Sunday, 14 April 2013

Logarithmic Graphs

What is it? A graph with a logarithmic scale, one which increases by multiplications in value rather than additions (e.g. 1, 10, 100, 1000 rather than 1, 2, 3, 4). The value by which the scale is multiplied by is usually 10 (i.e. log base 10). Both scales may be logarithmic or just one (semi-logarithmic graph). Semi-logarithmic graphs normally have time displayed on x

Benefits? Useful for studying data that changes exponentially. Can display a much larger range of data than an arithmetic scale. Allows one to see increased detail at smaller values, while larger values are compressed. Small values occupy a larger proportion of the scale in comparison with larger values. On an arithmetic scale, unless the graph paper was very large, the smaller values would appear too small to see properly. Allows comparison between trends in small and large values

Useful for showing rate of change. A steep gradient shows a fast rate of change while a shallow gradient represents a slowing rate of change.

A constant proportional rate of change (an exponential change) is represented by a straight line on a logarithmic graph (rather than a curved line on a arithmetic graph). This means logarithmic graphs are good for comparing rates of change.

Limitations? Zero cannot be plotted. Positive and negative values cannot be plotted on the same graph. Can be difficult to draw and interpret as scale is distorted.

Uses in geography?
Studying population data e.g. as in Gapminder
The Hjulstrom curve.
The Richter magnitude scale/The Moment magnitude scale
Magnitude-frequency flood risk analysis.

Example 1 (Logarithmic)

Example 2 (Semi-logarithmic)
nb - in this graph the scale is multiplied by 2 each time rather than 10 (i.e. log base 2).

Further information
Check out this video for a great explanation of logarithmic scales!
You can also find an introduction to logarithms here

Friday, 12 April 2013

The Formation of a Meander

Sometimes I find poems helpful for remembering things! So here's one I wrote about meanders, which includes lots of key geographical words you should be using to describe them!

Rivers always take the path of least resistance
Winding round obstacles into the distance
Even in straight channels bars of sediment seem to form
Alternating deep and shallow sections is the norm’
At alternating intervals of 5-7 times the bend*
The bars deposited when low flow conditions tend
Riffles and pools are they names these features go by
Weaving in between then, the thalweg must comply.

Riffles will reduce the river’s efficiency
Slowed by friction the water has no energy
To carry its load, so it drops it right there
Forming what’s known as a slip-off slope or point bar
While the inner bend is built up by deposition
On the outer bend the river’s flowing fast with a mission
The high hydraulic radius in pools is the reason for
Undercutting by abrasion and hydraulic action more.

This process is perpetuated by helicoidal flow
A corkscrew like movement about which you need to know!
This erodes the river cliff of one meander’s outer bend
Depositing downstream in the next one’s inner bend
As these processes continue the meander slowly migrates
Moving both laterally and downstream at a steady rate.

* 5-7 times the width of the channel – I wrote ‘bend’ because width’ didn’t rhyme!