1. OCEAN RESPONSE TO AIR-SEA FLUXES Oceanic and atmospheric mixed
The main mechanism: mechanical and convective mixing in the surface layer. Both work to provide a deepening of the upper ocean mixed layer.
Temporal seasonal evolution
of the surface mixed layer
Oceanic and atmospheric mixed
layers in contact

2. Simple mixed layer model: Vertical heat exchange equation:
2 non-dimensional
parameters: T z h H Ts TH
Integration within surface mixed layer gives:
Surface
net flux
Vertical heat exchange equation:
Integration within surface
mixed layer gives:

3. Integration from h to H:
This integral can be written as
where :

4. Ocean circulation characteristics from sea-air interaction parameters
Meridional Transport of Heat (MHT): OCEAN VIEW:
The total MHT can be represented as the sum of the advective and diffusive transports of heat:
Advective MHT can be decomposed into an overturning component which corresponds to the transport of the zonally averaged circulation, and a gyre component which corresponds to the transport by horizontal gyres:
where  is the zonal averaging operator and prime stands for the variations of temperature T and meridional component of velocity v around the zonal mean.

5. Qnet = SW-LW-Qh-Qe If we know surface net heat flux, can
we say something about the MHT? Q2 Q1 M0 S N M1 M2
M1=M0+Q1
M2=M1+Q2=
M0+Q1+Q2
Estimates of MHT can be obtained from the integration of
Qnet = SW-LW-Qh-Qe
over the ocean surface north of the latitude considered:
where Mo is a boundary condition at the north which should be taken from alternative source (observations) or set to zero.

6. Being computed from a balanced surface flux, global MHT should converge to zero at the north and at the south
Meridional heat transport shows basic features of the ocean general circulation, in particular it marks a specific role of the Atlantic Ocean, which indicates the northward MHT at all latitudes in both Hemispheres.

7. Ocean heat fluxes are influenced by the uncertainties (observational, sampling, etc.), which impact on the zonal heat balance and propagate quickly to MHT through the integration: MHT, being physically a very important parameter, remains not very effective measure of the reliability of surface flux fields from a methodological viewpoint. Uncertainty of 10 W/m2 for the Atlantic Ocean results in 0.5 PW error in MHT at 20S
Closure of surface heat balance is not achieved in most climatologies of sea-air fluxes:
SOC (Josey at al. 1999):
-30 W/m2, negative MHT at
12N in the Atlantic
UWM (Da Silva et al. 1994) :
- 30 W/m2

8. Water mass formation characteristics from surface fluxes
Ocean waters are characterized by temperature and salinity. Equation of state links density with these characteristics.
Highest
density
Smallest
density
Surface density in the North Atlantic

9. dzdS Volumetric T,S - diagram T,S – diagram is the ocean analog of
Typical density of ocean waters are from 1023 to 1028 kg/m3. For practical reasons ocean densities are estimated in relative units:
=-1000
Surface water
dzdS
Bottom
water
T,S – diagram is the
ocean analog of
P,T - diagram
Volumetric
T,S - diagram

10. To change the ocean water density we can:
provide heating/cooling by surface net heat flux (W/m2)
provide precipitation/evaporation (m3/sec)
But how to know how many kilograms we added (or extracted) to (from) the ocean by the joint application of these two processes?
The density flux (in fact a virtual mass flux since it has the unit of kgm2s-1) at the sea surface has been derived as:
This flux is applied as a surface boundary condition to ocean models
where CP is specific heat of sea water at constant pressure, 0 is a reference density of sea water, s is salinity in portions of unity,  and  are the thermal expansion and haline contraction coefficients:
 = /T,  = /S

11. North Atlantic surface density flux in kg/m2s, computed from the net flux and evaporation minus precipitation

12. Water mass transformation by surface density flux
Integration in space and time of the density flux gives the transformation rate of waters at given density, F(ρ), which represents the time average over a period T (generally one year) of the density change of a unit water volume of density ρ which results from the action of the atmospheric forcing:
where the  function samples the density flux f over the area where waters of density  are outcroping within the integration area . This quantity has a unit of kgs-1 and can be scaled with the unit density to be expressed in m3s-1 or Sv. In this form the transformation rate shows the volume of water of density 0 which is transformed, during a given period, into higher densities (F(0) > 0) or lower densities (F(0) < 0).

13. Трансфрмация вод на поверхности
Surface tropical
waters
STMW
LSW

14. Thermal versus haline contributions
ATL6
ATL1

15. Water mass formation:
The formation rate was defined by the differentiation of the transformation rate, as the gradient of F(T,S) orthogonal to isopycnals:
M(T,S) = -[F(T,S)  (T,S)] / ,  = (S0S, T0T).
Strong formation of STMW.
Strong formation of LSW.

16. Overturning induced by the water mass transformation
ATL1
ATL6

17. The role of surface fluxes in forming ocean circulation
Incorrect position
Correct position
Importance of the correct location of the Gulf stream in relation to
air-sea fluxes