Heat and freshwater budegts, fluxes,
and transports
Reading: DPO Chapter 5
Heat budgets, fluxes, transports
Tropics
shortwave radiation
450Wm-2
150Wm-2
Polar
longwave
250Wm-2
atmosphere
shortwave radiation
150Wm-2
50Wm-2
longwave
200Wm-2
atmosphere
evaporation
evaporation
-100Wm-2 -50Wm-2
-100Wm-2 -50Wm-2
225Wm-2
ocean
Net heat flux (gain) 75Wm-2
75Wm-2
ocean
Net heat flux (loss) -75Wm-2
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= c T ρ V [J]
p
per volume h= cp T ρ [J/m3]
Heat flux Q = heat/time/area W/m2
may be radiation like Qsurface, or water transporting heat like Q1 = u1 h1
Heat transport F = Q x area [W]
ΔH/ Δt= ρ cp V ΔT/ Δt =
Qsurface A + Q1 S – Q2 S
(*)
Qsurface
Surface heat flux
top area A
side area S
u2
Q2
side area S
h1
h2
volume V
u1
Q1
divergence of ocean
heat transport
Can calculate ocean heat transports F from only surface flux data :
Q1=-50W/m2
A1
Q2=-50W/m2
Q3=+50W/m2
A2
A3
F1=-Q1A1
F2=-Q1A1
-Q2A2
F3=-Q1A1
-Q2A2
-Q3A3
Or from oceanic measurements of currents v and temperature T
everywhere… 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 transport
Surface 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
Qsfc
Ocean heat balance
= 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”)
Qsfc
Ocean heat balance
= 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.
Qsfc
Ocean heat balance
= 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.
Qsfc
Ocean heat balance
= 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 transport
Heat 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 area
e.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 ρo So
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