Can Thor Ice-skate in a “Jorgumand” World?: An evaluation of the likelihood and ramifications of a
Jormungand-state for the Neoproterozoic.
Abstract:
There is evidence of at least two intervals of widespread glaciation during the late
Neoproterozoic (600-800 Mya), which are commonly referred to as “Snowball Earth” episodes. The
global nature of these events is indicated by the fact that glacial deposits are found at low paleolatitudes
during this time. Models of a global glacial event have produced a variety of solutions at low latitudes
including thick ice, thin ice, slushball, and open ocean. The latter two models are similar, except that the
slushball model has an ice-line at higher latitudes. To be viable, a model must account for the survival of
life through the glaciations and also explain the existence of cap carbonates and other glacial debris
deposited at low latitudes. The “thick-ice” model is not viable because kilometers of ice prevent the
penetration of light necessary for the photosynthetic biota below. The “slushball” model is also not
viable as it does not allow the formation of cap carbonates. The “thin-ice” model has been discussed
previously and can account for continuation of photosynthetic life and glacial deposits at low
paleolatitudes. The recently proposed “open-ocean” or “Jormungand” model also satisfies these
requirements. The validity of these modifications is assessed individually and the overall likelihood and
plausibility of a “Jormungand state” for the late Neoproterozoic glaciations is discussed.
INTRODUCTION
There is geological data indicating that during the Neoproterozoic there were at least two glacial
periods (~630Ma and ~715Ma), when ice sheets flowed into the ocean near the equator. These glaciers
formed at high latitudes and migrated down to the equator or they formed at low paleo-latitudes
(Kirschvink, 1992; Hoffman et al., 1998). Evidence for these low latitude glaciers comes from a variety of
sources such as cap carbonates and carbon isotopes (Hoffman et al., 1998); paleomagnetic data
(Sumner et al., 1987); biological data (Knoll, 1992); glacial deposits such as dropstones, evaporates, and
varves (Williams, 1975); and banded iron formations (Ilyin, 2009). The Late Precambrian had a different
paleogeography from modern day. According to Hyde (2000), there was clustering of the continents in
the southern hemisphere leaving the north a large ocean. To explain these features, scientists have
been using models to try and recreate the conditions and to compare the evidence seen in the rock
record to the solutions. To be a viable solution, the model will have to explain the existence of cap
carbonates and glacial debris at low latitudes and account for the continuation of photosynthetic life.
An early proposed solution is Snowball Earth, by Joseph Kirschvink. This proposes that ice
reached the equator during a full glaciation. Once the cooling started, it would slow the cycling of CO2 of
the atmosphere and oceans, which creates a feedback loop further cooling temperatures. Earth’s
surface would also become more reflective due to the high albedo of ice, and this would cool the planet
by reflecting infrared radiation (Kirschvink, 1992). This Snowball Earth hypothesis explains the presence
of cap carbonates as well as the cycling of the underlying glacial rocks. The glacial deposits are from
glaciers moving across the continents and reaching the ocean, where they drop large rocks into the
sediment at the ocean floor. As the ice covered the oceans and temperatures were low, productivity
was low. When heating began, the ice melted leaving the glacial deposits; productivity then increased
creating the carbonates above (Kirschvink, 1992). There is a problem with the story, however. Life had
to survive this massive glaciation. Kirshvink (1992) has proposed a theory that warm tropical “puddles”
existed in the seas where life survived. Survival in these refugia would be extremely difficult and
micropaleontological data shows that life thrived before and immediately after the event (Knoll, 1985).
As all the evidence is backed by global glaciations, different ice solutions have been proposed (Hyde et
al., 2000; McKay, 2000; Pollard and Kasting, 2005; Abbot et al., 2011).
Hyde et al. (2000) proposed a “slush ball” model. This would allow for liquid water to be present
at the surface for photosynthetic life and could explain their survival. They used a coupled climate/ice
sheet energy balance model (Deblonde and Peltier,1991), with a reduced solar constant and varied
carbon dioxide levels. These open water/floating sea ice results are not consistent with carbon isotopes
of the Neoproterozoic; they are close to abiotic values, not biotic. This solution also increases salinity by
close to 20%, but the volume matches data for the Pleistocene last glacial maximum (Hyde et al., 2000).
This model does not explain cap carbonate formation, because the ice would retreat slowly. It is also
only a metastable state, so it is not a viable solution (Pollard and Kasting, 2005).
The next solution was from Christopher McKay in 2000 and was a “thin ice” solution. Ice would
be at the equator, would retreat quickly, and stop oceanic cycling. The only limiting factor for this theory
is life. The thickness and clarity of the ice at the equator would determine whether life could survive.
McKay’s model was run to see if the thickness of ice at the equator would be thin enough to permit
light, but thick enough not to be a “slushball” solution. This includes slow cooling to produce relatively
clear ice and a lack of brine channels to affect the transmissivity. With over thirty meters of ice, no light
can penetrate. Another limiting factor is albedo and temperature for the ice. At values of -30ºC and
higher, and albedos of .75 or lower, sunlight will limit thickness. Values of ice thicknesses of 5m or less
could not be modeled correctly, but this thickness allows for high productivity of photosynthetic
organisms (McKay, 2000). However, Warren et al. (2002) argued that this ice would be bubbly, with high
albedo, which would not allow for light to penetrate. Thick sea ice should have also flowed to the tropics
and disrupted the thin ice. They theorized the only solutions could be thick (opaque) ice or none at all at
the equator. Pollard and Kasting (2005) disagreed with that assumption and used their own model to
show that theory was incorrect.
Pollard and Kasting (2005) developed a coupled energy-balance climate/sea-glacier model,
which accurately models dynamic sea-glacier flow. One of the controlling parameters in this model is the
single scattering albedo of the ice, which was set for “bubbly” and “clear” ice. Bubbly ice had a value of
.999 while less bubbly, “clear” ice, was .994. The model was run with sea-glacier flow on and off, and in
both cases it was clear that the value of the single scattering albedo is very important. For bubbly ice
the solution was thick ice with nearly 103 m of ice at the equators. For clear ice the solution was thin ice
(about 2m) at the tropics with thick ice near the poles. The thin ice also stays in a band at the tropics of
+13º and -13º for single scattering albedos of less than 0.995. Through this thin ice, photosynthesis can
continue across the entire tropic region. Once carbon dioxide levels rise in the atmosphere, the ice
would thin, dropping the albedo and allowing the system to move back to open waters, taking only
about 5 m.y. The recovery time in previous models, such as Caldeira and Kasting (1992), was close to 30
m.y. However, the solution is not robust because a slight change in the inputs can result in full snowball
solutions, because the sea glaciers would flow all the way to the equator. Regardless, this model does
provide a viable solution to the Neoproterozoic glaciations (Pollard and Kasting, 2005).
The most recent proposed solution is the “Jormungand” state, so named because it exhibits a
band of open water at the equator that when varied seasonally appears to “snake” across the globe.
(Abbot et al., 2011). In Norse mythology, Jormungand is a serpent so large that he is able to surround
the world and grasp his own tail, and his arch-enemy is the god Thor (Sturluson, 2008). This open water
solution was generated from an EBM, with input parameters generated on two different General
Circulation Models (GCMs). The first was the National Center for Atmospheric Research’s Community
Atmosphere Model v3.1 (CAM) (Collins et al., 2004; McCaa et al., 2004), and the second was the Mac
Planck Institute’s atmospheric model v5.3.02p (ECHAM5) as a follow up (Roeckner et al., 2003). CAM
was run in an aquaplanet regime, with a mixed layer ocean of 50m, thermodynamic sea ice, no ocean
heat transport, no aerosols, full diurnal and annual cycles, and 94% solar luminosity. Abbot et al.
interpret the results to be stable in the open water system because when the ice latitude is near the
poles, there is snow covering the ice, therefore making albedo high (2011). When sea ice is near the
equator, it is bare and the albedo feedback is weak enough that the negative radiation feedback
stabilizes the climate. The result has thick ice from the poles to around 20º latitude, and then thin ice
which reaches 10º latitude then there is open water to the equator (Abbot et al., 2011).
Below we examine the physical constraints necessary to generate a “Jormungand” state and the
reality of these constraints. Additionally, we propose the idea that with a more advanced treatment of
the solar radiation penetrating the ice, the “Jormungand” state is simply a reproduction of Pollard and
Kasting’s thin-ice solution and it may, in fact, be possible for Thor to ice-skate in the tropics.
Model Descriptions:
1-D Energy Balance Model
For this project we used the EBM from Pollard and Kasting (2005). It is a coupled energy-balance
climate/sea-glacier model, with penetrating solar radiation, internal ice melt, and sea-glacier flow. The
model is broken into three basic sections: atmosphere, surface, and ice shelf (ice flow), which are
individually calculated before being brought together for final calculations. It is zonally symmetric,
seasonal, and an all ocean planet (no continents) with 1º latitudinal gridding with first of the time steps
being 5 days. There are two loops that run in the model for timing: steps of 5 days up to a year, then a
year step up to the designated end time. A single layer atmosphere is used. Additional layers were
explicit for snow, ice, and the upper ocean, which all exchange heat and water vertically with the
atmosphere. The ocean is a slab ocean of 50m thick, and snow and ice thicknesses varied seasonally and
on longer timescales than other parameters. For thin ice, less than 15cm, the thickness is maintained at
15 cm for numerical stability and the fraction of ice cover is varied to conserve ice mass. Solar radiative
fluxes are treated as transmission, reflection, or absorption by a single atmospheric layer. Surface
radiative fluxes are important when dealing with sea ice and snow for modeling. The delta two stream
model calculates values for infrared and visible light differently because they interact with the surface
differently (Pollard and Kasting, 2005). Ice dynamics include tensile stresses that induce horizontal
velocities, which equalize thickness and causes spreading. The climate and the sea-glacier flow models
were coupled. The EBM provided the local net annual surface and basal budgets used by the sea-glacier
model, and the sea-glacier transport modifies the latitudinal distribution of ice thickness used in the
EBM (Pollard and Kasting, 2005).
3-D GENESIS Global Climate Model
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RESULTS:
We begin by repeating the Pollard and Kasting (2005) thin-ice solutions for the Neoproterozoic
using the same energy balance model as that study. To do this we did series of runs with and without
sea-glacier flow. Calculations were performed with two different single scattering albedos, w0s: 0.999
and 0.994. These values correspond to bubbly ice and clear ice, respectively. We were able to
effectively reproduce the thin-ice solution at the equator from Pollard and Kasting (2005). From here
we modified the energy-balance model one variable at a time to see if we could isolate the variable (or
variables) that separates a thin-ice solution from an open-water, Jormungand-state. Varying the CO2
amount, the albedos of snow and ice, the freezing temperature of seawater, the melting temperature of
sea-ice, and the ocean heat transport did not produce open-water at the equator. However, when we
turned off the penetrative solar radiation into the sea-ice, thereby making it purely absorbing at the
surface of the ice, we were able to produce a very thin open-water solution (See Figure). In Abbot et al.
(2011), the open-water band at the equator went from +/- 10ᵒ, even in the EBM solution. In our EBM
solution, the largest band we were able to get was approximately 6ᵒ in width. The 14ᵒ difference in
width is most likely due to the inherent dissimilarities in the two models.
Our 4 runs with CO2 values (1000, 1700, 2500, and 10000 ppm) superimposed on Figure 1 from Abbot et
al. (2011). Based on the positioning of our solutions it appears that we will have a different curve than
Abbot et al. (2011).