Earth_heat_budget

Earth's Heat Budget

Copyright 2010 - 2025 by Marek A. Suchenek

An article written in April 2010, expanded in November 2010, cartoon added in November 2019.

The calculations included in this article require knowledge of high school physics.

Mass of Earth's air

The atmosphere has a mass of about five quintillion kilograms, that is

Atm_mass = 5x10^18 kg

Earth's oceans and ice


	Volume in Thousands of Cubic Kilometers	Percentage of Total Water on Earth	Remarks
Oceans	1,310,302	97.3	This is salty sea water.
Ice	29,492	2.2	Much of this ice is in the Antarctic
Adapted from: Environment Canada

(Source: Volume of Earth's Oceans

http://hypertextbook.com/facts/2001/SyedQadri.shtml, An educational, Fair Use website)

Factor k (the weight of 1 cubic kilometer of water)

1 cu m of water weights 1 metric ton or 10^3 kg. So,

1 cu km = (1 km)^3 = (10^3 m)^3 = (10^3)^3 cu m = 10^9 cu m = 10^3x10^9 kg = 10^12 kg = 1 gigatonne.

k = 10^12 kg/cu km = 1 gigatonne/cu km

Mass of Earth's water

Water_mass = 1.3x10^9 cu km = 1.3x10^9x10^12 kg =
= 1.3x10^21 kg = 1,300,000,000 gigatonnes

Mass of Earth's ice

Ice_mass= 2.9x10^7 cu km = 2.9x10^7x10^12 kg = 2.9x10^19 kg = 29,000,000 gigatonnes

Specific heat of water

Water_sh = 1 cal/g x Cdeg = 1kcal/kg x Cdeg

Specific heat of air (atmosphere)

Atm_sh = 0.241 cal/g x Cdeg = 0.241 kcal/kg x Cdeg

Water/ice heat of fusion

Ice_fh = 79.72 cal/g = 79.72 kcal/kg

How much melting ice would balance 1 Cdeg increase of the atmosphere temp?

M [kg] = H [Kcal] / Ice_fh [kcal/kg] =
= 1 [Cdeg] x Atm_mass [kg] x Ath_sh [kcal/kg x Cdeg] / Ice_fh [kcal/kg] =
= 5x10^18 / 80 = 5x10^18 / 0.8x10^2 =
= 6.25x10^16 kg

The same things as volume in cu km:

V [cu km] = M [kg] / k [kg/cu km] = 6.25x10^16 / 10^12 =
= 6.25x10^4 cu km

The same thing as the percentage of Earth's ice:

M_i% = M [kg]/Ice_mass [kg] = 6.25x10^16 / 2.9x10^19 = 2.2x10^-3 = 0.22x10^-2 =
= 0.22 %

The same thing as the percentage of Earth's water:

M_w% = M [kg] / Water_mass [kg] = 6.25x10^16 / 1.3x10^21 = 4.8x10^-5 = 0.0048x10^-2 =
= 0.0048 %

Ocean area

Ocean_area = 361x10^6 sq km = 3.61x10^8 sq km

How much deeper the oceans would become as a result of balancing of 1 Cdeg increase of the atmosphere with melting ice:

D [km] = V [cu km] / Ocean_area [km] = 6.25x10^4 / 3.61x10^8 = 1.73x10^-4 km =
= 1.73x10^-1 m = 0.173 m = 17.3 cm

The Archimedean law would nullify this effect, at least partially.

Although about 98% of Earth's ice is grounded, most (about 75%) of the ice that melted since 1960 was floating, as the following table shows:

Earth's ice	Volume (km³)	Fraction of world ice	Est. change in volume since 1960 (km³)
Grounded ice only	~29,340,000	97.9 %	-2,250
Floating ice only	~620,000	2.1 %	-6,900

(Table has been adopted from "What If All the Ice Melts?" Myths and Realities http://www.johnstonsarchive.net/environment/waterworld.html.)

Because floating ice does not rise water level significantly, only about 25% of melting ice might have contributed to rising of the sea level. So, the actually observed sea level increase in the mentioned above scenario would be approx. 17.3/4 cm = 4.3 cm.

Here is a link to a vidio with an experiment with melting ice floating in a glass tank of water: http://oceandrilling.coe.tamu.edu/curriculum/Sea_Level/Ice_Volume/floatingice.html. (A similar experiment was used to incorrectly conclude that grounded ice melting will rise the sea level by the volume of water obtained from the ice; a more adequate experiment should rest the right hand side of the platform with ice on a floating buoy rather than on the bottom of the tank; here is a link to that flawed experiment: http://oceandrilling.coe.tamu.edu/curriculum/Sea_Level/Ice_Volume/ice.html.)

Since the grounded ice rests on crust that is floating on Earth's core, the melting of grounded ice must cause rising of the crust below the melting ice and lowering the oceans' floor, diminishing the rising of the sea level even more.

Exercise: How much lava (in cubic kilometers) will melt the same amount of ice?

How much ocean temp increase would balance 1 Cdeg increase of the atmosphere temp?

T_delta [Cdeg] = H [Kcal] / (Water_mass [kg] x Water_sh [Kcal/kg x Cdeg]) =
= 5x10^18 /(1.3x10^21 x 1) = 3.8x10^-3 = 0.0038 Cdeg =approx (1/3)x10^-2 Cdeg =
= 1/300 Cdeg

In other words, the proportionality constant between the same increase of ocean temp and atmpsphere temp is 1/300.

Measured annual Earth's ice loss

Sources:

East Antarctic Ice Loss

December 9, 2009http://www.greenmuze.com/climate/heat/1951-east-antarctic-ice-loss.html

NASA has recently released updated measurements of ice loss in Antarctica, revising their predictions upwards by almost 40%. Previously, the East Antarctic ice sheet was thought to be stable but now an estimated 57 gigatons (57,000,000,000 tons) of ice per year has been lost over the last 3 years. West Antarctic ice loss is also confirmed at 132 gigatons of ice per year.

NASA Uses New Method to Estimate Earth Mass Movements
September 14, 2010
http://www.jpl.nasa.gov/news/news.cfm?release=2010-298

"Using the new methodology, the researchers, led by Xiaoping Wu of JPL, calculated new estimates of ice loss in Greenland and Antarctica that are significantly smaller than previous estimates. According to the team's estimates, mass losses between 2002 and 2008 measured 104 (plus or minus 23) gigatonnes a year in Greenland, 101 (plus or minus 23) gigatonnes a year in Alaska/Yukon, and 64 (plus or minus 32) gigatonnes a year in West Antarctica. A gigatonne is one billion metric tons, or more than 2.2 trillion pounds."

Personal communication from Xiaoping Wu of NASA-JPL (November 11, 2010):

The trend in East Antarctica is a loss of 23 Gt/yr. It is separate from
that of the West Antarctica.

gigatonne = 1 billion metric tons = 10^9 tones = 10^12 kg

So, measured annual loss of ice mass between 2002 and 2008 was:

57 + 104 + 101 + 64 plus or minus (23 + 23 + 32) gigatonnes/year = 326 plus or minus 78 gigatonnes/year <= 404 gigatonnes/year

So, it would take at least 29,000,000 gigatonnes/404 gigatonnes/year = 72,000 years to melt all Earth's (Arctic and Antarctic) ice at this rate.

Estimate of the actual rate of global warming

Since, acording to the calculations presented above, melting of 6.25x10^16 kg of ice nullifies 1 Cdeg increase of Earth's atmospheric temperature, the measured loss of ice corresponds to 4.04x10^14/6.25x10^16 Cdeg = 0.65x10^-2 Cdeg = 0.0065 Cdeg warming of the Earth's atmosphere, and 17.3x0.0064 cm = 0.1 cm rise of oceans' level per year.

It appears that the above is the actual rate of the global warming. It amounts to about 0.7 Cdeg increase per 100 years. Until most of Earth's ice is melted (est. 72,000 years from now), it will not cause actual increase of atmosphere's temperature increase.

I wonder how did the scientists that reached consensus on "anthropogenic global warming" (AGW) theory come up with a figure that is roughly 100 times larger? Is it a fault of computer models and simulations that they used? Or is it because they forgot some physics that they learned in high school? Even if, for sake of an argument, one assumed that their estimate was correct, it would still take some 840 years to melt all Earth's ice and see the actual permanent increase of average temperature of atmosphere after that. So, where is the urgency that they propagate in their alarmist calls to stop the AGW now?

"Dissenters" to anthropogenic global warming (AGW) theory write:

Re: East Antarctic Ice Loss
http://www.greenmuze.com/climate/heat/1951-east-antarctic-ice-loss.html

I am a geophysicist working on Antarctic digital elevation models and I have just read your comment about potential sea level rise. I am afraid you are wrong...the work you quote is by Chen et al 2009 using GRACE satelite data....the total ice loss for the continent as a whole is estimated at 220 giga tonnes per year...this amount of ice when melted will raise the global sea level a total of 0.7 millimetres per year......if you do not believe this, then please check it for yourself.......so in 10 years it will be 7mm and in 100 years it will be 7 cms and not the and I quote you ......

"The ice loss has the potential to raise sea levels by anything from a few metres to over 70 metres (230ft) if the high melt rate continues over the coming decades."

Also you should tell your readers that the total amount of ice in Antarctica is 30,000,000 cubic kms or to put it into your terms
30,000,000,000,000,000,000 tons so in actual fact the current ice loss for Antarctica is actually 0.00065% of its total mass.

written by snowmaneasy , January 12, 2010