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									OC210 TOPIC 1:                         BASIC CONCEPTS
Online Reference Material:
1. Chapter 6 in “Introduction to Physical Oceanography” by Robert Stewart at

PART 1         Seawater Properties

I. Introduction: Importance of Ocean Circulation

a. Currents are a major pathway (along with winds) of redistributing heat on earth (Fig. 1)
    i. Current delivers excess solar heat in the tropics to the heat deficient poles. (Fig. 2)
    ii. Changes in ocean heat transported by currents has affected past climate (ice ages)
and could affect future climate (although not as dramatically as the “Day after
Tomorrow” scenario)

c. Changes in equatorial circulation (associated with El Nino events)
        i. Pool of warm water in equatorial Pacific expands eastward (Fig. 3)
        ii. Affects global temperature and precipitation patterns on land (e.g., warm and
dry in Pacific NW) (Fig. 4)
        iii. Affects fisheries (anchovy abundances off Peru) (Fig. 5)

d. Ocean is a major sink for anthropogenically (human) produced carbon dioxide (CO2)
       i. ~30% of CO2 emitted from fossil fuel burning is adsorbed by the ocean (Fig. 6)
       ii. this removes CO2 from the atmosphere (a good thing)
       iii. anthropogenic CO2 distribution in the ocean depends on circulation (Fig. 7)

e. Circulation affects the photosynthesis rates by plankton in the surface ocean (Fig. 8)
        i. Currents are pathways that deliver needed nutrients to the phytoplankton in
        surface layer of ocean
        ii. Surface current patterns cause certain ocean regions to be nutrient rich and
        others to be nutrient poor
                 - the large surface circulation cells located between ~15º and 40º, called
        „subtropical gyres” (Fig. 1), have the lowest nutrient concentrations and
        photosynthesis rates in the surface ocean
        iii. Phytoplankton are at the base of the ocean‟s food chain
                 -plankton distribution affects fish distributions

II. Importance of Seawater Density

1. The density of seawater largely controls the tendency for water parcels to move
        -if the density of water at the surface is higher than below, the water parcel will
sink to a level of its own density
                 -in this situation the water column is „unstable‟

       -if density of water at surface is lower than below, the water parcel will not sink
                -in this situation the water column is „stable‟
       -in a stable situation it takes energy input (usually from the wind) to "push" water
                -e.g., like submerging a floating rubber duck in the bathtub (you supply
                the energy to push it under the surface)

2. The density of seawater depends on three properties
       -Salt content (called salinity), temperature and pressure
       -Seawater density is increased by increasing salt content, lowering temperature
       and increasing pressure

3. Surface water is dense enough to sink to great depths when it is cold and saline enough
for its density to reach a critical value
         -this situation is found at high latitudes, in particular near Greenland and
         -at these sites, cold air temperature during winter cools surface water (typically to
< 2ºC) which, in turn, increases its density
                  -surface waters during winter in these regions often become dense enough
         to sink thousands of meters
         -sinking of surface waters is a very important mechanism to replenish waters in
the Deep Sea (the part of the ocean deeper than ~1500m)

4. For most of the ocean that lies within ~50° north and south of the equator (85% of the
total ocean area), however, the surface waters are much warmer (and less dense) than the
cold waters found below them (Fig. 9)
        -in these „warm water‟ regions, surface waters do not sink and thus there is no
direct contact between surface water and the deep sea
        -one can view this situation as a shallow lens (<200m or so) of warm (15º-20ºC)
less dense seawater lying on top of a deep column (~4000m) of cold (<5ºC) dense seawater

III. Seawater Properties that Control Density (Temperature, Salinity and Pressure)

1. Density is defined as the mass of water per unit volume
       -use rho (ρ) as the symbol for density
       -density units are in kilograms per cubic meter (kg/m3), i.e, mass/volume
                -the “cgs” units for density are grams per cubic centimeter (gm/cm3), but
       these are used less often than „mks‟ units in oceanography

2. Useful Conversions:
       1 cubic meter (m3) = 1000 liters (L)
       1 L = 1000 cubic centimeters (cm3)
       thus 1 m3 = 1,000,000 cm3 = 106cm3

3. Water density

       -density of freshwater at 4°C is 1000 kg/m3 (that is, 1.0000 gms/cm3)
       -one gram of mass is defined as the weight of one cm3 of freshwater at 4°C
       -why do you think “gram” is defined at a specific temperature?

4. Changes in seawater density are caused mainly by variations in temperature, salinity,
and pressure.
       -colder water is more dense
       -saltier water is more dense
       -increasing pressure causes density to increase
                -pressure increases with depth in the ocean due to the weight of water

5. Density (ρ) variations in the ocean are in the parts per thousand range
        -between the minimum and maximum observed seawater density of 1020 kg/m3
and 1070 kg/m3, the density changes by about 50 parts out of a thousand (5 parts per
hundred or 5%)
        -oceanographers use σ (sigma) to denote density, where σ = ρ (in kg/m3) - 1000
        -σ is very useful to express the small changes in density (parts per thousand or
less) that are typically observed in the ocean
        -for example, if density (ρ) of water is 1025 kg/m3, then σ = 25
        -to convert a σ value to density (ρ), add 1000 to the σ value
                 -e.g. σ = 28 means ρ = 1028 kg/m3

A. Salinity Effects on Density

1. Salt in seawater makes it denser than freshwater
         -How much salt is in seawater?
         -Typically seawater contains between 33 to 37 gms of salt per kilogram of
         -although the extreme surface ocean salinity range is 28 to 40 gms/kg

2. Salinity is defined as the grams of salt per kilogram of seawater

3. Lab Experiment:
       a. Start with 1 liter of freshwater at 4.00°C and a density of 1000 kg/m3 ( = 0 )
                -add 35 gms of salt (primarily NaCl)
       b. Explain why the resulting salinity is 33.8 not 35.

4. Typically, the salinity decrease from the surface ocean to deep waters is very small,
from about 36 in the surface to ~34.7 in the deep water
       -thus there is a corresponding very small density decrease with depth of about 1.2
kg/m due to only the salinity change

B. Temperature Effects on Density

1. Temperature affects seawater density
        -seawater density increases as water cools
        -as water cools, H2O molecules pack more closely together (because the
molecules are vibrating less at lower temperatures) and take up less volume
        -the same number of water molecules (same mass) packed into a smaller volume
yields higher density (Remember: density = mass/volume)

2. How much does the seawater density increase upon cooling from 20° to 0°C?
       -seawater density increases from 1024.0 kg/m3 at 20°C to 1027.3 kg/m3 at 0°C (at
a constant salinity = 34 ‰)
       -thus σ increases from 24.0 to 27.3

3. On average, there is about a 20°C temperature decrease from the surface to bottom of
ocean which causes about a 3.3 kg/m3 increase in density
       -Notice that the density increase with depth (+3.3 kg/m3) caused by the
temperature decrease more than offsets the smaller density decrease with depth (about -
1.2 kg/m3) caused by the average salinity decrease with depth.

4. Generally, the density increase resulting from the temperature decrease with depth in
the ocean dominates over the density decrease caused by the salinity decrease in the
ocean, which makes the deeper water more dense than surface water in the ocean
        -this means that in most regions the ocean is a stable fluid, that is, it will take
energy to mix the ocean vertically
        -however, this is not necessarily the situation in the polar regions where cold
surface water temperatures approach temperatures in the deep sea

C. Pressure Effects on Temperature and Density

Pressure Effect on Temperature

1. Pressure (P) increases water temperature because the water molecules are packed
tighter and collide with each other more frequently and these collisions produce heat
        -if you take a parcel of seawater at the surface and submerge it without losing any
heat to the surroundings (this is called adiabatic warming), then the in-situ water
temperature will increase as pressure (or depth) increases
        -the term “in-situ” means measured at the actual location (depth) of the water
        -in this situation the in situ temperature is measured by recording the temperature
using a thermometer reading at the depth of the water parcel

2. Pressure increases as depth in the ocean increases because the in situ pressure depends
on the weight of water above the in situ depth
        -the deeper the water parcel, the higher the column of water above and the higher
the pressure

3. The pressure exerted by the entire column of air at the surface of the earth is equal to 1
atmosphere of pressure
        -10m of seawater exerts approximately the same pressure as the entire column of
air above us
        -for every 10m increase in depth, the pressure in the ocean increase by ~1
atmosphere (a unit of pressure)

4. Units of Pressure
        1 atmosphere = 760 mm Hg
        1 bar = 0.987 atmospheres

5. Since a 10 meter column of seawater exerts a pressure of ~1 bar, then a 1 meter high
column of seawater exerts a pressure of ~1 decibar (1 dbar = 0.1 bar)
        -thus in the ocean, the pressure in dbars is approximately equal to depth in meters
(e.g. we measure 100 dbars of pressure at about 100m depth in the ocean) (Fig. 10)

6. The in situ temperature increase rate resulting from increasing pressure ranges from
about 0.05°C per 1000dbars (between 0m and 1000m) to ~0.15°C per 1000dbars
(between 3000m and 4000m)
        -thus the average in situ temperature increase rate due to pressure increase is about
0.1 ºC per 1000 dbar.
        - we can express this mathematically as: ΔT/ΔP = 0.1 ºC / 1000 dbars, where the
symbol Δ represents „change‟, T = in situ temperature and P = pressure.

7. In terms of depth (Z), the average rate of in-situ temperature increase resulting from the
pressure increase with depth is about 0.1°C per 1000m. This represents the average rate
of adiabatic heating in the ocean due to pressure increase.
         -For example, if a surface water parcel with a temperature of 0.0ºC is submerged
adiabatically to 4000m, the in-situ temperature at 4000m would be about 0.4°C
         -i.e., ΔTemp = ΔTemp * Depth increase
                           Δ Depth
                 ΔTemp (ºC) = 0.1 ºC * 4000m = 0.4ºC
         -there is no pressure effect on temperature if a water parcel moves „horizontally‟
at the same depth (same pressure level)

8. Oceanographers use the term Potential Temperature (denoted by theta or the symbol θ)
to describe the temperature that a seawater parcel would have if it was moved from its in-
situ depth to the surface without any loss or gain of heat, i.e. adiabatically
        -mathematically this is expressed as:
                - thus θ = T – P * (T/P)
                - or θ = T – Z * (T/Z)
        -for example, the potential temperature of a water parcel that has an in-situ
temperature of 0.40°C at 4000m is about 0.00°C
                -i.e., θ = 0.40°C - 4000m*(0.10ºC/1000m) = 0.00°C

       -this means that the act of moving the water parcel from the surface to 4000m
accounted for about 0.4°C of its measured in-situ temperature

9. For example, if you filled a large beaker (4000m deep) with water that had a
temperature of 20.0 ºC, you would measure an in situ temperature of 20.0 º C at the
surface and an in situ temperature of ~20.4 ºC at the bottom of the beaker.
        -this measured in situ temperature difference would be a result of the difference in
pressure exerted on water parcels at the surface and 4000m
        -note that the potential temperature for any water parcel in the beaker (at any
depth between the surface and 4000m) would be 20.0 ºC in this hypothetical situation

10. Why do oceanographers use Potential Temperature, rather than in-situ temperature, to
compare the temperature of different water parcels in the deep ocean?
       -for example, if two water parcels found at different depths in the ocean have the
same Potential Temperature but different in situ Temperature, no in situ heat input is
needed to cause the difference in in-situ temperature.
       -that is, the heating caused by the pressure (or depth) difference between the two
water parcels alone is enough to cause the observed in situ temperature difference at the
two depths

11. Note that Potential Temperature () is a calculated (not measured) value
        -need to measure both the in-situ temperature and in situ pressure to calculate .
        -oceanographers do this using a device called a “CTD” which measures the in-
situ conductivity (C) (which depends on salinity), in situ temperature (T) and in situ
pressure (Fig. 11)
        -one can convert the pressure measured by the CTD to depth by knowing the
average density of the water column above the depth of the measurement
                -Note: Pressure = g * ρ *Z, where g = gravitational acceleration.

Pressure Effects on Density

1. As pressure (P) increases, so does water density (Fig. 10)
       -the water molecules pack together tighter as pressure increases, which reduces its
       -because pressure increase with depth in the ocean, due to the weight of the
seawater above, this pressure increase causes the in situ seawater density to increase with
       -this pressure induced density increase is much greater than the density increase
       resulting from either temperature or salinity changes with depth in the ocean

2. If we take surface water with density of 1028 kg/m3 and sink it to 4000m depth, the in-
situ density increases to ~1046 kg/m3 (Fig. 10)
        -this 18 kg/m3 density increase is due to pressure increase only, not temperature or
salinity changes

        -in comparison, the density changes due to the typical temperature and salinity
differences between surface and deep water were ~+3.3 and –1.2 kg/m3, respectively.
        -thus the in-situ density increase between surface water and waters at depth in the
ocean is dominated by the pressure increase

3. Oceanographers define a term called Potential Density to correct for pressure effects on
both density and temperature
         -this is analogous to using Potential Temperature to describe temperature at depth
         -oceanographers use the symbol sigma-theta (σθ) for Potential Density that
describes the density of a seawater parcel assuming it was at the sea surface rather than
its in-situ depth
         -σθ removes the pressure effects on both density and temperature
         -changes in σθ are due only to changes in Potential Temperature and Salinity (but
not Pressure)
         -Thus σθ = ρsurface - 1000 (in kg/m3), similar to the relationship between σ and ρ

4. Oceanographers most often use Potential Density () to describe the density of
subsurface water parcels (not in situ density)
       -σ is a calculated parameter and not measured directly

5. Using θ allows oceanographers to:
        a. compare the Potential Density of water parcels in the ocean with the Potential
            Density of surface waters to look for locations where these deep water parcels
            may have originated at the sea surface
                - one couldn‟t compare in situ densities of water parcels at different depths
                because the strong pressure dependence of in-situ density (Fig. 10)
        b. determine the stability of a column of water, which is independent of pressure
effects on temperature and density
        c. determine the depth distribution of equal potential density “surfaces” or
contours (called isopycnals), which often indicate the path of mixing in the ocean.

6. Note: The  and θ of a water parcel at the surface of the ocean are equal. Why?

D. Quantifying the dependence of Density on Temperature, Salinity and Pressure

1. Do we actually measure the density of seawater?
       -No. We measure the salinity, temperature and pressure of seawater in-situ (using
a CTD) and then calculate density from the Equation of State which describes the
dependence of seawater density on temperature, salinity and pressure. (Fig. 12)

2. The Equation of State is experimentally determined in the lab and is therefore referred
to as an empirical relationship.

3. The equation has lots of terms and thus is very cumbersome to use for calculations

        -putting the equation of state into a spreadsheet or algorithm, however, makes it
relatively easy to calculate density from temperature and salinity and pressure data

4. To calculate the in situ density, input the measured salinity, in situ temperature and
pressure into the Equation of State.

5. To calculate Potential Density, input the Potential Temperature and salinity into the
Equation of State and set pressure (P) = 0.
       -remember σθ represents the density of a water parcel if it located at the surface of
the ocean (which removes the pressure effect on in situ temperature and density)

6. The form of the Equation of State (polynomial equation) indicates that there is not a
linear relationship between changes in density and changes in temperature and salinity
        -that is, there are exponents in the T and S terms in the polynomial equation
        -the non-linearity (curvature) is most pronounced between density and
temperature (Fig. 10)

7. An approximation of the equation of state is expressed as follows:

       ρ – ρo =  * (T – To) + β * (S – So)

       -where ρo = 1027 kg/m3, To = 10 ºC and So =35,  = -0.15 kg/m3/ºC and β = 0.78
       -for example: if T= 15ºC and S =36, then calculated ρ = 1027.03
       - Why is the sign negative for  and positive for β?

8. Connecting the Temperature and Salinity characteristics of water masses that have the
same density yields a curved line (Fig 13)
        -lines of constant θ are curved on a plot of T vs S
        -Note: seawater parcels with different T and S characteristics can have the same
        -that is, one seawater parcel can be warmer and saltier than another but have same
        -Generally, the least dense seawater is warmer and fresher, while the most dense
seawater is colder and saltier

9. One interesting consequence of the non-linear relationship between density, T and S is
that a mixture of two water parcels with the same density (falling on the same σθ line)
yield a water parcel that is denser than the density of the original water parcels.
        -see if can you picture this situation using the T-S plot in Fig 13?

10. The salinity of seawater affects both the temperature of maximum density of seawater
and the freezing point of seawater (Fig 14)
       -freshwater has maximum density at 4°C and freezing point at 0°C
       -seawater at S=35 has maximum density at ~ –3.5°C and freezing point at ~ -2°C

       -the ~ –2ºC freezing point for seawater means that we can observe below zero
temperatures in certain polar regions of the ocean (primarily near Antarctica)
       - the salinity effect on temperature of maximum density and temperature of
freezing explains why it is much easier to form ice on a lake (freshwater, S=0) than on a
bay (seawater). Can you explain why?


A. Potential Temperature Distribution

1. Entire temperature range in ocean is from ~ -2°C (close to freezing point at S=35) to
        -the high temperature extremes are usually found in closed seas, like the Red Sea
        -the surface ocean has much lower temperature range than air, which varies from -
60°C to +60°C over the earth‟s surface
        -on land, the continental regions away from the ocean have the largest seasonal air
temperature swings (e.g., Siberia, middle of Canada)
        -thus the ocean moderates air temperatures over land
                -most pronounced in Europe due to heat transport by Gulf Stream

2. Cross-section of temperature through an ocean basin (Fig. 15)
       -we can compile a series of depth profiles of temperature (measured with a CTD)
to form a cross-section of potential temperature across an ocean basin
       -in Fig. 15, a north-south series of depth profiles of temperature has been
compiled and contours of equal potential temperature (called isotherms) are drawn and
the temperature ranges are identified by color

3. Cold isotherms in the deep sea intersect the surface at high latitudes (south of 50ºS) in
the South Atlantic (Fig. 15)
        -this is one indication that water in the Deep Sea originated at the surface in polar
        -if this potential temperature cross-section continued northward of Iceland, we
would find that deep isotherms intersect the surface at latitudes northward (poleward) of

4. Question- If the ocean had a uniform salinity, how would the location of contours of
constant potential density (called isopycnals) compare to the location of contours of
constant potential temperature (isotherms)?

5. The potential temperature (θ) decrease with depth is greatest in top 1000m (Fig. 16)
        -the depth region where temp decrease is greatest with depth is called the
        -the rate of change of temperature with depth is called the temperature gradient
        -Generally, the word „gradient’ is used to express the rate of change of one
variable relative to another variable,

        -e.g., the depth gradient of Potential Temperature is expressed as /Z, where
the Δ symbol represents “change”
        -in words, /Z represents the change in Potential Temperature (in ºC) divided
by the change in depth (in meters) over some depth interval of interest
        -the steepness of the depth gradient in temperature depends on location and depth
                 -/Z is greatest near the surface in the warm tropical ocean and least in
the cold polar ocean

6. The ocean is divided into three depth regions based on an average depth profile in
Potential Temperature (Fig. 16)
       -surface mixed layer which is the uniform temperature layer at the surface
       (typically the upper 50-100m or so)
       -thermocline is the depth region where /Z is largest (~100m to ~1000m)
       -deep sea where temperatures are cold and fairly uniform and /Z is small
       (typically at depths >1500m)

Question: Why is /Z in the thermocline much smaller at high latitudes than low

7. Surface ocean is warmest at equator and coldest at poles (Fig. 17)
        -mean sea surface temperature (referred to as SST) in the global open ocean is
about 18°C, with a range of –1.5° to 29°C
        -the equator to pole decrease in SST is about equal to the temperature decrease
observed in a typical depth profile at low latitudes (see Fig. 16)
        -Why is the similarity of these ranges not a coincidence?

8. In the surface ocean, isotherms tend to follow latitude lines (Fig. 17)
        -east-west variability in SST much less than north-south variability
        -generally, isotherms follow the latitudinal trends in solar radiation (sunlight)
received at earth's surface (Fig 18)
                -this isn‟t surprising since solar insolation is the primary heat source for
the surface of the earth (including the oceans)

Question- What is the likely trend in surface isopycnals given the trend in isotherms?

Class Exercise: Graph the trend in annual average SST versus latitude between 60°S and
60°N (at 10° intervals) along 160°W (use information in Fig. 17).

9. The potential temperature variations in the Deep Sea (>1500m) are much smaller than
the SST variations. (Fig. 19)
       -the „open‟ surface ocean (excluding enclosed Seas) temperature range is ~ –1.5° to
       -the Deep Sea (depths >1500m) has a much smaller temperature range between ~
       –1.5º and 4ºC

B. Salinity Distribution

1. Salinity (S) range in the surface ocean is about 30 to 37 (gms salt per kg seawater)
(Fig. 20)
        -highest values in the Subtropical Gyres (~20-30° north and south of the equator)
                 -these are large pools of salty surface water found in all ocean basins
        -lowest surface salinity are at high latitudes, especially Arctic Ocean, where
salinity approaches 28
        -generally, salinity is higher in the Atlantic Ocean compared to the Pacific or
Indian oceans
        -contours of equal salinity are called isohalines

2. What controls the salinity of the surface ocean?
        -mainly the rates of evaporation (E) and precipitation (P) (Fig. 21)
        -where E exceeds P, the surface ocean salinity is high
        -where P exceeds E, the surface ocean salinity is low
        -evaporation causes a loss in water (as vapor), but not salt
                 -the salt that is not evaporated (left behind) increases the salinity
        -in contrast, precipitation adds freshwater (which has a salinity of zero)
        -E minus P (E - P) is the highest at mid-latitudes (~ 30º) which causes the high
salinity in Subtropical Gyres
        -river input of freshwater (Salinity=0) at high northern latitudes causes low
salinity in the Arctic Ocean
        -the units for E and P are in m/yr or cm/yr and represent the amount (depth) of
water lost to evaporation (E) or added by precipitation (P) per unit time

3. Salinity varies with latitude and depth in the deep Atlantic Ocean (Fig 22)
        -salinity, generally, is higher in the surface ocean than in the Deep Sea
                -Why is this expected given the latitudes where Deep Water contact the
        surface ocean? (see Fig. 20)
        -there are pronounced salinity features in the Deep Sea (e.g., low salinity waters at
~1000m in the S. Atlantic, which aren‟t seen in Potential Temperature

4. There is much less salinity variation in the Deep Sea (range from 34.4 to 35) compared
to the surface ocean (30 to 37) (Fig. 23)

C. Potential Density Distribution

1. In the surface ocean, temperature changes dominate density changes so the average
surface density increases poleward as surface water gets colder (Fig 24)
        -at surface of ocean,  = θ because there is no pressure effect at surface
        -remember:  = ρ – 1000, when density is expressed in kg/m3

2. A poleward surface temperature decrease from 29° to 0° C causes density to increase
from 1022 to 1028 kg/m3, (σ = 22 to 28 ) which approximately equals the density range
observed in the surface ocean (Fig 24)

3. Contours of equal potential density are called isopycnals
       -in the surface ocean, the pattern of isopycnals looks similar to the patterns of
isotherms (Fig. 24)
       -Why is this not surprising?

4. In contrast, the poleward decrease in surface salinity from 36.5 to 33 (Fig. 20) causes
density to decrease from 1026 to 1023 kg/m3 (σ = 26 to 23)
        -opposite to the poleward temperature effect on surface density

Question: If salinity only controlled the density of the surface ocean, at what latitudes
would the densest surface water be located?

5. In the deep sea, the typical potential density (θ ) range is smaller at about 27.5 to 28
(Fig 25)
        -this density range is >10x less than the θ range observed in surface waters

6. A cross section of potential density in the Pacific Ocean indicates a continuous increase
with depth (Fig. 26)
        -the ocean has a shallow warm, low density, lens of water sitting on top of a cold
column of deep water
        -deep isopycnals reach the surface off the coast of Antarctica in the Pacific

7. In the deep sea (in contrast to the surface ocean), both potential temperature and
salinity distributions have significant effects on potential density.


1. Generally, the Potential Density of seawater increases with depth (Fig 26)
        -typically θ increases from ~24.5 to ~27.8 between surface and bottom of ocean
2. That θ (not σ) increases with depth indicates that the density increase it is not a
pressure effect
        -since θ eliminates pressure effects on both density and temperature
3. Because θ typically increases with depth, then the ocean typically is a stable fluid
        -in most regions of the ocean (within about 50° of the equator) there is resistance
to vertical motion of water in the ocean because vertical motion would require mixing
denser water upward and less dense water downward
4. However, in polar regions (>60º latitude) there are small temperature and salinity
changes with depth (e.g., south of 50ºS in Fig. 16), and thus the σθ increase with depth is
        -in these regions, the isopycnals can be almost vertical (Fig 26)

      -when this occurs, the resistance to vertical mixing is low and surface waters can
mix downward to great depths (1000‟s of meters)

5. Does this mean there is no vertical motion in the warm portion of the ocean?
        -No. Energy derived from winds can overcome stability and vertically mix water
even when it is stably stratified
               -e.g., mixing derived from wind energy keeps the surface mixed layer well
        -seasonal cooling of surface waters can periodically reduce stability and cause
vertical mixing (convection), especially during fall and winter when air temperatures cool
               -during these times the depth of the surface mixed layer increases
               -this happens in the N. Atlantic where wintertime surface mixed layer
depths can reach down to ~500m

6. Generally, however, the increase in potential density with depth observed in most of
the ocean means that horizontal mixing of water parcels is much easier to accomplish
(takes less energy) and is many times faster (>106 x) than vertical mixing
        -picture injecting a patch of dye in the thermocline of the ocean. After a few
weeks, mixing would cause the dye patch to look like a pancake where the horizontal
extent of the patch was kilometers and the vertical extent was centimeters.

7. Thus parcels of water tend to move and mix along isopycnal surfaces where there is
constant potential density and little buoyancy resistance to movement
       -in most regions of the ocean, where isopycnals are almost flat (horizontal), this
means „horizontal‟ mixing is much, much faster than „vertical‟ mixing rates
       -however, in regions of the ocean where isopycnals dip downwards (Fig. 26),
under these conditions, movement along isopycnals can result in “vertical” displacement
or movement of water parcels

7. Stability is an indicator of the resistance to vertical water movement and is measured as
the rate of change of density with depth, i.e. the depth gradient of potential density
        -the rate of change of density relative to change in depth is mathematically
expressed as θ /Z (units: kg/m3 per m or kg/m4)

8. Why do we use θ to calculate stability and not in-situ density (σ)?
        -pressure effects on density do not affect stability because the in-situ density
increase that sinking water parcels experience due to increased pressure is lost if they
return to their original position

9. Let‟s demonstrate that pressure doesn’t affect stability with a hypothetical example
Example: You fill a 5000m deep beaker with seawater that has a uniform temperature and
salinity (θ= 0°C and S= 35).
        -You measure the in-situ density versus depth and it increases from 1028 at the
top to about 1050 kg/m3 at the bottom of the beaker.
        -Is the water in the beaker stable, i.e., is there any resistance to vertical motion?

        -Picture moving a parcel of water from one level (say at 1000m) to another deeper
level in the beaker (say 3000m). Is the in situ density of that parcel of water at 3000m
any different from the in situ density of its neighboring water parcels at that depth?
Would there be any tendency for that parcel of water to be more or less buoyant that its
neighboring parcels (any instability)?
        -No! Thus pressure effects on seawater density does not make the ocean a stable

10. Stability in the ocean is much greater in the tropics than in the polar regions (Fig. 27)
        -surface waters in polar regions are colder and thus denser, thus density difference
between deep water and surface water is (Δσ/ΔZ) less in polar regions
        -warm surface water in tropics means density difference between deep water and
surface water is greater than in polar regions

11. Only in polar regions (poleward of 60°), where density of surface water approaches
that of deeper water (vertical isopycnals) is there the opportunity for surface waters to
sink downward into the Deep Sea because the stability of the water column is low (see
Figs. 25 and 26)
        -therefore the polar regions are the Deep Sea‟s "window" to the atmosphere
        -in the polar regions, water destined for the Deep Sea has resided temporarily at
the surface and contacted the atmosphere before sinking to depth
        -we‟ll see that the oxygen gas content of seawater, which is an important control
on biological and chemical processes, is very sensitive to ocean water being exposed to
the atmosphere (as are nutrients concentrations).

12. The atmospheric conditions in the polar regions, mainly cold air temperatures, cause
surface waters to cool and increase their density
        -also during sea ice formation in these cold regions, the ice rejects salt, which
increases the salinity of the seawater which, in turn, increases its density

13. In the far north Atlantic Ocean (near Greenland, Labrador and Norway) and in the far
south Atlantic around Antarctica (primarily in the Weddell Sea), the surface waters get
cold enough in winter to sink to great depths (between 2000m and the bottom at ~5000m)
        -these are the primary sites of „deep water‟ formation
        -also the Ross Sea off Antarctica in the Pacific Ocean (Fig. 25) has been shown to
be an additional site of occasional deep water formation

14. Note: Oceanographers sometimes assume that depth is a negative number when
expressed in an equation. This results from the convention to express the altitude above
the earth‟s surface as a positive distance above earth‟s surface and depth in the ocean as a
negative distance below the earth‟s surface.
        -However, in the lecture notes and equations I will express depth below the sea
surface as a positive value.

Question: Why would surface heating and precipitation promote water column stability
whereas surface cooling and evaporation diminish stability?


1. Range in temperature and salinity of surface ocean is much greater than in the deep sea.
2. Seawater density depends on pressure, temperature and salinity and increases with
increasing pressure and salinity and decreasing temperature.
3. Sea surface temperatures are greatest near the equator and decreases poleward,
generally following latitude lines and contours of solar insolation.
4. Potential temperature corrects the measured in-situ temperature for the heating due to
the pressure.
5. Potential Density corrects in-situ density for pressure effects on both density and
6. Surface salinity is controlled by evaporation minus precipitation and is highest in
7. Temperature changes in upper ocean (<1000m) are the primary cause of density
changes, whereas in the Deep Sea (>1500m) both salinity and temperature contribute
significantly to density changes.
8. Density of surface waters increases poleward generally following temperature decrease.
9. In most regions of the ocean, the Potential Density increases with depth and indicates
that the ocean is a stable fluid, but this isn‟t necessarily the situation at high latitudes
(>60ºN and S).
10. Stability is the rate of change of density with depth and is greatest in tropics and least
in polar regions. The depth region where stability is greatest is in the upper portion of the
11. Vertical mixing of water parcels is high in regions of low stability and low in regions
of high stability.
12. At high latitudes cold surface waters can sometimes sink to great depths because of
low stability.


1. Which of the three factors (temperature, salinity or pressure) primarily controls the
density of surface seawater? Which of these three factors primarily controls the in-situ
density of seawater in the Deep Sea?
2. Calculate the volume change that occurs when a seawater parcel is cooled from 20° to
0°C and the density has increased from 1024 to 1027 kg/m3 . Assume the initial mass of
seawater was 1000.0 kg and the salinity was kept constant. What percent change in
volume does this represent?
3. What would be the approximate temperature, at the sea surface, of a parcel of seawater
that was raised from 2000m and had an in-situ temperature of 4.00°C? What would be
it‟s approximate potential temperature at 2000m?
4. Where does the range of surface and deep (>2000m) water plot in T-S coordinates?
What is the corresponding range in potential density? (see Fig. 13)

5. Calculate the stability of the water column at 10 ºN in the Pacific Ocean between 200
and 500m, between 500 and 1500m and between 3500 and 4500m based on information
in Fig 26. Check the units. Over which depth region is the stability the greatest? Why?
6. Why does theta equal σ at the surface of the ocean?
7. Explain why pressure effects on density do not contribute to stability.


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