Wednesday, August 12, 2009

Measuring Past Climates

Climate is a collection of all the long-term averages of the daily weather variables, such as rainfall, wind speed and direction, humidity, hours of sunlight and temperature. It is usually considered that a minimum data-base of thirty years is required to provide a useful description of the climate of a particular area.

In Australia weather information has been collected by various sources for about 150 years, and this information is now proving valuable in comparing our climate today with that of previous eras.

In Europe and America formal weather records date back much further – typically back to around 300 years ago, with the British Navy in particular accumulating weather information from localities all around the globe.

Records from other sources such as church registers, family histories and even art and literature also provide some useful information on past climate trends. But in reality these sources do little more than scratch the surface of climate investigation.

The Earth is estimated to be around 4.6 billion years old, so 300 years of recorded climate history is really only a drop in the ocean. Instead we must go to other sources to look for evidence of climate patterns and fortunately there are many. Climatologists look for what is called proxy data - evidence left behind in the natural world that is either the direct or indirect result of the climate at the time. This has proved to be a fascinating and revealing area of climate research.

Fossil evidence
The interpretation of fossil evidence enables us to look through a keyhole and catch intriguing glimpses of long ago climates that were experienced across our planet.

Many fossils are millions of years old and provide valuable insights into climates that were experienced in the times of the dinosaur and even well before. Ferns, for instance, require warm and humid conditions to survive and the discovery of fossilised specimens provides evidence of a past climate of this nature. Dating procedures can then put some sort of time frame on this. Changes in vegetation patterns over time that are also revealed through fossil evidence can be valuable indicators of climate change.

Petrified pine cone from the Jurassic Era ~210 million years ago collected from Patagonia. (Image from Wikipedia Commons - click to enlarge)

The fossilised evidence of the presence of large grazing animals also infers the likelihood of an abundant cover of vegetation and again points to a warm and wet climate at the time.

Ice Cores
Ice caps in the Antarctic and Greenland are hundreds of metres thick in some areas, and are the result of snow falling over the millennia and gradually compacting into huge ice sheets. The ice that lies down towards the base of these sheets in Antarctica is over half a million years old and minute bubbles captured inside contain samples of the ancient atmosphere. Scientists drill deep down into the sheets and retrieve long ice cores that contain a great deal of information about past climates.

Ice cores taken at the Russian Antarctic base at Vostok
(Image from Wikipedia Commons - click to enlarge)

Analysis of the trapped air bubbles enables scientists to reconstruct the gas concentrations contained in the atmosphere of the time and compare this with modern day figures. The thickness of the annual ice layers also reveal in which years there were heavy snowfalls and trapped dust particles point to eras in which there was increased storminess and volcanic activity.

These large rivers of ice travel at very slow speed down mountain sides under the influence of gravity and are capable of gouging out huge “U” shaped valleys as they do so.

Geologists have learned to identify these valleys and the associated rock debris trail that is produced along each side of the ice flow and can therefore identify where glaciers have been in the past.

There are many areas in Europe, particularly through parts of France and Switzerland where valleys of this type are found and this indicates that there have been much colder epochs in earlier times than now. Glacial valleys that contain no ice are therefore evidence of climate change, and processes that can estimate the age of these give us some idea of when these cold periods occurred. There are some good examples of old glacial valleys across the central plateau area of Tasmania.

The Aletsch Glacier in Switzerland
(Image from Wikipedia Commons - click to enlarge)

In 1840 the Swiss scientist Louis Agassiz was the first to suggest that there had been “ice ages” in the past, and although initially disbelieved by the scientists of the day, it is now recognised as proven theory.

Stalactites and Stalagmites

These amazing icicle like rock formations that grow in caves have fascinated humans for centuries and in more recent times have also found to be valuable climate indicators for the local area.

Stalactites extend down from the ceilings of caves, whereas stalagmites grow upwards from the cave floor. They are produced by dripping water rich in calcium carbonate. This forms deposits that gradually grow and harden over time. Many formations around the world are at least 100,000 years old, with some even far older.

Stalactites in Treak Cliff Cavern, Derbyshire, UK. (Image from Wikipedia Commons - click to enlarge)

But the way they grow carries with it a great deal of information about the past climate in the local area as geologists are able to deduce periods of rapid or slow growth by examining the small-scale structure of the formations. And this rate of growth depends on the rainfall with wet periods producing more dripping water within the cave and higher growth rates.

Scientists are then able to determine the age of the formations using standard dating techniques and deduce a rainfall timeline. In addition to rainfall patterns, stalactites and stalagmites also contain information about past temperature trends across the area.

Oxygen atoms are bound up within water, and these come in two forms, known as “heavy” and “light”. The ratio of these is temperature sensitive, and this data can be retrieved from stalactites and stalagmites allowing a temperature timeline to be constructed.


Coral formations that are common in tropical oceans around the world are quite ancient, typically between 5 and 10 thousand years old, and because they are highly sensitive to the state of the environment, they have proved invaluable in reconstructing past climates in tropical areas.

Corals react strongly to three main variables. These are the temperature, salinity and acidity of the surrounding seawater and these factors are all the end result of the climate of the area.

During periods of high rainfall, ocean waters near coastlines become minutely diluted by the excess of fresh rainwater and become less saline or “salty”. This produces a slightly different growth pattern in the coral than at other times. Scientists have learned to detect and date this difference and deduce past rainfall patterns across the area.

Pillar Coral located at The Florida Keys National Marine Sanctuary (Image from Wikipedia Commons - click to enlarge)

The ideal water temperature in which coral thrives is around 27C but it is remarkably sensitive to any long-term variations from this, even by only a few degrees. Changes in the structure of coral growth patterns during periods of temperature change have enabled climatologists to build up long-term temperature profiles of sea surface temperatures in many tropical oceans.

In particular, the phenomenon of coral bleaching, observed with increasing frequency during modern times, is a change in the structure of the coral produced by warmer than normal ocean temperatures. And if these temperatures remain high the corals can actually die. The Great Barrier Reef of Australia is one of the world’s most important stands of coral and is particularly vulnerable to coral bleaching. It is being closely monitored to detect any long-term damage from rising sea temperatures across the area.

Ocean and Lake Deposits

A great deal of climate information has also been locked away in the sediments that lie at the bottom of lakes and oceans – information that is proving to be of immense value in reconstructing past climates.

Of great assistance here have been the remains of tiny shell like creatures called foraminifera – normally less than 1 mm in size and difficult to see with the naked eye. Foraminifera live in the upper levels of oceans, normally near the surface, and after dying sink to the bottom in a continuous soft “rain”. Over thousands of years this forms a sediment which ultimately becomes fossilised.

Fossil foraminiferans collected near Al Ain, United Arab Emirates(Image from Wikipedia Commons - click to enlarge)

Foraminifera evolved into many thousands of varieties that were and are temperature sensitive, and as scientists learned to interpret the countless layers of sediment they produced, many going back millions of years, a long term picture of changing ocean temperatures was assembled.

Interestingly some of the older freshwater lakes around the world also carry information from past climates in the form of pollen deposits that can sometimes be retrieved from the lakebeds. These can be dated and used to identify what sort of plant species were about in ancient times, and from these plant types, the prevailing climate deduced.

Tree Rings

Just as living coral formations contain a great deal of climate information within their structure, so do their land based equivalent – trees – that develop growth patterns that are also very dependant on the climate of the time.

If we look at the cross section of the trunk a tree that has been sawed through we notice it is made up of a number of concentric rings – the older the tree the larger the number. Each of these rings represents a year of growth and the width of each provides a valuable clue as to the climate of the time.

Series of well developed tree rings from an old tree. Each ring represents a year of growth (Image from Wikipedia Commons - click to enlarge)

A broad ring points to a year in which growth was rapid – a time of good rainfall and a suitable range of temperatures. During a season when the tree was stressed, the ring is narrower, representing a year in which the tree grew more slowly due to less suitable rainfall and temperature conditions.

The study of past climate through the analysis of tree ring growth is called dendrochronology and has proved of considerable value in the reconstruction of past climates, particularly when the trees in question are very old. This is certainly the case with the Bristlecone pines of Colorado and California that in some cases produce living specimens more than 4000 years old.

In addition, dendrochronological studies are not confined to living specimens – fossilised tree remains containing ring information that can be dated and analysed in the same way to produce information about far more ancient climates.

Temperature Timeline

From this mountain of evidence climatologists have been able to build up a rough picture of past climates, and the temperature trends have been shown to be highly variable over long periods of time. Before 600 million years ago (mya) little is known because of the lack of reliable proxy evidence available.

The approximate temperature trends of our past climate. The increased temperature variability in more recent times may be due to the increased amount of proxy data available.
(mya means "million years ago"). Click on the image to enlarge.

The causes of these temperature variations is the subject of a great deal of research.

For information on the likely causes of climate change go to

Reference: "Understanding Climate Change", Richard Whitaker, New Holland Publishers, 2008

Saturday, August 8, 2009

The Australian Coastline - How Long Is It?

If we check out official Government figures we find that the mainland coast of Australia has a length of 35877 km, but this is a somewhat contentious matter, as is the measurement of all coastlines around the world.

The problem is that the figure we come up with is very much dependent of HOW we measure, and this is an important issue in arriving at an estimate.

If we measure the coastline with a ruler 1400 km long (specifying that both ends of our ruler must touch the coast with each measurement) we come up with a total of around 10800 km.

(Click on image to enlarge)

However we see that large parts of the coastline are omitted in this way and obviously a more accurate result will follow from using a smaller ruler.

If we use one about 700 km long, our new result is about 11300 km – an increase of 500 km or 4.6% with respect to our first measurement. (Click on image to enlarge)

But we are still missing a large amount of coastline including all the bays and inlets, so a smaller ruler should be used.

But proceeding in this way, we realise that by using smaller and smaller rulers, so that we can even measure around mangroves and individual rocks on beaches, our measured coastline will appear to become ever longer.

So we are left with the apparent paradox - the smaller our ruler the longer the coastline.

However, instinctively we feel that our estimates, although increasing with smaller rulers, will eventually converge to a limit that will be the true figure. But this may not be the case.

In the 1980’s the mathematician Benoit Mandlebrot pioneered a new type of geometry that was composed of figures called fractals. These much more closely resembled nature than the cubes, spheres, straight lines and triangles of traditional geometry.

Fractals have the interesting property of being “self-similar” – if you zoom in for a closer look at the side of a fractal the same detail of the full figure is maintained. No matter how many times you zoom in the same picture emerges without limit. You can see this effect here:

This produces the rather amazing fact that the “coastline” of a fractal is infinitely long – the smaller your measurement ruler the longer the coastline. (Click on image to enlarge)

The obvious question is therefore “is a continental coastline a fractal?” Here academic opinion is divided and to a certain extent we enter the realm of philosophy.

If we consider the Australian coastline is a fractal it is therefore infinitely long, just as are the coastlines of Tasmania, Europe and the United States. If not, we can stick with the official Government figure of 35877 km as given above.

A similar, but much simpler situation arises in many Australian backyards. We can ask “How long is the back fence” and if this consists of a paling structure, the answer is probably longer than you think.

(Click on image to enlarge)

Lets say the fence consists of 200 palings 10 cm wide and 1 cm deep. If we measure it with a string we will come up with a figure of 20 metres. But if we measure around the palings as shown, our back fence will become 22 metres long.

If we want to be really precise and measure carefully around each wood splinter it will be longer again and further, if we consider that the palings are fractals then we will have an infinitely long back fence. But don’t tell the Council – they might increase your rates.

Tuesday, August 4, 2009

Tessellation - Just Plane Fun

Tessellation is the filling of the plane with various shapes, and has ancient roots in various cultures.

In art, it takes the form of mosaics, and in building and construction it appears as various forms of tiling for pathways and in decorative flooring.

The Islamic nations were the world leaders in tessellation for many centuries. Whereas much western art of the time concentrated on depiction of the human form, Islamic art was more of a geometric nature, with advanced tessellation a significant feature.

The Girh tiles are a set of five shapes used in producing striking tessellation patterns in Islamic architecture from about the year 1200 onwards. The patterns produced are highly complex, and are underpinned by some advanced mathematical concepts that were well ahead of their time. For some more details on the Girh tiles go to

The Alhambra Palace, Granada, Spain
Image: Wikipedia Commons (Click to enlarge)

Wonderful examples of tessellation can be found at the Alhambra palace in Granada, Spain, that was built in the early 1300’s. Although over 650 years old, highly advanced tessellations are present that would have been very difficult to construct at the time, without the benefits of computer technology.

Today, the computer makes tessellation accessible to everyone, with the Power Point software ideal for experimentation and manipulation of all types of shapes, either straight sided or curved.

There are many different approaches to tessellation, but here we will look a simple “freestyle” method which begins by constructing closed straight line figures of any shape, and then producing tessellations from these.

(Click on images to enlarge)

(Click on images to enlarge)

(Click on images to enlarge)

In this case all the four shapes have equal area - the original shape plus the space between. (Click on image to enlarge)

We now find that we have created a shape - outlined in red here, that is self tessellating and is composed of four shapes of equal area that are also self-tessellating. (Click on image to enlarge)

The obvious question is can we say this in reverse - that is can we subdivide any self tessellating shape into four equal areas that are also self tessellating?

The answer to this lies well beyond my abilities but I'm sure there are those out there in cyber-space that will know. I'd love to hear from you!

Power Point also allows you to fill the shapes with images, producing interesting artistic effects. (Click to enlarge)

The master tessellator of modern times was undoubtedly M.C.Escher, a Dutch artist who combined the geometry of tessellation with conventional pictorial art. He was said to have been inspired by the tessellations he saw at Alhambra. The results are highly intriguing and produce a distinctive and unique art style.

Some of the exquisite tessellation
of the Alhambra
Image: Wikipedia Commons

An Intricate Escher tessellation
Image: Wikipedia Commons

Sunday, August 2, 2009

The Tri State Tornado of 1925

Tornados, or “twisters”, are violently rotating funnels of air that are spawned by severe thunderstorm activity, and are capable of producing extreme winds in excess of 300 mph (485 kph). This level of severity will produce catastrophic damage to even the strongest buildings and is capable of flinging houses off their foundations, and hurling automobiles and people through the air for considerable distances.

Flying debris produced by tornados is often lethal to anyone caught outside, and many people have also been killed by structural collapse when trying to seek shelter inside a building or trailer.

“Tornado alley” in the United States is the world’s twister hotspot, and covers parts of Texas, Oklahoma, Kansas, Nebraska, Illinois, Missouri and Indiana. This is the rolling open country of the Great Plains where cold air streaming southwards from Canada can collide with warm, humid air moving up from the Gulf of Mexico to generate lines of massive, severe thunderstorms, together with their violent tornadic offspring. This set of circumstances can occur almost anytime, but is most common during the months of spring and summer.

Perhaps the most infamous and extreme event of this type in modern recorded history occurred on March 18 1925, when a severe thunderstorm developed across southeast Missouri and generated a particularly violent twister. This turned out to be unlike any other tornado encountered before or since, and it cut a swathe of unparalleled death and destruction across three states before finally dissipating over 200 miles (322 km) from its place of origin. This was the deadly Tri State Tornado or TST.

The “normal” twister will only last a fairly short period, typically around half an hour or so. But TST was different – it lasted about three and half hours, producing an extended period of almost continuous destruction as it ripped its way across the countryside, travelling at speeds of up to 60 mph (97 kph). The actual wind speed inside the funnel was estimated to have been towards the top end of the tornado scale, with later analysis of the damage trail indicating possible winds around 300 mph (485 kph).

TST ripped through some twenty sizeable townships, including Gorham, Murphysboro, DeSoto, West Frankfort and Parrish, all in southern Illinois, killing a total of 488 people, and causing utter destruction right across the area. Parrish, in particular, was so completely ruined that it was never rebuilt, and contemporary photographs taken in some of the other areas show settlements that closely resemble some of the French and Belgian villages destroyed by shellfire in World War One.

The town of Griffin Indiana - all but flattened by the Tri State Tornado. Image: Wikipedia Commons (Click on image to enlarge)

Perhaps most tragically, because it was a Wednesday, school was in and several schoolhouses were directly hit, with 17 students dying in Murphysboro and another 33 at DeSoto.

Eventually the tornado crossed the border into Indiana, where it inflicted massive damage to the townships of Griffin and Princeton, before finally abating after the longest continuous rampage of any known twister.

In all, 695 people died - still the record by far for an American tornado, over 2000 were injured and some 15,000 homes demolished.

Subsequent investigation of the twister’s path revealed a monstrous gouge of destruction across the countryside, some 219 miles (353 km) long and about three quarters of a mile (1.2 km) wide.

Illustrated report of the disaster in the Herald Examiner describing the destruction of Murphysboro.
The number of casualties in the report was happily an overestimate.
Image: Wikipedia Commons

The Tri State Tornado remains the benchmark of severity against which all US tornados are measured, and is a perpetual reminder of how deadly twisters can become under the right conditions.

For a comparison of this event with the recent Oklahoma disaster see

Reference: “Disasters, Events and Moments that Changed the World”, Richard Whitaker, New Holland Publishing, 2007

Karen Carpenter - We've Only Just Begun

During the late 1960’s rock and roll ruled the airwaves perhaps like never before or since, and for those somewhat tired of the endless bump and grind, there was little respite on the horizon. Then, unexpectedly it came, from a totally unlikely source out of middle America.

Karen and Richard Carpenter were a brother and sister act that evolved gradually from a family interest in music. They had formed a trio with another artist in 1966, but launched out on their own in 1969, calling themselves simply “The Carpenters”.

Richard was an extremely clever musician, and his vocals formed an airy background to most of their work. However it was Karen’s magical voice that really launched the pair to stardom. She was a flawless light contralto, and her melodic interpretations of contemporary popular tunes remain as some of the musical yardsticks of the era.

Their first album was called “Offering”, followed by a song that would reach number 1 in several countries, called “Close to You”. This was the beginning of a sensational run of top twenty singles that would propel the Carpenters into international stardom.

Richard revealed his genius for music selection when he noticed an obscure Californian bank television commercial showing a newlywed couple about to embark on their life together, backed with a melody written by the song-writing team of Paul Williams and Roger Nichols.

The Carpenters remake of this song, called “We’ve Only Just Begun”, was not only a worldwide smash hit but also became the anthem of many newlyweds of the 1970’s.

You can hear it on this link:

Success followed success, with The Carpenters also becoming one of the most popular international touring acts of the time. Several of their songs became amongst the best sellers of the era, including “Top Of The World”, Rainy Days And Mondays”, “Yesterday Once More” and “A Kind Of Hush”. It seemed that The Carpenters had become the first choice for those weary of the endless "chain saw" fare served up by the music industry. With millions of records sold and legions of adoring fans, their life had become a fairytale success story.

Karen and Richard - The Carpenters - meeting President Richard Nixon in 1972
Image: Wikipedia Commons

But behind all the glitz and glamour, all was not well. Karen had slowly, inexplicably and inexorably, fallen into the grip of what was then a little publicised psychological condition called anorexia nervosa. Playfully called “chubby” in her earlier years, she became obsessed with keeping her weight down, even though she had a naturally slender physique, and illogically, she starved herself for extended periods.

Her face became noticeably gaunt during the mid to late 1970’s and although she was able to hide her emaciated body from the public to a certain extent by clever choice of clothes, her family were aware of the situation and became frantic with worry.

Finally she collapsed on stage in 1975, and after being rushed to hospital was found to be nearly 35 pounds (16 kg) underweight. Visits to doctors and therapists followed and for a time it appeared as though she was cured. However her body had been chronically weakened by the years of starvation, and she suddenly died of a heart attack in 1983 at the age of only 32.

Her death had the immediate effect of raising the public awareness of the then seldom - mentioned condition of anorexia nervosa, with thousands then seeking treatment for the elusive but deadly disease. Even in death Karen Carpenter had given hope to those who followed.

Reference: “Disasters, Events and Moments that Changed the World”, Richard Whitaker, New Holland Publishing, 2007