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When defining an area average of sea ice thickness, it is important to distinguish between an average taken over an ocean area

$$h_1 = \sum \frac{\text{sea ice thickness (in area)}}{\text{area}_\text{ice} + \text{area}_\text{water}}$$

and an average taken over the ice covered area

$$h_2 = \sum \frac{\text{sea ice thickness (in area)}}{\text{area}_\text{ice}}$$

The notations $h_1$ and $h_2$ are mine. I've seen both quantities referred to as “effective ice thickness”. I might go with Holland et al 2014 and call $h_1$ “effective ice thickness” and $h_2$ “average ice thickness”.

As an example think of a multi-category sea ice model: Let's say an ocean grid cell has a sea ice concentration of 50 %. Thus 50 % of the ocean grid cell is covered by water. The other 50 % of the grid cell is half-filled with 50 cm thick ice and half filled with 30 cm thick ice. For this case $h_1$ and $h_2$ would be 0.2 m and 0.4 m:

$$\begin{align} h_1 &= 0.5 \times 0 \text{m} + 0.25 \times 0.5 \text{m} + 0.25 \times 0.3 \text{m} = 0.2 \text{m} \\ h_2 &= 0.5 \times 0.5 \text{m} + 0.5 \times 0.3 \text{m} = 0.4 \text{m} \end{align}$$

Both variables can be useful. As I have seen conflicting names, I am a bit puzzled with the naming for $h_1$ and $h_2$. What are the standard names for $h_1$ and $h_2$ used in the sea ice community?

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  • $\begingroup$ This particular Google search should help you. google.com/… $\endgroup$ – Aabaakawad Oct 23 '15 at 17:59
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It would appear that you are spot on with the commonly used terms in your question. A well-referenced post on the Arctic forums (not by me) entitled 'Average sea ice thickness vs effective sea ice thickness', provide information about this very question. Specifically:

Average Sea Ice Thickness = Volume of Sea Ice/Ice Covered Area

Effective Sea Ice Thickness = Volume of Sea Ice/Grid Cell Area

According to the author of the post, (an Administrator of that site), these terms are imbedded in a lot of the published literature - for example, in the article "Uncertainties in Arctic sea ice thickness and volume: new estimates and implications for trends".

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