contribution is due to the heat storage change.
The divergenceof heat advection has a predominant period of
15-20 days from the beginning of the observation to year day
75. This is primarily north to south movement of the edge of
14,010
IMAWAKI ET AL.' NEW METHOD FORTURBULENTHEAT FLUX ESTIMATION
140
125
TH I0
I000
IOOO
8OO
8oo
6OO
600
4OO
400
200
2OO
2
1984
3
4
12
1985
1984
I
2
3
4
5
7
1985
8
9
I
II
12
I I • I I• I I I I
I
1984
2
3
4
5
6
7
8
9
1985
Fig. 7a
Fig. 7b
Fig. 7. Monthlymeanheat budgetestimatedat mooringstations(a) 140 and THI0 and (b) 125.The day-to-night
difference
(I7tD- iqtN, opencircles)of the localheatcontentchange,the net solarirradiance
- D, solid line), and the
(Qsol
night-to-day
difference
(qturb
N-- (•turb
D,crosses)
of theturbulentheatfluxareshown.The barsaretheerrorsof themean.
The abscissa is time in months from 1984 to 1985.
5.
DISCUSSION
the cold pool and is related to the equatorial mesoscalefluctuation, which is clearly seen in satellite AVHRR sea surface
It should be noted that in the presentheat budget estimates,
temperature data [Legeckis, 1977] and moored current meter only relative accuraciesof temperature measurementsare redata [Philander et al., 1985].
quired; systematicbias errors in temperature sensorsdo not
The part of the divergenceof advectiveheat flux associated causean error in estimationof the local heat contentchange.
withthemeridional
velocity,ApchvTy,
is estimated
fromdaily The estimated error tSH is proportioned to the calibration
velocity data at 10-m depth at mooring station THI0 and
error7 (in per cent)of sensorsensitivity;
namely,tSH= 7(/•tD
from daily temperaturedata at 10-m depth at mooringsta- -/•tN). Thereforetemperature
sensors
havinga 5% accuracy
tions 140 and TH11 (Figure 8b). The divergenceof advective giveusableestimates
(with an error of 35 W/m2) of the day-toheat flux (Qadv)(Figure 8a) estimated as a residual of heat night difference of the local heat content change (provided
budget(equation(4)) and this divergenceof meridionaladvec- that the true valueis some700 W/m2).
tive flux (ApchvT•.)
are correlatedvery well with eachother
The most important issue about the accuracy of the tech(correlationcoefficient0.72). The least squareregressiongives nique is the vertical resolution and number of daily cycles
A of 1.3,whichindicates
possible
underestimation
of Ty,from averaged. Let N temperature sensors be deployed evenly
moorings 3ø apart. The record length average of the diver- throughout the layer of thickness h, each sensor have a
gence of advective heat flux estimated from (4) is 53 + 33 measurementaccuracy of s(øC),and averagesbe made over M
W/m2.The recordlengthaverageof dailymeandivergence
of
daily cycles; then the random error tSH in the estimate of the
day-to-night difference of the local heat content change is
data and (6) is 48 _+24 W/m2. It comeslargelyfrom the south- given by
ward flowing mean meridional velocity t5and the southward
(6)x/2pchs
increasing
mean temperature
gradient•; Apcht• = 61
At(NM) •/2
W/m 2. At this longitude it appears that the excessheat at
meridional
advective heat flux estimated from current meter
1ø30'S is transferred away from the equator by the mean
southward flow. The divergence of the eddy heat flux is a
smaller quantity.
TABLE 2.
Number
Station
140
TH10
125
125
Note that if the depth is doubled, four times the number of
sensorsare required to keep the error the same.For h = 25 m,
as in the presentcase,tSH= [4.85 x 103t•/(NH)
•/2] W/m2.
Average Heat Budget
of
Observation
Period
Cycles
•,D __•,N
0sol
o
0turb
m -- 0turb
o
Oct. 1984to April 1985
Dec. 1984 to June 1985
April-Sept. 1984
Oct. 1984to Oct. 1985
178
185
145
331
705 -+ 32
638 -+ 25
728 _+53
674 -+ 26
523 -+ 4
519 _+4
510 +_4
513 _+4
181 _+32 (149-213)
119 _+25 (94-144)
218 _+53 (165-271)
161 _+26 (135-187)
Values are given as mean _ error in wattsper squaremeter. Rangesin parenthesesare mean + error
to mean
-
error.
IMAWAKI
ETAL.'NEWMETHOD
FORTURBULENT
HEATFLUXESTIMATION
14,011
--D
Qsol
5OO
--D
Qsurf
• ; ..,;2•,
, ',,•""•,•
Qadv
I
I
-20
I
I
I
0
I
I
I
I
I
I
20
I
I
I
I
I
40
I
I
I
60
I
I
80
I
I
I
I
I00
I
I
I
,
120
!III80
IIIII00
IIII120
-500-20
0 2040i0
YEAR
YEAR DAY OF 1985
Fig. 8a
DAY OF 1985
Fig. 8b
Fig. 8. Timeseriesof dailymeandivergence
of advective
heatflux((Jaav)
at mooringstationTHi0, (a) showntogether
with components
from whichit is estimatedby useof the heatbudgetequation(4) and (b) shown(thesolidline)together
with thedivergence
of themeridionaladvective
heatflux(dottedline)estimated
directlyfromthe velocityandtemperature
data by use of (6).
Since the calibration errors of the VACM temperature sensors The present resultssuggestthat such a night-to-day difference
are 0.02øC (P. Bedard, personal communication, 1987) and of turbulence is prevalent over the entire eastern tropical Pa-
N - 3 in the presentcase,the estimatedaccuracyis 56 W/m 2
for daily estimatesand 10 W/m 2 for monthly averages.The
cific.
There is also a suggestionthat the estimated nighttime turbulent heat flux is a little larger on the equator (mooring
station 140) than at 1ø30'S (mooring station TH10). It might
be related to the strong vertical shear associated with the
South Equatorial Current and the Equatorial Undercurrent
the upper 25-m layer, the estimatederror is 20 W/m 2 for on the equator. Recently, Newell [1986] has suggestedthat E1
monthly averages,which is also reasonable.It should be kept Nifio conditions in the eastern Pacific can be caused by drain mind, however, that the actual estimatescontain large tem- matic changes of the upper ocean vertical turbulent fluxes
poral fluctuations due to high-frequency advective processes, (rather than horizontal heat advection). Our computations at
and the error due to those fluctuations is generally much 110øW lend credenceto this hypothesis as they suggesta sealarger than the error due to measurements.
sonal cycle in night-to-day differencesin the daily heat storage
In the present paper the solar irradiance is assumed to be and a concomitant changein vertical turbulent transports.
absorbed completely in the surface mixed layer (to 25-m
The most advantageouspoint of this method is that it does
depth), but actually some of it penetratesto deeper layers. We not require the net surfaceheat flux data, which requires sevdo not have the measurementsfrom which the water type at eral meteorological measurements at the sea surface. Only
the sites can be specified accurately, but 4-11% of the solar hourly-averaged upper layer temperature profiles are required
irradiance at the sea surfaceis expected to penetrate to 25 m twice a day (at 0600 and 1800 local time), as well as an accu(the estimate is based on the equation by Paulsonand Simpson rate estimate of the net solar shortwave flux at the sea surface.
[1977] and water classifications by $imonot and Le Treut
The former can be obtained more easily than the meteorologi[1986]). The net solar irradiance absorbed in the surfacelayer cal data, for example,by drifting or moored thermistor chains,
(shown in Table 2 and Figure 7) should be reduced by 4-11%,
provided that a sufficient number of sensors with adequate
latter seems satisfactory. The sensor number of three is the
minimum requirement for the present purpose and should be
increasedin future. For example, if a thermistor chain having
five sensorswith measured accuracy of 0.05øC is deployed in
whichresultsin a 20- to 60-W/m2 increasein the night-to-day accuraciesare installed in the daily thermocline. The latter can
difference
of the turbulent
heat flux.
The presentmethod dependsupon the assumptionthat significant and persistentday-to-night differencesof the advective
heat flux divergenceand the sea surfacecooling do not exist. If
internal wave activity has a day-to-night bias, then our inter-
pretationof (t/tø -/-•t N- •solD) as the increaseof nighttime
turbulence is flawed. The suggestionto view the moored array
data in this manner came, of course, from turbulence measurements during the Wecoma observationswhich showed significant night-to-day differencesin the turbulent dissipation activity [Moum and Caldwell, 1985]; in the Wecoma observa-
tions,two thirdsof the verticalflux occurredduringthe night.
be obtained
from routine
satellite
observations.
Acknowledgments. Judy Illeman and Jian-Hwa Hu prepared the
data sets. S. I. (Geophysical Institute of Kyoto University, Japan)
received support from the Tropic Heat research project while visiting
ScrippsInstitution of Oceanography. This work was supported by the
National Science Foundation, grants OCE-83-14402 and OCE8521510, and the National Oceanic and Atmospheric Administration,
EPOCS Program.
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'•
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