Humanity has always built models to better understand complicated observations -AND- serve as teaching tools. Building a
working model proves "you are in possession of all the facts". Deviation from observation proves that your model needs to be
improved or replaced.
Early Mechanical Models of the Solar System
In ancient times people built mechanical models of our solar system to predict the current location of the planets and stars.
These models were based upon naked-eye observations and worked well until better observations proved otherwise. Model builders
responded by adding epicycles to the planetary positions
(perhaps this was just the easiest fix for a mechanical model).
In medieval times, Nicolaus Copernicus suggested that a heliocentric system would simplify the models but this idea seemed too revolutionary to most people (even
though it had first been suggested in 300 BC by Aristarchus
of Samos). Improved (but non-magnified) observations by Tycho Brahe
coupled with mathematical analysis by Johannes Kepler proved that
planetary orbits needed to be changed from circular to elliptical (how would the mechanical model builders accomplish this?).
Telescopic observations by Galileo proved the heliocentric
system was correct but now the Roman Catholic Church stood in the way of scientific progress. Many scientists avoided
controversy (including burning at the stake) when they stated "we don't really believe in the heliocentric system, it
just simplifies our models".
Although work done by people such as Urbain Le Verrier (who
used pen and paper to predict the location of an unknown planet eventually named Uranus) is unbelievably impressive, a computer
is required to model known planetary and stellar motion. In short, a mechanical model is no longer possible or practical.
Furthermore, if the Earth was the only planet orbiting the Sun, the shape of Earth's orbit would eventually degrade into a
circle. However, the gravitational tugs of other planets causes the shape of Earth's orbit to change from circular to elliptical
and back in a time period of 400,000 years. This theory was
also worked out using only pen-and-paper by the Serbian mathematician
Milutin Milankovitch but remained a mathematical abstraction until computer modeling was applied. BTW, other aspects of Milankovitch Cycles combine in such a way to enable glaciations
(ice ages) every 120,000 years or so. Our current inter-glacial period (known as the Holocene)
started 11,700 years ago.
Computer Limitations (and Science Limitations)
Because computers can be used to calculate equations many millions of times faster than any human, modern life would be
impossible without them. For example, who could imagine any government manually processing our income tax claims? However,
computers do have limitations most people are not aware of.
Experiment: the next time you pour cream into your coffee, carefully watch the swirling clouds as the
two fluids (liquids in this case) mix. This turbulent behavior is partly
based upon a combination of chaos theory and fluid
dynamics. Unfortunately no computer on the planet now (2010), or any time soon, is able to accurately model this. Think
about it: you are only mixing two liquids so why is the resulting action so complicated? To make matters worse, every time you
perform the coffee-cream experiment you will observe a slightly different result. So maybe we need to consider more details
like: exact volumes and temperatures of each liquid, height the cream is poured from, place where it has been poured into, exact
components of the cream, exact components of the coffee, viscosities of both liquids, smoothness and shape of the container,
swirling speed of the coffee from the initial filling event, etc.
It turns out that an accurate computer model will require us to mathematically compute the properties and trajectory
of every molecule. Since computers won't be doing this anytime soon, perhaps we can cut corners by only computing
the average action of each deciliter (one tenth of a liter) at ten second intervals. As long as the simulation gives
us a homogeneous mixture after 2 minutes and possibly allows the cream to settle to the bottom after a couple of hours then our
computer simulation might be good enough.
Future improvements in computer technology along with advances in computer programming techniques might allow us to slowly
reduce the average volume modeled along with the average time-period being simulated. And yet we are still only talking about a
cup of coffee.
Modeling Earth's Climate
Simulating Earth's Weather with Pencil and Paper
The first attempt to do a model Earth's weather was done with pencil and paper using something called the two-box
model. This scheme (which is still used today to teach science students) uses two boxes to model the whole earth. The
top box represents Earth's atmosphere while the bottom box represents Earth's surface. It is obviously very simplistic but a
little tinkering provides a good starting point to other more complicated models.
The two-box model was replaced with two-dimensional models, three-dimensional
models, then finally cell models. A complete description of these models is beyond the scope of
this introduction but you can Google the phrases to investigate further.
I recently stumbled upon a first serious attempt to do a cell model which was attempted in 1922 obviously without the aid of a
computer. Excerpt from: www.aip.org/history/climate/GCM.htm (please
read this constantly updated article)
In 1922, the British mathematician and physicist Lewis Fry Richardsonpublished a more
complete numerical system for weather prediction. His idea was to divide up a territory into a grid of cells,
each with its own set of numbers describing its air pressure, temperature, and the like, as measured at a given hour. He would
then solve the equations that told how air behaved (using a method that mathematicians called finite difference
solutions of differential equations). He could calculate wind speed and direction, for example, from the difference
in pressure between two adjacent cells. These techniques were basically what computer modelers would eventually employ.
Richardson used simplified versions of Bjerknes's "primitive equations," reducing the necessary arithmetic computations to a
level where working out solutions by hand seemed feasible. Even so, "the scheme is complicated," he admitted, "because the
atmosphere itself is complicated". The number of required computations was so great that Richardson scarcely hoped his idea
could lead to practical weather forecasting. Even if someone assembled a "forecast-factory" employing tens of thousands of
clerks with mechanical calculators, he doubted they would be able to compute weather faster than it actually happens. But if he
could make a model of a typical weather pattern, it could show meteorologists how the weather worked. So Richardson attempted to
compute how the weather over Western Europe had developed during a single eight-hour period, starting
with the data for a day when scientists had coordinated balloon-launchings to measure the atmosphere simultaneously at various
levels. The effort cost him six weeks of pencil-work. Perhaps never has such a large and significant set
of calculations been carried out under more arduous conditions: a convinced pacifist, Richardson had volunteered to serve as an
ambulance-driver on the Western Front. He did his arithmetic as a relief from the surroundings of battle chaos and dreadful
wounds. The work ended in complete failure. At the center of Richardson's simulacrum of Europe, the computed barometric pressure
climbed far above anything ever observed in the real world. "Perhaps some day in the dim future it will be
possible to advance the calculations faster than the weather advances," he wrote wistfully. "But that is a dream."
Taking the warning to heart, meteorologists gave up any hope of numerical modeling
Weather vs. Climate
We all know that weather reports today are not very accurate, and yet, they have improved considerably since the 1950s. In
certain instances, such as tropical depressions which can develop into hurricanes, weather reports may be reasonably accurate
over a period of 7-10 days. But just like our cup-of-coffee example described previously, skipping over the short-term details
will allow us to predict long-term trends. This is the major difference Weather and Climate and I should point out that "climate
models" are much better than "weather models".
"Climate vs. Weather"
modeling of the environment in a period of 1 to 100 years
modeling of the environment in a period of days to weeks
Even if it was possible to accurately model climate or weather, you cannot mathematically model all the inputs. For example,
here are two (of many) events which appear to act randomly:
There are 500 active volcanoes on Earth today with as
many as 1,500 potentially active volcanoes. However, there does not appear to be any mathematical
pattern which would describe their frequency or intensity. To make matters worse, all active volcanoes release a variable
(random) volume of CO2 which will increase the greenhouse effect. To make things more complicated, while some
volcanoes release larger volumes of dark-colored particular matter which absorbs sunlight, other volcanoes release light-colored
particulate matter which directly reflects sunlight back into space. Some volcanoes also release sulphur dioxide compounds which
stimulate cloud formation (silvery clouds are the perfect sunlight reflectors). Inspect the chart to the right and notice how
the black line drops in 1991 due to the effects of Mount Pinatubo
Added Complication: CO2 can remain in the atmosphere for 100 years or more. The effects of white
particulate matter and/or sulphur dioxide will only last one to two years. So what might initially appear to be a short-term
cooling event eventually will be a long term warming event.
One cigarette improperly discarded in a National Park occasionally will start a massive forest fire resulting in a
massive release of heat, smoke, and CO2 into the atmosphere.
These seemingly random events (along with the previously mentioned turbulent behavior of fluids) need to be manually inserted
into our climate models.
Simulating Earth's Climate (a very simple starting model)
simple 16-cell model
Imagine for a moment, a spinning Earth which is cut vertically into 4 columns and horizontally into 4 rows which results in 16 zones. We now need to write an a single equation for each zone which would simulate:
the quantity of solar energy entering each zone over the course of a day
the quantity of energy temporarily absorbed by: soil, melting ice, warming water, and evaporation
the quantity of energy being radiated back into space; especially at night
the quantity of energy temporarily released by: freezing water, and precipitation.
Because there is more sunlight at the equator, a greater amount of sunlight will be absorbed in rows A + B than rows N + S. In
fact, you may wish to visualize an oval of light stretched from North to South and wide enough to cover two columns at the
equator. Because the surface of the globe is spinning west-to-east (left to right), our view of the solar oval will be seen to
Because the surface of the globe is spinning west-to-east while the atmosphere wants to stay put, an apparent east-to-west wind
will be blowing over the equator so we'll need equations to describe that as well. Depending upon how you handle parameter
communication between zone boundaries, you will probably need at least 28 (12v+16h) inter-zone calculations.
(column 4 zones are connected to column 1 zones; there are no zones above row N or below row S because these are actually
This means that each simulated tick of the clock will require at least 44 (16 zone + 28 inter-zone)
calculations. You might be able to try this with pen and paper but it will be time consuming and error prone. Moving
the simulation into a computer will allow you to introduce larger (more accurate) equations into each location.
If you are brave then you'll need to introduce seasonal changes. This means that the A1 would receive peak daylight in June
while B3 would receive peak daylight in December. It might be easier to visualize a single sine wave superimposed upon our model
where the phase shifts one full cycle over the course of a year.
Simulating Earth's Climate (more layers)
Although solar energy directly heats the ground wherever it falls on land, heated ocean water tends to redistribute energy via
events as small as evaporation and as large as hurricanes, which all occur in the atmosphere. Ocean energy is also responsible for
water currents as small as the Gulf Stream and as large as the
Thermohaline Circulation which all occur at, or below, the surface. This means we might want to introduce a second layer so
atmospheric events could be simulated in the upper layer while ocean events would be simulated in the lower layer.
Doubling the zones from 16 to 32 means the number of zone calculations must double from 44 to 88 but but we need to add 16
additional calculations to handle the flow of energy between adjacent zones in each layer. We now require 104
(88 + 16 interlayer) calculations for each tick of the simulation clock. Yikes!
But do we have enough squares? More land exists in the Northern Hemisphere so more squares would allow us to code for that.
Also, since uplift formed the Panamanian Land Bridge ~ 3 million
years ago (cutting off the Atlantic from the Pacific in Panama), ocean currents are blocked in certain areas while making
glaciations are more common. If we want to model ocean currents then we will need a lot more zones.
JASON - Climate Models commissioned by the U.S. Government
It is an historical fact that the US government commissioned a climate study in 1978 by a group of scientists known associated
with JASON. This group created a computer model with the
audacious name "The
JASON Model of the World" which produced a report in 1979 titled:
preindustrial CO2 concentrations in the atmosphere expected to double by 2035 (today's models indicate 2050-2100
depending upon human actions)
temperatures would rise by 2-3 C by the end of the 21st century (current models agree)
temperatures at polar caps would rise much faster; perhaps by 10-12 C (current models agree)
caveat: some temperatures in this report are given in degree changes Celsius while
others are given in degree changes Kelvin. Multiply either of these numbers by 9/5 to get degree
Simulating Earth's Climate in Large Data Centers
associated image and text in this section was borrowed from a NOAA (National Oceanic and Atmospheric Administration) web site.
It appears to be using at least 3 layers and thousands of zones.
Climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry.
To "run" a model, scientists divide the planet into a 3-dimensional grid, apply the basic equations, and evaluate the results.
Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and
evaluate interactions with neighboring points.
This is a data-derived animation of ocean surface currents from June 2005 to December 2007 from NASA satellites. Watch
how bigger currents like the Gulf Stream in the Atlantic Ocean and the Kuroshio in the Pacific carry warm waters across
thousands of miles at speeds greater than four miles per hour (six kilometers per hour); how coastal currents like the
Agulhas in the Southern Hemisphere move equatorial waters toward Earth's poles; and how thousands of other ocean currents
are confined to particular regions and form slow-moving, circular pools called eddies.
The visualization covers the period June 2005 to December 2007 and is based on a synthesis of a numerical model with
observational data, created by a NASA project called Estimating the Circulation and Climate of the Ocean,
or ECCO for short. ECCO is a joint project between the Massachusetts Institute of Technology and NASA's Jet Propulsion
Laboratory in Pasadena, California. ECCO uses advanced mathematical tools to combine observations with the MIT numerical
ocean model to obtain realistic descriptions of how ocean circulation evolves over time.
Departing Thoughts on Modeling
What climate professionals say "about climate models"
Climate models are mathematical representations of the interactions between the
atmosphere, oceans, land surface, ice – and the sun. This is clearly a very complex task, so models are built to estimate trends
rather than events. For example, a climate model can tell you it will be cold in winter, but it can’t tell you what the
temperature will be on a specific day – that’s weather forecasting. Climate trends are weather, averaged out over time - usually
30 years. Trends are important because they eliminate - or "smooth out" - single events that may be extreme, but quite rare.
Climate models have to be tested to find out if they work. We can’t wait for 30 years to see if a model is any good or not;
models are tested against the past, against what we know happened. If a model can correctly predict trends from a starting
point somewhere in the past, we could expect it to predict with reasonable certainty what might happen in the future.
So all models are first tested in a process called Hindcasting. The models used to predict future global
warming can accurately map past climate changes. If they get the past right, there is no reason to think their predictions
would be wrong. Testing models against the existing instrumental record suggested CO2 must cause global warming, because the
models could not simulate what had already happened unless the extra CO2 was added to the model. All other known
forcings are adequate in explaining temperature variations prior to the rise in temperature over the last thirty years, while
none of them are capable of explaining the rise in the past thirty years. CO2 does explain that rise, and
explains it completely without any need for additional, as yet unknown forcings.
Where models have been running for sufficient time, they have also been proved to make accurate predictions. For example, the
eruption of Mt. Pinatubo allowed modelers to test the accuracy of models by feeding in the data about the eruption. The models
successfully predicted the climatic response after the eruption. Models also correctly predicted other effects subsequently
confirmed by observation, including greater warming in the Arctic and over land, greater warming at night, and stratospheric
note: the text above is is an excerpt from this article
Facts based on modern (direct-measured) data:
All 25 accepted climate models are able to accurately model Earth's past climate from 1860 forward (1860 provided humanity
with accurate world-wide temperature measurements due to the manufacture and sale of inexpensive thermometers).
Scientists do not pick one model while discarding others; they publish the results from all models then plot them all
between confidence lines.
In the case of unexpected natural events like the volcanic explosion of Mount
Pinatubo, climate models must produce similar results when the unexpected natural event is inserted in the simulation.
All models all agree that:
Earth's climate is getting warmer, and this is mainly due to a combination of anthropogenic (human-made) warming COMBINED WITH natural warming (the previous glaciation ended 11,700 years ago with no help from
human population increases by one billion every 12 years. Anthropogenic
warming will increase faster as humanity releases evermore green-house gases.
Not one climate model shows our environment getting cooler.
The models do disagree with the point-of-no-return dates being anywhere from 2015 to 2050.
There are more weather satellites in orbit now than at any previous time and their measurements are being used to fine-tune
climate models. Some satellites continuously measure Earth's surface (land and water) temperature over every 16 km (10 mile)
square. Others measure glacial flow.
Caveat: Humans can not "directly" measure temperatures from space. Why? Temperature is inferred
Measuring the microwave radiation emitted by atmospheric gases (works like a microwave oven in reverse)
Measuring infrared radiation which is partially absorbed by ever-changing atmospheric gases between the heat-source
and the measuring instrument.
These readings are mathematically translated (the subject of some debate) into atmospheric temperatures. It is virtually
impossible to use satellites to measure temperature (with certainty) from various atmospheric altitudes.
The Arctic and Greenland are melting at an unprecedented rate. The resulting influx of fresh water could affect the ocean
currents like the Gulf Stream and the Thermohaline
Circulation which distribute equatorial heat to places like Northern Europe. This means the current effects of global
warming will cool some locations which will convince many people that global warming is not real.
Increased heat is causing increased evaporation which causes rain to fall sooner. Many locations are now getting too much
rain while locations down-wind are getting little or none. Therefore, Global warming brings shifting in
Facts based upon pre-modern proxy data
based upon data before 1860 can be useful but are less reliable. Why?
First off, while temperature measurements before 1860 exist, they are usually spotty. For example, the first known
temperature measuring device is the Thermoscope produced by
Galileo around 1592, but their restricted temperature range restricted them to [mostly] indoor use.
Development continued with various people creating a sealed tube then adding an external scale, but it was Christian Huygens in 1665 who first proposed the idea of
a standard scale based upon the melting and freezing points of water
In 1724, Daniel Fahrenheit creates a
thermometer scheme based upon a scale with freezing point of 32 F and a boiling point of 212 F
In 1742, Anders Celsius creates a thermometer scheme
based upon a scale with freezing point of 0 C and a boiling point of 100 C
There are numerous accounts of people keeping local records in England and Ireland some which are now held by
Britain's Royal Society of London. One very notable record
was created by Thomas Hughes for Stroud (Gloucestershire) between 1775 and 1795.
since the majority of trees which contain grow rings are found at mid latitudes (trees don't grow at either pole;
trees at the equator do not have annual growth rings) this proxy measurement is only of use in the northern hemisphere
since coral only grows in warm water, this proxy measurement is only of value in a thick band around the equator.
Pollen, Dust, and in Ice Cores
While CO2 in ice cores provide a fairly accurate measurement of atmospheric carbon dioxide at the time
the ice was formed, trapped pollen and volcanic dust only indicate those particles were in the vicinity of the
freezing water. However, Ice Cores are available from Antarctica which are over 800,000 years old and contain trapped
CO2 which can be mapped and proxied.
Okay so what do the climates models based upon proxies tell us?
Sunlight seems to vary by no more than one half of one percent. On its own, changes in sunlight do not do much but can add
to other anomalous effects. Sunlight is somehow involved in small changes in the jet stream (which can have large effects upon
Northern Hemisphere weather)
Global climate (and weather) are continually affected by both El Nino
and La Nina. This should be of little surprise since almost 50% of the
Earth (the Pacific side) is covered by water.
Volcanoes affect global climate and weather more than anyone ever realized. On average, they tend to cool more than heat.
Some heating effects in one area may temporarily cause cooling in other areas. Remembering that the British Isles are warmed
by the Gulf Stream (London and Moscow are almost at the same latitude so London should be a lot colder than it is), then
anything which affects the Gulfstream could have devastating effects on North-Western Europe
Facts and derivations:
The Medieval Warm Period was 2-3 degrees warmer in
the UK but only a degree warmer in both Labrador and Northern Europe (based upon various proxies including tree rings).
Proxies indicated lower warming elsewhere.
This warming coincides with a period of very low volcanic dust (observed in ice cores) combined with slightly higher
solar output (C14 Dating).
Since volcanoes stimulate cloud formation by releasing of sulphur dioxides, a reduction in volcanic activity will result
in more solar energy reaching the Earth
More solar energy reaching the Earth drove the gulf stream a little harder which primarily warmed: Greenland, Iceland,
The British Isles, and Norway.
This warming anomaly appears to have lasted at least 300 years (950-1250).
Three hundred years of heating resulted in an acceleration of ice melt (as compared to the rate since the end of the ice
age 11,700 years ago)
Any fresh water, including water from ice melt, can poison the descending (northern) end of the gulf stream
Once the gulf stream was partially poisoned with fresh water, any decease in solar energy (increased volcanic activity
producing more clouds, deceased solar output, etc.) would flip warming in the other direction. This happened and we now
know as the Little Ice Age which is thought to have started
between 1250 and 1275 and ended ~ 1700 Notes:
Starting and ending dates vary greatly depending upon which data are referenced
Some documents based upon human historical records use a starting date of 1350
Data based upon ice pack and glacial ice use 1250
Although solar energy was slightly reduced during this time, the effect was tiny compared to the loss of cloud cover
Like the medieval warm period, places affected the most by warming were similarly affected by cooling
Energy absorbed by Earth but not transported north by the Gulf Stream goes elsewhere and this is noticed in proxy
records from other locations
Emission Scenarios (Using Computers to Model Alternatives for Humanity)
Many citizens are unaware of a related activity done by scientists who coupled computer-based climate models to
computer-based economic models to project humanity's possible actions 100 years into the future.
This is done by restarting each climate simulation (computer run) using one of four different emission
scenarios labeled: A1, A2, B1, B2. The outputs are based upon ~40 different outcomes (averaged across more than 25
The "ones" column continues our trend to globalization while the "twos" column is a shift back to a more regional economy. The "A"
row places more emphasis on a economic health (continuing to burn fossil fuels) while the "B" row places more
emphasis on environmental health
Since globalization exports education and also promotes the education of women, birth rates should slow and family sizes should
drop. Therefore, Column 1 showed human population hitting a 9 billion peak in 2050 then dropping off while column-2 hit a 9
billion peak in the year 2100 (no modeling was done after 2100 so we do not know if that population will plateau or drop).
The "A1" scenario is subdivided into 3 basic subcategories:
A1F1 (a.k.a. A1FI)
Fossil Intensive (same as "make no changes to current activity")
The first official chart published by the IPCC contained the typo "A1F1" where they meant to publish "A1FI". All subsequent
publications contain this typo (I guess they just want to remain consistent)
The USA and Canada are firmly in A1
Despite what has been reported in the Western press, China is shifting from A1F1 toward A1B and may end up at A1T just by
inertia. Once they begin running their factories with zero-cost energy (e.g. no fossil fuels) they will permanently dominate
the world economy.
There are too many humans on Earth to believe we would ever go extinct but I am convinced that current human culture will
not survive unless humanity switches to scenarios A1T or B1
Humanity is expected to hit 7 billion sometime in 2012 but there many scientists are now coming around to the idea that this
number needs to drop back to 6 billion or perhaps even 5. It is one thing to have human beings living off the land in a
pre-industrial fashion; it is quite something else to have 7 billion people living like Americans (a.k.a. homo technologicus).
Since humanity has had no success in voluntarily limiting our population in the past, I fear that continued climate change
will lead to food shortages. Hunger and compromised immune systems will lead to disease, war, pestilence, and death.
When I first stumbled onto IPCC Emission
Scenarios, I couldn't help recalling an Isaac Asimov short
story written in the 1940s titled "The Evitable Conflict"
which happens to be Chapter 9 of his 1950 book titled "I,
"The Machines", powerful positronic
computers which are used to optimize the world's economy and production, start giving instructions that appear to go against
their function. Although each glitch is minor when taken by itself, the fact that they exist at all is alarming. Stephen Byerley, now elected World
Coordinator, consults the four other Regional Coordinators and then asks Susan Calvin for her opinion.
She discovers that the machines have generalized the First Law of Robotics to now mean "No machine may harm humanity; or,
through inaction, allow humanity to come to harm" (years later known as the Zeroth Law). Dr. Calvin concludes that the "glitches" are deliberate acts by the
Machines, allowing a small amount of harm to come to selected individuals in order to prevent a large amount of harm coming to
humanity as a whole.
In effect, the Machines have decided that the only way to follow the First Law is to take control of humanity, which is one
of the events that the three Laws are supposed to prevent. Asimov returned to this theme in The Naked Sun and
The Robots of Dawn, in which the controlling influence is not a small conspiracy of Machines but instead the aggregate
influence of many robots, each individually tasked to prevent harm to humanity.