Evaporative heat flux (Q e ) 51% of the heat input into the ocean is used for evaporation. Evaporation starts when the air over the ocean is unsaturated with moisture. Warm air can retain much more moisture than cold air. The rate of heat loss: F e is the rate of evaporation of water in kg/(m 2 s). L t is latent heat of evaporation in kJ. For pure water,. t~ water temperature ( o C). t=10 o C, L t =2472 kJ/kg. t=100 o C, L t =2274 kJ/kg. In general, F e is parameterized with bulk formulae: K e is diffusion coefficient for water vapor due to turbulent eddy transfer in the atmosphere. It is dependent on wind speed, size of ripples, and waves at sea surface, etc. de/dz is the gradient of water vapor concentration in the air above the sea surface.

In practice: V wind speed (m/s) at 10 m height above sea. e s is the saturated vapor pressure over the sea-water (unit: kilopascals, 10mb) The saturated vapor pressure over the sea water (e s ) is smaller than that over distilled water (e d ). For S=35, e s =0.98e d (t s ). V is wind speed (m/s). T s is sea surface temperature ( o C) e a is the actual vapor pressure in the air at a height of 10 m above sea level. If the atmospheric variable is relative humidity (RH), e a =RH x e d (t a ). Example: T a =15 o C, e d = 1.71 kPa = 12.8 mm Hg, RH=85%, then e a = 1.71 x 0.85 kPa= 1.45 kPa., and(very crude parameterization). This empirical formula is an approximation of eddy diffusion formula because:

In most region, e s > e a,  F e and Q e are positive,  there is a heat loss from the sea due to evaporation. In general, if t s -t a > 0.3 o C, Q e >0. In some region, t s -t a <0 o C (surface air is warmer than SST) and RH is high enough to cause condensation of water vapor from the air into the sea, which results in a gain of heat in the sea. Fogs occur in these regions due to the cooling of the atmosphere over the sea.

Annual Mean Latent Heat Flux (W/m 2 )-COADS

Mean Latent Heat Flux (W/m 2 ), January, COADS

Mean Latent Heat Flux (W/m 2 ), July, COADS

Sensible heat flux (Q h ): On average, the ocean surface is about °C warmer than the air above it (exception: upwelling regions). Direct heat transfer (transfer of sensible heat) therefore occurs usually from water to air and constitutes a heat loss. Heat transfer in that direction is achieved much more easily than in the opposite direction for two reasons: 1. It takes much less energy to heat air than water. The energy needed to increase the temperature of a layer of water 1 cm thick by 1°C is sufficient to raise the temperature of a layer of air 31 m thick by the same amount. 2. Heat input into the atmosphere from below causes instability (through a reduction of density at the ground) which results in atmospheric convection and turbulent upward transport of heat. In contrast, heat input into the ocean from above increases stability (through a reduction of density at the surface) and prevents efficient heat penetration into the deep layers.

Empirical formula of Q h Bulk formula: Wyrtki (1965):  a = 1.2 kg/m 3 (density of air). C d = 1.55 x (drag coefficient at sea surface). V surface (10 m) wind speed in m/s. C p =1008 J/(kg K). Then.

More recent bulk formula (Smith 1988): where. Surface sensible heat flux is specific humidity Surface latent heat flux K e and K h are mainly functions of stability and wind speed. K e ≈1.20K h

Annual Mean Sensible Heat Flux (W/m 2 )-COADS

Mean Sensible Heat Flux (W/m 2 ), January, COADS

Mean Sensible Heat Flux (W/m 2 ), July, COADS

Annual Mean Net Surface Heat Flux (W/m 2 )-COADS

Mean Net Surface Heat Flux in January (W/m 2 )-COADS

Mean Net Surface Heat Flux in July (W/m 2 )-COADS

Magnitudes of heat budget terms

As a consequence, there is a continuous upward heat flux in the top few millimeters of the ocean and a negative temperature gradient of a few tenths of a degree per millimeter in the surface skin of the ocean, which creates the surface skin (a few centimeters, measured by satellites) and bulk temperature (1 or 2 meters below the surface, measured by buoys or ships). Their difference is around 0.1 o C (day) to 0.3 o C (night). Although most of the solar radiation is rapidly absorbed near the oceanic surface in a layer that is centimeters to meters thick, the processes that control heat loss occur in a even thinner layer, i.e., the surface skin of the ocean.

Where does the heat go in the ocean? If the relation doesn’t hold, there should be long-term change. To achieve a steady state, we should at least average over a year. i.e., in global average, 1. Globally, conservation for steady state is : heat in = heat out (It’s trivial!) 2. Locally, ocean gains heat in low latitudes but loses heat in high latitude. To maintain a steady state, heat has to be transported from low to high latitudes to make it up. i.e.,

The horizontal heat convergence is Integrate for an x-z section from west to east coast of an ocean, we have the meridional heat transport Integrating from the northern most extent (y n ) where the transport vanishes, We can determine from the net surface heat flux.(The small sub-grid transport is negligible.)

Heat Storage For oceanic variations (e.g., seasonal cycle), the heat storage is important It can be contributed by all the surface fluxes and transport terms.

Seasonal heat storage Heat is gained in the surface layer in the summer and then is released to the atmosphere in winter, which causes the formation of the seasonal thermocline.

Seasonal thermocline:  develops in the upper zone in summer.  high stability within the seasonal thermocline  become shallower and stronger as summer progresses  weakens in fall, as daily loss exceeds the heat gain  is driven deeper in fall, as it becomes less stable and as winds increase  disappears in late winter (the cycle restarts in summer again) Example: Seasonal thermocline at Ocean Weather Station “P” (50 o N, 145 o W) March is nearly isothermal in upper 100 meters. March-August, SST increases, (absorption of solar radiation). Mixed layer  30 m. August-March, net loss of heat, seasonal thermocline eroding due to mixing.

Diurnal heat storage This heat storage generates the diurnal thermocline.

Diurnal thermocline develops during the day at depth ~10-20 meters. can mix down a few meters further mix and cool (weaken) during the night anomalies often persists for many days