Presentation by Kai Rasmus, Luode Consulting Oy, Finland, at the Delft3D - User Days (Day 2: Hydrodynamics), during Delft Software Days - Edition 2019. Tuesday, 12 November 2019, Delft.

1. Using Hypothetical Snowball
Earth Conditions as a Sanity
Check on Sea Ice Models
Kai Rasmus, Luode Consulting Oy, Finland
Credits also go to:
Joose Mykkänen, Luode Consulting Oy, Finland
Reimer de Graaff, Deltares
Erik de Goede, Deltares

2. Introductory slide
• First we will talk about Snowball Earth
• Then an anecdote needs to be given
• The Delft3D ice-model will be presented
• Some validation results
• Finally the results of Delft3D ice-model simulation in Snowball Earth
conditions will be given
• Then the presentation will end

3. Snowball Earth
A hypothesis

4. Snowball Earth, what?
• 3-4 periods in Earth’s history when it has been totally ice-covered
• The last one was in the Proterozoic era 650 million years ago
• The hypothesis argue that it best explains sedimentary deposits
generally regarded as of glacial origin at tropical palaeolatitudes
• Formation related to the global carbon cycle on geological timescales
• Due to the distribution of continents, the tropical ocean was relatively
shallow
• i.e. perfect for a Delft3D application

5. A nut shell description
• Carbon dioxide fixing -> sedimentation of organic matter ->
sedimentary rock formation -> plate tectonic movement -> uplift into
volcanic regions -> ejection of carbon from volcanoes

6. An Anecdote
Let this be a lesson to you all

7. Way back in the beginning of this century…
• I was working as a PhD student at the University of Helsinki on the
optical properties of ice and snow
• A Snowball Earth guru from America came to give us a presentation
on it
• He made a point that at tropical latitudes the ice would still be thin
enough for photosynthesis to still be possible (a prerequisite for life
as we know it today to exist)
• I thought: ”Hey, this is easy to test with our models”

8. And so
• I setup the University of Helsinki ice model for Snowball Earth
conditions by mainly setting the global air temperature to negative
values and setting the ocean depth to something small similar to
Proterozoic conditions
• The result was that ice didn’t really grow at the equator
• My conclusion then was that the model was not working


9. However
• Then papers with similar results to mine started to come out

10. Even one in Nature

11. And a corresponding letter

12. Some observations from the literature
• McKay (GRL, 2000) found that when applying models developed for
the Antarctic dry lakes to Snowball Earth conditions, the ice thickness
would be 10m or less and photsynthesis would still be possible.
• Hyde et al (Nature, 2000) find that when a general circulation model
is included then a belt of open water is formed at the equator even
though ice sheets could extend that far.
• Lewis et al (JGR, 2007) find that when dynamics are included then a
hard snowball Earth (total ice cover) is more probable. When only
thermodynamics are considered then a soft snowball (some open
water) is possible.

13. So I was on the right track after all
• The moral of this story is that always publish your results ☺
• Also even though you do not subscribe to the Snowball Earth
hypothesis (as many don’t) then it does give one a platform for
testing ice-models
This is me still not subscribing to
the Snowball Earth hypothesis

14. Delft3D ice-model
Serious science
Also I have Reimer de Graaff and Erik de Goede to thank for this part

15. Delft3D Sea Ice Model
Atmosphere
(wind, air temp/press., solar rad.,..)
Hydrodynamics
2DH/3D
currents
temperature/salinity
properties
weathering
advection
spreading
wave forces
frequency
Morphology
bed changes
Water quality
Ice / snow
accumulation
melting
advection
internal stress
transport processes
Waves Oil

16. Delft3D Sea Ice Model
Combination of 2DH/3D hydrodynamic
model (Delft3D) with:
1. Thermodynamic model (vertical) based
On a single ice layer concept with or without
snow on top
An extension of the Delft3D thermodynamic
module
2. Dynamic model (horizontal) based on
The elastic-viscous-plastic (EVP) sea-ice
rheology
Based on open-source Lim3 code from Belgium
(advanced Louvain-la-Neuve Sea Ice Model)

17. Numerical implementation in Delft3D-FLOW
• ice ≈ floating structure (rigid lid approach)
• including drying and flooding
• same time step as hydrodynamic model (dynamic modelling)
• same computational grid and depth as hydrodynamic model
• wind/currents act on ice (where present)

18. Validation – Sea ice thickness

19. Validation – Sea ice extent
Satellite image reference USGS/NASA Landsat Program, SYKE

20. Validation – Lake ice thickness

21. Ice model – some observations
• The ice model seems to be working in present day conditions
• Thickness data still not generally available, especially for freeze and
thaw periods
• A problem for validation
• Ice extent can be obtained from satellite images
• Snow has a large impact on the ice growth
• Snow-ice formation component not implemented
• Snow-ice can be more than 50% of the overall thickness
• The ice model does not have boundary conditions implemented yet

22. What We Use it For and Why
• Study of ice effects of thermal discharges
• Development of factories
• Development of powerplants
• The ice model is usually included if an overwinter simulation is made
• Ice has a recreational usage component that needs to be conserved if
possible

23. Delft3D Ice Model in Snowball
Earth conditions
The actual purpose of this presentation

24. Setup for Hypothetical Snowball Earth
Conditions
• Rectilinear grid setup from latitude 25°S to 25°N and longitude 50°E
to 100°E
• Air temperature set to -25°C globally
• Northern winter (from December onwards)
• 2 senarios:
• No wind – equal to a purely thermodynamic model
• Wind varying with latitude in direction
• Dynamic ice
• The models were run for 4 months to achieve a steady state

25. Results

26. Results
• With no wind the Southern hemisphere is ice free
• The southern summer sun is able to melt the ice that is formed during the night.
• Delft3D does not produce thermohaline circulation (nor is it built to do so)
• If the model is run over the Northern summer then the Southern hemisphere should
freeze as well
• The dynamic (with wind) model produces as at all latitudes except for a
thin band at the equator
• The wind increases coolling at the surface
• The wind causes currents which redistribute heat
• The latitudinal distribution of ice is a result of the fictional wind
distribution
• Different winds would produce a different distribution

27. Comparison With Measurements
• Deltares has not released its ice observations from 650 million years
BC
• We are still waiting

28. Conclusions
• The Delft3D ice model is able to simulate present day conditions
• In its current form it does not produce euqatorial ice in Snowball
Earth conditions
• This result is in line with other research
• The Delft3D ice model is sane
• Always publish your results