ICE
The feedback of expanding and contracting ice sheets has often been offered as a
plausible explanation for how the contrasting climates of the glacialinterglacial times can be both (relatively) stable. Ice cover is, in general, much
more reflective than the surfaces it covers. The annual variation of surface
albedo is controlled by snowcover (Figure 9.2). Ocean surfaces at high latitude
have albedos of ~ 10% while sea ice at the same latitudes is ~60%. The
contrast been coniferous forest and an ice sheet is equally large.
Hartmann
1
Ice albedo feedback is strong and positive. Consider a forcing that cools the
surface at high latitude. Such a cooling will produce an equatorward
expansion of the ice fields producing further cooling. In contrast, consider
a forcing during glacial times that drives the surface temperatures higher.
Such a forcing would reduce ice coverage, increasing insolation producing
further warming.
The influence of ice cover will be
most significant during between
the vernal and autumnal
equinoxes when insolation at high
latitudes is large. As we will
discuss later, orbital scale forcing
of summer insolation at high
latitudes is a popular explanation
for the forcing that drives the
climate between ice to ice-free.
Hartmann
The timescales for accumulation and ablation of ice
sheets are quite different (and uncertain). This
reflects the temperature dependence of these
processes. Ablation occurs via absorption of solar
radiation, by uptake of sensible or latent heat
delivered by warm air (and or/rain), and by calving
or shedding of icebergs to the ocean or lakes. The
mass balance illustrated in the figure above (from
Ruddiman) illustrates that there is a relatively
narrow temperature range over which the net
accumulation is large. Below -20 oC, the growth rate
slows as the amount of humidity the air can deliver
is reduced. The mass balance becomes highly
negative above -10 oC because ablation accelerates
and overwhelms accumulation. The temperature
where accumulation and ablation balance is known
as the equilibrium line. Stable equilibrium for an
entire ice sheet occurs when these processes are
balanced when averaged over the extent of the ice
sheet. For most icesheets, net accumulation with
little ablation is characteristic of the center while
ablation characterizes the margins. Ice flows
between these regions in great ice rivers (Kamb). It
is obvious from the temperature dependence of the
ice mass balance that the critical issue is summer
temperatures (and wind).
2
The physical position of the equilibrium line
for ice accumulation depends on latitude
and altitude (left, from Ruddiman). The
so-called "climate point" is the position
of the last permanent ice cover. This
position has shifted by nearly 10 olatitude
over a period of tens of thousands of
years. The extent of ice cover at the
LGM is illustrated in the figure below.
Much of Siberia and Europe remained ice
free while the Laurentide ice sheet
covered much of North America.
The lack of ice in the eastern sector is thought to result from the desiccation of the air
as it passed over the northern ice. Once ice sheets begin to grow, a positive feedback
(in addition to the albedo feedback) occurs. The "ice elevation feedback" results
from the fact that at higher altitude, temperatures are colder. An ice sheet 2 km thick
with a 6 oC/km lapse rate will be fully 12 oC colder at top than at the margin. Once
ice sheets begin to grow, the accumulation rate can increase as the elevation of the ice
field increases. Note that even at +0.3 m yr-1 growth rate, nearly 10,000 years is
required to grow a 3 km ice sheet. Under a climate forcing, note that the maximum
size of the ice sheet reflects the time when the glacier moves from net accumulation
to net ablation. This will happen long (thousands of years) after the climate begins to
warm. This phase lag can be modeled using a simple sinusoidal forcing function and
will be part of future homework.
The weight of the ice sheet can force significant
alteration to the bedrock. The density of ice is
less than 1/3 that of the underlying rock (3.3 g/
cm3). Nevertheless, the weight of a 3 km deep
ice sheet is enormous and can depress the local
bedrock by ~ 1km. Because of the influence of
the lapse rate on ice sheet growth, such a
depression can influence the growth and decay
of a large ice field. Bedrock responds to the
forcing by ice with two distinct time constants.
Almost immediately, the bedrock sags in an
elastic response (about 1/3 of the total
alteration). On much longer time scales, the
slow flow of rock in the softer layer of the upper
mantle (100-250 km below surface) produces a
viscous response that occurs with a time
constant ~3000 years. With the removal of ice,
the opposite forcing occurs and today some parts
of Canada and Scandinavia are still rebounding
from the last glaciation. The slow viscous
response acts as a positive feedback for both
growth and decay of ice sheets. Finally, getting
back to the figure of the rate of ice sheet growth
and decay as a function of temperature, it is
clear that the retreat of an ice sheet can be
substantially faster than its growth. This is
undoubtedly part of the explanation for the 'saw
tooth' pattern of glaciation evident in the
paleoclimate records.
3
The ice albedo feedback was first incorporated in simple models by the Russian
scientist, Mikhail I. Budyko of the Leningrad Geophysical Observatory.
Contemporaneously, WD Sellers published a similar result. Both models
produced very sensitive climates such that small forcings (such as changes in
solar illumination) could drive the climate from completely ice covered to ice
free. These models assumed that everything about the climate could be
characterized by the surface temperature, and that the only independent
variable was latitude (compare to ice extent illustrated above at the LGM).
The models were based on simple conservation of energy and such models
are now dubbed "energy-balance climate models". These models asked about
how growth and retreat of the ice caps would influence the climate forcing.
The steady-state model balances three terms, insolation, IR emission, and
horizontal transport of energy by the atmosphere and ocean.
QABS(x,Ts) - F∞↑(x,Ts) = ∆Fao(x, Ts)
where x = sin φ (sine of latitude), QABS is the absorbed radiation, ∆Fao is the
meridional transport in the oceans and atmosphere. For each term, a
parameterization is used to characterize the latitudinal variability. The
absorbed solar radiation, QABS, is written as the product of the solar constant,
So, a function that describes the latitudinal dependence of the solar flux, S(x),
and the absorptivity for solar radiation, ap(x,Ts) = 1- αp(x,Ts):
QABS(x,Ts) = So/4 × S(x)ap(x,Ts).
In these models, the annual mean
insolation is given by something
like:
s(x) = 1.0 - .477 P2(x)
where P2(x) = ½(3x2-1) – the Legendre
polynomial of order 2 in x.
This pattern of insolation can be
compared with that shown in
Figure 2.7.
Hartmann
4
The emitted longwave flux is specified as a linear function of surface
temperature, e.g.:
The coefficients can be chosen to match the response illustrated in Figure 9.1.
The transport term (ΔFao) can be
specified in different ways.
Budyko assumed a linear form,
such that at every latitude the
transport relaxes the temperature
back towards its global-mean
value:
Slope = B
Hartmann
The coefficient γ is chosen so as to reproduce the meridional heat transport
observed for the existing temperature gradient.
Albedo feedbacks is introduced by assuming that ice forms when the temperature
falls below some critical value and that when this happens, the albedo responds
instantaneously. As discussed above, this critical temperature is ~ -10 oC. So:
where αice = 0.62 and αicefree = 0.3.
With these assumptions, Budyko's model equilibrium condition becomes:
A + BTs + γ(Ts-Ts(average)) = So/4 × s(x)ap(x,xi)
The absorptivity is a function of only latitude and the position of the ice
line, xi. Next, we define a new variable, I, the ratio of the local terrestrial
radiation to the global average insolation:
Substitution into the equilibrium model yields:
Where δ = (γ/B). If δ is large, then meridional transport is efficient compared
to longwave cooling, and the equator-to-pole gradient in I will be small.
5
The global area average of this expression is:
The global average value of the terrestrial emission divided by the insolation is
equal to the global average of the product of the absorptivity and the distribution
function for insolation. Thus the global average will be high when the absorptivity
is high where the insolation is high. Since I is related to Ts linearly, the global
mean temperature follows in the same manner. The albedo increase associated
with icecover will have its greatest influence as this ice extends equatorward (no
surprise).
The Budyko model can be solved for the latitude of the ice boundary as a function
of solar constant for particular values of δ. The solution is obtained by specifying
the position of the iceline and then solving for I at the iceline latitude. Because the
albedo specification is discontinuous at the iceline, I and Ts are discontinuous and
the solution for xi as a function of So is not unique. To remove this discontinuity,
we solve the for the albedo on each side of the ice line and use the average at the
line itself.
The general solution is shown in Figure 9.5. The model is highly non-linear
(driven by the albedo contrast). For many values of the solar constant,
three solutions are found. For So above 1.2 (normalized for the value of So
that puts xi at 72 oN), the solution is a stable, ice free world. For So below
0.95, only one stable solution is present, namely an ice-covered world.
In between, we have interesting
behavior. If the ice line stays at
latitude > 45o, the solution is
stable - increases in So produce
retreat of the ice. However,
once the ice moves equatorward
of 45o latitude, the solution is
unstable, and we plunge into a
snowball Earth. Note that only
a small change in So is required
(5%).
Hartmann
6
As designed, Budyko's model is highly sensitive to small solar forcing
changes. The answer is, however, quite sensitive to the choice of
parameters. In Figure 9.6 the solutions are shown for varying δ. For larger
values (more efficient transport), xi is more sensitive to So. This results
because large δ implies a small temperature gradient with latitude. Budyko
used a value of B = 1.5 W m-2 K-1 whereas more recent estimates are closer
to 2.2 Wm-2K-1. The resulting value of δ in Budyko's calculation was 2.6
and this high value contributed to the great sensitivity of his model.
Hartmann
Finally, as illustrated in Figure 9.7, the assumption of single values for
planetary albedo for ice and ice free conditions in a poor assumption and
one that the model results are quite sensitive to. As we have seen, albedo
at high latitudes is also associated with the larger average SZA and the
presence of clouds. In figure 9.7 the albedo for ice free conditions is taken
to be ap(x) = ao +a2P2(x) and ap(x) = bo for ice conditions with δ = 1.9, bo
= .7, and ao = 0.38. The value of a2 range from 0 to -.32 (ice-free and
icecovered albedo equal at pole). In Budyko's model, a2 = 0 whereas a
more realistic value is ~-.175.
Hartmann
7
Snow Ball Earth?
Budyko and Seller’s energy-balance climate models were built to
understand how ice-albedo feedbacks could have produced the observed
oscillation between ice free and glacial conditions. These models are
found to be hyper sensitive to changes in So, and suggest that if the
equilibrium iceline moved equator ward of ~45o latitude, global
glaciation could result and the Earth would find itself in an irreversible
cold climate. These results cast considerable doubt on the validity of
these models as it was assumed that Earth had never experienced such a
climate (and if it did, how would it escape and how would like persist?).
Recent studies have suggested, however, that the Earth may have entered
a nearly completely glacial state (and more than once). The evidence is
geological / geochemical and it comes from the Precambrian, before the
appearance of macroscopic metazoans.
During the neoproterozoic (550-1000 Myrs ago), the fragmentation of a longlived super continent seems to be accompanied by several lengthy periods of
global or near global ice (750 and 600 Myrs ago). These glacial deposits of
clays and fine silt contain a number of ice-rafted boulders. Evidence has been
presented, primarily from geomagnetic data, that these glaciers existed in the
tropics and reached to the ocean. This is the just the catastrophe predicted by
Budyko’s and Seller’s model. The ice growing thicker, the atmospheric
hydrological cycle is slowed to a crawl. Only the internal heat released from
Earth’s interior prevents the oceans from freezing to the bottom. In this lecture,
we will examine evidence put forward in support of this hypothesis and
describe how (if it happened) the Earth escaped from this hell.
8
The Evidence
In 1964, Harland (U. Cambridge) pointed out that glacial deposits occur in neoproterozoic
rock in nearly every continent (figure from Ruddiman). Dating and placing these
rocks is (like all such very old material) difficult. Harland, based on paleomagnetic
data, suggested that the glacial deposits described a clustering of these landmasses in
the tropics following the breakup of a super continent (Rodinia – 1000-800 Myr ago).
Small magnetic crystals in the glacial rocks align themselves to the Earth’s magnetic field as
the sedimentary rocks form. If they had formed near the pole, these crystals would be
oriented nearly vertically; in fact, they are nearly horizontal. For a period in the early
1990’s the low latitude location of these glacial deposits was called into question but
recent studies suggest that Harland had it right. The most recent paleomagnetic data
suggests that in the late precambrian, these land area were arranged as follows (Hyde et
al., Nature, 405, 425, 2000):
Notice that a number of these glacial deposits are located in the tropics (15S-15N). We
know these are glacial deposits (limestone and dolomite) and that some reached the
ocean because of the presence of ice-rafted drop stones. How is this possible? To
continue our storytelling, the argument goes that with the breakup of the super
continent, the increased weathering would produce a significant decrease in CO2 (more
on this later and in 148C). Because the continents are in the tropics, the negative
feedback on weathering typically associated with ice formation doesn’t occur. As the
ice line moves equatorward, the Earth rapidly cools and over a period of 10s of million
years, the Earth is encased in ice.
9
With the oceans frozen over, biological activity slows. In the meantime, CO2
emissions from the mid-sea ridges and volcanoes continues (you can’t stop plate
tectonics!). This leads to very low δ13C values – essentially in equilibrium with
CO2 venting from Earth's interior (– 7 ‰). Carbonates of organic origin have
significant carbon fractionation because of their preference for the lighter
isotope. Hoffman et al. presented evidence of large anomalies in δ13C in the
glacial deposits and in the large ’cap carbonates’ that lie above. They argue
that the δ13C are consistent with essentially a secession of marine life. In the
rocks that lie below the glacial deposits, nearly 50% of the carbonate would
seem to be of organic origin. In the glacial and cap carbonates above, nearly all
the carbonate must be inorganically precipitated. With the end of photosynthesis
in the oceans, the water would quickly becomes anoxic and iron dissolves (in
the presence of O2, iron is essentially insoluble). Evidence for this happening is
suggested by the banded iron formations that are seen in and just above the
glacial deposits. Such mobilized iron deposits are found elsewhere only during
Earth's early history when it is argued, O2 had not evolved into the atmosphere.
How does it end? With the land and ocean frozen and the hydrological cycle
shut down, our very own Joe Kirschvink suggested that because CO2 would
continue to vent from the volcanoes, atmospheric CO2 would slowly build up. In
a period of some 10s of million years, atmospheric CO2 increases to perhaps 0.1
- 0.3 bar and deglaciation begins. Once it starts, it is catastrophic. Temperatures
increase from – 30 oC to + 50 oC rapidly and global deglaciation occurs.
Oxygen, mixing into the oceans, precipitates the iron. In the high CO2 and moist
climate that follows, massive amounts of CO2 are deposited in the warm tropical
oceans as ‘cap carbonates’ – very large carbonate rocks the lie on top of the
glacial deposits.
Cap Carbonates along the Skeleton Coast of
Namibia. The crystal fans of indicate that they
accumulated extremely rapidly, perhaps in only a
few thousand years. For example, crystals of the
mineral aragonite, clusters as tall as a person, could
precipitate only from seawater saturated in CaCO3
[Hoffman et al., Science, 281, 1344; Scientific
American, 2000]
Great story! Truth or Fiction or a bit of both? It is
still unclear. What is reasonably well established is
that: 1). glaciers were present at or near sea level in
the tropics; 2) the solar ‘constant’, So, was 6% below
today’s value. It is unknown what the concentration
of CO2 was before, during, or immediately
following the glaciation. Following the terminal
glaciation a great diversity of multicellular life
occurred in the Cambrian explosion. We now turn to
the physics - could global glaciation occur?
http://www.sciam.com/print_version.cfm?articleID=00027B74-C59A-1C75-9B81809EC588EF21
10
We begin with Budyko’s and Seller’s energy-balance models (EBM).
Remember that these models suggested that with only a 5 or 6% reduction
in So, global scale glaciation could occur. Since the 1960s EBMs have
continued to be used to investigate paleoclimate issues. Palegeography,
dynamic ice sheets, and the efficiency of heat transport have been
identified as important for understanding ice growth and ablation (Poulsen
et al, GRL, 29, 1575, 2001). Recently, much more sophisticated
atmospheric GCM have been used to simulate the neoproterozoic
glaciation. Unlike the EBMs, the GCM study (Jenkins and Smith, GRL, 26,
2263, 1999) suggested that a snow ball solution required very specific
boundary conditions (very low CO2, low luminosity). More recent GCM
studies in fact have failed to find a full ice-covered solution (e.g. Hyde et
al., Nature, 405, 425, 2000). In this study an equatorial belt of ocean
remained ice free. Hyde et al. argue that this finding is not at odds with the
paleo δ13C provided that the band is sufficiently small and not too
productive. In a recent paper Crowley, Hyde and Peltier, calculate that for
this slosh ball Earth, much smaller amounts of CO2 are required to exit to
an unglaciated state (4 ´ present) with significant hysteresis (see Figures 3
and 4 from their paper) and thus the deglaciation could occur both faster
(much less CO2 build up required) and more paced (the exit is much less
abrupt).
Poulsen, Pierrehumbert, and Jacob [GRL, 29, 1575, 2001], performed the first
study of the neoproterozoic using a fully-coupled ocean-atmosphere model. In
this analysis, there is no snowball earth solution. In both the EBMs and the
GCMs, heat transport within the ocean is not treated explicitly. The results are
shown in Figure 1 of their paper. With a simple ocean mixed layer model (50 m)
with and without diffusive heat transport, tropic glaciation occurs quickly within 50 yrs (analogous to the EBMs). With the fully coupled model, however,
the ice margin oscillates seasonally and never approaches the tropics and
essentially no snow falls on the continent.
11
In diagnosing what produces the termination of glacial advance, Poulsen
et al. point to radiative cooling of the ocean during the winter producing
convection at the ice margin. Their simulations suggest that this process
alone warms the margin by 7 oC. The warm intermediate and bottom
water are produced in the simulation by convection at the poleward edge
of the subtropics. The authors argue that the ocean dynamics used in
previous models (EBMs and GCMs) are tuned to produce the present
climate and may not be suitable for understanding climates far from
today’s (e.g. the role of convection at the ice margin.) The conclusion of
this study is that IF the Earth got into a snowball condition it remains
unclear how it did so. The dynamics of ocean heat transport are critical
and not well understood. Is there something magical about the paleo
ocean topography that moved the intermediate water formation to higher
latitude (and colder water)? Or perhaps the forcing function was much
more dramatic than a slow, CO2 and orbital driven cooling (e.g. huge
volcano or meteor impact) producing sufficient cooling of the tropics to
produce an icehouse. The theoretical and experimental work on Snow
Ball Earth continues.
12