TOPIC 3: SURFACE OCEAN CIRCULATION
PART 2: Surface Ocean Response to Winds
Textbook Reading: Ocean Circulation: Chap 3, Chap 4 (sec 4.3, pgs. 107-113)
Physical Oceanography (on-line): Chap 9 (sec 9.2). Chap 10 (sec 10.3 – 10.6), Chap 11
(sec 11.2-11.4)
I. INTRODUCTION
1. The driving force for the ocean’s surface currents comes from winds
 Winds push the water at the surface of the ocean (<100m)
 Horizontal Pressure Gradients are produced when winds pile up surface water in some
regions and remove surface water from other regions
 The strength and direction of surface ocean currents depends on strength and direction of
winds, horizontal pressure gradient forces and the Coriolis Force
2. There are consistent features of the ocean’s surface circulation (Fig. 1)
 Subtropical Gyres are large regions of clockwise or counterclockwise rotating currents found
in both hemispheres and in all ocean basins
 East-west (zonal) currents are found in the Equatorial Ocean and the Antarctic Circumpolar
Current in the Southern Ocean
3. NOTE: The surface circulation shown in Figure 1 represents the generalized typical pattern of
surface circulation averaged over many years
- there are day to day, month to month and year to year changes in this pattern because
wind patterns change over these time scales
4. Why is there an organized pattern to the surface currents in the ocean? Why don’t currents move in
random directions?
- because winds that drive surface currents have an organized pattern of motion on large
spatial scales (hundreds and thousands of kilometers) and over long time scales (years or decades)
II. WHAT HAPPENS WHEN WIND BLOWS OVER THE OCEAN?
A. Wind Stress
1. Winds blowing over the ocean exert a force on the surface water that it contacts
 this transfer of energy between the wind and ocean occurs because of friction
 friction couples the water movement to the air movement
 without friction there wouldn't be any transfer of wind energy to the ocean
2. The wind force acting on the surface of ocean is called wind stress and is denoted by Tau ()
 wind stress is a force that acts in the direction that the wind is blowing on the surface
 in contrast, pressure is a force that acts perpendicular to the surface
3. Wind stress depends strongly on wind speed, i.e., the faster the wind, the greater the stress
 Tau () = *c*U2, where U is wind speed (m/s at ~10m height), ‘c’ is a proportional constant
(unitless), and  is air density (~1.3 kg/m3)
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c is called the Drag Coefficient and accounts for the ability of wind to drag the ocean water
with it and is a measure of the efficiency of transfer of wind energy to the ocean
c has been empirically (by experiment) determined to be in the range of 0.001 to
0.003 (unitless)
c depends in part on roughness of the ocean surface (presence of waves)
4. Forces
 Remember that a Force = mass * acceleration (F = ma)
 Where acceleration is the time rate of change of velocity (how fast the velocity is increasing
or decreasing)
 Thus the units for Force must be, for example, kg *(m/sec2)
 Newtons are the units of Force, where 1 Newton = 1 kg (m/s2)
 Thus, it takes 1 Newton of force to increase the speed of 1 kilogram of mass by 1 meter per
second every second
5. Wind stress () is a Force per unit area
 Thus  = mass*acceleration/area
 the units of stress should be kg*(m/s2)/m2
 so  is in Newton/m2
 Stress is a force that acts in the same plane as the water surface
6. Example of wind stress calculation
 Assume wind speed = 10 m/s, drag coefficient [c] = 0.002 and air density = 1.3 kg/m3
 so  = 0.002 * 1.3 kg/m3 * (10 m/s)2
= 0.26 kg/m3 * m2/s2 = 0.26 kg*(m/s2)/m2
= 0.26 Newtons/m2
7. Wind stress is the force that causes the surface layer of the ocean to move
8. Does wind stress drag only a very thin layer of water molecules in direct contact with the wind?
 No. Water has a property called viscosity that ‘links’ neighboring parcels of water
 the viscosity of a fluid transfers the movement of parcels of water to neighboring water
parcels
 viscosity also results in a friction force that opposes motion, that is, the linkages to other
neighboring water parcels resists the movement of the parcel of water (viscosity causes the
neighboring water parcels to exert a drag on the moving water parcel)
9. Mixing (or turbulence) in the ocean is a process that effectively uses the viscosity of seawater to
transfer the energy of the wind downward through the ocean.
 turbulence is the random movement of parcels of waters
-in contrast a current is organized flow of water in a certain direction
 without turbulence, the currents produced by wind blowing on the ocean’s surface would not
be measurable below a depth of 2m even after 2 days of constant winds
 with turbulence, this same wind produces water motion to a depth of ~100 meters
10. Viscosity and turbulent mixing transfers the wind stress force exerted at the surface of the ocean
downward to water parcels that are not directly exposed to the wind
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B. Steady Surface Currents Resulting from Constant Winds
1. Despite being exposed to steady winds, the surface ocean current velocities aren’t continuing to
increase with time. Why not?
 Let’s start with an ocean at rest (no motion) and no wind
 When the wind starts, the water begins to move because there has been a force (wind stress)
exerted on the surface layer of the ocean
 Since Force = mass * acceleration, when the wind stress force begins the ocean water begins
to accelerate and increase its velocity
 However as the wind continues to blow (assuming a constant wind speed and direction), we
notice that eventually the current reaches a constant speed (no longer accelerating) and
constant direction. Why does this happen?
2. When a water parcel is no longer accelerating despite the continued input of wind stress, this
situation implies that the net force exerted on the water must be zero. Another way to say this is that
there is a force balance when the net force equals zero and, as a result, acceleration equals zero.
 A force balance exists when the force causing the currents to accelerate (wind stress) is
exactly offset (or balanced) by a force (or forces) opposing the wind stress force
 thus under steady winds, ocean currents ultimately reach a velocity and direction that cause a
force balance to exist in response to a constant input of wind stress force
3. A force balance must exist in the surface ocean to keep ocean currents from constantly
accelerating over time as the winds continue to blow day after day (year after year, etc.)
 to achieve a force balance a force is needed that opposes current flow
 Frictional force is one such force
4. Frictional force opposes current flow and increases as the current speed increases
 Thus the frictional force would build up, as current speed increases, to a point where the
frictional force opposing motion equaled the wind stress force causing motion
 at this point, a force balance between wind stress and friction would exist, the net force on
the water parcel would be zero, thus acceleration would be zero and, as a result, the current
speed would no longer increase
 frictional forces are most important near the ocean boundaries (i.e., the atmosphere-ocean
boundary, ocean-sea floor boundary)
5. However, on a rotating earth the Coriolis Force also impacts the force balance affecting currents
-once the water begins to move, in response to wind stress, a Coriolis Force is exerted which
will attempt to deflect the current (to the right in the northern hemisphere and to the left in the
southern hemisphere).
6. Thus there are three forces that influence the speed and direction of currents in the surface layer
of the ocean, i.e., wind stress, friction, and Coriolis forces.
7. Thus in the surface ocean, a constant current speed (and direction) occurs under the influence of
steady winds, when a force balance exists between wind stress, friction and Coriolis forces.
-note that both Frictional force and Coriolis force increase as the current velocity increases.
-in contrast, if the wind speed is steady, then wind stress force remains constant over time
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D. Ekman Transport
1. In 1890, a Norwegian oceanographer Fridtjof Nansen attempted a trip to the North Pole by
freezing a ship called the Fram into the ice and letting the ship travel with the ice for three years.
They reached 86ºN. (Fig. 2)
2. During the trip, Nansen observed that icebergs in the Arctic moved at about a 20-45° angle to the
right of the wind direction. He took this to indicate that the direction of surface currents was not
aligned with the wind direction. (Fig. 3)
-Since ~90% of the iceberg is below the surface, the direction of iceberg flow depends on the
direction of the surface current flow.
3. To understand Nansen’s observations, in 1905 Walfred Ekman theorized that under conditions of
steady winds, the speed and direction of the surface current was determined by a force balance which
was reached when the Wind stress force (W) was offset (or balanced) by the combination of
Frictional force (F) + Coriolis force (C). (Fig. 4)
4. To attain a force balance where the current speed and direction aren’t changing with time, then the
combined forces (Resulting Force) of both the Frictional and Coriolis forces must act in the opposite
direction of the Wind Stress force, which is in the same direction as the wind. (Fig. 5)
5. In response to a Wind Stress force on the ocean’s surface (Fig. 5)
 the Coriolis Force acts, as soon as the surface water starts to move, at a right angle to the
direction of the current (to the right in the Northern Hemisphere and left in the Southern
Hemisphere)
 a Frictional Force acts, as soon as the water starts to move, in the opposite direction to the
direction of the current flow
 a Resulting Force is the force vector that results from the combined effects of the Coriolis
Force and Frictional Force
 as the surface current speeds up (accelerates) both Frictional Force and Coriolis Force
increase and thus the Resulting Force vector increases
6. In response to a wind stress force, the current speed begins to increase and the current is deflected
from the wind direction by the Coriolis Force, until the Resulting Force is equal in magnitude and
opposite in direction to the Wind Stress Force
- at this point in time, there is a force balance
- when a force balance exists, the surface current no longer accelerates (remains at a
constant speed) and remains at a fixed angle of deflection relative to the Wind Stress
Force vector
7. In order for a force balance to exist, the surface current must have a direction to the right of the
wind in the northern hemisphere and to the left of the wind in the southern hemisphere because the
Coriolis force is exerted (perpendicular) to the right of the current direction in the northern
hemisphere and to the left of the current direction in the southern hemisphere
 Note: the current itself is not a force.
 There are only three forces in this force balance: Wind Stress Force, Frictional Force and
Coriolis Force.
 The Resulting Force represents the combined force effect of the Coriolis Force and
Frictional Force and exactly opposes Wind Stress force at a force balance
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8. The deflection angle at which the surface current flows, relative to the wind direction, depends on
the magnitude of the Coriolis Force.
-if the magnitude of the Coriolis Force was equal to the magnitude of the Fractional Force, then
the current would flow at a 45 º angle to the wind
9. Class Problem: Draw the Force Balance for the Ekman layer in the Southern Hemisphere using a
force vector picture like that shown in Fig. 5
10. The Ekman Layer and Ekman Spiral (Fig. 6)
 Ekman viewed the surface ocean under the influence of wind as a series of layers
 a force balance between wind stress, friction and Coriolis forces is attained in the top layer
 for the ‘layers’ below the top layer, the current in the layer above exerts stress on the layer
below it, analogous to the wind exerting stress on the top layer, and drags the water in the
layer below
 this ‘layering’ implies that the currents in the layer below move to the right in northern
hemisphere (and to the left in the Southern Hemisphere) of the direction of the current in the
layer above it which is dragging the water along (just like the current in the top layer moves
to the right of the wind in the northern hemisphere)
 this causes a spiraling of the current direction with increasing depth in the Ekman layer and
is known as the Ekman Spiral
 in reality there is a continuum (rather than series of discrete layers) of currents over depth
with each current moving to the right (in northern hemisphere) and at a slower speed than the
current above it
 the force exerted by the currents in each deeper layer is less than the force exerted by the
current in the layer above because some of this force has been used to overcome frictional
resistance to motion in each layer, thus the speed of the currents in the Ekman Spiral
decrease with increasing depth
11. The direct response of water movement (i.e., currents) to wind stress is restricted to the upper 50
to 100m of the ocean, which is referred to as the Ekman Layer. Below this depth frictional forces are
small (negligible) compared to horizontal pressure gradient forces and Coriolis forces.
12. The Ekman Spiral has been observed in the surface layer using a string of current meters (Fig. 7)
-not easy to observe since the current speeds are slow and a constant wind direction is needed
13. It is important to realize that the average direction of water flow integrated over the depth of the
Ekman Layer is perpendicular to the direction of the wind stress, to the right in the northern and left
in the southern hemispheres (Fig. 6)
 that is, if you add up the current speeds and directions of flow of each of the “layers” within
the Ekman Spiral, the average water transport direction is perpendicular to the direction of
the wind
 this average water flow in the Ekman Layer is called the Ekman Transport and occurs within
the upper 50-100m of the ocean
14. To calculate the total volume of water transported in the Ekman layer we would multiply the
average current speed in the Ekman layer by the cross sectional area defined by the depth of the
Ekman layer and the length scale of interest.
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thus in the Ekman Layer, the volume transport (m3/s) = length scale of interest (m) * Ekman
layer depth (m) * average current velocity (m/s)
typical current velocities in the Ekman layer are 1-5 cm/sec
15. Class Calculation: If we took the length scale of interest as the entire width of the Pacific Ocean
at 40ºN (i.e., 120° of longitude) and average current velocity of 5 cm/s and Ekman layer depth of
50m, then calculate the volume transport in the Ekman Layer.
Ekman Volume Transport (m3/s) = Cross section area * velocity
= 120° (110km/°)*cos(40°) * (1000m /km) * 50m *0.05 m/s
= 25x106 m3/s
= 25 Sv
-Note that because of the earth’s spherical shape, the east-west distance between lines of
longitude decreases poleward. At the equator, there is 110km per degree of longitude. At any other
latitude, the east-west distance between longitude lines equals 110km*cos (latitude). [At the limit
(poles), when the latitude = 90 º, the cos (90) = 0.]
16. Volume transports in the Ekman Layer can be large, if the length scale is long (as in above
example), despite the Ekman layer depth being shallow (<100m) and the currents being slow.
E. What is the impact of Ekman Transport on the surface ocean circulation?
1. Generalized global wind regimes (Fig. 8)
 Two wind regimes have the greatest impact on surface ocean currents
 Trade winds are the strong easterly winds between 0º and 30° in both hemispheres
 Westerlies are the strong westerly winds between 30º and 60° in both hemispheres
2. Because the average water transport in the Ekman layer is perpendicular to the wind direction (to
right in NH and to left in SH) then we can expect the following patterns of Ekman transport (Fig. 8)
 net poleward and westward surface water flow away from the equator in the Trade Wind
regime (0° to 30°)
 net equatorward and eastward surface water flow in the Westerlies regime (30° to 60°)
 Remember: the water flow directly caused by wind stress occurs in a surface layer which is
<100m deep (Ekman layer)
3. This large scale (global) pattern of Ekman transport implies that, generally, there is a net surface
transport of water towards 30°, away from 60° and away from the equator. (Look at the directions of
the black arrows in Fig. 8 to see this pattern).
4. The Ekman transport resulting from steady Trade and Westerly winds distorts the sea surface
height causing slight “hills” near 30° and slight “valleys” at 0º and near 60° in both hemispheres
5. These sea surface height distortions (from a level or flat ocean surface) have a very important
impact on ocean circulation by producing geostrophic currents, which dominate the large-scale
circulation patterns in the upper ocean.
III. GEOSTROPHIC CURRENTS
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A. Horizontal Pressure Gradients
1. Under steady winds, Ekman transport causes surface water to pile up in certain regions of the
ocean and be removed from other regions (Fig. 9).
 Thus the winds cause small elevation distortions from a level sea surface
 the total range in sea surface height is small, at ~2.5 meters
 these small height changes occur over 1000s of kilometers of horizontal distances and are
much too small to be detected by sight
-however, they can be detected and accurately measured by satellites
2. What prevents the water from continuing to pile up in certain regions (e.g. gyres) as winds
continue to blow?
- A steady-state condition is reached where the rate of piling up surface water via Ekman
transport (resulting from winds) is exactly balanced by the loss of water via surface currents
away from the region.
( Likewise, in regions where Ekman transport is removing surface water (e.g. equator), this loss
rate of water is exactly balanced by the flow of water via surface currents input to the region.)
3. What causes water to leave the regions where surface water is being piled up?
 increased pressure caused by the piling up of surface water increases the pressure in these
regions and causes water to flow away
 Remember: Water, like air, moves away from regions of high pressure towards regions of
low pressure
4. Pressure is a force that is exerted downward (it is a force per unit horizontal area)
 Pressure at any depth equals the mass of water above the depth times gravitational
acceleration per unit area
- Remember: Force = mass*acceleration
- In this case, Pressure = mass of the water column * gravitational acceleration
5. The mass of the seawater column above a chosen depth depends on the height of the seawater
column and the average density of the seawater above the chosen depth
6. Thus Pressure (P) equals the gravitational acceleration * density*column height (Fig. 10)
- thus P = g *  * z, where  is the density of water (kg/m3), g is gravitational acceleration
constant on earth (g = 9.8 m/s2) and z is depth in meters
- since Pressure is a force per unit area, the units are:
P = Force / area = mass acceleration /area = (kg * m/s2 )/(m2)
- Remember: the units of Force are Newtons, where 1 Newton (N) is the force required to
accelerate 1 kg of mass by 1 m/sec2
- thus the units of Pressure are Newtons/m2
(Note: A negative sign is sometimes used to express pressure (P = -*g*z) when the depths in the
ocean are expressed as negative numbers.)
7. If you consider a column of seawater as a series of layers then the pressure change across one of
these layers is
 P = *g*z (Fig. 10)
 since the seawater density usually increase with depth then you usually have to calculate the
P over z increments using the average density (ρ) for each layer
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
thus the total pressure at a chosen depth equals sum (Σ) of all the individual pressure above
that depth (P =  g**z or Ptotal = g*ρ1*Δz1 + g*ρ2*Δz2 + g*ρ3*Δz3 + ….. until you reach
the depth of interest
8. By the way, the relationship between pressure and depth (P = *g*z) is how oceanographers
calculate depth from a CTD’s measurement of pressure
-this depth calculation requires a calculation of density for the water column above the chosen
depth, which is calculated from the CTD’s continuous measurements of temperature and salinity and
pressure.
9. In regions of the ocean where surface water is piled up by winds (as a result of Ekman Transport),
there is higher pressure than in regions where less or no piling of surface water has occurred because
the sea surface height (ΔZ) is slightly greater (Fig. 11)
10. These slight differences in pressure, as a result of slight differences in sea surface height,
between various locations in the ocean yield significant horizontal pressure gradients (HPG)
-an HPG is the difference in pressure at two sites in the ocean divided by the distance between
the two sites (P/x) (Fig. 11)
Pa at A = ρa*g*z
Pb at B = ρb*g*(z+Δz)
-where ΔZ is the difference in sea surface height between sites A and B
11. The Horizontal Pressure Gradient (HPG) between A and B is (Fig. 11):
ΔP/Δx = (Pb - Pa) / (Xb - Xa)
ΔP/Δx = [(ρb*g*z) - (ρa*g*(z+Δz))] / Δx
-if we assume for now that density at the two sites is the same (ρb = ρa),
-then ΔP/Δx = ρb*g*Δz/Δx,
12. For example: if ρ = 1025 kg/m3 , Z = 2m and X = 10° latitude
-then ΔP/Δx = g * ρ * Δz/Δx
=9.8 m/s2 * 1025 kg/m3 * 2m/(10° *110km/° *1000m/km)
= 0.018 m/s2 *kg/m3 = 0.018 Newtons/m3
13. If θ represents the angle of the linear sea surface slope (Fig. 11)
-then ΔP/Δx = g* ρ * Δz/Δx
ΔP/Δx = g* ρ * tan θ (because tan θ = Δz/Δx)
14. HPG is a force exerted per unit volume, i.e., ΔP/Δx = (ΔF/Area)/ Δx = ΔF/(Area*Δx) = ΔF/ΔV
-that is, pressure is a force per unit area and it is divided by length (Δx)
-thus, HPG represents a Force/volume (Newtons/m3)
15. The convert the force/volume exerted by the horizontal pressure gradient to force/mass, one
divides the HPG by density:
• HPG/ ρ = (Force/volume) / ρ = Force/(volume* ρ) = Force/mass (because mass = volume* ρ)
• HPG Force / ρ = (Force/volume) / ρ = (1/ ρ)*(ΔP/Δx)
• HPG Force / ρ = (1/ ρ)*(g * ρ *Δz/Δx) = g * Δz/Δx = g*tan θ (see Fig. 11)
-the units are m/s2 (units of acceleration)
16. The HPG Force/mass is important because it equals acceleration
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-Remember: Force = mass * acceleration
-therefore, Acceleration = Force/mass
17. The greater the HPG/mass, then the greater the potential acceleration rate of horizontal currents
- thus, the greater the horizontal gradient in sea surface height (z/x), the greater the
HPG/mass, the greater the potential acceleration, and the greater the potential geostrophic current
velocity.
-that is, the greater the horizontal gradient in sea surface height (ΔZ/Δx), the faster the
resulting geostrophic current velocity
18. Summary: In the upper ocean, Ekman transport of surface water caused by winds produces
horizontal pressure gradients (ΔP/Δx) because winds pile up surface water in some regions and
remove surface water from other regions
 these horizontal pressure gradients (HPGs) are the forces that initiate horizontal water
movement and accelerate currents
 HPGs in the ocean, generally, produce currents that move water away from the regions of
piled up water (higher pressure) towards regions where surface water has been removed (low
pressure).
 The water transported by these currents moving away from regions of high pressure exactly
offsets the surface water transported towards these regions by wind-induced Ekman transport
 This water volume balance in the upper ocean prevents the “hills” in the sea surface from
continually growing and the “valleys” from continually deepening while winds continue to
blow over the ocean.
B. Geostrophic Currents
1. Water flows away from high pressure and towards low pressure, so horizontal gradients in
pressure cause water parcels to move.
2. However, water parcels moving away from high pressure are influenced by Coriolis Force (Fig.
12)
 water parcels moving away from high pressure will be deflected to the right in the northern
hemisphere and to the left in the southern hemisphere because of Coriolis Force
3. To see the effect of the Coriolis Force on currents caused by HPGs, let’s start with a level ocean
surface and no motion. Then let winds blow over the ocean and pile up water in the east that, in turn,
produces a horizontal pressure gradient force towards the west (Fig. 12). Let the winds continue to
blow at the same speed and in the same direction.
What is the ocean’s response? (Fig. 12)
 Initially, the HPG force causes water to move westward in the same direction as the HPG
force is exerted.
 However, the current is deflected towards the right (in the Northern Hemisphere) due to the
Coriolis Force.
 The HPG is a force which accelerates the current, so the current speeds up. The Coriolis
Force keeps turning the current towards the right in the northern hemisphere (to the left in
the Southern Hemisphere) and increasing in magnitude as the current speed increases.
 The current speed increases until it reaches a velocity where the Coriolis Force on the current
equals (and opposes in direction) the HPG force. (The Coriolis Force is proportional to
current speed.)
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This force balance occurs when the current is moving perpendicular to the HPG force
because the Coriolis Force acts at a right angle to the direction of current flow.
At a force balance situation, the current speed remains constant over time
- a force balance occurs because the HPG force is exactly offset by the Coriolis Force
- under conditions of a force balance, the net force = 0 and, as a result, acceleration = 0
- as a result the current speed remains constant
4. Currents that result from a force balance between HPG force and Coriolis Force are called
Geostrophic Currents
 Geostrophic currents flow at right angles (perpendicular) to the HPG force (Fig. 12)
 one can determine the direction of geostrophic currents by assuming that the Coriolis Force
opposes the HPG force and the Coriolis Force is oriented perpendicular to current direction
 thus Geostrophic Currents run in a circle around a high pressure dome (Fig. 13)
o the currents run clockwise in the northern hemisphere and counterclockwise in the
Southern Hemisphere
o this hypothetical situation resembles the circular pattern of flow around the
subtropical gyres observed in the ocean
 in the Northern Hemisphere, the high pressure is to the right of the current flow direction
(and in the Southern Hemisphere the higher pressure is to the left) as one looks in the
direction of the current flow.
 use Fig. 13 to help visualize the relationship between the directions of the geostrophic
current and HPG force in both hemispheres.
5. The general pattern of surface current flow in the ocean is a result of geostrophic currents that
respond to the horizontal pressure gradients caused by differences in sea surface height
-thus geostrophic currents flow perpendicular to HPGs and, thus, flow along the contour lines of
sea surface height (look at the arrow directions along contours of sea surface height in Fig. 14)
6. Note: Frictional force is assumed to be negligible for Geostrophic Currents
 it is assumed that in the interior of the ocean the magnitude of the frictional force is small
(negligible) compared to the magnitude of the Coriolis and HPG forces
 in contrast, at the edges (or interfaces) of the ocean (near sea floor or at the air-sea boundary)
frictional forces must be accounted for (as they are in the Ekman layer)
 velocity shear (Δvel/Δx or Δvel/Δz) is greatest near boundaries (air-sea, basin walls and
bottom) which increases frictional forces
 this simplification of a frictionless geostrophic force balance is reasonable for most of the
ocean, i.e., generally, the predicted pattern of geostrophic current velocities (away from the
ocean boundaries) agrees reasonably well with observed surface current patterns
C. Calculating the Velocity of a Geostrophic Current
1. The importance of the geostrophic current velocity calculation is that it allows
oceanographers to calculate current speeds in the upper ocean based on estimates of sea
surface height
a. Traditionally sea surface heights were calculated from CTD measurements of depth
profiles of T, S and P, as is discussed below
b. More recently sea surface height is estimated from depth profiles of T, S and P
measured remotely by floats (ARGO float program)
c. Additionally satellites (TOPEX) can measure sea surface height remotely
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d. The bottom line is that is becoming significantly easier to measure sea surface height
and thus easier to estimate geostrophic current velocities in the ocean
e. Thus oceanographers can get a very good picture of the direction and speed of
surface currents in the ocean (like that pictured in Fig. 1) based on maps of sea
surface height (Figs. 9 or 14)
f. These calculated geostrophic current velocities are much easier to obtain than direct
measurements of current speeds from current meters which are expensive to deploy
everywhere in the ocean.
2. We calculate the geostrophic current velocity assuming there is a force balance between Coriolis
Force and HPG force under steady wind conditions
3. The Coriolis Force = Mass * Current Velocity * f
-where f = 2* *sin and  is a constant that represents the rotational velocity of the earth
(7.3x10-5 sec-1) and  represents the latitude at which the current is located
-the units for Coriolis Force are kg * m/sec * 1/sec = Newtons Δ
4. The Horizontal Pressure Gradient Force = mass * 1/ ρ * ΔP/Δx
-the units for HPG Force is kg * 1/(kg/m3) * Newtons/m3 = Newtons
4. Since Geostrophic currents are the result of a force balance between HPG and CF in the ocean,
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
then Coriolis Force = HPG Force under a force balance condition
Setting those two forces equal to each other at a force balance yields:
mass* velocity * f = mass * (1/ ρ) * ΔP/Δx
 The mass term on each side of the equation cancels. Rearranging to solve for velocity (v)
yields:
v = (1/ ρ) * (1/f) * ΔP/Δx
v = 1 ΔP
ρ f Δx
 where v is geostrophic current velocity (m/s),  is the angular speed of rotation of earth
(7.3x10-5 /sec) which is constant,  is latitude (°),ρ is density (kg/m3) and ΔP/Δx is the
horizontal pressure gradient with P in Newtons/m2 and x in meters.


units: velocity(V) = 1/(kg/m3) * (1/s-1) * (N/m2 /m) = m3/kg * s * kg*m/s2 * 1/m3 = m/s
(remember, Pressure=Force/area=mass*acceleration/area)
Note: 1 atmosphere of pressure = 1 bar = 105 Newtons/m2
- Remember: Pressure is force per area
 1 Newton/m2 = 1 Pascal (units of pressure)
4. Geostrophic current velocities depend on the magnitude of the sea surface height gradient between
the two locations and the latitude (Fig. 11)

since velocity =
1 ΔP
 f Δx
11
 assume, for now, that density () is equal between the sites and ΔP/Δx = g**z/x
 Substituting g**z/x for ΔP/Δx yields (after canceling the density term):
v = g z
f x
-one can express this geostrophic velocity in terms of the angle of the sea surface slope
v = g tan , where tan θ = Δz/Δx
f
-units: m/s = (m/s2) / (1/s) * (m/m)
5. Characteristics of Geostrophic Surface Current Speeds
 The calculated geostrophic current speed represents the average surface current speed
between the locations over which HPG is determined (between A and B in Fig 11).
 The calculated surface current speed represents only the component of current velocity
perpendicular to the observed horizontal pressure gradient (e.g., if you measure a north-south
HPG, then the component of geostrophic velocity calculated is in the east-west direction only)
7. Note: You should understand the force balance that causes geostrophic currents and the orientation
between HPG force, Coriolis Force and geostrophic current direction. Quantitatively, you should be
able to calculate the surface speed of a geostrophic current given a gradient in sea surface height and
latitude.
D. Estimating Surface Ocean Circulation from a Map of Sea Surface Height
1. Determining a global map of sea surface height provides a means to estimate the direction and
speed of surface geostrophic currents on a global scale in the ocean. (Fig. 14)
2. Oceanographers use dynamic height or geopotential height to describe the sea surface height
because changes in sea surface height represent potential energy.
-that is, if the wind stopped blowing, the surface water piled up in the "hills" would flow
towards the "valleys" and, in doing so, would convert potential energy to kinetic energy.
-because of this ability for a fluid to convert potential to kinetic energy, oceanographers refer to
the sea surface height as dymanic height (DH).
3. In practice, oceanographers calculate the dynamic height of the sea surface at any location by
measuring the vertical density distribution down to a chosen isobar or pressure level, e.g., 1000 or
2000 dbar
 since pressure (P) = g*ρ*z, one can calculate z (the height of the water column above a
constant isobar surface) from CTD measured values of P and calculated values of ρ (from
measured temperature and salinity)
 one repeats this calculation at many sites in the ocean always calculating the depth to a
constant chosen isobar (e.g. typically 1000, 1500 or 2000 dbar)
 since the depth distribution of density varies from site to site in the ocean (g does not vary),
then the depth z of the water column above a constant isobar will vary
 thus sea surface height will vary from site to site in the ocean
12
4. Class Problem: Calculate the height of the sea surface above the 1000 dbar isobar from measured
pressure and calculated density.
 Assume the average density above the 1000dbar pressure is 1026 kg/m3
 (Note: 1bar = 105 N/m2 or 1 dbar = 104 N/m2 and 1 N/m2 = 1 m/s2 * kg /m2 =kg/(m s2 ))
 Since P = g * ρ * Z, therefore
 Z = P/(g*ρ)
 Z= 1000 dbar * (104 kg/(m s2) / dbar) / (9.8m/s2 * 1026 kg/m3)
 Z= 994.6 m
 this means the sea surface is 994.6 m above the 1000dbar surface at this location
 if the mean density above the 1000 dbar surface was higher at another location, then Z would
be lower and the sea surface height above 1000 dbar surface would be lower
 in the above example, if the mean density was 1027 kg/m3 (rather than 1026 kg/m3), then Z
would be 993.6 m
 thus the difference in height between these two sites would be 1.0m (994.6m – 993.6m)
5. Dynamic Height distribution in surface ocean (Fig. 14)
a. Dynamic Height (DH) is often presented as an anomaly, that is, the lowest measured DH for
the surface of the world ocean is subtracted from the measured DH at any location. This way
all the DH values are positive and represent the height difference between any location and
the lowest value for the sea surface.
b. The total range in the ocean is about 2.5 dynamic meters or 250 dynamic centimeters
6. The highest dynamic heights are found in the western portions of the subtropical gyres (20-30°
latitude bands) because this is where the Ekman transport from the Trade Winds and Westerlies
converge and “pile up” water.
7. The lowest DHs are found in the regions of cold waters (near Antarctica and Greenland)
Question: Why would the lowest dynamic heights occur in the regions of coldest water?
-Hint: look at the Pressure equation (P = g*ρ*z) and consider the effect of temperature on
density.
8. The steepest horizontal gradients in DH occur in the regions where the DH contours are bunched
together (Fig. 14)
- a contour map of DH is like a contour map of topography. Where the contours of DH are
bunched together, this represents maximum in horizontal gradients of DH (maximum Δz/Δx).
- DH contours are closest (maximum Δz/Δx) where the western boundary currents, like the Gulf
Stream and Kuroshio Currents, are located.
9. The steeper the horizontal DH gradient (DH/x, which is the same as Δz/Δx), the greater the
horizontal pressure gradient and the faster the geostrophic current.
-remember: geostrophic velocity = g/f*Δz/Δx
10. The direction of geostrophic current flow follows the contours of dynamic height.
 at steady-state, a force balance between Coriolis force and horizontal pressure gradient force
implies that the current flows in a direction perpendicular to the HPG (Fig. 14)
 the HPG is perpendicular to the contours of dynamic height
 thus the geostrophic currents flow along the contours of DH in order to have the Coriolis
Force oppose the HPG Force. Look at Fig. 13 to help visualize this situation.
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11. The pattern of geostrophic current flow based on the map of dynamic height shows the major
features of surface circulation, like the subtropical gyres, western boundary currents (like the Gulf
Stream and Kuroshio Current) and the Antarctic Circumpolar Current (Fig. 14)
- another map of sea surface height (Fig. 9), from ARGO float measurements, shows essentially
the same pattern of surface currents
- compare Figures 1, 9 and 14 to see how the generalized surface ocean circulation is derived
from maps of sea surface height
12. By following the DH contours in Fig. 14, you can see the pathway of surface geostrophic
currents lead away from regions of Ekman convergence (at ~ 30°) towards regions of Ekman
divergence (latitudes of 0° and 60°)
 this current pathway results in flow away from the subtropical gyres and towards the equator
and subpolar gyres
13.The direction of surface geostrophic current flow opposes the direction of Ekman transport in the
surface layer (<100m) which moves water towards the subtropical gyres and away from 0º and 60º.
 The opposition of Ekman transport and geostrophic current flow results in a balance between
Ekman flow towards regions of convergence (‘hills’) and geostrophic flow away from
regions of convergence. Such a balance must exist or otherwise the ‘hills’ would continue to
grow in size over time, which isn’t happening.
- an analogous balance exists between Ekman transport away from regions of divergence
(‘valleys’) and geostrophic current towards these regions (0 and 60º)
14. Class Problem: Estimate the surface velocity of the eastward flowing Kuroshio Current
Extension in the N. Pacific at ~35°N and 180ºW (use Fig. 14 to estimate Δz/Δy)
 the northward change in DH is from about 180 to 150cm between 30° and 40°N
 use the geostrophic equation to calculate the surface current speed
 assume surface density is constant in this region
Velocity


= g/f * [Δz/Δy]
= 9.8 m/s2 / (2*7.3x10-5 /s * sin(35°)) * [0.30m/(10°*110km*1000m/km)]
= 0.028 m/sec
= 2.8 cm/sec
where f = 2 Ω sin (latitude), and Ω = 7.3x10-5 /sec.
Note: This calculation represents the component of the surface current velocity oriented
perpendicular the direction of the HPG. Since we estimated the northward sea surface height
gradient (Δz/Δy) and thus the HPG was directed northward, we have calculated the eastward
component of the surface current velocity.
E. Barotropic and Baroclinic Conditions
1. Barotropic conditions exist when the shape (or slope) of the isopycnals (contours of constant
density) are parallel to the shape (or slope) of the sea surface height (Fig. 15)
- this causes the shape (or slope) of contours of equal pressure (isobars) to be parallel (follow)
the shape (or slope) of the sea surface height
2. Under barotropic conditions, the horizontal pressure gradient at depth is equal to the HPG
occurring at the surface of the ocean caused by changes in sea surface height (Δz/Δx).
-the slope of the isobars remains constant with increasing depth
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3. Importantly, the geostrophic current speed remains constant with increasing depth under
barotropic conditions because the HPG remains constant with increasing depth. (Fig. 15)
4. Baroclinic conditions exist when shape (or slope) of the isopycnals oppose the shape (or slope) of
the sea surface height (Fig. 15)
 thus isopycnals are inclined to the isobars (rather than parallel to isobars as they are under
barotropic conditions)
 thus there is a horizontal gradient in density along an isobars under baroclinic conditions
5. Under baroclinic conditions the horizontal pressure gradient decreases with depth (Fig 15)
 this results from the slope of isobars decreasing with increases depth
 this decrease in HPG and isobar slope with depth results from having denser water
underlying regions of low sea surface height (SSH) and less dense water underlying regions
of high sea surface height
 since pressure depends on the density of the water column, the pressure increases at a greater
rate with depth (ΔP/Δz) where the water is denser (under regions of low SSH) than where
the water is less dense (under regions of high SSH) (Remember: ΔP = g*ρ*Δz)
6. Geostrophic current speeds decrease with increasing depth under baroclinic conditions (Fig 16)
-this is a result of the HPG force decreasing with increasing depth
7. If ones goes deep enough under baroclinic conditions, then the density distribution ultimately
causes the horizontal pressure gradient to approach zero (Fig. 16)
 at the depth where the HPG approaches zero (ΔP/Δx → 0), the geostrophic current speed
approaches zero (Remember: Geostrophic Velocity = 1/(ρ*f) * ΔP/Δx)
 this depth is called the level of no motion and is typically located at around 1000-2000m
 if, at a specific location, a measurable current is present at the assumed level of no motion,
this current speed is added to the calculated geostrophic current speed (see Fig. 16b)
 although there are currents in the deep sea (below 2000m) their speeds are much slower than
surface current speeds (see Fig. 16), so assuming a level of no motion exists is a reasonable
assumption for calculating the surface speeds of geostrophic currents and usually adds only a
small error in the calculated current speed
8. Baroclinic conditions are much more prevalent in the open ocean than barotropic conditions
 thus the ocean adjusts its density distribution (the slope of the isopycnals) to reduce
horizontal pressure gradients with increasing depth
9. Isopycnals dip downward under regions of high sea surface height (e.g. under subtropical gyres)
and upward under regions of low sea surface height (e.g. equator and poleward of 40-50º) (Fig. 17)
 thus the meridional trend in the depth of an isopycnal surface is the mirror image of the
meridional trend in sea surface height
10. The density (isopycnal depth) adjustment under baroclinic conditions occurs in part by having
water move downward (downwell) in regions of high sea surface height and having water move
upward (upwell) under regions of low sea surface height
-these vertical water motions help yield the depth trend in isopycnals required to maintain
baroclinic conditions
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F. Upwelling and Downwelling in Gyres
1. In regions where the wind, via Ekman transport, has piled up surface water the increased pressure
in theses regions causes surface water to move outward and downward (downwell).
2. In regions where the wind, via Ekman transport, has removed surface water the decreased pressure
in theses regions causes subsurface water to move inward and upward (upwell).
3. The direction Ekman transport caused by the Trades Winds and Westerlies cause surface waters to
converge (pile up) in the subtropical gyres at around 30ºN&S and to diverge (be removed) from the
subpolar regions at around 60ºN&S and at the equator (see Fig. 8)
4. Thus the subtropical gyres are regions of downwelling.
5. In contrast, the equator and subpolar regions are areas of upwelling, with the strongest upwelling
rates occurring at the equator.
6. Upwelling and downwelling have a major impact on the concentration of nutrients in the surface
layer.
- upwelling increases the supply of nutrients to the surface layer because nutrient concentrations
increase with depth
- downwelling reduces the supply of nutrients to the surface layer because the surface layer has
low nutrient concentrations
7. As a result, in the subtropical gyres, where there is downwelling, the concentrations of nutrients in
the surface layer is very low and in the subpolar regions (especially the Southern Ocean) and at the
equator, where there is upwelling, the concentration of nutrients in the surface layer is high (Fig. 18)
-similarly in certain regions of the coastal ocean (e.g. in particular off Peru), there is strong
coastal upwelling that supplies nutrients to the surface ocean
8. Since photosynthesis depends, in part, on the availability of nutrients, the rates of photosynthesis
are generally higher in upwelling regions where nutrients are available in the photic layer (upper
~100m).
9. Distribution of chlorophyll in the surface ocean generally indicate that chlorophyll abundances are
higher in upwelling regions where there are high nutrient concentrations in surface waters (e.g,
equatorial ocean, subpolar regions and certain coastal regions) than in downwelling regions with low
nutrients concentrations in surface waters (Fig. 19)
-chlorophyll is the compound plankton use to capture sunlight (energy) required for
photosynthesis and its concentration in surface waters can be estimated by satellites
-generally, there is a positive correlation between higher levels of chlorophyll and higher rates
of photosynthesis by plankton
-however in certain regions, like the Southern Ocean, other factors (possibly the supply rate of
iron from dust in the atmosphere and light during winter) limits the photosynthesis rate despite high
concentrations of nutrients in the surface layer
10. The subtropical gyres, regions of downwelling and low surface nutrient concentrations (Fig. 18),
have the lowest chlorophyll levels observed in the surface ocean (Fig. 19)
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G. Gulf Stream
1.The Gulf Stream (GS) is probably the best-studied geostrophic current in the ocean.
- originally identified during period of sea going exploration in late 1500s
- mapped in late 1700s by Ben Franklin (Fig. 20)
2. It lies at the western edge of the subtropical gyre in the N Atlantic Ocean. (Fig. 20)
-it is an example of a Western Boundary Current
-it is relatively narrow (50-100 km wide) and deep (1500m)
-it is one of the fastest currents in the ocean (up to 3 m/s or 300 cm/s)
3. The GS flows northeastward along the eastern coast of the US. It turns eastward (off the coast of
around Newfoundland) and heads across the N. Atlantic where it is called the N. Atlantic Current.
-some of the N Atlantic Current flows northward into the far N. Atlantic where a portion of its
transport cools, sinks and forms North Atlantic Deep Water (off the coasts of Greenland, Norway
and Labrador) (Fig. 20)
-much of the N Atlantic Current flows eastward across the Atlantic towards Europe where it
becomes part of the southward flowing Canary Current
4. The volume transport of the GS is about 100 Sv when it off of North Carolina and then decreases
to ~ 40 Sv when leaves the coast of Newfoundland and heads eastward as the N Atlantic Current.
5. There is a Western Boundary Current analogous to the Gulf Stream for the subtropical gyre in
each of the ocean basins (see Fig. 1).
a. The Kuroshio Current in the N. Pacific
b. The East Australian Current in the S. Pacific
c. The Brazil Current in the S. Atlantic Ocean
d. The Agulhas Current in the S. Indian Ocean
6. The Gulf Stream (and all the Western Boundary Currents) is a geostrophic current that lies in a
region of strong sea surface height gradients at the western boundary of the subtropical gyres (see
Figs. 9 and 14)
7. The Gulf Stream is located at a front between the warm/salty water flowing northward and the
cold/less saline water near the coast (Fig. 21).
-this front is seen in the rapid southeastward increase in depths of the isotherms and isohalines
8. Remember that the trend in the depth of the isopycnals is the mirror image (opposite) of the sea
surface height trend under baroclinic conditions
- thus the strongest increase in sea surface height occurs at the location where there is the
sharpest increase in depth of the isotherms
Class Exercise: Draw the trend in sea surface height across the temperature cross section in Fig 21
assuming the isotherms approximate the trend in isopycnals.
9. The Gulf Stream lies at the location of the steepest gradient in sea surface height (Fig. 14)
- this means the Gulf Stream is a fast geostrophic current (~2m/s)
-Remember: the velocity of a geostrophic current depends on the gradient in sea surface height
17
- thus Velocity = g/f*(Δz/Δx), where Δz/Δx is the sea surface height gradient
- Western Boundary Currents are some of the fastest currents in the ocean
10. Estimates of geostrophic velocities across the Gulf Stream, off the coast of North Carolina, show
a maximum surface current speed of almost 2 m/s (200 cm/s) or 4 knots northward (Fig 22)
-there is evidence for southward flow beneath the Gulf Stream (>~1500m) at this location
11. Class Problem: Using the east-west trend in geostrophic current speeds shown in Fig 22, sketch
the east-west trend in sea surface height. Notice that the geostrophic current switches direction (from
northward to southward towards the east in this velocity cross section. What does this imply about
the direction of the horizontal pressure gradient at 1000-1500m compared to the surface?
12. In contrast to Western Boundary Currents, the equatorward flowing currents at the other side of
the subtropical gyres have much slower speeds (e.g. Canary Current in the N. Atlantic, California
Current in the N. Pacific, Peru Current in the S. Pacific, see Fig. 1)
13. Western Boundary Currents (WBC) effectively transport heat poleward (Fig. 23)
-generally, the fast WBCs transport more heat poleward than their slower counterparts in the
eastern edge of the gyres transport heat equatorward
- WBCs are fed by tropical currents that supply warm and salty water (e.g., the North Equatorial
Current feeds the Gulf Stream) (see Fig. 20)
-in contrast, the slower and broader equatorward flowing currents at the other side of the
subtropical gyres (like the Canary Current in the N Atlantic) carry colder water towards the
equator
-thus the subtropical gyre circulation scheme in each ocean basin are major pathways of
poleward heat transport on earth
14. An interesting aspect of the Gulf Stream are the rings or eddies that are produced from the Gulf
Stream’s meandering path of flow (Fig. 24)
-both warm core and cold core rings are produced by the Gulf Stream
15. Warm core rings are eddies of warm water surrounded by cold water and Cold core rings are
patches of cold water surrounded by warm water (Fig. 25)
-these rings are typically 100-300km in diameter and can last for 1-3 years before they
completely mix with surrounding water
-these rings are a very efficient mechanism for transporting heat between the cold subpolar
waters and warm subtropical waters
16. These GS rings are also an effective mechamism to transport nutrients between the warm,
nutrient poor subtropical gyre and the cold, nutrient rich coastal waters lying to the northwest
- these rings often have anomalous biological properties than the surrounding water
- cold core rings typically have higher nutrients and chlorophyll levels than surrounding
subtropical water and warm core rings typically have lower nutrients and chlorophyll levels than
surrounding continental slope water
VIII. KEY POINTS
1. The patterns of surface winds have a strong influence on both surface current speeds and
directions.
18
2. Viscosity is the water property that allows the transfer of energy and momentum between winds
and ocean and within the ocean
3. Surface currents, under steady winds, move at an angle to the wind direction (to the right in the
northern hemisphere and to the left in the southern hemisphere).
4. Surface Ekman currents exposed to steady winds are not accelerating or changing direction (over
the long term), which implies that a force balance exists (acceleration = 0) where wind stress force
is balanced by the combination of Frictional and Coriolis forces.
5. The depth-integrated average water transport in the Ekman layer is perpendicular to direction of
wind stress (to right in northern hemisphere and to left in southern hemisphere)
6. Ekman transport, given the global pattern of surface winds, piles up surface water is some regions
(generally at ~30°) and removes surface water from other regions (generally at 0° and 60°)
7. Irregularities in sea surface height caused by Ekman transport, result in horizontal pressure
gradients (HPGs), which in turn cause water to move from regions of high to low pressure.
8. The irregularity of the sea surface elevation is measured in dynamic meters (which represents
potential energy).
9. Geostrophic currents result when a force balance exists between the Coriolis and HPG forces
(frictional force for most of the ocean (away from boundaries) is negligible compared to the
Coriolis and HGP forces). The geostrophic current moves at right angles (perpendicular) to the
direction of the HPG force.
10. The geostrophic current velocity (v) depends on the magnitude of the HPG and latitude and is
expressed as v = (1/ρ) * (1/f) * ΔP/Δx or, when expressed in terms of sea surface height gradients,
then v = g/f * ΔZ/Δx.
11. Geostrophic surface currents move along contours of equal dynamic height. Thus the general
pattern of surface current circulation can be approximated by a contour map of sea surface height.
12. Under baroclinic conditions the isopycnals are inclined to the sea surface, which cause the HPG,
and thus geostrophic current speed, to decrease with depth. This is the result of a sub-surface
adjustment of the density field that has dense water under regions of low sea surface height and
less dense water under regions of high sea surface height.
13. In subtropical gyres, where sea surface height is high, there is downwelling of surface water,
whereas at the equator and in the subpolar gyres where sea surface height is low there is
upwelling of subsurface water.
14. Surface nutrient concentrations and chlorophyll levels are generally higher in regions of
upwelling and lower in regions of downwelling.
15. The Gulf Stream in the N Atlantic is the most notable example of a geostrophic current and an
example of a strong Western Boundary Current in a subtropical gyre.
16. The asymmetry between fast poleward flowing Western Boundary Currents and slower
equatorward flowing currents along the eastern boundary of the subtropical gyres provides an
efficient mechanism for the poleward transport of heat.
IX. QUESTIONS/ PROBLEMS
1. If the wind direction is from east to west, what would be the compass direction of the average
Ekman transport in the northern hemisphere? What is the compass direction of the current at the
surface of the Ekman Layer (z = 0m)? Is this an easterly or westerly wind? What is the typical depth
of the Ekman Layer?
19
2. At 30°N, there is a 2m increase in sea surface height in the eastward direction that occurs over 10°
of longitude. What is the direction and speed of the resulting geostrophic surface current? Assume
uniform density.
3. Assume at locations A and B the average seawater densities above the 990 dbar isobaric surface
are 1024 and 1026 kg/m3, respectively (1 dbar= 1.01m). Calculate the difference in column height of
water above the 990 dbar surface (~1000m) between these two sites. Does this situation represent
baroclinic or barotropic conditions?
4. In which region of the ocean are the lowest sea surface dynamic height anomalies located? Why?
(see Fig. 14).
5. Plot the north-south (meridional) trend in sea surface dynamic height from 60ºS to 60ºN along
180°W in the Pacific (use Fig. 14).
 Indicate the direction of the zonal component (east or west) of the resulting geostrophic
currents at 40°N, 10°N, 30°S, and 60°S.
 Draw the trend in the depth of the isopycnal layers in the thermocline versus latitude
6. Calculate the geostrophic current speed at the surface of the Gulf Stream if the sea surface height
increases by 1.4m over a distance 115 km at a latitude of 35°N?
-How does this compare to the geostrophic velocity calculations presented for the Gulf Stream
in Fig. 22?
7. What is the compass direction of the horizontal pressure gradients at 1000m based on the
southward flowing current below the Gulf Stream (Z>1000m) seen in Fig. 22?
 Is this an example of baroclinic or barotropic conditions?
 How does the slope of the isobar (ΔP/Δz) at ~1000m compare to the slope of the isobar
represented by the sea surface in the portion of the cross section between 100 and 160 kms
shown in Fig 22?
8. How does the sea surface height of a Warm Core Ring compare to the sea surface height of its
surrounding water (see Fig. 25)? What would be the likely rotational direction (clockwise or
counterclockwise) of a cold core ring? How would the photosynthesis rate inside a cold core ring
likely compare to the photosynthesis rate outside?
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