(stuff about ocean depth and my figuring that the oceans may rise a meter
from thermal expansion)
How long would it take the oceans to rise in temp by 2 degrees ?
Let me try an estimate for that...
The first graph in the Wiki article on global warming looks to me like
rising at a rate of about .035 degree C per year after 1979. Suppose this
rate gets sustained.
I somehow remember doing a calculation in the past for thermal time
constant of the ocean mass, and came up with a century or somewhat more.
Feed a .035 degree per year slope starting from 1979 into a first order
lowpass filter with a time constant of a century, and I come up with a
guess of 130 years, or 2109.
And half this warmup of the ocean mass would occur in roughly the last
50 years of this 130 year period. And with the thermal expansion
coefficient being non-constant and increasing, the halfway point of the
sea level rise of this 130 year period will be even farther into it.
==================================================================
Let me take a new stab at thermal time constant of the ocean mass...
Solar constant at sea level with sun at zenith and really clear air is
1100 watts per square meter if I remember correctly. It could be closer
to 1,000. Ratio of a sphere's surface area to cross section is 4, so
divide 1100 by 4 to get 275 watts per square meter. Half this for average
extent and opacity of cloud cover, for average insolation of 137.5 watts
per square meter. Multiply by .96 for water being about 4% reflective,
for 132 watts per square meter.
Average Earth surface temperature is nearly enough 288 K. So I will use
132 watts per square meter and 288 K.
Let's suppose the radiation absorbed takes a 1% jump from 132 to 133.32
watts per square meter. In a first order of approximation, a 1% increase
in incoming radiation will increase the surface temperature by .25%. This
is neglecting interaction of spectral shift of outgoing radiation with
ability to radiate it changing with wavelength, and this neglects feedback
mechanisms such as change of the Earth's ability to absorb radiation.
So that extra 1.32 watt per square meter in a first order approximation
is expected to warm things up by .72 degree K.
Water has a specific heat of 4.19 joules per gram per degree K, maybe a
bit less for salt water. I would guess 4.15.
A 1 square meter column of average depth sea water 3.71 km deep has a
mass of close enough to 3.75E9 grams. Multiply this by 4.15 and .72, and
it looks like about 1.12E10 joules is needed to warm a square meter of
ocean all the way down by .72 degree.
Divide that by 1.32 watts, and I get a thermal time constant of about
8.5E9 seconds, or about 270 years.
With a thermal time constant of 270 years and planet surface temperature
rising .035 degree per year, I would expect the average ocean mass
temperature to be 2 degrees warmer than it was in 1979 sometime around
2150-2170.
- Don Klipstein (
[email protected])