The same applies with the rainfall levels. I do not know the position of these reading stations and so therefore do not know whether possibly one station was in a rain shadow etc. I must assume that each average for every month of every year is a representative average and that these stations or recording equipment have already been placed around the country carefully and strategically. I am assuming that the data has been collected using stratified sampling. Which is where the population (the weather recording stations) have been split into identifiable groups and then used accordingly. For example the data might have only been taken from stations at the same altitude for example. This is stratified sampling and I am assuming that the met office, the producers of this data have used some kind of this stratified sampling to obtain and release these sets of data.
Also it is hard to know whether the average is representative, there might be the factor that describes how many stations where were. For all I know there might only be one station in Northern Ireland taking only one reading. So again i must assume that enough stations have been placed in the country to obtain a representative average to cover all underlying factors.
The data used is from the Met Office UK:
This is the official weather processing station in the UK and is what supplies TV and newspapers with official weather reports. I can therefore confirm from this that is true weather reports and not some biased set of data. If for example I had received data from a British Ski tourist board then I would expect my results to be slightly different and biased as they would try and promote tourism in the desired areas by explaining how the climate was ideal for their industry.
Firstly I will look at two simple sets of data. One of the Mean temperature (Degrees C) on England and Wales together and then of the average rainfall levels (MM) in England and Wales both together. The data given to me is set out in the format of monthly readings. So for each of the 42 years I have 12 readings (one for each of the 12 months in the year). What I did was to take the average for each whole year so my result was 42 separate yearly averages. This is easier comparing years than months because it means I do not have to worry about different seasons of the year (obviously the months of January and February would be colder being in winter) and also that it is easier to look at the general trend of a yearly average over 42 years than a trend of all the months over 42 years.
I will expect there to be in both examples a positive gradient as this will show there to be an increase in data over the past 42 years from 1961 to 2003.
As you can see there is a positive trend here. After making the graph in Excel as it is quicker to make and also to edit and show trend lines than drawing by hand I then inserted a trend line into the points of the graph and also calculated the gradient using an Excel tool. The gradient is the number highlighted. As you can see it reads 0.03Degrees C/annum which indicates that it is a positive gradient. From this I can say then that over the past 42 years there has been a definite increase in average yearly temperate. There was however a strange reading, an anomaly. When included in the graph it gave a gradient of 0.0318 so therefore it affected the gradient. The readings for that year of 1979 were:
-0.3, 0.9, 4.1, 7.2, 9.3, 3.4, 5.5, 4.4, 12.8, 0.8, 6.3, 5.3 giving an average of 5.0
This was a ‘freak reading’ and was unlike any other yearly average as it bears no relation to any other year, or the pattern of the graph.
So I decided not to include it in the graph or the data as I felt it did not show a true reading of the average yearly temperature of England and Wales. As it bears no relation to any other year, or the pattern of the graph. I concluded that there must have been a mistake in the instruments possibly or the way in which these instruments were read for this one reading was far too unbelievable.
Looking now at the levels of Rainfall in England and Wales I would also expect there to be a positive gradient, indicating an increase in rainfall levels over the past 42 years. I think this because due to the slight increase in temperatures, there would have been substantial melting of the polar ice caps and therefore more water in the sea enabling more rainfall. Especially as the UK has a very maritime climate.
Again you can see that I have added a trend line and also highlighted the gradient of the graph. It shows again that there is a positive increase in the rainfall levels over the past 42 years. The gradient reads 0.1681 MM/annum
What I now would like to do is to find out the standard deviation this graph. This enables me to find the fluctuation levels of the data on the graph. I will find the standard deviation of certain time segments of the graph. I will split the data up into groups of:
1961-1970, 1971-1980, 1981- 1990, 1991-2003.
The last group is of a different time segment to the others. The others are in segments of 9 years whilst the last is of 12 years. This is because 1961-2003 is slightly hard to put into equal time slices. Using standard deviation in Excel I can find out the deviations and therefore the different fluctuations over the different time slices of the rainfall levels:
This shows that there has been a higher fluctuation of rainfall ranges over the past 12 odd years. In 1961-1970 the standard deviation result was a value in the middle of my other values. Whereas there seemed to be a slight fall in 1981-1990 as it reached approx. 5mm. But then since 1981-1990 it has increased up to 12mm. From this I can give a rough estimate. That in the 80’s there was some factor that decreased the amount of emissions into the atmosphere, causing global warming. Since then it has increased dramatically possibly due to the fact of modernisation, and the explosion of cars.
I can now see if the two are correlated. I said in my hypothesis that the two sets of data of Mean temperature and Rainfall Levels are linked because obviously as the earth heats up so therefore there will be high sea levels and therefore more rainfall levels etc. I can check this by looking at a correlation graph of the two.
This done it isn’t too clear what is being shown. Again there was this anomaly of the year 1979 which again like the previous time I took out. I ignored it.
Positive correlation graphs are defined as one that would look a little like this:
The above graph does show this slightly but it is very minute. The dots do seem to be scattered around in one single area on the graph and be rather situated on a flat line.
To gather a better correlation idea I used the correlation tool in Excel to tell me exactly the correlation. The result was 0.133333
This correlation figure provides evidence that there could be a link between mean temperature and rainfall levels and tells us that as one varies so too does the other.
Although I believe this figure is relatively small. Using the MEI structured Mathematics handbook I looked up that the critical value for a 42 part correlation figure to be positive is 0.2573. My correlation was 0.133333. This means that the correlation is relatively small.
My first hypothesis was
- That the data will show a definite increase from 1961 to 2003 in mean yearly temperature and therefore also in rainfall levels. I will want to show this as in the last few years there have been increasingly higher levels of media hyper about increasing global warming and its affects on the plant.
I have now provided evidence to show this to be correct although I would not state that the data shows a DEFINATE increase as the gradients in both graphs are quite small, and also that the correlation between the two are small.
But one must remember that we are talking very large scale readings. These temperatures are an average of two whole countries with areas of many miles.
Gradients of the Graphs of average yearly temperature and Rainfall respectively of England and Wales = 0.03 degrees C/annum, 0.1681mm/annum and the correlation between mean temperature and Rainfall levels in England and Wales was 0.13333
If I was to put it into context then things would look a bit different. If I look at the gradient for the Temperature of England and Wales as being 0.03degrees C/annum. This means that every year the temperature increases by 0.03. Which theoretically means that in one hundred then every year’s temperatures would be 3 degrees hotter. And then in a thousand years time every yearly average would be 30 degrees hotter. Neither are certainly not going to happen without devastating effects. This will not happen because there are many other factors affecting this gradient and that certainly will do in the near future like what people will actually do to prevent these emissions and therefore stop global warming hopefully.
As with the periods of time before and after the sets of data I have been given there have been and will be many other factors affecting the rate or increase/decrease. Obviously I cannot possibly include every factor but in the period given to me from 1961-2003 I can say from my evidence that I have worked out that there was an increase in mean yearly temperature and therefore also in rainfall levels.
My second hypothesis:
- I will then compare my results from England and Wales to both Scotland and Northern Ireland and see if there is any relation as England and Wales are on different latitudes to Scotland and Northern Ireland. In this I will be comparing gradients of graphs and seeing which of the two is possibly higher or has a more positive correlation etc. Because of this I would expect there to be a bigger increase in rainfall levels and lower mean temperature in the Northern most countries.
The data for England and Wales was given to me as an average of the two:
ENGLAND & WALES MEAN TEMPERATURE (DEGREES C)
Whereas the data given to me for Northern Ireland and Scotland are both separate:
NORTHERN IRELAND MEAN TEMPERATURE (DEGREES C)
SCOTLAND MEAN TEMPERATURE (DEGREES C
So I must gather both sets of results (the averages of each) and make an average of the two to make the same type of graphs like I did before to make for comparison.
The gradient of this graph as you can see is 0.0249 degrees C/annum (shown in the yellow highlighted box). The gradient of the mean temperature of England and Wales was 0.03 degrees C/annum. This is what I expected so see! From these two results it tells me that Scotland and Northern Ireland have had a lower increase in mean temperature than England and Wales together. One cannot tell whether Northern Ireland and Scotland’s lower increase in mean temperature is significantly lower. To prove this I would have to look at a much longer stretch of time and its data just to make a more educated guess. But it does provide evidence to suggest that Northern Ireland have had a lower increase in mean temperature than England and Wales
Again looking at rainfall levels for Scotland and Northern Ireland I must add the two
together as they are both separate averages so I must make an average of them both.
From the graph I created I can see that the gradient is again as expected positive and reads 0.2848 mm/annum. The gradient of the England and Wales graph is 0.1681 mm/annum. This provides evidence to show me that there has been a greater increase in rainfall in Scotland and Northern Ireland over the past 42 years. This follows true to my hypothesis.
As I did previously I will again take a standard deviation calculation of the rainfall graph above as there seems to be a very high fluctuation of readings as time progresses. I will then compare the standard deviation numbers to that of the standard deviation calculations of England and Wales.
I will split the data up into groups of:
1961-1970, 1971-1980, 1981- 1990, 1991-2003.
The last group is of a different time segment to the others. The others are in segments of 9 years whilst the last is of 12 years. This is because 1961-2003 is slightly hard to put into equal time slices. Using standard deviation in Excel I can find out the deviations and therefore the different fluctuations over the different time slices of the rainfall levels:
This shows that there has been massive fluctuation over the years, from 9.5 to 28.9. Telling me that of late the increase has been much bigger than that recorded in these 42 years.
I can now compare the standard deviation calculations of Northern Ireland and Scotland to that of England and Wales.
There is now only one more calculation I can perform so that I can gather the most evidence I can to compare England and Wales to Scotland and Northern Ireland. That is to create a correlation graph between the mean temperature and rainfall levels of Northern Ireland and Scotland to see if there is a bigger link between the two sets of data.
The correlation of this graph is 0.090969812
This correlation figure provides evidence that there could be a link between mean temperature and rainfall levels and tells us that as one varies so too does the other.
Although I believe this figure is relatively small. Using the MEI structured Mathematics handbook I looked up that the critical value for a 42 part correlation figure to be positive is 0.2573. My correlation was 0.090969812. This means that the correlation is relatively small.
Conclusion:
- That the data will show a definite increase from 1961 to 2003 in mean yearly temperature and therefore also in rainfall levels. In my case as I will be drawing graphs I will expect to see positive gradients or positive correlation between the inputs. I will want to show this as in the last few years there have been increasingly higher levels of media hyper about increasing global warming and its affects on the plant.
For the graph on Mean temperature of England and Wales look at page 5
For the graph on Average rainfall levels of England and Wales, look at page 6
The gradient of the Mean temperature graph of England and Wales was 0.03 degrees C/annum
The gradient of the Average rainfall levels of England and Wales 0.1681 mm/annum
Looking at the graphs of the mean temperature and rainfall levels of England and Wales and using the gradients and calculations I made can come to the conclusion that from 1961 to 2003 I have provided evidence to suggest that there has been an increase in Average temperature readings and in Rainfall readings in England and Wales. I would also like to suggest that this increase is due to the effects of global warming and gaseous emissions caused by man. Which is true to my hypothesis of higher levels of temperature and rainfall and all the media hype surrounding it.
- I will then compare my results from England and Wales to both Scotland and Northern Ireland and see if there is any relation as England and Wales are on different latitudes to Scotland and Northern Ireland. In this I will be comparing gradients of graphs and seeing which of the two is possibly higher or has a more positive correlation etc. Because of this I would expect there to be a bigger increase in rainfall levels and lower mean temperature in the Northern most countries.
Graph to show comparison between gradients in graphs of Mean temperature and average rainfall levels in England and Wales to Northern Ireland and Scotland
From this I can conclude that I have provided evidence to support my hypothesis. That there was a bigger increase in rainfall levels and a smaller increase in Mean temperature levels in Northern Ireland and Scotland compared to England and Wales. I predicted this due to the fact that the two separate areas are located on different latitudes. The northern two countries I can conclude are getting colder and receiving more rain due to the fact that global warming is melting the polar ice caps, causing a rise in sea temperature and also the lowering of the sea temperature. As Scotland and Northern Ireland have an extremely maritime climate and also because they are closer to the polar region than England and Wales (latitude), this is why there are experiencing the change that they do.
Standard deviation of rainfall levels
This shows me that approximately from 1961 to around 1990 Northern Ireland and Scotland have had the larger fluctuation in Rainfall levels. But of late, from 1991 to 2003 Northern Ireland and Scotland has had a huge fluctuation in rainfall levels. Just over twice as many times as much than that of England and Wales. This evidence further more supports my hypothesis showing me that of late rainfall levels have greatly fluctuated due to what I can imagine to be a boom in emissions from humans resulting in greater global warming and therefore higher rainfall levels. The reason being the melting of the polar ice caps.
Lastly I can look at the correlation of Mean Temperature and Rainfall levels and compare the two correlation graphs for England and Wales and Northern Ireland and Scotland.
The correlation of the two graphs were as follows:
England and Wales = 0.133333
Northern Ireland and Scotland = 0.090969812
This tells me the relationship between the two factors of mean temperature and average rainfall levels. How much they are related to each other. Using the data I was given and calculating the correlation co-efficient enabled me to conclude that the mean temperature and average rainfall is more related in England and Wales than in Northern and Ireland although the relation is extremely small if actually positive. As stated in the MEI structured mathmatics handbook the critical value for a 42 part correlation figure =0.2537. My two correlation figures are both below this and would suggest that they are very low indeed.
This would suggest to me that in Northern Ireland there are other factors that would seem to affect the relationship between Mean temperature and rainfall levels that do not affect the relationship in England and Wales. If I was to carry on this investigation I would probably like to find out these other factors.
Evaluation:
Overall I am pleased with the investigation I did. I am happy that I chose the right question for me and that my knowledge of techniques of analyzing data worked well for the question I chose.
Obviously In the very first section after the Plan I talked about what global warming was. I explained how global warming could not just be measured by looking at mean temperature levels and rainfall levels. There are many more results of global warming that I could look at to determine whether it is actually having any affect on England and Wales and certainly whether any levels are on the increase or decrease.
My method of using gradients and comparing them between two different areas I thought worked very well. It allowed me to compare the two between each other and see whether there was a difference. One problem however was knowing how big the difference was. Within this project I only used two different places having done no work on these types of graphs and these specific gradients and their values before hand. This meant that I really did not know whether the gradients were significantly bigger than each other. If I was to carry on this investigation I would just beforehand prepare some more gradients of a variety of countries, for example Zimbabwe, Russia, Japan, Brazil and Iceland. This would allow me to get a few more values for the extremities that these gradient values could take. This would ultimately allow me to compare my two gradients between England and Wales and Scotland and Northern Ireland better.
I also talked about how in this project I am assuming that global warming is caused by emissions of gas into the atmosphere heating up the earth by layering the atmosphere with an extra ‘blanket’ of gases trapping in heat. There are of course other factors for example cosmic rays that affect the causes of global warming which I cannot and would not be able to get hold of data for and therefore not analyze and include in any investigation of mine. That is just an example as there are many other factors. If I was to repeat or carry on with the project I would like to obtain as many other factors as possible by researching into these ‘cosmic rays’ and finding some data for them. Then if I can try to incorporate them as best I can into my investigation.