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Average sea ice thickness vs effective sea ice thickness
« on: September 29, 2014, 11:09:07 PM »
Someone sent me a mail and asked me to post this here on the ASIF for anyone who is interested:

Sea Ice Thickness

There are two ways in which sea ice thickness is presented, Average Sea Ice Thickness and Effective Sea Ice Thickness, the two should not be confused.

The following explanation of the difference between the two is based on information found embedded in many scientific papers, one of the more accessible is Uncertainties in Arctic sea ice thickness and volume: new estimates and implications for trends, M. Zygmuntowska, P. Rampal, N. Ivanova, and L. H. Smedsrud 2014.

Average Sea Ice Thickness

This is what is normally meant by the term average thickness and reflects what a real world observer would experience.

It is calculated by dividing the volume of sea ice by the area of sea covered by the ice.

Effective Sea Ice Thickness

This is how sea ice thickness is often presented in scientific papers, and is how it is reported in the PIOMAS results.

It is calculated by dividing the volume of sea ice in a grid cell by the whole area of the grid cell, including the area of that fraction of the grid cell containing no ice.

Effective Sea Ice Thickness is useful scientists because it makes it easy to calculate volume.

Effective Sea Ice Concentration is the answer to the question; "How many cubic metres of sea ice are there in a square metre of sea?" Which is not the same as asking the question; "How thick is that ice?" It is expressed terms of metres because "cubic metres per square metre" simplifies to "metres".

When used in a real world context, Effective Sea Ice Thickness is probably best regarded as Minimum Average Sea Ice Thickness because it only reflects actual average sea ice thickness when there is 100% concentration. At concentrations less than 100% Average Sea Ice Thickness is always greater than Effective Sea Ice Thickness (with the obvious exception of zero concentration).

Comparison of Average Sea Ice Thickness and Effective Sea Ice Thickness

The diagram and tables below illustrate the definitions of average thickness and effective thickness. The diagram and part of the tables are taken from the NSIDC Data: Terminology page where they form part of an excellent explanation of Sea Ice Extent and Area. They are used with full acknowledgement of the NSIDC copyright.

The diagram shows four grid cell square grid cells containing various amounts of sea ice. For clarity each grid cell is taken as having sides 8 metres long, rather than 8 kilometres long. Giving a grid cell area of 64 square metres.

    In A, there is no ice.
    In B, one fourth of the cell is covered by ice one metre thick.
    In C, one half is covered by ice one metre thick.
    In D, the entire cell is covered by ice one metre thick.

As can be seen, as concentration decreases Average Sea Ice Thickness remains constant. This is because the sea ice is uniformly one metre thick. Effective Sea Ice Thickness on the other hand decreases as concentration decreases.

For the situation in the above example to be reversed and Effective Sea Ice Thickness remain constant while concentration varies, sea ice volume must also remain constant. As shown in the example below:

In the second example sea ice thickness increases as concentration decreases to keep the Effective Sea Ice Thickness constant. As a result Average Sea Ice Thickness increases as concentration decreases, and the increase becomes more dramatic at lower concentrations.

Converting between Effective Sea Ice Thickness and Average Sea Ice Thickness

Converting from Effective Sea Ice Thickness to Average Sea Ice Thickness can have some surprising results, particularly at low sea ice concentrations.

NSIDC use a 15% cut off for concentration in calculating sea ice extent, and PIOMAS has a 0.15 Metre cut off for their thickness graph. A grid cell with these limits of 0.15% concentration and 0.15 metre Effective Sea Ice Thickness is shown in column A of the table below. The table is completed for a uniform Effective Sea Ice Thickness of 0.15 metres.

In terms of the 64 square metre grid square, an Average Sea Ice Thickness of 1 metre at this joint lower limit equates to a block of ice 3.1 metres a side and 1 metre thick.

Although the above conversion is mathematically correct its results are subject to real world constraints. When a block of ice becomes too tall for its width and becomes unstable, at some point it will simply topple over and become long and thin rather than tall and thin. At low sea ice concentrations Effective Sea Ice Thickness is possibly the most useful measure as the sea ice is broken up into a multitude of ice flows of widely varying characteristics and Average Sea Ice Thickness becomes a less reliable indicator of the state of the ice.
« Last Edit: September 30, 2014, 01:18:14 PM by Neven »
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