Thermobaric Effect: Potential Temperature as a Measure of Ocean Stability

2. Thermobaric Effect

4. Potential temperature In situ temperature is not a conservative property in the ocean.   Changes in pressure do work on a fluid parcel and changes its internal energy (or temperature)        compression => warming        expansion => cooling The change of temperature due to pressure work can be accounted for Potential Temperature: The temperature a parcel would have if moved adiabatically (i.e., without exchange of heat with surroundings) to a reference pressure. • If a water-parcel of properties (So, to, po) is moved adiabatically (also without change of salinity) to reference pressure pr, its temperature will be ΓAdiabatic lapse rate:  vertical temperature gradient for fluid with constant θ When pr=0, θ=θ(So,to,po,0)=θ(So,to,po) is potential temperature. • At the surface, θ=T. Below surface, θ<T. Potential density:σθ=ρS,θ,0 – 1000 where T is absolute temperature (oK) αT is thermal expansion coefficient

6. A proximate formula: t in oC, S in psu, p in “dynamic km” For 30≤S≤40, -2≤T≤30, p≤ 6km, θ-T good to about 6% (except for some shallow values with tiny θ-T) In general, difference between θ and T is small θ≈T-0.5oC for 5km

7. An example of vertical profiles of temperature, salinity and density

8. θ and σθ in deep ocean Note that temperature increases in very deep ocean due to high compressibility

9. Definitions in-situ density anomaly: σs,t,p = ρ – 1000 kg/m3 Atmospheric-pressure density anomaly : σt = σs,t,0= ρs,t,0 – 1000 kg/m3 Specific volume anomaly: δ= αs, t, p – α35, 0, p δ = δs + δt + δs,t + δs,p + δt,p + δs,t,p Thermosteric anomaly: Δs,t = δs + δt + δs, t Potential Temperature: Potential density:σθ=ρs,θ,0 – 1000

10. Static stability Simplest consideration: light on top of heavy Stable: Moving a fluid parcel (ρ, S, T, p) from depth -z, downward adiabatically (with no heat exchange with its surroundings) and without salt exchange to depth -(z+δz), its property is ( , S, T+δT, p+δp) and the Unstable: environment (ρ2, S2, T2, p+δp). Neutral: (This criteria is not accurate, effects of compressibility (p, T) is not counted).

11. Buoyant force (Archimedes’ principle): where (δV, parcel’s volume) Acceleration: For the parcel: is the hydrostatic equation (where or , C is the speed of sound)

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

13. 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.

14. A Potential Problem: E is the difference of two large numbers and hard to estimate accurately this way. g/C2 ≈ 400 x 10-8 m-1 Typical values of E in open ocean: Upper 1000 m, E~ 100 – 1000x10-8 m-1 Below 1000 m, E~ 100x10-8 m-1 Deep trench, E~ 1x10-8 m-1

15. Simplification of the stability expression Since For environment, For the parcel, Since and , Г adiabatic lapse rate, Then m-1

16. The effect of the pressure on the stability, which is a large number, is canceled out. (the vertical gradient of in situ density is not an efficient measure of stability). • In deep trench ∂S/∂z ~ 0, then E→0 means ∂T/∂z~ -Г (The in situ temperature change with depth is close to adiabatic rate due to change of pressure). At 5000 m, Г~ 0.14oC/1000m At 9000 m, Г~ 0.19oC/1000m • At neutral condition, ∂T/∂z = -Г < 0. (in situ temperature increases with depth).

17. θ and σθ in deep ocean Note that temperature increases in very deep ocean due to high compressibility

18. Note: σt = σ(S, T) Similarly, , , ,