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THESIS

THE CLIMATOLOGICAL SEASONAL RESPONSE

OF THE OCEAN MIXED LAYER IN THE

EQUATORIAL

AND TROPICAL PACIFIC OCEAN

by

Harry J. Ries, Jr.

March 1988

Thesis Advisor Roland W. Garwood, Jr.

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TITLE (Include Security Classification)

THE CLIMATOLGGICAL SEASONAL RESPdJSS OF THE OCS.\N MIXED
LAYER III THE SQUATCRIAL AND TROPICAL PACIFIC OCEAN

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Ries, Harry J,

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Ocean Mixed Layer

Equatorial and Tropi cal Pacific Ocean

■JABSTRACT {Continue on reverse if necessary and identify by block number)

The seasonal changes of mixeci layer ciepth (MLD) can be related to
the forcing by the net surface heating and wind speed. This is shown in
this study by comparing the monthly mixed layer depth from temperature
profiles in the Bauer-Robinson Numerical Atlas with monthly net
surface heating and wind speed obtained from the Weare Marine Climatic
Atlas of the Tropical Pacific Ocean. Using a conceptual model based on
mixed layer physics, ocean response and atmospheric forcing are examined
using the Obukhov mixing length. A pattern in the seasonal variation of
upwelling along the Equator is also examined. The model links the
atmospheric and oceanic climatologies through the derived MLD (oceanic
data) and Obukhov mixing lengths (forcing data). The results show a
high degree of pattern similarity between the seasonal response of the
ocean and the seasonal changes in atmospheric forcing. The pattern of

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seasonal influence on KLD at the Equator is very weak in
comparison to that of the tropics and sub-tropics.

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The Climatological Seasonal Response

of the Ocean Mixed Layer in the Equatorial

and Tropical Pacific Ocean

by

Harr\^ J. Ries, Jr.

Lieutenant, United States Navy
B.A., Pennsylvania State University
University Park, Pennsylvania, 1979

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY

from the

NAVAL POSTGR.'\DUATE SCHOOL
March 1988

ABSTRACT

The seasonal changes of mixed layer depth (MLD) can be related to the forcing
by net surface heating and wind speed. This is shown in this study by comparing
the monthly mixed layer depth from temperature profiles in the Bauer-Robinson
Numerical Atlas with monthly net surface heating and wind speed obtained from the
Weare Marine Climatic Atlas of the Tropical Pacific Ocean. Using a conceptual model
based on mixed layer physics, ocean response and atmospheric forcing are examined
using the Obukhov mixing length. A pattern in the seasonal variation of upwelling
along the Equator is also examined. The model links the atmospheric and oceanic
climatologies through the derived MLD (oceanic data) and Obukhov mixing lengths
(forcing data). The results show a high degree of pattern similarity between the
seasonal response of the ocean and the seasonal changes in atmospheric forcing. The
pattern of seasonal influence on VI LD at the Equator is very weak in comparison to
that of the tropics and sub-tropics.

TABLE OF CONTENTS

I. INTRODUCTION 10

II. CLIMATOLOGICAL DATA AND MIXED LAYER

DYNAMICS 11

A. THE CLIMATOLOGICAL DATA SOURCES 11

1. The Bauer-Robinson Numerical Atlas 11

2. The Weare Marine Climatic Atlas . 12

B. METHODS OF DETERMINING MIXED LAYER

DEPTH . 16

C. A ONE-DIMENSIONAL MODEL OF THE MIXED

LAYER 17

1. The Temperature Equation 18

2. The Structure Equation 20

3. The Equilibrium Solution 22

4. The Equilibrium Solution in the Presence of Vertical
Advection 22

D. SUMMARY OF EQUATIONS IN THE CONCEPTUAL
MODEL 23

III. RESULTS: SEASONALLY CHANGING CLIMATOLOGICAL
ASPECTS OF MIXED LAYER DEPTH 24

A. LARGE AREA CONTOURS OF MIXED LAYER DEPTH 24

1. The Slope of the Equatorial Thermocline 24

2. Seasonal Changes of Mixed Layer Depth Contours in

the Eastern Pacific Ocean 26

B. SMALL AREA ANALYSIS OF ATMOSPHERIC

FORCING AND MIXED .30

1. Atmospheric Forcing 30

2. The Oceanic Response 35

C. THE FLUCTUATION FIELDS 41

1. The Derivation of Fluctuating Quantities 41

2. Statistical Analysis .42

D. THE VERTICAL INTEGRAL OF TEMPERATURE

WITHIN THE SURFACE LAYER 51

E. THE OBUKHOV MIXING LENGTH 51

IV. CONCLUSIONS 60

APPENDIX A: MERIDIONAL SECTIONS OF TEMPERATURE 62

APPENDIX B: MONTHLY MLD CONTOURS 70

APPENDIX C: ENHANCEMENT OF DEEPENING AND

SHALLOWING OF MLD ^

APPENDIX D: MODIFIED MIXING SCALE 8?

LIST OF REFERENCES ^^

INITIAL DISTRIBUTION LIST ^

LIST OF FIGURES

2.1 Numbers of Temperature Profiles for the North Pacific Ocean from

the Robinson Atlas (1976) 13

2.2 Zonal Sections of Temperature (oC) at 1 oN for (a) February and (b)
August 14

2.3 Density of Atmospheric Data from Weare, et. al.(19S0) 15

2.4 A Conceptual Model of the Ocean Mixed Layer 18

3.1 Yearly Average Mixed Layer Depth Contour Interval is 15 meters ......... 25

3.2 Maximum and Minimum Westward Extent of the 30m MLD

Contour 27

3.3 Annual Cycle of North-South Movement of 30m MLD Contour 28

3.4 Annual Cycle of Movement of 30m MLD Contour 29

3.5 Meridians Cross-secting the Area of Study 31

3.6 Net Surface Heating for the Area of Study 32

3.7 Net Surface Heating at 155 oE Contour Interval is 30 W/m 36

3.8 Wind Speed at 155 ©E Contour Interval is 0.5 m/s 37

3.9 Pattern of Seasonal Influence 38

3.10 Mixed Layer Depth at 155 oE Contour Interval is 15 m 39

3.11 Time Rate of Change of Mixed Layer Depth at 155 oE Contour

Interval is lOm/month 40

3.12 Fluctuation in Wind Speed at 155 oE Contour Interval is 0.5m/s 43

3.13 Fluctuation in Net Surface Heating at 155 oE Contour Interval is 20

W;m2 44

3.14 Fluctuation in Mixed Layer Depth at 155 °E Contour Interval is

10m ' 45

3.15 A Seasonal Pattern of (a) Wind Speed and (b) Net Surface Heating in

the Equatorial Pacific Ocean 46

3T6 A Seasonal Pattern of (a) Mixed Layer Depth and the (b) Time Rate

of Mixed Layer Depth 47

3.17 Correlation CoefTicients vs. Latitude along 155<»E (a) Net Surface

Heating and (b) Wind Speed with MLD 48

3.18 Correlation Coefficients vs. Latitude along 155oW (a) Net Surface

Heating and (b) Wind Speed with MLD 49

3.19 Correlation CoefTicients vs. Latitude along 105 ©W (a) Net Surface

Heating and (b) Wind Speed with MLD 50

3.20 Time Rate of Change of Heat in the Water Column at 155 «£

Contour Interval is 35W,'m ^ 52

3.21 Difference of Net Surface Heating and Heat in the Water Column at

155 oE Contour Interval is 35 W/m 53

3.22 Obukhov Mixing Length at 155 «£ Contour Interval is 15m 55

3.23 / Ratio of Mixed Layer Depth and Obukhov Mixing Length at 155 <ȣ 56

3.24 Ratio of Mixed Layer Depth and Obukhov Mixing Length at 155

oW . 57

3.25 Ratio of xVIixed Layer Depth and Obukhov Mixing Length at 105

oW . . . . ^ ■ 58

3.26 Ratio of Mixed Layer Depth and Obukhov Mixing Length at the

Equator 59

A.l Meridional Sections of Temperature ("C) at 90 oW for (a) February

and (b) August 63

A.2 Meridional Sections of Temperature {°C) at 100 oW for (a) February'

and (b) August 64

A. 3 Meridional Sections of Temperature (oC) at 120 ©W for (a) February

and (b) August 65

A. 4 Meridional Sections of Temperature ("C) at 140 oW for (a) February

and (b) August 66

A. 5 Meridional Sections of Temperature (oC) at 170 oW for (a) February

and (b) August 67

A. 6 Meridional Sections of Temperature (oC) at 170 oE for (a) February

and (b) August .68

A. 7 Meridional Sections of Temperature (©C) at 140 °E for (a) February

and (b) August 69

B.l January Vlixed Layer Depth 71

B.2 February Mixed Layer Depth 72

B.3 March Mixed Layer Depth 73

B.4 April Mixed Layer Depth 74

B.5 May Mixed Layer Depth 75

B.6 June Mixed Layer Depth 76

B.7 July Mixed Layer Depth 77

B.8 August Mixed Layer Depth 78

B.9 September Mixed Layer Depth 79

B.IO October Mixed Layer Depth 80

B. 1 1 November Mixed Layer Depth 8"'

B.12 December Mixed Layer Depth °^

C.l (a) Areas of Upwelling and Downwelling and Lines of Zero Surface

Heat Flux (b) and Enhanced Deepening and Shallowing at 155oE ^

C.2 Same as Fig. C.l but at 155oW 85

C.3 Same as Fig. C.l but at 105oW 86

D.l Modified Mixing Scale at 155 oE ■ 89

D.2 Ratio of Mixed Layer Depth and Modified Mixing Scale at the

Equator

I. INTRODUCTION

Numerical modeling of the oceanic planetary boundary' layer (OPBL) has been
advancing steadily since the pioneering work of Kraus and Turner (1967). All
numerical models must be able to accurately reproduce the mean state of the
phenomenon under study to give the predicted variations geophysical relevance. An
understanding of the actual mean state of a fully turbulent OPBL (for a given
geographical region and time scale) is quite often gained from the many climatic atlases
and environmental data sets available to the researcher. The resolution, density, and
qualitv of these atlases and data sets are hishlv variant from one resion of the world's
oceans to another and from one time scale to another.

This study focuses on the mean seasonal response of the OPBL in the equatorial
and tropical Pacific Ocean on a seasonal time scale. The study has been carried out to
provide the numerical modeler with a more definite depiction of the mean state and
seasonal variations of the OPBL in the equatorial and tropical Pacific Ocean.

Several climatic information sources have been examined and evaluated for their
suitability for integration into this study. The Bauer-Robinson Numerical Atlas
(containing oceanic data) and the Weare Marine Climatic Atlas (containing
atmospheric data) were both available in a digitized format on microcomputer hard-
disk storage. All of the computationally derived data were produced and processed by
microcomputer.

A one dimensional conceptual model is utilized to relate the seasonal variations
of atmospheric forcing on the OPBL to the variations of the ocean boundary layer.
These seasonal variations are related using the Obukhov length scale (a modeling
approach) and statistically based correlation coefficients.

The thesis is organized as follows. First, the sources of climatological ocean and
atmospheric forcing data are reviewed, in light of the understanding of mixed layer
dynamics and how mixed layer physics should influence determination of climatological
or average values of mixed layer depth. Next, climatological ocean data are analyzed
to determine the climatological mixed layer depth in the tropical Pacific Ocean.
Finally, seasonal changes in atmospheric forcing are related to to the seasonal changes
in the of mixed layer depth.

10

II. CLIMATOLOGICAL DATA AND MIXED LAYER DYNAMICS

A. THE CLIMATOLOGICAL DATA SOURCES

L The Bauer- Robinson Numerical Atlas

The Bauer-Robinson Numerical Atlas provides monthly temperature profiles
from the ocean surface down to a typical depth of 150 meters at 30 meter intervals.
These monthly temperature profiles represent an average profile for a one degree (of
latitude by longitude) quadrangle. Coverage of the atlas includes all of the world
ocean basins except the Arctic Ocean. A secondary set of data contains the annual
mean temperature and salinity at 30 meter intervals from the ocean surface to the
bottom (or to a 7000 meter depth). Data for the Pacific Ocean portion of the atlas,
the geographical area germane to this thesis, have two categorical differences. Data for
the North Pacific portion was derived from hand digitized mechanical
bathythermograph (MBT) files, prior to 1967. At the present time, the MBT files are a
part of the Master Oceanographic Observation Data Set (MOODS) maintained at the
Fleet Numerical Oceanography Center. Data for the Southern Pacific portion were
compiled up to 1981, and were utilized in assembling the atlas.

Each of the individual observations was interpolated to the 30 meter interval
levels. Then, a mean profile was computed for each of the one degree quadrangle for
each month and level. For the Northern Pacific data, it was necessarv to use a slishtlv
different technique. Mechanical bathythermograph data have good relative accuracy,
but limited absolute accuracy. A system of an average difference mean was employed,
whereby the mean at the surface was used as a starting point. Then, average
temperature differences in each interval were successively added to this starting point.
By this method, false-positive temperature gradients were not produced. The density of
observations contributing to the mean of a particular one degree quadrangle could vary
by as much as two orders of magnitude. This variation of the density of observations
is largely contiguous for particular regions within the equatorial and tropical areas of
study (as charted in Bauer and Robinson 1976).

The data densities for the North Pacific Ocean are displayed in Fig. 2.1. The
data density is lowest along the Equator and increases significantly in subtropical
latitudes. It is clear that high data densities occur along the major shipping routes.

11

For detailed analysis, three meridians were selected: 155E,155W, and 105W. The data
density along these meridians is highly variant. This variation will be considered later
in the results section.

Zonal sections of temperature in the surface layer at IN are presented in Fig.
2.2. Of particular note is the westward deepening of the thermocline between HOW
and 150W, This westward deepening is steeper in August than in February'. The pool
of water warmer that 2SoC in the western Pacific is greater in August as is the volume
of water cooler than I40C and above 150m in the Eastern Pacific. Selected meridional
cross-sections are presented and discussed in Appendix A.
2. The Weare Marine Climatic Atlas

The atmospheric forcing data (e.g. wind speed, zonal wind stress, and the
components for net surface heating) were obtained from the numerical version of the
Marine Climate Atlas of the Tropical Pacific Ocean, by Weare, et. al. (1980). The
area covered by this atlas is the same as the area of study for this thesis (i.e. 40S to
30N and from llOE to 75W). All of the atmospheric data was obtained either directly
or indirectly, using bulk formula, and derived from five million individual marine
weather reports for the years 1957 to 1976. Data from this 240 month period are
condensed into an average climatic year. The data is resolved on five degree
quadrangles. Long term monthly means, and standard deviations for variables such as
wind speed were calculated and examined for gross errors. Bulk, formulas, which are
discussed in detail in Weare er. al. (1980), were applied to each report to obtain the
flux quantities which were then averaged and evaluated. A detailed error analysis is
presented in a companion paper, Weare (1981), for the principal flux quantities utilized
in this thesis, namely latent and sensible heat flux, and solar and infrared back
radiation.

The density of observations varies considerably in space and time (Fig. 2.3).
The data density is lowest south of the equator and east of the date line, between SOW
and 140W in the eastern Pacific Ocean and below 20S. Several quadrangles ofT the
coast of eastern Australia have as many as 3000 total observations, while half of the
240 months have no recorded observations. The eflect of these variations, must 'be
considered in evaluating the analysis. A large region along the Equator (from 160E to
125W) has only 50 (out of a total of 240) months with ten or more observations,
whereas the subtropical regions have four times as many months with ten or more
observations.

12

prrsra

TrrrrrrrTCTTTTTTT

»K;= = = = =TiC'=et:

-I e « Br fc jc = 3= = a it a ■

. - = a « a a

■" " ^ 3 « C S a a O ** B = -*^^ * fe

~ " — saca«c(

-3 tool T* ■■;::£ = "*--• I ^,

Fig. 2.1 Numbers of Temperature Profiles for the North Pacific Ocean from
the Robinson Atlas (1976).

13

February

August

I.', 1 '

V

.-'V* ,,/

ou laj \MJt \MLJt ma laj -m^ so.* mu aj ou >«j

Fig. 2.2 Zonal Sections of Temperature (oQ
at 1 oN for (a) Februar>' and (b) August.

14

U5NC TERM ANNUAL VEJJi
LOC 10 or THE .NtWBER OF OaSERVATIONS

». "JV 1

I ' ' ' I

I I I I I

IZSTE MOTE iwrc JBCW IflCTW MOTW IZCTW lOO"!

ecT

3QrN
20rN

0*

icra

20*3
30*3

40*3

LOMC TTUi ANNUAL UCA.<(
NUMBER OP MONTHS irTH 10 OR MORE 0BSERVAT10H3

izrz i4cra iwz iktw iwrw ucrw laorw joorw aorw

Fig. 2.3 Density of Atmospheric Data
fromWeare, et. al.(1980).

15

B. METHODS OF DETERMINING MIXED LAYER DEPTH

In this study, the depth of the mixed layer is defined as the base of that portion
of the turbulent ocean planetary boundary' layer that is well mixed and homogeneous
in the temperature of the sea water contained in this layer. It is important to note that
ever\'where there is an air-ocean interface (or ice-ocean interface), there will be a
turbulent, well mixed boundary layer dynamically distinct from underlying layers.

The vertical temperature profile is typically the only available indicator of the
extent of the mixed layer depth, although there are known to be conditions of deep
isothermal temperature structure where mixing is controlled by the presence of a
halocline. In the case of convective overturning due to salinity elTects, the mixed layer
depth is known to extend deeper than that which is to be indicated by the temperature
profile. For this reason, Levitus (1982) utilized a density criterion to determine mixed
layer depth. A temperature criterion of sea surface temperature (SST) minus 0.5 oC
(SST - O.50C) was equated to a sigma-t change of 0.125. The direct comparison of a
strictly temperature-derived mixed layer depth (MLD) field, and one that is derived
from the density criterion is misleading. The coefficient of expansion for sea water is a
strongly non-linear function of temperature. A temperature increment of 0.5 oC
corresponds to a broad range of temperatures and salinities extant in the world ocean.
In water with a salinity of 35.0 parts per thousand, the 0.5 oC temperature dilTerence
corresponds to a sigma-t change of 0.075 in the 60C to lO^C range, and, to 0.15 in the
24 oC to 26 oC range. This method of mixed layer depth determination, based on a
density change was attempted in the initial stages of this thesis, but was later
abandoned, due to the absence of monthly salinity data in the numerical atlas. Use of
monthly temperature data and yearly average salinities produced ambiguous results.
However it must be noted that this method would produce physically meaningful
results had salinity data been available in the same temporal and spatial resolution as
the temperature data.

A statistical approach was employed in Bathan (1972) in which a Student-t test
(at the 5% level) evaluated the average of successive groups of three temperatures.
This was continued down the temperature profile until an average was encountered
that was significantly different from the surface value. MLD was determined to be at
this point. Also utilized was a method oi' fitting lines through successive three-step
increments, and comparing the slope of these lines with the slope of a test line.
Neither of these methods were used in this study because the temperature data are

16

based on 30 meter levels and they are too coarsely resolved in the vertical for the above
techniques.

Another method, using an average of two techniques, was employed in Colburn
(1975) and Wyrtki (1962). The first technique derived a depth that was based on a
simple difference of 0.5 «€ from the SST (SST - 0.5 oC). The second technique
examined the temperature profile for the maximum temperature gradient. A depth
was determined from the intersection of this maximum gradient line with a constant
temperature line equal to the SST.

A simple SST - LO^C difference method was used in Robinson (1976) to
determine the top of the seasonal thermocline. In this study, a simple linear
interpolation technique was used to estabhsh the depth at which there existed a
temperature value of sea surface temperature minus 0.5 <»C (SST - 0.5 oC). A visual
inspection of this method using sample temperature profiles indicates that a non-
absolute measure of MLD is obtained. A non-absolute measure of MLD is one that,
when the temperature profile is plotted versus depth, the MLD so determined does not
fall on or within the entrainment zone (see Fig. 2.4). The mixed layer depth value falls
just above the entrainment zone. This non-absolute, but accurate, measure of mixed
layer depth is considered better suited for analysis of fluctuations (Levitus, 1982) and
for comparison with the atmospheric forcing variables, and so is used in this study.

C. A ONE-DIMENSIONAL MODEL OF THE MIXED LAYER

In Kraus and Turner (1967) a one-dimensional model of the seasonal movements
of the thermocline is proposed. The rate at which the ocean mixed layer will deepen or
shallow is dynamically dependent upon the conversion of turbulent kinetic energy
(TKE) to potential energy (PE). This conversion results from a balance, or imbalance,
in the rate of production of TKE, due to wind stirring, and the rate of buoyant
damping within the turbulent mixed layer, due to surface heating (conversion of TKE
to PE). The temperature of such a dynamic mixed layer is determined by the sum of
the surface heat flux and the entrainment heat flux. The entrainment heat flux, at the
base of the mixed layer, with an active entrainment zone, is depicted in Fig. 2.4, which
also depicts the conceptual model used in the analysis of data in this study.

The seasonal changes in MLD can be related to seasonal changes in wind stress
and surface heating. The wind stress provides the turbulent energy required for mixing
the ocean boundary layer. The gain or loss of heat at the top of the ocean boundary
layer will either augment or dampen the turbulence caused by wind mixing. A solution

17

Fig. 2.4 A Conceptual Model of the Ocean Mixed Layer.

18

for a diagnostic depth of retreat (the depth to which MLD, h, will shallow or retreat)
can be obtained which is proportional to the Obukhov Mixing Length when the mixed
layer achieves steady state ^h,'^t = 0, or is no longer entraining cold water from below
the mixed layer.

1. The Temperature Equation

The time rate of change of temperature within the surface layer is derived
from a one-dimensional heat equation (2.1). Averaged quantities are denoted by an
overbar (-), while fluctuation quantities are denoted by a prime ('). The subscripts h
and 0 respectively denote quantities at MLD and at the surface.

dJidt = ' d;dz(yrT\ + d!dz{Wf\ - W 8T;dz + k(^2T;^z2) (eqn 2.1)

Starting from the right hand side (RHS) of equation 2.1, term (1) is the
vertical turbulent heat flux (entrainment heat flux); term (2) is the net surface heat flux
(Q^/pC ); term (3) is the vertical temperature advection (resultant from internal
adjustments); and term (4) is the eddy diffusion.

Scale analysis, from Garner (1983), of equation 2.1, uses similar values for
variables found in the climatologies, currently under study on a seasonal time scale,
and permit the omission of the eddy diffusivity (term 4). Eddy diffusivity typically
ranges from approximately 0.1 to 0.5 (cm^,'sec), while the second derivative of
temperature is 5 degrees C,(5000cm)^, which is on the order of 1/10'' (all other terms in
the above are I/IO''). Thus, equation 2.1 is simplified to the form of equation 2.2

5T/at=-a,5z(WT')j^ + ^;5z(W'T')q - W (^T/^z). (eqn 2.2)

Term 1 on the RHS of equation 2.2, i.e.. the entrainment heat flux at the base of the
mixed layer, is equal to the magnitude of the temperature jump (AT) in the
entrainment zone multiplied by the entrainment rate (W ) as in equation 2.3

(WT\=-ATW^. (eqn 2.3)

After a vertical integration and using (WT')|q = Q^/pC , equation 2.2 simplies to
equation 2.4

5T/^t= Q/(pCph) - (AT W^)/h. (eqn 2.4)

19

The density of seawater is p and the specific heat of seawater is C . Vertical advection
does not appear in equation 2.4, since it does not affect the time rate of change of
temperature in the mixed layer. Vertical advection can actually advect the thermocline
to the surface only in coastal waters and thus directly affect SST. Interior adjustment
(due to advective processes) can indirectly alTect mixed layer temperature. Advection
can reduce, via the variables W and AT, h which in turn can increase the
entrainment.

The rate of change of turbulent heat flux as a function of depth within the
(well-mixed) turbulent ocean boundan,' layer is Unear. The vertical turbulent heat flux
at the base of the mixed layer is usually negative, given the predominant climatological
conditions of ^T/5z > 0 in the world's oceans. The entrainment rate becomes zero
when the mixed layer is in a steady state or in retreat. It is physically impossible to
unmix the water in the mixed layer upon application of the Second Law of
Thermodynamics. For this reason, a Heaviside step function (A), which is zero when
in steady state or when in retreat, is introduced into equation 2.4 so that the fmal
equation is 2.5

^T;^t= Q^/(pCph) - A (AT W^)/h. (eqn 2.5)

2. The Structure Equation

The structure of the turbulent mixed layer is best examined by evaluating the
time rate of change of mixed layer depth (h). The time rate of change of MLD is
represented dynamically by the difference between the entrainment rate and the rate of
movement of the interface at the base of the mixed layer due to advective processes as
expressed in equation 2.6

^h,at = W^ - W(z = -h). (eqn 2.6)

From the shear production term of the TKE equation as developed in Kraus and
Turner (1967) we know that the kinetic energy (KE) of wind stresses is converted into
TKE, which in turn is used in the entrainment process to maintain or deepen the mixed
layer. The entrainment rate is identically equal to the rate of work done in the
production of turbulence by wind stresses as applied at the ocean surface. As shown in
equation 2.7, the wind stress (t) is computed as the product of the density of air (p^), a

20

drag coefficient (C ,), and the wind velocity measured at ten meters above the ocean
surface, and is also equal to the product of the density of air and the vertical turbulent
momentum flux at the surface:

Let the last term in equation 2.15 be representative of a velocity scale for the
atmospheric boundary layer or friction velocity (u"), then the vertical turbulent
momentum flux across the air-ocean interface can be related to u*" for each of the
respective layers. Given that the density of seawater is SOO times greater than that of
air, an important comparison of the velocity scales of the atmospheric and oceanic
boundary' layers is shown in equation 2.8.

u*^(ocean) = u*^(atmosphere),'800 (eqn 2.8)

The velocity scale for the ocean boundary layer will be represented by u*. This
velocity scale is representative of the largest eddies in the wind driven mixed layer.

The effect of surface heating is to make the water of the mixed layer more
buoyant. More work must then be expended to mix this warm water down towards
the entrainment zone. Under conditions of a net surface flux into the water of the
mixed layer (Q^ > 0), the heating term is a sink of turbulent energy, as represented in
equation 2.9, where a is the coefficient of expansion for seawater, g is the gravitational
acceleration, Cj and C2 are proportionality constants.

W^ X C^iu^'f - qagQ^/lpCp) (eqn 2.9)

As shown in equation 2.10 the conversion rate of TKE to potential energy
(PE), due to entrainment, (term I) is expressable as a diflerence between the rate of the
creation of turbulent kinetic energy by wind stirrmg (term 2), and the conversion o'i
TKE into PE due to buoyant damping (term 3).

agh AT W^ = C^(u-^=)^ - C.agh [Q^/(pC )] (eqn 2.10)

21

Windspeed is proportional to u*-^ Thus it can be shown in equation 2.10 that
by doubling the wind speed the entrainment rate (W ), and hence the deepening rate
(^h/5t), increases by a full order of magnitude.

3. The Equilibrium Solution

In the absence of vertical advection and in the steady state (i.e. ^h,^t = 0), an
equiUbrium depth of retreat (h^) be derived. Solving equation 2.10 for W^ and
substituting equation 2.10 into equation 2.6 subject to the prescribed steady state
conditions (and W(z=-h) = 0), the depth of retreat is:

h^ = (Cj/C,) ((u*)^' [ag Q,;(pCp)]} a: L . (eqn 2.11)

The depth of retreat is proportional to the Obukhov length scale (L). This length scale
is physically representative of the maximum depth of turbulent mixing, constrained by
the surface boundary' conditions of heat flux and wind stress, for a mixed layer in
equilibrium and not afTected by vertical advection (Muller, Garwood, and Garner,
1983).

4. The Equilibrium Solution in the Presence of Vertical Advection

The term W /D in equation 2. 12 is a measure of the vertical advective velocity
at the base of the mixed layer. If vertical advection is present and MLD is at
equilibrium (i.e dh/dt = 0), then it can be shown from equation 2.10 that the vertical
advective velocity must be balanced by the rate of mechanical production of turbulence
(by wind stirring) minus the buoyant dampmg of the turbulence (by surface heating).
Such a balance is shown in equation 2.12. Equation 2.13 is derived from 2.10 when the
Heaviside step function is set to zero. When the dilTerential equations 2.12 and 2.13
are solved numerically, the results indicate that mixed layer depth adjusts to an
equilibrium depth equivalent to one-half the Obukhov mixing length (L/2) as in
equation 2.14.

W^h/D = (C^u*^),(agh AT) - (C2Q,)/(pCp AT) (eqn 2.12)

dJldt = Q„/(pCph) - [AT \V^/h](A = 0) • (eqn 2.13)

h = [Cd + c^)] [(u-^=-');(ag Q,/pC ) = L;2 (if C-,= 1) (eqn 2.14)

22

As shown in equation 2.14, MLD is not sensitive to the rate of vertical advection, but
the numerical solution for the equilibrium time of adjustment indicates that it is
sensitive to variance in the rate of upwelling of downwelling. The subject of enhanced
time rate of change of MLD in the presence of downwelling and upweUing is discussed
in Appendix C.

D. SUMMARY OF EQUATIONS IN THE CONCEPTUAL MODEL

A Summary' of principle equations from the preceding sections is used to relate
seasonal fluctuations in MLD to seasonal fluctuations in atmospheric forcing in the
tropical and equatorial Pacific Ocean. This summary of equations forms the basis of
the conceptual model that is used to estabhsh and evaluate the relationship between
the seasonal response of MLD to atmospheric forcing in this study. The first four
equations use atmospheric forcing data and the fifth uses oceanic data. The
temperature equation (Equation 2.16) is obtained from Equation 2.4. The structure
equations (Equations 2.17 and 2.18) are obtained from Equations 2.10 and 2.6. The
equilibrium solution for depth of retreat (Equation 2.19) is obtained from Equation
2.11. Mixed layer depth (Equation 2.20) is determined to be at the depth at which the
temperature equals the SST minus 0.5 «»C.

5T/^t= Q/(pC h) - (AT WJ/h (eqn 2.16)

p ^

agh AT W^ = Cj(u*)^ - qagh [Q^/(pCp)] (eqn 2.17) .

ah/at = W^ - W(z = -h) (eqn 2.18)

h^ = 2u^=^ / (agQ^/pCp) cc L (eqn 2.19)

MLD = (Depth where temperature = SST -0.5oC) (eqn 2.20)

23

III. RESULTS: SEASONALLY CHANGING CLIMATOLOGICAL
ASPECTS OF MIXED LAYER DEPTH

A. LARGE AREA CONTOURS OF MIXED LAYER DEPTH

Here we examine a region of the Pacific Ocean that lies between 40S and 30N,
and llOE and 75W. It is within this region that the two principle climatologies under
study overlap. The seasonal variations of MLD will be examined within this region,
since recent efforts of numerical modeling have beaun to focus on this resion, and
useful information about climatoloaical seasonal variations is needed. Mixed laver
depths for each one degree quadrangle were computed using the SST minus 0.5 oC
criterion method which was described in Chapter II. For those quadrangles covered by
land, and consequently with no data, filler values were inserted so as not to distort
adjacent contours. Each of the monthly fields were then contoured on a Mercator
projection, producing minimal distortions and inaccuracies.

An average annual field of MLD was computed from the average of the monthly
temperature profiles in each quadrangle. Fig. 3.1 shows the yearly average mixed layer
depth. The monthly variations of mixed layer depth from the annual mean are shown
in Appendix B.

1. The Slope of the Equatorial Thermocline

The westward deepening of the equatorial thermocline is an observed
phenomenon that is generally well understood. A westward deepening of the region of
tightly packed isotherms is evident in the latitudinal cross-section at IN in Fig. 2.2.
Moreover, a seasonal change is evident in the slope of this region. In the February
plate (Fig. 2.2a) the 25 oC isotherm intersects the surface at 120W and is at a depth of
80 meters at 130E, while in the August plate (Fig. 2.2b) it intersects the surface at
145W and it is at a depth of 90 meters at 130E.

As described in Pickard and Emery (1982), the wind over the equatorial Pacific
Ocean is predominantly westward. As a result, the South Equatorial Current flows
towards the west. As the westward flowing currents encounter the land barriers on the
western side, a surface slope develops that is upward toward the west, and a pressure
gradient develops toward the east. A thicker surface layer is developed, and the
thermocline has a slope opposite to the surface slope. This upward sloping (toward the
east) thermocline has an important etlect on the mixed layer, in both the western and
Eastern Pacific Ocean, according to Gill (1982).

24

HE-'

Fig. 3.1 Yearly Average Mixed Layer Depth
Contour Interval is 15 meters.

25

This effect is evident in the reduction of the time rate of change of mixed layer
temperature. In equation 2.4, MLD (h) appears in the denominator of the surface heat
flux and entrainment heat terms. An increase in MLD reduces both terms in equation
2.4. In the Eastern Pacific Ocean, cold water exists close to the surface due to
up welling (see below). Again examining equation 2.4, it is evident that a shallower
iMLD (h) will increase the time rate of change of the temperature of the mixed layer.
The role of a shallower MLD (h) is also important in the structure equation (equation
2.10), where h also appears in the denominator of both terms on the RHS when the
equation is rearranged so that only the entrainment rate (W ) appears on the LHS. A
smaller h will result in an increased entrainment rate. The effect of an increased
entrainment rate is evident in equation 2.6 and an increase in the time rate of change
of MLD will result. The water of such a shallower layer is thusly more easily mixed,
and cooling of the surface waters during periods of active entrainment. During inactive
periods, the surface layer can become a thin, relatively warm skin of water, in response
to the hish levels of surface heating. The surface lavers above the thermocline in the
western Pacific are warm and deep. Changes in entrainment, or heating rates, do not
affect the surface temperature a great deal.

2. Seasonal Changes of Mixed Layer Depth Contours in the Eastern Pacific Ocean

The most prominent feature of the yearly average field (Fig. 3.1) is the tongue
of shallow mixed layer depths protruding westward, along the equator, from the
Eastern Pacific Ocean. Further inspection of the monthly fields (see Appendix A)
reveals that this feature moves meridionallv and zonallv throughout the vear. The 30
meter contour recedes to its minimum westward extent in December, and extends to its
maximum extent in April. The minimum and maximum longitudinal extent of the 30
meter contour is shown in Fig. 3.2, and the full annual cycle is shown in Fig. 3.3 The
annual cvcle of latitudinal movement is shown in Fie. 3.4 .

The general appearance of this 30 meter mixed layer depth contour closely
resembles the patterns of SST which feature a tongue of cold water extending east-west
along the equator. This cold tongue is associated with strong upwelling occurring in
the water column. In Wyrtki (1981), the tongue of surface cold water was investigated
and determined to be maintained by the process of advection of cold water from the
east, and by upwelling of cold water from below. Wyrtki (1981) further established
that the cause of this tongue was due to the upwelling process.

26

Westward Extent of 30m MLO Contour

ISO W

D

f-N
0

-s

-A

■J
•J
-M
•A

M

F

HOW

M

o
n
t
h

Fig. 3.2 Maximum and Minimum Westward Extent
of the 30m MLD Contour.

27

Latitudtnal Movement of 30m MLO Contour

Month

D N 0 S A

J M A M f I

Fig. 3.3 Annual Cycle of North-South Movement
of 30m MLD Contour.

28

d

J'

u

a

O
O

3aniLLvi

Fig. 3.4 Annual Cycle of Movement
of 30m MLD Contour.

29

The seasonal variation of upvvelling rates are related to the annual fluctuations
in the trade winds. The upwelling is stronger on average from September to
November. The upwelled water is found to "preferably go to the winter hemisphere,
while the supply comes from both hemispheres" (Wyrtki, 1981). This seasonal cycle in
upwelling, due to Ekman divergence, corresponds to the minimum and maximum in the
westward extent of the 30 meter mixed layer depth contour, as illustrated in Figs. 3.2
and 3.3 In Fig. 3.4, the 30 meter contour appears to be shifting toward the winter
hemisphere,

Although these results are not conclusive, they seem to suggest that on
seasonal time scales in the equatorial region of the Eastern Pacific Ocean, the
dominant term in equation 2.18, which most affects changes in mixed layer depth with
respect to time, would appear to be the upwelling rate rather than the entrainment
rate. A measure of vertical advection W(z = -h) is presented later in this chapter in the
Difference of Net Surface Heating and Heat in the Water Column data fields.
Comparison of the magnitude of these data fields indicate that advective processes are
most dominant in the Eastern Pacific Ocean.

B. SMALL AREA ANALYSIS OF ATMOSPHERIC FORCING AND MIXED

Layer Depth

The large area contours of mixed layer depth do not prove useful for detailed
analysis of atmospheric forcing and mixed layer response, since many of the contours
are poorly resolved. For this reason, the area of study has been cross-sectioned by the
Equator and three principal meridians at 155E, 155W, and 105W, as shown in Fig. 3.5.
In this way it becomes easier to focus on the seasonal variations of MLD and how
these variations differ by latitude and by meridional region within the area of study.

1. Atmospheric Forcing

The net heating of the sea surface (Q ) is the algebraic sum of the primary
sources of heating, to solar radiation (Q.), minus the losses of heat due to long wave
back radiation (Q^). 'ind latent (Q.) and sensible (Q. ) heating of the atmosphere by the
sea, as described in equation 3.1 .

Qo = Qs-(Qb + Ql + Qh). {eqn3.1)

Large area contours of the atmospheric forcing variables for the area of study
are included in Weare (1980). Only the annual mean is included here (Fig. 3.6) which

30

Fig. 3.5 Meridians Cross-secting the Area of Study.

31

Fig. 3.6

Net Surface Meatin.2 for the Area of Study.

32

shows a maximum region of heating in the Eastern Pacific Ocean protruding westward
along the Equator to 135W and a much lower maximum of 60 W/m" along the
Equator in the Western Pacific Ocean. The variance of the mean values (of net
oceanic heating) can vary as much as +/- 30 watts per square meter, with a 95%
confidence interval (Weare, 1981). Therefore, any qualitative consideration of the
results in this section must be evaluated in light of these stated variances.

One of the atmospheric circulation patterns dominant in the equatorial and
tropical Pacific Ocean is that of a Walker circulation. The Walker circulation pattern is
that part of the meridionally averaged How which is primarily due to the atmospheric
heating symmetric about the Equator. This circulation, discussed in Gill (1982),
originates in a region of rising motion over the longitudes of greatest atmospheric
heating (in the western Pacific), and is perpetuated by eastward latitudinal flow aloft to
a region of sinking motion over the eastern longitudes. Cyclonic motion in the air
column is centered on the western flank of the heating zone. A system of easterly
winds at the surface connects the sinking and rising regions. The zonally averaged
flow, in the area of study, is typified by Hadley cell circulations, with rising motion
occuring over and on each side of the Equator. In the northern cell, the upper air flow
turns to the north, where the flow will eventually sink to the surface and flow south,
completing the circulation. The converse is true south of the Equator, where the upper
air part of the circulation turns southward. The combined averaged flow at the
surface, for the most part, produces the Easterly Trade Winds. In the southern
hemisphere a regime of southeasterly flow converges on a region of calm winds known
as the Doldrums. The Doldrums occur between 4N and ION (Pickard and Emer>',
1985). In turn, the northeasterly trade regime converges upon the doldrums in the
northern hemisphere. Divergent flow within the wind-driven, westward flowing South
Equatorial Current along the Equator is the primary cause of the equatorial upvvelling
referred to in the last section.

It is within the context of these atmospheric circulation patterns that fields of
surface heating and wind speed must be discussed. The surface heating field, in Fig.
3.7, presents seasonally varying regions, within the area of study, that are very different
from each other.

In the Western Pacific Ocean the average annual ocean heating is less than in
the Eastern Pacific, as seen in Fig. 3.6 A seasonal pattern is evident, in Fig. 3.7. at
155E with a strongly pronounced region of upward heat flux (Q is negative), located

33

in the southern latitudes below 5S, during the southern hemispheric winter months of
March through September. Directly to the north is a weaker pattern of downward heat
flux (with a maximum of +120 Watts, m^) during the northern hemispheric summer
months. In the central Pacific region, the summer heating and winter cooling of the
sea surface is not as strong as it is to the west. In the Eastern Pacific Ocean, strong
winter cooling occurs in the southern tropics and sub-tropics. Along the Equator, a
narrow band of strong heating is prevalent through nine months of the year. In the
northern hemisphere, heating decreases and a minimum occurs during the summer
months. To explain this summer minimum, it is necessary to recall that large scale
subsidence exists in the air column above the eastern Pacific Ocean as part of the
Walker Circulation. The latent heating losses from the sea surface to the atmosphere
are at a maximum when cloud cover is also at its maximum in the Eastern Pacific
ocean. This is caused by low level cloud cover which becomes thickest during the
summer months and is associated with a subsidence produced inversion. However,
throughout most of the year the largely cloud free air column permits a greater amount
of solar radiation to become incident on the sea surface than in the Western Pacific
Ocean. In the plot of equatorial net heating a minimum heating in the eastern Pacific
Ocean during June and July is also evident. Surface heating is greater in the eastern
ocean than in the western ocean. A heating cycle that is not as highly variant is
observed in the central longitudes.

The contours of wind speed at 155E (Fig. 3.9) all exhibit a seasonal pattern.
Winds increase at about the time of the vernal equinox and decrease upon the
approach of the autumnal equinox. The seasonal pattern decreases at lower latitudes.
In each of the meridional fields of wind speed a curved locus connecting wind minima
can be drawn through the low tropics and equatorial region. This locus of wind
minima is interpreted as a line or band of minimum convergence between the
southeasterly and northeasterly trade winds. A diagrammatic and general pattern of
seasonal influence along with a curved line of wind minima are shown in F"ig. 3.8 In
the western Pacific Ocean, Fig. 3.9, the curved line of wind minima bulges from the
winter into the summer hemisphere. This was the eflect noted by Wyrtki and Meyers
(1976), such that the trade wind regime of the winter hemisphere is the larger and
stronger of the two regimes. The wind minima line is not as symmetrically shaped in
the central Pacific Ocean as is that occurring in the west. The wind minima line does,
however, conform to an irregular seasonal influence pattern. In the Eastern Pacific

34

Ocean, the magnitudes of the wind minima are lower and it is apparent that the
southeasterly trade wind pattern extends far into the northern hemisphere. The
southeast trades do, in fact, extend far into the northern hemisphere for most of the
year as indicated in the wind vector diagrams in Weare (1980) and the Handbook of
Oceanographic Tables (Bialek, 1966). The equatorial section of wind speed is lower
than in either the Central or Eastern Pacific Ocean. The Central Pacific Ocean has the
strongest wind speeds along the equator, and the Eastern Pacific Ocean wind speeds
are greater than those in the Western Pacific Ocean.
2. The Oceanic Response

The fields of MLD (Fig. 3.10) exhibit pronounced patterns of seasonal
influence. In the Eastern Pacific Ocean and north of lOS, the pattern is not so
pronounced. One probable explanation is that equatorial and tropical upwelling is
dominant in determining changes of the mixed layer in this part of the Pacific Ocean.
Examining equation 2.6, the seasonally changing wind speed and surface heating are
part of the the entrainment rate term which is balanced by the rate of vertical
advection. If their respective maxima are out of phase, then a mollified pattern of
MLD is possible. This is examined in detail in Appendix D.

The fields of time rate of change of MLD show a response to atmospheric
forcing that is predicted by the one-dimensional model used in this study. In the
Western Pacific Ocean in Fig. 3.11, the ^h/^t contour lines enclose the regions of
shallowing MLD. When this pattern is compared with corresponding wind speed and
surface heating fields, the relationship of atmospheric forcing to the depth of retreat
(see equation 2.11) becomes apparent. Namely, a small decrease in wind speed (raised
to the third power), coupled with a linear increase in heating, does produce the
expected shallowing or retreat of the mixed layer. The converse is true for the region
of deepening. Deepening also occurs at a greater rate in the tropics at the onset of the
winter storm season (between March and May). This rate is greater than it is in any
other time of the year. This is consistent with the mid-latitude results of Elsberry and
Camp (1978). The ^h,{3t = 0 contour enclosing the region of southern hemispheric
shallowing extends far into the northern hemisphere in Fig. 3.11 This corresponds to a
sharp decrease in wind speed associated with the southeast trade winds that extend far
to the north in this region.

35

155 E
Q(NET)

(WATTS/METER ' )

o

-40.0 -30.0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.7 Net Surface Heating at 155 ©E
Contour Interval is 30 W/m.

36

155 E
WIND SPEED

(METERS/SECOND)

-40.0 -30.0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.8 Wind Speed at 155 oE
Contour Interval is 0.5 m/s.

37

•

0)

o

c

u

s

♦^"

«*>

' c

o

""

MM

s

o

o

^•i

(/)

^^

re

flj

o

fiu

/

</5

^ £
« .5

021 0"n OOT 06

OS 07. 09

HINOK

OS oy OS 02

Fig.

3.9 Pattern of Seasonal Influence.

38

loo E
MIXED LAYER DEPTH

(METERS)

-40.0 -30.0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.10 Mixed Layer Depth at 155 "E
Contour Interval is 15 m.

39

155 E
DH/DT

(METERS/MONTH)

..io-""\

-40.0 -30.0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.11 Time Rate of Change of Mixed Layer Depth

at 155 oE
Contour Interval is 10m,'month.

40

C. THE FLUCTUATION FIELDS

1. The Derivation of Fluctuating Quantities

As expected, the atmospheric forcing fields and the fields of oceanic response
show that the seasonal pattern becomes more pronounced as latitude increases north
and south of the equator. The contoured fields of fluctuation from average quantities
also illustrate this pattern. Both the atmospheric forcing fields and the oceanic
response fields for any particular month at a particular location are the sum of a mean
value for that location and a perturbation quantity for that location for that month.
This relation can be expressed:

h(x,y,t) = h(x,y) + h'(x,y,t) . (eqn 3.2)

The fluctuation from average quantities was computed by subtracting the annual
average of the variable in question from the monthly value:

h' = h - h . (eqn 3.3)

The fluctuation fields of wind speed, net surface heating, and mixed layer depth so
determined are shown in Figs. 3.12, 3.13, 3.14 The oceanic response of the monthly
fluctuation in MLD to the monthly fluctuation in atmospheric forcing of wind speed
and net surface heating is easily compared on these diagrams. The expected correlation
between these variables based on the conceptual model developed in the last chapter is
readily apparent in the higher tropical latitudes (greater than ION and lOS), but the
correlation degrades considerably along the Equator. For example, figure 3.14 shows a
deeper than average MLD in the northern latitudes during the winter months of
January and February. As would be expected from the conceptual model the
fluctuation in wind speed in Fig. 3.12 shows a large positive fluctuation. The
fluctuation in surface heating is a large negative one as shown in Fig. 3.13. This
pattern of correlation varies with the seasons in the respective hemispheres and with
position. Stronger correlations exist along the 155E and 155W meridians and weaker
correlations along 105\V. This is a possible consequence of the strong influence of
vertical advection in the eastern tropical Pacific Ocean. The special utility of this
analysis technique is revealed upon examination of the equatorial cross-sections of
each variable. A very weak seasonal pattern that varies in position and time becomes

41

apparent across the equatorial region from east to west and from January through
December. This is the seasonal response of the equatorial MLD to seasonally var\'ing
atmospheric forcing variables.

A distinct region of wind speeds that are below average is diagonally centered
in Fig. 3.15 a. A similarly distinct heating pattern, although with a higher degree of
variance, emerges in the net surface heating field in Fig. 3.15 b. The oceanic response,
in a region of below average winds and strongly positive (downward) surface heat flux,
will be to produce a region of shallower VILD. A region of distinctly shallower mixed
layer depths is observed along the diagonal of the contour of the fluctuation field (Fig.
3.16 a). This pattern is somewhat broken. This disruption in the pattern is probably
the result of vertical advection which may be very strong along the equator. In Fig.
3.16 (b), a region of negative time rate of change of MLD (shallowing) occurs earlier in
the year along the center of the diagonal region of interest and a region of positive
time rate of change of MLD (deepening) occurs later in the year. Such a pattern of
shallowing and deepening supports the result found in the preceding figures.
2. Statistical Analysis

The statistical analysis using correlation coefficients between the atmospheric
forcing by wind and surface heating and the oceanic response of the mixed layer is
examined along the meridians at 155E, 155W, 105W in Figs. 3.17. 3.18, 3.19
respectively. A statistical model is proposed that is based on equation 2.17 of Chapter
II, wherein fluctuations in MLD are positively correlated with wind speed and
negatively correlated with surface heating. A general pattern of negative correlation
with surface heating and positive correlation with wind speed is evident in the figures.
The strongest correlations occur above ION and below lOS.. The degree of correlation
of MLD with surface heating and wind speed is strongest along 155E in Fig. 3.17.
Each of the respective correlation patterns becomes weakest between lOS and ION.
These results are insufficient to indicate whether the statistical model itself is
inadequate or the spatial resolution and seasonal time scale are incorrect for the
equatorial region. The data presented in Figs. 3.15 and 3.16 show that the conceptual
model seems to adequately describe MLD response to atmospheric forcing, but that
the MLD response is verv' weak on a seasonal time scale.

42

155 E
FLUCTUATION IN WIND SPEED

(METERS/SECOND)

§- ''--.. ^^- 0)

o

-40.0 -30.0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.12 Fluctuation in Wind Speed at 155 ȣ
Contour Interval is 0.5m,'s.

43

155 E
FLUCTUATION IN 0(NET)

(WATTS/METER^)

-40.0 -30.0

-20.0

-10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.13 Fluctuation in Net Surface Heating

at 155 oE

Contour Interval is 20 W;m.^

44

155 E
FLUCTUATION IN MLD

(METERS)

-40.0 -30.0 -20.0

-10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.14 Fluctuation in .Mixed Layer Depth

at 155 oE

Contour Interval is 10m.

45

Wind Speed - -

•.

- —

e
•Jj-

e

is-

v.

/ / y k

^r ^\^^j^^ ^

<P<Mtk

'A

2-

>vkyy/

Yy^

V"

Z-

'//.

//

. "■

•

///

//

e

*

^^y

///

Y/

BS.6 143.0 165.0

183.0 203.0 223.0

DECREES EAST LONGirUDE

243.0

263.0 .

....

^et Surface Heating _. .

vc <— . ....

o

• o

e
e-

^^^,

'^Us.lXi

/;

//

^1

«60

/

/

e
• -

^^Oy\ >8o \ /\

xyiy>s\0

^/ /

X.

e

/x^

<^\) (

»,

%

e

y ^>80^ y^ y\

/-'^-^

<./1

o
• e

/jJ///

>80

a

N'

/ / / / /

e

/ / y / y

1

23.0 140.0 t«9.0'

133.0 203.0 223.0

DECR'sKS EAST LONGITUDE

24i3.0

2S9.0

Fig. 3.15 A Seasonal Pattern of (a) Wind Speed
and (b) Net Surface Heating in the Equatorial Pacific Ocean.

46

.MLD -- Shallower than Average (<0)

IZi.O

14S.0

183.0

las.o 20SO 22S.a

DEGR£ZS EAST LONGITUDE

2«S.O

263.0

Deepening Rate-- Supports Above Pattern

129.0

143.0

183.0

183.0 203.0 223.0

DEGREES EAST LONGITUDE

243.0

283.0

Fig. 3.16 A Seasonal Pattern or(a) Mi.xed Layer Depth
and the (b) Time Rate of Mixed Layer Depth.

47

Net Surface Heating with MLD

♦ 1

Wind Speed with MLD

♦ 1

-1

40$ 31

20

10

10

20

30 N

Fig. 3.17 Correlation CoefTicients vs. Latitude along 155oE
(a) Net Surface Heating and (b) Wind Speed with MLD.

48

Net Surface Heating with MLO

♦ 1

us it

Wind Speed with MLD

* 1

as 30 20 10 0 11 21 30 N

Fig. 3.18 Correlation CoefTicients vs. Latitude along I55oW
(a) Net Surface Heating and (b) Wind Speed with MLD.

49

Net Surface Heating with MLD

♦ I

0

48S 3S 21 10 I II :i JON

Wind Speed witti MLD

♦ 1

-1

40S 30 20 10 0 10 20 30 N

Fig. 3.19 Correlation CoefTicients vs. Latitude along 105oW
(a) Net Surface Heating and (b) Wind Speed with MLD.

50

D. THE VERTICAL INTEGRAL OF TEMPERATURE WITHIN THE SURFACE
LAYER

The three dimensional temperature equation (eqn. 3.4) consists of the following

terms on the RHS: the advection term (1), vertical dilTusivity term (2), and horizontal

diffusivity (3). In this analysis only the one dimensional case is considered, terms 1 and

3 are dropped.

aT,5t = -V-VT - ^(T'W')/^z + AjjV^T (eqn 3.4)

In equation 3.5 the vertical integral is taken over the surface layer and the temperature
flux at the base of the surface layer is neglected.

J dT;dx dz = -T'W'o = Q^/pCp (eqn 3.5)

The temperature profiles in the areas under study have been numerically integrated to
produce fields of the time rate of change of the heat content of the surface layer. These
fields are shown in Fig. 3.20.

An indication of vertical advection, assuming horizontal advection and dilTusivity
are negligible, is obtained when the time rate of change of heat content in the surface
layer is compared to the net heating at the ocean surface. The net surface heating is
subtracted from the heat in the water column as shown in Fig. 3.21. If the dilTerence is
less than zero, then upwelling is assumed to account for the disparity in heat content
and heat supply. Contoured diagrams similar to Fig. 3.21 were produced for 155W and
105W, but are not shown. A comparison of the three diagrams indicates that
upwelling is stronger in the Eastern Pacific Ocean along 105W than it is along either
the 155W or 155E meridian.

E. THE OBUKHOV MIXING LENGTH

The diagnostic depths of mixed layer retreat were computed using the
atmospheric forcing data and equation 2.19 The depth of retreat is only a physically
meaningful quantity when there is no active entrainment, and the surface heat fiux is
positive. When the net downward surface heat fiux becomes ver\' small or negative the
mixing length becomes ver>' large or negative, hence it retains no physical meaning. A
standard value greater than 150 meters was inserted in the data matrices in place of

51

155 E
D/DT Q(WATER COLUMN)

OUTTS/METER^)

-40.0 -30. 0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.20 Time Rate of Change of Meat in the Water Column

at 155 oE
Contour Interval is 35W/m.2

52

155 E
Q(WATER COLUMN) - Q(NET)

(WATTS/METER ^ )

o

°i^

-40.0 -30.0

-20.0

-10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.21 DifTerence of Net Surface Heating and

Heat in the Water Column at 155 oE

2
Contour Interval is 35 W/m.

53

those lengths having no physical meaning. This was done prior to contouring so that
those regions at equilibrium would be unafiected by contouring problems.

The Obukhov mixing length fields are presented in Fig. 3.22, and a modified
mi.xing scale (Garwood, et. al., 1985 a and b) and discussion are presented in Appendix
D. The Obukhov mixing length fields show reasonable equilibrium depths in the
tropical and subtropical parts, both north and south of the equator during the
respective Summer times. All show equatorial depths that are either far too shallow or
are not at equilibrium.

When the MLD is divided by the Obukhov length (producing an H/L ratio) for a
given month and location, the fact that the subtropical summer regions reach a brief
state of equilibrium is demonstrated more clearly. This ratio is presented in Figs. 3.23
through 3.26. Higher ratios are found along the equator. There is a large section in
the eastern Pacific Ocean that does reach equilibrium (with ratios close to one),
whereas in the western Pacific Ocean, the ratios are much higher. The results of this
section are inconclusive in determining the role of advection in the seasonal adjustment
of the mixed layer depth in the equatorial and tropical Pacific Ocean. Although
inconclusive on the above stated point of inquiry, the Obukhov mixing length results
results do illustrate a successful attempt to relate two separate climatologies (one
oceanic and the other atmospheric) with a conceptual model based on the physics of
the mixed layer to produce a single additional piece of oceanographic information
(MLD).

■ The H/L ratio presents the same information contained in the statistical
approach using the correlation coefficients. The Obukhov length formulated in
equation 2.11 is computed using the atmospheric forcing variables of wind speed and
surface heating from Weare Marine Climatic Atlas (numerical version). The contours
of Obukhov mixing length shown in Fig 3.22, within those regions at or approaching
steady state from Fig. 3.11. nearly parallel those of MLD (h) in Fig. 3.10. The MLD
was derived from the Bauer-Robinson Numerical ,'\tlas. This modeling approach does
not uniformly work well along the Equator from lOS to lOX. This region has H, L
ratios of 5 or more as shown in Figs. 3.23 through 3.26.

54

155 E
OBUKHOV iMIXING LENGTH)

(METERS)

-40.0 -30.0 -20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.22 Obiikhov Mixing Length at 155 oE
Contour Interval is 15m.

55

155 E
H / OBUKHOV MIXING LENGTH""

(RATIO)

-40.0 -30.0 -20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.23 Ratio of Mixed Layer Depth and
Obukhov Mixing Length at 155 oE.

56

155 W
H / OBUKHOV MIXING LENGTH

(RATIO)

-40.0 -30.0

-20.0 -10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. 3.24 Ratio of Mixed Layer Depth and
Obukhov MLxin? Lencth at 155 oW.

57

105 W
H / OBUKHOV MIXING LENGTH

(RATIO)

-40.0

-30.0

-20.0

-10.0

LATITUDE

0.0

10.0

20.0

Fig. 3.25 Ratio of Vlixed Layer Depth and
Obukhov Mixing Length at 105 o\V.

58

fxq

... o

C— I I — I o

w

o

PQ
O

K

HlNOFl

Fig. 3.26 Ratio of Mixed Layer Depth and
Obukhov Mixing Length at the Equator.

59

IV. CONCLUSIONS

The dilTerence in the resolution between the two climatologies must be
considered when evaluating seasonal patterns in the area of study. The atmospheric
forcing data, resolved on a five decree arid, is much coarser than the one decree arid
on which the oceanic grid is resolved. The one degree grid of the oceanic data misses
many of the most interesting seasonal variations along the Equator which occur on the
scale of +/- 25km. A series of hand plotted temperature profiles were executed in the
bednning of studv to evaluate each of the numerical methods of determinina mixed
layer depth. The location of the temperature profiles varied from the subtropics and
tropics to the equatorial regions in the east, central, and west of the area of study. It
was stated by Levitus (1984) that, of the several methods of determining VILD from
climatological data, no one method seemed superior to any other. It must be noted
that the more interesting approach would have been to use temperature and salinity
data together in a density defined MLD criterion. However, the lack of monthly
salinity data (only annual values for each of the standard depths were available)
precluded the use of this method.

A careful examination of the data obtained from the two climatologies does show
close similarities in seasonal patterns. Although a measure of the relative strength of
vertical advection is presented, it is difficult to establish that disparities in the patterns
of forcing and oceanic response are caused by this advection. The use of statistical
correlation coefficients verified the applicabihty of the conceptual model developed in
Chapter Two in the tropics and subtropics at latitudes greater than lOS and ION.

Three additional patterns were studied. The relationship between seasonal
changes of the MLD and the seasonal changes in upwelling along the equator was
established. A seasonal response of the mixed layer to seasonal changes in atmospheric
forcing along the equator was also presented. The theor\' that enhancement of mixed
layer deepening or shallowing can occur from interior vertical motion seems to be
validated in those regions of the eastern and central Pacific Ocean where advection is
strongest.

Clearly a need for more comprehensive and rehable climatological (large scale)
data is demonstrated by this study. Because of the large variations in the quality of the

60

data within and between the two data sets, more advanced and complete statistical
methods were not attempted. Instead graphical patterns were examined to establish
seasonal relationships. Future large scale studies, such as the one attempted here, will
require much more detailed and accurate observational data sets so that the patterns
that have been shown to be are graphically evident can receive meaningful statistical
validation. This suggests an avenue for future investigation. The use of the Obukhov
mixing length and MLD to Obukhov mixing length ratios (in a modeling approach) is
equally well suited for this purpose and has been, to a large extent, successful in this
study. The use of an expanded area analysis (vice the use of meridians) is necessar>' to
to fully examine and test the application of mixed layer physics in the calculation of
climatological mixed layer depths (on a seasonal time scale) for large parts of the world
ocean. To accomplish this in the equatorial regions, a much more finely resolved (in
both space and time) oceanic data set is required on a grid at least one order of
magnitude more dense than the one used in this study. The results of this study
suggest that the seasonal time scale is not the most appropriate framework within
which to examine mixed layer response to atmospheric forcing very near the Equator.

This study is unique since it initially involved a broad investigation of oceanic
and atmospheric climatological data sources. The study then successfully synthesized
the two distinct data sources, using mixed layer physics and tested these results using a
conceptual model of the ocean mixed layer, into a second generation source of
climatological data. The original motivation for this study was to make this
synthesized information available to the numerical modeler. Unfortunately, the utility
of this synthesized climatological information is limited due to the coarse resolution of
the original climatologies. This suggests that the horizons of oceanographic modeling
are expanding and outpacing our abiUty to reliably modify and verify models against
accurate and detailed observational data. Studies like this one illustrate the need for a
comprehensive world ocean data set that is absolute in coverage and fine in resolution
(in both time and space). Sampling requirements for future large scale observational
expeditions should include salinity measurements taken at the same time and space
intervals as the more easily obtained temperature and pressure measurements.
Endeavors such as the World Ocean Circulation Experiment (WOCE) are crucially
important to the future of physical oceanography.

61

APPENDIX A
MERIDIONAL SECTIONS OF TEMPERATURE

The following meridional sections of temperature (Figs. A.l - A. 7) were extracted
from the Bauer- Robinson Numerical Atlas during the initial stages of this study. The
individual data arrays were useful in testing the several methods of determining VI LD
discussed in Chapter II. These figures are included in this appendix because they
further illustrate the westward sloping equatorial thermocline and provide additional
descriptive detail to the area of study.

62

February

www V //^-x \ y I

•40 S
Latitude

■2(r

'ION

August

«•

5 .

w i :

f ■ i = i =

• I •. \

'40 S
Latitude

ION

Fig. A.l Meridional Sections of Temperature (oC)
at 90 o w for (a) February and (b) August.

63

February

; ' •. X • 1 •

Latitude

»■

\ \ \

August

'40 S
Latitude

i <*

ION

Fig. A. 2 Meridional Sections of Temperature («>C)
at 100 oW for (a) Februar}- and (b) August.

64

February

'« S ' '20

Latitude

'30 N

r

• a

^ ■

: ij •; S

August

/ «/'?/^/ « i

« ■■ s

/7 v\\\y>///

'« S ' '20

Latitude

30 N

Fig. A. 3 Meridional Sections ofTemperature (oQ
at 120 oW for (a) February- and (b) August.

65

February

'40 S ' '20

Latitude

'30 N

August

30 N

Latitude

Fig. A. 4 Meridional Sections of Temperature (oC)
at 140 oW for (a) February- and (b) August.

66

February

?

r

III*

N\\\\\\W.'

. V . . . ^ K

MU\\M\\\ \\ \ ///:::

ilili\\li\\\\\^4^

'40 S '20

Latitude

'30 N

August

'40 S '20

Latitude

30 N

Fig. A.5 Meridional Sections of Temperature (©C)
at 170 oW for (a) February and (b) August.

67

February

r

. « iSi Si ^ \ »

'l * i 5 ■•. a ■;

•»

'40 S
Latitude

'20

'30 N

August

••

i « •;

S; • : » ; S : S

: K I

i / «

• «

1 ai Si 2

i7

» * / -' '• \ / / /•':/;

W V \ \/;VVv.'id^X^ / // /

miiWWv-Mfi^

/■••

UO S ' '20

Latitude

30 N

Fig. A. 6 Meridional Sections of Temperature (oC)
at 170 oE for (a) February and (b) August.

68

February

Latitude

'30 N

August

x* "••.> "^••. y / /

Latitude

< I

30 N

Fig. A. 7 Meridional Sections of Temperature {°C)
at 140 oE for (a) February' and (b) August.

69

APPENDIX B
MONTHLY MLD CONTOURS

The monthly contours of MLD that follow were numerically extracted and
processed within the micro-computer environment of the IBM-PC AT''". The
resolution of the MLD contours is one degree of latitude by one degree of longitude
and each field contains 12,496 data points.

70

aaniiivi

Fig. B.l January Mixed Layer Depth.

71

iin n.i.i.T.VT

Fig. B.2 February Mixed Layer Depth.

72

o

<

aaniiivi

Fig. B.3 March Mixed Layer Depth.

73

<^3

aaniiivi

Fig. B.4 April Mixed Layer Depth.

74

^

Q

Q.

X

(—1 ■

00

* *•• •

1"'!.

aaniiivi

Fig. B.5 May Mixed Layer Depth.

75

V

••• H

. .1 .

-^■^^^'^^ I

if: I V ' • ■ .: C; /-".•

'-^^-^ ;U'' / ;.T //\ ^ ,'rV

)

'^C^

^^^^10,

fV\iX i':T'

'^^..;.:i ;vi :v.;-4---^U;--fc/---:-"i---"

I : ; VA n 1 • ' < :

, , .. . r, ;l_A til O \ , I " '

/^ ;-.A...y\....kNi u...^

-V !\ ' V - ,-0^,-i-N "... -- .^

^qs^

':!«^

mm

o

- o

. O

U

u

u

o
n

o

CM

X

•a

M

aaniiivi

Fig. B.6 June Mixed Layer Depth.

76

■ K ..

■ • Q

• H
. X

i - •

I-.- ;

riTimmtwc^-

X
o

Q

H

O

2
O

aaniixvi

Fig. B.7 July Mixed Layer Depth.

77

■..■• H

s

aaniiivi

Fig. B.8 August Mixed Layer Depth.

78

o

[£\ I— 1

t.';?Si*-'%»-"^

aaniiivi

Fig. B.9 September Mixed Layer Depth.

79

I 1

2^S

aaniuvi

Fig. B.IO October Mixed Layer Depth.

SO

K_

tq:5

<a

;;j^j2i:i.;'.-;/^,T«

aaniiivi

Fig. B.ll November Mixed Layer Depth.

81

<:S

,-f-.. s

,.< ;.V.. . Si...'' 'A ....... j!LCv----r\--/-'-

\ I cj : . ) »» ,rf'i ,:\ » III 1: »/

V I-

■^<NA--,

0 liv.

:j ,' fa I ,';<0 .M V e> H _W.

1 ^ '

<?•

. ■ o

o

o
a

u

aaniuvi

Fig. B.12 December Mi.xed Layer Depth.

82

APPENDIX C
ENHANCEMENT OF DEEPENING AND SHALLOWING OF MLD

The theory that a strong enhancement of mixed layer coohng and deepening can
result from upvvelling between the heating and cooling seasons (MuUer, Garu'ood, and
Garner, 1983) is tested in the composite diagram, Figs. C.1,C.2,C.3. In figure C.2 a,
the clear areas (non-cross-hatched) are those areas where upwelling is indicated from
Figs. 3.21. Downwelling is indicated by the cross-hatched areas. The lines containing
the star symbol are the lines of zero net surface heating indicating a transition between
surface heating and cooling. In Fig. C.2 b, the corresponding field of mixed layer
depth contains areas of probable enhancement of deepening or shallowing that are
indicated within an ellipse. The mixed layer depth contour contained within the ellipse
occurs over a transitionar\" zone and shows an indication of enhanced deepening or
shallowing by its shape. That is to say, there is an obvious protrusion of the contour
line. In the Western Pacific Ocean (Fig. C.l), enhanced deepening and shallowing is
not as prevalent as it is in the Eastern Pacific Ocean, where upweUing and downwelling
may be much stronger. These results tend to verify the theory presented in Muller,
Garwood, and Garner (1983) using climatological data on a seasonal time scale.

83

_155!_E.

°40.0 -JO.O

-10.0 0.0

UTITUDE

10.0

20.0

30.0

-tO.O 0.0

UTITUDE

3o.e

Fig. C.l (a) Areas of Upvvelling and Dowmvelling and

Lines of Zero Surface Heat Flux (b) and

Enhanced Deepening and Shallowing at 155oE.

84

153LyL

-10.0 0.0

LATITUDE

-40.0 -30.0 -10.0

-10.0 0.0

UTITUDE

10.0

20.0

3o.e

Fig. C.2 Same as Fig. C.l but at 155 oW.

85

JLOSl-W.

-40.0 -30.0 -ao.o

>io.o 0.0

UTITUDE

10.0

20.0 30.0

O

a.

-40.0

-30.0 -lO.O

-10.0 0.0

UTITUDE

10.0

20.0

30.e

Fig. C.3 Same as Fig. C.l but at 105oW.

86

APPENDIX D
MODIFIED MIXING SCALE

The one-dimensional model of Kraus and Turner is ver>' heavily dependent upon
the role of vertical advection, W(z = -h), to prevent open ended mixing of the entire
water column on an annual or greater time scale. In Garwood (1977), the. full TKE
budget was utilized to model the mixed layer with certain special considerations.
Garwood proposed a bulk layer model in wliich the rate of entrainment was based on
the total averaee turbulent kinetic eneray in the mixed laver, and on the relative
distribution of this energy among three kinetic energy component equations. In
particular, the redistribution of TKE into the vertical direction is critical for the
occurance of mixing. In addition, the time scale for viscous dissipation of TKE
depends on planetary rotation. The conclusion from Garwood (1977) was that these
special considerations allow a cyclical steady state solution for seasonally van-ing heat
fluxes since dissipation increases with mixed layer depth.

Both the pressure redistribution terms and the rotational stress terms in each of
the component equations of the TKE budget vanish in summation. In Garwood
(1977) the importance of the pressure redistribution terms in the transformation of
horizontal TKE to vertical TKE was proposed as an important energy source for the
process of entrainment. The rotational stress term, within which the Reynolds stresses
interact with the northerly component of planetary rotation, is now believed to be an
important redistribution term within the total TKE budget, as examined in Garwood,
et. a/ (1985 a and b). The direction of turbulent kinetic energy exchange depends upon
the sign of the east-west component of wind stress. Vertical mixing and MLD are
reduced for a westerly wind regime, while easterly winds increase vertical mixing and
MLD. When this theory is applied in the equatorial Pacific Ocean the westward
deepening of the equatorial thermocline is effectively simulated.

Because of these results a new modified diagnostic equation for the equilibrium
mixed layer depth is taken from Garwood (1985 a and b). The modified mixing scale
L(<I>) in equation D.3 is computed by dividing the Obukhov length (L) by the
additional factors in equation D.l. The northward component of planetary rotation is
represented by H and the zonal wind stress represented by T . The surface buoyancy
flux B^ is computed in equation D.2.

87

O = (12y t^) / (p^ B^) (eqnD.l)

B„ = ag{Q^/(pCp) (eqn D.2)

L(<D) = L / [1 + (12/7) <D] (eqn D.3)

The contoured fields of the modified mixing scale (Figs. D.l and D.2) are noisier than
the corresponding Obukhov length fields (presented in Chapter III). This is believed to
be due to the zonal wind stress value used in computing the modifying factor. The
zonal wind stress component was computed using a variable drag coefficient that was
highly dependent upon the stability of the air just above the surface. Comparison of
this zonal wind stress with one derived from hand calculation, using a constant drag
coefficient showed the Weare zonal component to be too small and highly variable.
This additional source of error and variance, given the high degree of the same in
surface heat flux and wind speed, has produced inconclusive results in the fields of the
modified mixine scale.

S8

155 E
MODIFIED MIXING SCALE

(METERS)

-40.0

-30.0

-10.0 0.0

LATITUDE

10.0

20.0

30.0

Fig. D.l Modified Mixing Scale at 155 °E.

89

HiNOH

Fig. D.2 Ratio of Mixed Layer Depth and
Modified Mixing Scale at the Equator.

90

LIST OF REFERENCES

Bathan, K.H., 1972: On the Seasonal Changes in the Depth of the Mixed Layer in the
North Pacific Ocean. Journal of Geographical Research, 11, No. 36, 7138-7149.

Bialek, E.L., 1966: Handbook of Oceanographic Tables (SPSS), U.S. Naval
Oceanographic Office Special Publication, Naval Oceanographic Office,
Washington D.C., 130 pp.

Colburn, J.G., 1975: The Thermal Structure of the Indian Ocean. University of Hawaii
Press, Honolulu, HI., 173 pp.

Elsberry, R.L., and N.T. Camp, 1978: Oceanic Thermal Response to Strong
Atmospheric Forcing. 1, Characteristics of forcing events. Journal of Physical
Oceanography, 8, 206-214.

Garwood, R.W., Jr., 1977: An Oceanic Mixed Layer Model Capable of Simulating
Cyclic States. Journal of Physical Oceanography, 1, 455-468.

Garwood, R.W., Jr., P.C. Gallacher and P. Muller, 1985: Wind Direction and
Equilibrium Mixed Layer Depth: General Theor\-. Journal of Physical
Oceanography, 15, 1332-1338.

Garwood, R.W., Jr., P. Muller and P.C. Gallacher, 1985: Wind Direction a nd
Equilibrium Mixed Layer Depth in the Tropical Pacific. Journal of Physical
Oceanography, 15, 1332-1338.

Gill, A.E., 1982: Atmospheric Ocean Dynamics, Academic Press, Inc., London,
England, 662 pp.

Kraus, E.B., and J.S. Turner, 1967: A One-dimensional Model of the Seasonal
Thermocline II. The General Theor>' and Its Consequences. Tellus, XIX, 1,
98-105.

Levitus, S., 1982: CUmaiological Atlas of the World. NOAA Professional Paper
Number 13, U.S. Government Printing Office, 173 pp.

Muller, P., R.W. Garwood and J. P. Garner, 1984: Effect of Vertical Advection on the
Dynamics of the Oceanic Surface Mixed Layer. Annales Geographicae, 2,
387-398.

91

Pickard, G.L. and W.J. Emery, 1982: Descriptive Physical Oceanography: An
Introduction. Pergamon Press, 249 pp.

Robinson, M.K., 1976: Atlas of North Pacific Ocean Monthly Mean Temperatures and
Mean Salinities of the Surface Layer, U.S. Naval Oceanographic OfTice Reference
Publication 2, Naval Oceanographic Office, Washington D.C., 173 pp.

Weare, B.C., P.T. Strub and M.D. Samuel 1980: Marine Climate Atlas of the Tropical
Pacific Ocean. University of California Press, Davis, California, 147 pp.

Weare, B.C., P.T. Strub and M.D. Samuel, 1981: Annual Mean Surface Meat Fluxes in
the Tropical Pacific Ocean. Journal of Physical Oceanography, 11, 705-717.

Wyrtki, K., 1971: Oceanographic Atlas of the International Indian Ocean Expedition.
National Science Foundation, NSF-IOE-1, Washington, D.C., 74 pp.

Wyrtki, K., 1981: An Estimate of Equatorial Upwelling in the Pacific. Journal of
Physical Oceanography, 11, 1205-1214.

Wyrtki, K., and G. Meyers, 1976: The Trade Wind Field Over the Pacific Ocean.
Journal of Applied Meteorology, 15,698-704.

92

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7. Prof. Peter Muller 1
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CICESE

P.O. Box 4803

San Ysidro, CA 92073

22. Library

School of Oceanography
Oregon State University
Corvallis, OR 97331

23. Conunander

Oceanographic Systems Pacific

Box 1390

Pearl Harbor, HI 96860

24. Chief, Ocean Services Division
National Oceanic and Atmospheric
Administration

8060 Thirteenth Street
Silver Spring, MD 20910

25. Department of Oceanography
University of British Columbia
Vancouver , B.C. Canada

V6T 1W5

26. Library

Bedford Institute of Oceanography
P.O. Box 1006
Dartmouth, N.S., Canada
B2Y 4A2

95

3i(,.%9)

The climatological
seasonal re^nn,,

o^ean mixed ^r °' ''^
^^Juatorial and f ^" ''^^'
^--ific Ocean '°^'^"^

5 K^y c.

3 7 U C 2

»

Thesis

R463

c.l

Ries

The climatological
seasonal response of the
ocean mixed layer in the
equatorial and tropical
Pacific Ocean.

L.