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Predication of the thermocline depth online

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than are convergent conditions.

Each ocean area (some of which are perhaps 5 degrees or less square)
possesses individual geographic characteristics which affect formation of
the mixed layer and thermocline. In some cases, such as in areas of perma-
nent convergence or divergence, these characteristics may be sufficiently
strong to preclude conventional mixing processes. Beyond such extreme
cases, local effects are assumed as always present in some degree, acting
in different proportions and ways from one area to another. Local conditions
seem to be especially effective on mixed-layer changes due to convergence
or divergence. Actually, local factors probably exert initial influence
on convergence and divergence resulting in a chain effect on the mixed
layer.



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At= 7°F(6°-8°)


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OC0RRESP0N0 TO NORMAL WIND WAVE FIELD










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B CONVERGENCE FIELD OF PURE WIND CURRENT




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& DIVERGENCE FIELD OF PURE WIND CURRENT
























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50


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0.2 0.4 0.6


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4 16 1.8 2.0 2.2 2 4


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FIGURE 23 EMPIRICAL POINTS OF K VERSUS T/ FOR At= 6"-8° F



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FIGURE 24 RELATIONSHIP OF TYPICAL ASSUMED CONVERGENT
AND DIVERGENT FIELDS AS APPLIED TO PRESSURE
SYSTEMS FOR CHOICE OF r, CURVES
(C = CONVERGENCE, D = DIVERGENCE)



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FIGURE 25



50



RELATIONSHIP OF TYPICAL ASSUMED CONVERGENT
AND DIVERGENT FIELDS AS APPLIED TO PRESSURE
SYSTEMS FOR CHOICE OF v CURVES
(C = CONVERGENCE, D= DIVERGENCE)



Figure 23 shows the distribution of three types of points of k (17)
for the At interval of 6° to 8° F. The upper points, designated by square
symbols, correspond to convergent conditions; central points (circles) are
normal values in the wind field with horizontal flow of pure wind current;
and the lower group (triangles) correspond to divergence areas. Each group
of points follows the same functional pattern and spreads from the central
(normal) group increasingly with k and 17 . The same pattern occurs in all
At intervals. Largest p values for all 3 groups of points lie in the At
interval of 0° to h° F, and smallest p values for all 3 groups lie in the
At interval of l6° to 18° F.

p values computed for convergence and divergence curves by least

squares for all available At intervals show a certain variation of the

P P
ratios ^"^"and ^^ within each interval. This variation is probably

conv norm
due to sparsity of data. The total range of variation of these ratios in
all At intervals is 0.339 to 0.505; overall distribution of values indicate
a constancy of ratio from one At interval to another and no apparent dif-
ference between convergence and divergence. Therefore, the mean value of
all ratios, O.436, was used for computation and plotting of k(^) curves
for convergence and divergence. Constancy of ratios from one At interval
to another indicates constant decrease of convergent and divergent effects
with increasing stability, because the convergence and divergence curves
approach the normal curve as the stability index increases. Logical inter-
pretation of this constant decrease indicates that stability resists all
mixing forces equally.

Corresponding equations of convergence and divergence curves for a
given At are :

\onv = [o^ (K - k 'conv) 2 Pnor m ] ,/2 =[4.58p norm (k-k' conv )] |/ 2 (n)
\ v =[o.436(k-k , dlv )2p norm ] l/2 =[o.873p norm (k-k' dlv )] ,/2 ( 12 )

WhSre ''conv = k 'nor m "^ «* *'d,v = ''nor. +0.07

Mixed-layer thickness is still correlated to wave parameters which
must be taken from the wind field producing convergence or divergence at
the point under consideration. This wind field usually lies outside the
point of observation. Tnis idea is based on the assumption that the area
of observation or prediction was initially in the wind field where normal
mixing occurred. Because of propagation of the wind field, the area later
became a convergent or divergent zone, and the mixed-layer thickness was
altered accordingly.

The upper and lower solid curves in Figures 15 through 22 for con-
vergent and divergent conditions of pure wind current were computed by
Equations (11 ) and (12). Only k and 77 values showing no intermixing of
normal and convergent or divergent points (transition zones) were used



51



in computation of p values (Figure 23). Consequently, these curves must
"be considered to represent well-developed strong convergence or divergence
effects on the mixed layer. In cases of -weak or moderate convergent or
divergent effects on the mixed layer, interpolations can be made "between
normal and convergent or divergent values. Successful interpolation depends
considerably on experience and knowledge of local conditions.

h Curves

The broken-line curves in Figures 15 through 22 are used for determin-
ing the mixed-layer thickness h and were computed by Equation (7) after
application of Equation (6) to determine k values for the various At inter-
vals with known mixed-layer thickness and given wave parameters. After
determination of the k(^) curves, k values along with given wave parameters
and the sea state parameter 77 were considered to be known, h values could
then be computed and plotted as curves related to the k(7j) curves. The
central h curve applies to normal mixing, the upper h curve applies to
convergence, and the lower h curve applies to divergence. Mixed-layer
thickness h is measured in feet and can be determined by means of the right
half of the scale in the left margin of Figures 15 through 22. Inter-
mediate values for weak or moderate convergent or divergent effects on the
mixed layer may be interpolated between the normal and convergent or diver-
gent values.

The h curves rise quite steeply for low 77 values, rise less steeply
with moderate values, and finally level off at high 17 values. This level-
ing off occurs only with rather high 77 values at low stability indexes.
With high values of stability index, leveling off begins for moderate values
of 77. The normal h curve for the At of 2 F is almost horizontal at an
approximate 77 value of 620. This value of 77 corresponds to a fully developed
sea in a wind field of 38 or 39 knots, where mixed-layer thickness is about
310 feet. Further increase of wind force would not appreciably increase
the mixed-layer thickness, if normal conditions (no convergent effect )_
persist and At remains constant. In case of convergence the limit of h
for the At of 2° F is about ^50 feet at an 77 value of 885, which corre-
sponds to about 43-knot winds and fully developed sea.

The normal h curve for the At interval of 17° F levels off when 77
equals 170, which corresponds to about 27-knot winds and fully developed
sea. With such stability under normal mixing conditions (no convergent
effect), further increase of wind force would not increase the mixed-layer
thickness. Mixed-layer thickness at the At of 17° F is thus limited to
80 feet; the thickness could increase to about 135 feet, when 77 is 270 in
the presence of a strongly developed convergent effect.

All h values and their limits apply only when AT is constant. If the
mixed-layer thickness increases rapidly, At does not usually remain con-
stant. A mixture of cool water from the thermocline decreases the mixed-
layer temperature and simultaneously decreases 5£, so that the initial AT
value does not apply during the entire active mixing period. Lower At values
must be substituted near the end of the mixing period; consequently, mixing



52



may be deeper than indicated by use of the initial stability index. If
the surface temperature can be measured during the mixing period, a A"t
value can be determined for use at the end of active mixing. The fore-
going statements apply to all h curves.

Salinity Gradient

The surface and the '400-foot depths have been discussed as being the
most convenient limiting levels for determination of the temperature dif-
ference between the surface and a level below the thermocline. A somewhat
deeper level would be more convenient, because the thermocline sometimes
extends below ^00 feet. This temperature difference is used instead of
the temperature gradient in the thermocline to represent stability; however,
stability is a function of both temperature and salinity gradients. Inter-
nal waves and possibly other factors cause fluctuation of these gradients.

These fluctuations justify substitution of At for the mean temperature
gradient in the thermocline without any great loss of accuracy, because
At is considered proportional tc; the actual temperature gradient. When
At remains nearly constant, the temperature gradient in the thermocline
changes with decreasing thermocline and increasing mixed-layer thicknesses;
however, change of the temperature gradient is incorporated in the function
k(7;), and At efficiently substitutes for the actual temperature gradient
in the thermocline .

Effect of the salinity gradient on stability has not been considered
in calculations to this point. If the salinity gradient is positive, the
maximum value is usually located somewhere in the deeper part of the thermo-
cline, at a point below which salinity decreases slowly. The maximum value
sometimes occurs below the thermocline. If the salinity gradient is nega-
tive its value usually decreases through the depth of the thermocline.

In order to simplify the stability factor, salinity differences in
the thermocline are expressed as temperature differences and are designated
At'. Thus At' is an equivalent temperature difference that would produce
a density change equal to that produced by a given salinity change in the
thermocline. Temperature differences equivalent to salinity differences
have been computed for a wide range of mean temperatures in the thermo-
cline. Pressure and mean salinity effects in the thermocline are esti-
mated to be negligible and have therefore been disregarded in this study.
Increasing salinity with depth produces positive equivalent temperature
changes (At* ), and decreasing salinity with- depth results in negative
values (At'").

The result of 2k Kansen casts made in the thermocline at station CHARLIE
in September i960 is shown in Figure 26A. A~t' is O.89 F. Data for sa-
linity gradients in the thermocline during other months at this location
were not available; however, an additional ^3 observations from the same



53




At = 0.89° F 24 OBS
OCEAN WEATHER STATION
CHARLIE, SEPTEMBER I960




At'=0.99° F 43 OBS
B. VARIOUS LOCATIONS, YEARS, AND MONTHS
NORTH OF THE NORTH ATLANTIC CURRENT




C. COMBINED DATA OF A AND B

FIGURE 26 FREQUENCY DISTRIBUTIONS OF DENSITY CHANGES IN THE
THERMOCLINE DUE TO SALINITY DIFFERENCES EXPRESSED
AS TEMPERATURE DIFFERENCES At' IN ° F



general area were available. The k-3 observations are spread over several
years and all months, excluding those of winter, and extend over a 10-degree
square located immediately north of the Worth Atlantic Current. The result,
shown in Figure 26b, is in good agreement with the data at station CHARLIE
for September and more or less indicates the same salinity distribution
throughout the months of the seasonal thermocline. These data are combined
in Figure 26c.

The mean of the combined data (At"' = 0.9^- F) must be the salinity
effect on the k(rj) curves in Figures 15 through 22. It is assumed that
this effect is incorporated in the stability indexes of these curves, so
that the stability index of the k(rj) curves not only represents the mean
temperature diff erence A"T, but also At', the mean equivalent temperature
difference which represents the mean salinity effect in the thermocline.
Thus, At is the summation of AT and At'. The value of At ' near station
CHARLIE and in other temperate areas of the North Atlantic seems to be
rather uniform and close to 1° F. If there is no salinity difference in
the thermocline, 1° F should be subtracted from the temperature difference
between the surface and 1+00 feet in order to obtain the correct value of
At.

5^



The salinity gradient is apparently of little importance in areas north
of the North Atlantic Current. The gradient "be comes important to the south
of this current, especially in major currents. Figure 27 shows the fre-
quency distribution of At ' based on random observations in the area between
the North Atlantic and the North Equatorial Currents. The range of At ' is
-3° to + 3° F; more than hair of the salinity gradients were negative. In
this area actual stability may be considerably different from that indi-
cated by At, especially with negative salinity gradients. Since k(?7) curves
correspond to 1 F higher stability indexes, the correction C = -At'-1° must
be applied in case of negative salinity gradients. For example, if
T -T],qq = 10° F, and the salinity difference in the thermocline corresponds

to At 1 = -2°, the correction would be C=-2 -1 =-3 , and the actual stability
index would be 7° F. This would correspond to stability produced by
T -T^qq = 7° F at constant salinity. If salinity increases with depth the

correction is C sAt'-l ; that is, no correction applies when At 1 = 1°, a
1° correction applies when At ' =2 F, etc.




-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.5 10 1.5 2.0 2.5 3.0 at'

At = -0.44°F 31 OBS

A. RANDOM OBSERVATIONS SOUTH OF THE NORTH ATLANTIC CURRENT



i,,,:,,,::,t„ , ,;, , , , .^L




II ZTTV -



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B. RANDOM OBSERVATIONS IN THE NORTH EQUATORIAL CURRENT
GULF STREAM, AND NORTH ATLANTIC CURRENT

FIGURE 27. FREQUENCY DISTRIBUTIONS OF DENSITY CHANGES IN THE
THERMOCLINE DUE TO SALINITY DIFFERENCES EXPRESSED
AS TEMPERATURE DIFFERENCES At' IN °F



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56



Corrections are computed in Table h for various salinity differences
for given mean temperatures in the thermocline. The above rules apply to
the correction values taken from the table. For example, with mean tempera-
ture of 55° F and salinity difference of 0.h2%o±n the thermocline the gen-
eral correction is 3°. If salinity decreases with depth ^° must be sub-
tracted from Tq-T^qo " fco obtain the corrected value of A~t; if salinity
increases 2° must be added to Tq-T^qq.

Figure 27 shows the frequency distribution of At' in the North Equa-
torial Current, the Gulf Stream, and North Atlantic Current. Only 2 of
the 36 observations showed negative salinity gradients. The remainder,
which showed positive gradients, cover an extremely wide range of values.
Analysis indicates that conclusions concerning stability in the currents
based on temperature gradient alone have little meaning. For example, if
Tq-T^oo " 10 ° F and At' ■ 9° the actual stability index is 18° F, under
constant salinity conditions. Therefore, the k(^) curves in Figures 15
through 22 cannot be applied for prediction of thermocline thickness in
currents ,when salinity distribution in the thermocline is not known.

Excluding areas of permanent currents, salinity gradient corrections
are required where salinity of surface water is increased by high evapora-
tion during the time of the seasonal thermocline. In the Mediterranean Sea
only k out of 25 observations showed a positive salinity gradient; the
remainder showed negative gradients. Stability seems to be lower in the
Mediterranean Sea for more time than the mean temperature difference
(T -T4oo) indicates. This is also probably true in all subtropical areas
of the North Atlantic.

Weak Thermocline

Within the mixed layer a small thermocline, termed "weak thermocline,"
appears very often during decay of the mixed layer, when surface tempera-
ture rises and surface conditions supply only a small amount of mixing
energy. There is probably no essential difference in formation of the
weak thermocline, whether surface temperature increases are caused by advec-
tion or by other heating processes.

Temperature difference in the weak thermocline seldom exceeds 2° F;
however, resulting stability is considerably stronger than normally ex-
pected. Figure 28 shows a plot of 21 k values determined for a weak thermo-
cline by Equation (6). The normal (central) curve for the At interval of
11° F (Figure 19) has been fitted to the points to indicate how well their
distribution agrees with the curve. In view of the small temperature dif-
ference in the weak thermocline, the point distribution would be expected
to correspond more closely to the normal k(^) curve for the At interval of
2° F (Figure 15) • Such a high stability index, with consequent strong
resistance to mixing by the weak thermocline, is difficult to explain.
One possible explanation is that salinity increases considerably in the
weak thermocline; however, the salinity increases could hardly account for
the increase of equivalent stability index by as much as 8° F. The steep
vertical temperat ire gradient in the weak thermocline may provide extra
stability until a critical level of mixing energy prevails. This critical

57




0.2 0.3



0.8 0.9



0.4 0.5 0.6 0.7
K

FIGURE 28 COMPARISON OF k{rj) POINTS FOR A WEAK THERMOCLINE TO
THE NORMAL k(i?) CURVE FOR /Vfc=ll°F



level appears when the value of 77 reaches anywhere from 120 to 140, corre-
sponding to a fully developed sea with 2k- to 25-knot winds. Stronger
surface conditions tend to destroy the weak thermocline and may eventually
affect the main seasonal thermocline.

If the weak thermocline persists for several days, the lower part of
the mixed layer often becomes part of the main thermocline, and eventually
the weak thermocline becomes the interface between the mixed layer and the
main thermocline as shown in Figure 29.




FIGURE 29 CONVERSION OF THE WEAK THERMOCLINE TO THE INTERFACE
BETWEEN THE MIXED LAYER AND THE MAIN THERMOCLINE



53



The rather widely scattered distribution of points in Figure 28 does
not permit definite conclusions. However, the normal curve for the At
interval of 11° F (Figure 19) can "be used to predict the weak thermocline
depth, if there is evidence of surface temperature increase. Convergence
and divergence effects probably enter the problem of predicting the weak
thermocline depth and could partly account for the wide scattering of the
points in Figure 28. Extent of decay in the lower part of the mixed layer
depends largely on the strength of flow in the upper part of the thermo-
cline .

Variation of Thermocline Depth With Latitude

Theoretical studies of thermocline depth have indicated a considerable
increase of mixed-layer thickness with decreasing latitude, if wind con-
ditions are the same. No empirical evidence to support such an increase
can be found, and such conclusions are not substantiated by this study.
Data from the North Atlantic at various locations between 35° and 56 N
do not indicate measurable differences of mixed-layer thickness. Perma-
nent convergence areas in subtropical zones may often be misleading; the
rather thick mixed layer in such areas cannot be attributed to mechanical
mixing. Strong negative salinity gradients in the thermocline often per-
mit deeper mixing in these areas because of reduced stability. Tnis fact
may be one reason for the fictitious influence of latitude. If some small
latitude effect is present, it may have been lost among several errors
involved. For the time being, however, its existence and magnitude remain
uncertain, and this prediction method can be considered valid for any
latitude .

PRACTICAL PREDICTION OF THE THERMOCLINE DEPTH

Verification

The thermocline depth predicted by this method is the mean depth of
the interface between the mixed layer and the thermocline. Consequently,
verification of the prediction cannot be made with an individual BT obser-
vation, but must be determined from several (preferably 6 or more) BT
observations taken over a period of about one day, because the amplitude


1 2 4 6 7

Online LibraryPaul A MazeikaPredication of the thermocline depth → online text (page 4 of 7)