1. MAST602: Advection, transports, budgets Flux, transport Radiation, Advection, Diffusion Conservation of volume Continuity Conservation of salt Freshwater transport Heat budget Heat transport Reading: Knauss Chapter 4 Adapted from Dr. Lynne Talley’s SIO class notes

2. Transport processes In lieu of an animation, pretend that this is animated. (1) The surface heat balance, including radiation, makes the ocean warmer to the south. (2) The Gulf Stream flows northward, advectting warm water. (3) Eddies diffuse the heat.

3. Continuity

4. Flux and transport Transport Velocity times concentration integrated (summed) over area normal to the velocity (same as Flux normal to an area integrated over that area.) Flux of a property Velocity times concentration (same as Transport per unit area)

5. Transport definitions Volume = integral of velocity v m 3 /sec Mass = integral of density x velocity v kg/sec Heat = integral of heat x velocity c p Tv J/sec=W Salt = integral of salt x velocity Sv kg/sec Freshwater = integral of Fwater x velocity (1-S)v kg/sec Chemical tracers = integral of tracer x velocity Cv moles/sec Where “integral” is the over the area normal to the velocity Flux is just these quantities per unit area

6. Conservation of volume, salt and freshwater (1) Mass conservation:  o V o -  i V i = (R + AP) - AE  F (2) Salt conservation: V i  i S i = V o  o S o (3) F =  i V i (S i /S o - 1) or F =  o V o (1 – S o /S i ) (4) Also from (2), V i  i S i /S m = V o  o S o / S m where S m is a mean salinity, so (5) F =  i V i (1- S i /S m ) -  o V o (1 - S o / S m ) which is useful if we have to assume that  i V i ~  o V o given error in observations

7. Mediterranean and Black Seas Evaporative basin Runoff/precipitation