Chapter 7: Thermodynamics 7.1 Sea surface heat budget In Chapter 5, we have introduced the oceanic planetary boundary layer-the Ekman layer. The observed T and S in this layer are almost uniform vertically, thus it is also referred to as the surface mixed layer. This layer is in direct contact with the atmosphere and thus is subject to forcings due to windstress (which enters the ocean as momentum flux), heat flux, and salinity flux. Heat and salinity fluxes combine form buoyancy flux. Below, we will discuss the heat fluxes that force the ocean, and examine the processes that can cause mixed layer temperature changes by introducing the mixed layer temperature equation. Why is the surface heat budget important? Heating and cooling at the ocean surface determine the sea surface temperature (SST), which is a major determinant of the static stability of both the lower atmosphere and the upper ocean. For example, the wintertime cold SST in the North Atlantic and in the GIN Seas (Greenland, Ice land, and Norwegian Seas) increase density, destabilizing the stratification of the ocean, resulting in deep water formation and therefore affecting the global thermohaline circulation. On the other hand, in the equatorial Western Pacific and eastern Indian Ocean warm pool region, SST exceeds 29◦C and thus destabilize the atmosphere (because the atmosphere is heated from below), causing convection. Convection in the warm pool region is an important branch for the Hadley and Walker circulation and therefore is important for the global climate. The surface heat fluxes at the air/sea interface are central to the interaction and coupling between the atmosphere and ocean. Before we discuss the processes that determine the SST variation, let’s first look at the annual mean SST distribution in the world oceans (Figure 1). Why SST is generally warm in the tropics and cold poleward? Solar shortwave flux is high in the tropics and low near the poles. There is net heat flux surplus at lower latitudes and deficit at high latitudes (Figure 2). Why the SST is cold in the eastern Pacific (cold tongue)? Upwelling - Ocean processes. Therefore, SST distribution is determined from both surface heat flux forcing and from the oceanic processes. For simplicity, we will examine the temperature equation for the surface mixed layer, and assume solar shortwave radiation is completely absorbed by the surface mixed layer. In fact, this is a mixed layer model for temperature. [RECALL that some light can penetrate down to the deeper layers, depending on the turbidity of the water.] The processes that determine the temperature change of a (Lagrangian) water parcel in the surface mixed layer are: • net surface radiation flux Qnr; • the surface turbulent sensible heat flux Qs; • the surface turbulent latent heat flux Ql; i Figure 1: Annual mean SST in the Pacific, Atlantic, and Indian Oceans. Figure 2: Latitudinal distribution of net surface radiative fluxes. ii • heat transfer by precipitation (usually small) Qpr; • entrainment of the colder, subsurface water into the surface layer Qent. The first law of thermodynamics tells us that heat absorbed by a system is used to increase the internal energy of the system and used to do work to its environment. An example is a metal box that is full of air with a sliding door on one side. Initially air pressure on both sides of the door are the same, which equals the atmospheric pressure. When the box is heated up from below, air temperature inside the box will increase because its internal energy increases and molecules motion increases. This will increase the air pressure on the inner side of the door and thus pushes it to move outside. If the sliding door is fixed, all the heat will be used to increase the internal energy of the air inside the box. For the oceanic mixed layer, energy absorbed by the mixed layer per unit area is used to increase the internal energy (temperature) of the water column. Now, let’s apply the first law of thermodynamics to the oceanic mixed layer with depth hm for a unit area (Figure 3). Figure 3: Schematic diagram showing the oceanic mixed layer and heat fluxes that act on the ocean. For a water column of the mixed layer with an area of ∆x × ∆y, internal energy increase is: dTm dTm ρwcpw dt hm∆x∆y. For a unit area, it is: ρwcpw dt hm, ◦ where ρw is water density, cpw is specific heat of water (J/kg/ C). This energy increase will be caused by the net heat flux due to both heating from the surface and cooling from the bottom of the mixed layer. That is: dT ρ c m h = Q + Q + Q + Q + Q , (1) w pw dt m nr s l pr ent − − where Qent = ρwcpwwent(Tm Td) and Td is the temperature of the thermocline. dTm ∂Tm · ∇ Tm−Td Rewriting the equation by expanding dt = ∂t + V Tm + w hm we have: iii ∂Tm Qnr + Qs + Ql + Qpr Tm − Td Tm − Td = − V · ∇Tm − w H(w) − went = Qnet. (2) ∂t ρwcpwhm hm hm Next, we’ll discuss each term in detail and Qnet is the net surface heat flux. (a) Qnr The net surface radiation flux, Qnr, is the sum of the net solar and long wave fluxes at the surface. − sw lw − 4 Qnr = (1 α0)Q0 + Q0 ǫ0σT0 . (3) Figure 4: Schematic diagram showing radiative fluxes. In the above, sw Q0 - downward solar radiation flux at the surface; α0 - is the shortwave surface albedo (reflectivity); lw Q0 - is the downward infrared radiation flux at the surface. 4 -ǫ0σT0 - outgoing longwave radiation of the ocean. This is from the Stefan-Boltzman’s law of radiation. To a fairly high accuracy, a black body (100% emmisivity) with temperature T emits radiative flux as E = σT 4 where σ =5.67 × 108wm−2K−4. T0 is the skin temperature at the very surface; but if we consider the mixed layer is well mixed, T0 represents the mixed layer temperature Tm. ǫ0 - surface longwave emissivity (0.97 for the ocean). The ocean is close to a black body. sw lw The surface downward short wave and long wave fluxes Q0 and Q0 depend on the amount of radiation incident at the top of the atmosphere and on the atmospheric conditions: Temperature profile, gaseous constituents, aerosols, clouds. Radiative transfer processes and models are covered by the radiation class. So we will not get deep into this part here. iv (b) Qs and Ql The surface turbulent sensible and latent heat fluxes. Turbulent is a small-scale irregular flow that often occurs in atmospheric and oceanic planetary boundary layers (PBL). It is characterized by eddy motion. It has a wide range of spectra in spatial and temporal scales. Unlike the large scale deterministic flow whose horizontal scale is much larger than its vertical scale, turbulent flow has comparable horizontal and vertical scales and thus is bounded by the planetary boundary depth 1km. Its smallest scale is 10−3m. These eddies produce efficient mixing in the PBL, bring heat from the oceanic surface to the top of the PBL and bring the cooler air from the PBL top to the surface. Since it is not possible to predict the behavior of the wide range of eddies using analytical or numerical methods, we usually determine the turbulent motion using statistical approximations. To do so we separate the total flow into mean (deterministic) and the turbulent component, and obtain empirical formulae. That is, uT = u + u′ where uT , u, and u′ represent total, mean, and turbulent flow. − ′ ′ Qs = ρacpd(w θ )0, (4a) − ′ ′ Ql = ρaLlv(w qv)0, (4b) ′ where w′ - turbulent vertical velocity; θ is the turbulent potential temperature, overline “-” is time mean, qv is air specific humidity, and Llv is the latent heat of evaporation. Potential temperature of a water or air parcel is defined to be the temperature of the parcel when it is adiabatically bring to the sea level pressure. It is used here rather than in situ temperature for convenience (so that we don’t have to worry about the temperature change due to pressure). Figure 5: Schematic diagram showing eddy sensible and latent heat transport. In Figure 5, SST is higher than air temperature and thus it warms up the air right above the sea surface. Eddies bring the warm air from the surface upward and bring the colder air down to the sea surface, producing the mixing. As a result, the ocean loose heat to the atmosphere. The latent heat flux in fact is turbulent moisture transport. Why moisture v transport is related to heat flux? Because evaporation, which produces the moist air, needs to cost the internal energy of the ocean to overcome the molecular attractions of sea water to become water vapor. As a result, SST decreases and the ocean looses heat to the atmosphere. ′ ′ ′ ′ The covariances (w θ )0 and (w qv)0 can be determined from high-frequency measure- ments of w, θ, and specific humidity qv. However, such measurements are rarely available. Therefore, we usually use bulk aerodynamic formulae to estimate them. The bulk formu- lae are based on the premise that the near-surface turbulence arises from the mean wind shear near the surface, and that the turbulent fluxes of heat and moisture are proportional to their gradients just above the ocean surface. According to these assumptions, we obtain the bulk formulae: − − Qs = ρacpdCDH (Va Vo)(Ta To), (5a) − − Ql = ρaLlvCDE(Va Vo)(qva qvo), (5b) ◦ where cpd = 1004J/kg/ C-specific heat of air, CDE is close to CDH under ordinary con- ditions.