Heat and freshwater budegts, fluxes, and transports Reading: DPO Chapter 5

Heat budgets, fluxes, transports atmosphere ocean 450Wm Wm Wm Wm Wm Wm -2 evaporation shortwave radiation longwave Net heat flux (gain) 75Wm -2 Tropics atmosphere ocean 150Wm -2 50Wm -2 75Wm Wm Wm Wm -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 = 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 p T ρ V [J] per volume h= c p T ρ [J/m 3 ] Heat flux Q = heat/time/area W/m2 may be radiation like Q surface, or water transporting heat like Q 1 = u 1 h 1 Heat transport F = Q x area [W] top area A side area S volume V Q surface u1u1 h1h1 Q1Q1 u2u2 h2h2 Q2Q2 ΔH/ Δt= ρ c p V ΔT/ Δt = Q surface A + Q 1 S – Q 2 S (*) Surface heat flux divergence of ocean heat transport

Q 1 =-50W/m 2 Q 2 =-50W/m 2 Q 3 =+50W/m 2 A1A1 A2A2 A3A3 F 1 =-Q 1 A 1 F 2 =-Q 1 A 1 -Q 2 A 2 F 3 =-Q 1 A 1 -Q 2 A 2 -Q 3 A 3 Can calculate ocean heat transports F from only surface flux data :

Or from oceanic measurements of currents v and temperature T everywhere… over a section across the ocean. Heat transport = H =   c p T v i A i =  c p T vdA 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 (u out -u in ) 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/m 2 ) into ocean DPO Figure 5.16

Ocean heat balance, including radiation Q sfc = Q s + Q b + Q h + Q e Total surface heat flux = Shortwave + Longwave + Latent + Sensible

Ocean heat balance, including radiation Q sfc = Q s + Q b + Q e + Q h Total surface heat flux = Shortwave + Longwave + Latent + Sensible This diagram shows a net global balance, not a local balance

Ocean heat balance Q sfc = Q s + Q b + Q e + Q h in W/m 2 Shortwave Q s : incoming solar radiation - always warms. Some solar radiation is reflected. The total amount that reaches the ocean surface is Q s = (1-  )Q incoming where  is the albedo (fraction that is reflected). Albedo is low for water, high for ice and snow. C monthly mean fractional cloud cover, θ N is the noon solar elevation. (So-called “bulk formulas”)

Ocean heat balance Q sfc = Q s + Q b + Q e + Q h in W/m 2 Longwave Q b : 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, σ Sb Stefan-Boltzmann constant.

Ocean heat balance Q sfc = Q s + Q b + Q e + Q h in W/m 2 Latent Q e : 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) C e transfer coefficient for latent heat, u wind speed at 10m height, q s is 98% of saturated specific humidity, q a is actual specific humidity, L is latent heat of evaporation.

Ocean heat balance Q sfc = Q s + Q b + Q e + Q h in W/m 2 Sensible Q h : heat exchange due to difference in temperature between air and water. Can heat or cool. Usually small except in major winter storms. C h 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 T a is measured.

Annual average heat flux components (W/m 2 ) DPO Figure 5.15

Heat flux components summed for latitude bands (W/m 2 ) DPO Figure 5.17

Heat transport Heat input per latitude band (PW) 1 PW = 1 “Petawatt” = 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 m 3 /sec Mass transport = integral of density x velocity v kg/sec Heat transport = integral of heat x velocity c p Tv 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 =  v i A i =  vdA m 3 /sec Mass transport = M =   v i A i =   vdA kg/sec Heat transport = H =   c p T v i A i =  c p T vdA J/sec=W Salt transport = S =   S v i A i =  S vdA kg/sec Freshwater transport = F =   (1- S) v i A i =  (1 - S) vdA kg/sec Chemical tracers = C =   C v i A i =  C vdA 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:  V o - V i = (R + AP) – AE  F (total of freshwater inputs over basin) (2) Salt conservation: V i ρ i S i = V o ρ o  S o or approximately V i S i = V o  S o

Combining these equations gives V i = F S o / ΔS V o = F S i / ΔS or approximately (V i ≈ V o  V, S i ≈ S o  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