heat and freshwater budegts, fluxes, and transports
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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
h2Q2
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
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