Description of the annual cycle

With the basic terms introduced, it is instructive to step through the mean annual cycle of the energy budget. Our ability to assess the budget components has improved since the Nakamura and Oort (1988) study. More accurate TOA radiation fluxes have been obtained by ERBE, although these only cover about a four-year period. Trenberth and Stepaniak (2003) used data from the NCEP/NCAR reanalysis to compute grid cell values of vertically integrated energy fluxes, divergences and tendencies for the period 1979-2001. These data allow direct computation of budget terms for the polar cap except the net surface flux, which they also computed as a residual. Their computation of the net surface flux uses ERBE and NCEP/NCAR data over their common period of coverage (February 1985-April 1989).

The values in Table 3.1 for Fwall and the change in atmospheric energy storage are based on the 1979-2001 NCEP/NCAR record assembled by Trenberth and Stepaniak (2003), while the radiation fluxes and residual net surface heat flux are based on the ERBE period. As such the terms in Equation (3.3) will not sum to zero. We use Nakamura and Oort's (1988) values of So (the rate of storage of heat in the Arctic Ocean), and hence get estimates of the latent heat exchange from ice growth/melt (Sm) as another residual. Estimates of the planetary albedo from the APP-x data set are also provided for months with a significant solar flux.

Consider first the annual cycle in the rate of energy storage in the atmosphere AE/At, starting with August, which represents late summer. There is a net loss of

Table 3.1 Estimates of the components of the energy budget of the north polar cap



Table 3.1 Estimates of the components of the energy budget of the north polar cap



1 swn

F lw

( Frad)


( Fwall)

( Fsfc)



























































































































Notes: All values except the planetary albedo are in W m . Fswn is the net shortwave radiation. See text for discussion of data sources. Because of the use of data sets covering different time periods, the budget terms as expressed in Equation (3.3) (in parentheses) will not sum to zero.

energy from the atmospheric column in this month of -20 W m-2. The net loss is at its maximum in September (-30Wm-2), is roughly maintained in October (-25 W m-2), then declines through the winter. It turns positive in February. The net energy gain increases during spring to a maximum of +22 W m-2 in April, and is slightly negative in July. This annual cycle is consistent with the observation that the longwave loss from the top of the atmosphere falls most sharply in autumn, falls less sharply through winter, and rises through spring and summer to its highest values in July. The annual cycle in the atmospheric energy content can be readily seen in atmospheric variables averaged for the region north of 70° N, such as the mean height of the 300 hPa pressure surface (Figure 3.6) and mean precipitable water (Figure 3.7) as evaluated from NCEP/NCAR data.

The annual cycle in the energy storage of the atmosphere is determined by the interactions of the three terms on the right of Equation (3.3). A useful starting point is to consider an idealized (but obviously unrealistic) polar cap for which there are no horizontal atmospheric fluxes and no vertical heat transfers between the atmosphere and the ocean-ice-land column (Fwall and Fsfc equal zero). Consider in this simple model the effects of the solar radiation flux on the atmospheric energy content. Solar radiation is the external energy source to the system. Remember that the atmosphere is approximately transparent to shortwave radiation but absorbs longwave radiation strongly outside the "atmospheric windows" (3-5 and 8-12 ^m regions). Solar radiation heats the surface. The atmosphere is then heated from the bottom up by sensible and latent

Arctic Reanalysis Data
Figure 3.6 Mean annual cycle of 300 hPa geopoten-tial height for the region 70-90° N. Results are based on NCEP/NCAR reanalysis data over the period 1970-99 (by the authors).
Arctic Reanalysis Data
Figure 3.7 Mean annual cycle of precipitable water averaged for the region 7090° N. Results are based on NCEP/NCAR reanalysis data over the period 19792000 (by the authors).

heat fluxes and the absorption of upwelling longwave radiation emitted by the surface. The system radiates longwave radiation into space. In radiative equilibrium, the net solar radiation at the top of the atmosphere must equal the longwave loss to space. With the assumption of radiative equilibrium, the energy content of the atmosphere would follow the annual cycle of the solar radiation flux. The energy content would be largest in summer, when the solar flux is strongest, and smallest in winter, with intermediate values during the shoulder seasons. The change in energy storage would be positive as the solar flux increases, and negative as the solar flux decreases.

The observed annual cycle of the change in atmospheric energy storage bears qualitative resemblance to that expected from this simple model. The observed values are most positive in spring, when the solar flux is increasing rapidly, and are most negative in autumn, when the solar flux is decreasing rapidly. However, it is clear from Table 3.1 that, except for June and July, the system actually departs quite radically from radiative equilibrium. The obvious explanation is that we have ignored Fwall and Fsfc. We have furthermore ignored seasonality in the planetary albedo.

Consider autumn. The TOA net solar flux is small and becoming smaller, resulting in a decrease in the heat content of the atmosphere. The decline in the solar flux and hence the cooling of the atmospheric column is greater in high as compared to middle latitudes. Hence the zonal mean temperature gradient in the atmosphere increases. This means that Fwall increases, adding energy to the system to slow the cooling rate. As the atmosphere continues to cool, the surface fluxes turn positive. The ocean loses sensible heat to the atmosphere. With continued cooling, sea ice forms, also releasing heat to the atmosphere to slow the cooling rate. By our convention, snowfall also represents a net heat transfer to the atmospheric column. Hence, although the atmosphere is cooling strongly in autumn, the braking effects of Fwall and Fsfc mean that it cools at a slower rate than expected from the decline in the solar flux.

Autumn turns to winter. The atmosphere continues to lose energy, but as the winter solstice approaches, the rate slows. In part, this is because there is little change in the net solar flux (the flux is essentially absent from October through February). The atmosphere is cold, but not becoming a great deal colder, so that although Fwall is large, it is not changing much. Fsfc remains positive as sensible heat continues to be drawn out of the ocean reservoir and the growth of sea ice and snow cover continue. The mean winter (December through February) surface flux of 41W m-2 includes the marginal seas, where values are comparatively high. Surface-based measurements by Maykut (1982) indicate that the upward flux over the central Arctic pack ice is closer to 21 W m-2.

Spring approaches and the change in energy storage of the atmosphere turns positive, allied with an increase in the longwave loss to space. This is due to the growing input of solar radiation and the continued heat inputs via the surface flux. However, the effect of the higher solar declination is strongly offset by the high planetary albedo, largely due to the extensive sea ice, snow cover and clouds. But as the atmosphere warms, Fwall begins to decline. By April, the positive change in atmospheric energy storage attains its seasonal maximum due in large part to the much stronger inputs of solar radiation, related to both the increase in solar declination and the first hints of a reduction in the planetary albedo. The strong energy gain of the atmosphere continues in May, but by June, when the solar input is largest, the rate of gain begins to decline. This occurs in part because of a weakening of the atmospheric circulation, and in part because of the surface fluxes. By June, sea ice and snow are melting (the latter over both ocean and land), drawing heat from the atmospheric column. A large part of the solar input is also used to warm open-water areas, also representing a loss of atmospheric heat. In July, the change in atmospheric storage is close to zero, as is the TOA net radiation budget. For this month, the budget is determined by the roughly equal and opposing effects of the atmospheric transport and the net surface flux.

The planetary albedo is at its minimum in July and August. This primarily relates to the exposure of snow-free land, open-ocean waters and the removal of snow cover from the remaining sea ice cover. These influences outweigh the effects of the summer maximum in (highly reflective) cloud cover seen over most of the Arctic (see Chapter 2). The lower albedo of the sea ice cover does not result in sensible heating of the atmosphere (when melt is occurring, the skin temperature is fixed to the freezing point). By contrast, the stronger absorption of solar radiation by the sea ice promotes stronger ice melt, which represents a loss of energy in the atmospheric column.

Nakamura and Oort (1988) also examined the Antarctic polar cap. The Antarctic results are less reliable than the Arctic results because of the paucity of data. Annual cycles for the two polar caps are similar in a qualitative sense, but differ markedly in the magnitude of the fluxes. Of interest is that the surface fluxes are much larger in the Arctic. In the Arctic, the seasonal variation in Fsfc accounts for about 70% of the amplitude of the net radiation at the top of the atmosphere (Frad). What this means is that the ocean-cryosphere heat reservoir is as important as the atmospheric influx of energy from the middle latitudes in compensating for the radiation loss at the top of the atmosphere. In the Antarctic, the seasonal variation in the surface flux seems to account for only a small fraction of the variation in Frad. As discussed by Nakamura and Oort (1988), the differences in budget terms between the two polar caps are not surprising given the radically different geography. While the north polar cap is relatively flat and primarily ocean covered, the south polar cap is a high-elevation, ice sheet covered region.

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