How "Hot Water" is getting us into Hot Water

One of climate science’s favorite facts and infographics to use to convince people that climate change is real is rising ocean temperatures.  “If the ocean’s average temperature rises by 2⁰C we cannot recover!”  They tell human’s that this will affect marine and coastal eco systems (which is true) and to care about other species outside of humanity.  As is the theme with all of my posts, we are told to care about these topics via buzzwords and declaratives while the science and facts are deemed "too confusing."  So let’s peel back why we need to be worried about ocean temperature outside of the fishes and crustaceans and focus on what we are really after: our future.  As with all of my posts this is not all encompassing and tries to give you a framework to think about the changing climate.

This post will rely on Easy Being Green, Being John Milankovitch, and Deep Ocean Currents , and assumes you have read them.

Photosynthesis

If there is one thing they do not let you get out of grade school without learning these days it is “Photosynthesis!” Plants take in “sunlight” and convert it to “energy”.  While this is not incorrect it is neither the whole, nor most important part of the equation when it comes to climate science.  Here is the chemical reaction for photosynthesis:

CO₂ + H₂O + light ==> CH₂O + O₂

A chemical reaction is kind of like a recipe and this one reads: Take one part Carbon Dioxide, one part Water and mix with light.  After some time you will have a cake made of Sugar (CH₂O) and Oxygen.  Photosynthesis, in terms of climate science, can be seen as a Carbon Dioxide removal mechanism, like a CO₂ sponge.  While Oxygen is also a Greenhouse gas it has a much lower absorption rate for earth’s radiation than Carbon Dioxide (see previous post).  Taking our last blog post into consideration photosynthesis does not technically make the planet cooler, but it prevents it from getting warmer; it slows down the positive feedback machine that is the Greenhouse effect by limiting Carbon Dioxide in the atmosphere. 

What does any of this have to do with ocean temperature?  This is where these little guys come into play:

These tiny organisms are known as “phytoplankton”.  You have most likely spent your life calling them “algae” and spending your summer fending them off from your pool.  The earth is not your swimming pool however and we require the billions of tiny and large algae to live.  It is estimated that 55-85% of all oxygen in the earth’s atmosphere is produced by these little organisms.  While we cannot estimate directly how much CO₂ this process draws out of the atmosphere it is clearly some non-zero number. The difficulty in accessing the information is CO₂ being absorbed and released by the Ocean in many ways and attributing the exact amount of CO₂ absorbed by phytoplankton photosynthesis is currently not possible.  What we need to consider is the effects of rising ocean temperatures on our friend the phytoplankton.  The following video shows changing ocean temperatures alongside the total amount of photosynthetic algae on the ocean’s surface:

You can see that as the ocean cools CO₂ “eating” algae prosper.  They are also most prevalent in areas where we saw deep ocean currents sinking and rising out of the depths (the second part of this blog post).  A warming ocean is not good for algae that remove CO₂ from the atmosphere.  It is also great for algae that do not contribute to this (i.e. red algae and red algae “blooms”) and can push beneficial algae out of the eco system.  Again we are dealing with a positive feedback system as additional man made CO₂ “can” have drastic effects on the global climate.  We have man made greenhouse gas added to the Milankovitch cycles warming the planet, causing algae to consume less greenhouse gas, causing the planet to heat more… etc.

Surface Reactions:

Our next example relies on a little chemistry and a little on our previous post about deep ocean currents.  In addition to our little algae friends eating up the atmosphere’s CO₂ the ocean’s surface itself can react with CO₂  .  Here is an example:

This says that Carbon Dioxide and Water under the right conditions will make Carbonic Acid, Hydrogen and Bicarbonate. If the ocean water simply stayed on top of the ocean some of Carbonic Acid, hydrogen and bicarbonate would spread out through the water, and some would recombine to form CO₂ and H₂O (the opposite reaction).  The Carbonic Acid, hydrogen and bicarbonate would only spread so deep into the ocean as there isn’t any force to spread it out throughout the rest of the ocean. This process would be self-contained in the surface of the ocean however – absorbing and emitting the same amount of CO₂ ; not having much of a changing effect on the climate.  This is where we revisit our first blog posts!

At three places on the globe the surface ocean water is driven to the ocean floor and moved incredibly slowly throughout the globe.  The driving force for the sinking water is density and the driving force for the density is… ocean temperature.  This means that some of the carbonic acid and bicarbonate at these locations is driven all the way to the ocean floor, where it will remain for ~1000 years.  This gives it the entire ocean to distribute the carbonic acid and bicarbonate.  Instead of just the ocean surface and atmosphere we now have the entire ocean to distribute our used CO₂.  The following map shows where in the ocean our CO₂ is “stored”

As expected a majority of CO₂ is found where surface currents sink to the ocean floor in the northern and less so southern poles. This process “buries” many CO₂ sources not just the one in this example.  From our algae example, as algae dies its “corpse” can be turned back into the CO₂ we hoped it was getting rid of and released into the atmosphere.  Algae corpses that get pushed into the deep ocean current however remove this potential CO₂ from the atmosphere all together and “store” it in the ocean.

As discussed in the first blog post rising ocean temperatures slow down the deep ocean currents.  As deep ocean currents slow, the amount of CO₂ consumed by the deep ocean currents lowers, the more CO₂ is in the atmosphere, the warmer the planet gets, the more the deep ocean currents slow… Yet another positive feedback system.

Final Thoughts

Examples like these are why some scientists respond with such hyperbole and hysterics when talking about climate science.  The system in question is based on many, many intricate positive feedback systems that point to a situation that does not get better.  It is not just one input/output that snowballs downhill but many.  The next blog post will talk about current levels of CO₂ in the atmosphere compared to the past, however I will bury the lead a little and tell you our current CO₂ level is almost twice that of any previous time in known history.  While the ice cores can tell us about past climates, no known atmosphere has ever been this greenhouse rich.  We are taking one of the inputs into our feedback system and turning it up to 11, and while the results are likely to be drastic, the scarier part is that they are also unpredictable. 

Sources:

http://earthobservatory.nasa.gov/GlobalMaps/view.php?d1=MYD28M&d2=MY1DMM_CHLORA

 http://earthsky.org/earth/how-much-do-oceans-add-to-worlds-oxygen

http://www.pmel.noaa.gov/co2/story/Ocean+Carbon+Storage

"It's not that easy being Green" - What makes a Greenhouse Gas

 
Happy Holidays!  Today’s post is a little longer but you have the whole holiday to read it!  It also condenses a lot of complex science into what I believe is a very digestible chunk – if I am wrong please let me know!

The Greenhouse effect is something politicians and scientists bandy about however never try to explain.  Heck they do not even mention the most common Greenhouse Gas – Water Vapor.  Today we are going to describe what makes a greenhouse gas, how they heat the planet, and why more of them may not be the best thing!

Everything in the Universe is constantly emitting energy.  Some things, like say the desk I’m typing at, do not have much, if any energy to emit.  Other things, like the Sun, have a ton of energy.  Since there is nothing touching the Sun, and there is no air for it to immediately heat up, the only way it has to get rid of that energy is radiation.  Radiation is typically measured by two numbers: Amplitude, and Wave Length.  Since all waves are described the same way, we’ll use our friendly analog of water to describe Amplitude and Wave Length.

Amplitude measures how “high” the wave is.  If two waves are exactly identical, but one has a greater Amplitude than the other, it is carrying more energy.  Let’s think about two sets of beaches with waves crashing every 30 seconds.  The waves on the first beach are 10 ft high and the waves on the second beach are 30ft high.  The waves on the second beach are going to be moving much more water than the first beach.

Wavelength measures how often the waves occur.  It is the distance between two peaks of the wave.  If all things between two waves are the same, the one with the smaller wave length will have more energy. Going back to our beaches assume the exact same waves except looking out from beach 1 you see a wave crest every 50 ft and at beach 2 you see a wave crest every 25 ft. It’s easy to see that the waves at beach 2 are going to be moving more water as they crash twice as often.

Radiation

Sun’s Radiation at Sea Level

This is a graph of the Sun’s radiation at sea level.  The horizontal axis shows the wavelength and the vertical axis shows the energy.  We can see most of the suns energy is radiated at between 400 and 800 nanometers (a nanometer – nm – is very small, it is .000000001 meters or .00000004 inches).  The important message from this graph is that the sun releases energy at all types of wavelengths along the scale.

The earth, as an object in space, also radiates heat.  Some of this heat is generated internally – by the very hot core - and some is external caused by the sun beating down on the earth.  The earth is much less hot than the sun so we expect it to have less energy to radiate away.  Thus the wavelengths of its radiation are expected to be larger and their amplitudes to be less (remember the beach).  This is what the radiation from the earth, out to space looks like (The blue part!).

Notice earths radiation has a wavelength that is greater than 10 times that of the sun

Where Does the Energy Go?

A fundamental law of the universe is that Energy Is Conserved.  What this boils down to is when two things exert energy on each other the energy MUST go somewhere.  When you push a ball, it moves.  When you push down on a spring it gets tighter and tighter (you can feel it push back on you).  When you rub your hands together you get heat!  The energy you put into the system must be put out some way.  This is as close to a truth in science as you can get.

When radiation energy comes in contact with any matter (matter is the science term for a solid, liquid or gas) it has 3 possible interactions.  The first is to simply pass on by.  Some energy waves have such tiny wave lengths, and are so high energy they kind of just miss the matter, or the just ding off the matter and do not interact with it in any meaningful way.  Think about an X-ray passing through your soft tissue.

The next option is reflection.  We use this all the time.  Think about wearing a white t-shirt in the blazing sun.  The shirt reflects most of the light hitting you and keeps you cooler.

Finally the most dynamic and confusing of all is Absorption.  This means the energy hits the matter and is absorbed.  The most obvious version of this case is when you leave your car with black leather seats in the sun.  As the sun beats down on the seats, the smaller wave length light we can’t see likely passes through it,  some of the light is reflected (giving it the shininess), and most of it is absorbed and then emitted as heat. The seats get hotter and hotter as they absorb more and more energy.  This is how liquids and solids generally absorb radiation – it hits them and they convert this energy into heat.

Gas on the other hand has a weirder interaction with radiation.  Since it is so spread out it cannot easily release the energy as heat, it must find another way to convert the radiation energy.  The radiation must cause some sort of rotation, or vibration so that the energy has somewhere to go.  The following Gifs show Carbon Dioxide (CO2) and Methane (CH4) common greenhouse gasses vibrating.

This adds the final piece to our greenhouse puzzle.  Gases need some specific requirements to absorb radiation energy.  First they need a structure that allows them to vibrate or spin or some way to absorb some energy.  If these were just something like Nitrogen gas (~70% of our atmosphere) the energy simply passes by or bounces off of it – there is nowhere for the energy to go in the system.

Next we need the correct wavelength to stimulate the movement.  As you look at the CO2 and CH4 molecules wiggle back and forth, imagine you are holding one end of a jump rope and I am holding another.  I’m just going to hold my end and you are going to move your arm up and down.  If you go too slow it will look like this:

 

If you go too fast the rope will be going up and down all along it in no pattern.  However when you get exactly the right speed you will get this motion: 

You see one peak as your arm goes up and one valley as your arm goes down.  This synching up of energy input wavelength and its response’s wavelength is exactly what is needed for a gas to absorb radiation.  This yields charts like the following:

Gray where CO2 absorbs radiation, white where it doesn’t

This shows the “Absorption spectrum” for CO₂.  The horizontal axis is wavelength.  The vertical axis is % of energy absorbed.  As you look around 2000 nm, 4000nm, and 20knm you see almost all radiation is absorbed.  These are the wavelengths of radiation that cause CO2 to vibrate and twist and wiggle in the right way.  Anywhere that is not gray CO₂ will absorb NONE of the energy.

Putting it All Together

We now have everything we need to model the planet.  Here is a model with no greenhouse gasses.

Under this model the temperature of the Earth would be pretty stagnant.  Yes some days there would be more clouds so the Earth reflects more radiation, other days less clouds and a warmer earth.  Aside from our previously discussed “Milankovitch Cycles”, the sun would always supply “W” radiation, the Earth would absorb “X” radiation.  The earth would supply “Y” heat and radiate away “Z” energy.  The temperature of the Earth would always be “X+Y-Z” and those numbers would change little throughout the years.

Here is the actual picture of our system:

The new addition is the absorption of Earth’s radiation by the atmosphere.  This energy is then absorbed and re-radiated back towards earth in the process we described above.  THIS IS THE GREENHOUSE EFFECT.  Let’s stack the Sun and Earth’s radiation spectrums with the 4 major greenhouse gas absorption spectrums.

I hope you can see the issue at hand.  These four gasses all absorb energy at the same wavelength the Earth emits radiation.  They also happen to not interact with sunlight at all.  This is where the “Greenhouse” property is attained.  As the sun beats down the earth will heat.  As the earth heats it radiates energy.  This energy is absorbed by greenhouse gasses and is then radiated back toward the earth.  This heats the earth more.  This means more radiation is coming off the earth (greater amplitude).  This causes even more energy to be transferred to the greenhouse gasses and the process spirals on.

In engineering we call this a positive feedback system.  You put some amount of energy in and the system builds and builds and builds until it goes out of control.  We almost never design a system to do this.  The human body uses positive feedback for one process… child birth.  It’s pretty easy to see why this is not an ideal situation for the earth.  It’s also easy to see that adding more gas to the system adds more energy returned to the earth – it makes the process more drastic.

 

Problems with Greenhouse Gasses and Man Made Global Warming

Here is a pretty easy wrench you could throw into this whole situation with just the past 4 blog posts.  The southern hemisphere’s summer is currently occurring when the earth is closest to the sun (Axial procession from the Milankovitch Cycle) which will naturally cause the Southern Hemisphere to heat up with no humans necessary.  As the Southern Hemisphere gets hotter naturally more and more water vapor will be in the air as the oceans see more energy.  Since water vapor is both the most bountiful and absorbing of the greenhouse gasses the planet will start a greenhouse process with this alone.  This heating of the planet causes more water vapor to get into the atmosphere, causing a greenhouse effect all on its own.  More water vapor causes more heat, causes more greenhouse effect. Since there is no way to stop Axial procession nor water evaporation you cannot blame people for global warming?

This scenario is what these first 4 blog posts have been preparing for.  From our last blog post we know we can reconstruct climates and temperatures of the past; from “Being John Milankovitch” we know how to trace large increases in global energy; from the first blog post we have the long term results of those thousand year old changes.  Scientists need to take everything they have learned and are honestly still deciphering about the past and apply it to the climate they are seeing today.  They need to compare CO2 in the past to CO2 in the present etc.

Image Credits:

http://www.bbc.co.uk/staticarchive/df504ecc44f0690dc88a53b7532182d8dc2e80ba.gif

http://ffden-2.phys.uaf.edu/631fall2008_web.dir/wallace_webpage/8_Sun.html

http://tek-think.com/2015/03/11/understand-power-standing-wave/

http://2012books.lardbucket.org/books/introduction-to-chemistry-general-organic-and-biological/section_11/62049a0bf48e2cb0b024d238707590e3.jpg

"If only Climate Change was an Asteroid heading towards Earth" - Or How We Learn About the Past

The title is in reference to "Armegeddon" I would listen to "Don't wanna Miss a Thing" while reading

If I asked you what the weather was yesterday between 6:00 AM and 7:00 AM in Bali how would you look it up?  You would Google “Bali Weather 11/20” and have the information in seconds.  What about in Kansas in 1910?  You’d have to find an old newspaper from that time or an almanac but you could most likely find it.  What about Chile in 2000 BCE or Tokyo in 10,000 BCE?  This is what we need to unlock in order to study the climates of the past.  

If I have a theory about the current climate and where it is heading, but have to wait 2 human life times to see it come to term, I am going to have one hell of a time testing anything.  However if I knew the exact climate and make-up of the earth throughout all of its history I would be able to match my theories about the climate with the climates of the past.  Since we did not have meteorological instruments or chemists stationed in Chile in 2000 BCE we need a different type of Almanac. Luckily the earth has provided just that in Glaciers; giant, as old as the earth has been cold, and constantly recording the state of the earth in their layers of ice.  Imagine every summer since the inception of ice you wrote down the hottest day of the summer and the coldest day of winter. Then you stacked these pieces of paper every year… for a couple million years (the age of the current glaciers in Antarctica).  Every couple of years you also wrote down a description of the weather that year and stuck that in there too. This is what we are going to use to study the past climate.

Digging up the Past

So we have miles and miles of history frozen all over the world. The issue is this history is incredibly brittle, has to remain frozen, and needs to remain intact and in sequence for the miles and miles it exists.  In good news, throughout the course of American history we have been great at getting things out of the ground (thanks oil industry!) and can drill for days. Imagine you had a 2 inch hole-saw and drilled a hole in a 2x4.  The 2x2 inch slug of wood that we throw away is now what we are looking to extract.  Instead of a couple of inches of wood slug however, we are looking to harvest more than 2 miles of ice – therefore we use much bigger hole-saws!  Since these have years and years of engineering behind them it would be insincere to pretend like I could summarize all the ways we have come up to extract cores so I’m just going to throw up some pictures and let you imagine from there.

What a Core Can Tells Us

Water Ratio

Cores contain three important history “logs” we use to recreate the atmospheres of the past. The first “log” we look at will be the frozen water itself. Most of us know that water is made up of Hydrogen and Oxygen or “H₂O”, however not all H₂O is created equal.  Eventually we will cover “isotopes” in a Not So Simply Science however this is what you need to know: There are two common forms of water, one is heavier than the other.  As most of us learned in grade school snow is precipitation, it literally falls from the sky.  In order for it to get up in the sky it takes energy to evaporate – think boiling a pot of water.  The heavier the water the more you have to heat it.  As in most of our examples the energy we need to evaporate the water comes from the sun.  The warmer the planet, the more heavy water can get into the air, the more heavy water ends up in snow, the more it is frozen in the glaciers!  The first important fact we get from the core is this ratio of heavy water to light water.

Important Note: O18 is heavier than O16 - that's what you need to know!

While we do not have weather records for all of recorded history, we still have a ton of weather records from both current and ancient civilizations.  We take our weather records and compare them to core samples from that time. With the expected heavy/light water ratio and the temperature, we can reconstruct the history of temperature by analyzing the ratio throughout the core.  Even more importantly we can measure the history of temperature change! This information is invaluable – it is how we anchor all of our climate science.  Without knowing the temperature of the planet in the past we cannot predict what will happen in the future.

Air Pockets

The next “log” of glacier cores is basically the climate science equivalent of Jurassic Park!  Just like the tiny mosquitos filled with dino blood were trapped in tree sap, tiny pockets of atmosphere get pressed and frozen into the layers of the glacier.  These are basically tiny windows into the atmosphere of the past and the time when it was present.  If the first log gives us the global temperature at the time, this second log gives us both the potential causes and effects of this temperature.  Scientists use these tiny atmosphere samples to recreate the greenhouse gasses of the past atmosphere.  While the effects of greenhouse gasses will have to explored in further blog posts here is chart that shows changing temperature along with the concentration of CO₂ for the last 400,000 years.  While this does not show which is cause or effect, it shows a clear link between the two in some way.

Dust

The last “log” we will talk about is dust and debris. In our daily lives dust is a simple nuisance, dust that has been trapped beneath ice for millions of years can let us know a lot about other atmospheric conditions we cannot get from temperature and gas breakdown alone.  Firstly dust and debris are actually pretty specific in their origin.  Sand from Arizona is different than sand from the Jersey Shore is different than sand from the Gobi desert.  Secondly dust gets into the atmosphere by being blown around.  More wind means more dust and the further travel.  The dryer the climate is the more dust is available to get into the air.  When they want to keep dust down at large construction sites they are constantly spraying water everywhere – the earth does the same thing.   As an example of how any of this is useful, dust in Greenland’s cores is seen to be 10-100 times more prevalent during glacial periods.  This lets us know that in the deserts where the dust originates from, during glacial periods, it is much dryer and windier than when the climate is warm.  The amount of dust and specific origin let us infer even further into the climate's conditions.  The previous chart shows the inverse relationship of “dustiness” to temperature.

Potential Issues

While I have painted a pretty simple picture of the benefits of glacial cores, they are more like a long Indiana Jones corridor of booby traps than the almanac I presented.  Firstly as we get further and further back in time it gets harder and harder to date the ice core.  Close to the surface the core looks a lot like a tree, there are layers you can see when the ice melted and refroze in the summer and winter.  As you get deeper and deeper, under more and more pressure these lines become essentially non-existent.  This is where we use things like known volcanic explosions and other geological events to look for changes in the ice composition.  It is a highly advanced guessing game.

The black line is from a Volcanic Eruption ~21,000 years ago

Next, molecules (the little parts that make up everything) do not tend to just sit still for millions of years.  While the bubbles of atmosphere are trapped in the ice and put under immense pressure many of their molecules will travel out of the bubble and spread into the ice.  It is then up to scientist to calculate what the atmosphere would contain based on more recent bubbles we know the correct concentrations for as well as the amount of time these old bubbles have been in the ice.

Finally (not really finally there are just too many issues to look into) as we handle cores whether by drilling them out, transporting them, or keeping them cool they are constantly changing.  Imagine you were reading a history book, but the more you read it the more the content changed.  They can change so much that what you thought you read the day before about Greece defeating the Persians now reads the Persians defeated the Greeks. It is that difficult.  We cannot recreate being 2 miles beneath the surface of the earth, being undisturbed for thousands of years as we rip the ice out of the earth, our handling of the core has to change it. All of these factors need to be worked into any analysis that is done on an ice core.

Regardless of all of these issues, these are our premier way of comparing today's changing climate of the future into known quantities of the past.  The power of knowing how the climate reacted in the past is immeasurable.  I have spent a lot of time talking about just how long geological time is, and how it can be hard to even see the end of a current hypothesis about the climate come to fruition.  With Ice cores however we get to test our theories out on hundreds of thousands of years of climate data!

Image Credit: 

http://pages.uoregon.edu/rdorsey/geo334/O-isotopes.html

http://icecores.org/icecores/drilling.shtml

http://insectcop.net/two-mosquito-mistakes-that-the-first-jurassic-park-movie-made/

http://climatechange.umaine.edu/icecores/IceCore/Ice_Core_101.html

https://upload.wikimedia.org/wikipedia/commons/b/b8/Vostok_Petit_data.svg

http://icecores.org/indepth/2015/spring/nsf-press-release_waisdivide_01.jpg

http://www.crowcanyon.org/images/photos/learn_about_archaeology/ice_core.jpg

Not So Simply Climate: The Love Song of J. Alfred "Proof"rock

I have always felt that there are a couple of jumping off points for people and mathematics.  A point where the teacher says “just do this” and someone says “…What?” and that is it for them.  The first is most like when the teacher says “then we just solve for ‘x’”.  The second is when they explain proofs, “We’ll be proving this is true;” “Prove there are 180^o in a triangle.” There is no why or how, just do.  These Not so Simply Climate posts will hopefully show you that it really isn’t that bad and can even be fun in the right context.

Proofs are like building blocks in math and science; for your house it is plywood and studs, for a bank it may be cinderblock, for science it is proofs.  If we want to build up large, powerful ideas we need much smaller ones to build from. If you are going to build predictions or solutions from these ideas, you want to make sure your foundation is strong.  You can’t build a skyscraper from poorly made cement.  In our last blog post we said that as the earth gets closer to the sun it gets warmer.  Can you prove that?  How much warmer?  Even simple ideas such as these need to be proven.

Finally remember Math and Science are like a game, or puzzle.  You are encouraged to be clever and thoughtful while finding your way through.  Sometimes you get stuck, but they will never lie to you.

-

.

That was what I would call a rigorous proof.  We had a well-defined problem statement and cleanly proved its validity   Just knowing that this information is true doesn’t really serve us and purpose however, now we must use it to further our understanding of the natural world!  We will use our previous proof to help support the last blog post, when the planet gets closer or further from the sun it sees much more or less heat than the distance closer. 

Inverse Square Law

This proof isn’t formal or super rigorous but it will validate what we expect and show the process of scientific thinking.  Say I told you that "the further you get away from a heat source the less hot you get" you would say "Of course you goof".  Unfortunately "Of course" or "Because I believe it" is not enough to base our reality on.  

The surface area of a sphere is 4πR² (this also requires a proof which is linked at the end)

4π is simply a number ~12.  R is the radius of the sphere.  The radius is the distance from the very center of the sphere to its surface.  If we could actually dig through the center of the earth, the Radius of the earth would be half the distance you would dig.  

When you are ordering tile for a floor you measure two sides of the floor, multiply them together and order that many "square feet".  If you were going to tile a sphere however you would measure across it and divide that number by two and then plug that number into 4πR²  and order that many square feet. This is what we mean by “Surface Area”.

Now imagine you had a sphere of heat where the heat was the same at all points on the surface, and only on the surface, like a balloon of heat.  We will say the total heat at the surface is some number H^o and the sphere has some radius R.  Since we said the heat at any point on the surface is the same, the heat at any point on the surface is the total heat divided by its surface area or 

H_point = H^o/4πR²

No let’s pretend we have the exact same situation except the radius of this sphere is R+200, it is larger than the old sphere. Now:

This is like inflating the balloon.  Same amount of heat, but spread out more.

Since the radius is always positive we know R²+ 400*R+40000 > R² .  Now we use our proof from earlier!

The larger and larger our radius, the less heat at any point on the surface sees.  Also the smaller the radius the more heat any point sees.  We also know that this difference goes with square of the distance (R²) so if you move 10ft away, you reduce the heat by 100 times etc…

Sure this proof isn’t perfect.  Sure we took some liberties; obviously the sun doesn’t have uniform heat across its surface, all of its heat isn’t only located on its surface.  The last little part about H_point-new < H_point requires some more algebra to really prove, however all of this is close enough to reality to prove what we needed to prove, i.e. the basis of natural occurring global warming.

"Being John Milankovitch" or Natural Causes of Climate Change

Some housekeeping before we start.  I'm going to update the blog every Monday and Thursday.  Those posts will always be aimed to further the goal of the blog, simply explain the science of climate change.  I will try not to do more or less, just exactly Monday and Thursday!

The secondary goal of the blog is to show people that Science and Math aren't terrifying, and are more like games and puzzles than water torture.  So weekend posts which I will throw in sporadically will be much less focused and just discuss whatever I feel like.  Hopefully these are interesting as well.

Anyway on to the post!  This post has way more bananas in it than I ever intended.

In my opinion there are two facts about Climate Change: 
          1- It is an incredibly complex problem with maybe millions of inputs and millions of outputs.
          2- The climate was shifting drastically before any sentient being ever burned a fossil fuel   

This second fact doesn't relieve us of our responsibility to discover what we are doing to the planet, but gives us a framework to base our results on.  Just because your ship sinks in the roughest waters doesn't mean you stop trying to make your ships float all together... 

Out of all of the factors that affect the climate there are three powerful ones we have no control over.  All three have to do with how the earth makes its way around the sun.  All three affect each other; constantly adding and subtracting energy from our climate. These effects are called the “Milankovitch cycles” and have been changing the climate of the planet for millions and millions of years without any help from us.

Orbital Shape

One of the first things we learn in science class is that the earth goes around the sun.  They show us a picture with the sun in the middle and 9 (now 8 I guess?) circles representing the order of the planets from the sun.  The earth doesn’t go around the center of the sun however (take that Capernicus); two masses actually rotate around their center of mass.

Imagine Center of Mass as an average in space (The red square in the image above).  If you and I were the exact same size (first set of circles), our center of mass would be exactly halfway between the two of us.  If I was twice the size of you our center of mass would be 1/3 of the way from me to you (second set of circles).  If I were the sun and you were the earth I would be ~ 330,000 times as massive as you and our center of mass would be somewhere super close to my center, but not exactly my center.  Therefore as you moved around me it wouldn’t be exactly around my center, but we would both rotate slightly off my center and make an ellipse (third set of circles)! Simultaneously all of the other stuff in the universe is technically all revolving around each other’s centers of mass.  Since the sun is so massive and close to the earth in comparison to everything else this will only change the center of mass of the system slightly but this will change our orbit constantly.  It will become slightly more, and slightly less elliptical.  As it becomes more elliptical parts of the orbit get closer to the sun obviously warming up the earth, parts of the orbit are further from the sun – cooling the earth.

A+ art! Also this picture represents a much more dramatic change than what actually happens

This process has ~ a 100,000 year cycle.  Yup, 100,000 years.  Again geological time is incredibly long.  Mathematically Orbital Shape is expected to have the least effect on global climates.

Axial Tilt

Another early fact we learn about the planet is that the earth is “tilted” when compared to its daily rotation.  This is what makes our seasons.  When the top of the earth is tilted towards the sun, it is both closer and receives more direct sun light causing Summer.  The opposite is true for winter.  It is like you leaning closer and further from a fire.  This tilt is caused and also affected by all of the other things in the universe constantly pulling on the earth.  The axis of the earth changes from ~21.5^o to 24.5^o.  At a higher degree we see more drastic summers and winters (close/further and more direct light) than at a lower degree.  

This process takes 41,000 years to complete. Mathematically Axial Tilt is expected to have the most effect on global climate.

Axial Procession

Axial procession gets the honor of the coolest name, most confusing effect to explain, and least effect on the climate.  The effect is most easily described in the following two pictures:

Basically, as the earth spins on its axis it is not always pointing in the same direction.  Imagine you are playing dizzy bats (Warning Dizzy Bats is Dangerous!); you place your head on the bat and start spinning in a circle.  The bat does not stay perfectly perpendicular though because you are most likely intoxicated and as you spin in the circles the top of the bat also travels in a circle.  This is basically what the earth does.  In conjunction with the changing orbital shape we now get different types of “Summer”. When the earth is tilted directly at the sun (either North or South Pole) and its orbit brings it closest to the sun we get the most direct light possible, and are closest to the sun (marked as “Hottest Summer!”). The opposite of all of that is also true for winter.  

Axial Procession has never been the most dominant of the three cycles, it makes the effects of the previous two more or less drastic.  A full procession takes 26,000 years.

Issues with the Cycles

Prior to ~ 1 million years ago for well over 2 Million years the earth saw periods of glaciation ~ every 40,000 years.  Periods of glaciation refer to times when the planet cools and glaciers grow with varying severity.  This matches up nicely with the Axial Tilt cycle we talked about earlier.  This is also a comfortable result for a physicists or mathematician, they expect Axial Tilt to have a major effect on the planets temperature and if glacial periods occur every 40,000 years we would seem to have identified the cause of climate change. 

“Joe at the beginning of this blog you said there are all those inputs into the climate how can we just ignore all of them!?”  We do approximations like this all the time in math and physics; if one part of an equation is so dominant we can approximate the other parts as 0.  

Imagine you were a Banana Tycoon and lost 1 banana out of every 100 million you ship due to your very cheap shipping containers.  You lost 1 million  more due to moisture in your ships hulls.  Depending on your profit margins you may ignore both problems, address the moisture issue and likely never address your cheap containers.  We do the exact same thing in science and engineering all the time when we solve problems.

The last million years have thrown a wrench into this result however as periods of glaciation have slowed to almost exactly 100,000 year cycles.  While this cycle does line up with our Orbital Shape cycle it does not explain no longer following the Axial Tilt cycle.  Also while the Orbital Shape cycle varies from 90,000 years to 120,000 years, the periods of glaciation have stayed stagnant at 100,000 years.  This result is basically the opposite of our Axial Tilt result.  

Imagine now you are a small town Banana stand owner who sells 100 bananas a day.  You lose 1 banana a day to rot.  If you stay a small town Banana stand owner you'll just ignore this rot forever.  As you grow into a Banana mogul however your 1/100 becomes 10,000/1,000,000 a real issue!  When a physicists or mathematicians has used an approximation but the formulas do not reflect reality they have to go through and consider all of the effects they approximated away.  We have all seen videos of old bridges that have gone wild in the wind (if you haven’t (see ya later bridge).  This is the result of someone not understanding that when they scale there small models the itty bitty terms they treated as 0 become huge, bridge shattering terms. 

Basically the climate

It is because of these shifts in glacial periods that we must consider all of the factors affecting the climate. Things like fossil fuel emission, deforestation, urban sprawl which you reasonably could approximate as 0 with a 40,000 glacial period need to be looked at much closer. 
No matter what we do the planet will get colder, it will get warmer, crops will thrive and struggle, but being able to accurately predict the result, as well as trend our effect on the planet, is invaluable.  While it would be naïve to assume our total control of climate change – it is also incredibly naïve to not see the merit in studying it.   

Next UP: Not Simply Science: The Inverse Square Law; Simply Climate: How we Measure the Climate of the Past


Image Credit: 

http://empowereddollar.com/money-in-the-banana-stand/
https://upload.wikimedia.org/wikipedia/commons/4/43/Earth_precession.svg
https://upload.wikimedia.org/wikipedia/commons/6/68/Precession_and_seasons.svg
http://www.engineergirl.org/what_engineers_do/FunFacts/TacomaNarrows.aspx

"Crank you For Being a Crank" - How we Make Electricty

 The goal of this post is to explain the different forms of Electricity production we use in the United States.  There is a lot of hand waving and we'll be skipping most of the nitty gritty physics, but none of that is important to talk intelligently about alternative energy!  We are constantly bombarded by "clean energy" and "alternative energy" but if you do not know how energy is currently being produced, how could you understand the alternative.  While the sexy topics will always be products like Teslas and Priuses, electricity is a giant consumer of fossil fuel.

Alternating Current

Almost all electricity we create is “Alternating Current” or AC.  We’ve all heard things like 120 Volts AC @ 60 Hertz (or 50 Hertz if you are chilling on another continent).  AC simply means the current is constantly swapping back and forth from positive to negative.  Image you had a fish tank and were shaking it back and forth so that a wave was going back and forth 60 times a second (yes your arms would get mighty tired).  We then fix a ball which can go up and down in the middle of tank at the surface of the water.  This up and down motion of the ball is what we are trying to harness when we use AC electricity.  For heavier balls we would need to shake our arms harder or use more water.  Making a ball move up and down may not seem like the most efficient use of our energy, but now let’s imagine that coming out of the front of the ball is a rod, and this rod is attached to one end of an old water pump.  As we shake back and forth, the ball goes up and down, the pump fills and expels water and now we are cooking.  With this stream of water we can get up to all sorts of hijinks.

Producing AC Current:

To make AC Current we need two things from our example, Boundaries and the Energy to move these boundaries back and forth.  The water in the example is electrons, the little guys that move around to transfer the energy, and the ball is whatever we are plugging into the outlet.

For boundaries we are going to use large, strong magnets.  Magnets by themselves will not cause the electrons to move they simply tell them where to go.  They are like the tank in the example.  They will force the electrons back and forth once we start to introduce energy.  Due to how magnets and coils of wire interact the energy we need to put into the system is to spin a coil of wire between the magnets.   As we spin the coil the electrons start to go back and forth and an AC current is caused.  The more coils of wire and the stronger the magnets the more electricity we make.  We now have a goal – take something large spin it about an axis.

We have been spinning things around an axis since the wheel was invented.  Any type of engine you can imagine can be used to generate AC power – combustion, coal, steam, water, hand crank (Unbreakable Kimmy Schmidt style).  Your classic power plant is basically a giant fossil fuel eating machine.  Large engines spin large coils around and around.  The rest of the plant is concerned with regulating the voltage and current coming out of it, but for the sake of this blog we can pretend a traditional power plant is a huge car engine and the only thing it is driving is the alternator.  No matter your opinion on fossil fuel exhaust, the traditional power plant produces a ton of it.

The primary way we spin stuff around stuff is steam.  Unlike a combustion engine we aren’t exploding anything to spin the engines but heating water or gas to create steam.  Tremendous pressure can be created to then spin a turbine, spinning a coil, creating electricity.  The simple steam engine uses coal for fuel.  You light it on fire, place it under some water and it burns for a long time; we have been doing it for forever.  Coal has questionable emissions and a huge lobby behind it.  Clean coal… also has questionable emissions and a huge lobby!  Recently natural gas has taken up the flag alongside coal as our largest electricity producing fuel.  Similar to boiling water on your stove, you just burn the natural gas to create heat and boil water or gas to create steam.

66% of our Electricity is estimated to come from burning Coal (30%+), Natural Gas(30%+) and Petroleum (1%).  90% of all coal produced in the US went to electricity in 2016.

The much harder way to create steam is nuclear power.  That’s right, the end goal of a nuclear power plant, which uses the sum of all human knowledge from the beginning of time until now, is to create the same thing your gas stove cane make.  A nuclear reactor utilizes nuclear fission (topic of another post) to create heat.  The important take-away of nuclear fission is that it produces a ton of energy, once started uses very little fuel and creates waste we have no way currently of getting rid of.  Newer and newer reactors are being designed which either create very little waste, or can re-seed old waste to reuse as fuel.  These are what the fossil fuel lobbies are fighting against.  I could spend the rest of forever talking about how I feel nuclear power plants will become Americas new “New Deal” but I’m trying to wrestle my bias into submission.

20% of our Electricity is estimated to come from Nuclear Power.

Finally we use nature to make AC power.  Naturally occurring sources of energy like wind and water can be used to turn generators.  We have been using dams and wind turbines for a long time.  Their advantages are free fuel and little to no environmental impact.  Their disadvantage is they are limited in location by the existence of the naturally occurring energy.  You cannot create a dam where there is no moving water; you could put all the wind turbines in the world in Camden County, NJ and would be better served hand cranking your generator.

6% of our Electricity comes from Water power, and 5% from Wind.

Direct Current

Direct current or DC, unlike AC is “one direction”.  It is much more like pushing water through a hose.  At the end of the hose is a ball we want to move.  If the ball is heavier we either need to increase the pressure of the water, increase the width of the hose to let more water through or both.  It’s pretty easy to see the appeal of DC; if I want to move the ball forward I point my hose at it and shoot; no intricate system of energy exchanges as seen in our water tank example.  For this reason (and others) we use DC to drive pretty much everything.  Your appliances, car, electronics, are almost all all DC circuits.  “Liar!” you say!  “My house has AC coming into it from the street and you just spent 10 minutes telling me that all of our Electricity is AC”.  Producing DC is difficult and expensive.  It is much easier to shake the tank back and forth and lose some energy along the way than constantly push water through the hose.

Generating DC current:

The DC current producers we are most familiar with are batteries.  Batteries utilize chemical reactions to create a constant flow of electrons.  To compare to our analogy, the chemical reaction would be the water pressure required to push the water through the hose.  New batteries are constantly being researched and advertised however think about how often you have to recharge your iphone or laptop.  The amount of energy needed to put back into the system to create DC power via chemical reactions is just too high to be commercially viable, which is why we only use it for portability’s sake.

What if the energy to recharge DC power cells was free though?  This is what solar panels attempt to capitalize on.  The sun can provide energy that is not only free but also unlimited and incredibly powerful.  They utilize the light of the sun to stimulate electron flow.  The power is then used to recharge batteries to provide constant current (the sun isn’t always out), or converted to AC power and used as before.  For a long time solar faced all types of setbacks.  Solar panels were difficult to make, expensive and so inefficient it did not make sense to use them for anything aside from small power and academic reasons.  This has become less and less true as more and more research has gone on and they are now much more competitive.

 

Next Two Posts: Natural Causes of Climate Change -- Crash course in Electrical Engineering

Image Credit: https://s-media-cache-ak0.pinimg.com/originals/2c/63/fd/2c63fdef57811e14971a972ad71350eb.jpg

 http://www.hnashe.com/

Energy Statistics Credit:  https://www.eia.gov/tools/faqs/faq.cfm?id=427&t=3