1. OEAS 604: Introduction to Physical Oceanography Surface heat balance and flux Chapters 2,3 – Knauss Chapter 5 – Talley et al. 1

2. Outline Review heat budget components Bulk flux calculations for sensible and latent heat flux Heat content versus heat flux Heating and cooling and the seasonal thermocline The diurnal warm layer 2

3. Heat is exchange between the ocean and the atmosphere by the following processes: Short-wave radiation (insolation) received from the sun [Q s ] Long-wave radiation (net infrared radiation) [Q b ] Latent heat flux (evaporation) [Q e ] Sensible heat flux (air-sea temperature difference) [Q h ] Change in Heat content with time Flux in Flux out Advection 3

4. Short- and long-wave radiation can be measured by radiometer (pyranometer) Need to measure both incoming and outgoing radiation: Short-wave radiation : r is reflectivity or albedo Long-wave radiation: 4 t w =water temperature; e a =humidity above water; C =cloud cover

5. Direct measurements of latent and sensible heat flux are difficult Direct measurements require “covariance” measurements of turbulent fluctuations of vertical velocity and temperature/humidity. More on turbulent fluxes and Reynolds averaging in a later class ρ a = density of air (~1.2 kg m -3 ) c a = specific heat capacity of air (1030 JKg -1 K -1 ) w'=vertical velocity fluctuations (m s -1 ) t' = temperature fluctuations (°C) L e = latent heat of vaporization (~ 2.26×10 6 Jkg -1 ) q' = specific humidity fluctuations (ratio of mass of water vapor, m_v, per unit mass of dry air m_a) 5

6. ρ a = density of air (~1.2 kg/m 3 ) c a = specific heat capacity of air (~1030 J/kg K) C S = bulk transfer coefficient (Stanton number) U 10 = wind speed @ 10 m T w = temperature of water (°C) T a = temperature of air (°C) Because of difficulty with direct measurements, sensible and latent heat fluxes are often estimated using bulk formulations 6 Sensible Heat A h – eddy conductivity (diffusivity) rate of transfer of heat between layers A h = ρ a C d W dz C d = drag coefficient at sea surface – measure of resistance (1.55 x 10 -3 ) W = wind speed (m s -1 ) dz = distance over which T measured (2 m) Stanton number = empirical coefficient derived from data dimensionless ~1 x 10 -3

7. 7 ρ a = density of air (~1.2 kg/m 3 ) L e = latent heat of vaporization (~ 2.26×10 6 J/kg) C L = bulk transfer coefficient (Dalton number) U 10 = wind speed @ 10 m (m/s) q s = specific humidity at saturation q a = specific humidity of overlying air Latent Heat F e = rate of evaporation of water kg s -1 m -2 L t = latent heat of evaporation (kJ kg -1 ), depends on temperature A e – eddy diffusivity, rate of transfer of water vapor e – water vapor concentration in air above sea surface [1.4(e a – e s ) W] Dalton number = empirical coefficient derived from data dimensionless – relates humidity difference to evaporative fluxes ~1 x 10 -3

8. Heat Content in the Ocean The change in the amount of heat due to a change in temperature ΔT is given by: Change in Heat Content Specific heat mass Change in temperature Normalize by Volume 8

9. Change in heat content: c w = 4.186 J/gC° = 4186 J/kgC° ρ = 1028 kg/m 3 10°C20°C h = 10m A 10 m thick column of water warms by 10°C in 10 days. a) What is the change in heat content? b) If no heat was transferred through the sides or the bottom, what was the surface heat flux? 9

10. Change in heat Content: c w = 4.186 J/gC° = 4186 J/kgC° ρ ~ 1028 kg/m 3 10°C20°C Dimensionally, change in heat content has units: The total heat content over the whole water column is obtained by vertically integrating: h = 10m The rate at which heat content is changing is a function of time. 10 days This has same units as heat flux 10

11. Heat Budget Change in Integrated Heat Content per time =Flux InFlux Out- 1m Q in Q out 1m 11

12. HEAT FLUX = Q is defined as the amount of heat passing through a unit area in a unit time So the amount of energy entering the ocean surface through area A (m 2 ) in time Δt is: Joules 1m Q Heat Flux 12

13. Heat Flux QTQT h ML This input of heat goes into a volume (V = A×h), where h is the depth of the surface mixed layer, changing its temperature by ΔT A 13

14. Thermocline Depth Changes in thermocline intensity and position indicate changes in the the heat content of the ocean 14

15. a)What is the total change in heat content? b)If the profiles were taken 10 days apart, what was the net surface heat flux? 15

16. a)What is the total change in heat content? a)If the profiles were taken 10 days apart, what was the net surface heat flux? b)Is there any heat flux within the water column? 16

17. a)What is the total change in heat content? b)If the profiles were taken 10 days apart, what was the net surface heat flux? 17

18. Diurnal Heating and Cooling Over the course of the day, the incoming shortwave radiation is cyclic while the heat loss is roughly steady. 18

19. Diurnal Warm Layer 19

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23. 23 Nieves et al. (2015, Science)

24. Next Class Quiz – Thursday, 10 September Stratification and Stability – Chapter 1 – Knauss – Chapter 1 – Talley et al. 24