Geoscience Reference
In-Depth Information
The strong relationship between the growth rate and freezing degree days for
young (thin) ice is explained in that the temperature gradient in the ice is essen-
tially linear. In the simplest case, it can be assumed that the temperature gradient in
the ice is the difference between the temperature at the ocean-ice interface (at the
salinity-adjusted freezing point) and the ice surface temperature, divided by the ice
thickness. As outlined in
Chapter 5
, the rate of growth (or ablation) at the bottom
of the ice is represented by the sum of the ocean heat flux (F
w
) and the conductive
heat flux through the ice (K
i
∂T
i
/∂z). When their sum is negative, growth (accretion)
occurs. When their sum is positive, ablation occurs. With the assumption of a linear
temperature gradient, the thickness responds immediately to changes in the thermal
forcing at the surface.
The rate of growth of young ice is very sensitive to H. As H increases, the tem-
perature gradient in the ice decreases, slowing the growth rate. This is a fine exam-
ple of a negative feedback - although one needs to conduct heat through the ice
to the surface to form ice, the very formation of the ice acts to inhibit its further
production. Turning back to
Chapter 3
, it should come as no surprise that the heat
release to the atmosphere in winter associated with ice production is primarily in
the marginal ice zones, where most new ice is formed. The growth rate decreases
by almost an order of magnitude between H = 10 cm and H = 100 cm. Clearly, the
growth rate depends on the magnitude of F
w.
If the ocean heat flux becomes larger,
ice growth decreases. Snow cover is also important. If one includes a layer of snow
and specifies that the conductive flux through the snow is equal to that in the ice, the
growth rate decreases. This is because with the snow, the ice is effectively thicker.
In reality, conduction through snow tends to be much less efficient than through ice
(
Table 5.1
), leading to still slower growth rates.
As ice becomes thicker than about 100 cm, the relationship between the growth
rate and freezing degree days (or air temperature) weakens. To describe the growth
of MYI or thicker FYI, one must abandon the idea of a linear temperature gradi-
ent in the ice. As discussed by Maykut (
1986
), the growth of thicker ice depends
more on its thermal history than on the surface heat balance at one moment in time.
Observations have shown that in early summer, accretion may occur at the bottom
of the ice while melt is occurring at the top, the reason being that the summer warm-
ing has not penetrated to the lowest part of the ice. Conversely, in October, when ice
is growing quickly in leads, thick ice is generally decreasing in thickness owing to
bottom ablation, the reason being that the autumn cooling has not yet affected the
lowest part of the ice.
The formation of a typical thick (3.5-4.5 m) MYI floe can be conceptually viewed
in terms of a process leading to quasi-equilibrium condition. Consider an FYI floe
that has survived the summer melt season. By definition, it is now multiyear ice.
During the second winter, there will be ice growth at the bottom of the MYI floe.
The thickness that is added to its bottom, however, is less than what will be added
to nearby FYI. This is because the MYI floe is thicker than the FYI, meaning that
the bottom growth starts later in autumn, and, once stared, proceeds at a slower rate.
Still, it ends up thicker than it was at the end of the first winter. In subsequent years,
