Melting ice hidden temperature increase calculation required.... 
If we know how many million tonnes of ice melts per year, i.e. net
total
from one year to another, we can calculate how much heat we have 
moved into melting this ice.
Then we also know that melting one tonne of molten ice requires the
same amount
of heat as heating 50 tonnes of water 1 degree....
So if we know both ocean water mass (OWM) and net molten ice mass per
year(NMIM) in ice sheets, land ice, glaciers and molten permafrost, we
can solve the equation below for corresponding temperature increase,
dT:
dT*OWM=NMIM*50; 
The dT we obtain can then be added to measured global warming,
to get a better understanding of how much the melting is masking the
current warming. It may be 0.0001 dgr/year, so we do not have to
consider
it. Or the masked increase may be a significant number. 
Awaiting your response,
Best Regards Sten

 

 
global

It does not appear to me that the annual energy required to melt the
ice which melts each year, is relevent unless we subtract the annual
energy required to produce the ice. The difference is likely small and
varies from year to year in an almost random maner. Is the ice that
melts on the mountain peaks of Equador (near the Equator) just as
relevant as the ice that melts inside the Arctic Cirle or near the
South Pole where it often refreezes within hours even in January,
which is the warmest month. Does it matter if the melt water enters an
underground aquifer, evaporates or reaches the ocean? More important
estimates are likely + or minus 10% or more. Also several % of the ice
evaporates = sublinates and this energy is mostly recoverd elsewere
when clouds, frost or dew is formed. Doesn't this complicate your
calculation? In the case of clouds some of the energy of formation is
radiated back into space.  Neil

The question precisely stressed NET melted ice, which already includes
new ice formed minus melted. THis is valid question and correctly
formulated question. However, I believe that heating ocean waters is
immensely more potent masking of global warming due to very high heat
capacity of water. Using the notation in the question, masking of
global warming is dT=q*OWM, where dT is change in average temperate of
OWM and q is heat capacity of water.

Thank you for reply, Neil.
With  "net total from one year to another" I mean the difference. I.e.
annually net molten, i.e. ice not refrozen the following year.
Yes the difference is likely small.  I  want to know  if it is small
enough to ignore over  50 years.
To eliminate the apparent randomness from year to year, please compare
present ice volumes with past ice volumes 10, 50 and
100 years ago, as far as data is possible to obtain.
It doesn't matter where the ice ends up, we are looking for how much
heat the net melting of it consumes.
Pls ignore evaporation combined with or following the melting. 
(That may be a further masking of temperature increase, since soft
water evaporates faster than salt water, and
 each tonne cold  water evaporated corresponds to the heating of some
600 tonnes water 1 degree C. - Another question! )
The question to be answered now by the calculation is "How much would
the temperature increase per year if there
was no ice left before the freezing season starts each year",
considering only the latent heat of fusion..
Once that number is known as a function of "tonnes ice net molten per
year",
better predictions of  future temperature rises are possible.

At a scenario  "no ice left", simply add the dT calculated. (worst
case scenario..)
Regarding mentioned potential scenarios "where the water ends up", we
shall probably include heating of this water
from zero to ocean mean temperature.  If this is 10 dgr.C(?) and
included, the factor 50 shall be changed to 60.
The fact that the total volume of sea water increases year by year can
 be ignored now as it can easily be adjusted
for afterwards in equation.
Some interesting differential calculations can also be setup based on
that only a small percentage "surface water"
is prevented to heat up quicker from the effect . The time constant 
is some 100 years for the bulk of the water in
the depths of oceans to be affected by surface water heating.  That
also buffers any surface warming, i.e. acts as
another huge heat sink, but to be left out for now.
With the constants in the basic equation asked for in the questions
other equations can easily be set up.
Please provide both "annualy average molten ice" and present total
ice.

 
The question was prompted by recently published  predictions that
"there will be no permanently frozen sea ice left
around the north pole by 2080", accurate or not.
Best Regards Sten

Thank you jigari.
The discussion  raises the question of what the definition of global
warming is?
I thought it was the mean temperature of the ocean, but I may be
wrong. Please advise.
We need figures for both  mean ocean surface temperatures and mean
ocean temperatures, plus
figures for mean atmosphere temperatures. 
Regards Sten

If I only could define global warming... If changes in average
temperatures of deep ocean are not accounted, then plenty of warming
is masked in deep ocean, which is the bulk of world's water mass and
has huge heating capacity. Considering that residence time of deep
ocean waters can be 500 years, however, the uptake of heat can be slow
but an inevitable process. But your question is on faster time scales
(decades) so the question is how much of masking by deep ocean (if it
is not already accounted) is relevant.