Heat budget

Figure 2.2 Annual mean zonally averaged net radiation flux (W/m2) at the upper atmospheric boundary (a), and its seasonal variability (b). (After Stephens et al, 1981.)

Figure 2.2 shows the time-space variability of zonally averaged net radiation flux at the upper atmospheric boundary. Note three features: asymmetry of seasonal oscillations which is most distinct in high latitudes in both hemispheres, the local winter maximum in tropical latitudes in the Southern Hemisphere and marked increase in seasonal oscillations in the Southern Hemisphere compared with the Northern Hemisphere. The first and third features are connected to the specific character of the spatial distribution of the outgoing long-wave emission; the second feature is due to an increase in assimilated short-wave solar radiation because of a reduction of the planetary albedo.

The same features are inherent in net radiation flux at the surface of the World Ocean (Figure 2.3), though they manifest themselves less distinctly than in net radiation flux at the upper atmospheric boundary. The cause of this is a reduction in the effective emission of the ocean surface due to the existence of downward long-wave atmospheric radiation. The same cause explains the total increase in net radiation flux at the ocean surface compared with its value at the upper atmospheric boundary.

Denote the radiation heat influx in the atmosphere (the difference in net radiation fluxes at the upper atmospheric boundary and at the underlying

surface) by (Qi + Q2), where Qi and Q2 are influxes of short-wave and long-wave radiation respectively. Then (QÍ + Qf), together with the incoming sensible heat from the underlying surface which is equal and of opposite sign to the sensible heat flux H at the underlying surface, and the heat release = LP due to water vapour phase transitions, as well as the divergence V-cpmAvArA of the mass-averaged sensible heat transport and the conversion C(0,1) of internal energy I into potential energy <D (see Section 2.5), has to be balanced by changes in the internal energy of a unit atmospheric column, that is,

~cvmATA + V-cpm"^>A = <£ + Qk2 + <& + Qi - C(<D,/), (2.3.1)

where here, and above, TA is the air temperature, L is the heat of condensation, cp and cv are the specific air heat for constant pressure and volume; the remaining designations are the same.

Similarly, the net radiation flux (Qf + Qf) at the underlying surface plus the heat release LlEl at the expense of phase transitions of water vapour and minus the fluxes of sensible heat Q\ = H and latent heat = LE, as well as the divergence of the integral sensible heat transport, have to be balanced by changes in the heat content of a unit column of the ocean or land, that is, dt

^ c0m0f0 + V • c0/Wo = + Qf - Qf - Q? - LXEX, (2.3.2)

where c and T are the specific heat and temperature; m is the mass of a column with unit area; L, is the heat of melting (sublimation); subscripts O and L signify belonging to the ocean and land, double superscripts OS and LS signify belonging to the ocean and land surfaces, the symbol signifies, as mentioned above, averaging over the mass of the ocean or over the mass of the active land layer.

The terms appearing on the right-hand sides of Equations (2.3.2) and (2.3.3) completely describe the resulting heat flux at the underlying surface. Note some distinctive features of the time-space distribution of this flux within the World Ocean area not covered by ice (L,£, = 0). Judging from Figure 2.4, for annual mean conditions, the ocean gains heat from the atmosphere in low latitudes and loses it in middle and high latitudes (the secondary maximum in the middle latitudes of the Southern Hemisphere arises from a

Figure 2.4 Annual mean zonally averaged resulting heat flux (W/m2) at the ocean surface (a) and its seasonal variability (b). (After Strokina, 1989.)

Figure 2.4 Annual mean zonally averaged resulting heat flux (W/m2) at the ocean surface (a) and its seasonal variability (b). (After Strokina, 1989.)

III V VII IX XI

III V VII IX XI

reduction in the latent heat flux). In the Northern Hemisphere the heat inflow from the atmosphere is lower and the heat transfer from the ocean into the atmosphere is higher than in the Southern Hemisphere. The seasonal variability of the resulting heat flux in the Northern Hemisphere also appears to be greater. This feature can be explained by the difference in the ocean/land area ratio in both hemispheres.

We supplement the system (2.3.1)—(2.3.3) by the budget equations for the latent heat LmAqA in the atmosphere and sea ice L,m, (here, qA is the mass-averaged air specific humidity; m, is the sea ice mass referred to a unit of surface area). These equations take the form

8t where v, is the horizontal vector of the sea ice drift velocity.

Integrating Equations (2.3.1)—(2.3.5) over the longitude and then summing we obtain the equality

2na cos q> — ([cvmAfA] + [c0m0f0']f'0 + [cLmLfjf'L at

= 2na cos <p([0f] + [£>?]) - 2na cos <p[C(<D, /)], (2.3.6)

where mhta =

o is the meridional sensible and latent heat transport in the atmosphere,

(foCoMoVoTo + fmrtiiVi + f'LcLmLvLTL)a cos q> d<p o is the meridional sensible and latent heat transport in the ocean and active land layer; v0, vI and vL are the meridional components of current velocity, of sea ice drift and of river and ground water movement; f'Q, f[ and f'L are fractions of the ocean, sea ice and land in the zonal belt of the unit meridional extent.

Equation (2.3.5) relates the net radiation flux ([Qf] + [gj]) at the upper atmospheric boundary (here, Qf is the flux of the absorbed short-wave solar radiation, Qf is the flux of the long-wave emission into space) to the divergence of the meridional heat transport, and energy change in the atmosphere-ocean-sea ice-land system. Let us discuss the time-space variability of the last two components. But first of all we consider the seasonal variability of the global heat budget, which is described by the equality

-({cvmAfA} + {LmA4A} + {c0m0T0}f0 + {cLmLTL}fL + {AmJ/,) ot

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