"Sally Sells Sea Shells In the Sea Floor" - How we measure the sea level of the Past

Today we are going to move onto another topic we hear about all the time which NO ONE bothers to explain: Rising Sea Level (RSL).  This may be because at its core RSL is pretty simple to understand --  As the earth heats up, glaciers melt – As glaciers melt there is more free water on the planet – the water has to go somewhere so the oceans and seas rise.  Like most of climate science, the effects of a warming earth are not really debatable – this is happening and has happened for a long time.  Also like most climate issues we are attempting to figure out how much humans have already and will impact these changes.  In future posts we will go into the effects of a rising sea level but for now we are going to show how scientists learn about sea levels of the past.  Learning about the planet's past is our only way of accurately predicting its future.

As technology has advanced we are able to measure sea level changes very accurately.  Just like with greenhouse gasses though we need to look into the earth to unlock past sea levels.  This post will walk through how scientists have unlocked the history of sea levels throughout the last several glacial periods.  This process "hopefully" will highlight just how clever scientists have to be to validate their ideas and data.  There's not such thing as a free lunch - and there is no such thing as a free hypothethis!

Sea Levels of The Past

At the largest scale, the easiest way to determine past sea levels is to look at the make-up of the land borders of large bodies of water.  Along these borders (think cliffs along the ocean) we will see rock formations that seem to be formed by tides coming in and out much higher along the cliff than the tide will ever reach now.  Similarly if we put our scuba masks on and dived beneath the tidal line of today we would see similar formations much deeper in the water.  These geological formations aren’t going to give us any exact information but they at least give us some perspective – the earth’s sea level has been all over the place throughout its history.

Using similar thinking as we did for learning about the atmosphere of the past (Ice Cores) – we are looking to find out how the sea level has changed over the last several hundred thousand years.  This information will give us climate cycles that are similar to the one we are in now; letting us make educated guesses about our future and giving us thousands of years to test those guesses against.  When scientists were looking to find out about the past atmosphere they needed to find somewhere the earth stored this information and came up with glaciers.  What on earth has spent its history storing information about sea level?

Globigerinoides ruber d'Orbigny

This little guy is known as Globigerinoides ruber d'Orbigny but we are just going to call him a plankton (plankton are always rearing their heads when we talk about the climate). Plankton like these live in the ocean and have hard outer shells, like tiny single celled coral.  To make their shells they take calcium, carbon and oxygen in the water and combine them to form something like limestone, typically having a chemical formula: CaCO₃.   These plankton then die and their skeletons get turned into fossils and are embedded in the ocean floor.  Hopefully something from the ice core blog post sticks out in your mind (if not read up about it there J ); there are two distinct types of Oxygen in our atmosphere “heavy” and “light” oxygen. 

“But Joe we know that heavy and light Oxygen levels change with global temperature not sea level!” This is true, especially for areas of the ocean near the poles – but let’s think about areas that might be home to our tiny plankton friends whose heavy to light oxygen ratio should stay the same regarless of temperature.

Both the Mediterranean sea and the Red sea are exactly what we are looking for.  Our tiny plankton friends thrive in their salt water bodies, their climates have stayed relatively stagnant over much of recent (500,000+ years) past and they only have one way to interact with the ocean both through narrow (comparative to their size) straights.  If sea levels never changed in these seas, especially the Red sea, the ratio of heavy to light oxygen in our plankton shells would remain the same. 

We (and scientists) are going to use the Red Sea for our example as its oxygen ratios and interaction with the ocean are more stagnant than the Mediterranean Sea.  As temperatures rise and glaciers melt more heavy oxygen evaporates out of the ocean.  This “less heavy” ocean then feeds into the Red sea from the Indian Ocean (the extra water has to go somewhere) and new plankton shells are created.  As temperatures fall and sea levels go down, the previous “lighter” ocean leaves the Red sea leaving a “heavier” ocean than before.  We then core the Red Sea bottom like we do a glacier to extract the sea level data of the past.

Issues with our Cores

The biggest issue with the Red Sea cores for a very long time (until 2012/2014) was there was no great way to date them.  The Red sea plankton shells give very detailed sea level information – unlike an ice core where the oxygen can escape and spread throughout the core – the oxygen in the plankton fossils are stuck, basically forever.  This is exactly what we are looking for, however without knowing the time these sea levels happened at we cannot compare them to the climate at the time.

For a long time scientists attempted to use glacial cores to date Red sea cores.  If we assume that a warmer climate gives us a higher sea level you can sort of line up the sea level peaks with temperature peaks.  This gives you some date to work with however it has many issues. First, the glacial cores are hard to date themselves; basing data off of already difficult to verify data is not a winning combination.  Next and maybe even more problematic is this does not allow us to see the relationship between climate, CO₂ and sea level.  We are kind of arbitrarily matching up temperature and sea level;  not allowing the data to tell us what the relationship is.

Luckily the earth provided scientists what they needed to accurately date the Red sea – “speleothems!”

Salt Monster!

A speleothem is a fancy word for Salt Castle!  They are created when ocean air blows into a cave; the air then condenses on the roof of the cave and leaves the salt behind somewhere i.e. the cave ceiling.  The caves in question are the “Soreq” caves on the south east of the Mediterranean Sea which you can visit as a tourist in Jerusalem.  These are basically mineral stalactites which contain – you guessed it- Oxygen!  The heavy to light oxygen in the Soreq speleothems is not nearly as “locked in” to sea level as the plankton fossils in the Red Sea (the Med. Sea is affected by temperature more than the Red Sea), however it is very easy to date.  While we cannot use the speleothems to give the exact changes in sea level it accurately tells us when the changes occured.

 

We now have a very accurate measure of sea level changes from the Red Sea and a very accurate time line of the changes from the Soreq caves which yields graphs like this:

With this information in our pocket we can now start predicting the sea level in response to temperature and green house gasses.  The study from above was not completed until 2014 and more and more research is constantly being done in the field. For some reason climate deniers pretend that everything we need to know about the environment is known already – in reality the science is still being discovered, being analyzed.  We are gaining more and more knowledge about things we could only make guesses about before.

The first 3 links in the citation are the studies most of this information is based off of- they are pretty dense reads but incredibly informational and worth at least parusing at your liesure ;)

Citations:

https://www.researchgate.net/publication/233418145_Rapid_coupling_between_ice_volume_and_polar_temperature_over_the_past_150000years

http://www.nature.com/articles/ncomms6076?WT.ec_id=NCOMMS-20141001

http://earthobservatory.nasa.gov/Features/Paleoclimatology_OxygenBalance/

http://www.nature.com/scitable/knowledge/library/drip-water-hydrology-and-speleothems-26394838

http://phys.org/news/2014-04-million-year-sea-temperature.html

https://us-static.z-dn.net/files/d50/8b8583c00559d0d1dc9103094e30601e.png

Not So Simply Climate- "Hey Kid I'm a Computer!" or Boolean Logic Explained

We spent the weekend in NYC with the family and visiting friends so I wrote up this "Not So Simply Science" post and never got to publish it.  Thus it will take Monday's post spot- hope you all enjoy it.

Today’s post is a detour from the pretty heavy climate talk of the last two weeks.  We’re going to talk about something I truly love working with and basically spend most of my day thinking about – Boolean logic.  Since this is a Not So Simply Climate it legitimately has nothing to do with climate science, however Boolean logic is what defined the late 20^th and early 21^st century so it can’t hurt to learn about it!

Boolean just means any variable can only be in two states.  The two we typically use are “True and False” or “0 and 1”.  You have most likely heard of it called “binary logic” and it is how we design almost all consumer electronics.  Using electricity to do complex math and logic is tedious and fickle.  Using electricity to do very very simple things incredibly fast is easy and super repeatable.  Breaking everything down to the simplest form possible then, True/False, is what we are trying to take advantage of.

If any of this seems interesting to you maybe pick up programming or micro electronics as a hobby.  Or make your kids take up Computer or Electrical Engineering --- it’s a pretty good time.  

Operations

There are 7 basic “operators” in Boolean logic.  An operator is something like ‘+’ or ‘x’ it tells you what to do between two variable.  If we see “3+3” and “3x3” we know that one yields 6 and the next yields 9.  However what does “True + True” mean? What does “True+False” mean? What does “True * True” mean?  We need to define these operators to then build even more complex operations from them.

NOT

Not is the only logic operator which acts on a single input.  It simply “flips” the input into whichever state it isn’t.  So a 0 becomes 1, 1 becomes 0, False become True, True becomes False.  NOT is incredibly useful – it lets you figure out a way to do something, and then whenever you need the “opposite” you just throw a NOT on the end.  NOT is denoted a couple ways.  In programming we put a “!” in front of the variable or equation we are working with.  In a logic equation we put a line over the variable or equation.  Finally in a logic circuit it is represented by a triangle with a circle on the end:

“Not” has a pretty simple Truth Table:

Y = NOT(X)
X	--->	Y
0	--->	1
1	--->	0

AND

“AND” operates on two inputs (as will the rest of the operators).  AND will only ever be “True” if both inputs are “True”.  So if one input is false and another true I cannot say “A is True AND B is True” So it is false.

“AND” is denoted by “&” in programming, the multiplication symbol in equations and this symbol:

 “AND” has the following truth table:

X*Y = Z
X	Y	--->	Z
0	0	--->	0
0	1	--->	0
1	0	--->	0
1	1	--->	1

OR

“OR” is true if any input is True.  If A is True and B is False I can say “A or B is True” and be correct.  Or is represented by “|” in programming, an addition symbol in equations and this symbol:

 “OR” has the following truth table:

X+Y = Z
X	Y	--->	Z
0	0	--->	0
0	1	--->	1
1	0	--->	1
1	1	--->	1

Our next two operators are going to be the “opposite” of the previous two.  Their names are not all that clever. 

NAND

 “NAND” is simply the opposite of AND.  NAND is represented by: 

You can think of it in two ways:

-          This will only be true when both inputs are False

-          I can simply perform an “AND” and then a “NOT”

The truth table for NAND is:

!(X*Y) = Z
X	Y	--->	Z
0	0	--->	1
0	1	--->	1
1	0	--->	1
1	1	--->	0

NOR

“NOR” is simply the opposite of OR.  NOR is represented by:

You can think of it in two ways:

-          This will only be true when Neither input is True

-          I can simply perform an “OR” and then a “NOT”

The truth table for NOR is: 

!(X+Y) = Z
X	Y	--->	Z
0	0	--->	1
0	1	--->	0
1	0	--->	0
1	1	--->	0

XOR

“XOR” is the “Exclusive OR” operator.  I have always said it as “zore” like sore with a Z.  This is not how you say it but I don’t care – it’s been 10+ years and I’m not changing.  The XOR is only TRUE if one and only one of its inputs are TRUE.  We think of it as A or B is TRUE, but NOT both A and B. Later we’ll explain why it is important but it is the foundational operation in our computer processors.  Xor is represented by ⊕ or:

The Truth table for XOR is:

(X⊕Y) = Z
X	Y	--->	Z
0	0	--->	0
0	1	--->	1
1	0	--->	1
1	1	--->	0

XNOR

Finally we have the “Exclusive NOR” or “Ex NOR”.  Hopefully you can see the pattern… this is the opposite of the Exclusive OR.  It is only True if both inputs are the Same.  We think of it as “Are A and B both True or Both False”.  XNOR sadly doesn’t have a cool symbol, you just put a line over an XOR equation, the circuit symbol looks like: 

The truth table for XNOR is:

!(X⊕Y) = Z
X	Y	--->	Z
0	0	--->	1
0	1	--->	0
1	0	--->	0
1	1	--->	1

Making Operators from other Operators

The easiest operator to make in the physical world are NAND and NOR operators.  This has to do with how transistors are made and maybe we’ll go into it in a later post but for now you need to know they take up the least amount of silicone, space, and can be crammed next to each other easily. When we say “new computer chips have X billion transistors” most of those transistors go to making NOR or NAND operations.

Here is a super simple example.  Lets imagine some variable X.  What if I made X BOTH inputs to my NOR function. 

NOT

The truth table looks like this:

!(X+X) = Z
X	X	--->	Z
0	0	--->	1
0	1	--->	0
1	0	--->	0
1	1	--->	0

So if X is False, then Z will be true.  If X is True, Z will be FALSE.  We have now made a NOT operator! 

Well if we have a NOT operator, and we have a NOR operator… you bet we can make an OR operator:

OR

This is simply a NOR followed by a NOT.

Finally let’s make an AND operator.   Look at the truth tables for AND and NOR.

AND is only true if both inputs are TRUE.  NOR is only true if both inputs are FALSE.  So if we can take two “1’s” make them both “0” and input them into a NOR we will get a 1.  The logic circuit looks like this then:

AND

After the first line both A and B will be !A and !B, and finally Nor’d together.  The truth table looks like this:

!X = Z			!(X+Y)=Z
X	Y	--->	!X	!Y	--->	Z
0	0	--->	1	1	--->	0
0	1	--->	1	0	--->	0
1	0	--->	0	1	--->	0
1	1	--->	0	0	--->	1

We get exactly what we desire, the AND function!

The XOR function is more complicated and I do not think we gain a ton walking through it but I’ll show it and you can figure it out for yourself:

XOR

Addition

The last thing we’ll create is an Adder, i.e. we will be adding A and B together.  Remember we are using binary numbers so: 

-          0+0 =00

-          1+0 =01

-          0+1 = 01

-          1+1 = 10

o   Just like in our traditional base 10 system 5+5=10, in binary 1+1 = 10

Since we only have our logic operators we are going to use our friend the truth table to see what we need.  For the “1s” digit we have:

X+Y = Z
X	Y	--->	Z
0	0	--->	0
0	1	--->	1
1	0	--->	1
1	1	--->	0

I hope this looks familiar, as it is exactly the XOR function. So the ones digit will be solved with an XOR operator.

Let’s look at the 2’s digit or the “Carry” digit (just like 5+5 is 0 “Carry the 1” so is 1+1).  The look up table is:

Carry(X+Y) = Z
X	Y	--->	Z
0	0	--->	0
0	1	--->	0
1	0	--->	0
1	1	--->	1

Ding ding ding! This is just our AND operator.  So to make a single bit adder we need to put together our XOR and AND operators:

Single Bit Adder

Here are some ways we can expand on the single bit adder; how do we add in the carry bit so we can add more than 1 bit at a time i.e. add 3 bits together; how do we subtract two numbers; how do we multiply two numbers?  We can do all of these things with just the logic operators we have laid out in this post.  We just keep putting the small pieces together to build larger and more complex pieces. 

These 7 operators and the ADD are the foundations of our computers – hell they are why computers are called computers.  We are doing Boolean arithmetic millions to billions of time per second to shape our world!