Sunday, May 3, 2015

Does Earth Possess a Second Season?

Earth's changing distance from the Sun

Motivated by the observation that for approximately 18 years, global warming has been essentially constant -- a behavior on Nature's part that not a single climate model predicted -- I decided to look more closely at the scientific basis for Catastrophic Anthropogenic Global Warming (CAGW), recently sanitized (to protect the children?) to the more innocuous "Climate Change". Catastrophic Warmists claim that human production of Carbon Dioxide (CO2) is warming the Earth via the greenhouse effect and that the magnitude of this warming will soon be so immense as to be termed catastrophic. (See below for a "spaghetti graph" of climate model predictions versus Nature's response).

CAGW skeptics (sometimes termed "climate deniers") believe that the Earth is indeed warming and that some of this warming is surely due to human-produced CO2, but skeptics suspect that the magnitude of this CO2-induced warming has yet to be correctly modeled by climate scientists and has probably been exaggerated. While atmospheric CO2 continues to increase -- CO2 concentration recently exceeded 400 ppm compared to a pre-industrial level of 280 ppm (parts per million) -- the average global temperature has remained essentially flat since the beginning of the 21th Century.

Climate scientists quantify the warming strength of a greenhouse gas as a "forcing" measured in Watts per square meter. If you aimed a 200 Watt heat lamp at a 1x1 meter Muslim prayer rug, you would be subjecting that prayer rug to a "forcing" of 200 Watts per square meter. (W/m^2).

The physics of the greenhouse effect predicts the forcing due to a doubling of CO2 to be 3.7 W/m^2 -- about the same effect on that prayer rug as a tiny Xmas tree light instead of a heat lamp. But these tiny Xmas tree lights are spread over the surface of the entire Earth so this seemingly small forcing represents an immense total input of heat into the Earth's atmosphere.

The Earth's temperature rise due to 3.7 W/m^2 of CO2 forcing is estimated to be about 1.2 degrees Centigrade.

But CO2 forcing is only a small part of the story. Climate scientists argue that "feedback effects" will amplify this modest temperature rise to truly catastrophic values. Estimates of CO2 - induced warming WITH FEEDBACK range from 2 to 6 Centigrade degrees for a doubling of CO2. Differing estimates of this crucial feedback factor account for the spaghetti-like quality of climate model predictions.

The main source of this conjectured feedback is water vapor which is a more powerful greenhouse gas than CO2. When increased CO2 heats the atmosphere, more water vapor can be stored in the heated air. This extra water vapor causes more global warming than the CO2 alone.

BARE CO2 plus FEEDBACK = Catastrophic Anthropogenic Global Warming.

The crux of the global warming controversy is whether current climate models are reliable enough to guide public policy. The correct estimation of feedback factors is a big part of this controversy.

The global warming debate is much too large a topic for a blog post. Here I want to discuss a discovery that is probably not original but which I have never seen discussed in the global warming literature. Does Earth have a "second season"?

Everyone knows that the Earth goes around the sun and that Earth's orbit is not circular but is shaped like an ellipse (a fact discovered by Johannes Kepler in the 17th Century). Traveling this oval path, the Earth is closest to the Sun in January (producing record high winter tides in Santa Cruz) and furtherest from the Sun in July.

When the Earth is close to the Sun (perihelion) it should be gathering more heat. And at aphelion, less heat will fall upon us. Just for fun I decided to calculate this dependable yearly change in solar radiation and compare this number with the 3.7 Watts/m^2 forcing due to CO2 doubling.

This is a simple physics problem. The change in Earth-Sun distance between perihelion and aphelion is 3.33%. Elementary calculus shows that the inverse-square law turns this 3.33% distance change into a 6.66% intensity change in the amount of solar radiation reaching Earth.

I looked up the intensity of sunlight at the top of the atmosphere. Bare solar radiation is 1350 Watts/m^2. But not all of that sunlight reaches the Earth's surface. The fraction of light reflected from a planet's surface is called its "albedo" (from the Latin term for "whiteness"). Mainly due to its bright white clouds, Earth's albedo is about 30% (compared to the dull Moon's 12% reflectivity). Subtracting reflected sunlight gives a nice round number for solar intensity at the Earth's surface -- 1000 Watts/m^2.

The 6.66% change in solar intensity amounts to a yearly change of 66.6 Watts/m^2 at the Earth's surface. That's a change in radiative forcing that's 18 times greater than the forcing (3.7 Watts/m^2) due to CO2 doubling!!! What a surprise!! Periodic solar forcing is immense!

Not so fast, Nick. Most of this solar radiation strikes the (spherical) Earth at a slant. And none of this radiation strikes the night side. To get a fair estimate of the "effective yearly change in total solar forcing" this number must be divided by 4. (Books on climate change explain why this correction factor for the spherical Earth is just 4 and not some complicated factor of pi.)

Dividing by four gives an effective yearly change in total solar forcing of 16.6 Watts/m^2 -- a factor of 4.5 greater than the calculated forcing due to a doubling of CO2.

Nearly 5 times as intense as the CO2 forcing -- and many times faster: Rate of solar forcing is measured in months compared to decades for CO2!

And that's just the BARE solar forcing before water-vapor FEEDBACK is factored into the equation.


This simple calculation suggests that in addition to the familiar seasons due to the tilt of the Earth's axis -- an asymmetric effect that produces Winter in Melbourne while it's Summer in New York, Earth should enjoy a symmetric "second season" during which the whole Earth warms in January and the whole Earth cools in July.

Does Earth's second season actually exist? Is our much vaunted science capable of measuring this periodic pulsation in the Earth's heat budget. Does our planet possess instruments sensitive enough to register this regular thermal heartbeat superimposed on the ordinary seasons that we know so well?

[Added 12/22/15: The calculated "second-season forcing" is 4.5 times the "forcing due to a doubling of CO2". The factor 4.5 seems small, but its significance is immense. Let's be conservative and round off the ratio of SS forcing to CO2-doubling forcing to 4. Then the predictable global temperature forcing that occurs every 6 months due to the Earth's elliptic orbit is equal to 4 doublings of CO2 concentration.

The first doubling of CO2 from a preindustrial value of 280 ppm to 560 ppm is estimated to occur, IF WE DO NOTHING TO CURB CO2 EMISSIONS, by about the year 2100. This First Doubling will take approximately 150 years (from 1950 to 2100). The Second Doubling (from 560 ppm  to 1120 ppm) will take twice that long (300 years) if current CO2 emissions remain unchanged). The Third Doubling (from 1120 ppm to 2240 ppm) will take 600 years. And the Fourth Doubling (from 2240 ppm to 4480 ppm) will take 1200 additional years. To increase the CO2 global temperature forcing by a factor of 4 at the current rate of fossil fuel consumption will take 150 + 300 + 600 + 1200 years which is equal to 2250 years or 22-1/2 centuries. Ignoring the question of where we are going to find 2200+ years worth of fossil fuels, this calculation puts the second-season global temperature forcing in an appropriate perspective.

Namely: Every 6 months the Earth's eccentric orbit creates a global temperature forcing (not including feedback) equal to more than two thousand years of CO2 emissions due to fossil fuel burning at current levels of consumption. Certainly I cannot be the first person to have carried out this simple calculation. Is this conclusion silly or profound? And where is the evidence?]

Since the magnitude of second-season temperature forcing is a direct consequence of uncontested laws of physics, the Earth's observed temperature response to this forcing offers a golden opportunity to measure the magnitude of the short-term FEEDBACK FACTOR which despite its importance and the input of billions of tax-payer's dollars is still immensely uncertain -- ranging from 1.0 (no feedback to 5.0 (lots of positive feedback)

Therefore I am suggesting a new goal for 21th-Century climate scientists comparable to the search for a new planet or a new elementary particle. I propose we mount a well-funded international search to measure the magnitude (in Centigrade degrees) of the yearly heartbeat of warmth due to Earth's Second Season.

Spaghetti Graph: comparison of 90 climate models compared with satellite-measured average global temperature..(Click to enlarge.)


danamassie said...

Take a look at Milankovitch cycles.

Anonymous said...

"**SOME** CAGW skeptics (sometimes termed "climate deniers") believe that the Earth is indeed warming and that some of this warming is surely due to human-produced CO2, but **SOME** skeptics suspect that the magnitude of this CO2-induced warming has yet to be correctly modeled by climate scientists and has probably been exaggerated. Others lie their asses off all day long for laughs."

Fixed for you. No charge.

Anonymous said...

Right here

nick herbert said...

turns out NASA is flying a CERES satellite that measures incoming/outgoing radiation. Change in solar radiation due to the Second Season is easily visible in the record and is about the same magnitude as calculated in this post. See

Anonymous said...


nick herbert said...

While trying to refute my own seemingly outrageous claim, I came up with this:

While the calculation is correct, it is not the power (W/m^2) that raises the Earth's temperature but the energy (power x time).

So for a fair comparison we should calculate how much ENERGY the second season pumps into the Earth during its heating cycle. And then compare that with the amount of ENERGY trapped by CO2.

Second season ENERGY (SSE): We divide the max power 16.66 W/m^2 by 2 to get average power. And then multiply by six months to get energy in W-months/m^2. This number is 49.98 or about 50 W-month/m^2 injected into the Earth's climate in the first half of the second season. In the second half of the season, this same amount of energy is withdrawn from the Earth's account.

Trapped CO2 ENERGY (TCE). Since present-day CO2 is only 1/2 way to doubling, we divide 3.7 W/m^2 by 2 to obtain the present power, then multiply by six months to fairly compare the CO2 energy input to the SSE input. This number is about 11.1 W-month/m^2.

Conclusion: During the 6-month SS warming phase, approximately 5 times as much energy flows into the Earth than is trapped by CO2.

Another way of expressing this relationship is that, at present, 6 months of second-season warming should give rise to the same measurable temperature increase as 2-1/2 years of CO2.

I do not know if satellite measurements are sensitive enough to detect global warming due to Earth's second season, but because of its close connection to CO2-based warming, this number would be important to look for.

chas said...

Pardon my ignorance--wouldn't your scenario result in warmer summers and colder winters for the southern hemisphere?