Dud: ry

l 93943

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESIS

ONE-DIMENSIONAL MODEL HINDCASTS OF
COLD ANOMALIES IN THE NORTH PACIFIC OCEAN

by

Gary L. Stringer

December 19 83

Thesis

Advisor: R. L.

Elsberry

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4. TITLE (and Subtitle)

One-Dimensional Model Hindcasts of
Cold Anomalies in the North Pacific
Ocean

5. TYPE OF REPORT 4 PERIOD COVERED

Master's Thesis;
December 19 83

6. PERFORMING ORG. REPORT NUMBER

7. AUTHORS

Gary L. Stringer

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Naval Postgraduate School
Monterey, California 9 3943

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Naval Postgraduate School
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December 19 83

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North Pacific Ocean

Cold Anomalies

One-Dimensional Model Hindcasts

TRANSPAC

20. ABSTRACT (Continue on reveree tide II nmcoammrr «nd Identity by block number)

Two cases of pronounced, long-term cold anomalies from
the North Pacific Ocean Experiment TRANSPAC monthly analyses
during 1976-79 are studied. The first case developed after
October 1977 and persisted to June 1978. Two periods of
amplification of the anomaly are identified. The second
anomaly was the most extreme cold anomaly in the four-year
sample. The relationships between local atmospheric

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forcing, and the development, existence and decay of the
anomalies are examined with the Garwood ocean mixed layer
model. In the first case, the fall deepening period was
hindcast very well. However, the period of spring
transition and seasonal warming were not well predicted,
is deduced that the most likely cause of the errors is
inaccurate atmospheric forcing. In the second case, the
model predictions are very sensitive to the surf ac e heat
flux. This anomaly cannot be satisfactorily simulated with
the Garwood model. This appears to be due to large
uncertainties in the surface heat flux fields in the summer.

It

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One-Dimensional Model Hindcasts of
Cold Anomalies in the North Pacific Ocean

by

Gary L. Stringer

Lieutenant Commander, United States Navy

B.S., University of Washington, 1975

Submitted in partial fulfillment of the
requirements for the degree of

MASTER OF SCIENCE IN METEOROLOGY AND OCEANOGRAPHY

from the

NAVAL POSTGRADUATE SCHOOL
December 19 83

ABSTRACT

Two cases of pronounced, long-term cold anomalies from
the North Pacific Ocean Experiment TRANSPAC monthly analyses
during 1976-79 are studied. The first case developed after
October 1977 and persisted to June 1978. Two periods of
amplification of the anomaly are identified. The second
anomaly was the most extreme cold anomaly in the four-year
sample. The relationships between local atmospheric
forcing, and the development, existence and decay of the
anomalies are examined with the Garwood ocean mixed layer
model. In the first case, the fall deepening period was
hindcast very well. However, the period of spring transi-
tion and seasonal warming were not well predicted. It is
deduced that the most likely cause of the errors is inaccu-
rate atmospheric forcing. In the second case, the model
predictions are very sensitive to the surface heat flux.
This anomaly cannot be satisfactorily simulated with the
Garwood model. This appears to be due to large uncertain-
ties in the surface heat flux fields in the summer.

TABLE OF CONTENTS

I. INTRODUCTION 14

A. PURPOSE AND HYPOTHESIS 14

B. STUDY DESCRIPTION 16

C. DEFINITIONS 18

1. Spring Transition 18

2. Mixed Layer Depth 19

II. DATA SOURCES AND PROCEDURES 21

A. DATA SOURCES 21

B. MEAN AND ANOMALY FIELDS 2 3

C. PREDICTION MODEL 24

III. LARGE-SCALE LONG-DURATION CASE 2 6

A. COLD ANOMALY 12 DESCRIPTION 26

B. MODEL HINDCAST 42

C. ERROR DISCUSSION 65

1. Analysis Error 68

2. Model Parameterizations 69

3. Model Forcing ^0

4. Model Physical Processes 79

IV. LARGE-SCALE RAPID TRANSITION CASE 82

A. COLD ANAOMALY 1 DESCRIPTION 82

B. MODEL HINDCAST 98

C. ERROR DISCUSSION 10°

1. Data Quality 10°

2. Model Physics 102

3. Model Forcing 104

D. REVISED HEAT FLUX CORRECTION 110

V. CONCLUSIONS 121

APPENDIX 125

LIST OF REFERENCES 132

INITIAL DISTRIBUTION LIST 134

LIST OF TABLES

Table 1. Comparison of analyzed CA 12 and model
MA 12 development for each month. The
locations and temperatures given are the
location of the lowest temperature in
CA 12 and MA 12 for each month.

30

Table 2

Table 3

Analyzed and model hindcast heat content
(xl04 cal/cm2) relative to 200 m at
36.0°N, 150. 0°W, their difference, and
the relative error in heat content
above 200 m between analyzed and
hindcast temperature profiles.

Relative error in model hindcast heat
content relative to 20 0 m at the central
point 36.0°N, 150. 0°W when the model was
initialized on 15 February 1978 (column
labeled Hindcast) and when an additional
5 cal/cm^/h was added to the downward
surface heat flux from 15 March to
18 June (last column) .

67

75

Table 4. CA 1 development for each month during

1976. The location (s) and temperature (s
are for the lowest temperatures in the
region of CA 1 for that month.

87

LIST OF FIGURES

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.
Figure 8.
Figure 9 .
Figure 10.
Figure 11.
Figure 12.
Figure 13.

Anomaly Dynamics Study region.

Points at 36°N, 150°W and 40°N, 165°E

mark the location of maximum intensity

for the two anomalies examined. 17

Temperature (°C) anomaly CA 12 at

surface during (A) October 1977 and

(B) November 1977. 32

The ratio of change in analyzed
temperatures (°C) from 15 October to
15 November 1977 to the climatological
temperature change for the same period. — 33

Temperature (°C) anomaly CA 12 during
December 19 77 at (A) surface and
(B) 60 m. 34

Temperature (°C) anomaly CA 12 during

January 1978 at (A) surface,

(B) 60 m and (C) 120 m. 35

Similar to Fig. 3 except for the

period from 15 December 1977 to

15 January 1978. 36

Similar to Fig. 5 except for

March 1978. 37

Similar to Fig. 5 except for

April 1978. 38

Similar to Fig. 5 except for

May 1978. 39

Similar to Fig. 5 except for

June 1978. 40

Similar to Fig. 3 except from

15 April to 15 May 1978. 41

Similar to Fig. 3 except from

15 May to 15 June 1978. 41

Daily maximum model mixed layer depth

and corresponding model mixed layer

temperature (MLT) compared to

objectively analyzed MLT at the center

of cold anomaly 12, 36.0°N, 150. 0°W

from 15 October 1977 to 18 June 1978. 49

8

Figure 14. Model temperature (°C) anomaly MA 12

at surface during November 1977. 50

Figure 15. The ratio of the change in model

temperatures (°C) from 15 October to
15 November 19 77 to the climatological
temperature change for the same period. 50

Figure 16. Model temperature (°C) anomaly MA 12
during December 1977 at (A) surface
and (B) 60 m. 51

Figure 17. Model temperature (°C) anomaly MA 12
during January 1978 at (A) surface
(B) 60 m and (C) 120 m. 52

Figure 18. Similar to Fig. 15 except from

15 December 1977 to 15 January 1978. 53

Figure 19. Similar to Fig. 17 except for March 1978. - 54

Figure 20. (A) Objectively analyzed monthly vertical
temperature (°C) profiles centered on the
15th of the month for October (squares) ,
November (circles) and December
(triangles) 1977. (B) Model monthly
vertical temperature (°C) profiles
averaged over five days centered on the
15th of each month for October (squares),
November (circles) and December
(triangles) 1977. 55

Figure 21. Similar to Fig. 20 except for January
(squares) , February (circles) and
March (triangles) 1978 . 56

Figure 22. Similar to Fig. 20 except for April
(squares) , May (circles) and
June (triangles) 1978. 57

Figure 23. Similar to Fig. 17 except for April 1978. - 58

Figure 24. Similar to Fig. 17 except for May 1978. 59

Figure 25. Similar to Fig. 17 except for June 1978. — 60

Figure 26. Similar to Fig. 15 except from

15 April to 15 May 1978.

61

Figure 27. Similar to Fig. 15 except from

15 May to 15 June 1978. 61

9

Figure 28. Similar to Fig. 13 except at grid

point 38.0°N, 135. 0°W.

Figure 29. Similar to Fig. 13 except at grid

point 40.0°N, 160. 0°W.

Figure 30. Similar to Fig. 13 except at grid

point 34.0°N, 160. 0°W.

Figure 31. Daily maximum model mixed layer

depth and corresponding model mixed
layer temperature at the central
point of cold anomaly 12, 36.0°N,
150. 0°W. The model was initialized
on February 1978 and 5 cal/cm^/h was
added each time step to the downward
surface heat flux from 15 March to
18 June 1978. The objectively
analyzed MLT are denoted by x on
the 15th of each month.

Figure 32. Predicted temperatures (°C) during
March 1978 at (A) surface, (B) 60 m
and (C) 120 m from the model
initialized on 15 February 1978 and
integrated with the addition of
5 cal/cm2/h each time step to the
downward surface heat flux from
15 March to 18 June 1978.

Similar to Fig. 32 except for

April 1978.

Temperature (°C) anomaly CA 1 at
surface during June 1976.

The ratio of change in analyzed
temperatures (°C) from 15 June to
15 July 1976 to the same climatolo-
gical temperature change for the
same period.

Figure 36. Temperature (°C) anomaly CA 1 during
July 1976 at (A) surface (B) 60 m
and (C) 120 m. ■

Figure 37. Similar to Fig. 35 except for period
from 15 July to 15 August 1976.

Figure 33.
Figure 34
Figure 35

62

63

64

76

77

78

88

88

89

90

10

Figure 38. Similar to Fig. 36 except for

August 1976. 91

Figure 39. Similar to Fig. 36 except for

September 1976. 92

Figure 40. Similar to Fig. 36 except for

October 1976. 93

Figure 41. Similar to Fig. 35 except for the

period 15 September to 15 October 1976. — 94

Figure 42. Similar to Fig. 36 except for

November 1976. 95

Figure 43. Similar to Fig. 35 except for the

period 15 October to 15 November 1976. 96

Figure 44. Similar to Fig. 36 except for

December 1976. '• 97

Figure 45. Model temperature (°C) anomaly MA 1 at
the surface during August 1976. The
model used the surface heat flux
correction relative to 200 m as
determined by Elsberry et al. (1982) . 99

Figure 46. Histogram showing the occurrence of
cold anomalies during the period
January 1976 to December 1979. 101

Figure 47. Daily maximum model mixed layer depth
and corresponding model mixed layer
temperature (MLT) resulting from no
surface heat flux corrections being
applied compared to objectively analyzed
MLT at the center of CA 1 40.0°N,
165. 0°E from 15 June to 18 December
1976. 108

Figure 48. Model temperature (°C) anomaly at the

surface during August 1976. No surface
heat flux correction was applied in the
model. 109

2
Figure 49. Correction field (cal/cm /h) relative to

200 m for 15 June to 18 August 1976 to

be applied to the FNOC surface heat

flux fields. 117

11

Figure 50. Model temperature (°C) anomaly at the
surface during August 1976 resulting
from the correction field relative to
200 m being applied to the FNOC
surface heat flux fields. H'

Figure 51. Daily maximum model mixed layer depth
and corresponding model mixed layer
temperature (MLT) resulting from the
new correction field relative to
200 m being applied, compared to
objectively analyzed MLT at the center
of CA 1 40.0°N/ 165°E from 15 June to
18 August 1976. 118

Figure 52. Similar to Fig. 49 except for

correction field relative to 100 m. 119

Figure 53. Similar to Fig. 50 except for the

application of the correction field

relative to 100 m. 119

Figure 54. Similar to Fig. 49 except for

correction field relative to 50 m. 120

Figure 55. Similar to Fig. 50 except for the

application of the correction field

relative to 50 m. 120

12

ACKNOWLEDGEMENTS

The author would like to thank Drs , Warren White and
Buzz Bernstein for providing the TRANSPAC analyses of
ocean thermal structure. The data archiving division of
Fleet Numerical Oceanography Center provided the atmo-
spheric forcing fields. Appreciation is due to Dr. Roland
Garwood who provided the ocean mixed layer prediction
model. Miss Arlene Bird deserves thanks for her assistance
in computer programming. A special thank you goes to
Mr. Pat Gallacher for interpolating the FNOC atmospheric
forcing fields, providing valuable comments and assistance
during the study and for his review of the manuscript. The
computing was done at the W.R. Church Computer Center.

The author would like to express his sincerest gratitude
and appreciation to Dr. Russ Elsberry for the time and
effort he has spent assisting in the defining and analysis
of this study, and in the preparation of this thesis.

Finally, and most importantly, I want to give my
heartfilled love and thanks to my wife, Linne; without her
support and encouragement this thesis would not have been
possible.

13

I. INTRODUCTION

A. PURPOSE AND HYPOTHESIS

The purpose of this study is to test the applicability
of the Garwood (1977) one-dimensional bulk mixed layer
model for hindcasting the cold ocean thermal anomalies
found in the Anomaly Dynamics Study (ADS) domain. Elsberry
(1983) describes numerous cold anomalies and selects
several anomalies that are particularly suitable for
testing ocean prediction models. Two of these cold
anomalies were chosen for this study. The ability to pre-
dict departures from climatology provides a useful test of
a model's capabilities relative to either a persistence or
a climatological (zero anomaly) forecast. The study of
anomalies also lends insight into the large-scale variability
of the ocean thermal structure. A second purpose of this
study is to demonstrate the usefulness of the corrections
derived by Elsberry et al. (1982) to Fleet Numerical
Oceanography Center (FNOC) surface heat flux estimates in
North Pacific Ocean predictions. These corrections are
necessary to offset a systematic bias in the FNOC heat
fluxes which was discovered in the prediction experiments
of Elsberry et al. (1979), Budd (1980) and Steiner (1981).

The seasonal variation in heat content of the upper
ocean, away from the major current systems, is primarily

14

determined by the net heat flux across the ocean-atmosphere
interface. This heat is distributed in the vertical almost
exclusively by turbulent mixing. During and after the
formation of the seasonal thermocline, the gradual increase
in the solar flux tends to be offset by upward surface heat
fluxes and increases in entrainment mixing associated with
strong atmospheric storms. That is, a decrease in sea-
surface temperature is found during periods of higher wind
speeds (Elsberry and Garwood, 1978) . These higher wind
events occur less frequently during the spring and summer.
The balance between periods of net warming and net cooling
is in favor of increasing sea-surface temperature from the
spring transition until early autumn. After this time,
the net surface cooling and entrainment mixing associated
with strong storms reverses the balance, and the sea-surface
temperature decreases. Superposed on these seasonal trends
are periods with above or below normal temperatures.

Anomalous sea-surface temperatures can be caused by
anomalous solar radiation and surface heat fluxes or by
anomalous entrainment heat flux at the mixed layer base
generated by wind stirring and convective overturning
(Elsberry and Garwood, 1978) and by horizontal advection,
Ekman pumping and upwelling. The basic hypothesis of this
study is that near-surface cold temperature anomalies in
the North Pacific Ocean during 1976-1978 were primarily
generated by local vertical mixing processes.

15

B. STUDY DESCRIPTION

An objective of the North Pacific Ocean Experiment
(NORPAX) was the study of the interaction between large-
scale ocean temperature anomalies and weather. One observa-
tional component of NORPAX was a ship-of-opportunity
expendable bathythermograph (XBT) program (TRANSPAC)
designed to observe the ocean thermal structure on space
scales of thousands of kilometers (White and Bernstein,
1979) . The TRANSPAC analyses provide the initial and
verifying temperature profiles that are required to validate
ocean prediction models (Elsberry and Garwood, 1980) .
Because all of the TRANSPAC observations made within a
particular month are used in the objective analysis, this
defines the time and space scales for the initialization and
verification of the model.

The NORPAX ADS area (Fig. 1) is the oceanic region
examined in this study. The ADS region is bounded by 30 °N-
50°N and 130°W-160°E and encompasses midlatitude regions
that contain large-scale thermal anomalies. This region
also has strong atmospheric variability. In this study, two
cold anomalies are examined. The first is a large-scale,
long-duration event that began in the fall of 1977, and
extended into the spring of 1978 in the vicinity of 36°N,
150°W. The second anomaly is a shallow, large-scale, rapid
transition event occurring in the summer of 1976 in the
vicinity of 40 °N, 165°E. These two anomalies provide an

16

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opportunity to test the Garwood model and the vertical
mixing hypothesis.

C. DEFINITIONS

Several terms that will be used throughout this thesis
are defined and discussed in this section.

1 . Spring Transition

The transition from a winter mixed layer regime to
a summer regime occurs during the spring, when the occur-
rence and magnitude of storms (and thus high wind speeds)
are diminishing and the net daily insolation is increasing.
The increase of absorption of solar radiation in the near-
surface layers promotes stability,

Tully and Giovando (196 3) noted that the spring
transition appeared to be rapid. Elsberry and Garwood (1978]
combined an oceanic model simulation and observations to
demonstrate that the spring transition can occur during a
single daytime heating cycle. Budd (1980) reported that
the spring transition usually occurred within a 36-hour
period; however, the time period for transition was longer
for steady wind conditions. The key synoptic feature ini-
tiating the transition is an extended period of light winds
coinciding with a period of net downward heat flux (Elsberry
and Raney, 1978). A layer of warmer (less dense) water
near the surface is established during the diurnal heating
cycle. If the mechanical generation of turbulent kinetic
energy is sufficiently small, the layer will remain intact

18

through the night. A repetition of this cycle through the
next several days can lead to the formation of the seasonal
thermocline .

A set of criteria based on the mixed layer depth
and temperature was used to determine when the ocean
boundary layer changed from a winter to a summer regime
(similar to Budd, 1980) . The transition period was defined
as the first period of sustained shallow mixed layer depths
(<40 m) that followed a period of greater than 80 m depths.
Occasionally the predicted and/or analyzed depths may later
exceed 80 m for a short period a week or more after the
establishment of the stable layer. Consequently, the
transition period was specified as that period which also
coincided with a significant increase in mixed layer tempera-
ture. As the TRANS PAC temperature analyses were available
monthly, only an approximate time frame can be given for the
spring transition.

2 . Mixed Layer Depth

There is no consensus method for determining the
mixed layer depth of a vertical temperature profile. Various
definitions have been applied in different studies depending
on the requirements (operational or research) and profile
resolution. In this study, the mixed layer depth has been
defined to be that depth at which the vertical temperature
gradient exceeds 0.10°C/5m. For regions with a very slight

19

negative gradient above a marked thermocline and for which
the criteria of 0.1°C decrease in 5 m was too stringent,
the mixed layer depth was manually determined from the
vertical temperature profile. This was done to reduce
any bias in mixed layer depth due to definition as found
by Steiner (1981) .

In the Garwood model , a minimum mixed layer depth
of 5 m was set. This is consistent with the analyses, as
the wake turbulence of a ship from which an XBT was launched
would destroy an shallow (<5 m) surface layer (s) , and thus
these layers would not be present in the analyses. The
maximum model mixed layer depth was set at 19 0 m to prevent
the model vertical profiles from becoming isothermal.

20

II. DATA SOURCES AND PROCEDURES

A. DATA SOURCES

This study is based on data between January 1976 and
December 1979 from two separate sources. The FNOC atmo-
spheric forcing and TRANSPAC temperature analyses are over
the ADS domain bounded by 30°N, 50°N, 130°W and 160°E. The
grid resolution is 2° latitude by 5° longitude.

Atmospheric forcing data (wind speed and direction,
solar heat flux and total surface heat flux) were obtained
from the archived FNOC northern hemispheric atmospheric
analyses and short-term predictions. The wind components
were available at six-hour intervals, and the solar and
total surface heat (latent plus sensible plus back radia-
tion minus solar) flux values at 12-hour intervals. The
Garwood model requires atmospheric forcing fields on hourly
time scales to resolve the oceanic response to the diurnal
heating cycle. Garwood (1977) found that this diurnal
component can modulate the seasonal trend. A complete
description of the procedures and programs for editing and
interpolating the forcing fields to one-hour intervals is
in Gallacher (1979).

The TRANSPAC data sources and analysis procedures are
described in White and Bernstein (1979) . XBT observations
were made by ship-of-opportunity personnel along ship

21

tracks between Japan and the west coast of the United
States. Due to ships tending to avoid rough weather there
is a seasonal and a "fair weather" bias in the data. During
the summer, the ship tracks are farther north and there is
good data coverage over the domain. However, the northern
part of the domain is not well sampled during the winter.
It was found that the northwest and the southwest corners
of the grid were not well sampled (Elsberry, 1983). Conse-
quently, these areas are excluded in this study and will
appear as cross-hatched areas on all appropriate figures.

The XBT profiles have been objectively analyzed at
depths of 0, 30, 60, 90, 120, 150 and 200 m. These
objectively analyzed fields produced by White and Bernstein
(1979) are not vertically coupled. Since the analyzed
temperature profiles are available monthly, they are taken
to be representative of the "observed" temperature profile
on the 15th of the month. To assure a continuous record,
wherever minor data gaps existed along the edge or in the
interior of the ADS grid, time and space interpolations
were made at 0, 60, 120 and 200 m (Elsberry, 1983). Since
data gaps were not removed in the analysis at the other
analyses levels, only the analyses at 0 , 60 and 120 m were
used to describe the horizontal temperature anomaly
structure. The horizontally edited values at the above
levels, plus objectively analyzed values (if present) at
30, 90 and 150 m, were then vertically interpolated to a

22

5 m spacing between 0 and 200 m. These gridded monthly
oceanic temperature fields were used to initialize the model
simulations and to verify the model output.

The following comments should be kept in mind during
subsequent discussions of the analyses over the entire
domain. Due to the sparse ocean data, differences between
the Garwood model predictions and the TRANSPAC observations
of less than 0.5°C are probably not significant (Budd, 1980).
The baseline study conducted by White and Bernstein (1979)
indicated that the region west of 175 °W was dominated by
strong mesoscale (300 km) baroclinic eddies or waves, whereas
east of 175 °W the larger scale variability dominated. The
temporal and spatial data coverage and the 2° latitude by
5° longitude grid interval are inadequate to resolve eddies
in the region west of the dateline and in the California
current. Furthermore, the analyses in regions north of
45°N and south of 35°N are less reliable due to the seasonal
variation in data coverage (Elsberry, 1983).

B. MEAN AND ANOMALY FIELDS

The monthly mean temperature (climatological) fields
used in this study are an average of the TRANSPAC monthly
objectively analyzed fields over the four years, 1976-1979.
These mean temperature fields are based only on the TRANSPAC
vertical temperature profiles, and do not include any other
source of temperature observations. The advantage of the

23

four-year mean is that the analysis method is consistent
in both the mean and the anomaly fields (Elsberry, 1983).
The disadvantage is that the anomaly fields will differ
from those generated using the long-term NORPAX mean fields
(Barnett and Ott, 1976) . This is particularly true because
two of the four winter periods (1976 and 1977) include
extreme conditions in the Central Pacific (White and
Bernstein, 1979; Elsberry et al., 1979; White et al.,
1980; Haney, 1980; Budd, 1980). Thus cold anomalies during
these winters have a smaller magnitude in this study than
in the NORPAX fields. Elsberry (1983) found that there is
an overall trend toward a warm bias in the four-year surface
TRANSPAC mean fields relative to the long-term Barnett and
Ott (1976) fields.

The anomaly fields were formed by subtracting the four-
year mean (climatclogical) fields from the analyzed fields
at 0, 60 and 120 m. The resulting horizontal anomaly fields
are taken to be the anomalous conditions on the 15th of the
month.

C. PREDICTION MODEL

The Garwood (1977) ocean mixed layer model is a second
order closure bulk model. Since the model is one-dimensional,
no advection or Ekman dynamics are included. A more complete
description of the Garwood model is contained in the
Appendix.

24

The Garwood model is initialized with the initial
(TRANSPAC objectively analyzed) temperature profile fields
for the 15th of the month. The model is used to predict
the evolution of the oceanic thermal structure over the
ADS area due to local surface forcing. The model predicts
vertical temperature profiles in 5 m increments to 20 0 m
over the entire grid every hour. For this study, the
model output consists of the vertical temperature profiles
averaged over 5 days centered on the 15th of each month,
and the mixed layer temperature at the time of maximum
mixed layer depth for each day.

The model anomaly fields were formed by subtracting
the four-year mean (climatological) fields from the model
predicted fields at 0, 60 and 120 m. The resulting hori-
zontal model anomaly fields are taken to be representative
of the conditions on the 15th of the month.

25

III. LARGE-SCALE LONG-DURATION CASE

A. COLD ANOMALY 12 DESCRIPTION

The cold anomaly (CA) described below was designated
and described by Elsberry (1983) as CA 12. CA 12 is a
large-scale, long-duration event which persisted for
approximately eight months and encompassed a vast region
of the ADS grid.

The entire domain had above average temperatures during
October 1977 (Fig. 2A) . For orientation purposes, the
ultimate location of maximum intensity or central point
(36°N, 150°W) for CA 12 is marked as a dot on the appli-
cable figures. Starting in November 1977 (Fig. 2B) , CA 12
began to develop at the surface in the northeast region.
The temperature decreases in this region are noteworthy
relative to the climatological cooling during this period.
In the northeast region, which changed from a warm to cold
anomaly between October and November 1977, the surface
temperature decrease was greater than 1.5 times the
climatological decrease (Fig. 3) . The cold anomaly con-
tinued into December 1977 (Fig. 4) ; however, the temperature
decrease was almost the same as climatology. At this time,
the majority of the region had below normal temperatures
and the anomaly had penetrated 60 m (Fig. 4). From
December 1977 to January 1978 (Fig. 5) , the rate of tempera-
ture decrease (Fig. 6) slowed to half that of climatology

26

in the northeast region, whereas the rate increased to

1.5 times climatology in the southeast region as the anomaly

expanded southward.

The anomaly continued to increase in amplitude and
spatial extent between January and March 1978. Temperature
decreases became more erratic over the area during this
period. The vertical structure of CA 12 during January
1978 and March 1978 is shown in Figs. 5 and 7. The cold
anomaly penetrated to 120 m in January 1978. A warm
anomaly, extending to 120 m, was found along the eastern
boundary in January 1978. This resulted in an anomaly
pattern with a north-south orientation. During February
(not shown) and March 1978 this warm anomaly extended
westward in the vicinity of 44 °N, 140 °W. Thus CA 12 had
a maximum amplitude in the southeast region. During
March 1978, CA 12 reached maximum intensity (-1.91 °C at
36 °N, 150 °W) and areal extent. The western anomaly pattern
in the vicinity of 38°N, 170°E in March 1978 was due to the
formation of CA 18 (Elsberry, 1983) which persisted through-
out the remainder of the existence of CA 12 .

The vertical structure for April through June 1978 is
shown in Figs. 8 to 10. The anomaly amplitude diminished
from March to April 1978. During this period, the tempera-
ture in the vicinity of the central point increased at a
rate (not shown) of 1.5 times the climatological rate as
this area underwent spring transition. However, the

27

temperature in the eastern portion of the region remained
below normal through June 1978 (Figs. 8-10). Through that
time, the anomaly center was maintained but the pattern
changed shape. From April to May 1978 the surface features
of the anomaly became more diffuse, but the anomaly ampli-
tude at 60 m showed little change. The most rapid surface
temperature increase took place during these two months
(Fig. 11) ; it was associated with the very late spring
transition throughout the remainder of this region
(Elsberry* 1983). In the region of CA 12, the temperature
increase during May to June 1978 was much the same as the
expected climatological increase (Fig. 12). However, the
region of CA 18 increased in temperature at twice the
climatological rate. In May 1978 the surface signature of
CA 12 was absent, although there was a 10° longitude west-
ward displacement of minimum temperatures at 60 and 120 m.
By June 1978 (Fig. 10) , the cold anomaly 12 became diffuse
at 60 and 120 m, but interestingly, it intensified again
at the surface. In June 1978, there was substantial vertical
tilt between the surface and 60 m but not between 60 and
120 m. After July 1978 (not shown) , the region was generally
cold throughout the remainder of the year and periods with
above normal temperatures did not persist (Elsberry, 1983).

In summary, CA 12 was a long-duration, large-scale
event with multiple periods of amplification followed by
sustaining periods. The location and minimum temperature

28

for CA 12 each month is given in Table 1. CA 12 formed
between October and November 1977 at about 44°N, 145°W and
was only sustained by the expected cooling during the
southward expansion in December 1977. In January 1978 the
anomaly progressively expanded southward. The anomaly
reached its maximum amplitude and areal extent in March
1978. By April 1978, the anomaly reached its southern
most location (32°N, 155°W) and had started to diminish in
size and amplitude, although portions of the regions
remained colder than climatology for several months. In
May 1978, the surface signature of the anomaly disappeared.
In June 1978, CA 12 was displaced northward to about 38°N,
155 °W and the signature of the anomaly had all but disap-
peared at depth and had reappeared at the surface. This
cold anomaly was clearly a major climatolgoical event.

These changes in the analyzed strength of CA 12 (Table 1)
could be due to several effects: (1) atmospheric forcing
pulses due to localized atmospheric effects; (2) oceanic
response to seasonal climatic changes; (3) anomaly-anomaly
interactions; and (4) advection effects resulting from
Ekman and/or Sverdrup mass transport. An effect of the
above physical mechanisms is that CA 12 could be interpreted
as being composed of several consecutive cold anomalies
that have monthly life spans and appear in a region that
is anomalously cold. It is not possible to separate
completely the above effects with the available data.

29

TABLE 1

Comparison of analyzed CA 12 and model MA 12 development for
each month. The locations and temperatures given are the
location of the lowest temperature in CA 12 and MA 12 for
each month.

ANALYSIS MODEL

Month Year Location Temperature Location Temperature

Nov 1977 44°N/145°W -1.63°C 46°N,140°W -2.51°C

Dec 1977 40°N,145°W -1.61°C (1) 46°N, 140°W -1.69°C

(2)30°N/155°W -1.48°C

Jan 1978 38°N,145°W -1.36°C (1) 46°N, 140°W -1.99°C

(2) 34°N,155°W -2.14°C

Feb 1978 34°N,145°W -1.76°C 34°N/150°W -2.23°C

Mar 1978 36°N,150°W -1.91°C 34°N,150°W -2.15°C

Apr 1978 32°N,155°W -1.85°C 30°N,155°W -3.10°C

May 1978 34°N,150°W* -1.31°C 30°N/150°W -2.65°C

Jun 1978 38°N/155°W -1.65°C 36°N,150°W -3.79°C

* at 60 m

30

There may be some tilt present in the vertical structure
of the anomalies. These tilts will not be examined here
because the objective analysis of the temperature field
is done independently at each level, and the horizontal
resolution of these analyses is not appropriate. The
next section describes the model hindcast of CA 12 .

31

50N

(A)

(B)

35N -

30N

160E 170E 180 170W 160W [SOW MOW 130W

Figure 2. Temperature (°C) anomaly CA 12 at surface

during (A) October 1977 and (B) November 1977.
The horizontal temperature analysis for each
month is centered on the 15th of that month.
Negative (dashed) lines represent regions with
temperatures less than climatology, zero (heavy
solid) same as climatology and positive (light
solid) temperatures greater than climatology.
The interval is 0.5 °C. Cross hatched areas
have insufficient data for analysis. Dot marks
the ultimate location of maximum intensity or
central point (36°N, 150°W) for CA 12.

32

50N

45N

40N

35N -

30N

160E 170E 180 170W 1 60W 150N MOW 130W

Figure 3. The ratio of change in analyzed temperatures
(°C) from 15 October to 15 November 1977 to
the climatological temperature change for
the same period. Values greater than 1.0
during this period indicate above-average
temperature decreases.

33

(A)

(B)

50N

45N

40N

35N -

■----0-

& /

) \ A^

30N
50N

45N

40N -

35N -

30N

■ t i ii

160E 170E 180 170W 1 60W 150W MOW 130W

Figure 4. Temperature (°C) anomaly CA 12 during

December 1977 at (A) surface and (B) 60 m,

34

(A)

(B)

(C)

50N

45N

40N -

' J 0

o

35N

30N
50N

45N

40N -

35N -

30N
50N

45N

40N -

35N -

301

' «/ < fi

Figure 5.

160E 170E 180 170W 160W 1 SOW MOW 1 30W

Temperature (°C) anomaly CA 12 during January
1978 at (A) surface, (B) 60 m and (CI 120 m.

35

50N
45N
40N
35N

* OM

30N

160C 170E 180 1 70W 160W 1 50W MOW 130W

Figure 6. Similar to Fig. 3 except for the period from
15 December 1977 to 15 January 1978.

36

50N

(A)

* OM

30N
50N

(B)

(C)

40N -

35N -

30N

160E 170C 180 17GW 160W 150W HON 130N
Figure 7. Similar to Fig. 5 except for March 1978.

37

(A)

(B)

(C)

SON

45N

agggggg^ u

>< 0 M

40N -i

35N -

30N
50N

45N

40N

35N -

i ~\

30N

50N

45N
40N

35N 4

30N

r >
i

i
i

>

0*

.-t.O-1

• 1

160E 170E 180 170W 160W 150W MOW 130W
Figure 8. Similar to Fig. 5 except for April 1978

38

50N

(A)

(B)

(C)

40N -■■

35N

30N

V-0.5-' \

160E 170E 180 170W I SOW 150W 1 40W 130W
Figure 9. Similar to Fig. 5 except for May 1978

39

(A)

(B)

50N

45N

40N -•

35N

30N
SON

45N

40N -

35N -

30N
50N

45N

40N -

351

30N

160E 170E 180 170W 160W 150W MOW 130W

Figure 10. Similar to Fig. 5 except for June 1978

(c)

40

50N i

45N

40N

35N

30N

160E 170E 180 170W 160W 1 BOW MOW 130W

Figure 11.

Similar to Fig. 3 except from 15 April to
15 May 1978. Values greater than 1.0 indicate
greater temperature changes than the normal
monthly change. Negative (dashed) values
indicate temperature decrease during a period
in which seasonal warming is taking place.

50N

45N

40N -

35N

30N

160E 170E 180 170W 160W 150W MOW 130W

Figure 12. Similar to Fig. 3 except from 15 May to
15 June 1978.

41

B. MODEL HINDCAST

The Garwood model was initialized with the ocean tem-
perature analysis from 15 October 1977 and integrated
through 18 June 1978 to cover the life span of CA 12. As
may be seen in Fig. 13, the model does a rather remarkable
job in predicting the mixed layer temperature through
March 197 8 during the deepening and maintenance phases of
the anomaly at the central point (36.0°N, 150. 0°W) . From
April through June 197 8 however, the model-predicted mixed
layer temperatures remained too low.

Recall that the model was initialized with the October
1977 fields which showed the region covered by above average
temperatures (Fig. 2A) . By November 1977 (Fig. 14) , the
model developed a cold anomaly on the surface in the north-
east region. The model anomaly (MA) underwent rapid
temperature decreases (Fig. 15) from October to November
1977 as did CA 12. in the northeast region, the analyzed
surface temperature decrease was greater than 1.5 times the
climatological decrease (Fig. 3), while the model surface
temperature decrease was greater than twice the climatologi-
cal decrease (Fig. 15). From November to December 1977,
the model sustained the anomaly by a cooling rate much the
same as climatology. By this time the majority of the
region had below normal temperatures. The model-derived
anomaly penetrates to 60 m at the central point in December
1977 (Fig. 16) , which is one month earlier than analyzed

42

(Figs. 4 and 5). That is, the model decreases in mixed
layer temperature (and increases in depth) are slightly
larger than observed in CA 12 from October to November 1977.
The model anomaly in the northeast (MA 12N) at 46 °N, 140 °W
is in the locality where CA 12 first appeared. MA 12N
remains in the same location for three months, and disap-
pears as a separate center by February 197 8.

In December 1978, another cold model anomaly (MA 12)
center appears on the surface in the southeast (-1.48°C at
30°N, 155°W) . Both centers (MA 12 and MA 12N) are con-
sidered to be part of the model's representation of CA 12.
As the southeast center (MA 12) development after December
1978 closely parallels that of CA 12, the discussion below
will focus on MA 12. From December 1977 to January 1978
(Fig. 17) , the predicted rate of temperature decrease
(Fig. 18) slowed to that of climatology in the northeast
region, but stayed at 1.5 times climatology in the southeast
region as the anomaly expanded southward. This general
pattern is consistent with the analyzed changes in the
eastern half of the domain (Fig. 6) .

The vertical structure for January and March 19 7 8 can
be seen in Figs. 17 and 19. The model predictions are
noisy at 60 and 120 m, although the features of CA 12 are
still very discernable. The model prediction takes on a
weak north-south orientation similar to the analyses. The
warm anomaly along the eastern boundary is not predicted in

43

January 1978 except at 120 m, where it is correctly oriented
north-south but has a larger areal extent. By March 1978
(Fig. 19), this warm anomaly at 120 m has moved eastward
to along the eastern boundary of the ADS area, where it
remains through June 1978. Since this warm anomaly has a
large areal extent in the eastern region at 120 m, MA 12
does not penetrate to 120 m in the vicinity of 36°N, 150°W
until February 1978 (not shown) , which is one month later
than analyzed.

The model does a fairly good job in hindcasting the
marked changes in shape of the vertical thermal structure
for the central point of CA 12. The model mixed layer
temperatures (MLT's) are in close agreement, albeit on the
cold side, with those analyzed through March 1978. The
analyzed and predicted vertical temperature profiles for
October through December 1977 can be seen in Fig. 20A and
20B and those for January through March 1978 in Fig. 21A
and 21B. The October 1977 profiles are, of course, identical
as this is the initial time. The predicted mixed layer
temperatures (MLT's) for November and December 1977 were
nearly the same as analyzed, while the remainder of the
vertical profiles approximated the analyses. One exception
is the higher thermoclime temperatures analyzed during
November 1977 only. It is during the period from January
to March 197 8 that the model predictions come the closest
to hindcasting correctly the vertical temperature profiles

44

at the central point down to 2 00 m, The mixed layer depth
is also largest during this period. The model MLT ' s for
January through March 1978 are less than 0.5°C lower than
the analyzed MLT and the thermal structure below the
mixed layer is in fair agreement with the analyses.

The analyzed spring transition at the central point
occurred between March and April 1978 using the criteria
described in Chapter I, Section CI. Determination of the
mixed layer depth for both the model and analyzed profiles
was made using the criteria described in Chapter I,
Section C2. The analyzed March 1978 vertical temperature
profile (Fig. 21A) appears to have a mixed layer depth (MLD)
of about 80 m, although the temperature gradient below
this level is quite small. By April 1978 (Fig. 22A) , the
analyzed MLD has shallowed to about 40 m and the MLT has
increased by 1.0°C. Using the same criteria as for the
analyzed spring transition, the model spring transition
does not occur until between April and May 1978. As may
be seen in Fig. 22B, the model MLD in April 1978 is 150 m.
By May 1978, the model MLD has shallow-d to about 5 m and
the model MLT has increased by 1.0°C. Using the daily
maximum model MLD and corresponding MLT from Fig. 13, the
predicted spring transition would be during the latter
half of April 1978.

Throughout the spring, the model mixed layer temperature
remained too low (Fig. 13). In the southwest region, the

45

model predictions continued to decrease in temperature
from March to April 1978, whereas the region actually had
undergone spring transition and the cold anomaly was
diminishing. The model-derived vertical structure for
April through June 1978 can be seen in Figs. 23 to 25. It
is during April 1978 that MA 12 reaches maximum intensity
(-3.10°C at 30°N/ 155°W) and areal extent. The model
anomaly center in April 1978 is southwest of the analyzed
central point. Between April and May 1978, the surface
temperature in the model began to increase at a rate
(Fig. 26) close to twice the climatological rate, which is
consistent with the analyzed changes (Fig. 11) . This rapid
increase in temerature did not persist long enough for the
model mixed layer temperature to increase to the analyzed
temperatures. In May 1978 (Fig. 24), the predicted anomaly
is quite intense rather than having somewhat diffuse surface
features, as was analyzed. The model prediction does
maintain the eastern portion at below normal temperatures
through June 1978. From May to June 1978, the predicted
rate of temperature increase (Fig. 27) is less than that
of climatology, and is approximately equal to the analyzed
rate of temperature increase (Fig. 12) in the region of
CA 12. By June 19 78, at the central point, the model-
derived anomaly is still quite prominent, -1.79°C, at
60 m, whereas at 120 m the anomaly has diminished to only

46

-0.65°C. The model correctly predicts the intensification
of the surface anomaly at the central point in June 1978
(Fig. 25) ; however, the model anomaly is twice as intense
as analyzed.

In summary, the Garwood model does a very notable job
in hindcasting CA 12 as it developed during the autumn of
1977 and reached the maximum amplitude and area extent
during the winter of 1978. The mixed layer temperature
and depth, and corresponding vertical temperature profiles
at the center of the anomaly, are fairly close to those
analyzed. The model spring transition is late compared to
the analyzed spring transition, and the model mixed layer
temperatures remain too low, A summary of the locations
and minimum temperatures during the life spans of both
CA 12 and MA 12 is provided in Table 1 (Chapter III,
Section 3B) . It is very satisfying to see numerous similari-
ties during the life span of the cold anomaly. The model
hindcast of CA 12 is slightly on the cold side as seen in
Fig. 13. These results show that CA 12 can be accounted
for the most part by local atmospheric forcing.

It is interesting to look at other grid points around
the central point of CA 12. One grid point examined is
located to the northeast of CA 12 near the persistent warm
anomaly along the eastern boundary of the ADS area. The
model predictions there are not as good, as the model does

47

not hindcast the warm anomaly along the eastern boundary.
At 38°N, 135°W (Fig. 28) , the model mixed layer temperature
is also consistently too low throughout the integration.
However, the monthly trends of temperature change are well
simulated. At the northwest edge of the anomaly (40°N/
160 °W) , themodel prediction (Fig. 29) is much better than
at the central point of CA 12. Thus, the temperature
changes in the central area of the ADS region appear to be
explained by one-dimensional processes. Furthermore, the
anomalous thermal structure appears to be generated by
local atmospheric forcing. The hindcast for 34°N, 160°W
(Fig. 30) is also quite good. At this location, the model
captures the trend during the autumn-winter temperature
decrease and also does a good job in the spring, except for
April 197 8. In April, the model mixed layer temperature is
significantly colder than the analyzed monthly mixed layer
temperature.

48

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50N

45N

&XXW^

40N -

35N

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160E 170E 180 1 70W 1 SOW 150W MOW 130W

Figure 14. Model temperature (°C) anomaly MA 12 at
surface during November 1977.

50N

45N

40N

35N

30N

160E 170E 180 170W 160W 150W MOW 130W

Figure 15.

The ratio of the change in model temperatures
(°C) from 15 October to 15 November 1977 to
the climatological temperature change for the
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this period indicate above-average temperature
decreases.

50

(A)

50N

45N

'1.0

40N -;\ --//•Jo.o-^

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35N -\ v '•*•

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35N -

30N

V. ?Z /Di

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x-.-0

160E 1 70E 180 170W 160W 150W HOW 130W

Figure 16. Model temperature (°C) anomaly MA 12 during
December 1977 at (A) surface and (B) 60 m.

51

(A)

(B)

(C)

SON

45N

35N -

30N
50N

45N

4on -)) \ V$<0 ---,; yy-'-^ ,<V-

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50N ^^E

| 120 M

35N -

30N

-0.5. V

160E 170E 180 170W 160W 150W MOW 130W

Figure 17. Model temperature (°C) anomaly MA 12
during January 19 78 at (A) surface,
(B) 60 m and (C) 120 m.

52

50N

45N

40N -

35N

30N

160E 170E 180 170W 160W 150W MOW 130W

Figure 18.

Similar to Fig. 15 except from 15 December
1977 to 15 January 1978. Values greater
than 1.0 indicate greater temperature changes
than the normal monthly decrease. Negative
(dashed) values indicate a temperature
increase during a period in which seasonal
cooling is expected.

53

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50N

45N

40N -

35N -

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160E 1 70E 180 170W 1 60W 150W MOW 130W
Figure 19. Similar to Fig, 17 except for March 1978

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-i.s-

/ \
/ \

-0.5'

30N

o

•v

35N \ ; .,

-\.0

^A

160C 170E 180 170W 160W 150W MOW 130W
Figure 23. Similar to Fig. 17 except for April 1978.

58

(A)

(B)

50N

45N

40N -

35N -

30N
50N

45N

40N -

35N -

30N

(C)

45N

* 120 M
2

40N -

30N

o.s^-

9 .' / <>S '

<V <«.

: #\

■& >

i 'o

/ / /

i,V, J Ca

160E 170E 1 80 ' 1 70W 160W 150W HOW 130W
Figure 24. Similar to Fig. 17 except for May 1978

59

(A)

(B)

50N

45N

40N

35N

30N
SON

45N

40N

35N -

1 x //~i^"^

(c)

30N
50N

45N

40N •>

35N -;

i / / r

: ' 3 i i 1 1

L>

C5

30N -•

160E 170E 180 1 7GW 160W 150W MOW 130W

Figure 25. Similar to Fig. 17 except for June 1978

60

SON

45N

40N

35N -

30N ■ ''" v ' i r ■ ■ i ■ ' i ' ' ' r

160E 170E 180 170W 160W 150W MOW 130W

Figure 26. Similar to Fig. 15 except from 15 April to
15 May 1978.

50N

45N

40N -

35N -

30N

160E 170E

70W 1 SOW 1 50W MOW 130W

Figure 27.

Similar to Fig. 15 except from 15 May to
15 June 1978.

61

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64

C. ERROR DISCUSSION

A later (earlier) than normal mixed layer spring
transition is expected to be related to the development of
lower (higher) than normal sea-surface temperatures. This
relationship held rather well for the 19-year sample at
Ocean Weather Station "P" (50°N/ 145°W) (Elsberry and
Garwood, 1978) and also during 1976 and 1977 in the ADS
region (Budd, 1980) . If the timing of spring transition
is not correct (for example, due to incorrect forcing), the
model predictions after that time will be in error.

One may observe these errors in the heat content of the
model vertical temperature profile. The difference in heat
content relative to 200 m between analyzed and model
profiles, AQ, is given by:

AQ = p C ( (T . (z) - T , (200) ) dz

° P -inn anal anal

, (1)
0
- / IT -la) - T (200) dz
-200 mod mod

where p is the density, C is the specific heat and z is
the depth below the surface. The relative error in the
heat content relative to 200 m is given by:

relative error = - . (2)

0

p C / IT (z) - T . (200) ) dz
Mo p J anal anal

-200

65

Trapezoidal integration is used in the determination of the
heat content. The heat content is calculated relative to
the 2 00 m temperature with the intent of removing some of
the change in heat content due to vertical displacements
of the thermocline and also due to horizontal effects. To
remove completely the change in heat content due to vertical
displacements, one should integrate with respect to an
isotherm in the thermocline. However the analyses have
insufficient resolution to allow such an integration.
Another motivating factor for calculations relative to
200 m was that the calculations to determine the correction
fields to the surface heat flux fields were also relative
to this depth (Elsberry et al., 1982).

Values for the analyzed and model hindcast heat content
relative to 200 m from November 1977 to June 1978 are given
in Table 2. Also shown in Table 2 are the differences in
heat content for each month and the relative error in the
heat content between analyzed and model profiles. The
model heat content is derived from the temperature profiles
averaged over five days centered on the 15th of each month.
Using averaging periods of 10 and 20 days showed little
change in the heat content of the averaged model tempera-
ture profiles relative to 200 m. Thus all of the model
profiles used in this study are based on the five-day
averaging period.

66

TABLE 2

2
Analyzed and model hindcast heat content (xl04 cal/cm )

relative to 200 m at 36.0°N, 150. 0°W, their difference,

and the relative error in heat content above 200 m between

analyzed and hindcast temperature profiles.

Month Year Analyzed Hindcast Difference Relative Error

Nov

1977

6.33

6.64

-0.31

-0.049

Dec

1977

6.33

5.79

0.56

0.086

Jan

1978

4.09

3.95

0.14

0.036

Feb

1978

2.97

3.01

-0.04

-0.013

Mar

1978

2.38

2.48

-0.10

-0.043

Apr

1978

3.24

2.45

0.79

0.244

May

1978

3.88

2.89

0.99

0.255

Jun

1978

4.47

3.43

1.04

0.233

The relative errors in Table 2 show a seasonal trend.
During winter, the mixed layer is deep and the relative
error is small. During summer, the mixed layer is shallow
and the relative error is increased over five-fold. This
is not surprising. When the mixed layer is shallow and
warm during the summer, there is a greater possibility that
the model profile below the mixed layer will be in error,
since it is essentially unchanged once the mixed layer
shallows.

The relative error is a function of (1) analysis error;
(2) model parameterizations; (3) model forcing; and
(4) model physical processes. Each of these areas will be
examined in more detail in the next four sections.

67

1. Analysis Error

The number and distribution of ship XBT reports that
are included in the objective analysis (White and Bernstein,
1979) determine the accuracy of the fields. One problem
appears to be a "fair weather bias" because ships tend to
avoid bad weather. During the winter, the ship tracks are
further south, and consequently the analysis in the northern
portions of the ADS grid is extrapolated from data in the
southern portions. Another problem is that merchant ships
do not transit the region at equally spaced time intervals.
There is no assurance that the reports will be well distri-
buted in space or in time. A candidate for a varied temporal
distribution of XBT reports is the month of April 1978.
Since CA 12 is in the southern portion of the ADS grid,
where the monthly mean wind fields indicate persistent anti-
cyclonic flow, it is unlikely that ships would avoid the
region due to bad weather. As seen in Fig. 13, the model
mixed layer depth has shallowed to about 25 m at the beginning
of April 1978, however, it is predicted to deepen again to
about 70 m in the middle of the month and then shallow to
approximately 10 m in late April. If ship observations were
taken at the beginning and end of the month, when the mixed
layer was warm and shallow, this would result in an erroneous
analysis of MLT. As noted in Fig. 30, a comparison of the
observed and model MLT's to the southwest of the central
point also shows that the model MLT was lower than the
observed MLT for April 1978.

68

2 . Model Parameterizations

There are four constants that are critical to the
parameterization of the physical processes in the Garwood
model. These constants, m^ , p,., r and y, must be evaluated
empirically (a more complete description of these constants
and the parameterizations is contained in the Appendix) .
The model parameters itu and p., are important in predicting
the seasonal cycle of sea-surface temperature. The values
of these constants were empirically determined by Gallacher
et al. (1933) for the ADS region using data between January
1976 to December 1978.

The model constants r (fraction of solar flux
absorbed in first meter) and y (absorption coefficient)
determine the predicted vertical distribution of heat in
the water column, and are functions of the turbidity of the
water. These parameters are most important during the
spring and summer when the mixed layer depth is small. To
determine the model sensitivity to r and y / the model was
rerun from 15 February to 18 June 1978 with r decreased
from 0.5 to 0.4 and y increased from 0.001 to 0.002. These
values will lead to more heat being absorbed into the
surface layers of the column. However, the new mixed layer
temperature prediction was not a significant improvement on
the model results shown in Fig. 13. This was not surprising
since the model constants have already been adjusted to be
as consistent as possible with the atmospheric forcing

69

(Gallacher et al., 1983). Thus, some other reasons/
processes are responsible for the analysis-model differences
in the spring.

3 . Model Forcing

It is necessary to first determine if the errors are
due to an initial value problem associated, in this case,
with the long integration period. That is, the accumulated
errors in the model forcing or in model constants could have
led to incorrect profiles prior to the spring period. To
test the contribution from this source of error, the model
was initialized with the 15 February 1978 analysis. The
daily maximum mixed layer depth and corresponding tempera-
ture plots when the model was initialized in February 1978
were very nearly the same as in Fig, 13. The relative
errors in Table 3 for this experiment are similar to those
in Table 2, which shows that there is minimal improvement
by initializing the model in February 1978. To determine
if the model could produce the correct trend after the
spring transition had occurred, the model was also
initialized with the 15 April 1978 analysis. Even in this
case, the model did not predict the correct trend in the
mixed layer temperature, and the predicted June 1978 sea-
surface temperatures continued to be too low.

Since the errors were not due to an initial value
problem, the actual model forcing from October 1977 through
June 19 78 was examined. As the model predictions were good

70

through March 1978, it is assumed that the forcing through
that time were reasonably correct. Earlier studies
(Elsberry et al., 1979; Budd, 1980; Steinder, 1981) found
that the monthly integrated FNOC surface heating did not
have a sufficiently large seasonal amplitude. There was
also a persistent bias toward excessive heat loss to the
atmosphere especially along the southern boundary of the
domain. Elsberry et al. (19 82) calculated bimonthly heat
flux correction fields to be added to the FNOC surface
heat flux fields to reduce this excessive upward flux.

There was a downward heat flux correction of about

2

4 cal/cm /h applied during April-May (Elsberry et al.,

1982) . The fraction of the correction fields that should
be attributed to the solar heat flux was not determined by
Elsberry et al. (1982), as previous studies (Elsberry et
al., 1979; Budd, 1980; Steiner, 1981) indicated that the
solar heat flux fields were reasonably correct. The
resulting heat fluxes were used in the model forcing for
this study.

As mentioned earlier, the model predicted inadequate
ocean warming in the spring. This suggests that the most
likely cause of the observed errors is inaccurate atmo-
spheric forcing. It is important to point out that the
predictions during the spring are very sensitive to the
magnitude of the downward surface heat flux. There is a
delicate balance between the heat flux tending to form a

71

stable and shallow layer near the surface and the wind
mixing tending to erode the stable layer to re-establish a
mixed layer characteristic of winter. Once the shallow
mixed layer is formed, the greater the downward flux, the
more rapid the warming, and the less likely that wind
mixing will erode the layer. Thus, the magnitude of the
heating has a double effect in the spring transition period.
As discussed earlier, this was the period when the relative
errors in heat content relative to 200 m began increasing
dramatically .

Budd (1980) found that the time changes in fluxes
of solar radiation and total heat flux were apparently of
much less importance than variations in wind speed during
the change of the mixed layer from a winter to a summer
regime. Thus the effect of errors, even small ones, in
wind speed forcing are enhanced during the period of spring
transition. It is not possible to determine corrections to
the FNOC wind fields as no indpendent wind reports are
available. However, one would expect the FNOC analyses to
be biased toward lower wind speeds, due to the fair weather
bias. Since the model mixed layer depth is too deep, the
FNOC winds would have to be too high, which is unlikely.

To illustrate the sensitivity of the model predictions
during this period, an additional downward heat flux was
added to the surface heat flux correction determined by
Elsberry et al. (1982) . Several model runs with additional

72

downward heat flux were made. These runs were initialized
in February 1978 to reduce computer time. It was found
that to predict correctly the trend from March to June 1978

(Fig. 31) , an additional downward heat flux of about

2

5 cal/cm /h had to be added each time step from 15 March

to 18 June 1978. With the additional heat, the relative
errors in heat content dropped dramatically (Table 3) and
the spring transition occurred during the same period as
the analysis. The resulting horizontal structure features
for March and April 1978 (Figs. 32 and 33) were closer to
the analyzed structure (Figs. 7 and 8) of CA 12 than the
original model predictions (Figs. 19 and 23). The addi-
tional heat also created a small warm anomaly along the
eastern boundary of the ADS region in March 1978. By
April 1978/ this warm anomaly covered a larger section of
the northeast than was analyzed, but the anomaly features
are still closer than the original predictions to the
analyzed features. The improvement of the model features,
the presence of a warm model anomaly along the eastern
boundary and the reduction in relative errors suggests
that the most likely cause of the errors at the central
point for March and April 1978 is inaccurate atmospheric

forcing. However, the downward surface heat flux of

2

5 cal/cm /h did not improve the horizontal temperature

anomaly structure for May and June 1978 (not shown) . Those
fields had much too strong thermal anomalies which did not

73

resemble the analyzed horizontal structure, although the
relative errors in heat content were decreased substantially

(Table 3) . This suggests that a correction of about

2

5 cal/cm /h of heat should be added, but not entirely as

surface heat flux. It is also possible that some other
reasons or processes are responsible for the analysis-model
differences found in May and June 1978.

74

TABLE 3

Relative error in model hindcast heat content relative to
200 m at the central point 36.0°N, 150. 0°W when the model
was initialized on 15 February 1978 (column labeled
Hindcast) and when an additional 5 cal/cm^/h was added to
the downward surface heat flux from 15 March to 18 June
(last column)

Hindcast

+ 5 cal/cm2/h

-0.026
0.133
0.062

-0.033

Month

Year

Hindcast

Mar

1978

-0.021

Apr

1978

0.255

May

1978

0.260

Jun

1978

0.236

75

MARCH
1978

APRIL

MAY

JUNE

Time

Figure 31.

Daily maximum model mixed layer depth and
corresponding model mixed layer temperature
at the central point of cold anomaly 12,
36. 0°N, 150. 0°W. The model was initialized
on February 1978 and 5 cal/cm /h was added
each time step to the downward surface heat
flux from 15 March to 18 June 1978. The
objectively analyzed MLT are denoted by x
on the 15th of each month.

76

(A)

(B)

(C)

50N

45N

40N -

35N

30N
SON

. 45N

40N

35N

30N
50N

45N

40N

35N -■

q

■5.-'

• O if'

30N
Figure 32.

160E 170E 180 170W 160W 150W MOW 130W
Predicted temperatures (°C) during March 1978
at (A) surface, (B) 60 m and (C) 120 m from
the model initialized on 15 February 1978 and
integrated with the addition of 5 cal/cm2/h
each time step to the downward surface heat
flux from 15 March to 18 June 1978.

77

(A)

(B)

(C)

SON

45N

40N -

35N -

30N
50N

45N

40N

35N -

30N

50N -r

45N

40N -

35N

30N

120 M

160E 170E 180 170W 160W 150W MOW 130W
Figure 33. Similar to Fig. 32 except for April 1978

78

4 . Model Physical Processes

This one-dimensional version of the Garwood model
does not treat advective effects. Of the physical processes
not included in the model, horizontal advection is the most
likely to contribute to the erroneous prediction during the
spring of 1978. To examine this effect it is necessary to
describe the synoptic situation during the spring. The
monthly mean streamf unction fields, calculated from the
FNOC winds over the ADS grid, were used to examine the
interannual variability in the monthly mean surface pressure
fields. The streamf unction is generally proportional to and
parallel to the isobars.

During March of 1976, 1977 and 1978 a large anti-
cyclone was centered near 35°N, 135°W and covered most of
the eastern North Pacific south of 45 °N. This general
anticyclonic pattern continued through April with the cell
weakening in both 1976 and 1977, but intensifying in 1978.
In the northern portions of the ADS area during March and
April the winds were generally westerly. During May, the
anticyclone was replaced by a cyclonic pattern, except in
1978. The anticyclone was anomalously weak over the
southeast of the region (centered approximately 34 °N,
145°W) during May 1978. In June of all three years, the
eastern Pacific subtropical anticyclone was re-established
over the eastern half of the ADS grid.

Two arguments can be given to explain why the model
temperatures were too low in May and June 1978. The first

79

argument concentrates on the atmospheric effects of the
anomalous anticyclonic circulation over the eastern part
of the ADS area during May 1978. With an anticyclonic
circulation, there would be an increased downward solar
heat flux due to the clear skies and light winds. Neither
of these conditions is conducive to turbulent mixing in
the ocean, so that an increase in downward solar heat flux
may account for the errors in the spring.

The second argument examines the anomalous surface
Ekman and Sverdrup mass transport. The anticyclonic winds
during May 197 8 are southeasterly over the region of the
central point. This is expected to produce a surface Ekman
mass transport of warmer water towards the northeast (since
the depth-integrated Ekman mass transport is 90° to the
right of the wind stress) into CA 12. To balance this
convergence and subsequent downwelling caused by Ekman
pumping under the atmospheric anticyclone, there must be a
geostrophic mass transport such that the total Sverdrup
mass transport balances the negative curl of the wind stress
The balancing mass transport is southward bringing colder
water into the region of CA 12. There is not sufficient
data to say which mass transport is dominant. The observed
vertical temperature profiles below the mixed layer for
April, May and June 1978 (Fig. 22A) do show that there was
warm advection in April, cold advection in May followed
again by warm advection in June.

80

In summary, the synoptic scale flow over the region
of CA 12 during April and May 1978 was more anticyclonic
than during 1976 or 1977. During March and June the synoptic
scale flow over the region of CA 12 was anticyclonic all
three years. Either an additional downward heat flux or an
Ekman transport of warm water would be consistent with the
synoptic conditions. It is not possible to determine which
effect is more important due to lack of data.

81

IV. LARGE-SCALE RAPID TRANSITION CASE

A. COLD ANOMALY 1 DESCRIPTION

The cold anomaly described below was designated and
described by Elsberry (1983) as CA 1 . CA 1 is a shallow,
large-scale, rapid transition event that persisted for
approximately seven months. It was the most intense cold
anomaly detected in the ADS region during 1976-1979
(Elsberry, 1983) .

This cold anomaly is especially dramatic as it occurred
after at least six months (the first available map is
January 197 6) of above-normal temperatures at all depths
(Elsberry, 1983) . The conditions on the surface during
June 1976 (Fig. 34) show that the majority of the ADS region
had above-normal temperatures due to a large-scale, warm
anomaly centered 36°N, 160°W. For orientation purposes, the
ultimate location of maximum intensity or central point
(40°N, 165°E) for CA 1 is marked as a dot on the figures.
The rate of temperature increase (Fig. 35) from June to
July 1976 (Fig. 36) along the western boundary was less
than 0.5 times the expected climatological rate. This gave
rise to CA 1, which during July 19 76 (Fig. 36) included two
centers at 42°N, 165°E and 36°N, 165°E with temperatures of
-2.47PC and -2.18°C respectively. The southern center
appeared to be relatively deep as it penetrated to at least
120 m, but this center did not persist. The eastern anomaly

82

pattern in the vicinity of 42°N, 140°W in July 1976 (Fig. 36)
was designated CA 2 by Elsberry (1983) . This anomaly per-
sisted throughout most of the life of CA 1. The very slow
rate of temperature increase relative to climatology
(Fig. 37) continued into August 1976 (Fig. 38). It was
during August 1976 that CA 1 reached maximum intensity
(-4.41°C at 40°N/ 165°E) and areal extent. At this time
CA 1 eradicated the surface signature of a warm anomaly
which was located near 42°N, 175°E during July 1976. Even
though this cold anomaly is very intense, it is interesting
that it was a very shallow feature. As may be seen in
Fig. 38 , CA 2 also reached maximum intensity (-1.76°C at
42°N, 140°W) and areal extent during August 1976.

Summer warming continued erratically from August to
September 1976 (Fig. 39) over the region of CA 1, whereas
a cooling trend would have been expected based on clima-
tology. By September 1976 (Fig. 39), CA 1 began to diminish.
The northern section of CA 1 was sustained, although the
center of -2.32°C was displaced to 42°N, 170°E. The
southern section diminished during September 1976, perhaps
in response to the arrival of an intense warm anomaly at
60 m and below.

The expected fall cooling occurred between September
and October 1976 (Fig. 40) over the entire grid as the
rates of temperature decrease (Fig. 41) were of the same
order as climatology. During October 1976 (Fig. 40), CA 1

83

took on a two-cell appearance with centers at 42°N/ 180°
and 38°N, 165°E and with temperature anomalies of -1.81°C
and -1.35°C respectively. The western center extended
below 120 m. Between these two centers was a strong warm
anomaly at 60 m. From October to November 1976 (Fig. 42) ,
the rate of temperature decrease (Fig. 43) over the entire
grid was again much the same as climatology. Thus the
anomaly is simply being maintained during September to
November rather than being significantly strengthened or
diminished. In November 1976 (Fig. 42), CA 1 increased in
intensity with depth and extended through 120 m. By
December 1976, CA 1 was greatly diminished and had a two-
cell appearance through 60 m, with the strongest signature
at 120 m (Fig. 44). Above-normal temperatures were present
over much of the ADS region in December 1976 (Fig. 44), as
the rates of temperature decrease (not shown) were slightly
less than climatology. The cold anomaly was not discernible
after December 1976.

CA 1 often had a two-cell appearance (Table 4) . These
changes in the analyzed strength of CA 1 may be the result
of the physical mechanisms described in Chapter 3, Section A,
In November 1976 at 36°N, 165°E and in December 1976 at
36 °N, 16 0°E, the strength of the anomaly increases with
depth. There are several explanations for the decrease in
anomalous temperature with depth. A possible explanation
is that there was surface Ekman mass transport of warmer

84

water into the region. Based on the monthly mean stream-
function fields for 1976, 1977 and 1978, there was anomalous
westerly flow over the region of CA 1 in November and
December 1976. This flow would not result in the transport
of warmer surface water into the region by surface Ekman
mass transport. Instead, it would tend to increase the
surface intensity of CA 1. Another possibility is cold
advection at depth. However, a complete description of
the cause of this anomalous decrease in temperature with
depth is not possible due to lack of data and grid
resolution.

In summary, CA 1 was a shallow, long-duration, rapid
transition event. CA 1 formed between June and July 1976
in the west central section of the ADS domain with two
centers of low temperature (Table 4) . Anomaly development
was rapid over a region in which the temperature increased
at a much slower rate than expected from climatology. The
cold anomaly reached maximum amplitude and areal extent
during August 1976, The intensity of this anomaly was
truly remarkable considering that it occurred during the
summer. In September 1976, the anomaly started to diminish
in size and amplitude. Up through September 1976, the
center of lowest temperature tended to be in the vicinity
of 41°N, 163°E. As CA 1 diminished, the centers of lowest
temperature erratically moved southward. The anomaly
persisted above 60 m until October 1976. Portions of the

85

regions remained colder than climatology through December
1976. The next section describes the model hindcast of
CA 1.

86

TABLE 4

CA 1 development for each month during 1976. The location (s)
and temperature (s) are for the lowest temperatures in region
of CA 1 for that month.

Month Location Temperature

Jul

(1)

42°N,

165°E

-2.47°C

(2)

36°N,

165°E

-2.18°C

Aug

40°N,

165°E

-4.41°C

Sept

42°N,

170°E

-2.32°C

Oct

(1)

38°N/

165°E

-1.35°C

(2)

42°N,

180°

-1.81°C

Nov

36°N,

165°E

-0.72°C

Dec

(1)

38°N,

165°E

-1.35°C

(2) 34°N, 160°E -0.76°C

87

Figure 34

50N

45N

40N -

35N -

30N

160E 170E 180 1 70W 160W 150W MOW 130W
Temperature (°C) anomaly CA 1 at surface during
June 1976. The horizontal temperature analysis
for each month is centered on the 15th of that
month. Negative (dashed) lines represent
regions with temperatures less than climatology,
zero (heavy solid) same as climatology and
positive (light solid) temperatures greater than
climatology. The interval is 0.5°C. Cross
hatched areas have insufficient data for
analysis. Dot marks the ultimate location of
maximum intensity of central point (40°N,
165°E) for CA 1.

Figure 35.

SON

45N

40N

35N -

30N -»

160E 170E 180 170W 160W 150W MOW 130W
The ratio of change in analyzed temperatures
(°C) from 15 June to 15 July 1976 to the same
climatological temperature change for the
same period. Values greater than 1.0 during
this period indicate above-average temperature
increases .

88

50N

(A)

(B)

(C)

35N -

30N

160E 170E 180 170W 160W 150W MOW 130W

Figure 36. Temperature (°C) anomaly CA 1 during July

1976 at (A) surface (B) 60 m and (C) 120 m.

89

50N

45N

40N -

35N -

30N

160E 170E 180 1 70W 160W 1 50W MOW 1 30W

Figure 37.

Similar to Fig. 3 5 except for period from
15 July to 15 August 1976. Values greater
than 1.0 indicate greater temperature changes
than the normal monthly seasonal increase.

90

(A)

(B)

(C)

50N

45N

40N -

35N -

30N
5DN

A-

,' i ' i i

/ ' V i i

1 / /

V /

30N

150E 170E 180 170W 160W 1 SOW MOW 130W
Figure 38. Similar to Fig. 36 except for August 1976

91

50N

(A)

(B)

(C)

30N

160E 170E 180 170W 160W 150W MOW 130W
Figure 39. Similar to Fig. 36 except for September 1976

92

(A)

SON

45N

(B)

(C)

160E 170E 180 170W 160W 150W MOW 130W
Figure 40. Similar to Fig. 36 except for October 1976

93

50N

45N

40N -

35N -

30N

160E 170E 180 i 70W 160W 1 SOW MOW 130W

Figure 41.

Similar to Fig. 35 except for the period
15 September to 15 October 1976. Values
greater than 1.0 indicate greater temperature
decreases than the normal monthly change .
Negative (dashed) values indicate a
temperature increase during a period in which
seasonal cooling is taking place; except, in
the lower right hand corner where the dashed
lines indicate a temperature decrease in an
area where climatology is warming.

94

(A)

50N

45N

40N -

(B)

(C)

30N J

160E 170E 180 170W 1 60W 150W MOW 130W
Figure 42. Similar to Fig. 36 except for November 1976

95

50N

45N

40N -

35N -

30N

160E: 170E 180 170W 160W 1 50W HOW 130W

Figure 43.

Similar to Fig. 35 except for the period
15 October to 15 November 1976. Values
greater than 1.0 indicate greater temperature
decreases than the normal monthly seasonal
change.

96

(A)

SON

45N

^^

(B)

(C)

40N -

35N -

30N
50N

45N

40N

35N -

30N
50N

45N

40N

35N

30N

160E 170E 180 170W 160W 150W MOW 130W

Figure 44. Similar to Fig. 36 except for December 19 76

97

B. MODEL HINDCAST

The Garwood model was initialized with the TRANS P AC
temperature analysis from 15 June 1976 and integrated
through 18 December 1976 to cover the life span of CA 1.
Instead of hindcasting the extremely intense CA1 , the first
model prediction created an extremely shallow and warm
anomaly. The model results for August 1976 at the surface
can be seen in Fig. 45. The daily maximum model mixed layer
depth and corresponding mixed layer temperatures (not shown)
at the central point (40°N, 165°E) of CA 1 shows that the
temperatures are over 15 °C higher than analyzed. By
December 1976, the mixed layer temperature is about 5°C
higher than analyzed. As shown in Fig. 45, these high
surface temperatures are part of a zonal surface temperature
pattern with temperatures much too high in the regions south
of 42°N and too low in the northern regions. The predicted
surface temperatures are particularly high to the west of
180° longitude. The next section will investigate the
reasons and processes that could produce erroneous results.

98

50N

45N

40N

35N -:

30N

160E 170E 180 170W 160W 150W 140W 130W

Figure 45.

Model temperature (°C) anomaly MA 1 at the
surface during August 1976. The model used
the surface heat flux correction relative to
200 m as determined by Elsberry et al. (1982

99

C. ERROR DISCUSSION

The model anomaly field bore little resemblance to that
analyzed, and did not produce a cold anomaly in the region
of CA 1. The poor model results could be a function of
(1) data quality; (2) model physics; and (3) model forcing.
Each of these areas will be examined in more detail in the
next three sections.

1. Data Quality

The original objective analysis procedure used by
White and Bernstein (1979) generates values at all grid
points regardless of whether any observations are present
in the vicinity of the grid points. In a data-sparse region,
a faulty XBT could significantly degrade the quality of the
monthly objectively analyzed values at the surrounding grid
points and cause a temperature bias with depth. However,
one would expect that the objective analysis technique
would tend to eliminate such a bias if other correct profiles
are in that region.

CA 1 is the most intense anomaly observed by Elsberry
(1983) during 1976-1979 (Fig. 46). CA 1 is about 2.5°C
colder than the next coldest anomaly. It is possible that
the extreme intensity of CA 1 is due to erroneous data.
However, neither the XBT profiles nor the data distribution
maps for the life span of CA 1 are available to determine
if this factor can explain part of the model discrepancy.

100

CD -|

<^4 _

w
o

<

06
O

o
o

0

n l I i

i 1 1 r

-i 1 1 r

-i r^^i r

-1 -2 -3 -4
TEMPERATURE RNOMHLY (C)

-5

Figure 46.

Histogram showing the occurrence of cold
anomalies during the period January 1976 to
December 1979. CA 1 is on the extreme right
in the histogram (from Elsberry, 1983) .

101

2 . Model Physics

Because Garwood (1977) found that shear production
significantly affected entrainment mixing in relatively
limited conditions, the version of the model used here does
not contain equations for mean momentum or a term for shear
production in the turbulent kinetic energy equation.
However, there is some evidence as reported by Price (1981) ,
Kraus (1981) and Martin (1982) for the importance of shear
as a mixing mechanism. Martin (1983) suggests that the
Garwood model would benefit from the inclusion of shear
production due to the mean current, in that augmented shear
production should prevent overly shallow mixed layers from
persisting. In the Garwood model, the time derivative
terms in the entrainment equation are dropped when the layer
is shallowing, and the new mixed layer depth is solved for
algebraically. The absence of entrainment shear production
may account for some of the model tendency toward too high
sea-surface temperatures during the spring and summer.

The parameterization of the absorption of solar
radiation in the vertical may be another source of error.
A discussion of the parameterization of the flux of solar
radiation, Q , in the Garwood model is provided in the
appendix. Fifty percent of the incoming solar radiation is
absorbed in the upper meter of the ocean. The fraction
that penetrates to greater depths can have a significant
effect on the development of the upper ocean thermal

102

structure. In spring and summer, solar radiation provides
a direct means of heating the seasonal thermocline below
the mixed layer. During cloudy periods and storms, the
reduction of the solar radiation means less heat will be
directly absorbed in the mixed layer, which reduces the
thermal gradient below the first meter, and allows for
deeper mixing. The turbidity of the water also affects the
distribution of solar radiation in the vertical. An increase
in turbidity (not included in the model) during the spring
and summer could increase the sea-surface temperature and
the stratification below the mixed layer, while decreasing
the mixed layer depth and the warming of the ocean below the
mixed layer.

CA 1 might also be caused by the .advection of a cold
ocean eddy into the region. White and Bernstein (19 79)
emphasize that the baroclinic eddy activity west of 175°W
was considerably greater than to the east, where the large-
scale variability dominates. The transition near the
Emperor seamount chain between the strong and the weak eddy
regions was quite abrupt, of the order of 5-10° of longitude
(Bernstein and White, 1977). Eddies south of the Kuroshio
extension would be cold, which agrees with the anomalous
temperatures in the region of CA 1. The decay of a cold
eddy is also consistent with the analyzed temperature
structure. That is, a cold core eddy could have arrived
in the region of CA 1 between July and August 19 76 and as

103

the eddy decays the region would be increasing in temperature
ans still be colder than climatology. The transitional
speed of CA 1 can not be determined accurately using the
monthly position(s) of maximum intensity (Table 4). The
grid size of 2° latitude by 5° longitude is too coarse to
describe the evolution of mesoscale events. Using the -2.0°C
isotherm in Fig. 37 to define the edge of CA 1 in August
1976 gives a radius of about 650 km. This radius is approxi-
mately 13 times the baroclinic Rossby radius of deformation.
Thus if CA. 1 was a cold eddy, one would expect a large
vertical extent. However, this is not seen as CA 1 in
August 1976 (Fig. 38) is completely above 60 m. Since the
vertical extent is so small and the horizontal scale so large,
it is unlikely that CA 1 is one large eddy.
3 . Model Forcing

It is necessary to first determine if the errors are
due to an initial value problem associated with initializing
after the spring transition when the mixed layer is shallow
and warm. According to Martin (1983) , errors due to model
initialization are minimized by initializing during the
winter when the mixed layer is deep. After the mixed layer
shallows in the spring and the seasonal thermocline begins
to form, the model results are fairly independent of the
initial conditions. To test the contribution from this
source of error, the model was initialized with the
15 February 1976 analysis and integrated through

104

18 December 1976. The results of this test showed that the
errors are not due to an initial value problem as again the
mixed layer was too shallow and too warm throughout the
integration period, and especially during the summer months.
Since the first model predictions with the bimonthly
heat flux correction fields determined by Elsberry et al.
(1982) were too warm in the region of CA 1, the model was
run without the surface heat flux corrections. The inte-
gration period was from 15 June to 18 December 1976. The
daily maximum model mixed layer depths and corresponding
mixed layer temperatures at the central point (Fig. 47)
were substantially improved over the first prediction. The
predicted mixed layer temperature anomaly for August 1976
was within 1°C of the -4.41°C value. However, large negative
temperature errors occurred in the remainder of the ADS
domain. This can be clearly seen in the model hindcast for
the surface during August 1976 (Fig. 48) . The errors were
largest along the southern boundary of the ADS region.
Plots (not shown) of daily maximum mixed layer depth and
corresponding temperature at 38°N, 160°W and at 42°N, 135°W
showed that a seasonal thermocline was not established.
These results agree with earlier studies (Elsberry et al.,
1979; Budd, 1980; Steiner, 1981) which found that the
monthly surface heating from FNOC does not have a suffi-
ciently large seasonal amplitude. These studies also found
a persistent bias toward excessive heat loss along the

105

southern boundary of the domain. Thus a downward surface
heat flux correction is definitely needed in the region,
even if it is not at the location of CA 1. Consequently,
it was decided to examine carefully the June-August surface
heat flux correction fields as determined by Elsberry et
al. (1982).

For comparison, the model results with the correction
field during the summer of 1978 were examined. The model
was initialized with the 15 June 1978 analysis and inte-
grated through 18 August 1978 to illustrate the effect of
the June-August surface heat flux correction fields. If
the model did not predict the anomalous conditions by
August, then it would not get the anomalous conditions after
August correct either. Model runs were made with and without
surface heat flux correction fields. From the model inte-
gration without the correction fields, it was very apparent
that as for 1976, a downward heat flux correction is needed
to correct a bias of excessive upward heat flux over the
ADS region. The model integrations with the correction
fields predicted mixed layer temperatures that were too
cold in 1978 compared to being too warm in 1976. Thus,
the model integrations suggest that the corrected heat
flux underestimates the heat flux required for June to
August 1978, and overestimates that required for 1976 in
the region of CA 1.

106

The analyzed vertical temperature profiles at
40°N, 165°E for June, July and August of 1976, 1977 and
1978 were examined. The evolution of the profiles during
two (1977 and 1978) of the three years were very similar,
while the period of CA 1 development during 1976 was quite
different. The analyzed vertical temperature profiles for
August of 1977 and 1978 were characterized by shallow,
warm (<5 m, about 24°C) mixed layers. Even though the
mixed layer was also shallow in August 1976 (<-5 m) , the
temperature was about 7°C colder.

A comparison of the model forcing without the
surface heat flux correction from June to December for the

three years showed that 1976 had noticeably less (about

2
10-20 cal/cm /h) total upward flux than the other two years

over most of the period. This is consistent with the

analyzed mixed layer temperature for August 1976 being much

lower than during the other two years. There were no

dramatic differences in the wind speed or solar radiation

fields among the three June-August periods.

In summary, the surface heat flux forcing is

definitely a potential error source. Although the heat

correction field derived by Elsberry et al. (1982) may be

appropriate to the normal large-scale evolution, it is not

appropriate to model predictions of the development of

CA 1 from June to August 1976. Thus a new surface heat flux

correction field for the period June-August 1976 is

described in the next section.

107

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o*o o

o-trv- o-09i- o'oaie'ooc-

O'OC 0"5l O'Ol

(3) sjnpjaduuajL jsAd-] paxi/vj

Cn o

a -p g

•HO 4-1 0

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G 0) «M

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a o <d -p w

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Q) 4-1 g rH O

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H (T> O <D LH

O G SZ^O

U -H T3 -P H

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C 3 <H 0 2

(d w a o

a; a x o

,g h <d

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a,--* Cni3 «=r

QJ Eh G

t3 rJ -H T3 H

s <u a)

n^ja +> rt!

0) 0 u

>i(D W C

id m a a><M

•

HDOT30

VO

-P -H — '

P*

T3 fd -P M

ffl

<U M U En 0)

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g g H <U

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rH -P O CD

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«a M x >ix!

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ai

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Q

id m-i c -p

g rH re ra

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<-H

g T3 (d >i— .

■H d) (1) H £

O

X X A <D -P

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fd -h > G

g g <U -H 0

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O -P g

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108

SON

45N

40N -

35N -

30N

* /
»«

! ; ; ; ; /' 'V//7

^y / / / / / , , ' i

iii/,
/tit/

160E L70E 180 170W 160W 150W 140W 130W

Figure 48. Model temperature (°C) anomaly at the surface
during August 1976. No surface heat flux
correction was applied in the model.

109

D. REVISED HEAT FLUX CORRECTION

CA 1 occurs during a period of ocean warming (AH > 0)
and net downward ( but less than expected from climatology)
surface heat flux (Q > 0) which produces excessive warming
(AH - QT > 0). Elsberry et al. (1982) determined that this
type of error would occur 26.8% of the time using the
corrected total heat flux. The heat flux correction fields
for the June-to-August period as determined by Elsberry et
al. (1982) are based on only three years. Their basic
assumption is that the error in the surface heat flux is
systematic and that an average over the three years will
give a stable estimate of the required correction. However,
it was shown above that the changes in heat content during
1976 were markedly different. Therefore a new heat flux
correction field is derived specifically for the 15 June to
18 August 19 7 6 period. The purpose is to determine if the
model can predict the correct vertical distribution of the
heat if an improved estimate of the total surface heat flux
is provided.

The change in oceanic heat content relative to 200 m
is

AH = H(t + At) - H(t) , (3)

where At = two months (June - August 19 76) and H relative
to 200 m is given by

0

H = p C f (T(z) - T(200) ) dz . (4)
° P -200

110

It is expected that AH will be positive during this period
of net downward heat flux (roughly between April and
September ) . A two-month interval was used to be consistent
with the heat correction field derived by Elsberry et al.
(1982) . They found that bimonthly correction fields were
simple to apply and representative of the seasonal variation.
This two-month interval is also the time during which CA 1
reached maximum intensity and spatial extent.
The following budget equation is assumed:

At
AH = / Qdt + Residual = Q At + Residual . (5)
0 T

The integral sign indicates that the air-sea flux is summed
over the same time interval that AH is evaluated. Q is
defined as the total surface heat flux and can be expressed
as the time integral of:

QT = Qs - (Qb + Qh + Qxl = Qs - Qsfc , 161

where the subscripts s, b, h and 1 refer to solar, back,

sensible and latent heat fluxes through the sea surface.

Q ,. is surface heat flux. The residual term includes non-
sfc

local physical effects (especially horizontal advection) and
the errors in estimating the heat content changes and the
surface fluxes. This budget equation assumes that vertical
processes dominate the horizontal, and for the space and

111

time scales in this study, that the local change in heat
content over the given period should be balanced by the
vertical flux of heat at the air-sea interface.

The analyzed temperature fields and the model physics
were assumed correct. Using predicted temperature fields
for August 1976 determined without any heat corrections and
the analyzed temperature fields for August 1976, a new
bimonthly surface heat flux correction relative to 200 m
at each grid point is

correction = (AH ,._ > - AH , ,_ N)/At

mod (Aug) anal (Aug) '

(H -, /, s - H n ,, . )/At
mod (Aug) anal (Aug) '

(7)

2
The correction field (Fig. 49) with units of cal/cm /h

was added to the FNOC surface heat flux each hour in the

model integration. The solar radiation fields are assumed

to be correct. Negative values in the resulting correction

field (Fig. 49) indicate that the upward heat flux is to be

reduced by the amount shown. It can be seen that H , and

H . are approximately equal at the central point (40 °N,

165°E) , so that only a small correction is required.

The model was initialized with the 15 June 1976 analysis

and integrated through 18 August 1976 (Fig. 50) . The

intensity of CA 1 is correctly hindcast, although the

gradients around the anomaly are too large. There is also

a warm anomaly along 170 °E which is not present in the

analyzed anomaly field (Fig. 38A) . The shape of the

112

anomalous warm region in the mid-southern section of the
ADS domain is in agreement with that analyzed, albeit with
much too high temperatures. It may also be seen in Fig. 50
that there is some weakening of the anomalous features
through the middle of the ADS domain. The model does
hindcast the eastern region as cold, which agrees with the
analysis.

At the central point of CA 1 (Fig. 51) , there is very
good agreement between the monthly objective analyzed mixed
layer temperature and the temperature corresponding to the
daily maximum mixed layer depth. The good agreement at this
point was expected from Fig. 47 since the new correction is
almost zero. Major improvements due to the new correction
field relative to either the original (Fig. 45) or no
(Fig. 4 8) correction are found through most of the domain.

To determine if further improvements in the surface
anomaly field could be made, two other correction fields
were derived. As the summer mixed layer is shallow and
warm, the local atmospheric effects are only felt in the
upper 100 m. Thus a correction field based on the heat
content changes relative to 100 m was produced (Fig. 52).
The model was then initialized with the 15 June analysis
and integrated with this correction field added to the
FNOC surface heat flux fields through 18 August 1976. The
resulting surface anomaly field (Fig. 53) is less representa-
tive of that analyzed than in Fig. 50. The eastern, middle

113

and southern sections were not hindcast well. In the
region of CA 1, the temperature of the predicted anomaly
is too low and the anomaly center is displaced northward.

Since the anomaly in August 1976 is present above 60 m,
it is possible that the heat flux correction field should
be based on the heat content changes in the upper 50 m.
Therefore, a correction field relative to 50 m (Fig. 54) was
also produced. The model was then integrated over the same
time period as previously. The resulting surface anomaly
field (Fig. 55) is a much poorer representation of the
analyzed field (Fig. 38A) than the predicted fields with
surface heat flux correction fields relative to 100 and 200 m.
One region of improvement in Fig. 55 is in the eastern section,
although the improvement is small relative to Fig. 50.

The pattern correlation was calculated between the
analyzed and predicted temperature changes between 15 June
and 15 August 19 76. These calculations are over an area
bounded by 34°N, 44°N, 170°E and 135°W. The pattern correla-
tion for the model integration with the surface heat flux
correction relative to 200 m was 0.49, while the pattern
correlation for the model integration with the correction
field relative to 100 m was -0.05. Based on these and the
previous results, the new correction field relative to 200
m was judged to be better. The improved results with
the larger depth suggest that this calculation is more
effective in removing some of the effects of horizontal
advection and changes in heat content due to vertical

114

displacements of the thermocline. Waking the correc-
tions relative to 50 and 100 m may intertwine these
effects with the effects of local atmospheric forcing.

In summary, if the best possible estimate of the surface
heat flux is provided, the model predictions were improved,
although they were only a fair representation of the
analyzed August 1976 fields. One possible source of error
is the assumption that the total correction should be
applied to the surface heat flux. Perhaps a fraction of
the correction field should be applied to the solar heat
flux. The areas of erroneous high temperatures in the
model predictions may also be due to the absence of shear
production due to the mean current. It is possible that
non-local atmospheric forcing and events may contribute to
the poor model performance. Given the available data, it
is not possible to separate the effects of three-dimensional
processes, poor forcing, inaccurate ocean analyses and
incomplete model physics and parameterizations.

The very strong anomalous conditions associated with
CA 1 are at least partly due to the anomalous atmospheric
forcing during the period. Unfortunately, the magnitude of
the anomalous forcing appears to be of the same order of
magnitude as the bias in the FNOC surface heat flux fields.
When the uncertainties in the heat correction field are
large, the ability of the model to predict anomalous ocean
conditions cannot be satisfactorily tested. These tests

115

with a single case would suggest that improvements in the
FNOC surface heat flux are required. It is hoped that the
new Navy Operational Global Atmospheric Prediction System
will provide these improved fields.

116

50N

45N

40N

35N -

30N

\\\H* s *',',- ~ ,U \ • i i ' ' *

i • ' "\ **'v -' rrrIfi — * * * » ■ » \ *

*\ " * \* / / ' / *>. x v v * * v s > '

Figure 49.

160E 170E 1B0 170W 1 SOW 150W HOW 130W

2
Correction field (cal/cm /h) relative to

200 m for 15 June to 18 August 1976 to be

applied to the FNOC surface heat flux fields.

Negative values indicate that the upward heat

flux is to be reduced by the amount shown.

50N
45N
40N

35N

30N

><0M »;3f;>\;v.'// \ -////^

^-^v Wi.'i it " ' ' > ' / «•- v*\v. \\

&$foM??!['!?\ \v>fc> \sCZJJkX \

Figure 50.

160E 1 70E 180 170W 160W 150W MOW 130W

Model temperature (°C) anomaly at the surface
during August 1976 resulting from the
correction field relative to 200 m being
applied to the FNOC surface heat flux fields.

117

JULY
1976

AUGUST

Time

Figure 51.

Daily maximum model mixed layer depth and
corresponding model mixed layer temperature
(MLT) resulting from the new correction field
relative to 200 m being applied, compared to
objectively analyzed MLT (denoted by x on the
15th of each month) at the center of CA 1
40.0°N, 165°E from 15 June to 18 August 1976.

118

50N

45N

40N

35N

30N

160E 170E 180 170W 1 60W I50W 140W 130W

Figure 52. Similar to Fig. 49 except for correction
field relative to 100 m.

50N

45N

40N

35N

30N

|0M |ggp

XT

2.0"

\wv ','.,x"xxxr

160E 170E 180 170W 160W 150W HOW 130W

Figure 53. Similar to Fig. 50 except for the application
of the correction field relative to 100 m.

119

50N

45N

40N -

35N

30N

yxv^x--.

1..

~2.

V

9. \ f. i

> <5> P

160C 170E lBO 170W l SOW 150W MOW 130W

Figure 54. Similar to Fig. 49 except for correction
field relative to 50 m.

MOM RS^

40N -..

30N

1 1

|6fi7'.\»V v *\ / ^ N n ' --in '"

/ .I'Ml., v> ~N s v„ -- \

v\\Y''/ ** . v '" ' / / .' — •» v-" — ■""""

\/ '.

■0 .„

\V.)/C^

160E 170E 180 170W 160W 150W MOW 130W

Figure 55. Similar to Fig. 50 except for the application
of the correction field relative to 50m.

120

V. CONCLUSIONS

The Garwood model does a very commendable job of hind-
casting the large-scale long duration anomaly CA 12 through
the autumn of 1977 and winter of 1978. Errors in the model
prediction increased substantially in the spring, following
the analyzed spring transition between 15 March and 15 April

1978. It was found that an additional downward surface heat

2
flux of 5 cal/cm /h during this period produced improved

predictions. With the additional heat flux correction the

model spring transition occurred during the same period as

the analysis. For March and April 197 8, the improvements of

model features, the presence of a warm anomaly along the

eastern ADS region boundary and the reduction in relative

heat content errors, suggest that the most likely cause of

errors at the central point for these two months is

inaccurate atmospheric forcing. However, the additional

downward surface heat flux did not improve the horizontal

temperature anomaly structure for May and June 1978. Those

fields had much too strong thermal anomalies which did not

resemble the analyzed horizontal structure, although the

relative errors in heat content were decreased substantially

2

This suggests that a correction of about 5 cal/cm /h of heat

should be added, but not entirely as a surface heat flux.
In May and June 1978, there was anomalous anticyclonic flow

121

over the region of CA 1. Thus, either an additional down-
ward solar heat flux and/or Ekman transport of warm water
could be the process by which the additional heat needs to
be distributed in the model.

These results verify the hypothesis that CA 12 was
primarily generated by the vertical mixing processes during
the autumn of 1977 and the winter of 1978. That is, the
mixed layer temperature change is related to one-dimensional
processes to the first order. The usefulness of the heat
flux correction fields, derived by Elsberry et al. (1982),
for FNOC surface heat flux estimates in North Pacific Ocean
predictions was demonstrated during the autumn of 197 7 and
the winter of 1978. The model results for CA 12 in the
spring suggested that in periods of rapid change (i.e.,
spring transition) a better estimate of the surface heat
flux is required. The results for CA 1 emphasized this.

It was found from the hindcast of CA 1 that the heat
flux correction fields derived by Elsberry et al. (1982)
were not satisfactory for June to August 1976. A new
surface heat flux correction field was derived specifically
for 15 June to 18 August 1976. This new heat flux correction
exactly accounts for the difference in the predicted (without
correction) and analyzed temperature profile heat content
relative to 200 m. With this more correct estimate of the
surface heat flux, the model did produce an improved result

122

which was a fair representation of that analyzed for August
1976. However, there were still errors in the model results.
Perhaps some of the heat flux correction needs to be applied
to the solar heat flux. There is also the possibility of
model physics being the source of error. The Garwood model
may benefit from the inclusion of entrainment shear production
This entrainment may reduce the sensitivity of the model by
preventing overly shallow mixed layers from persisting
during the spring and summer.

The uncertainties in the heat flux correction fields
are fairly large in the spring and summer. This limits
tests of the ability of the model to predict anomalous
ocean conditions during the spring and summer. It is
recommended that the model's capability for spring and
summer predictions be further examined.

The results of this study are generally encouraging.
The most encouraging aspect is that a one-dimensional mixed
layer model, such as the Garwood model, has the capability
to predict anomalous conditions over long integration
periods. The validity of a vertical mixing hypothesis for
the formation and maintenance of cold anomalies in the
North Pacific Ocean is also demonstrated. However, these
predictions illustrate the crucial role of the surface heat
and momentum fluxes in predicting the ocean mixed layer
characteristics. The FNOC surface heat fluxes from the

123

hemispheric, primitive-equation model need to be improved,
especially during the spring and summer. It is hoped that
the new NOGAPS model at FNOC will provide these improved
fields.

124

APPENDIX

GARWOOD MODEL

The Garwood (1977) model is a bulk or vertically
integrated model for the oceanic planetary boundary layer
(OPBL) or mixed layer. It is comprised of a closed system
of seven equations.

The entrainment buoyancy flux equation,

T 1/2

m. <w > <E>
-bw(-h) = — i H ; (1)

the horizontal component of turbulent kinetic energy,

1 3 ,. 2, 2 . bw(-h) |AC|2
j -^ (h <u +v > ) = m3u, 2AB '

T - 1/2 2ml - 1/2 m5~~ -
- m0(<E> - 3<w >) (E) ' -± (<E> + ~ fh)<E>; (2)

the vertical component of turbulent kinetic energy,

I ft (h <^> ) = I hbw(-h) - \ hu*b*

_ 1/2 -^ 1/2
+ m2 (<E> - 3<w >) <E> '

nu , ,„ m

- Ji(<E>1/2 + -1 fh) <E> ; (3)

3 it^

125

the mean buoyancy and mean momentum equations

h £|2£ = bw(-h) - bw(0) + -23- Q , (4)

po p

h -5— = cw(-h) - cw(0) + if<C>h ; (5)

and the jump conditions at the bottom of the mixed layer
(relating entrainment fluxes to the rate of deepending,
and the changes in mean momentum and buoyancy at the base
of the mixed layer) ,

■cw(-h) ■ AC |~ , and (6)

■bw(-h) = AB || . (7)

The time-dependent model forcing consists of the
surface fluxes of momentum and buoyancy. In the present
experiments, the contribution to the buoyancy due to
salinity is neglected due to the lack of salinity data.
Thus, the surface boundary conditions required to compute
these fluxes are the total heat flux (Q ) , the solar
radiation (Q ) and the wind speed. Model outputs are the
entrainment fluxes, turbulent kinetic energy, mixed layer
depth and mixed layer temperature.

The mechanism Garwood (1977) envisioned in the initial
destabilization of the interface (between the mixed layer

126

and the denser water beneath) and the resulting entrainment
is a "local" Kevin-Helmholtz instability (also known as a
Benjamin (1963) class C instability) . This instability is
triggered by shear across the interface provided by the
local turbulent eddies. The shear due to mean flow only
is assumed to make a minor contribution to the achievement
of this critical shear value; thus (5) can be neglected.
By using the equation for the flux Richardson number evaluated
at z = -h,

Rf " .— au — w: ' (8)

(uw __ _ vw ^)

and the jump conditions (6) and (7) , one can find that
shear production is a fixed fraction of buoyant damping in
the entrainment zone. This zone may have a flux Richardson
number greater than 1.0 and still possess enough turbulent
kinetic energy for mixing to continue. In the Garwood model
the shear production is only a secondary energy source for
mixing, which can only be made available by entrainment
initiated by another source. According to Garwood (1977),
the most significant source of energy for mixing within an
active entrainment zone is the convergence of flux of
turbulent energy,

- (fz» [ W (l - f » ]

o

127

Thus, the critical parameter to determine the entrainment
rate is not Rf but the ratio, P, of buoyancy flux to the
convergence of energy flux:

P = S*

|_ I w C| + -B-) ]

O

The Garwood model uses separate vertical and horizontal
equations (2) and (3) for the turbulent kinetic energy.
This allows the convergence of turbulent kinetic energy
flux to be included in the model. Mixed layer retreat
occurs when the vertical component of turbulence is
inadequate to transport heat, momentum and turbulence to
the earlier depth of mixing.

As explained by Tennekes and Lumley (1972) , the dissi-
pation rate can be estimated from the rate at which large
scale eddies supply energy to the smaller scale eddies.
This gives rise to a dissipative time scale

*« - *- • <10>

Where the vertically integrated averaged turbulent kinetic
energy is defined as

<e> = 2& + ^ + 2t>- , (11)

128

0

0

/ e dz =

/

-h

-h

and the net rate of dissipation is

3u. 3u.

v ax1 sx1 dz • (12)

3 3

There are two time scales in the oceanic mixed layer.
The first is a convective time scale formed from the
turbulent velocity and the length scale of the large scale
turbulent flow, t, = h/u* . This scale can be thought of
as the time required for a large turbulent eddy to overturn.
The second scale is imposed by planetary rotation, t~ = 1/f .
In deeper boundary layers, planetary rotation turns the mean
shear direction with depth and t~ is the characteristic time
scale of the resulting vortex stretching. In Garwood's
model, both of these time scales are incorporated into the
parameterization of the dissipation time scale, which is
defined as

t = t ~1 + t ~2 . (13)

£ 1 2

The parameterization of the absorption of solar
radiation used in the Garwood model is described by
Gallacher et al. (1983) as a double exponential model for
which one of the extinction depths approaches zero.
Computationally, this reduces to absorbing a fixed fraction
(1-r) of the flux of solar radiation, Q , in the first

129

meter, and exponential absorption for depths greater than
one meter.

Due to the process of Reynolds averaging in the turbu-
lence equations and the subsequent formation of correlations
(moments) of the fluctuating variables, there are more
unknowns than equations. This problem can not be corrected
at a fundamental level with additional equations since each
new equation for a higher order of moment introduces addi-
tional yet higher order moments. To close the system of
equations, the chosen highest moments must be parameterized
in terms of lower order moments and mean values. The Garwood
model employs a second order closure scheme; thus the triple
correlations (second order moments) are parameterized in
terms of zeroth order moments (mean values) and first order
moments (autocorrelations and cross correlations) .

The process of parameterizing the high order moments
generates constants of proportionality. In the set (l)-(3),
m-, through m- are constants of proportionality which must
be determined from geophysical data. The values used in
this study were itu = 2.0, p, = m./m, = 1.0, p2 = m^/m^ = 1.0,
p3 = m5/m = 0.5, r = 0.5 and y = 0.001. The critical
constants are nu , p^, r and y. In order for the model to
produce accurate forecasts it must be able to simulate the
fall deepening, which is particularly sensitive to nu; the
winter maximum mixed layer depth, which is sensitive to p^;
the spring transition, which depends on the interaction of

130

nu and the surface heat fluxes; and the summer maximum
mixed layer temperature, which depends on r and y« Tne
values of the critical constants listed above were
empirically determined by Gallacher et al. (1983) to be as
consistent as possible with the atmospheric forcing used
in this study.

131

LIST OF REFERENCES

Barnett, T.P., and J.D. Ott, 19 76: Average features of
the subsurface thermal field in the Central Pacific.
Scripps Institute of Oceanography Reference Series
76-20, 13 pp.

Benjamin, T.B., 1963: The threefold classification of
unstable disturbances in flexible surfaces bounding
inviscid flows. J. Fluid Mech. , 16, 435-450.

Bernstein, R.L., and W.B. White, 1977: Zonal varia-
bility in the baroclinic eddy field of the mid-
latitude North Pacific. J. Phys . Oceanogr. 1_, 123-126.

Budd, B.W., 1980: Prediction of the spring transition
and related sea-surface temperature anomalies. M.S.
Thesis, Naval Postgraduate School, 9 5 pp.

Elbsberry, R.L., 1983: A synoptic case study analysis of
the ocean temperature anomalies in the Central
Pacific region during 1976-79. Unpublished manuscript,
Naval Postgraduate School Tech. Rep. NPS 63-83-0 0,
50 pp.

, P.C. Gallacher, A. A. Bird, and R.W. Garwood,

Jr., 19 82: Deriving corrections to FNOC surface heat
flux estimates for use in North Pacific Ocean predic-
tions. Naval Postgraduate School Tech. Rep. NPS 6 3-
82-005, 67 pp.

, P.C. Gallacher, and R.W. Garwood, Jr., 1979:

One-dimensional model predictions of ocean temperature
anomalies during fall 1976. Naval Postgraduate
School Tech. Rep. NPS 63-79-003, 30 pp.

, and R.W. Garwood, Jr., 1978: Sea-surface

temperature anomaly generation in relation to atmos-
pheric storms. Bull. Amer . Meteor. Soc, 59 , 786-789.

, and R.W. Garwood, Jr., 1980: Numerical ocean

prediction models — goal for the 19 80 's. Bull. Amer.
Meteor. Soc, 61, 1556-1566.

, and S.D. Raney, 19 78: Sea-surface temperature

response to variations in atmospheric wind forcing.
J. Phys. Oceanogr., 8^ 881-887.

132

Gallacher, P.C., 1979: Preparation of ocean model forcing
parameters from FNWC atmospheric analysis and model
predictions. Naval Postgraduate School Tech. Rep.
NPS 63-79-005, 24 pp.

_, A. A. Bird, R.W. Garwood, Jr. and R.L. Elsberry,

19 83: A determination of the constants for a second
order closure turbulence model from geophysical data.
Naval Postgraduate School Tech. Rep. NPS 63-83-004,
35 pp.

Garwood, R.W. Jr., 1977: An oceanic mixed layer model capa-
ble of simulating cyclic states. J. Phys . Oceanogr.,
7, 455-468.

Haney, R.L., 1980: A numerical case study of the develop-
ment of large-scale thermal anomalies in the central
North Pacific Ocean. J. Phys. Oceanogr. , 10, 541-556.

Kraus, W. , 1981: The erosion of a thermocline. J. Phys.
Oceanogr. , 11, 415-433.

Martin, P.J., 19 82: Mixed-layer stimulation of bouy

observations taken during Hurricane Eloise. J. Geo-
phys. Res., 87, 409-427.

Martin, P.J., 1983: Simulation of the mixed layer at OWS
November and Papa with several models. Unpublished
manuscript, Navy Oceanographic Research and Development
Activity, 4 6 pp.

Price, J.F., 19 81: On the upper ocean response to a moving
hurricane. J. Phys. Oceanogr., 11, 153-175.

Steiner, E.F., 1981: One-dimensional model predictions of
upper ocean temperature changes between San Francisco
and Hawaii. M.S. Thesis, Naval Postgraduate School,
79 pp.

Tennekes, H., and J.L. Lumley, 1972: A First Course in
Turbulence. MIT Press, Cambridge, Massachusetts,
300 pp.

Tully, J. P., and L.F. Giovando, 1963: Seasonal temperature
structure in the eastern subarctic Pacific Ocean.
Roy. Soc. Can. Spec. Publ., 5_, 10-36.

White, W.B., and R.L. Bernstein, 1979: Design of an

oceanographic network in the midlatitude North Pacific.
J. Phys. Oceanogr., 9_, 592-606.

, R. Bernstein, G. McNally, S. Pazen and R. Dickenson,

1980 : The thermocline response to transient atmospheric
forcing in the interior North Pacific 19 76-78. J. Phys.
Oceanogr. , 10 , 372-384.

133

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Pacific Ocean.

-"•'Oh

""hesis

S852T

c.l

Stringer

One-dimenstional mo-
del hindcasts of cold
anomalies in the North
Pacific Ocean.