What is meant by (1) LTER sea-ice extent and (2) LTER sea-ice area?

(1)
Sea-ice extent refers to the total surface area inside the ice-edge.
This area inside the ice-edge is not necessarily covered by 100%
sea-ice, because sea-ice concentrations inside the ice-edge can be
anywhere from 15-100%.

Satellite sensors can usually detect the ice-edge with fairly good
accuracy because the physical properties of open water versus sea-ice
are very different (the most obvious is that one is a liquid, the other
is a solid, but also sea water is both warmer and saltier than
sea-ice).  The satellite senses these different physical properties so
that large areas of open water can be distinguished easily from large
areas of sea-ice.

The satellite sensor used here detects microwave signals from the
surface, and with the use of some mathematical formulae, we can
interpret those microwave signals in terms of percent ice cover.  From
field experiments we have determined that when the satellite senses 15%
sea-ice cover, it is detecting the ice-edge.  So we map where the
ice-edge is, then we determine the area inside that ice-edge and call
that sea-ice extent.  Again, note that the area inside the ice-edge
could be covered with sea-ice in concentrations anywhere from 15-100%.

(2) 
Sea-ice area refers to the area of ocean inside the ice-edge that
is covered by sea-ice only. 

Here we use the information about the percent sea-ice cover and add
only the area inside the ice-edge that is actually covered by sea-ice.


EXAMPLE. 

Let's say that the LTER study region is a rectangle where the length is
900 km and the width is 200 km.  Then the surface area would be 900 km
x 200 km which equals 180,000 km2.  (Notice however that in using the
satellite data we actually use a surface area of 194,319.8 km2.)

If the ice-edge was north of the LTER study region, then we would say
that sea-ice extent is 180,000 km2 (ie., the total area of the LTER
region because it all lies within the ice-edge).  But let's say the
half of the LTER study region is covered by 50% sea-ice and the other
half is covered by 90% sea-ice, then sea-ice area would be:

Half of the LTER study region = 180,000 km2 / 2 = 90,000 km2

sea-ice area = (90,000 km2 * 0.50) + (90,000 km2 * 0.90)
             = 45,000 km2 + 81,000 km2
             = 126,000 km2


GOOD QUESTION:

When would one want to use sea-ice extent and when would one
want to use sea-ice area?

Because satellites can easily detect the difference between large areas
of open water and large areas of sea-ice covered waters, the satellite
estimates of sea-ice extent are fairly consistent - even between
different kinds of sensors (for example, sensors that detect visible
versus infrard versus microwave signals).  So the measure of sea-ice
extent is fairly robust and can be consistently observed over time and
space.

Sea-ice area is in general a less accurate estimate, and its accuracy
is strongly dependent on the sensor being used.  Each sensor, and the
mathematical formulae that convert the signals into sea-ice
concentrations, all have caveats.  However, if one is aware of these
caveats, then the estimate of sea-ice area can be used to interpret
general changes in sea-ice cover over time and space.  There is no
doubt that we need more validation studies to fully understand the
errors involved in the estimate of sea-ice area, and in general this is
an area of active research.