Heat and freshwater budegts, fluxes, and transports

Reading: DPO Chapter 5

Heat budgets, fluxes, transports

atmosphere

ocean

450Wm-2

150Wm-2

225Wm-2

250Wm-2

-50Wm-2-100Wm-2

evaporation

shortwave radiation longwave

Net heat flux (gain) 75Wm-2

Tropics

atmosphere

ocean

150Wm-2

50Wm-2

75Wm-2

200Wm-2

-50Wm-2-100Wm-2

evaporation

shortwave radiation longwave

Net heat flux (loss) -75Wm-2

Polar

This imbalance needs to be compensated by transporting heat poleward in atmosphere and ocean.

Total (atmosphere + ocean) ≈ 6 PW (1 PW = 1015 J/s) (can be determined just from satellite radiation observations).

Atmospheric measurements allow estimate of atmospheric part: 4PW, so total ocean “meridional” heat transport 2 PW (no ocean observations needed for this….)

Heat flux at edge of atmosphere versus latitude

Total (atmosphere+ocean) global heat transport versus latitude

Total global atmospheric heat transport versus latitude

Simple heat budget example Heat content H= cp T ρ V [J] per volume h= cp T ρ [J/m3]Heat flux Q = heat/time/area W/m2may be radiation like Qsurface, or water transporting heat like Q1 = u1 h1 Heat transport F = Q x area [W]

top area A

side area S

side area S volume V

Qsurface

u1

h1

Q1

u2

h2

Q2

ΔH/ Δt= ρ cp V ΔT/ Δt = Qsurface A + Q1 S – Q2 S (*)

Surface heat flux divergence of ocean heat transport

Q1=-50W/m2 Q2=-50W/m2 Q3=+50W/m2

A1 A2 A3

F1=-Q1A1 F2=-Q1A1

-Q2A2

F3=-Q1A1

-Q2A2

-Q3A3

Can calculate ocean heat transports F from only surface flux data :

Or from oceanic measurements of currents v and temperature Teverywhere… over a section across the ocean.

Heat transport = H = cpTviAi = cpTvdA J/sec=W

CARE is necessary to balance the MASS first. If more water flows INTO a volume than OUT, then the heat/temperature equation like (*) earlier has a term like(uout-uin) T which can give an arbitrary (possibly HUGE) error depending on choice of temperature scale (e.g. Celsius vs. Kelvin)

Heat and heat transportSurface heat flux (W/m2) into ocean

DPO Figure 5.16

Ocean heat balance, including radiation

Qsfc = Qs + Qb + Qh + Qe

Total surface heat flux = Shortwave + Longwave + Latent + Sensible

Ocean heat balance, including radiation

Qsfc = Qs + Qb + Qe + Qh

Total surface heat flux = Shortwave + Longwave + Latent + Sensible

This diagram shows a net global balance, not a local balance

Ocean heat balanceQsfc = Qs + Qb + Qe + Qh in W/m2

Shortwave Qs: incoming solar radiation - always warms. Some solar

radiation is reflected. The total amount that reaches the ocean surface is Qs = (1-)Qincoming where is the albedo (fraction that is reflected).

Albedo is low for water, high for ice and snow.

C monthly mean fractional cloud cover, θN is the noon solar elevation.

(So-called “bulk formulas”)

Ocean heat balanceQsfc = Qs + Qb + Qe + Qh in W/m2

Longwave Qb: outgoing (“back”) infrared thermal radiation (the ocean

acts nearly like a black body) - always cools the ocean

C monthly mean fractional cloud cover, T is air and water temperature,e water vapour pressure, k an empirical cloud cover coefficient,ε emittance of the sea surface, σSb Stefan-Boltzmann constant.

Ocean heat balanceQsfc = Qs + Qb + Qe + Qh in W/m2

Latent Qe: heat loss due to evaporation - always cools. It takes energy to

evaporate water. This energy comes from the surface water itself. (Same as principal of sprinkling yourself with water on a hot day - evaporation of the water removes heat from your skin)

Ce transfer coefficient for latent heat, u wind speed at 10m height,qs is 98% of saturated specific humidity, qa is actual specific humidity,L is latent heat of evaporation.

Ocean heat balanceQsfc = Qs + Qb + Qe + Qh in W/m2

Sensible Qh : heat exchange due to difference in temperature between air

and water. Can heat or cool. Usually small except in major winter storms.

Ch transfer coefficient for sensible heat, u wind speed at 10m height,T is surface water and air temperature, γ is adiabatic lapse rate of air and z the height where Ta is measured.

Annual average heat flux components (W/m2)

DPO Figure 5.15

Heat flux components summed for latitude bands (W/m2)

DPO Figure 5.17

Heat transportHeat input per latitude band (PW)

1 PW = 1 “Petawatt” = 1015 W

Heat transport (PW)

(meridional integral of the above)

DPO Figure 5.24

Heat transport

• Meridional heat transport across each latitude in PW• Calculate either from atmosphere (net heating/cooling) and

diagnose for ocean• OR from velocity and temperature observations in the ocean. Must

have net mass balance to compute this.

DPO Figure 5.23

Transport definitions

• Transport: add up (integrate) velocity time property over the area they flow through (or any area - look at velocity “normal” to that area)

• Volume transport = integral of velocity v m3/sec• Mass transport = integral of density x velocity v kg/sec

• Heat transport = integral of heat x velocity cpTv J/sec=W

• Salt transport = integral of salt x velocity Sv kg/sec• Freshwater transport = integral of Fwater x velocity (1-S)v

kg/sec• Chemical tracers = integral of tracer concentration (which is in

mol/kg) x velocity Cv moles/sec

• Flux is just these quantities per unit area

Transport definitions

• Volume transport = V = viAi = vdA m3/sec

• Mass transport = M = viAi = vdA kg/sec

• Heat transport = H = cpTviAi = cpTvdA J/sec=W

• Salt transport = S = SviAi = SvdA kg/sec

• Freshwater transport = F = (1-S) viAi = (1 - S)vdA kg/sec

• Chemical tracers = C = CviAi = CvdA moles/sec

• Flux is just these quantities per unit areae.g. volume flux is V/A, mass flux is M/A,

heat flux is H/A, salt flux is S/A, freshwater flux is F/A, C /A

Conservation of volume, salt

(1) volume conservation:

Vo - Vi = (R + AP) – AE F (total of freshwater inputs over basin)

(2) Salt conservation: Vi ρi Si = Vo ρoSo

or approximately Vi Si = Vo So

Combining these equations gives

Vi = F So / ΔS Vo = F Si / ΔS

or approximately (Vi ≈ Vo V , Si ≈ So S)

V = F S / ΔS

“Knudsen relations”.

Useful for calculating transport/influx/outflux from F and S, or for estimating F from flow measurements….

Note what happens when ΔS becomes very small (“overmixed” case….)

Mediterranean and Black Seas

Evaporative basin Runoff/precipitation

DPO Figure 5.3

Precipitation minus evaporation (cm/yr): what freshwater transports within the ocean are required to maintain a steady state salinity distribution in the ocean given this P-E?

NCEP climatology• Consider N. Pacific box, Bering Strait to north, complete east-west

crossing between net P and net E areas, for example• Total freshwater transport by ocean out of this box must equal the P-E• FW transport across the long section must equal take up all the rest of the

net P-E in the area to the north, after Bering Strait is subtracted

Global ocean freshwater transport

Wijffels (2001)

• Continuous curves show different estimates of ocean FW transport based on observed P-E+R (atmosphere and rivers)

• Diamonds with error bars are estimates of FW transports based on ocean velocities and salinities

Freshwater transport divergences from velocity&salinity observations.Blue/positive means is net precipitation, red/negative net evaporation.Arrows/color show circulation and relative salinity being transported