# Presentation: 206501

## A Calving Law for Ice Shelves:Spreading-Rate Control of Calving RateR.B. Alley, I. Joughin, H.J. Horgan, T.K. Dupont,   B.R. Parizek, S. Anandakrishnan, and K.M. Cuffey 

- _x0003_Considering cold, floating termini;
- A first estimate, not a final one;
- But, this matters;
- We suggest the tendency for ice shelves to fall apart (the near-front spreading rate) controls the rate at which they fall apart (the calving rate).

- G. Comer Foundation

## Unbuttressed;  friction from local high in bed not stabilizing ice sheet.

- Buttressed;       friction from local high in bed is stabilizing ice sheet.

- Does it calve here
-                 or there?

- ICE

- ICE

**To the best of our knowledge, no ice-sheet model calculates this physically. We should do better.**

## Very good reason why predicting hard for:

- <date/time>

- Earthquakes;
- New volcanoes;
- Whether your ceramic coffee cup will break when you drop it on the floor;
- Iceberg calving from ice shelves...

## Fracture mechanics is a mess!  Depends on:

- <date/time>

- Forcing (for ice shelves: tides, storms, collisions from passing icebergs, etc.);
- Material (temperature, c-axis fabric, impurities, density, etc.);
- Geometry (thickness, thickness gradient, transverse character, etc.);
- Pre-existing flaws (basal and surface crevasses, etc., hence history, such as tides at grounding line).

- Engineers like to calculate everything to several decimal places, then build 3x stronger, just in case...

## So, are we screwed?  We hope not...

- <date/time>

- Often, there is a “leading term” across a broad range of situations;
- A ceramic coffee cup over a hard floor will almost always survive a one-inch drop and almost always break from a ten-foot drop;
- Our hypothesis: tendency of ice shelves to fall apart (longitudinal stretching rate) controls the rate at which they fall apart (calving rate);
- Our hypothesis test: see if this explains a lot of the variance across a range of ice shelves.

## Procedure:

- <date/time>

- Measure longitudinal stretching rate about one iceberg-width from the front, especially near center-line of shelf (stress perhaps better, but strain rate more easily measured, and in some formulations strain rate controls);
- Measure calving rate (assume steady state--most ice shelves are recognizable across mappings, those that aren’t generate *Science* and *Nature* papers, so avoid nonsteady times/places, and near-frontal velocity is calving rate to close approximation);
- If hypothesis is correct, calving rate increases with stretching rate, so plot it up and see

## There are lots of “issues”

- <date/time>

- How steady is steady?
- Look how far back from the ice front?
- Smooth over what length of ice shelf?
- Etc.

- But, we are cautiously optimistic that these “issues” influence rather than control the outcome (I think that if you did the analysis, you’d get the same trend and similar numbers).

## =0.003/yr

- =0.003/yr

- V=1000 m/yr

- Calve

- Ice flow

- 600 km

- Amery

- Riiser

- Filchner

- =0.002/yr

- V=1275 m/yr

- =0.0008/yr

- V=275 m/yr

- Data Gap

- =0.001/yr

- V=1075 m/yr

- Ross

- 200 km

- 300 km

- 400 km

- .

- .

- .

- .

## Whole data set.  Positive slope is dominated by Jakobshavn (which is shown for three different times; J).

- Whole data set.  Positive slope is dominated by Jakobshavn (which is shown for three different times; J).
- Line is:
- Calv=1.6x104*strain_rate1/2
- The square-root relation is consistent with fits to various subsets of the data.

- J

- Blow-up of low-strain-rate data.  Pine Island (P) and McMurdo (M) dominate, but even omitting them leaves a positive-slope relation (but a noisy one with lowered confidence). The same line is included for reference.

- P

- M

## Calving rate increases with strain rate

- <date/time>

- We cannot yet find any obvious way out of this;
- This is what we hypothesized from common sense--ice shelves seem to fall apart in response to their tendency to fall apart;
- Regression gives calving rate Ck, k~1/2,         =strain rate
- Tendency for basal crevasse of height L to grow under stretching-stress  is measured by stress-intensity factor KIc~ L1/2With ~3 and L~, KIc~ 1/2Since C~1/2calving rate~ tendency for basal-crevasse growth?  (This is probably too simplistic, but interesting...).

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- .

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## If this is right, some interesting implications-- see Dupont poster!

- If this is right, some interesting implications-- **see Dupont poster**!
- Fast input, slow spreading, very long shelf (Erebus Glacier Tongue?)

- Slow input, fast spreading, unstable without buttressing (high-profile papers and low-profile ice sheets?)

- http://asterweb.jpl.nasa.gov/gallery/images/glacier-tongue.jpg

- http://svs.gsfc.nasa.gov/vis/a000000/a002400/a002421/index.html

## Synopsis

- <date/time>

- Accurate modeling requires better calving laws, including one for cold ice shelves;
- An accurate, all-inclusive law won’t be easy to find;
- We have gone looking for a first approximation;
- Our initial hypothesis--the calving rate increases with the longitudinal spreading rate (or, **the rate at which the ice shelf falls apart increases with its tendency to fall apart**) explains a lot of the variance across the ice shelves we have examined, with calving increasing as roughly the square root of spreading;
- Such a law may explain some ice-shelf behavior;
- We want more data, more-careful consideration of the physics, and more thought whether differences between shelves apply to single shelves;
- Pending those, we suggest calving_rate~strain_rate1/2