The Impasse By Ian Beardsley 2015
1
James Lovelock for some time had said his Gaia Hypothesis said that there was no stopping of catastrophic climate change, and that it would be upon us soon, and that there was no point in being green, recycling, and so forth that these ideas had become nothing more than for profit industries and as such were counter-‐ productive in the struggle to stop global warming, because they did nothing more than make people think by going green they were solving the problem which kept them from doing the real big things that needed to be done to solve a problem which was much bigger than they really knew. He said the only habitable places would be the northern latitudes, while the middle latitudes would become desert. That the most we could be hope for was to live life as best we could for what short time would be left for us. However, he has come out after that to say he made a mistake in his calculations and that he was alarmist, not intentionally, but explained that that is the nature of science, you admit when you were wrong. He is now working on a third book where he explains how he was wrong and the though the earth is having colder winters and warmer summers, the net result is that the net average temperature is remaining about the same; that the earth is managing to keep its temperature in a safe, reasonable range. Of course he did say that global warming will happen, because we are putting more greenhouse gases into the atmosphere by industry and burning fossil fuels, but that it just won’t happen as soon as he earlier thought it would. I recently took a course in global warming science at MIT, and it seems pretty clear to me that the earth has to be warming. The earth receives about 1,370 watts of radiation from the sun per square meter. About 30% of that is reflected back into space. What is left is intercepted be the earth’s disc and distributed over its entire surface area. This warms the earth to a particular temperature. Once it reaches that temperature, more radiation has already distributed itself over the planet’s surface. Light (radiation) is constantly coming in. Therefore, for the temperature of the earth to not increase, it must constantly be losing as much radiation (energy) as it receives. When the earth is in such a state, where the average temperature of the earth over a year averaged over all the planet remains constant, it is said the earth is in equilibrium. There are many ways in which the earth can lose radiation to be in equilibrium, but one of the major ways is for it to be absorbed into the vaporization of ocean water. It takes energy to vaporize water, energy that would otherwise go into heating the Earth. When ocean water is vaporized (goes from liquid to gas) this is the formation of clouds. When the clouds condense into water droplets (precipitate) this represents further loss of energy that would have otherwise warmed the earth. Through such mechanisms the earth has been able to remain in equilibrium for some time, that is, again, to lose as much radiation as it receives, so that its average annual temperature when averaged over all geographic locations, has been able to stay steady at about 15 degrees centigrade.
2
However, since the advent of the industrial era, we have burned more fossil fuels, putting more CO2 into the atmosphere, and CO2 is a greenhouse gas. A green house gas is a gas that retains heat and warms the planet. Greenhouse gases are necessary, in that they keep the earth from getting too cold. Without an atmosphere with its green house gases, the earth would be about 18 degrees centigrade below freezing. But, too much greenhouse gases, and the earth becomes too warm. Remember, the earth needs to be in equilibrium, which means it needs to lose as much radiation as it receives. Current measurements show that the earth receives about one watt per square meter more than it loses. A watt is a joule per second, where a joule is an amount of energy. A square meter is about the size of a patch of land, a square, about one yard on each side. How much heat is that, that is heating each square meter of the earth? Well consider a 100 watt light bulb. A lot of it its energy drawn from your lamp outlet goes towards making light to light, say, your bedroom, but some of it goes towards making the bulb hot. I would estimate this excess energy we have falling upon the earth that is not being lost would be around the heat caused placing a 100 watt light bulb in the center of every square meter of the planet. It does not sound like much, but think; we are adding more and more CO2 to the earth every day, so that value is increasing, and the increasing effects are affecting the planet in more ways than one. One of the effects is what is called a feedback loop; this is where a warming planet melts more snow in the northern and southern latitudes, decreasing the ability of those latitudes to reflect sunlight back into space. This in turn makes the earth get warmer, so even more snow is melted than before, causing still less light to be reflected back into space, causing still more warming, causing more melting of snow than before,… and so on; it is a runaway effect, that is why is called negative feedback. How does the atmosphere and its greenhouse gases keep the earth warm? As we said the earth receives radiation from the sun. This radiation warms the surface of the planet. However, the radiation that reaches the surface of the earth is bounced up to the lower layer of the atmosphere, the stratosphere, and the stratosphere sends it back down to the surface. However by that time the same amount of sunlight has come from the sun to the surface of the earth. So as you can see, the light coming in from the sun plus the light emitted back to the surface of the earth by the atmosphere doubles the amount of radiation warming the surface of the planet. The more greenhouse gases we have, the warmer the planet. Just how have human activities increased CO2 levels on earth? In 1958 CO2 levels were 315 parts per million of the atmosphere. It rose to above 400 parts per million in 2013, and this change was brought about by the industrial era. And here is the point: Lovelock has said that though the summers are warmer, the winters are colder, so that the earth has managed to keep a steady temperature. But in the MIT class I took, it was stated that measurements show the earth is not in radiative equilibrium, that it receives about one watt per square meter more than it loses and therefore has to be warming.
3
We have a real situation on our hands. I cannot help but think global warming will not happen at all because there are other cycles in earth climate that can override global warming due to other more potent forces. I speak of the precession of the equinoxes and slight changes in the earth orbit that about every 20,000 years cause an ice age that lasts about 100,000 years. However, these cycles don’t occur with any precise regularity; the numerous factors that determine the climate are far too complex to determine with any exacting precision what will happen. There is one thing we can all agree on, whether we are James Lovelock, or MIT, and that is burning fossil fuels puts heat retaining gases in the atmosphere, and that does cause the planet to warm. When I say situation, I mean we have a situation in that everyone is bickering over whether or not burning greenhouse gases does this when meanwhile the situation escalates, for example, in passing a bill to build the Keystone XL Pipeline, which as Senator Bernie Sanders put perfectly is taking us in a direction towards using fossil fuels when we should be going away from that route and towards clean, renewable energy, like, solar. The human situation can best be explained by what H.G. Wells wrote in his book Mind At The End Of Its Tether, around 1950. “The Writer finds very considerable reason for believing that, within a period to be estimated by weeks and months, rather than by aeons, there has been a fundamental change in the conditions under which life,…has been going on since its beginning. “If his thinking has been sound, then this world is at the end of its tether. The end of everything we call life is close at hand, and cannot be evaded. “The writer is convinced there is no way out or round or through the impasse. It is the end. “The present writer has experimented with a number of words and phrases,.. “The Antagonist is the term the present writer will employ to express the unknown implacable which has endured life for so long and has now turned against it so implacable to wipe it out. “It is possible that hard imaginative thinking has not increased so as to keep pace with the expansion and complication of human societies and organizations. That is the darkest shadow on the hopes of mankind.” For the more mathematically inclined, I present some of the topics covered here with some simple Algebra.
4
One can generate a basic model for climate with nothing more than high school algebra using nothing more than the temperature of the sun, the distance of the earth from the sun, and the earth’s albedo, the percent of light it reflects back into space. The luminosity of the sun is: L_0=3.9E26 J/s The separation between the earth and the sun is: 1.5E11 m The solar luminosity at the earth is reduced by the inverse square law, so the solar constant is: S_0=3.9E26/4(pi)(1.5E11)^2 = 1,370 watts/square meter That is the effective energy hitting the earth per second per square meter. This radiation is equal to the temperature, T_e, to the fourth power by the steffan-‐ bolzmann constant, sigma. T_e can be called the effective temperature, the temperature entering the earth. S_0 intercepts the earth disc, (pi)r^2, and distributes itself over the entire earth surface, 4(pi)r^2, while 30% is reflected back into space due to the earth’s albedo, a, which is equal to 0.3, so (sigma)(T_e)^4 = (S_0/4)(1-‐a) from (1-‐a)(S_0)(pi)(r^2)/4(pi)(r^2) But, just as the same amount of radiation that enters the system, leaves it, to have radiative equilibrium, the atmosphere radiates back to the surface so that the radiation from the atmosphere, (sigma)(T_a)^4 plus the radiation entering the earth, (sigma)(T_e)^4 is the radiation at the surface of the earth, (sigma)(T_s)^4. However, (sigma)(T_a)^4=(sigma)(T_e)^4 and we have: (sigma)(T_s)^4=(sigma)(T_a)^4 + (sigma)(T_e)^4 = 2(sigma)(T_e)^4 T_s=(2^(1/4))(T_e)
5
(sigma)(T_e)^4=(S_0/4)(1-‐a) sigma = 5.67E-‐8 S_0=1,370 (1,370/4)(1-‐0.3)=(1,370/4)(0.7)=239.75 (sigma)(T_e)^4=239.75 (T_e)^4 = (238.75)/(5.67E-‐8) = 4.228E9 T_e=255 degrees kelvin So, for the temperature at the surface of the Earth: (sigma)(T_s) = 2(sigma)(T_e)^4 T_s=(2^(1/4))T_e or T_s = 1.189(255) = 303 degrees Kelvin Let’s convert that to degrees centigrade: Degrees Centigrade = 303 -‐ 273 = 30 degrees centigrade And, let’s convert that to Fahrenheit: Degrees Fahrenheight = 30(9/5)+32=86 Degrees Fahrenheit In reality this is warmer than the average annual temperature at the surface of the earth, but, in this model, we only considered radiative heat transfer and not convective heat transfer. In other words, there is cooling due to vaporization of water (the formation of clouds) and due to the condensation of water vapor into rain droplets (precipitation or the formation of rain).
6
Summary The incoming radiation from the sun is about 1370 watts per square meter as determined by the energy per second emitted by the sun reduced by the inverse square law at earth orbit. We calculate the total absorbed energy intercepted by the Earth's disc (pi)r^2, its distribution over its surface area 4(pi)r^2 and take into account that about 30% of that is reflected back into space, so the effective radiation hitting the Earth's surface is about 70% of the incoming radiation reduced by four. Radiative energy is equal to temperature to the fourth power by the Stefan-‐ boltzmann constant. However, the effective incoming radiation is also trapped by greenhouse gases and emitted down towards the surface of the earth (as well as emitted up towards space from this lower atmosphere called the troposphere), the most powerful greenhouse gas being CO2 (Carbon Dioxide) and most abundant and important is water vapour. This doubles the radiation warming the surface of the planet. The atmosphere is predominately Nitrogen gas (N2) and Oxygen gas (O2), about 95 percent. These gases, however, are not greenhouse gases. The greenhouse gas CO2, though only exists in trace amounts, and water vapour, bring the temperature of the Earth up from minus 18 degrees centigrade (18 below freezing) to an observed average of plus 15 degrees centigrade (15 degrees above freezing). Without these crucial greenhouse gases, the Earth would be frozen. They have this enormous effect on warming the planet even with CO2 existing only at 400 parts per million. It occurs naturally and makes life on Earth possible. However, too much of it and the Earth can be too warm, and we are now seeing amounts beyond the natural levels through anthropogenic sources, that are making the Earth warmer than is favorable for the conditions best for life to be maximally sustainable. We see this increase in CO2 beginning with the industrial era. The sectors most responsible for the increase are power, industry, and transportation. Looking at records of CO2 amounts we see that it was 315 parts per million in 1958 and rose to 390 parts per million in 2010. It rose above 400 in 2013. Other greenhouse gases are methane (CH4) and Nitrous Oxide (N2O). Agricultural activities dominate emissions for nitrous oxide and methane. A healthy earth is one that is in radiative equilibrium, that is, it loses as much radiation as it receives. Currently we are slightly out of radiative balance, the Earth absorbs about one watt per square meter more than it loses. That means its temperature is not steady, but increasing.
7
Here are a couple programs I wrote in the language C that model not just climate for the earth but for planets around other stars. Discover 04 (Goldilocks.c) #include <stdio.h> #include <math.h> int main (void) { printf("This program finds the habitable zone of a star,...\n"); printf("And the surface temperature of the planet in the habitable zone\n"); float LC, r, L, HZ, AU, a, root, number, N, answer, C, F; printf("What is the luminosity of the star in Joules per second? \n"); scanf("%f", &L); AU=L/3.9E26; HZ=sqrt(L/3.9E26); printf("The luminosity of the star in solar luminosities is: %f\n", AU); printf("The habitable zone of the star is in AU: %f\n", HZ); r = HZ*1.5E11; LC=L/(4*3.141*r*r); printf("luminosity constant of star in watts per square meter: %f\n", LC); printf("What is the albedo of the planet? (between 0 and 1): "); scanf("%f", &a); N = (1-a)*LC/(4*(5.67E-8)); root = sqrt(N); number = sqrt(root); answer = 1.189*number; printf("The surface temperature of the planet is: %f K\n", answer); C = answer - 273; F = (C*1.8) + 32; printf("That is %f C, or %f F \n", C, F); }
8
Discover 08 #include <stdio.h> #include <math.h> int main(void) { float s, a, l, b, r, AU, N, root, number, answer, C, F; printf("This program calculates the temperature of a planet,...\n"); printf("Given the luminosity of the star and the albedo of the planet,..\n"); printf("What is brightness of the star in solar luminosities? "); scanf("%f", &s); printf("What is the albedo of the planet (0-‐1)? "); scanf("%f", &a); printf("What is the distance of the planet from the star in AU? "); scanf("%f", &AU); r=1.5E11*AU; l=3.9E26*s; b=l/(4*3.141*r*r); N=(1-‐a)*(b)/(4*(5.67E-‐8)); root=sqrt(N); number=sqrt(root); answer=1.189*(number); printf("The surface temperature of the planet is: %f K\n", answer); C=answer-‐273; F=(C*1.8)+32; printf("That is %f C, or %f F", C, F); printf("\n"); }
9
Here is a sample running of those programs: jharvard@appliance (~): cd dropbox/descubrir bash: cd: dropbox/descubrir: No such file or directory jharvard@appliance (~): cd Dropbox/descubrir jharvard@appliance (~/Dropbox/descubrir): ./discover04 This program finds the habitable zone of a star,... And the surface temperature of the planet in the habitable zone What is the luminosity of the star in Joules per second? 9E26 The luminosity of the star in solar luminosities is: 2.307692 The habitable zone of the star is in AU: 1.519109 luminosity constant of star in watts per square meter: 1379.603149 What is the albedo of the planet? (between 0 and 1): 0.618 The surface temperature of the planet is: 261.051056 K That is -11.948944 C, or 10.491900 F jharvard@appliance (~/Dropbox/descubrir): ./discover08 This program calculates the temperature of a planet,... Given the luminosity of the star and the albedo of the planet,.. What is brightness of the star in solar luminosities? 2.3 What is the albedo of the planet (0-1)? 0.618 What is the distance of the planet from the star in AU? 1.5 The surface temperature of the planet is: 262.489410 K That is -10.510590 C, or 13.080938 F
10
Ian Beardsley February 18, 2015
11