Snowball
oceanography
What is Snowball Earth?
Most extreme climate event in Earth history.
Characteristics:
• Occurred at least twice between 750-635 Ma.
• Global (or almost global) ice coverage.
• More than 1 km thick sea-glacier.
• Mean global temperature: -44oC.
(1992)
How do we know about snowball?
Glacial deposits at low paleo-latitude
Evidence for Snowball:
1) Low latitudes glacial
deposit.
2) Open water deposit.
3) Carbon isotope ratio.
4) Banded iron formation.
5) Cap carbonate rocks.
…
Glacial deposits:
Dropstone
Figs from Hoffman & Schrag 2002
For more: www.snowballearth.org
Goal
Study ocean circulation under global ice-cover.
Motivation
• Improve understanding of the climate system.
• Improve climate models.
• Photosynthetic life under the thick ice?
What do we do?
We use and coupled the following models:
• Ice-flow model of Tziperman et al. (2012).
• Oceanic MITgcm using shelf-ice package and
bottom geothermal heating. Idealized BC.
• Ice-flow and ocean models exchange
information every few hundred years (300 yr).
Models’ coupling
q—melting/freezing rate
Tf—freezing temperature
h—sea-glacier depth
T(z=0)—ice temp. at z=0.
(i) Lat./depth ocean (1D ice): 1o resolution (82oS to 82oN)
with 32 levels with 10 m resolution in vicinity of ice.
Ocean depth of 2 km plus 1 km ice.
(ii) Eddy resolving (1/8o), equatorial sector (0o—45oE and
10oS—10oN)
(iii)3D ocean (2D ice), 2o resolution globally. 73 levels.
Results:
2D ocean, 1D ice
Summary of the 2D results
(i) Strong equatorial currents.
(ii) Enhanced equatorial concentrated meridional
overturning circulation (MOC) cell.
(iii) Anti-symmetric and broad zonal vel. (u).
(iv) Symmetric & confined meridional vel. (v).
(v) u, v change sign with depth. w and MOC maximal
at mid-depth.
(vi) No MOC above above the maximum heating.
(vii) Difference in temperature of 0.2 oC.
(viii) Difference in salinity of 0.5 ppt.
We wish to understand why:
(i)—(vi).
Study a simplified set of equations
Model
Assumptions: (i) 2D (latitude-depth) (∂/∂x =0), (ii)
constant ice depth, (iii) steady state (∂/∂t =0), (iv) β-plane.
×× ×
×
××
Neglect terms based on “scaling” or numeric.
Equator: Pressure gradient is balanced by viscosity.
(i) Strong equatorial currents.
(ii) Enhanced equatorial concentrated meridional
overturning circulation (MOC) cell.
(iii) Anti-symmetric and broad zonal vel. (u).
(iv) Symmetric & confined meridional vel. (v).
(v) u, v change sign with depth. w and MOC maximal
at mid-depth.
(vi) No MOC above above the maximum heating.

Off-equator: “geostrophy”.

z=0 at mid depth.
Equator: Pressure gradient is balanced by viscosity.
(i) Strong equatorial currents.
(ii) Enhanced equatorial concentrated meridional
overturning circulation (MOC) cell.
(iii) Anti-symmetric and broad zonal vel. (u).
(iv) Symmetric & confined meridional vel. (v).
(v) u, v change sign with depth. w and MOC maximal
at mid-depth.
(vi) No MOC above above the maximum heating.

Off-equator: “geostrophy”.

z=0 at mid depth.
Equator: Pressure gradient is balanced by viscosity.
(i) Strong equatorial currents.
(ii) Enhanced equatorial concentrated meridional
overturning circulation (MOC) cell.
(iii) Anti-symmetric and broad zonal vel. (u).
(iv) Symmetric & confined meridional vel. (v).
(v) u, v change sign with depth. w and MOC maximal
at mid-depth.
(vi) No MOC above above the maximum heating.

Off-equator: “geostrophy”.

z=0 at mid depth.
Equator: Pressure gradient is balanced by viscosity.
(i) Strong equatorial currents.
(ii) Enhanced equatorial concentrated meridional
overturning circulation (MOC) cell.
(iii) Anti-symmetric and broad zonal vel. (u).
(iv) Symmetric & confined meridional vel. (v).
(v) u, v change sign with depth. w and MOC maximal
at mid-depth.
(vi) No MOC above above the maximum heating.

Off-equator: “geostrophy”.

z=0 at mid depth.
Equator: Pressure gradient is balanced by viscosity.
(i) Strong equatorial currents.
(ii) Enhanced equatorial concentrated meridional
overturning circulation (MOC) cell.
(iii) Anti-symmetric and broad zonal vel. (u).
(iv) Symmetric & confined meridional vel. (v).
(v) u, v change sign with depth. w and MOC maximal
at mid-depth.
(vi) No MOC above above the maximum heating.

Off-equator: “geostrophy”.

z=0 at mid depth.
Most features are explained!
Equatorial sector—
high resolution (1/8o simulation) simulation
Why?
(i) Parametrization of eddy viscosity coefficient.
(ii) Turbulence under complete ice cover?
Setup:
(i) Equatorial section: 10oS to 10oN & 0oE to 45oE with
1/8o resolution (360x168 grid); fixed (uniform) ice
depth; 20 vertical level (100 m each);
(ii) Two configurations: with and without island.
(iii)Maximum geothermal heating at 6oN.
(iv)Much lower viscosity coefficient!
Turbulence.
Melting rate
• Almost one order
of magnitude
larger than
atmospheric
value.
• The enhance
melting is
associated with
upwelling of
warm water.
• Can enhanced melting create hole in the ice?
• Can this resolve the question of photosynthetic life
under hard Snowball conditions?
Summary
(i) The ocean Snowball condition if far from
being stagnant. Rich and enhanced dynamics.
(ii) Mainly equatorial dynamics. Strong zonal jet;
strong & confined meridional overturning
circulation (MOC) cell as a result of rotation,
geothermal heating, and horizontal viscosity.
(iii)Turbulence.
Main oceanic characteristics are robust!