Post on 25-Mar-2022
transcript
Coastal Upwellings Part 1
Alma Mater Studiorum Università di Bologna Laurea Magistrale in Fisica del Sistema Terra
Corso: Oceanografia Costiera Marco.Zavatarelli@unibo.it
Main text G.T Csanady: Circulation in the coastal ocean. Chapter 3. The behaviour of the Stratified sea. Section 3.10
K.F. Bowden Physical Oceanography Of coastal water. Chapter 5: Coastal upwellings Section 5.2
Main references
Wind blowing over the ocean generates Ekman Layers, currents and transport Wind blowing along a coast generates an onshore/offshore Ekman drift to which the coast stand against as an obstacle.
Upwellings
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Drift is offshore/onshore if the wind blows with the coast at its left/right in the northern Hemisphere Vice-versa in the southern hemisphere
Upwellings
Northern hemisphere
Southern hemisphere
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Offshore drift causes water depletion in the upper layers, a low pressure set in, forcing water from below to preserve continuity Sea level at the coast is lowered, giving rise to a slope of the sea surface (upward in the offshore direction), producing a geostrophic current parallel to the coast
Upwellings
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Upwelled water is colder than the displaced surface water and rich in nutrient salts. Therefore upwelling regions have high biological productivity
Upwellings
Sea surface temperature Chlorophyll concentration Phytoplankton biomass proxy
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Major world ocean upwelling regions associated with eastern boundary currents.
Upwellings
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ECMWF Reanalysis
Average: June, July, August
Average: December, January, February Along the Ocean eastern boundaries means wind Are seasonally directed equatorward (low- & mid- latitude). Ekman tranport off-shore --->coastal upwelling
Major world ocean upwelling regions associated with eastern boundary currents.
Upwellings
SST
Chl-a
Currents
Winds
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Major world ocean upwelling regions associated with eastern boundary currents.
Upwellings
California
Canary
Humboldt Benguela
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In the Mediterranean……….. (sicily and aegean wind driven upwelling).
Upwellings
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Time variability Upwelling events occurs on a time scale of days, since they are linked to specific wind events
Upwellings
Upwelling
Temperature time series (20 days) at different depths For an upwelling event Lasting for about 5 days
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Time variability Upwelling events occurs on a time scale of days, since they are linked to specific wind events
Upwellings
Along shore flow Cross shore flow
Density
Time variability Upwelling events occurs on a time scale of days, since they are linked to specific wind events
Upwellings
Intermittent Upwelling conditions (Wafrica)
Two layers ocean. Steady Wind Blowing parallel to y axis:
Upwellings. The basic Theory: Ekman-Sverdrup
τ w(y)
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DE
Upwellings. The basic Theory: Ekman-Sverdrup
τ w(y)
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Two layers ocean. Steady Wind Blowing parallel to y axis:
Mx = ρudz =−DE
0
∫ τ w(y)
fThe Ekman mass transport is given by: DE= Ekman depth
∂u∂x+∂v∂y+∂w∂z
= 0From the equation of continuity:
∂u∂x
= −∂w∂z
∂v ∂y = 0Assuming uniform condition parallel to the coast: then:
Upwellings. The basic Theory: Ekman-Sverdrup
The mass transport across the vertical plane at x=L, taken down to a Depth H is:
Mx` = ρuL
−H
0
∫ dz = − ρ∂w∂z0
L
∫ dx−H
0
∫ dz
Marco.Zavatarelli@unibo.it
∂u∂x
= −∂w∂z
uL = −∂w∂z0
L
∫ dx
Consider the upper layer (thickness = H). Across a Vertical plane at distance L from the coast (L sufficiently large for the direct inflence of the coast to be negligible)
0 ≤ x ≤ LHorizontal transport across the vertical plane at x=L and from surface to depth H is balanced (by continuity) by the vertical transport at depth H computed for . N.B.: is not (yet) the “Ekman Transport Mx
`
Upwellings. The basic Theory: Ekman-Sverdrup
Mx` = ρuL
−H
0
∫ dz = − ρ∂w∂z0
L
∫ dx−H
0
∫ dz
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∂w∂z−H
0
∫ dz = w0 −wHsince:
Mx` = ρwH
0
L
∫ dx
with w0 and wH being the vertical velocities at surface and at depth –H.Assuming w0=0 we have:
if Then “Ekman” transport H ≥ DE Mx
` =Mx
DE
Upwellings. The basic Theory: Ekman-Sverdrup
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DE
Mx = ρwH0
L
∫ dx
Assuming wH uniform from x=0 to x=L , we can define the Ekman transport as:
Mx = ρwHL ρwHL =τw(y)
f or also: and: wH =
τw(y)
f ρL
Assuming: f=7.29 10-5 (ϕ=30°) L=50km ρ=1025 kg m-3
Mx=2.75 103 kg m-1s-1
wH=5.4 10-5 ms-1=4.6 m day-1
τ w(y) = 0.2Nm−2
Upwelling: divergent Ekman transport
The theory summarised in the preceeding slides is a re-statement of the definition of the “Ekman pumping” defined as divergence of the Ekman transport: See equation 6.4 in Pinardi’s notes
Mx
Mx +∂Mx
∂xΔx
0∂Mx
∂xΔx
C O A S T
Upwelling in a coastal barotropic Ocean
Consider (See lessons about barotropic circulation): Semi-infinite shallow basin with x≤0bounded by a straight infinitely long coast coincident with the y axis. The basin is forced by a constant (Negative!) wind parallel to the coast: Bottom stress is also neglected The transport equations are: .
y
x
-τ(y)
τ w(x )
ρ= 0
τw(y)
ρ= −u*
2
τ b(x ) = τ b
(y) = 0∂U∂t
− fV = −c2 ∂η∂x
∂V∂t
+ fU = −u*2
Non oscillatory Solutions for horizontal transport and for sea surface elevation are: The negative value in the sea surface elevation solution implies “depressed” elevation, approaching 0 moving from the coast to offshore.
U = −u*2
f1− ex R( )
V = −u*2tex R
η = −u*2
cex Rt
R = cf=
gHf
y
x
-τ(y)
The divergence of the horizontal transport reduces to With U coincident with Qx (the Ekman volume transport) far from coast and vanishing at the coast. And this is the upwelling vertical velocity (“ekman pumping”).
∂U∂x
= w−De
w−De
=∂U∂x
= −∂∂xu*2
f1− ex R( ) = − u*
2
f∂∂x1− ex R( ) = u*
2
f1Rex R = u*
2
cex R
Upwelling in a coastal barotropic Ocean