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RESEARCH ARTICLE10.1002/2014JC010383

An objective algorithm for estimating maximum oceanic mixed

layer depth using seasonality indices derived from Argo

temperature/salinity profiles

Ge Chen1 and Fangjie Yu1

1Qingdao Collaborative Innovation Center of Marine Science and Technology, College of Information Science and

Engineering, Ocean University of China, Qingdao, China

Abstract In this study, we propose a new algorithm for estimating the annual maximum mixed layerdepth (M2LD) analogous to a full range of local ‘‘ventilation’’ depth, and corresponding to the deepest sur-

face to which atmospheric influence can be ‘‘felt.’’ Two ‘‘seasonality indices’’ are defined, respectively, for

temperature and salinity through Fourier analysis of their time series using Argo data, on the basis of which

a significant local minimum of the index corresponding to a maximum penetration depth can be identified.

A final M2LD is then determined by maximizing the thermal and haline effects. Unlike most of the previous

schemes which use arbitrary thresholds or subjective criteria, the new algorithm is objective, robust, and

property adaptive provided a significant periodic geophysical forcing such as annual cycle is available. The

validity of our methodology is confirmed by the spatial correlation of the tropical dominance of saline effect

(mainly related to rainfall cycle) and the extratropical dominance of thermal effect (mainly related to solar

cycle). It is also recognized that the M2LD distribution is characterized by the coexistence of basin-scale

zonal structures and eddy-scale local patches. In addition to the fundamental buoyancy forcing caused

mainly by latitude-dependent solar radiation, the impressive two-scale pattern is found to be primarily

attributable to (1) large-wave climate due to extreme winds (large scale) and (2) systematic eddy shedding

as a result of persistent winds (mesoscale). Moreover, a general geographical consistency and a good quan-

titative agreement are found between the new algorithm and those published in the literature. However, a

major discrepancy in our result is the existence of a constantly deeper M2LD band compared with other

results in the midlatitude oceans of both hemispheres. Given the better correspondence of our M2LDs with

the depth of the oxygen saturation limit, it is argued that there might be a systematic underestimation with

existing criteria in these regions. Our results demonstrate that the M 2LD may serve as an integrated proxy

for studying the coherent multidisciplinary variabilities of the coupled ocean–atmosphere system.

1. Introduction

As a counterpart of the mixed layer in the lower atmosphere, the oceanic mixed layer is a global feature of

turbulence-induced quasi-homogeneous zone in terms of density in the upper ocean. The two coupled

mixed layers are home to major hydrodynamic and thermodynamic activities of the ocean–atmosphere sys-

tem which determine the fundamental patterns of the marine environment and climate change. Better

understanding of their formation, variation, and interaction are of critical importance to both oceanogra-

phers and meteorologists. In contrast to the atmospheric mixing height of tens to hundreds of kilometers,

the oceanic mixed layer depth (MLD, specified as MLDT , MLDS , or MLDD when defined with temperature,

salinity, or density) varies only from tens to hundreds of meters, but its dynamic complexity is no less than

the former, including buoyancy fluxes induced by radiative heating/cooling, surface precipitation/evapora-

tion, ice formation/melting, and mechanical mixing due to wind/wave stirring, eddy/current shear, as well

as Rossby and internal wave disturbance. As a result of immense diurnal, seasonal, and interannual ventila-

tions, the consequences of oceanic mixed layer are wide spread and far reaching, ranging from climatic

effects such as El Ni~no-Southern Oscillation, global warming and its hiatus, chemical effects such as nitrogen

and carbon cycles in an oxygen depleted environment, to biological effects such as phytoplankton blooms

and fishery population shift [P €ortner and Knust , 2007; Ravichandran et al ., 2012].

Tremendous efforts have been made in the past few decades to develop schemes and optimize algorithms

for identifying oceanic mixed layers over global and regional oceans, leading to numerous criteria for the

Key Points:

A new objective algorithm for

estimating annual maximum MLD is

proposed

The two-scale MLD pattern is related

to wind/wave climate and eddy

shedding

Correspondence to:

G. Chen,

[email protected]

Citation:

Chen, G., and F. Yu (2015), An objective

algorithm for estimating maximum

oceanic mixed layer depth using

seasonality indices derived from Argo

temperature/salinity profiles, J.

Geophys. Res. Oceans, 120, 582–595,

doi:10.1002/2014JC010383.

Received 12 AUG 2014

Accepted 29 DEC 2014

Accepted article online 7 JAN 2015

Published online 30 JAN 2015

This is an open access ar ticle under the

terms of the Creative Commons Attri-

bution-NonCommercial-NoDerivs

License, which permits use and distri-

bution in any medium, provided the

original work is properly cited, the use

is non-commercial and no modifica-

tions or adaptations are made.

CHEN AND YU VC 2015. The Authors. 582

Journal of Geophysical Research: Oceans

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estimation of MLD based on temperature, salinity, and density measurements. An early review on MLD-

related works carried out between 1970s and 1990s is presented by Kara et al . [2000] who separate them into

two general categories. The first is to define an isothermal layer depth from a temperature profile and assume

this to be the MLDT , and the second is to define a MLDD from a density profile with either a property differ-

ence or a gradient criterion. As they point out, however, none of these studies (see their Table 1) present a

quantitative analysis justifying a particular property difference value as the most appropriate criterion. A few

years later, an updated summary of criteria used to define the MLDT ,D is compiled by de Boyer Mont egut et al .

[2004]. Given the fact of criteria diversity as indicated in their Table 1 (e.g., the temperature threshold varies

from 0.1 to 1.0C with a changing reference depth of 0–10 m), the authors emphasize that most often both

the concept and the choice of thresholds are rather arbitrary. This view is shared by Lorbacher et al . [2006]

who argue that the estimated MLD is sensitive not only to choices of threshold and reference value, but also

to the vertical resolution and gradient at the base of the mixed layer. Dong et al . [2008], among others [e.g.,

Holte and Talley , 2009; Ohno et al ., 2009], also divide the criteria of MLD estimation into two groups: property

difference-based criteria and gradient-based criteria. They further quantify that in the first group, values of

potential temperature difference from 0.01C to 1.0C and values of potential density difference from 0.005

to 0.125 kg m23 are commonly used. A temperature gradient of 0.025C m21 and density gradient from

0.0005 to 0.05 kg m24 are applied to determine MLD in the gradient criteria. In addition to these straightfor-

ward schemes, more sophisticated approaches have also been proposed as attempts to minimize the uncer-

tainties associated with MLD estimates. For example, Lavender et al . [2002] use the intersection between a

straight-line fit to the upper layer and an exponential plus second-order-polynomial fit to the deep layer to

estimate the MLDT of individual temperature profiles in the Labrador Sea. Thomson and Fine [2003] introduce

a ‘‘split and merge’’ method, which fits a variable number of linear segments to a profile. Lorbacher et al .

[2006] calculate the MLDT on the basis of the shallowest extreme curvature of temperature profiles. Holte and

Talley [2009] develop a hybrid method which finds the MLD of individual ocean profiles, models the general

shape of each profile, searches for physical features in the profile, and calculates threshold and gradient to

assemble a suite of possible values before selecting a final MLD.

As clearly evident from the brief review above, and given the largely arbitrary and subjective nature of

existing criteria, there seems to be no single, optimal, and universal methodology for determining the

MLDs over global oceans. Kara et al . [2000] point out that differences in the criteria can lead to consid-

erable differences in the MLDs, which in turn, could influence the study findings. Lorbacher et al . [2006]

summarize three major uncertainties about the threshold method. First, if assuming that a DT 50.2

C (athreshold of temperature difference between the sea surface and a given depth, same as Dq below for

density) is representative of an adequate criterion, the resulting deviations of the estimated MLD T can

be sometimes in the order of MLDT itself. Second, the complicated dependence of MLD on the vertical

resolution is not desirable, especially when comparison studies are made with the low vertical resolution

output of numerical models. Third, because MLD depends on the sea surface temperature (SST) or a ref-

erence value and there is no rational choice for this value, leading us to be more than skeptical that

the turbulent region of the upper ocean is captured well by the threshold criterion. Dong et al . [2008]

perform a sensitivity test using alternate net difference values of temperature DT 50.1, 0.2, 0.5C and

density Dq50.01, 0.03, 0.125 kg m23, and find that the resulting MLDs differ significantly for the South-

ern Ocean. In addition, a value of criterion chosen subjectively for one region or season might not be

applicable to another region or season [Lorbacher et al ., 2006]. For example, the ‘‘intersection method’’

developed by Lavender et al . [2002] works nicely in the North Atlantic, but fails to produce realistic

MLDs in the Southern Ocean [Holte and Talley , 2009].

In this study, we develop a fundamentally different approach for finding the annual maximum mixed layer

depth (M2LD) from Argo float measurements based on the intrinsic concept of seasonality. Instead of using

the threshold or gradient-based criteria which have a straightforward geophysical background in theory

but a subjective and arbitrary nature in practice, we propose a new algorithm for estimating the M2LD,

which is totally independent of specific temperature, salinity, or density thresholds. The idea behind the

methodology is that, instead of using directly measured property profile data, pseudo ‘‘seasonality index

profiles’’ of an annual property amplitude are first derived, on the basis of which a local minimum of the

index corresponding to a maximum penetration depth can be determined. As will be demonstrated in the

following sections, this novel approach will eventually benefit from the basic fact that seasonal cycle, rather

Journal of Geophysical Research: Oceans 10.1002/2014JC010383



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than the dependencies on various complex local assumptions, is ultimately the decisive forcing for the

annual M2LD. The rest of the paper is organized as follows: a brief description of the Argo float data used in

this investigation along with the proposed M2LD derivation algorithm is provided in section 2. The results

are presented, analyzed, and compared in section 3. The mechanisms of M2LD formation are discussed in

section 4, and some final remarks are given in section 5.

2. Data and Method

Ten years of Argo (Array for Real-time Geostrophic Oceanography) data spanning from 2004 to 2013 are

used in this study. Argo floats are designed to observe large-scale (seasonal and longer, thousand kilo-

meters and larger) subsurface ocean variability globally [Roemmich et al ., 2009]. As the first observation sys-

tem of global subsurface ocean in history and one of the main sources of in situ temperature/salinity ( T / S )

measurements, the Argo project has an unprecedented spatial–temporal sampling and coverage, the aim

of which is to provide simultaneous T / S observations of the 022000 m upper ocean in near real time. By

January 2014, there are as many as 3613 active floats disseminated around the global ocean spacing nomi-

nally at every 3 of longitude and latitude. In this analysis, gridded Argo T / S data are obtained from the

China Argo Real-Time Data Center (http://www.argo.org.cn/ ). The original observations used to generate

the product are the so-called D-mode Argo data with pressure offsets corrected [Barker et al ., 2011]. There

are 48 vertical layers in our data set ranging from 5 to 1950 m with an interpolated spatial resolution of

1 3 1 and temporal resolution of 1 month, respectively [Chen et al ., 2014].

The accumulation of continuous time series from available Argo floats has exceeded one decade for the

first time. The annual harmonic of sea temperature and salinity with a periodicity of P 5 12 months for a

given layer can be derived through Fourier analysis of the time series T ( x , y , z, t ) and S ( x , y , z, t ) at each grid

point ( x, y ) of depth z ,

T ð x ; y ; z ; t Þ5 AT ð x ; y ; z Þ3cos ð2pt =P 1uT ð x ; y ; z Þ½ (1a)

S ð x ; y ; z ; t Þ5 AS ð x ; y ; z Þ3cos ð2pt =P 1uS ð x ; y ; z Þ½ (1b)

where AT and AS are the amplitudes of the annual component, uT and uS are the phase angles which deter-

mine the time when the maximum of the annual harmonic occurs, while t varies from 0 to 120 months for

the present Argo data set. The fact that the Argo array density is considered nonoptimal until 2007 will notsignificantly affect the result of this analysis since we are focusing on the annual and semiannual cycles,

and according to the Nyquist criterion, the time series of over 7 year densely distributed data are long

enough for resolving the T / S variability on seasonal time scales. Given a complete spatiotemporal data set

T ( x , y, z, t ) for temperature or S ( x , y, z, t ) for salinity, AT ( x , y, z ) and uT ( x , y, z ) or AS ( x , y, z ) and uS ( x , y, z ) can be

simultaneously retrieved and are supposed to carry full information of annual T / S variability in terms of

amplitude and phase for the global upper ocean.

Following the procedures described above, pseudoprofiles of AT and AS can be derived at each grid point

as indices for measuring the strength of T / S seasonality. Starting from the surface layer, our algorithm

searches progressively at each grid deeper layers until it finds a depth where AT or AS reaches its first signifi-

cant local minimum or its level of practical accuracy of 0.02 C for temperature and 0.01 psu for salinity

[Barker et al ., 2011]:

AT ð x i ; y j ; z TminÞ5min AT ð x i ; y j ; z k Þ k 5 1; 2; . . . ; 48ð Þ (2a)

AS ð x i ; y j ; z SminÞ5min AS ð x i ; y j ; z k Þ

k 5 1; 2; . . . ; 48ð Þ (2b)

where k is the index of depth layer, z Tmin ( z Smin) corresponds to the depth of the first minimum AT ( AS ). The

process is repeated for each ( x i , y j ) with i 51, 2,. . ., 360, and j 5260,259,. . ., 60. The final M2LD is

chosen as the deeper layer out of z Tmin and z Smin:

M2LDð x i ; y j Þ5max z Tminf jð x i ; y j Þ; z Sminjð x i ; y j Þg (3)

The geophysical validity of this simple approach lies in three aspects. First, since mixed layer depth can

vary by tens of meters over a diurnal cycle [ Thomson and Fine, 2003] and given the temporal resolution



http://www.argo.org.cn/http://www.argo.org.cn/


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of present Argo data [Roemmich et al ., 2009], it is actually difficult to track the evolution of MLD on

daily or instantaneous basis in a meaningful way. On the other hand, it is understood that the mixed

layer contains the ocean’s ‘‘memory’’ of air-sea exchange out to periods of a year or longer [Sprintall

and Roemmich, 1999], we therefore decide to focus on annual maximum MLD, which provides an over-

all dynamic connection (both hydro and thermal) between the atmosphere and the ocean and thus

plays a central role in climate variability. Second, seasonality indices of temperature and salinity at a

given location decrease monotonically with depth as a result of a normal ventilation until the first

‘‘abnormal bump,’’ i.e., ‘‘local minimum’’ is encountered, which signifies the termination of vertical mixing

dominance due to possible occurrence of other intervening processes such as the intrusion of a front

or a jet of sinking colder water which distorts the vertical structure of the homogeneous temperature

or salinity layer [Kara et al ., 2003]. This seasonality minimum coincides with the M2LD since annual cycle

of MLD is usually an order of magnitude larger over most of the world’s oceans compared with other

variabilities including diurnal cycle [e.g., Price et al ., 1986] or interannual oscillation [e.g., Keerthi et al .,

2013]. Alternatively, mixed layer is considered to be vanishing or insignificant when AT ( AS ) reaches the

Argo measurement accuracy. Third, as pointed out by de Boyer Mont egut et al . [2007], the base of the

mixed layer is usually defined as the top of the pycnocline, being the depth where the density has

increased by a certain threshold from its surface value. Presently, the available density profiles are about

an order of magnitude less than the temperature profiles [Lorbacher et al ., 2006]. Given also the lack of

salinity data, it is often concentrated on the temperature stratification, assuming that the top of the

thermocline and halocline have the same depth and thus together define that of the pycnocline. How-

ever, this view is oversimplified for the real ocean. Temperature and salinity can be stratified in dis-

tinctly different ways as a result of specific thermal and haline forcings [Lorbacher et al ., 2006; Mignot

et al ., 2007]. As a combined result, our algorithm of equations (1)2(3) can be justified in search of an

annual maximum MLD especially in the tropical oceans where the saline effect is supposed to

dominate.

Practically, we start by looking at the global distribution of recovered annual amplitude of sea temperature

and salinity variabilities at selected depths, as shown in Figure 1. Focusing on the left column, it is obvious

that the geographical pattern of sea temperature seasonality is highly inhomogeneous in each layer and is

largely dissimilar for different layers. For example, the near-surface temperature seasonality is most promi-

nent around the Japan islands in the northwest Pacific, and off the east coasts of the U.S. and Canada in the

northwest Atlantic (Figures 1a and 1b). Large annual variability is also apparent in the circumpolar beltbetween 25S and 40S of the Southern Ocean. The least dynamic region coincides with the western Pacific

warm pool (WPWP) [Chen et al ., 2004b]. In contrast, the most dynamic areas for seasonal sea temperature

changes are located in the Ni~no-3/4 and the WPWP regions at 100 and 200 m depths, respectively (Figures

1c and 1d). Localized strong seasonalities are also observed in deeper oceans such as the Gulf of Mexico at

500 m, and the Indonesia waters at 1950 m (Figures 1e and 1f). A similar degree of diversity can be

observed for salinity seasonality as well (see right column of Figure 1), particularly in the Asian monsoon

region (Figures 1g–1i) and the intertropical convergence zone.

Browsing through the color scales of the left and right columns in Figure 1, one finds a common characteris-

tic shared by temperature and salinity seasonalities that they both drop down rapidly as going deeper. This

can be quantitatively illustrated by plotting the spatially averaged seasonality of temperature and salinity

with respect to depth as shown in Figure 2 (also overlaid with dashed lines are the semiannual amplitudes

of sea temperature and salinity). As expected, the two indices decline monotonically with the dramaticreduction of solar penetration into the deeper ocean. Globally, it is estimated that only 1.1% of the surface

strength of seasonal variability is left for temperature and 2.5% for salinity at about 2000 m depth. Individ-

ually, however, the vertical reduction behaviors of seasonal signals are tremendously diverse. Three typical

examples of temperature seasonality profiles are shown in Figure 3a for (330E, 25S), (232E, 1S), and

(160E, 30N), where a local minimum can be first identified at approximately layers 8, 14, and 23 (corre-

sponding to 60, 120, and 220 m depths), respectively. Plots with similar features are also generated for salin-

ity (not shown). The existence of these well-defined seasonality minima justifies the validity of our

proposed scheme and enables us to practically determine the M2LD by maximizing the concurrent temper-

ature and salinity-derived depths, i.e., finding a deeper value out of z Tmin and z Smin, as described in equation

(3). It should be pointed out that, since our scheme searches for the first local minimum (rather than the




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global minimum in the whole profile) of the seasonality index corresponding to the initial termination of

turbulence, it is unlikely to be biased toward seasonal thermocline features as described in Brainerd and

Gregg [1995].

By definition, density is the most relevant parameter in constructing a MLD climatology. Variations in tempera-

ture and salinity combine to control the density of ocean surface water. The density increases with a decreas-

ing temperature and an increasing salinity. As evidenced in Lorbacher et al . [2006] and Mignot et al . [2007],

Figure 1. Global distribution of recovered annual amplitude (seasonality index) of (left column) sea temperature and (right column) salinity variabilities at selected depths: (a and g) 5 m;

(b and h) 50 m; (c and i) 100 m; (d and j) 200 m; (e and k) 500 m; and (f and l) 1950 m.




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the commonly used assump-

tion of temperature dominance

is found to be systematically

violated under certain circum-

stances such as intense precipi-

tation, river runoff, and even El

Ni~no events. They show exam-

ples of profiles where salinity

controls the depth of the

mixed layer due to the exis-

tence of the so-called ‘‘barrier

layer.’’ Accordingly, we are

motivated to assess the spe-

cific contribution of thermal

effect and haline effect in our

M2LD derivation scheme. To do

so, the spatial distribution of

the differences between

temperature-based and

salinity-based M2LDs is pre-

sented in Figure 4, and the

zonally averaged value of the

difference is shown in Figure 5 (note that positive values are used for z Tmin and z Smin in the calculation). It is

found that, as far as the seasonal convective circulation is concerned, 78.8% of the global ocean is thermal

driven, while 21.2% is haline driven. Combining Figures 4 and 5, one recognizes that the salinity-controlled

area and temperature-controlled area are basically latitudinally divided: the former covers a majority of the

tropical oceans while the latter dominates the extratropical oceans of the two hemispheres. Such a pattern

is in good agreement with Mignot et al . [2007] who locate their quasipermanent barrier layers in the equato-

rial and western tropical Pacific and Atlantic, in the Bay of Bengal and the eastern equatorial Indian Ocean,

in the Labrador Sea, and parts of the Arctic and Southern Ocean, thus suggesting that our M2LD estimation

algorithm is a robust one, effectively triggering the salinity criterion in deep tropics while activating the

temperature criterion in the rest of the world’s oceans.

Also, it is interesting to examine the effect of other seasonal harmonics on M2LD determination in addition

to the annual component. In doing so, two seasonality indices based on semiannual temperature and salin-

ity amplitudes are derived using the same algorithm described above, given the fact that semiannual cycle

is usually the second largest regime in seasonal variabilities (being roughly 1/4–1/2 of the annual amplitude,

see the dashed lines in Figure 2) and may even exceed the annual cycle in some areas of the ocean. It turns

out that semiannual dominance is significant in about 9.6% of the oceanic regions (Figure 6), in which 4.5%

of the cases are triggered by the temperature criterion and 5.1% by the salinity criterion. A majority of these

areas are located in the tropical oceans of the three basins, as well as the Southern Ocean along the Antarc-

tic Circumpolar Current (ACC). No particular geographic preference is found for the temperature or salinity

index, and the resulting deepening of the M2LD is estimated to be approximately 5–10 m at the affected lat-

itudes (e.g., 15S–20N and 50S–60S, not shown). Therefore, the semiannual indices provide slight but sig-

nificant regional corrections to the annual harmonic-based algorithms without changing the basic pattern

of the global M2LD.

3. Results and Comparisons

Following the procedures described in section 2, a global map of M2LD is created using the combined tem-

perature/salinity algorithm (Figure 7). The overall pattern of the M2LD climatology is characterized by a

zonally oriented three-band structure: (1) a band with largely deep M2LDs in the Southern Ocean between

30S and 60S; (2) a band with generally shallow M2LDs in the tropical oceans between 30S and 30N; (3)

two basin-wide zones with relatively deeper M2LDs between 30N and 60N in the North Pacific and North

Atlantic. In Figure 7, the deepest M2LDs in the Southern Ocean are found in the northern side of the

Figure 2. Globally averaged annual (solid lines) and semiannual (dashed lines) amplitudes

(seasonality index) of sea temperature (red) and salinity (blue) as a function of depth layer

corresponding to 0–2000 m.




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subantarctic front (SAF) resulting from the Antarctic intermediate water (AAIW) with relatively low salinity,

high oxygen, and low potential vorticity. It is the densest, deepest, and freshest portion of the subantarctic

mode water and is thought to form partly in the Southeast Pacific just before the ACC enters the Drake Pas-

sage [Dong et al ., 2008; Holte and Talley , 2009]. In the North Pacific and North Atlantic, the two deep M2LD

bands are located in the frontal zones between the subtropical and subarctic gyres in the western basin

due to the formation of a density compensated layer [Oka et al ., 2007].

The observed M2LD pattern is naturally related to prevailing wind and wave actions. But a careful compari-

son between Figure 7 and the global wind speed climatology [see, e.g., Chen et al ., 2003a, Figure 1] indi-

cates that the two distributions differ significantly: the trade wind belts and horse latitudes of oceanic

winds are all absent in the M2LD map. Instead, Figure 7 is rather similar in its general pattern to the global

significant wave height (SWH) climatology (a measure of dynamic degree of wave-induced total turbulence)

derived from satellite data [see, e.g., Chen et al ., 2002, Figure 3b], except that the zone of deepest M2LDs

appears in the North Atlantic while that of the maximum SWH is found in the southern Indian Ocean. The

Figure 3. (a) Annual amplitude (seasonality index) of sea temperature as a function of depth layer corresponding to 0–2000 m at selected grid points: red for (160 E, 30N), green for

(330E, 25S), and blue for (232E, 1S); overlaid plot of seasonality index (red), winter temperature (pink), and salinity (blue) profiles (corresponding to maximum MLD) for (b) (160 E,

30N) and (c) (232 E, 1S).




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two comparisons imply that wave stirring seems to be a direct forcing for the mixed layer generation.

Because SWH consists of both wind sea and swell sea (nonwind) contributions, whereas the latter has a

totally different spatial pattern with respect to wind climatology [see Chen et al ., 2002, Figure 3a], the result-

ing zonal pattern of mixed waves thus reduces to a three-band structure consistent with the M2LDs rather

than following the seven-band structure of the global wind climatology. Having demonstrated that ocean

wave action might be the main dynamics in mixed layer formation, we continue to examine the relationship

between M2LD (Figure 7) and the 10 year return wind speeds derived from satellite data using a methodol-

ogy developed by Chen et al . [2004a] (Figure 8). Surprisingly, the two maps resemble each other not only in

overall pattern but also in relative strength of major features in mid-to-high latitudes, which further sug-

gests that it is ultimately the extreme winds and the corresponding large waves (SWH) that play a critical

role in shaping the extratropical M2LD distribution.

Next, in comparison of our M2LDs with those reported in the literature, we find a general similarity in their

global patterns (see our Figure 7, Figure 14b of de Boyer Mont egut et al . [2004], and Figure 6c of Ohlmann

et al . [1996]). In particular, the result of this study is in quantitative agreement with that of de Boyer Mon-

t egut et al . [2004]: the M2LD varies from 10 m to approximately 150 m in the tropical oceans, while reaches

a belt of maximum exceeding 300 m in the midlatitudes of the two hemispheres. A close scrutiny of avail-

able maps reveals that our result contains numerous well-defined eddy-like patches with contrasted localM2LD highs and lows mostly in the westerlies of the two hemispheres (Figure 7), which is also evidenced to

some extent in Ohno et al . [2004] and predicted by Keerthi et al . [2013] using an eddy permitting numerical

model. This argument is supported by the fact that the deepest localized M2LDs in the Southern Ocean

exceed 550 m in our Figure 7, in contrast to the finding of 400 m on a regional scale by Dong et al . [2008],

Figure 4. Global distribution of the differences between (positive) temperature-based and salinity-based annual M2LDs. Positive values are

depicted in color while negative ones in black and white.

Figure 5. Zonally averaged differences between (positive) temperature-based and salinity-based annual M2LDs. The horizontal dashed

line indicates a zero value.




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confirming the statement that some profiles are even different from adjacent ones in the same year [Ohno

et al ., 2004].

In fact, using 16 years of sea surface height data during 1992–2008, Chelton et al . [2011] have identified and

tracked 35,891 mesoscale eddies (more than 3000 per year on average) over the global oceans. These long-

lived eddies have an average lifetime of 32 weeks and an average propagation distance of 550 km (which

enable them, at least most of the larger ones in middle and high latitudes, to be marginally resolved by the

present Argo floats with nominal intervals of 3 3 3 in space and 10 day in time). Their mean amplitude

and a speed-based radius scale are 8 cm and 90 km, respectively. In addition to these characteristic proper-

ties, there is a remarkable overall resemblance between the small circular patches in our M2LD distribution

and the origin and termination locations of the observed eddies (see bottom panel of Figure 1 and Figure 6

of Chelton et al . [2011]). Moreover, the mean eddy amplitudes are found to peak around 40 –50 in both

hemispheres (see the upper panels of their Figure 10). These geographically correlated features hint that

mesoscale eddies play a dominant role in modifying the large-scale pattern of M2LD determined jointly by

wind/wave climate and solar radiation (see also next section).

It is understood that the eddy-induced convective process is localized in space. Three phases can be identi-

fied in open ocean deep convection: (1) ‘‘preconditioning’’ on the large scale in the order of 100 km, (2)

‘‘deep convection’’ occurring in localized, intense plumes on scales of the order of 1 km, and (3) ‘‘lateral

exchange’’ between the convection site and the ambient fluid through advective processes on a scale of a

few tens of kilometers [Marshall and Schott , 1999]. The last two phases are not necessarily sequential and

often occur concurrently. Specifically, cooling events may initiate deep convection in which a substantial

part of the fluid column overturns in numerous plumes that distribute the dense surface water in the verti-

cal. The plumes have a horizontal scale of the order of their lateral scale (


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predominantly vertical heat transfer on the convective scale gives way to horizontal transfer associated

with eddying on geostrophic scales [Gascard , 1978] as the mixed patch laterally exchanges fluid with its sur-

roundings. Individual eddies tend to organize the convected water into coherent lenses in geostrophic bal-

ance, forming the cell-rich pattern in our M2LD map (Figure 7).

It is desirable to make a quantitative comparison of similar results obtained in this study and those by previous

investigators. Before doing so, we try to first compare the zonally averaged M2LDs for different oceans using the

proposed scheme (Figure 9a). It shows that there is a high consistency between 40 S and 35N for the derived

M2LDs, meaning that the mixed layers at these latitudes are basin independent to a large extent. M 2LDs are con-

siderably deeper in the North Atlantic (nearly 700 m at 57N) than in the North Pacific (around 200 m) and the

difference enlarges with latitude, being consistent with a similar result of Hosoda et al . [2010]. In the Southern

Ocean, however, the Pacific sector usually has deeper M2LDs than the two other basins. We find that the deep-

est average M2LDs can reach 300 m north of the mean SAF in the southeastern Pacific Ocean. Also within the

Pacific sector, a minimum M2LD occur at 53S, which is slightly shifted from the 57S value obtained by Holte

and Talley [2009], and is concurrent with the subsurface salinity minimum, a signature of AAIW.

As some of the investigators of previ-

ous methodologies have released

and updated a corresponding MLD

climatology product based on Argo

float data, it is possible for us to fur-

ther compare the zonally averaged

M2LDs computed using our scheme

and those from the JAMSTEC (Japan

Agency for Marine-Earth Science and

Technology [Hosoda et al ., 2010];

original MLD data at http://www.

jamstec.go.jp/ARGO/argo_web/

MILAGPV/index_e.html), IFREMER

(French Research Institute for the

Exploitation of the Sea [de Boyer

Mont egut et al ., 2004]; original MLD

data at http://www.ifremer.fr/cer-

web/deboyer/mld/Surface_Mixed_

Layer_Depth.php), and SIO (Scripps

Institution of Oceanography [Holte

and Talley , 2009]; original MLD data

at http://mixedlayer.ucsd.edu/ )

schemes as shown in Figure 9b. The

four lines agree generally well within

620 of the tropical oceans, but

Figure 9. Zonally averaged M2LDs for (a) the Pacific (red), Atlantic (blue), Indian

(green), and global (black) oceans using our scheme; and (b) the global ocean using

JAMSTEC (red), IFREMER (green), SIO (blue), and our (black) schemes.

Figure 8. Global distribution of 10 year return wind speed derived from merged TOPEX/Jason-1/2 altimeter data.



http://www.jamstec.go.jp/ARGO/argo_web/MILAGPV/index_e.htmlhttp://www.jamstec.go.jp/ARGO/argo_web/MILAGPV/index_e.htmlhttp://www.jamstec.go.jp/ARGO/argo_web/MILAGPV/index_e.htmlhttp://www.ifremer.fr/cerweb/deboyer/mld/Surface_Mixed_Layer_Depth.phphttp://www.ifremer.fr/cerweb/deboyer/mld/Surface_Mixed_Layer_Depth.phphttp://www.ifremer.fr/cerweb/deboyer/mld/Surface_Mixed_Layer_Depth.phphttp://mixedlayer.ucsd.edu/http://mixedlayer.ucsd.edu/http://www.ifremer.fr/cerweb/deboyer/mld/Surface_Mixed_Layer_Depth.phphttp://www.ifremer.fr/cerweb/deboyer/mld/Surface_Mixed_Layer_Depth.phphttp://www.ifremer.fr/cerweb/deboyer/mld/Surface_Mixed_Layer_Depth.phphttp://www.jamstec.go.jp/ARGO/argo_web/MILAGPV/index_e.htmlhttp://www.jamstec.go.jp/ARGO/argo_web/MILAGPV/index_e.htmlhttp://www.jamstec.go.jp/ARGO/argo_web/MILAGPV/index_e.html


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diverge significantly beyond those regions. Further poleward, the JAMSTEC M2LDs become the deepest

with the largest discrepancies exceeding 300 m in zonal mean. It should be noticed that, as proposed by

Reid [1982], the 95% oxygen saturation limit from CTD data gives a proxy for M2LD which is also called a‘‘bowl’’ by Guilyardi et al . [2001]. That is, the 95% oxygen saturation corresponds to the oxygen dissolved

during ventilation at the surface at the time of the deepest convective mixing during the year. Such a find-

ing appears to support our result of deeper M2LDs in midlatitude oceans global wide. It may serve as obser-

vational evidence for an improved accuracy of our proposed algorithm, and suggest its better performance

compared with other schemes in areas of strong seasonality (see Figures 1a and 1b) due to a potentially

higher signal-to-noise ratio.

4. Discussions

It is necessary to explore the mechanisms of annual M2LD formation and understand their consequences.

As is commonly known, oceanic MLD is ultimately determined by solar heating and wind forcing from the

atmosphere [Sall ee et al ., 2010]. Generally, the MLD is proportional to the intensity of combined forcings of

these two factors as illustrated in Figure 10, where the annual SST amplitude is considered as a proxy of

buoyancy forcing, and the 10 year return extreme wind speed is regarded as a proxy of turbulent forcing.

Specifically, as far as solar radiation is concerned, it is well known to have a dominant annual cycle. Spatially,

the combined effects of atmospheric path length and inclination of earth’s axis cause earth to receive more

solar heat in the tropics, less at the temperate latitudes, and the least at the poles. Temporally, however, tak-

ing into account the seasonal north-south migration of the sun, the annual cycle of average daily solar radi-

ation is most pronounced at the middle and higher latitudes where the angle at which the sun’s rays strike

earth and the length of daylight change dramatically from summer to winter. As a combined effect, the

annual flux of solar radiation is greatest at the midlatitudes, smallest around the equator, with polar regions

in between. Consequently, heat is transferred to and from the ocean at the sea surface in hemispheric

summer and winter, respectively. The net effect of these processes is a varying annual change in zonal SSTs

(see Figure 10): 1–2C in the tropics and 2–6C at the middle latitudes. The smaller 1–4C change in tem-

perature at polar latitudes results from the heat transferred locally in the formation and melting of sea ice.

Particularly, the solar forcing is intensified in the northern hemisphere as a result of the significant asymme-

try of land–ocean distribution. A good correspondence between the solar forcing and the M2LD response

appeared as a phase reversal is evident for the global oceans between 45 S–45N (especially the well-

defined regional feature within 35N–45N, see the red and black lines in Figure 10). For the subpolar lati-

tudes of the two hemispheres, solar effect becomes less obvious because of other important forcings such

as the annual cycle of large-scale sea ice variation and the hostile marine environment known as ‘‘furious fif-

ties’’ [e.g., Sverdrup and Armbrust , 2008].

Furthermore, heat that is absorbed at the ocean surface in hemispheric summer is transferred downward

by winds, waves, and currents. While in hemispheric winter, heat is transferred upward toward the cooling

surface. As a result, an obvious correspondence between the basin-scale M2LD pattern and the global

Figure 10. Zonal distributions of M2LD along with annual amplitude of SST variability and 10 year return extreme wind speed as well as

the bathymetry for the global ocean.




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distribution of 10 year return extreme wind speed as well as the SWH climatology is found, and an overall

similarity between the maps of mesoscale M2LD features and eddy evolution behaviors is observed. Note

that a direct correlation between zonal wind belt and M2LD bands does not appear as might be expected.

Instead, our analysis suggests that it is the large waves generated by extreme winds in tandem with non-

wind swells (as jointly represented by SWH, the mean value of the first 1/3 largest ocean waves) which are

virtually responsible for the observed large-scale M2LD pattern. Also, it is worth noting that extreme winds

seem to replace solar heating to be the primary forcing in higher latitudes beyond 645 given their clear

phase relationship with zonal M2LDs. In addition, the much shallower bathymetry within the 50N–60N

band (1000 m) compared with its southern hemisphere counterpart (4000 m) is thought to considerably

accelerate the convection process by enhanced tidal mixing across the water column over the North Atlan-

tic which is known to be an area of deep water formation due to substantial subduction [Nakamura et al .,

2006]. As for the mesoscale features, contributing factors other than eddy shedding may include violent

storms, heavy rain cells, and so on.

It is worth to further discuss the possible reasons behind the largest discrepancy between our result and

those published previously, i.e., the constantly deeper M2LDs in midlatitude oceans (Figure 9b). It should be

kept in mind that the regions of 6(20–45) are homes to all subtropical gyres including the world’s most

energetic western boundary currents such as the Kuroshio and the Gulf Stream. As reported by Guilyardi

et al . [2001], the oxygen-based estimate of the MLD is larger than the temperature-based one in all subtrop-ical gyres, which they ascribe to the persistent downwelling Ekman pumping. Moreover, these regions coin-

cide with the notorious ‘‘roaring forties’’ where extremely high sea state prevails throughout the year [see,

e.g., Chen et al ., 2002, Figure 3b]. The coupled effect of strong currents and waves makes the mixing proc-

esses of these zonal belts quite unique in that mechanical stirring (both lateral and vertical) is competing

with buoyancy forcing to form an insufficient state of mixing at a given location: the turbulence or disturb-

ance may have reached a certain depth while the thermohaline convection is still underway. As such, the

commonly used temperature-based MLD criteria are unlikely to work properly, while our approach appears

to be more effective in dealing with these specific cases from a density point of view. A joint look at the sea-

sonality index in combination with T/S profiles confirms that our algorithm is able to produce reasonable

M2LD estimates under complex thermohaline situations for both temperate and equatorial oceans (see Fig-

ures 3b and 3c). The fundamental difference to account for the observed discrepancy is that previous meth-

odologies mostly rely on individual or monthly averaged T/S profiles, while our seasonality-index-based

methodology takes into account the overall effect of the annual mixing progression. Since reaching theM2LD is a cumulative process which may last for nearly half a year especially in the midlatitudes where the

annual variability of SST has a maximum, our result is, therefore, expected to be closer to the reality, as also

supported by the oxygen-based estimation.

It is also interesting to relate the observed discrepancy to the concept of mixing layer and mixed layer

depths as distinguished by Brainerd and Gregg [1995]. According to their definitions, the mixing layer is the

depth zone being actively mixed from the surface at a given time and generally corresponds to the depth

zone in which there is strong turbulence directly driven by surface forcing. The mixed layer is the envelope

of maximum depths reached by the mixing layer on longer time scales that has been mixed in the recent

past. It generally corresponds to the zone above the top of the seasonal pycnocline. Obviously, our

approach basically deals with the mixed layer while many others might be more sensitive to the mixing

layer. The resulting difference thus corresponds to the so-called ‘‘remnant layer’’ [Brainerd and Gregg, 1995],

which is maximized in midlatitudes where the wave and current-induced turbulences as well as the solar

forcing are peaked (see Figure 10).

5. Final Remarks

Although enough have been said on the importance of MLD to the hydrodynamics and thermodynamics of

the coupled ocean-atmosphere system, it is believed that the special geophysical and biogeochemical

implications of the annual maximum MLDs have not yet been fully recognized. For example, using maxi-

mum monthly MLD ensures that thermal energy lost to the mixed layer in form of solar penetration is lost

on annual time scales and is not merely trapped within seasonal pycnocline or barrier layer waters that are

subsequently entrained into the mixed layer on seasonal time scales. Several studies suggest that changes




13/14

in the maximum depth of the mixed layer from one winter to the next may explain the reemergence of sea

surface temperature anomalies and thus persistence of wintertime SST patterns [ Alexander et al ., 2001; Car-

ton et al ., 2008]. Prakash et al . [2012] argue that the existence of perennial oxygen minimum zones is the

result of restricted ventilation which limits the recharges of the water column with oxygen. Ravichandran

et al . [2012] report a persistent occurrence of a subsurface chlorophyll a maximum just above the top of

permanent thermocline and euphotic depth (to which almost all biological activities are restricted). The

accumulation of multidisciplinary evidences all points to the need for an effective methodology which can

produce realistic estimates of the M2LDs over the global oceans.

With the above scientific backgrounds in mind, and considering the fact that all existing schemes for MLD

estimation are arbitrary and subjective to some degree, we are motivated to develop a truly objective algo-

rithm for deriving M2LD using the best available Argo data. In addition to its pure objectiveness, our criteria

have at least another unique characteristic: the introduction of two independent seasonality indices for both

temperature and salinity based on a decade-long concurrent T / S data set. The combined use of these two

indices is found to effectively optimize the contributions of thermal and haline convections with nearly 80%

of the cases from the former and over 20% from the latter. The proposed strategy is supposed to work glob-

ally, regionally or locally as long as significant periodic forcings such as annual and/or semiannual cycles are

available for one or more of the geophysical properties, but will not be applicable to nonperiodic forcings at

interannual or longer time scales. The validity of our methodology is further confirmed by the spatial correla-tion of the tropical dominance of the saline effect (mainly related to rainfall cycle [see, e.g., Chen et al ., 2003b,

Figure 4]) and the extratropical dominance of the thermal effect (mainly related to solar cycle [see, e.g., Chen

and Li , 2008, Figure 5c]). As far as M2LDs are concerned, a general geographical consistency and a good quan-

titative agreement are found between our new algorithm and those published in the literature by American,

French, and Japanese scientific groups (Figure 9b). Meanwhile, however, it is particularly worth noting that a

major discrepancy of our result is the occurrence of a constantly deeper zonal band compared with other

results of its kind in the midlatitude oceans of both hemispheres. This suggests that our algorithm produces

similar results like other schemes under fully mixed seas, but appears to be more effective under semimixed

(or mixing) seas (i.e., turbulent mixing precedes convective overturning, in which mechanical stirring occurred

without fully homogenizing the temperature). Given the better agreement of our result with the depth of the

oxygen saturation limit (a proxy of the maximum depth reached by the oceanic mixed layer every year), it is

argued that the M2LDs are likely underestimated by some of the existing criteria in these regions. Also, it is

recognized that our M

2

LD distribution is characterized by the coexistence of basin-scale zonal structure andeddy-scale local structure (Figure 7). The impressive two-scale pattern reveals that our new algorithm could

be more efficient in resolving finer structures associated with realistic M2LDs. As such, it is clear that the M2LD

may serve as an integrated proxy for studying the coherent multidisciplinary variabilities in the coupled

ocean-atmosphere system, whose roles will be further amplified by long-term deployment of physical, chemi-

cal, and biological sensors onboard future Argo floats.

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Acknowledgments

This research was jointly supported by

the Natural Science Foundation of

China under grants 41331172,

U1406404, and 61361136001 and the

Global Change Research Program of

China under grant 2012CB955603. We

would like to thank J. Buck from the

British Oceanographic Data Center andan anonymous Reviewer for their

thorough and helpful reviews on the

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Special thanks go to the China Argo

Real-Time Data Center for providing us

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CHEN AND YU 595
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an objective algorithm for estimating maximum oceanic mixed layer depth using seasonality indices...

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