Statistics Controlled Assessment

Climate

Joseph Babalola-Davies

Centre Number: 10834

I nvestigation:  

To find out if there is a correlation between the increase of hotter weather

in the summer and the increase of colder the weather in the winter and to

find out if the increased amount CO2 levels is the cause of these changes.

Aim:

My aim is to investigate whether increased CO2 emissions globally

correlate with increased annual temperatures and to investigate if there is

a correlation between the increased summer temperatures and the

decreased winter temperatures.

Hypothesis:

I predict that the winter and summer temperature over the last 10 years

have changed. Summer temperatures have become hotter and winter

temperatures have become colder.

Plan:

In my coursework, I plan to investigate the difference of temperatures

between this year and the previous 10 years. I will be investigating the

difference in temperature of the summers and winters of 2014 and 2005. I

will conduct this investigation, by using the Meteorological Office’s results

as the source of my data, from this I will investigate in what way that the

CO2 level shave affected the average temperature over the years.

I will collect temperatures from the summers and winters of 2005-2014. I

will get my results using summer and a winter temperature, as this is

where the coldest and hottest temperature are more apparent. After

collecting the data, I will calculate the mean average temperature for

summer and winter and then, I will the compare minimum temperatures

with the maximum temperatures of each respective year. After collecting

my data I will use Spearman's rank correlation coefficient to find out if my

data has a correlation between summer and winter, which will also

determine if there is a negative correlation or a positive correlation

between the data.

If there is a positive correlation, this can prove that the winter and

summer temperatures are going in the same direction in warmth or

coldness.

Data will be obtained from the Meteorological Office as I will use

secondary data to conduct my investigation. I will use this site because

the Met Office is gives of the most accurate forecast as they give a five

day prediction of the weather, for any location in Britain. The Met Office

weather forecasts are around 30-40% accurate when predicting weather

but since I am looking at past weather forecasts, that have already taken

place it will not affect the accuracy of my results. I also plan to use other

sites such as the NASA which shall be a source for CO2 levels.

I will analyse and compare the results with each other from each year’s

average results and compare the summer and winters results with each

year. Then I will calculate how much change there is within each year to

see if there is an increase or decrease in temperature. I have chosen to

investigate over the last 10 years as technology has been more accurate

at collecting data over the last 10, rather than using all the data from

before that, which may not be as accurate. I have not used a random

sample to get my results as, I am investigating the correlation

between the rise of temperature in the summer and the decrease of

temperature in the winter over the course of 10 years. If I was to use a

random sample, I will get inconsistent results as collecting random years

will mean I would not be able to see how temperature changed over the

years. So I have decided to use the recent 10 years, where temperature

fluctuation are more apparent for comparisons data

Collection of data

UK Minimum Temperature (Degrees C)

Year WINTER SUMMER ANNUAL

2005 1.88 10.53 5.88

2006 1.11 11.14 6.11

2007 2.79 10.22 5.95

2008 1.64 10.61 5.47

2009 0.39 10.58 5.55

2010 -1.18 10.40 4.24

2011 -0.46 9.43 5.98

2012 1.73 10.19 5.21

2013 0.68 10.66 5.21

2014 2.48 10.46 6.31

These Results are the average minimum temperature of the season of

each year in degrees Celsius, with the average annual minimum

temperature for each year. Looking at the data it seems that the annual

average minimum temperature has fluctuated over the recent past 5

years

Average CO2(ppm) Years

379.92 2005

381.79 2006

382.42 2007

385.56 2008

387.31 2009

389.73 2010

391.83 2011

394.28 2012

396.81 2013

398.78 2014

Average CO2 (ppm)

UK Maximum Temperature (Degrees C)

Year WINTER SUMMER ANNUAL

2005 7.55 19.07 13.05

2006 6.61 20.47 13.38

2007 8.34 18.07 13.26

2008 8.11 18.40 12.67

2009 6.05 18.99 12.82

2010 4.50 18.95 11.73

2011 5.34 17.95 13.34

2012 7.45 17.73 12.36

2013 6.03 19.73 12.36

2014 7.98 19.24 13.52

Looking the UK Maximum Temperature 2014 has the highest annual

temperature as well as the highest ever recorded since 1910. When

calculating with Spearman’s rank I will only use the annual temperature as

it is the average temperature for all the months and use it to compare

with the CO2 emission emitted. I will compare the summer temperatures

with the winter temperature to see if there is a correlation between these

two

Mini WIN Rank WIN Mini SUM Rank SUM Difference

(d)

d2

1.88 8 10.53 6 2 4

1.11 5 11.14 10 -5 25

2.79 10 10.22 3 7 49

1.64 6 10.61 8 -2 4

0.39 3 10.58 7 -4 16

-1.18 1 10.4 4 -3 9

-0.46 2 9.43 1 1 1

1.73 7 10.19 2 5 25

0.68 4 10.66 9 -5 25

2.48 9 10.46 5 4 16

∑d2 174

6∑d2 1044

Processing, analysing and representing data

Minimum temperature was used to calculate the link between winter and

summer temperatures. From using Spearman’s rank correlation I have

worked out that there’s a negative correlation between the two daters.

Spearman's rank correlation coefficient:

1 - (6 x 174)/ (103-10) = -0.0545454545455.

From the Spearman's rank correlation coefficient: -0.1 (to 1 significant

figure) we can say that it shows that the two set of data show a negative

correlation but it is a weak correlation.

To calculate the UK’s mean average temperature over the last 10 years, I

will use standard deviation to calculate the variability and diversity of these

results, collected from the Meteorological Office. A low standard deviation

indicates that the data points are very close to the mean, whereas high

standard deviation would have indicated that the data is spread out over a

large range of values, so this will mean that the data is accurate.

I used a sample population, which is the process of taking a subset of

samples that which represents an entire population. For this reason, a

sample standard deviation was used as it is used for a finite set of

samples whilst a population deviation requires all samples. I could not

attain data prior back to 1910 or evaluate all data from 1910 and

onwards. This is an impractical quantity of data to process, use and

compare. So a sample deviation would be more preferred over a

population deviation.

The standard deviation is a measure which summarises the amount by

which every value within a data varies from the mean. It effectively

indicates how tightly the values in the dataset are bunched around the

mean value, which is why I am using standard deviation. It is the most

robust and widely used measured of dispersion since, unlike the range

and inter-quartile range; it takes into account every variable in the

dataset. When the values in a dataset are tightly bunched together the

standard deviation is small. When the values are spread apart the

standard deviation will be relatively large.

For datasets that have a normal distribution, the standard deviation can

be used to determine the proportion of values that lie within a particular

range of the mean value. For such distributions, it is always the case that

68% of values are less than one standard deviation (1SD) away from the

mean value. 95% of values are less than two standard deviations (2SD)

away from the mean. 99% of values are less than three standard

deviations (3SD) away from the mean. The graph below shows this

concept in diagrammatical form.

Minimum winter temperature

X x –(1.106)mean (mean)2

1.88 1.88-1.106= 0.774 0.599076

1.11 1.11 -1.106= 0.004 1.6 x 10-5

2.79 2.79-1.106= 1.684 2.835856

1.64 1.64 -1.106= 0.534 0.285156

0.39 0.39 -1.106= -0.716 0.512656

-1.18 -1.18 -1.106= -2.286 5.225796

-0.46 -0.46 -1.106= -1.566 2.452356

1.73 1.73-1.106= 0.624 0.389376

0.68 0.68 -1.106= -0.426 0.181476

2.48 2.48 -1.106= 1.374 1.887876

11.06 14.36964

Mean

1.88+1.11+2.79+1.64+0.39+-1.18+-0.46+1.73+0.68+2.48= 11.06

11.06 ÷ 10=1.106(mean)

Sample Standard Deviation: √(14.36964 ÷ (10-1) = 1.2635769334

Minimum summer temperature

X x –10.422(mean) (mean)2

10.53 10.53 - 10.422=0.108 0.011664

11.14 11.14- 10.422=0.718 0.515524

10.22 10.22- 10.422=-0.202 0.040804

10.61 10.61- 10.422=0.188 0.035344

10.58 10.58- 10.422=0.158 0.024964

10.40 10.40- 10.422=-0.022 0.000484

9.43 9.43- 10.422=-0.992 0.984064

10.19 10.19- 10.422=-0.232 0.053824

10.66 10.66- 10.422=0.238 0.056644

10.46 10.46- 10.422=0.038 0.001444

104.22 1.72476

Mean

10.53+11.14+10.22+10.61+10.58+10.40+9.43+10.19+10.66+10.46 =

10.422

104.22÷10=10.422

Sample Standard Deviation :√( 1.72476 ÷ (10-1) = 0.437767061347

By calculating the standard deviation I got 0.437767061347 this is a

relative low number, this indicates that the mean of my minimum

temperature are close to the mean value.

Discussion

0

2

4

6

8

10

12

Winter Minimum temperature averages

Winter Minimum temperature averages

This graph shows the speared of the temperatures. A data set with a

mean of 1.106 which is shown by the blue line. 80% of the values lie

within 1 standard deviation of the mean. 90% of the values lie within 2

standard deviations of the mean. 100% of the values lie within 3 standard

deviations of the mean.

60%

of

the

values lay Within 1 standard deviation of the mean. 100% of the values

lay 2 within standard deviation of the mean. Line represents mean data

which is 10.422.

AverageCO2

Rank ANNUL Max Rank Difference

(d)

d2

379.92 1 13.05 6 -5 25

0

2

4

6

8

10

12

Summer minimum temperature averages

Summer Minimum tempera-ture averages

Year ANNUL Max Average CO2(ppm)

2005 13.05 379.92

2006 13.38 381.79

2007 13.26 382.42

2008 12.67 385.56

2009 12.82 387.31

2010 11.73 389.73

2011 13.34 391.83

2012 12.36 394.28

2013 12.36 396.81

2014 13.52 398.78

381.79 2 13.38 9 -7 49

382.42 3 13.26 7 -4 16

385.56 4 12.67 4 0 0

387.31 5 12.82 5 0 0

389.73 6 11.73 1 5 25

391.83 7 13.34 8 -1 1

394.28 8 12.36 2.5 5.5 30.25

396.81 9 12.36 2.5 6.5 42.25

398.78 10 13.52 10 0 0

∑d2 188.5

6∑d2 1131

1-(6x188.5)/ (103-10) = -0.142424242424. We can say that it shows that

the two sets of data show weak, negative correlation.

Looking at this graph I can clearly see that there is little correlation

between the annual temperature and CO2 levels.

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

CO2 (ppm) 379.919999999999

381.789999999999

382.419999999999

385.56 387.31 389.729999999999

391.83 394.28 396.81 398.78

ANNUL Temp(Celsius )

13.05 13.38 13.26 12.67 12.82 11.73 13.34 12.36 12.36 13.52

Temperature & Carbon dioxide levels

By calculating the correlation of these two data, I had found out that

there’s a negative correlation between the two data. This suggest the

amount of CO2 in the air globally has not in fact influenced the

temperature in the UK as the Spearman’s ranking shows there is a -0.1

correlation, which means there is a very weak correlation between the

two.

In my graph, the temperature moves in a similar direction, however the

change is too small to notice at some points, but in between 2007 and

2006 there are dips in both CO2 levels and temperature and gradually the

temperature also increases along with the CO2 levels showing there is a

correlation.

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014

WINTER 1.88 1.11 2.79 1.64 0.39000000000000

1

-1.18 -0.46 1.73 0.68000000000000

1

2.48

SUM-MER

10.53 11.14 10.22 10.61 10.58 10.4 9.43 10.19 10.66 10.46

-113579

11

UK Minimum TemperatureSummer & Winter

Tem

pera

ture

(°C

)

Looking at this graph, I can see there is some sort of correlation between

the summer temperatures and the winter temperatures, however there is

a weak correlation between the two data. On the other hand, there is a

trend where there is temperature fluctuation. The two line graphs have a

weak correlation, but this does support my hypothesis. I

had hypothesized, that the warmer summer was, the warmer winter would

be resulting, in a positive correlation as shown in the graph.

Interpretation of data and discussion of results

1 2 3 4 5 6 7 8 9 10

WINTER 1.88 1.11 2.79 1.64 0.39000000000000

1

-1.18 -0.46 1.73 0.68 2.48

SUMMER 19.07 20.47 18.07 18.4 18.99 18.95 17.95 17.73 19.73 19.24

-2.52.57.5

12.517.522.5

Max summer & Minimum winter temperature

tem

pera

ture

(Cel

sius)

To conclude, I believe that my hypothesis about the global temperatures

affecting the temperatures in the UK was correct, but it appears when

using Spearman’s rank to show a correlation it comes out with a

negative correlation, suggesting that two of my data’s are moving away

from each instead of the same direction. My data on CO2 emissions

suggest that CO2 levels and annual temperature have steadily gone up, as

it does correlate with NASA’s graph of CO2 levels.

These fluctuations may be due to natural respiration of plants which take

in carbon dioxide, causing these fluctuated movements on the

graph. However, I believe my hypothesis about the increased winter and

summer temperatures were correct as my graph shows when winter

temperatures increased so did the summer temperatures showing a

correlation to these yearly changes as shown in the maximum summer

and the minimum temperature chart.

When using Standard deviation on my minimum summer result, my

calculations had shown that the data was close to the average. My

minimum winter data was more dispersed in terms of averages, as shown

in the scatter graph, meaning it was not close to the average mean data.

This suggests there were outliers in minimum winter results. This may

have caused slight errors in my investigation.

When comparing CO2 levels with annual temperature, I had attained a

negative correlation coefficient due global warming’s effect upon climate

levels, which may have caused the temperature variations, as I did not

take into account that global warming can cause colder climates than

usual, such as in 2010 which had one of the coldest but also one of the

highest temperatures to date. Caused by the hot air around the globe

condensing into moisture, and then was released in the form of snow

which had caused the cooler temperature in 2010.

When storms occur, this added moisture can fuel heavier precipitation in

the form of more intense rain or snow, which causes these

abnormal temperatures, which I had not taken into account when forming

my hypothesis. Such years should have been omitted in my investigation.

The seasons we experience are a result of the Earth’s tilted axis as it

revolves around the sun. During 2010’s winter crises, our hemisphere was

tilted away from the sun and its light hits us at a different angle, making

temperatures lower.

An increased sample of data would have been better than to use,

however my results were only skewed due to climate change making

weather unpredictable. For such reason, there were negative correlations

in my data, as the weather has become more severe it was only natural,

that such investigation would have had irregular results.

Bibliography

 

http://www.metoffice.gov.uk/pub/data/weather/uk/climate/datasets/

Tmax/date/UK.txt

http://www.metoffice.gov.uk/pub/data/weather/uk/climate/datasets/Tmin/

date/UK.txt

http://www.epa.gov/climatechange/ghgemissions/global.html

http://simple.wikipedia.org/wiki/Standard_deviation

https://www2.ucar.edu/climate/faq/how-much-carbon-dioxide-and-other-

kinds-greenhouse-gas-already-atmosphere

https://statistics.laerd.com/statistical-guides/measures-of-spread-absolute-

deviation-variance.php

http://www.epa.gov/climatechange/ghgemissions/global.html

http://scrippsco2.ucsd.edu/data/data.html

ftp://aftp.cmdl.noaa.gov/products/trends/co2/co2_mm_mlo.txt

http://www.loc.gov/rr/scitech/mysteries/seasons.html