Water & Carbon Skills (AQA A Level Geography)

• Geographical skills are working skills essential to developing a synoptic approach to answering questions but also observing the 'bigger picture' in geography

Key terms 

• Quantitative data is measurable and can be expressed by numbers or placed into specific categories
  • Often used to test and prove previously specified concepts or hypotheses
  • Quantitative data is objective as it provides specific values
  • E.g. Barton-on-Sea beach in Dorset, UK is a short 1.75km, 20m wide, shingle and rock beach, backed by high, clay cliffs of between 5-10m
• Qualitative data is descriptive information, usually written and presents features (quality) in an intuitive way
  • Often used to formulate theories and hypotheses
  • Qualitative data is subjective because it 'describes' from the angle of the viewer
  • E.g. The river is fast and dangerous or the wood is dark and feels dangerous 
• Primary data is data collected first-hand usually during fieldwork
  
  • It is real-time data specific to the investigation
  • E.g. Photograph taken of flood defences or species count using a quadrat
• Secondary data is data collected by others and is used in support of primary data
  
  • It allows for studies of changes over time - census data collected by the government and compared 
  • E.g. Maps, textbooks, websites, journals etc. 
• Big data are large datasets that need computational manipulation 
  • Used to show trends, patterns and subsequent links
  • E.g. Geolocation, geospatial data, GIS (geographic information systems), Google Earth, satellite navigation etc. 
• Continuous data
  • Numerical data that can take any value within a given range
  • E.g. heights and weights
• Discrete data
  • Numerical data that can only take certain values
  • E.g. shoe size

Line graph

• One of the simplest ways to display continuous data
• Both axes are numerical and continuous
• Used to show changes over time and space

Table Showing Relative Strengths and Limitations of Line Graphs

Strengths	Limitations
Shows trends and patterns clearly	Does not show causes or effects
Quicker and easier to construct than a bar graph	Can be misleading if the scales on the axis are altered
Easy to interpret	If there are multiple lines on a graph it can be confusing
Anomalies are easy to identify	Often requires additional information to be useful

• A river cross-section is a particular form of line graph because it is not continuous data, but the plots can be joined to show the shape of the river channel

Flow lines

• Useful for showing the strength of interaction between variables
• Shows direction and volume along a specific path
• E.g. the water and carbon cycle use flow lines
• The lines can also be displayed to show proportion or importance using size or colour to highlight differences 

Image showing carbon cycle proportional flow lines 

Compound or divided bar chart

• The bars are subdivided to show the information with all bars totalling 100%
• Divided bar charts show a variety of categories

• They can show percentages and frequencies

Table Showing Relative Strengths and Limitations of Compound Graphs

Strengths	Limitations
A large amount of data can be shown on one graph	A divided bar chart can be difficult to read if there are multiple segments
Percentages and frequencies can be displayed on divided bar char	Can be difficult to compare sometimes

Image showing data presented on a compound graph

Triangular graph

• Have axes on three sides all of which go from 0-100
• Used to display data which can be divided into three
• The data must be in percentages 
• Can be used to plot data such as soil content, employment in economic activities
• Read each side carefully so you are aware of which direction the data should go in

Mass balance

• Mass balance is the input, output, and distribution of the water or carbon cycle between its flows/transfers within each stage of the system
• It accounts for all the material in a process and can be measured locally (a single system) or globally 
  • E.g. a student conducted a mass balance on a drainage basin and they concluded that approximately 84% of the water was directly recycled back to the river while 15% was indirectly returned via plant and sub-surface flows, with the final 1% being removed from the water cycle by deep aquifers
• A balanced carbon cycle is the outcome of different components working in dynamic equilibrium with each other
  • The atmosphere's carbon composition is partly regulated by ocean and terrestrial photosynthesis
  • Soil health is maintained through decomposition, combustion and carbon storage which is important for ecosystem productivity etc. 

Scatter graph

• Points should not be connected
• The best-fit line can be added to show the relations
• Used to show the relationship between two variables
  • In a river study, they are used to show the relationship between different river characteristics such as the relationship between the width and depth of the river channel

Table Showing Relative Strengths and Limitations of Scatter Graphs

Strengths	Limitations
Clearly shows data correlation	Data points cannot be labelled
Shows the spread of data	Too many data points can make it difficult to read
Makes it easy to identify anomalies and outliers	Can only show the relationship between two sets of data

Scatter graph to show the relationship between width and depth on a river X's long profile

Types of correlation

• Positive correlation
  • As one variable increases, so too does the other
  • The line of best fit goes from the bottom left to the top right of the graph
• Negative correlation 
  • As one variable increases the other decreases

  • The line of best fit goes from the top left to the bottom right of the graph

• No correlation
  • Data points will have a scattered distribution
  • There is no relationship between the variables

Percentage and percentage change

• To give the amount A as a percentage of sample B, divide A by B and multiply by 100
  • In 2020, 25 out of 360 homes in Catland were burgled
  • What is the percentage (to the nearest whole number) of homes burgled?

• • 

• A percentage change shows by how much something has either increased or decreased

• 

• • In 2021 only 21 houses were burgled. What is the percentage change in Catland?
  • 

• • There has been a decrease of 16% in the rate of burglaries in the Catland area
• Remember that a positive figure shows an increase but a negative is a decrease

• This is the study and handling of data, which includes ways of gathering, reviewing, analysing, and drawing conclusions from data

Mean, median, mode and range

• Mean = average value (all the values added and divided by the number of items)
• Median = middle value when ordered in size
• Mode = most common value
• Range = difference between the highest value and lowest value

Sample site	1	2	3	4	5	6	7
Number of pebbles	184	90	159	142	64	64	95

• Taking the example above to calculate:
• Mean -
• Median - reordering by size =  = 95 is the middle value
• Mode - only 64 appears more than once
• Range -

Upper, lower and inter quartile range

• These are the values of a quarter (25%) [lower quartile (LQ)] and three-quarters (75%) [upper (UQ)] of the ordered data

No. of shoppers	2	3	6	6	7	9	13	14	17	22	22
			Lower quartile			Median			Upper quartile

• The interquartile range (IQR) is the difference between the upper (UQ) and lower quartile (LQ)
• It measures the spread (dispersion) of data around the median
• A large number shows the numbers are fairly spread, whereas, a small number shows the data is close to the median
• UQ - LQ = IQ []

Standard deviation

• This measures dispersion more reliably than IQR and the symbol for it is 'σ' (sigma)
• The formula is  
• Σ means 'sum of' and  is another way of writing 'mean' and 'n' is the number of samples taken
• Work out individual aspects of the formula first e.g. the mean
• Sample results:

Sample site	1	2	3	4	5
Number of pebbles	5	9	10	11	14

1. Calculate the mean - 
2. Calculate  for each number
3. Square each of those values (the square of a negative number becomes positive)
4. Add the squared values to give 
5. Divide the total by 'n'
6. Finally, find the square root

			$(x-\overline{x})$
5	9.8	-4.8	23.04
9	9.8	-0.8	0.64
10	9.8	0.2	0.04
11	9.8	1.2	1.44
14	9.8	4.2	17.64
$\mathit{\Sigma }$ = 42.8

• $\mathit{\sigma }\mathbf{ }\mathbf{=}\mathbf{ }\sqrt{\frac{\mathbf{42}\mathbf{.}\mathbf{8}}{\mathbf{5}}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{2}\mathbf{.}\mathbf{93}\mathbf{ }\left(2 dp\right)$
• Numbers closely grouped around the mean shows a small deviation
• A large standard deviation would show a set of numbers that were spread out

Spearman's rank correlation coefficient

• A test to determine if two sets of numbers have a relationship
• Not the easiest to calculate
• Σ means 'sum of',  $\mathit{d}$ is the difference and 'n' is the number of samples taken
• The formula is ${\mathit{r}}_{\mathbf{s}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{-}\mathbf{ }\frac{\mathbf{6}\mathbf{\sum }{\mathbf{d}}^{\mathbf{2}}}{{\mathbf{n}}^{\mathbf{3}}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{n}}$

1. Rank each number in both sets of data, with the highest number given rank 1, second highest 2 etc.
2. Calculate 'd' which is the difference between ranks of each group e.g. ranks for group 5 are 4 and 6; difference will be 2
3. Square value 'd' and calculate the total ${\mathit{d}}^{\mathbf{2}}$ to find $\mathbf{\sum }{\mathit{d}}^{\mathbf{2}}$
4. Finally, calculate the coefficient of ${\mathit{r}}_{\mathbf{s}}$ using the above formula
5. The resulting number should always be between -1 and +1

GNP ($) per capita and Life Expectancy (years)

Country	GNP	Rank	Life Expectancy	Rank	$\mathit{d}$	${\mathit{d}}^{\mathbf{2}}$
1	15,124	5	73	5	0	0
2	20,535	4	72	6	2	4
3	10.432	9	68	8	1	1
4	7,050	11	62	11	0	0
5	22,950	3	76	3	0	0
6	14,800	6	75	4	2	4
7	23,752	2	77	2	0	0
8	36,875	1	79	1	0	0
9	5,525	12	61	12	0	0
10	8,678	10	66	9	1	1
11	12,211	8	65	10	2	4
12	13,500	7	70	7	0	0
$\mathit{n}\mathbf{=}\mathbf{12}$		$\mathit{\Sigma }{\mathit{d}}^{\mathbf{2}}$ = 14

• $\mathit{\Sigma }{\mathit{d}}^{\mathbf{2}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{14}\mathbf{ }\mathit{a}\mathit{n}\mathit{d}\mathbf{ }\mathit{n}\mathbf{ }\mathbf{=}\mathbf{12}$. 
• ${\mathit{r}}_{\mathbf{s}}\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{ }\mathbf{-}\frac{\mathbf{6}\mathbf{ }\mathbf{\times }\mathbf{14}}{{\mathbf{12}}^{\mathbf{3}}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{12}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{-}\mathbf{ }\frac{\mathbf{84}}{\mathbf{1716}}\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{048951}\mathbf{ }\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{)}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{95}$
• (0.048951 can be rounded to 2 decimal places giving 0.05)

• A positive result shows a positive correlation, where one variable increases so does the other
• The closer the number is to 1, the stronger the positive correlation
• A negative results shows a negative correlation, where one variable increases the other decreases
• The closer the number is to -1 the stronger the negative correlation
• If however, the correlation is 0 or near to 0, there is no relationship

Determining significance

• Spearman's rank may show that two sets of numbers are correlated, however, it does not show how significant the link between the two values are
• To check for significance; a table of critical values or a graph is needed
• This looks at the probability of the links occurring by chance 
• A 5% or higher probability of chance is not significant evidence for a link
• 1% or less is a significant evidence of a link
• This is the significance level of a statistical test
• The degrees of freedom needs calculating - $\mathit{n}\mathbf{-}\mathbf{2}\mathbf{ }\mathbf{ }\mathbf{ }$
  • Using the example above:  $\mathbf{12}\mathbf{ }\mathbf{-}\mathbf{ }\mathbf{2}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{10}$ degrees of freedom
  • As ${\mathit{r}}_{\mathbf{s}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{0}\mathbf{.}\mathbf{95}$ then the correlation has a less than 1% probability of being by chance
  • Therefore, there is a high significance level of a relationship between GNP and life expectancy

  Spearman’s Rank Correlation Significance Table