For environment: Then For small δz (i.e., (δz)2 and higher terms are negligible),

Therefore, in a neutral ocean, Static Stability: Stable: E>0 Unstable: E<0 Neutral: E=0 ( ) , Therefore, in a neutral ocean, . Since E > 0 means, Note both values are negative A stable layer should have vertical density lapse rate larger then the adiabatic gradient.

Г terms: 2 x 10-8 m-1 (near surface: 4 x 10-8 m-1) (∂δS,p/∂S) is much smaller than (∂ΔS,T/∂S) (10% at 5000 m and 15% at 10000 m, opposite signs) (∂δT,p/∂T) has the same sign as (∂ΔS,T/∂T), relatively small about 2000m, comparable below). First approximation, , or (reliable if the calculated E > 50 x 10-8 m-1) A better approximation, (σθ ,takes into account the adiabatic change of T with pressure) When the depth is far from the surface, σ4=σS,θ,4(p=40,000kPa=4000dbar) may be used to replace σθ.

In practice, E≈ -25 ~ -50 x 10-8 m-1 in upper 50 m. a) mixed layer is slightly unstable subtropics, increase of salinity due to evaporation, vertical overturning occurs when E ~ -16 to -64x10-8 m-1, because of the effects of heat conduction, friction, eddy diffusion, etc. b) observational errors Error of σt ~ 5 x 10-3 The error of σt at two depths Δσt ~ 10-2 for Δz=z1-z2=20 m.

σθ and σ4

Cabbeling

(Brunt-Väisälä frequency, N) Buoyancy frequency (Brunt-Väisälä frequency, N) We have known that , (depending on δz, restoring force) Since δz is the vertical displacement of the parcel, then or Its solution has the form where (radians/s)2 N is the maximum frequency of internal waves in water of stability E. Period: E=1000 x 10-8 m-1, τ=10 min E=100 x 10-8 m-1, τ=33 min E=1 x 10-8 m-1, τ≈6hr

Buoyancy Frequency and ocean stratification

Buoyancy frequency, an example

Typical Distributions of Water Characteristics in the Oceans

Ocean Mean State Sea Surface Properties Vertical Structure Thermocline

Global Statistics • The mean temperature of the world ocean is 3.5oC and the mean salinity is 34.7. (Even at the equator the average temperature is as low as 4.9°C). • 75% of the total volume of the ocean water has properties within the range from 0o to 6oC in temperature and 34 to 35 in salinity. • 50% of the total volume of the oceans has properties between 1.3oC and 3.8oC and between 34.6 and 34.8. • Both temperature and salinity are quite uniformly distributed below 1000 m depth. Volumetric temperature-salinity diagram of the world ocean. 75% of the ocean's water have a temperature and salinity within the green region, 99% have a temperature and salinity within the region colored in cyan. The warm water outside the 75% region is confined to the upper 1000 m of the ocean. From M. Tomczak, 1996: Introduction to Physical Oceanography (http://gaea.es.flinders.edu.au/~mattom/IntroOc)

Mean Sea Surface Temperature (SST) • roughly zonal (east-west) isotherm • meridional gradient follows solar radiation • diverted north-south near the eastern coast (cold tongues) • warm pool: SST > 28oC • sea ice at high latitudes (near -2oC) CPC Analysis, January 1982-December 2001

Mean Sea Surface Salinity (SSS) NODC WOA98, levitus et al • SSS distribution is mostly zonal (range: 33-37) • Minimum north of the equator (ITCZ) • Maximum in subtropics (trade winds) • Lower around coast (river) and polar region (melting ice) • Mediterranean, 39 and Red Sea, 41 (large evaporation ) Mean Sea Surface Salinity (SSS)