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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

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Climate Hustle

Evan

Evan and Nancy (wife) live 30 minutes north of Minneapolis, Minnesota (USA). We both grew up in Minnesota, but spent about 2 years in Europe (mostly Germany) and 9 years in Japan (just north of Tokyo). We graduated from the University of Minnesota with Mechanical Engineering degrees. Nancy works as a scientific editor, editing mostly for Japanese clients, and I work as a Chemical Engineering consultant.

My thesis work was modeling particle formation and growth dynamics. The model that I developed was adopted by the US Environmental Protection Agency for modeling particle dynamics in the atmosphere. This is my one tenuous link to climate science, because my professional career developed around modeling the formation and growth of particles in commercial chemical reactors, for making particles used in commercial products.

Nancy and I are committed to reducing our own carbon footprint while working to educate others on the severity of climate change and needed solutions. I have been heavily influenced by Kevin Anderson's professional message and personal example, which among other things recently motivated me to become vegetarian. We are also planning to build an energy-efficient house, and we recently traded in our truck for an electric vehicle. My Climate-Change communication efforts currently involve working with the SkS team to write analogies to clarify the science of Climate Change.

 

Recent blog posts


SkS Analogy 19 - A table full of crystal and ideal temperature

Posted on 7 March 2019 by Evan & jg

Tag Line

A table stacked high with delicate crystal is beautiful to look at, but impossible to move without significant breakage.

Elevator Statement

Stack crystal plates, bowls, glasses, and figurines on top of each other on a table. Done by a skilled artist it is a pleasure to look at. But try to move this delicate work of art from one place to another. The faster you move it the more damage there will be. The more crystal that is placed on the table and the higher it is stacked, the more precarious it is to keep balanced, and the more breakage occurs if the table is moved.

If the table had been placed at a different location before stacking the crystal, it could have been filled with the same crystal and created a similar, beautiful masterpiece at a different location. But stacking the table full of crystal and then moving it to a new place causes significant breakage.

Table full of crystal
So it is when we populate Earth with 8 billion beautiful people, inhabiting all of the available habitable zones, and then alter the location of the habitable zones through rapid changes in temperature, precipitation, and storms. Increasing the average temperature of the earth is not so much the problem as is the rate at which we are changing the temperature. The faster we raise the temperature, the faster climate changes, the quicker that habitable zones move, and the less time there is to adapt (i.e., move from one habitable zone to another).

Some ask rhetorically what Earth’s ideal temperature is. This is like asking what a table’s ideal location is. Damage occurs to the crystal on a table not because it is or is not in the ideal location, but because the table is moved after it is fully loaded with delicate crystal.

To minimize breakage, a table stacked high with crystal must either be moved extremely slowly, or left in its current location.

Read more...

13 comments


SkS Analogy 18 - Cliff jumping and temperature changes

Posted on 30 January 2019 by Evan & jg

Tag Line

Regardless the height of the cliff, jumping from cliffs is deadly.

Elevator Statement

Regardless of the height of a cliff, jumping from cliffs is deadly. Hang-gliding from cliffs thrills. Jumping from cliffs kills. Jumping 10 m from a cliff that is 1000 m above sea level hurts just as much as jumping 10 m from a cliff that is 900 m above sea level.

Increasing or decreasing the global average temperature causes sea level to rise or fall. Rapidly increasing or decreasing the global average temperature will likely cause sea level to rapidly rise or fall. It does not matter what the current global average temperature is. Causing the global average temperature to jump, as we are, causes sea level to jump. A snail can outrun sea level change, but houses, sky scrapers, buildings, subways, and roads move slower than snails. They sit where they are and drown. Are your children and grand children prepared for this coming future? Is there anything we can do to slow down the ongoing global temperature jump?

Cliff Jumping

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18 comments


SkS Analogy 17 - Lotteries, evaporation, and superstorms

Posted on 24 January 2019 by Evan & jg

Tag Line

Evaporation is like a lottery. Lottery winners finance our storms.

Elevator Statement

Each day 10,000 people each put $100 into a million-dollar lottery where winner takes all. Because lottery winnings are taxed, the winner receives $600,000 and the government receives $400,000. This leaves the people who bought the lottery tickets poorer, one person richer, and the government more powerful.

A puddle of water loses water due to evaporation. Evaporation occurs when many neighboring molecules share a little of their energy with a single molecule that gains enough energy to leave the puddle and fly away into the atmosphere. This molecule wins the lottery. The high energy required to send a single water molecule into the atmosphere causes the energy of the other molecules in the puddle to decrease (i.e., the temperature of the puddle decreases), while the amount of water vapor in the atmosphere increases. A fraction of the water vapor in the atmosphere is available to storms, so that as the total amount of water vapor in the atmosphere increases, the amount available to storms also increases (i.e., the fraction of a larger number means more is available).  Because storms get their power from condensing water vapor, as more water vapor is added to the atmosphere more water vapor is available to storms, which increases their power. Therefore, evaporation leaves the puddle with a less energy, the atmosphere with more water vapor, and storms with more power. This is how evaporation keeps Earth cool and supercharges storms.

Evaporation adds power to the atmosphere

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6 comments


Climate Carbon Bookkeeping

Posted on 20 December 2018 by Evan & jg

The question often arises as to how we know that the current year-to-year buildup of CO2 is due to human activities. One way is to do simple bookkeeping of how much of each of the major types of fossil fuels we burn each year, and the predicted CO2 buildup implied by the known yearly combustion rate. Burning fossil fuels produce two major products: CO2 and H2O. As long as we know the carbon and hydrogen content of each of the major types of fossil fuels, it is relatively straightforward to calculate the amount of CO2 released each year. The point of this article is to demonstrate how we do such a calculation, and to demonstrate that such a calculation clearly shows that the measured annual rise of CO2 is due to human activities.

Climate Carbon Bookkeeping

CO2 emissions occur primarily due to burning coal, oil, natural gas, and through deforestation. Because the consumption rates of coal, oil, and natural gas are known, and because other groups monitor the state of forests, it is easy to estimate the CO2 emissions from these sources. Part of the CO2 emitted accumulates in the atmosphere and remains there for centuries to millennia, but part of the CO2 emitted is quickly reabsorbed back into the biosphere (water, soil, and rocks). By using a rough estimate that about 50% of emissions are reabsorbed into the biosphere,  it is possible to estimate the atmospheric CO2 accumulation due to human emissions.

Before the Industrial Revolution (which started about 1800 AD) CO2 natural emissions were roughly in balance with CO2 natural sinks, for no net accumulation. This is demonstrated by CO2 estimated from ice-core samples for the period 1000 AD to present, shown in Figure 1. From the dawn of the Industrial Revolution until now atmospheric CO2 concentrations have been steadily increasing. It is easy to show that the atmospheric accumulation of CO2 since the dawn of the Industrial Revolution is due mostly to the burning of fossil fuels, because we know from year to year how much oil, natural gas, coal, and forest trees we are burning, and we know how many molecules are in the atmosphere. Given this data, we can calculate the expected annual increase in CO2 and compare it to the measured annual increase.

CO2 concentrations in Earth’s atmosphere are tracked as the number of CO2 molecules per million molecules [parts per million: ppm]. Figure 1 indicates that 200 years ago this value was about 280 ppm, whereas today it is close to 410 ppm, and from 2005 - 2014 it  increased an average of about 2.1 ppm/year. To see that this increase is due primarily to burning fossil fuels and deforestation, we simply divide the number of carbon atoms emitted from Anthropogenic sources by the number of molecules in the atmosphere. It requires a little math, but no computer models.

Figure 1. Atmospheric CO2 estimated from ice-core samples, combined with measurements that started in 1958 (represented by the dark blue line). This graph is available at https://www.co2levels.org/

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13 comments


SkS Analogy 16 - Arctic ice, sailboat keels, and wild weather

Posted on 3 December 2018 by Evan & jg

Tag Line

Slowly pull up the keel of a sailboat as it’s racing straight across a large lake, and soon it will begin to wallow around at the mercy of the wind.

Elevator Statement

In the physical world large differences cause the motion of things:

  • Heat flows from hot to cold (like from inside your warm house to the cold outside)
  • Water flows from high to low places (think waterfall)
  • Air flows from high to low pressure (like from inside an air compressor through the nozzle and out)

The temperature difference between the warm Equator and the cold Arctic causes large-scale air motion to the Arctic. Like a river raging straight down a steep mountain, a large temperature difference causes air to move northward from the Equator fast and straight, bending with the rotation of the Earth to create a well-behaved jet stream that moves from West to East.  The motion is reminiscent of a well-trimmed sailboat challenging the wind as it races straight and true across a large body of water.

It is well documented that the Arctic is warming at 2 to 4 times the global average rate (read here and here). This decreases the temperature difference between the Equator and the Arctic, which decreases the driving force for the Jet Stream winds. The weakened driving force allows the jet stream to wallow around, just like a river that slowly meanders back and forth when it hits an area with only a slight elevation change (think flat). The image is similar to how a sailboat flounders about when the keel is pulled up: moving at the mercy of the wind instead of challenging it. In the same way that healthy arctic ice is linked with a strong, healthy jet stream that tracks relatively straight and true around the earth, so too a strong, deep keel is linked to a sailboat that tracks straight and true.

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8 comments


SkS Analogy 15 - Ice Tea and Temperature Rise

Posted on 16 October 2018 by Evan & jg

Tag Line

Even on a hot day, as long as your glass of tea has ice it is a nice, cool drink. Only when the ice disappears does your drink start to warm up.

Elevator Statement

The height of a balloon above the ground is not proportional to the amount of hot air you put into the envelope.1 In fact, when you first start filling a balloon all that happens is that the hot air causes the envelope to lift off of the ground, applying tension to the basket and its occupants, but there is no upward motion of the balloon at that point. You pump in more and more hot air, and if select US Senators were standing by they would likely proclaim that there is absolutely no effect of hot air on the balloon.

The problem, of course, is that a huge amount of hot air must be injected into the balloon just to overcome the weight of the envelope, the basket, and its occupants. As long as the upward force is less than the downward, restraining force, nothing happens. But once the upward force overcomes the downward force, up you go, and any small addition of hot air2 at this point causes you to accelerate faster and faster skyward.

Ever wonder why you put ice cubes into your water and not cold rocks? The difference between ice and rocks is that the temperature of a cold rock will slowly increase along with the liquid it is trying to keep cold, and will do no better keeping the liquid cool than the cool liquid itself. Cold rocks do nothing to keep your drink cool.

However, ice is effective because as long as there is ice in your glass, the combination of ice and tea will stay near 0°C. As soon as the ice melts and is completely gone the temperature of your tea starts to rise, and soon your drink becomes warm and tasteless. We have all used ice in our drinks, but likely without ever realizing that the reason for using ice is that by definition, the temperature of ice cannot rise above 0°C, whereas a cold rock will easily warm up past 0°C. So if there is ice in your glass, it stabilizes the temperature to near 0°C. Read on in the next section to learn about the property of ice that keeps your ice tea near 0°C.

In the last 40 years we’ve lost about 50% of the Arctic ice area and about 70% of the volume.3 Time to ask Earth’s bartender for more ice for our drink, lest the temperature of the Arctic becomes too warm.

Ice balloons temperature rise

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7 comments


SkS Analogy 14 - Inertia and Inevitability

Posted on 10 October 2018 by Evan & jg

Tag Line

Inertia is your friend … until it isn’t.

Elevator Statement

Inertia delays the response …
  But for each CO2 level there is a guaranteed response …
        Be patient, the response is coming …
                     And when it finally comes there’s no going back.

Tie a rubber band to a weight. Move your hand rapidly1 away from the weight,2 stop your hand,3 wait, and the slowly accelerating weight will eventually slam into your hand.4

Think of your hand as CO2 concentration and the weight as atmospheric temperature. Moving your hand quickly is like rapidly increasing CO2 concentration.5 The motion of the weight is like rising atmospheric temperature, where the position of the weight is an indication of atmospheric temperature. A heavy weight causes a large time delay between the motion of your hand and the motion of the weight, similar to the delay between GreenHouse-Gas (GHG) emissions and warming caused by the thermal inertia of the oceans.

So just like connecting your hand to a weight with a rubber band, moving your hand quickly does not guarantee that the weight will initially move quickly. But if you are patient, and if you experiment by moving your hand at different rates, you will find that the quicker and further you move your hand the faster and harder the weight will eventually slam into your hand. You just have to be patient to let the weight catch up.

For another example of the effect of inertia in a system with a small force moving a large weight we turn to NASA. NASA uses solar-powered ion thrusters to power its current generation of deep-space voyagers. Ion thrusters use electrical energy provided by solar panels to accelerate individual xenon atoms, ejecting them at high velocity out the back of the rocket engine. The beauty of ion thrusters is that they combine an essentially infinite energy source (i.e., the sun), together with on-board fuel (xenon) to provide high-efficiency propulsion. The down side is that the thrust/weight ratio is so low that it may take months to years for the probe to reach maximum velocity.

Noting that the heating effect of GHGs in Earth’s atmosphere is relatively low, and that the mass of the oceans is massive, just as ion-thrust engines require months to years to accelerate their payload up to maximum speed, GHGs in Earth’s atmosphere require years to decades to accelerate their “payload” up to maximum temperature, with a typical cause-and-effect time constant of about 30 years: the length of a typical house mortgage.

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4 comments


SkS Analogy 13 - Water glasses and Greenhouse gases

Posted on 17 July 2018 by Evan & jg

Tag Line

How do you add water to a full glass?

Elevator Statement

Adding water to a full glass causes the water to rain over the sides.
    Adding water vapor to saturated air causes mist, clouds, or rain to form.

To add water to a full glass, first increase the height of the glass.
    Adding greenhouse gases to the atmosphere causes warming, raising the dew point.

Then add more water to the larger glass.
    The higher dew point allows more water vapor to be added to the air.

Water glasses and greenhouse gases

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3 comments


SkS Analogy 12 - A Sinking ship reaches new heights

Posted on 15 May 2018 by Evan & jg

Tag Line

A sinking ship reaches new heights.

Elevator Statement

For a sinking ship the stern may be unusually low, the bow unusually high, and on average, the whole thing is going down. We cannot infer what is happening to the ship just by what is happening to one part. We must look at the entire ship.

It seems that at least one US Senator did not understand this relationship between the environment’s local extremes and global means when he found snow in front of the US capital, in February, and thought it meant that Global Warming had stopped.1  If he had watched the news that night, he might have realized that just a few hundred miles to the south it was unusually hot in Florida.

If we wait to take action on Climate Change until it is obvious to everyone that the ship is sinking, we may all be swimming.

Sinkging_Ship

Climate Science

As the Earth warms, some parts will still be cold. Let’s face it, the North and South Poles are just cold places. Some parts may experience colder temperatures for a while in response to a modified jet stream that draws cold, Arctic air further south than in the past. Cold days still happen, just less frequently.

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0 comments


SkS Analogy 11 - Cabinets, airplanes, and frame of reference

Posted on 2 May 2018 by Evan & jg

Tag Line

The elevation of an airplane landing on a runway is only useful if measured relative to the ground (i.e., height), and not to sea level (i.e., altitude).

Elevator Statement

While determining the optimum height for kitchen cabinets, an industrious husband in Minnesota asks his wife

“Should we move the kitchen cabinets up by 0.1% from the position we originally discussed?”

“Why on earth are you bothering me about such a trivial amount?” came the reply. “Now if you were considering something ridiculous like raising them 1 ft. I would complain.”

In fact, the husband was considering raising the kitchen cabinets by 1 ft. His reference to 0.1% used the height above sea level of 1000 ft. as the reference point for making his measurements. A ridiculous analogy you say? Climate-change deniers and not-so-well-informed skeptics make similar errors, but they are not as obvious. Read on if you want to learn the error that a Nobel Laureate made by miscommunicating in a similar manner as this industrious husband.

Climate Science

Nobel Laureate Ivar Giaever stated the following in a talk he gave on climate science,1

“From ~1880 to 2013 temperature increased from ~288K to 288.8K (0.3%). If this is true, to me it means that the temperature has been amazingly stable.”

A 0.3% increase is kind of like the 0.1% the husband raised the kitchen cabinets. Dr. Giaever was using an absolute temperature scale for his comparison. Unlike the Celsius temperature scale where 0°C is the point where ice melts, 0K on the absolute temperature scale is the point where atoms “melt” and start moving. For comparison, on the temperature scale that Dr. Giaever was using, ice melts at a blisteringly hot 273K. If you live in a coastal city prone to flooding, do you care more about the temperature at which atoms “melt” and start moving (i.e., 0K), or do you care more about the temperature at which ice melts (i.e., 273K = 0°C) and continues moving ever closer to your home?

 

Read more...

22 comments


SkS Analogy 10 - Bathtubs and Budgets

Posted on 12 October 2017 by Evan & jg

Tag Line

Adding 101 gallons to a 100-gallon bathtub causes it to overflow, even if added slowly.

Elevator Statement

No matter how slowly a bathtub is filled, adding more than 100 gallons of water to a 100-gallon bathtub causes it to overflow. This principle is clear, obvious, and one we encounter every time we take a bath.

Similar to the finite volume of a bathtub, Earth’s atmosphere has a finite volume. Because Earth’s atmosphere has a fixed volume, human emissions of greenhouse gases (GHGs) are increasing the atmospheric concentration of CO2, because we keep adding GHGs into this closed system, similar to running water into a bathtub.1 The concentration of CO2 does not depend on how rapidly we add GHGs to the atmosphere, but only on the total amount added.2 Lowering emission rates is important for improving the air quality in a large city, but carbon emission rates are meaningless for determining the global warming we will eventually experience due to a revved-up greenhouse effect: only the total amount emitted matters.3

Climate Science

The atmosphere has a budget of carbon it can accept to keep overall warming below a certain level, and the bathtub in this analogy is intended to be a visual representation of such a budget. Although scientists do not know with certainty how much the climate will warm for a doubling of CO2 (the so-called climate sensitivity), a climate sensitivity of 3°C/doubling of CO2 (see Ocean Time Lag)4 is consistent with the warming observed since the 1970’s, and is mid-range in the IPCC estimates that range from a low of 1.5 to a high of 4.5°C. Using a climate sensitivity of 3°C/doubling of CO2, a rough guide of the carbon budget corresponding to a particular level of warming is as follows5

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44 comments


SkS Analogy 9 - The greenhouse effect is a stack of blankets

Posted on 29 June 2017 by Evan &

Tag Line

The greenhouse effect is like a stack of blankets on a winter night.

Elevator Statements

  1. More blankets = more warmth: The greenhouse effect is like blankets warming the Earth. If it is -18°C (0°F) in your bedroom, you need a few blankets to keep yourself warm. More blankets = more warming. Too many blankets and you sweat. So the point is that the greenhouse effect is a good thing, up to a point.
  2. More blankets means warmer inside, cooler outside: With an increasing number of blankets, the temperature above the blankets gets cooler, because more energy is trapped below the blankets. With increasing greenhouse gases (GHGs) in Earth’s atmosphere, the upper atmosphere gets progressively cooler, because more energy is trapped in the lower layers of the atmosphere. This is one way that scientists know that the recent warming is due to greenhouse gases and not due to increasing solar output. In the sleeping analogy, if you turned up the temperature in the room, it would get warmer both above and below the blankets. If the recent warming was due to a hotter sun, then both the upper and lower atmosphere would warm. But the upper atmosphere is getting colder, just as the top of the outer blanket covering you gets colder when you add more blankets but leave the room temperature the same. See the SkS article "Is the CO2 effect saturated?"
  3. It is not the rate at which you put blankets on, but the total number of blankets that determines your final warmth. CO2 emission rates don’t affect the final temperature due to global warming, except that if we slow the emission rates it buys us more time. It is the total CO2 emitted that determines the final temperature we will reach, just like it is only the total number of blankets over you that matters, and not the rate at which you put them on.1 Note: the emission rates are important for determining how rapidly the climate changes and increased emission rates will make it more difficult for animals and humans to adapt to the increased warming. But just like when filling a bathtub, to keep the bathtub from overflowing (i.e., keeping global warming to under 2°C), it is not the rate at which the bathtub is filled that matters, but the total amount of water put into the tub. Carbon budgets refer to the total amount of CO2 we can emit before we exceed a dangerous level of warming, just as a blanket budget represents the total number of blankets we can tolerate before we start to sweat and overheat. Some skeptics refer to a time about 100's of millions of years ago, during the late Ordovician when CO2 levels were higher, but earth was the same temperature as now, or cooler. They point to this time to imply that CO2 levels do not correlate to temperature. But during the Ordovician the sun was cooler (like a colder bedroom), so that the colder bedroom combined with more blankets = similar temperature as today. If you turn down the heat in your room, you need an extra blanket or two. Thus, with a colder room, your blanket budget is higher.

Read more...

20 comments


SkS Analogy 8 - I'll take the specialist

Posted on 15 June 2017 by Evan &

Tag Line

I’ll take the specialist, please.

Elevator Statement

Your child has an eye injury and needs a doctor. Who are you going to call?

A Ph.D. in chemistry? No, you need a medical doctor.
A family-practice medical doctor? No, you need an eye doctor.
Any eye doctor? No, you need an eye doctor who does surgery.
Any eye surgeon? No, an experienced eye surgeon.

Because this is your child’s eye, you decide to take your child to two, experienced eye surgeons to make sure they agree on the course of action. You want consensus from at least two recognized experts in their field of specialty before messing with something as precious as the eye of your child. You care about your child and are using common sense.

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22 comments


SkS Analogy 7 - Christmas Dinner and the Faux Pause

Posted on 9 June 2017 by Evan &

Tag Line

Saying “No warming” since the last El Nino is like
Saying “No weight gain” since the last Christmas dinner.

Elevator Statement

On Christmas eve you eat a big dinner, with lots of seconds, gravy, ooey gooey sweet potatoes with more sweet than potatoes. After the monster dinner, generous helping of pie, ice cream and lots more. You weigh yourself after the “dinner”. The next morning you find creative ways to get rid of the food you “ate” the night before, all of it (and more) ending up in the “waste” bin. You weigh yourself again, for comparison.

Hurrah, a new weight-loss technique. How to lose 5 lbs. (or more) in one delightful day. For the next month you note that you have not gained a single ounce since that gorging Christmas dinner. In fact, you’ve managed to keep your weight below the Christmas-eve measurement. Weight-loss is easy: just push your weight up momentarily to some unsustainably high weight, and then eat a more modest diet thereafter.

This tale would seem absurd, except this is exactly what educated, well-paid senators of the USA say on a regular basis. They substitute 1998 (the year of a monster El Nino) for Christmas dinner, they substitute temperature for body weight, and then say “No warming in __ years”, and neglect to note that the start of the “arbitrary” time period they’ve chosen was a monster El Nino. This Zombie Myth keeps on walking, eating the brains of many, despite the fact that we’ve notched record warm years 3 years in a row (i.e., 2014, 2015, and 2016). With the record warmth we’ve had, it’s possible we’re in the middle of the next Christmas “Dinner”.

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23 comments


SkS Analogy 6 - Speakers, tuning forks, and global warming

Posted on 29 May 2017 by Evan & jg

Tag Line

The physics of global warming by greenhouse gases is well understood and can be illustrated by items we use every day.

Elevator Statement

Simple, well-understood physics indicate the following:

  • Sound waves vibrate speakers (think microphone1) and vibrating speakers make sound waves
  • Sound waves vibrate tuning forks and vibrating tuning forks make sound waves (with a narrow range of frequencies)
  • Infrared waves vibrate CO2 molecules (increased vibration means more energy, which means warmer) and vibrating CO2 molecules make infrared waves (think CO2 lasers, which make waves with a narrow range of frequencies)

Almost everybody is familiar with microphones, speakers, and tuning forks. These are items you can see, touch, and feel, so they are familiar. Even though we cannot see greenhouse gases like CO2, they operate the same as speakers and tuning forks: they absorb and reemit waves, just on a very small scale. When they absorb waves they trap heat, warming the atmosphere.

Tuning fork and CO2 molecule

Excitation of tuning fork by sound and CO2 molecule by infrared radiation (graphics by jg).

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17 comments


SkS Analogy 5 - Linear, Non-linear, and Coastal Flooding

Posted on 23 May 2017 by Evan &

Tag Line

We age linearly and earn non-linearly.
In a warming world, coastal flooding occurs non-linearly … or faster!

Elevator Statement

Linear means a straight line, non-linear means a line that is not straight, and is often a simple, curved line. Consider the following examples from our everyday lives that illustrate linear and non-linear behavior.

  • Our age increases linearly, because our age increases at a constant rate, 1 year per year.
  • Our income increases non-linearly, because our income increases at a varying rate, x% per year.

When the change of your salary is related to your salary, you get a non-linear response. To illustrate, suppose you got a 3.5% raise each year.

  • Year 1: Start with a $30,000/year salary.
  • Year 2: 3.5% more than $30,000. New salary is $30,000 + 0.035*30,000 = 31,050.
  • Year 3: 3.5% more than $31,050. New salary is $31,050 + 0.035*31,050 = 32,137.
  • ...

Suppose a person is born in the year 2000. If we do the simple thing and plot their age on the “Y” axis and the year on the “X” axis, we get a straight line, as follows. We call this a linear relationship. If they start working at age 16, for $30,000/year, and if they get a pay raise of 3.5%/year until they retire at age 65, then we get the non-linear growth of income.

Linear and Non-Linear relationships

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39 comments


SkS Analogy 4 - Ocean Time Lag

Posted on 18 May 2017 by Evan &

Tag Line

Greenhouse gases (GHG) determine amount of warming, but oceans delay the warming.

Elevator Statement

To see how the oceans delay warming of the atmosphere, try the following thought experiment.

  • Imagine a pot that holds about 8 liters/quarts.
  • Hang a thermometer from the center of the lid so that it hangs in the middle of the pot.
  • Put the pot on the stove with no water, just air.
  • Turn the burner on your stove on very low heat.
  • Measure the time it takes for the thermometer to reach 60°C (about 140°F).
  • Remove the pot from the stove, let it cool, fill with water, and place it on the stove on very low heat.
  • How much longer does it take to reach 60°C (about 140°F) with water instead of air in the pot? A lot longer!
  • If you wanted to heat the water to 90°C (about 195°F) in the same amount of time, you would need to start this experiment with the burner on higher heat.

The longer time it takes to heat the pot of water than a pot of air explains why there is a delay between GHG emissions and a rise in temperature of the atmosphere: the oceans absorb a lot of heat, requiring a long time to heat up. This is why scientists such as James Hansen refer to global warming as an inter-generational issue, because the heating due to our emissions are only fully felt by the next generation, due to the time lag created by the oceans.

Climate Science

The earth is covered mostly in water. The large heat capacity of the oceans mean they soak up a lot of energy and slow down the heating of the atmosphere. Just how long is the delay between the time we inject CO2 and other GHG's into the atmosphere and when the effect is felt? The CO2 concentration is like the burner setting in the above example: more CO2 is like a higher burner temperature. However, even though turning up the heat creates hotter water, it takes a while for the water to heat up.

We can estimate the final temperature the atmosphere will reach for a given CO2 concentration by using the average IPCC estimate of 3°C warming for doubling CO2 concentration (this is called the “climate sensitivity”). Using the estimate of pre-industrial CO2 concentration of 280 ppm (parts per million), a climate sensitivity of 3°C implies that CO2 concentrations of 350, 440, and 560 ppm yield 1, 2, and 3°C warming, respectively. Using this estimate of climate sensitivity together with measurements of CO2 from 1970 to today, we can estimate the warming that has been locked in due to recent CO2 emissions. That is, knowing the burner setting, we can estimate the final temperature of the pot of water, even though we will have to wait some time for it to heat up.

We also use the GISS (Goddard Institute for Space Studies) data to plot measured global mean temperature above preindustrial to estimate the time lag between the temperature anomaly suggested by a particular CO2 concentration and the time when that temperature is observed. This and CO2 concentrations for 4 selected years are shown in the following figure.

Time lag between CO2 and final warming

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13 comments


SkS Analogy 3 - The Greenhouse Effect is Like a Cloudy Night

Posted on 9 May 2017 by Evan & jg

Tag Line

The greenhouse effect is like a warm, cloudy night.

Elevator Statement

  • At night clouds trap infrared radiation emitted from the ground, similar to greenhouse gases, and re-emit some of the absorbed radiation back to the ground.
  • More nighttime cloud cover means more trapped heat, and warmer temperatures near the ground, just as more CO2 in the atmosphere means more trapped heat, and warmer temperatures.
  • Because clouds are big and thick, their radiation-trapping effect is felt immediately, within a single night.
  • Because CO2 is diffuse, its effect is felt slowly, over many decades.
  • Increasing the concentration of CO2 in the atmosphere is like increasing the cloud cover at night: both warm the Earth by trapping infrared radiation.

Climate Science

The greenhouse effect describes the trapping of energy by Earth’s atmosphere: infrared radiation from the ground is absorbed by gases in the atmosphere such as CO2, H2O, CH4, and others. Although the greenhouse effect is active 24/7, it is most apparent at night. This is because with no background solar radiation, nighttime warmth occurs mostly by greenhouse gases and clouds grabbing and storing some of the infrared radiation emitted from the ground that is trying to make it to outer space. This is partly why nighttime temperatures have been steadily increasing as greenhouse gases increase: more greenhouse gases implies more heating.

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SkS Analogy 2 - Ferrari Without Gas

Posted on 24 April 2017 by Evan & jg

Tag Line

A Ferrari without gasoline goes nowhere.
Greenhouse gases without infrared radiation cause no warming.

Elevator Statement

  • The concentration of greenhouse gases is like the size of a car engine: higher greenhouse gas concentration is like a bigger engine.
  • Infrared radiation is like the gasoline in the tank of a car.
  • Just as gasoline is the fuel that drives an engine, infrared radiation is the fuel that drives the greenhouse effect.

Climate Science

Global warming occurs because infrared radiation emitted from the surface of the Earth is captured by greenhouse gases in the atmosphere, increasing the temperature of the atmosphere. Increased greenhouse-gas concentrations in an atmosphere with constant background infrared radiation will absorb an increasing fraction of the emitted infrared radiation, causing warming. Increased greenhouse-gas concentrations in the atmosphere combined with increased infrared radiation (e.g., due to reflective snow and ice melting exposing dark oceans that absorb solar radiation and reemit it as infrared radiation) causes even faster heating, such as is happening in the arctic.

Some skeptics point to Snowball Earth to “prove” that CO2 does not cause warming, by noting that 650 million years ago CO2 concentrations exceeded 1000 ppm yet the world was frozen solid, even down to the equator. Part of what allowed Snowball Earth to occur was because solar radiation was 4% lower than today, but a major reason that Snowball Earth persisted for so long is that snow and ice reflect 90% of incoming solar radiation, reducing infrared radiation to the point that the greenhouse effect was severely reduced.

Snowball and Dirtball Earth Radiation Balances

Snowball and Dirtball Earth radiation balance (graphics by jg).

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SkS Analogy 1 - Speed Kills

Posted on 19 April 2017 by Evan &

Tag line

Speed Kills

Elevator Statement

Deceleration from 60 mph to 0 in …

  • 30 seconds (base rate): Normal exit from a freeway; no drinks spilled, life goes on.
  • 3 sec (10 times base rate): Slam on the brakes. All drinks and loose items end up on dash board. People not wearing seat belts do ungraceful face plants. Survivable injuries.
  • 0.3 sec (100 times base rate): Like running into a parked car. Crumple zones in both cars absorb much of the energy, but people are seriously injured, some mortally.
  • 0.03 sec (1000 times base rate): Like running into a brick wall. Most don’t live to tell about it.

Climate Science

It is not only the CO2 concentration that is important, but the annual rate of increase of CO2 concentration, because the rate of increase determines the rate at which natural systems must adapt … or go extinct.

For 1 million years life on earth has adapted itself to going into and out of ice ages (i.e., glacial cycles) over approximately 100,000-year cycles. We come out of ice ages in about 10,000 years, with CO2 rising 100 ppm in that time. That is a rate of increase of about 0.01 ppm/year. If we use this as a typical rate to which nature has adapted, and has done so already for at least 10 cycles, then we can determine how much faster than this we are now moving. The idea is that if we limit CO2 rise to this rate, we expect nature will adapt; the further away we move from this base rate the more difficulty nature will have adapting.

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