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Thermodynamics: Mixed Layer Temperature Equation

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Thermodynamics: Mixed Layer Temperature Equation ATOC 5051 INTRODUCTION TO PHYSICAL OCEANOGRAPHY Lecture 20 Learning objectives: develop a physical understanding of ocean thermodynamic processes 1. Ocean surface heat fluxes; 2. Mixed layer temperature equation. Previous class: Ekman pumping Surface wind stress varies spatially, produces surface Ekman transport “convergence (& downwelling)” or “divergence (& upwelling)” � we = ���� = "!# $ &" $ &# − $% "!# $' "!# Negative (downward) We Vectors: interannual anomalies of surface wind stress Color: anomalous thermocline depth (D20) Mean D20 (m) & interannual SSTA Mean upwelling zone Question: In the white boxed area, do you expect (a) Ekman convergence or divergence (negative or positive) We? (b) Deeper or shallower thermocline? (c) Warmer or colder SST? Indian Ocean mean upwelling zone: driven by monsoon wind stress curl – Ekman divergence & positive Ekman pumping velocity � Positive we = ���� = "!# $ &" $ &# Sea surface temperature − $% "!# $' "!# (SST): Why not cold? 1. Ocean surface heat fluxes; Oceanic surface mixed layer: is subject to wind & buoyancy (heat and salinity) flux forcing: Properties (e.g., T, S,..) are pretty well mixed: Tm and Sm are often used to represent sea surface temperature (SST) and sea surface salinity (SSS). Winds: momentum flux, drive oceanic circulation; Heat fluxes: directly affect SST; Salinity flux (Evaporation minus precipitation) - SSS Importance for understanding SST change: Climate: Drives atmospheric circulation; air/sea interaction, Hadley and Walker circulation, atmospheric waves; global climate; SST & SSS (sea surface salinity) changes: affect deepwater – thermohaline circulation – climate. Marine biological activities, marine chemistry (CO2). Ocean: important Component of Earth’s Climate System & Water cycle Observations TRMM (satellite observed) global SST Processes that cause SST change? Meridional distribution of net surface heat flux Processes that determine the temperature change of a water parcel (Lagrangian) in the surface mixed layer are: (1). Net surface radiative flux Solar shortwave Outgoing longwave radiation radiation Units: J/s/m2=Watt/m2 (2) Surface turbulent sensible heat flux (3) Surface turbulent latent heat flux (4) Heat transfer directly by precipitation (usually small for long time scale) (5) Oceanic processes: upwelling & entrainment cooling – entraining waters from subsurface – �!"# 2. Mixed layer temperature equation The first law of thermodynamics says: heat absorbed by a system is used to increase its internal energy and do external work. Example: air Sliding door heating For oceanic mixed layer, energy absorbed is used mainly to increase its internal energy (temperature). Apply the first law of thermodynamics to the mixed layer with depth hm for a unit area. z y x For a water column of with an area of internal energy increase is: density (J/s) where is the specific heat of water For a unit area, it is: (J/s/m2 = W/m2 ) This energy increase is caused by net heat fluxes from both surface and bottom of the mixed layer. Here, we assume the shortwave radiation is completely absorbed within the surface mixed layer (without shortwave penetration into the deeper ocean). Because Parameterization of vertical mixing This is the mixed layer temperature equation; there should also be horizontal mixing but here it is neglected here. In a surface mixed layer model, the effects of entrainment and upwelling are difficult to separate. The equation is often written as: ! ∂Tm Qnet (Tm −Td ) = −Vm •∇Tm − w ∂t ρwcpwhm hm �ℎ Where Q = Q +Q +Q +Q � = ( ! + � ) ∇ℎ + � ) net nr s l pr & �� ! ! "#! w is the upwelling velocity (Ekman pumping velocity). −hm This equation is used to calculate mixed layer heat budget in many studies. In real ocean, properties within the surface mixed is not fully mixed and some vertical variations remain, even though small. A more accurate Tm equation that considers light penetration and turbulent transport is: ∂T Q ! (T −T ) 0 ! m = net −V •∇T − w m d − ∇• (V 'T ')dz a a ∫ −h(x,y,t) ∂t ρwcpwhm hm Q Q Q Q Q Q , net = nr + s + l + pr − −hm Q −hm is shortwave radiation that is left at the bottom of the mixed layer and the last term is: turbulent heat transport convergence/divergence. Below, we discuss each term in detail. a) Top of atmosphere atm radiative transfer Oceanic surface Q: Positive into the ocean b) Potential temperature Top of PBL SST Bulk formulae: See class notes for detailed values of Llv an Cpd c) d) T −T It includes the effects of both e) −w m d hm upwelling & entrainment cooling. Entrainment: turbulent mixing effect that entrains water from the thermocline into the surface mixed layer. Upwelling: vertical advection due to surface mass divergence; it involves isotherms tilting upward TAO data in the eastern Pacific: Color: SST; black arrow: winds;White arrow: Ekman transport Equatorial upwelling: meridional view Zonal view Question: The ocean surface mixed layer is forced by a counterclockwise wind stress, 40N 1) Ekman transport directions; 2) Geostrophic current directions; 3) Do you expect colder or warmer SST at center of wind region?.
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