Evaporative heat flux (Q e ) 51% of the heat input into the ocean is used for evaporation. Evaporation starts when the air over the ocean is unsaturated with moisture. Warm air can retain much more moisture than cold air. The rate of heat loss: F e is the rate of evaporation of water in kg/(m 2 s). L t is latent heat of evaporation in kJ. For pure water,. t~ water temperature ( o C). t=10 o C, L t =2472 kJ/kg. t=100 o C, L t =2274 kJ/kg. In general, F e is parameterized with bulk formulae: K e is diffusion coefficient for water vapor due to turbulent eddy transfer in the atmosphere. It is dependent on wind speed, size of ripples, and waves at sea surface, etc. de/dz is the gradient of water vapor concentration in the air above the sea surface.

In practice: V wind speed (m/s) at 10 m height above sea. e s is the saturated vapor pressure over the sea-water (unit: kilopascals, 10mb) The saturated vapor pressure over the sea water (e s ) is smaller than that over distilled water (e d ). For S=35, e s =0.98e d (t s ). V is wind speed (m/s). T s is sea surface temperature ( o C) e a is the actual vapor pressure in the air at a height of 10 m above sea level. If the atmospheric variable is relative humidity (RH), e a =RH x e d (t a ). Example: T a =15 o C, e d = 1.71 kPa = 12.8 mm Hg, RH=85%, then e a = 1.71 x 0.85 kPa= 1.45 kPa., and(very crude parameterization). This empirical formula is an approximation of eddy diffusion formula because:

1 and 1/2 layer flow Simplest case of baroclinic flow: Two layer flow of density  1 and  2. The sea surface height is  =  (x,y) (In steady state,  =0). The depth of the upper layer is at z=d(x,y)<0. The lower layer is at rest. For z > d, If we assume  The slope of the interface between the two layers (isopycnal) = times the slope of the surface (isobar). The isopycnal slope is opposite in sign to the isobaric slope. For z ≤ d,

A B C D E

Wind-driven circulation II ●Wind pattern and oceanic gyres ●Sverdrup Relation ●Vorticity Equation

Surface current measurement from ship drift Current measurements are harder to make than T&S The data are much sparse.

Surface current observations

Drifting Buoy Data Assembly Center, Miami, Florida Atlantic Oceanographic and Meteorological Laboratory, NOAA

Annual Mean Surface Current Pacific Ocean, Drifting Buoy Data Assembly Center, Miami, Florida Atlantic Oceanographic and Meteorological Laboratory, NOAA

Argo is a global array of 3,000 free-drifting profiling floats that measures the temperature and salinity of the upper 2000 m of the ocean. This allows, for the first time, continuous monitoring of the temperature, salinity, and velocity of the upper ocean, with all data being relayed and made publicly available within hours after collection.

Schematic picture of the major surface currents of the world oceans Note the anticyclonic circulation in the subtropics (the subtropical gyres)

Relation between surface winds and subtropical gyres

Surface winds and oceanic gyres: A more realistic view Note that the North Equatorial Counter Current (NECC) is against the direction of prevailing wind.

Sverdrup Relation Consider the following balance in an ocean of depth h of flat bottom (1) (2) Integrating vertically from –h to 0 for both (1) and (2), we have (neglecting bottom stress and surface height change) where (3) (4) are total zonal and meridional transport of mass sum of geostrophic and ageostropic transports

Differentiating, we have DefineWe have (3) and (4) can be written as (5) (6)

Using continuity equation And define Vertical component of the wind stress curl We have Sverdrup equation If The line provides a natural boundary that separate the circulation into “gyres”

is the total meridional mass transport Geostrophic transport Ekman transport Order of magnitude example: At 35 o N,  -4 s -1,  2  m -1 s -1, assume  x  Nm -2  y =0

Alternative derivation of Sverdrup Relation Construct vorticity equation from geostrophic balance (1) (2)  Integrating over the whole ocean depth, we have Assume  =constant

whereis the entrainment rate from the surface Ekman layer The Sverdrup transport is the total of geostrophic and Ekman transport. The indirectly driven V g may be much larger than V E. at 45 o N

then

Since, we have set x =0 at the eastern boundary, Further assume In the trade wind and equatorial zones, the 2nd derivative term dominates:

Mass Transport Since Let,,  where  is stream function. Problem: only one boundary condition can be satisfied.

1 Sverdrup (Sv) =10 6 m 3 /s