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The Southeast Pacific Warm Band and Double ITCZ
HIROHIKO MASUNAGA
Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan

TRISTAN S. L’ECUYER
Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado(Manuscript received 9 March 2009, in final form 11 August 2009)
ABSTRACTThe east Pacific double intertropical convergence zone (ITCZ) in austral fall is investigated with particularfocus on the growing processes of its Southern Hemisphere branch. Satellite measurements from the TropicalRainfall Measuring Mission (TRMM) and Quick Scatterometer (QuikSCAT) are analyzed to derive 8-yr
climatology from 2000 to 2007. The earliest sign of the south ITCZ emerges in sea surface temperature (SST)by January, followed by the gradual development of surface convergence and water vapor. The shallow
cumulus population starts growing to form the south ITCZ in February, a month earlier than vigorous deep
convection is organized into the south ITCZ. The key factors that give rise to the initial SST enhancement or
the southeast Pacific warm band are diagnosed by simple experiments. The experiments are designed to
calculate SST, making use of an ocean mixed layer ‘‘model’’ forced by surface heat fluxes, all of which arederived from satellite observations. It is found that the shortwave flux absorbed into the ocean mixed layer isthe primary driver of the southeast Pacific warm band. The warm band does not develop in boreal fall because
the shortwave flux is seasonally so small that it is overwhelmed by other negative fluxes, including the latent
heat and longwave fluxes. Clouds offset the net radiative flux by 10–15 W m22, which is large enough for thewarm band to develop in boreal fall if it were not for clouds reflecting shortwave radiation. Interannual
variability of the double ITCZ is also discussed in brief.

1. Introduction
The intertropical convergence zone (ITCZ) over theeast Pacific Ocean stays away from the equator by 58–108
latitude, and is only to its north most time of the year.
Many studies have investigated the possible origins of
this off-equatorial preference and meridional asymmetry. A high sea surface temperature (SST) may be a factor that is instrumental for the geographical constraint
on the ITCZ (Pike 1971), while other studies (Holton
et al. 1971; Waliser and Somerville 1994, and references
therein) attribute it to intrinsic atmospheric dynamics
rather than to the presence of warm ocean beneath. The
role of the underlying ocean, on the other hand, has been
considered as being crucial for explaining the absenceof the east Pacific ITCZ in the Southern Hemisphere.

Corresponding author address: Hirohiko Masunaga, Hydrospheric Atmospheric Research Center, Nagoya University,F3-1(200) Furocho, Chikusa-ku, Nagoya 458-0015, Japan.
E-mail: masunaga@hyarc.nagoya-u.ac.jp
DOI: 10.1175/2009JCLI3124.1
Ó 2010 American Meteorological Society

SST remains low in the southeast Pacific, arguably as
the result of an SST–wind–evaporation feedback (Xieand Philander 1994; Xie 1994), stratiform cloud decks(Mitchell and Wallace 1992; Philander et al. 1996), asymmetric coastline geometry (Philander et al. 1996), andother factors, including the seasonally varying solar forcing (Wang and Wang 1999).
A Southern Hemisphere branch of the ITCZ (hereafter ‘‘south ITCZ’’) often emerges from March to Aprilin the east Pacific, leading to a double ITCZ, together
with its Northern Hemisphere counterpart (hereafter thenorth ITCZ), as documented from time to time (Hubert
et al. 1969; Halpern and Hung 2001; Lietzke et al. 2001;
Zhang 2001; Gu et al. 2005). Aside from Zhang (2001),
who argued that SST could be a primary driver of the
double ITCZ, the physical processes that account for
how and why the south ITCZ develops have not been
explored extensively. It is reasonable to expect that themeridionally symmetric insolation in this particular season should create symmetric warm oceanic bands straddling the equatorial cold tongue (Mitchell and Wallace

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1992). This simple, intuitive hypothesis, however, is challenged by the fact that the south ITCZ is not observed at
all in the other equinoctial season. We have no satisfactory explanation to date for what promotes the eastern
Pacific ITCZ in austral fall and hampers it in boreal fall.
Solving this problem would help us understand not only
the transience of the south ITCZ, but potentially thestability of the north ITCZ as well.
In the present paper, the growing processes of theeastern Pacific south ITCZ are investigated from satellite observations. Data from a variety of satellite sensors,
including a microwave radiometer, radar, and a scatterometer are utilized to analyze SST, columnar water vapor(CWV), the surface convergence field, and shallow anddeep precipitating clouds (section 2). After the observed
climatology is outlined in section 3, the satellite datasets
are applied to evaluate the heat budget of the ocean
mixed layer (section 4). Section 5 is devoted to discussing
the factors that modulate mixed layer temperature variability. The present findings are concluded in section 6.

2. Data
It has been a decade since the Tropical Rainfall Measuring Mission (TRMM) satellite was launched in late1997, so TRMM now provides a long observational record that is suitable for climatological analysis. Shallow
and deep precipitating clouds can be distinguished using
TRMM Precipitation Radar (PR) echo-top height andVisible and Infrared Scanner (VIRS) infrared brightness temperature (IR Tb; Masunaga et al. 2005). Precipitating shallow cumulus is identified by rainfall witha PR echo-top height lower than 4 km. Cloud droplets
are undetectable by the PR, and therefore nonprecipitating low clouds are not included in the shallow category defined here. Masunaga et al. (2005) originallydefine the shallow category with an additional constraintof IR Tb . 265 K, which is not imposed in this study
in order to avoid missing shallow cumulus overcast by
higher-level clouds. Towering cloud systems, or ‘‘deep
stratiform’’ and ‘‘deep convective’’ systems combined
together in the Masunaga et al. (2005) terminology, aredelineated by PR echo tops that are higher than 4 km,
collocated with IR Tbs colder than 245 K. This infrared
threshold helps capture high cloud decks that would beleft undetected by the PR alone, given that the PR
sensitivity to ice condensates is marginal. The area coverage of shallow cumulus and towering clouds (hereafter
shallow cumulus coverage and deep storm coverage,
respectively) are used as the measure of convective activity for the individual cloud types.
SST and CWV are provided from the TRMM Microwave Imager (TMI) product created and distrib-

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uted by the Remote Sensing Systems. The near-surface
wind vector is provided from the Quick Scatterometer(QuikSCAT) SeaWinds level-3 daily gridded dataset.
The wind vector field is used for computing surface convergence and surface wind stress. The satellite datasets
are also applied to an ocean heat budget consideration
described later (section 4). SST and CWV are used forevaluating latent heat flux. The QuikSCAT wind constrains the latent heat and ocean upwelling fluxes. Surface
current data from the Ocean Surface Current Analysis–
Real time (OSCAR; Bonjean and Lagerloef 2002) are
employed to calculate the horizontal advection in theocean mixed layer. The OSCAR current is calculated
primarily from satellite altimeter and scatterometer products. Pentad time series of the filtered current velocity
is linearly interpolated in time to a daily data sequence.
The mixed layer depth is estimated with a variable density criterion using a dataset provided by de Boyer
Montégut et al. (2004). The World Ocean Atlas 2005
(WOA05; Locarnini et al. 2006) is adopted to estimate
the temperature difference between the mixed layer andupwelling water from beneath. Surface radiative fluxes
are provided by the Hydrologic Cycle and Earth Radiation Budget (HERB) product (L’Ecuyer and Stephens
2003; 2007; L’Ecuyer and McGarragh 2010), where theradiative fluxes are computed with the cloud and precipitation distribution observed from the TMI and VIRS
instruments aboard the TRMM. Methodologies for estimating the surface heat fluxes are described in the
appendix.
All satellite datasets are projected onto a common
18 3 18 global grid. The daily and monthly climatologies
of each parameter are then constructed from 8 yr ofobservation from 1 January 2000 to 31 December 2007.
El Niño Southern Oscillation (ENSO) is relatively moderate in amplitude during this period, so that no effort ismade to remove the ENSO components that might contaminate the climatological mean. Although the data are
available across the entire globe (except for high latitudes out of reach from the TRMM satellite), the target
area of the present work is limited to the tropical eastern
Pacific, zonally bound between 1508 and 758 or 858W.

3. Climatology of the east Pacific double ITCZThe observed characteristics of the east Pacific south
ITCZ are first illustrated as analyzed from the 8-yr climatology. Figure 1 shows the monthly mean SST, deepstorm coverage, and shallow cumulus coverage from
December to March. Consistently observed throughout
these months are the north ITCZ at 58–108N and thenortheastern edge of the South Pacific convergence zone
(SPCZ), in the bottom-left corner of each panel. The

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FIG. 1. Observed monthly climatologies of (left) SST (8C), (middle) deep storm coverage (%), and (right) shallow cumulus coverage(%) for 158S–158N, 1508–758W. SSTs of 248 and 278C are highlighted by thick contours. (top to bottom) Different rows show subsequentmonths from December to March.

south ITCZ is absent in December, with the exception ofa small area of warmer SST at 1008W. By January, thisarea has expanded into a band of warm water, hereafter
called the southeast Pacific warm band (or simply thewarm band), south of the equator, isolating the equatorial cold tongue from the cool water brought by the
Humboldt Current. However, shallow and deep clouds
do not show any corresponding pattern at this stage inthe evolution of the south ITCZ. The warm band keeps
growing through February, with a local SST maximum
developing around 58S, 908W. At the same time, shallow
cumulus begins to organize itself into the double ITCZ.
The 908W SST maximum extends westward and connects with the SPCZ in March, and the double ITCZ
finally becomes evident in deep storm coverage as wellas in shallow cumulus coverage.
Figure 2 illustrates the Hovmöller diagram, averaged
over 12.58–2.58S, of various parameters relevant to thesouth ITCZ. A steady sea surface warming is clearlyobserved from January through March in Fig. 2a, withthe rate of SST increase highest around 908W. The resultant ‘‘U’’-like pattern is also evident in the surface

convergence calculated from QuikSCAT wind (Fig. 2f).
The surface wind, which is divergent at the beginning,
becomes convergent near 908W at first, and then eventually across the entire tropical southeast Pacific. The
Hovmöller diagram of CWV (Fig. 2d) implies a gradual
but constant trend of moistening. The moistening results
solely from local evaporation initially as long as surface
convergence stays negative. The U pattern is again discernible in CWV, although it is not as well defined asthat observed in SST and convergence. The rapid moistening near 908W, once it starts to occur, implies thatmoisture convergence is now at work as the primary
driver of moistening, because the latent heat flux monotonically declines eastward with no 908W peak (Fig. 2e).
The tropical southeast Pacific is increasingly populated byshallow cumulus in February and March, while it is not
until March that deep storm coverage exhibits a systematic enhancement, as already seen in Fig. 1.
The parameters shown in Fig. 2 are projected together
on daily time series in terms of the regional mean overthe study area (12.58–2.58S, 1508–858W) in Fig. 3. SST
delineates a sinusoidal seasonal cycle, which is highest in

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FIG. 2. Hovmöller diagram of observed daily climatologies meridionally averaged over 12.58–2.58S. (a) SST (8C) with 248 and 278C
contours highlighted, (b) deep storm coverage (%), and (c) shallow cumulus coverage (%). (d) CWV (kg m22), (e) latent heat flux
(W m22), and (f) surface convergence (1026 s21) with negative values (i.e., diverging areas) unshaded.

late March or early April. Shallow cumulus and deepstorm coverage also vary seasonally but less sinusoidally
than SST. The period of enhanced shallow cumulus
population spans roughly a half-year from February to
July. Shallow cumulus coverage stays at the backgroundlevel of 0.3%–0.5% for the rest of the year. The periodof enhanced population does not last as long as 2 months
for deep clouds, and it shows a sharp rise and drop with
the narrow maximum in between. The background levelof deep storm coverage is nearly zero, indicating thatdeep convection is virtually absent, except when thesouth ITCZ is active. CWV and the surface convergencemaximize in late March, in phase with SST. Interestingly, surface convergence shares the overall variability
with shallow cumulus coverage, including the secondary
peak in late May or early June. This resemblance may

suggest the presence of a dynamical link between surface convergence and the development of precipitationin shallow cumulus. The latent heat flux does not bear
any apparent relevance to the south ITCZ in annual
cycle.
The climatological characteristics of the double ITCZ
are similar overall to that seen in past work (Halpern
and Hung 2001; Lietzke et al. 2001; Zhang 2001; Gu et al.
2005). Figures 1–3, however, illustrate some notableaspects of the south ITCZ that have not been studiedmuch before. First, a sign of the south ITCZ is visually
traceable in SST even in austral summer, when the south
ITCZ itself does not exist yet in terms of convergence
field and precipitating cloud coverage. The southeast
Pacific warm band steadily evolves for a few months
to follow, with the local SST maximum around 908W

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FIG. 3. Time series of observed daily climatologies regionally averaged over 12.58–2.58S, 1508–858W. (a) SST(8C; solid), deep storm coverage(%; dotted), and shallow cumulus coverage (%; dashed). (b) CWV (kg m22; solid),
latent heat flux (LHF; W m22; dotted), surface convergence (Conv; 1026 s21; dashed).

leading the rest. Second, surface convergence, CWV,
and shallow cumulus begin to form the south ITCZ
pattern one after another, followed ultimately by themature phase, which is marked with vigorous deep
convection. As such, the south ITCZ does not abruptly
manifest itself in austral fall, but instead undergoes aseries of evolutionary stages initiated in the precedingsummer.
The rest of this study is devoted to exploring the factors responsible for the observed SST variation in thetropical southeast Pacific, because the very initial sign ofthe south ITCZ seems to appear only in SST. To thisend, simple experiments to diagnose the heat budget ofthe ocean mixed layer are carried out in the following
section.

4. Diagnosis of SST controlling factors
In this section, the factors driving the southeast Pacificwarm band are sought by considering the individual
terms that contribute to the ocean heat budget. Results
are presented after a short description of experimental
setup.

a. Experimental setup
The heat budget of the ocean mixed layer may be
written as
rw H ml Cp,w

›T s
5Qadv 1Qupw 1QSW 1QLW›t
1QLH 1QSH ,(1)

where rw 5 1030 kg m23 is the ocean water density,
Hml the mixed layer depth, Cp,w 5 4.0 3 103 J kg21 K21
the specific heat of ocean water, Ts the SST, Qadv theheat transport by horizontal advection within the mixed
layer, Qupw the heat transport by upwelling through themixed layer bottom, QSW the shortwave energy flux
absorbed into the mixed layer, QLW the net longwave
flux at the surface, QLH the latent heat flux, and QSH thesensible heat flux. All Q terms are in watts per squared
meter. The eddy diffusion of heat has been neglected.
Each flux term in the RHS, except for QSH, is evaluatedfrom satellite observations. See the appendix for details
regarding the methodology for calculating each term in(1) with the exception of the sensible heat flux, which is

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TABLE 1. Experimental setup. See text for more detail.
Run

Austral fall experiment (initiated on 1 Nov)

Boreal fall experiment (initiated on 1 Jul)

Control
LW Y fixed

All fluxes are varied daily
F YLW is fixed at July

All fluxes are varied daily
F YLW is fixed at January

LW [ fixedSW fixed
LH fixed
ADV fixed
UpW fixed

F [LW is fixed at JulyQSW is fixed at JulyQLH is fixed at July
Qadv is fixed at July
Qupw is fixed at JulyF [LW is fixed at January
QSW is fixed at January
QLH is fixed at January
Qadv is fixed at January
Qupw is fixed at January

not important for tropical oceans and is given a constantvalue of 210 W m22.
Two sets of simple experiments are performed with(1), forced by satellite-derived heat fluxes. The first is an‘‘austral fall experiment,’’ where SST is initialized by theobserved climatology of 1 November. Equation (1) isthen integrated over time numerically at each 18 3 18
grid point. In the control run, all of the fluxes are varied
daily. Additional runs are conducted with one of thefluxes fixed at a ‘‘wrong’’ season, defined as the July climatology in this case, while the remaining terms arevaried daily as done for the control. Each of the flux
terms in (1) is ‘‘fixed’’ in turn, with the exception of
QSH, and the upwelling and downwelling components of
QLW, F [LW , and F YLW , are tested separately, resulting insix trials hereafter referred to as the LWY fixed, LW[
fixed, SW fixed, LH fixed, ADV fixed, and UpW fixedruns, as listed in Table 1. The second experiment is a‘‘boreal fall experiment,’’ which is identical to the austral fall experiment, except that the initial conditions are
initiated to 1 July and the ‘‘wrong’’ month fluxes are
fixed at their January climatologies.
These experiments are aimed at identifying the particular heat fluxes responsible for the southeast Pacificwarm band. The key factors controlling the warm bandmust be distinctly seasonal, because the south ITCZ
emerges only in austral fall and is suppressed for thereminder of the year. In the austral fall experiment, theflux terms critical for the development of the southeast
Pacific warm band may be inferred by the runs that failto reproduce the warm band under July conditions. These
fluxes should, in turn, lead to a spurious warm band in the
boreal fall experiment when forced by January conditions. The seasonal contrast in the individual flux terms
between January and July will be examined in section 5a.

b. Results
The control run of the austral fall experiment is firstcompared with the observation. Figure 4 presents monthly
mean SST for the first 3 months of the experiment. The
experiment overestimates SST across the tropical southeast Pacific, except in the equatorial cold tongue where

SST is largely underestimated. Given the simplicity of its
design, the current experiment is very limited in quantitative predictability and is by no means aimed at accurate forecasting of SST. In Fig. 4, nevertheless, theexperiment proves to have some ability to reasonably
reproduce the overall spatial pattern of SST. The estimated SST exhibits the southeast Pacific warm band as
observed. This result encourages us to proceed further
with the present analysis, provided the interpretation isrestricted to a qualitative assessment of SST.
Different runs of the austral fall experiment are shownin the Hovmöller diagram in Fig. 5. The U pattern isroughly captured in the control run, although it is somewhat washed out near its eastern edge by the contamination of the strong cold tongue. The overall result is notaltered when F YLW or F [LW is fixed at the July climatology(Figs. 5c,d). In contrast, replacing QSW with its July climatology results in a drastic change to SST (Fig. 5e)
where the warm band is completely absent. The LH
fixed run (Fig. 5f) yields little change to SST. The sea
surface warming near the eastern end of the Pacific almost
vanishes in the ADV and UpW fixed runs (Figs. 5g,h),
destroying the U shape in the Hovmöller diagram. The
advective and upwelling heat fluxes therefore havesome impact on the southeast Pacific warm band, although the impact is not as dramatic as the absorbed
shortwave flux.
Results from the boreal fall experiment are summarized in Fig. 6. Observed SST (Fig. 6a) shows no U pattern but only a monotonic eastward decline throughout
the 6 months studied. This is as expected from the factthat the south ITCZ is absent in boreal fall. The control
run (Fig. 6b) closely reproduces the observed SST for
the first 3 months. The first sign of the southeast Pacificwarm band appears in October in the control run a little
too early relative to the observations. The result is insensitive to a change to the longwave flux (F YLW andF [LW ) or to the latent heat flux as seen in Figs. 6c,d,f. It
is again the absorbed shortwave flux that totally alters
SST (Fig. 6e). The southeast Pacific SST rises quickly
to form into a U pattern, as if it were austral fall, when
QSW is prescribed with the January conditions. A vague

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FIG. 4. Observed monthly climatologies of SST (8C) for (a) November, (b) December, and (c) January. (d)–(f)Same as (a)–(c), but for estimated SST from the control run of the austral fall experiment. SSTs of 248 and 278C arehighlighted by thick contours.

resemblance of the U pattern is also seen in the ADV
fixed run.
Figure 7 illustrates the spatial distribution of SST estimated from different runs. In the austral fall experiment (left column), the southeast Pacific warm band isreproduced in all runs except the SW fixed one. All ofthese results are reversed in the boreal fall experiment(right column of Fig. 7). Only the SW fixed run allows asalient (but artificial) warm band to develop. The ADV
fixed run yields faint evidence of the southeast Pacificwarm band. All of the other runs from the boreal fallexperiment lack robust evidence for the warm band.
It is inferred from these results that the southeast
Pacific warm band is promoted or suppressed primarily
by the seasonal cycle of the absorbed shortwave flux.
The contribution of any other heat flux is negligible orat most secondary. Ocean advection is most dominantamong the secondary factors and may have some visible
impact.

5. Discussion
The analysis in section 4 focused on the temporal
evolution of SST in the tropical southeast Pacific. Discussed next is what determines the geographical structure of the southeast Pacific warm band, followed by theeffects of cloud shielding, interannual variability, andimplications for modeling studies.

a. Spatial structure of the warm band
Figure 8 is the regional map of the January mean heat
fluxes estimated by the control run from the austral fallexperiment. The total heat budget (Fig. 8a), or the RHSof (1) as a whole, for this month implies a warming tendency of the ocean surface everywhere outside the narrow equatorial cold tongue. The cold tongue is apparently
fed by the equatorial upwelling (Fig. 8f). To the south ofthe cold tongue, the total heat flux is about 60 W m22
around 1208W and gradually increases eastward until itreaches ;100 W m22 or larger off the South American
coast. This local enhancement of the total heat flux presumably explains the 908W maximum observed in thesoutheast Pacific warm band.
The absorbed shortwave flux (Fig. 8c) is by far largest in magnitude among the heat fluxes and accounts
for nearly all of the thermal energy absorbed into theocean mixed layer. All other fluxes primarily have cooling
effects that compete against the absorbed shortwave
heating. The absorbed shortwave flux shows a strong
meridional gradient, as expected from the seasonal solar
radiation, as well as a moderate zonal variability that iscaused by reflecting clouds and the westward-deepening
mixed layer. The latent heat flux (Fig. 8d) has a largescale zonal gradient, which is probably responsible forthe eastward increase in the total heat flux mentioned
earlier. The abrupt drop in the total heat flux at the very

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FIG. 5. Hovmöller diagrams of SST averaged over 12.58–2.58S from (a) observation and (b)–(h) different runs from the austral fallexperiment: (b) control, (c) LW Y fixed, (d) LW [ fixed, (e) SW fixed, (f) LH fixed, (g) ADV fixed, and (h) UpW fixed runs. SSTs of 248 and
278C are highlighted by thick contours. See section 4a for details on experimental setup.

eastern end of the ocean is ascribed to coastal upwelling.
Spatial inhomogeneity in Qadv in the vicinity of the equator is probably related to the tropical instability wave.
Figure 9 illustrates the July climatology of the surface
heat fluxes. The seasonal contrast between January andJuly is most prominent in the absorbed shortwave flux.
There are areas showing notable seasonal variation insome of the other fluxes, for example, well-known stratocumulus regions off the South American coast modulating QLW (Fig. 9b), but the amplitude of these variation(or difference between the July and January climatologies), which is ;50 W m22 at most, are much less thanthe overall changes in the total heat budget. This value islargely dominated by the absorbed shortwave flux, which
reduces by more than 100 W m22 from January to July inthe tropical southeast Pacific. As a result, the total heat
flux changes sign across the tropical southeast Pacific,
preventing the warm band from developing in this season.

In this study, sensitivity to the individual heat fluxes
is investigated without a possible linkage between different fluxes taken into account. Different flux terms,
however, are generally not independent of each other.
For instance, an enhanced solar flux would reinforce thewind blown into the convergence zone in response to anincrease of SST, resulting in a change of advective andlatent heat fluxes. An example was found in some coupled climate models (de Szoeke and Xie 2008), wherea northerly wind bias on the equator leads to a cold SST
bias there when the south ITCZ is too strong. The inclusion of such secondary effects in the sensitivity study
would possibly introduce additional impacts on themixed layer heat budget.

b. Cloud impact on the shortwave flux
Past studies (Mitchell and Wallace 1992; Philander
et al. 1996) argued that marine stratocumulus helps keep

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FIG. 6. Same as Fig. 5, but from the boreal fall experiment.

SST relatively low in the tropical southeast Pacific andthus is partially responsible for the meridional asymmetry of the ITCZ. Cloud impacts on the absorbed
shortwave flux are evaluated in this subsection. To thisend, a ‘‘clear-sky’’ run is performed using the cloud-free
shortwave and longwave fluxes provided by the HERB
dataset, which is calculated daily with all clouds removed. The run is initialized on 1 July, as done for theboreal fall experiment. The clear-sky run represents ahypothetical world where the shortwave penetrates down
to the ocean surface without being scattered by clouds
at all. The increase of insolation resulting from the absence of clouds is somewhat offset by a reduction of
downwelling longwave flux in the net heat budget.
Figure 10 shows southeast Pacific SST from the clearsky run together with the control run. It is evident thatthe southeast Pacific warm band would develop even inboreal summer and fall, although not as strong as theaustral fall event, if it were not for cloud-shielding effects. In a regional ocean–atmosphere model run by Xie

et al. (2007), the annual mean SST in the south ITCZ
area was found to increase by 28–38C if overlying clouds
were removed. As a result, this sea surface warming in
the absence of clouds gives rise to a warm band south ofthe equator as seen in the present result. It is noted thatcloud impacts on the radiative fluxes are not strongly
dependent on season but are more or less constantthroughout the year. Figure 11 demonstrates that theseasonal variation of QSW is virtually parallel between
the clear-sky (dotted) and control (solid) runs, differing
only by an offset of ;20 W m22 and day-to-day fluctuations. When the longwave contribution is subtracted
from the clear-sky QSW to delineate the net radiative
effect (dashed), the offset is reduced to 10–15 W m22
but is still consistent year-round. It follows that theseasonality of the southeast Pacific warm band is essentially driven by the annual cycle of insolation, withits magnitude reduced constantly by clouds, which peaks
from mid-October to late February for latitudes of thestudy area.

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FIG. 7. (left) January mean SST (8C) for (from top to bottom) the control, SW fixed, ADV
fixed, UpW fixed, LW Y fixed, LW [ fixed, and LH fixed runs from the austral fall experiment.
SSTs of 248 and 278C are highlighted by thick contours. (right) Same as left, but for September
mean SST for runs from the boreal fall experiment.

Figure 11 also shows QSW for the northeast Pacific
ITCZ (2.58–12.58N, 1508–808W). The magnitude of QSW
is smaller than in the southeast Pacific mainly because
the mixed layer is shallower north of the equator andtherefore absorbs less shortwave flux (see the appendix
and Fig. A2). The annual cycle of insolation is also slightly
weaker in amplitude in the Northern Hemisphere thanin the Southern Hemisphere because the earth passes
through the perihelion in austral summer in the presentday orbit. The reduction in QSW resulting from cloudshielding is more dramatic in the north ITCZ than in its
southern counterpart. In general, the north ITCZ is exposed to relatively moderate shortwave flux compared tothe south ITCZ. This result is somewhat counterintuitive,

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FIG. 8. January mean heat fluxes (W m22) estimated from the austral fall experiment (control run): (a) all fluxes summed together, (b)net surface longwave flux (QLW), (c) shortwave flux absorbed into the ocean mixed layer (QSW), (d) surface latent heat flux (QLH), (e)ocean advective heat flux (Qadv), and (f) ocean upwelling heat flux (Qupw). Positive (negative) values indicate warming (cooling) tendency.
Color shade is scaled as indicated. Contour interval is 10 W m22 except for negative fluxes in (a) and (f), where contours are omitted forclarity.

given that the total heat flux north of the equatorial cold
tongue stays positive in both summer and winter (seeFigs. 8 and 9). It is beyond the scope of the present study
to explore this problem, whereas it is potentially important in relevance to the persistence of the northeast Pacific ITCZ.

c. Dynamics of the growth of the south ITCZ
We have seen in section 3 that the growing processesof the south ITCZ involve a few distinct stages. The
emergence of the southeast Pacific warm band is followed by an increase in the population of shallow cumulus and eventually by the onset of vigorous deep
convection. The continuous development of surface convergence and moisture also accompanies the growth of
the south ITCZ. It is noteworthy that surface convergence starts rising much earlier than the onset of deep

convection. Liu and Xie (2002) pointed out that a weaksouth ITCZ is observed outside the period when the
double ITCZ is visible in deep convective clouds. They
attributed the weak ITCZ, without cumulus dynamics
involved, to the deceleration of surface wind in responseto an SST gradient flanking the southeast Pacific warmband. The moisture increase resulting from surface convergence and continuing sea surface warming would
generate thermodynamic conditions favoring moist convection in an area that is otherwise capped by the persistent trade inversion. The seasonal migration of solar
zenith angle makes QSW decline after March (Fig. 11).
This leads to the dissipation of the southeast Pacificwarm band, which disables the further maintenance ofthe south ITCZ.
A similar evolutionary sequence, that is, prior sea surface warming followed by tropospheric moistening and1200

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FIG. 9. Same as Fig. 8, but July mean heat fluxes estimated from the boreal fall experiment.

cloud deepening, is often documented in the context of
intraseasonal oscillations (Lin and Johnson 1996; Zhang
1996; Kiladis et al. 2005; Masunaga et al. 2006; Benedict
and Randall 2007). Because the south ITCZ is neither
oscillating nor propagating, wave dynamics do not account for its physical origins, but the resemblance is so
apparent that it may suggest that some generic processes
are common to the tropical oscillations and the south
ITCZ. For instance, shallow cumulus clouds developingon the leading edge of the Madden–Julian oscillation
arguably promote the moisture transfer from the boundary layer to the free troposphere, preconditioning a convective burst to come (Kemball-Cook and Weare 2001).
It is possible that the early increase of shallow cumulus
population may help to convectively activate the south
ITCZ as well.
A regional coupled ocean–atmosphere model simulation (Xie et al. 2007) showed that the cloud base isdecoupled from the atmospheric mixed layer beneathover the southeast Pacific from February through April.
This suggests that stratocumulus clouds should be broken

up into shallow cumulus during these months, consistent
with the present observational evidence. An increase ofshallow cumulus accompanying the dissipation of stratocumulus clouds leads to an enhancement of solar radiation reaching the sea surface. De Szoeke et al. (2006)
found that the south Pacific warm band does not develop,
and thus neither does the south ITCZ, in a coupled model
when the shallow convection parameterization is disabled. The transition from stratocumuli to shallow cumulus is probably an additional factor that promotes thedevelopment of the warm band.

d. Interannual variability
While the primary focus of this paper is limited toclimatological aspects of the east Pacific double ITCZ,
year-to-year variability is briefly explored here. Figure 12
depicts bimonthly (March and April) mean SST and the
deep storm fraction for each year studied. The south
ITCZ is consistently observed every year in these months,
but markedly varies in strength from year to year. A salient south ITCZ develops in 2000, 2001, 2004, and 2006,

1 MARCH 2010

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1201

FIG. 10. Hovmöller diagram of SST averaged over 12.58–2.58S for the (a) control run and (b) clear-sky run, and the regional map ofSeptember mean SST for the (c) control run and (d) clear-sky run from the boreal fall experiment. SSTs of 248 and 278C are highlighted bythick contours.

while it is relatively weak in 2002 and 2007 and barely
recognizable in 2003, as noted by Gu et al. (2005), and2005. The southeast Pacific warm band is discernible
even in the year with the faintest ITCZ, although it isless mature than in other years. The magnitude of thesoutheast Pacific warm band is closely related to thestrength of the south ITCZ in interannual variability as
also argued by Zhang (2001).
We have shown that the primary driver of the southeast Pacific warm band is the absorbed shortwave flux.
Figure 13 plots monthly mean QSW and the rate of SSTchange or dSST/dt averaged over the tropical southeast
Pacific. The time series demonstrates that the annual
cycles of QSW and dSST/dt are in phase, consistent withthe expectation that the rate of SST change is controlled
dominantly by QSW in Eq. (1). A closer examination ofFig. 13 reveals that the amplitude of the annual cycle isalso coherently modulated where dSST/dt is positive,that is, during the developing stage of the warm band. In
contrast, coherent amplitude modulation is virtuallyabsent when dSST/dt is negative. This contrast is confirmed by the scatterplot of QSW and dSST/dt. WhendSST/dt is greater than zero, dSST/dt is tightly coupledwith QSW, showing a clear positive correlation. The correlation is looser for dSST/dt , 0. It follows that thegrowth of the southeast Pacific warm band is modulated
by QSW not only in climatology but also in individualyears. A larger (smaller) QSW in austral summer results
in a warmer (cooler) SST in the tropical southeast Pacific, which in turn leads to a stronger (weaker) south
ITCZ in the subsequent austral fall. On the other hand,
the magnitude of sea surface cooling tendency in boreal
summer does not closely reflect the year-to-year variation of the incoming shortwave flux.
Because the seasonality of insolation is strictly invariable from a year to another on a decadal time scale,

FIG. 11. Daily climatology of control QSW (solid), clear-sky QSW (dotted), and clear-sky QSW offset by the cloud longwave impact(dashed) averaged over (left) southeast tropical Pacific (12.58–2.58S, 1508–858W) and (right) northeast tropical Pacific (2.58–12.58N,
1508–808W).

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FIG. 12. Bimonthly (March and April) mean SST (8C) and deep storm coverage (%) for each year from (top left) 2000 to (bottom right)
2007. SSTs of 248 and 278C are highlighted by thick contours.

the interannual variation of QSW is controlled by clouds.
Such cloud variability is, however, not the only factor
governing the interannual variation of the double ITCZ.
The largest source of interannual variability that has notbeen tested in this study is probably ENSO. It is known
that the east Pacific double ITCZ is either faint or absent
during El Niño events (Zhang 2001). Various effects,
including anomalous ocean upwelling, would be needed
to explain the key factors that suppress the southeast
Pacific warm band in El Niño years. Unfortunately, it isdifficult to extract robust ENSO signals from the study
period of the present work. The ENSO impacts on thesoutheast Pacific warm band, and its possible feedback
to ENSO, are left for future studies.

e. Implications for coupled climate models
It has been recognized for years that coupled ocean–
atmosphere general circulation models often have difficulties in simulating realistic SST in the tropical east
Pacific. While a limited number of coupled models are
successful in reproducing the seasonality of east Pacific
SST and ITCZ, some models tend to have a persistent
double ITCZ and some others exhibit a seasonally mi-

grating ITCZ across the equator (Mechoso et al. 1995;
Dai 2006; de Szoeke and Xie 2008). Causes for theseerrors are highly complicated and have yet to fully understand. Nevertheless, it would be beneficial to briefly
discuss the current findings in light of known problems incoupled ocean–atmosphere modeling.
We have seen that the absorbed solar radiation is the
key factor controlling the seasonality of the south ITCZ
and that cloudiness is required to suppress the southeast
Pacific warm band in austral winter and spring. Other
factors, which may not have been well recognized before
in conjunction with the south ITCZ, include the mixed
layer depth and mixed layer absorptivity of shortwave
radiation. The mixed layer depth (Hml) could exertcompeting effects on the ocean heat budget. While anincrease in Hml lowers the SST tendency for a given magnitude of the total heat flux [see Eq. (1)], it enhances theabsorbed shortwave flux in the tropical east Pacific where
the mixed layer is shallow [see Eq. (A16)]. The latter effect can be large enough to give rise to a spurious warmband in the southeast Pacific depending on the choice ofHml (not shown). An overestimated shortwave absorptivity would cause the same SST bias. A misrepresentation

1 MARCH 2010

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1203

FIG. 13. Regional mean QSW (W m22) and the rate of SST change (dSST/dt; 8C month21) for the tropical southeast Pacific (12.58–2.58S,
1508–858W). (left) Monthly time series of QSW (solid curve, labeled on the left ordinate) and dSST/dt (shaded bars, labeled on the rightordinate). (right) Scatterplot of QSW (abscissa) and dSST/dt (ordinate). All values are monthly mean.

of these parameters might be partly responsible for the
double ITCZ error in some coupled models.
The double ITCZ error has given way to an alternating ITCZ error in recent coupled models, where thenorth ITCZ weakens too much during the time when thesouth ITCZ strengthens (de Szoeke and Xie 2008). Interestingly, such seasonal migration of the ITCZ is what
would be expected if the north ITCZ were dominated by
the same dynamics as those controlling the south ITCZ.
Identifying causes for the alternating ITCZ error requires further understanding of the mechanisms thatsustain the north ITCZ perpetually against the seasonal
weakening of insolation.

6. Summary
The present study is aimed at determining the growthmechanism of the east Pacific double ITCZ in austral fall.
Satellite measurements from the TRMM and QuikSCAT
were analyzed to derive the 8-yr climatologies of SST,
surface convergence, CWV, shallow and deep precipitating clouds, and the surface heat fluxes from 2000 to2007. The initial signature of the south ITCZ emerges
in SST, referred to as the southeast Pacific warm band, as
early as in January. A pronounced feature of the warmband is a local SST maximum around 908W, resulting
from the sum of different surface heat fluxes having different signs and competing geographical patterns. Surface convergence and CWV gradually develop along thesoutheast Pacific warm band. The population of shallow
cumulus starts growing to form the south ITCZ in February, a month earlier than vigorous deep convectionthat finally organizes in the south ITCZ in March. The
double ITCZ therefore does not emerge abruptly in

austral fall, but results from a series of distinctive evolutionary stages in the preceding months, initiated by
SST in the previous austral summer.
Simple experiments were carried out in order to diagnose the key factors that give rise to the southeast
Pacific warm band. In the experiments, the heat budgetof the ocean mixed layer is calculated with the surface
heat fluxes (longwave, shortwave, latent heat, advection,and upwelling), all of which are derived from satellite
observations. The results suggest that the absorbed shortwave flux primarily drives the southeast Pacific warm
band, enhanced to a lesser extent by the ocean advection. Insolation remains near the annual maximum fromaustral summer through late February for a latitudinalrange of the south ITCZ, resulting in a peak in tropicalsoutheast Pacific SST and the south ITCZ in March. It is
now obvious why the double ITCZ is absent in boreal
fall: the incoming shortwave flux is minimum in the preceding solstice season, and thus incapable of maintaining a warm ocean surface in the Southern Hemisphere.
The heat budget calculation shows that the ocean mixed
layer exhibits a cooling tendency in July, where theshortwave flux is overwhelmed by negative fluxes suchas the latent heat and longwave fluxes.
Cloud impacts on the shortwave flux in the tropicaleast Pacific have also been quantified. Clouds offset the
net radiation by 10–15 W m22 throughout the year in
the tropical southeast Pacific. This offset is so large thatthe warm band would also develop in boreal fall if reflecting clouds did not exist. It was also found that a yearwith a robust (faint) southeast Pacific warm band has
a strong (weak) south ITCZ, supporting the strong SST
influence on the ITCZ. The ENSO modulation of the
austral fall double ITCZ would require a longer period

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to study than the current analysis and thus is not discussed
in this paper.
The meridional asymmetry of the east Pacific ITCZ
has generally been explored in the literature by asking
why the Southern Hemisphere lacks a permanent ITCZ
(Mitchell and Wallace 1992; Xie and Philander 1994;
Philander et al. 1996). The present findings suggest thatthe seasonal preference of the south ITCZ is a naturalconsequence of the annual cycle of insolation. This
supports the model result of Wang and Wang (1999) thatthe annual march of solar forcing is crucial for maintaining the meridional asymmetry of the ITCZ. It is,however, not completely clear why SST remains higheven in local winter north of the equator. The real
mystery might be not why the south ITCZ is transient
but why the ITCZ could persist all the year around in thenortheast Pacific.

QLH 5 ra Ly CE [qy  q*(T)]ju10 j,ys

APPENDIX
Method for Ocean Surface Flux Estimate
a. Latent heat flux
The latent heat flux through evaporation from theocean surface is estimated by use of the bulk formula,(A1)

where ra, Ly, qy, q*y(T), and u10 are the dry air density(1.22 kg m23), vapor latent heat per unit mass (2.5 3
106 J kg21), vapor mixing ratio, saturation vapor mixing
ratio for temperature T, and the wind velocity at 10 m
above the sea surface, respectively. The saturation vapor
mixing ratio is reduced by 2% from the value expectedfrom the Clausius–Clapeyron relation to take the salinity effect into account. The neutral, 10-m bulk transfer coefficients are obtained from the empirical formulas
derived by Large et al. (1994),
103 CE 5 34.6C1D/2 ,

(A2)

where
103 CD 5

Acknowledgments. The TRMM PR (2A25) and VIRS
(1B01) datasets were provided by the Japan Aerospace
Exploration Agency (JAXA) Earth Observation Research Center (EORC). The TMI-retrieved SST and
CWV datasets are produced and distributed by the
Remote Sensing Systems (http://www.ssmi.com). The
QuikSCAT SeaWinds ocean wind vector data and
OSCAR surface current product were obtained fromthe Physical Oceanography Distributed Active Archive
Center (PO.DAAC) at the NASA Jet Propulsion Laboratory, Pasadena, California (http://podaac.jpl.nasa.
gov). The Tropical Atmosphere/Ocean (TAO) Project
Office of the National Oceanic and Atmospheric Administration (NOAA)/Pacific Marine Environmental
Laboratory (PMEL) provided ocean buoy data. The
WOA05 temperature data were obtained from the
NOAA/National Oceanographic Data Center. The mixed
layer depth dataset was downloaded (http://www.lodyc.
jussieu.fr/;cdblod/mld.html). This work is supported by
the Ministry of Education, Culture, Sports, Science, andTechnology (MEXT) Grant-in-Aid for Young Scientists
No. 20740269. The HERB dataset was generated under
the support of National Aeronautics and Space Administration (NASA) Energy and Water Cycle Study(NEWS) Grant NAG06GC46G.

VOLUME 23

ju10 j2.70 m s1
1 0.142 1.
13.09 m s1
ju10 j(A3)

Microwave radiometer measurements provide SST
required for (A1), but not qy at any specified verticallevel. Existing studies to estimate latent heat flux fromsatellite data have explored a variety of algorithms toderive qy (Chou et al. 1995; Jourdan and Gautier 1995;
Schulz et al. 1997; Curry et al. 1999; Kubota et al. 2002,
and references therein). In this study, a simple formula isestablished, where qy is regressed from CWV and SST.
Figure A1a shows the scatterplot of in situ water vapor
density, or raqy, against CWV. The in situ water vapor
density is obtained from relative humidity data acquired
at nine of the Tropical Atmosphere Ocean (TAO) arrayed bouys that are moored in the southeast Pacific(i.e., 88S, 58S, and 28S and 1258W, 1108W, and 958W).
Satellite overpasses are extracted for each selected buoy
to pair the in situ water vapor with CWV.
Figure A1a appears to suggest that the in situ water
density is not accurately determined by CWV alone.
An additional constraint of underlying SST, however,breaks the plot down into distinct groups. Two example
cases of 278 6 0.58C and 218 6 0.58C are shown by dots
and crosses, respectively. The scatter turns out to be further reduced (and almost linearly correlated) when theordinate is redefined with
Hy 5

W
,
r a qy(A4)

where W designates CWV (Fig. A1b). Note that Hy
represents the water vapor scale height when the verticalprofile of raqy is approximated to be exponential. A
bivariate linear regression is applied to Hy as a functionof CWV and SST. The resultant empirical formula is1 MARCH 2010

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MASUNAGA AND L’ECUYER

FIG. A1. (a) Scatterplot of in situ water vapor density or raqy against CWV for different SSTs. Dots and crosses
denote SSTs of 278 and 218C, respectively, with other SSTs omitted for clarity of presentation. (b) Same as (a), but for
Hy or CWV/raqy instead of raqy. Solid and dashed lines are regressed curves for SSTs of 278 and 218C, respectively.
See text for details.

HyTW
 60.9 3 s , (A5)5 1961 1 40.3 3
2
[m]
[8C]
[kg m ]
orW
[kg m2 ]
,
5
Ts
W
[kg m3 ]
60.9
31961 1 40.3 3[8C][kg m2 ]
(A6)
ra qy

which is delineated in Fig. A1. The latent heat flux is
calculated using (A1) and (A6) for given CWV, SST,
and ju10j, all of which are provided by satellite observations.

Qadv 5 Cp,w Mml  $T s .

(A8)

An annual climatology of Hml is adopted from deBoyer Montégut et al. (2004) with a variable density
criterion corresponding to DT 5 20.28C applied against
the reference depth at 10 m. A variable density criterion
is used instead of a simple temperature threshold so thata barrier layer, known to develop in the tropical convergence zones, is detected and separated (Sprintall andTomczak 1992). Figure A2a shows the regional map ofHml, where Hml deepens southwestward in the tropicaleast Pacific.
Given the wind stress vector t estimated from
QuikSCAT wind,t 5 ra CD u10 u10 ,(A9)

b. Ocean advection and upwelling fluxes
The advective heat transport in the ocean mixed layer
Qadv is derived from the satellite-derived surface current(OSCAR product) and SST. The OSCAR current isdefined as the mean velocity averaged between thesurface and 30-m depth. The assumption of a constantdepth at 30 m may introduce a minor error in the present analysis because the mixed layer depth varies from10 to ;70 m in the study domain. Uncertainties in thehorizontal advection, however, are not critical for theheat budget analysis of the east Pacific warm bands,
where radiative and latent heat fluxes are virtually in balance (Xie 1994). The mixed layer mass transport Mml is
Mml 5 rw H ml u,(A7)

where u is the current velocity. The advective heat flux isthen evaluated as

the Ekman mass transport ME [ (ME,x, ME,y)T is evaluated fromrs ME, x  fME,y 5 t x ,(A10)

rs ME,y 1 fME, x 5 ty ,(A11)where rs is the drag coefficient, f the Coriolis parameter,
and tx and ty the zonal and meridional components of t,
respectively. The drag coefficient was empirically estimated by Lagerloef et al. (1999) to be 2.15 3 1024 m s21
for the Ekman layer with a depth of 32.5 m. In the present
formulation, rs is defined per unit depth and is given as
2.15 3 1024/32.5 or 6.62 3 1026 s21. The drag term isessential in the vicinity of the equator, where ME would
otherwise diverge to infinity as f diminishes to zero. Upwelling velocity wE is

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FIG. A2. The annual climatologies of (a) mixed layer depth (Hml)and (b) temperature difference between the mixed layer and upwelling water from beneath (DTE).

wE 5

1$  ME ,rw(A12)

and the upwelling heat flux is evaluated as
Qupw 5rw Cp,w wE H(wE )DT E ,(A13)

where H is the Heaviside function and DTE represents
the temperature difference between mixed layer waterand upwelling water from beneath. In this work, DTE isprescribed from the annual climatology of local temperature difference between the two reference depths,
that is, T(0.5Hml) 2 T(Hml 1 dh), where dh is arbitrarily
chosen to be 15 m. The regional map (Fig. A2b) showsthat DTE ranges from 0.68 to ;38C, which is a conservative estimate compared to 48C, as chosen by Wyrtki(1981). Because Hml is derived from a variable density
criterion, the estimated DTE does not closely reflect Hml
particularly in the presence of a barrier layer (Sprintall
and Tomczak 1992; de Boyer Montégut et al. 2004).

c. Radiative flux
The HERB product (L’Ecuyer and Stephens 2003,
2007; L’Ecuyer and McGarragh 2010) provides atmospheric radiative flux and heating profiles covering the
TRMM-observed region. Instead of directly using broadband spectral measurement, the HERB synthesizes radi-

VOLUME 23

ative fluxes from cloud and precipitation profiles retrieved
from satellite observations together with other parameters, such as air temperature, humidity, and aerosol,using broadband radiative transfer calculations. As such,
the HERB dataset provides radiative flux not only at the
top of the atmosphere, but at any vertical level. To
quantify the radiative effects on the mixed layer heatbudget, the downward shortwave and longwave fluxes atthe surface, or F YSW and F YLW , respectively, are takenfrom the HERB dataset. It has been shown that satellitebased surface radiative flux products, such as the International Satellite Cloud Climatology Project (ISCCP)
radiative flux profile data (FD), tend to overestimate
surface SW fluxes in tropical regions (Large and Yeager2009). Based on comparisons against in situ flux measurements at nine ocean sites, L’Ecuyer and McGarragh(2010) estimate that the HERB product may exhibit
similar biases of ;18 W m22. In the current study, theshortwave flux is reduced constantly by 20 W m22 inorder to avoid a potential overestimate of the shortwave
impact on the ocean heat budget. To test the potential
impacts of such an overestimate on the ocean heatbudget, separate experiments have been conducted withdifferent SW offsets that indicate that the behavior of
the mixed layer heat budget is qualitatively insensitive toerrors of this magnitude (not shown). It is further notedthat that the excess SW heating that may exist in regionswith shallow mixed layers can be partially compensatedfor by tuning both absorptivity and DTE over a realistic
range. Finally, L’Ecuyer and McGarragh (2010) demonstrate that, despite any potential biases that may exist
in SW fluxes, seasonal and interannual variability indownwelling SW flux estimates are well represented in
the HERB product.
The net longwave heat flux at the surface is written as
QLW 5 F YLW 1 F [LW 5 F YLW  sT 4s(A14)

where s 5 5.67 3 1028 W m22 K24 is the Stephan–Boltzmann constant. Note that the Q values defined inthis study represent heat fluxes (W m22) according tothe oceanographic convention and should not be confused with heating rates (K day21), which are often denoted by Q in the meteorological contexts. The net
shortwave flux absorbed by the ocean mixed layer is
QSW 5 (1  a)PF YSW ,(A15)

where a and P are the ocean surface albedo and thefraction of incoming shortwave energy that is absorbedby the mixed layer. While a, fixed at 0.06 in this work, isrelatively uniform across global oceans, P varies with

1 MARCH 2010

MASUNAGA AND L’ECUYER

different factors including the mixed layer depth andchlorophyll concentration. Ohlmann et al. (1996) estimated P as 0.80–0.93 for the eastern equatorial Pacific.
In the present study, P is assumed to simply depend on
the mixed layer depth as
H ml
P 5 1  exp 0.06
,
[m]

(A16)

which yields P 5 0.83 for Hml 5 30 m.

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