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?
