Lesson video

Hello, my name is Dr.

Rollinson, and the contents of today's lesson is absolutely fascinating.

I hope you found it interesting.

So let's get started.

Welcome to today's lesson from the unit of Maths and the environment.

This lesson is called Studying climate change.

And by the end of today's lesson, we will understand how Earth's polar ice caps are changing.

Here are some previous keywords that will be useful during today's lesson.

So you may want to pause the video, you need to remind yourself what I ever mean, and then press Play when you're ready to continue.

The lesson is broken into two learning cycles.

In the first part lesson, we're going to be taking a dataset for a large period of time and splitting it into smaller, separate periods of time and then making comparisons between them.

Then the second part lesson, we're going to use data to make predictions for the future.

Let's start with comparing data between different periods of time.

Here we have a graph that shows data from the Met Office and HadCRUT5, and now that second bit is just basically a large dataset, part of a research project.

The data is about the mean global temperatures each year from 1851 to 2024.

The vertical axis is frequency, so the height of each bar shows us how many years that bar represents.

The horizontal axis, however, is a little bit more complicated.

It shows global temperatures measured in degrees Celsius, but these are mean global temperatures for each year, and that's what it means when it says, "Annual global mean temperatures." But then look at the next part on the axis label, it says, "Expressed as a difference from pre-industrial conditions." So that means that these numbers do not represent actual temperatures.

Otherwise, it'll be quite cold.

So what the numbers show is how the mean global temperature in a particular year compares with what the temperatures were before industrialization.

So in other words, the horizontal axis shows whether it was warmer or colder than it was before industrialization.

For example, this bar, which is now highlighted, represents all the years where a mean global temperature was between 0.

8 and 1 degrees warmer than it was during pre-industrial conditions.

And then as the vertical axis shows us the number of years each bar represents, then we can say that there were 13 years with a mean global temperature was between 0.

8 and 1 degrees warmer than in pre-industrial conditions.

Now, don't worry if you're not quite sure what the specific numbers on the horizontal axis mean.

All really need to know for this part lesson is that the bars which are further to the right represent warmer years, and the bars which are further to the left represent colder years.

So let's now try and make some interpretations from this data.

There are 174 years represented in this graph, but it's not clear from the way this graph is presented whether the years which are later on are warmer or colder than the years that were earlier on.

So if we wanted to get a sense of whether temperatures have generally increased or decreased over time, this probably wouldn't be the best sort of graph for that, and we'll see some other graphs in the second part of the lesson, but we can still do something with the data we have here with this type of graph.

For example, we could compare different periods of time by splitting the data up into parts.

So rather than representing all 174 years in one single graph, we could split it into two equal time periods, have one graph that shows us the data from 1851 to 1937, and a separate graph that shows us the data from 1938 to 2024.

And it looks something a bit like this.

These graphs show the same data as the previous one, but each period of time is represented separately.

Now I might be thinking, those are quite odd years or choose, it's just chosen like that so that there is pretty much the same number of years in each of those two graphs.

So what might the benefits be for splitting up the data like this? Well, by representing each period of time separately, we can make comparisons between them and draw out some conclusions.

For example, if we look at the graph on the left, which represents years 1851 to 1937, we can see that all the annual global mean temperatures were between 0.

4 degrees colder and 0.

4 degrees warmer than pre-industrial conditions.

But if we look at the graph on the right, which shows us years 1938 to 2024, we can see that all the annual global mean temperatures here were between 0 and 1.

6 degrees warmer than pre-industrial conditions.

In other words, because the bars in the second graph are further to the right on the horizontal axis, it means that those years were generally warmer than the years represented in the first graph.

We could also compare the modal class for each time period as well.

We can look at the graph on the left for years 1851 to 1937 and see that the modal class is between 0 and 0.

2 degrees.

We know that's the modal class because it's the tallest bar, which means it has the greatest frequency.

Whereas with the graph on the right, which is years 1938 to 2024, we can see that the modal class, the tallest bar, is between 0.

2 and 0.

4 degrees Celsius.

So when it comes to comparing these two modal classes, if we're trying to work out whether or not temperatures have got warmer or colder over time, we don't wanna look at how high those bars are.

We only use the height to determine which is the modal class.

What we wanna look at is how far along the horizontal axis that bar is, which is the modal class.

And we can see with a graph on the right, that bar is further to the right along that horizontal axis, suggesting that the modal class is warmer on the right than it is on the left.

So we've compared this data in a couple of different ways and we've drawn a similar conclusion each time.

Now is this data which suggests that the annual mean global temperatures have been generally warmer since 1938 than they were before 1938.

That doesn't mean that every single year after 1938 is warmer than every single year before it.

If you look at the bars, you can see that's not necessarily the case, but generally, we can see that the vast majority of years tend to be warmer in the later time period than they were in the earlier time period.

Now in this case, we decide to split a data into two time periods.

We could use more than two time periods if we want to.

For example, if we split it into three equal time periods, it could look something a bit like this.

These graphs showed the same data again, but this time, in three separate time periods.

On the left, we had the earliest time period from 1851 to 1908.

In the middle, we have a slightly later time period, which is 1909 to 1966.

And on the right, we have the latest time period, which is 1967 to 2024.

Let's make some comparisons between these.

If we look at the left on the earliest time period, we can see that all the data is between -0.

4 and +0.

4 degrees Celsius.

Look at the middle time period, we can see that all the data is between -0.

3 and 0.

5 degrees Celsius.

So just a slight shift to the right there.

And then when we look at the graph on the right, which is for the latest time period, we can see that all the data is between 0 and 1.

6 degrees Celsius.

So that is a bit more of a shift towards the warmer numbers.

We can also compare the modal class in each period of time as well.

With the graph on the left, we can see the modal class is between -0.

2 and 0 degrees Celsius.

For the graph in the middle, we can see that there are two modal classes, and they are between 0 and 0.

4 degrees Celsius.

And with the graph on the right, we can see the modal class is between 0.

8 and 1 degree Celsius.

So the modal class has increased slightly between the first two graphs, has increased quite a bit for that third graph.

Based on these comparisons, the data would suggest that the annual mean global temperatures have been generally increasing over time since 1851.

Now we have justified that conclusion in a couple of different ways using numbers, but you can also see that just by looking at the graphs.

As you compare these three periods of time, you can see the bars gradually shift further and further to the right along that horizontal axis, showing us that the annual mean global temperatures tend to be getting warmer and warmer over time in this data here.

So let's now take a look at a different dataset.

This graph shows us different data from the Met Office and the OSI SAF.

That's again another large dataset based on a research project.

And this data is about sea ice in the Antarctic for each month from 1979 to 2024.

The horizontal axis this time shows us monthly data, and the data is about the extent of sea ice.

The extent of sea ice is measured as an area in millions of square kilometres.

But once again, the numbers and cells are not the actual areas.

They represent differences between the recording that is taken for a month and the average for that particular month over time.

For example, imagine a research has measured the extent of sea ice in November, 2024.

A negative number would indicate that there is less sea ice than average for November, and a positive number would indicate that there is more sea ice than average for November.

Again, if that's a little too complicated, don't worry about it.

You can think about it in this more simplified way that bars which are further to the right show us more sea ice and bars which are further to the left show us less sea ice.

So I'm gonna hand over to you now to interpret this data for yourself.

Which is the modal class based on this graph here? Choose from either A, B, C, or D.

Pause while you do it and press Play for an answer.

The answer is B, from -0.

5 to 0 million square kilometres, and you can see that from the graph because it's the tallest bar.

So that means it's the class with the greatest frequency.

So now we've taken the same data and split it into two separate periods of time.

The top graph shows us the monthly data from 1979 to 2001, and the bottom graph shows the monthly data from 2002 to 2024.

For which period of time is the modal class greater? Pause the video while you write down your answer and press Play when you're ready to see what it is.

The answer is 2002 to 2024.

If you thought it was a top graph, it might be because the modal class in that top period of time has a greater frequency than the modal class in the bottom period of time, but it's not the frequency we're concerned with here.

The frequency only indicates which class is the mode in each graph.

What we're looking for is which one has the greatest values in data.

And we can see that for the top graph, the modal class is between -0.

5 and 0, but for the bottom graph, the modal class is between 0 and 0.

5.

Therefore, that one has the greater modal class.

Let's now consider the consistency of data between these two periods of time.

True or false? The extent of sea ice in the Antarctic was more consistent between 1979 and 2001 than it was between 2002 and 2024.

Is that true or false? And please explain your answer.

Pause video while you do that and press Play when you're ready to take a look at an answer.

True.

So how could we justify it? Well, we could justify it in a few different ways, and here's one example.

We could say something like, "The data appears less spread out in the top graph than in the bottom graph." We can see in the top graph, there are only five bars, and the vast majority of data are just in those two middle bars, which is why the height of those bars are really high and the remaining bars are quite low.

Whereas in the bottom graph, there are more bars, and the data is more spread out generally between them, which is why all the bars are relatively low compared to in the top graph.

So that's one way we can justify it, but there are other ways as well.

For example, you could say something like this, "All the data for 1979 to 2001 is between the values -1.

5 and 1.

But when you look at the bottom graph for 2002 and 2024, the data is between -2.

5 and 2." So there is a wider range in the data.

Or you might have made a more descriptive comparison, a bit like this, "For the top graph, which is for 1979 to 2001, most of the data, not all of it, but most of it is between -0.

5 and +0.

5.

Whereas for 2002 to 2024, the data is more evenly spread." Okay, it's owe to you for task A.

This task has two questions and here is question one.

Pause video while you do this and press Play for question two.

And here is question two.

Pause while you do this and press Play to start going through some answers.

Let's go through some answers.

In question one, you've got two graphs that show you data about the sea ice in the Arctic for each month from 1979 to 2024, but that data is split up into two time periods.

One is from 1979 to 2001, and the modal class for that data is 0 to 0.

5 million square kilometres.

And the bottom graph shows the period of time from 2002 to 2024.

And the modal class of that data is between -1 and -0.

5 million square kilometres.

So in part C, you had to draw a conclusion from these two graphs, and it asks you, "Did the extent of sea ice generally increase or decrease between the two periods of time?" And explain your answer.

Well, the extent of sea ice is generally less for 2002 to 2024 than for 1979 to 2001.

So it is generally decreased.

How can we go about justifying that though? Well, there are lots of different ways you can do it.

So let's take a look at a couple examples.

One example could be to compare the modal classes for each time period.

The modal class is lower for 2002 to 2024 than it was for 1979 to 2001.

We can see in the top graph the modal class, which is the tallest bar, is between 0 and 0.

5, whereas in the bottom graph, the modal class is between -1 and -0.

5.

So it is lower in that later time period.

An alternative explanation could be something a bit like this, that the data for 1979 to 2001 is between the values -1 and +1.

5, while the data for the later time period, 2002 to 2024, is between -2.

5 and +0.

5.

So that means that both the upper and lower limits of the data has decreased as we've gone from the earlier time period to later time period.

And those are some justifications you can use with numbers, and there are other ways you can do it as well by using other statistics.

It's always worth just looking at the graphs as well, and you can see that for the bottom graph, the bars are further to the left than they are in the top graph.

So that gives you a more of a visual sense that the bars have shifted to the left over time, which means there is less sea ice over time.

Then question two, you were presented with three graphs, and these graphs show you data about sea-surface temperatures for each year from 1851 to 2024, and it split into three periods of time.

And you had to compare the sea-surface temperatures for the three periods of time and describe any conclusions that you can draw from the data.

Now there are lots of different things you could write for this, so let's just take a look at some examples.

One thing you might notice is that the annual mean sea-surface temperatures appear to only increase slightly between those first two periods of time.

If you look at the modal class for those top two graphs, you can see that they have both the same.

The modal class each case is between -0.

6 and -0.

4.

However, when you look at the upper and lower limits of the data in those two graphs, you can see that there is a slight change.

For 1851 to 1908, all the data is between -1 and -0.

2, whereas it's between -1 and 0 from 1909 to 1996.

Just the upper limit has come down ever so slightly there.

So based on the numbers given in the justification, it indicates that the data hasn't really changed very much between those two periods of time.

But when you look at the graphs themselves, it gives a slightly different impression.

When you compare the top graph with the middle graph, the bars do seem to have shifted ever so slightly to the right, particularly two tallest bars in each of those two graphs.

So maybe if you found some other statistics, like if you were able to work out the mean for each dataset, you might see a bit more of a change.

Which is why it's always worth looking at statistics, but also a visual representation like this.

So that's one conclusion you might make.

You may also look at the latest time period and say something a bit like this.

"For the majority of years from 1967 to 2024, the annual global sea-surface temperatures were higher than they were between 1851 and 1966." In other words, that last time period tends to have warmer sea-surface temperatures than either those two earlier periods of time.

And a way to justify that could be either by using the modal class or by looking at where the upper and lower limits are for the data you can see there.

There are more precise methods that can be used to compare datasets.

For example, using the mean or median, or there are some other statistics you can use as well, they may be a more precise way of making comparisons if you already know how to use them.

But if you've used any of those comparisons that we've previously talked about, well done.

You're doing great so far.

Let's now move on to the next part of this lesson, where we're going to be using data about sea ice to make predictions.

Here we have a graph that shows data from the Met Office and HadCRUT5 about the mean global temperatures each year from 1850 to 2024.

It's the same data that we worked with in the first part of this lesson, but represented in a different type of graph.

This time, the horizontal axis shows us the years for each data point and the vertical axis shows is the annual global mean temperature expressed as a difference from pre-industrial conditions given in the degrees Celsius.

So other words, each temperature shows whether it was warmer or colder than before industrialization.

For example, let's take a look at this data point, which is highlighted here.

The horizontal axes tells us that it was taken in the year 2020, and the vertical axis tells us that the mean global temperature was 1.

3 degrees Celsius warmer than it was during pre-industrial conditions.

So let's start interpreting this data now.

What do you notice about the data? Pause video while you think about this, think about any possible conclusions that you can draw out of what you can see on the graph there, and press Play when you're ready to continue together.

Well, there are plenty of different things you could say about this data.

Let's hear a few suggestions.

Sophia says, "The mean global temperatures go up and down each year." You can see that because as you compare one point with the next one, sometimes it goes up, sometimes it goes down, which is why the line is quite wiggly, going up and down all the time.

Jun says, "For most years between 1850 and 1940, the mean global temperatures stayed within a similar set of values." It can stay somewhere roughly between -0.

3 and at +0.

3.

But Aisha says, "The mean global temperatures also stayed between a similar set of values for 1940 to 1970.

But these are higher than they were from 1850 to 1940." Visually, you can see the data kind of step up a bit around about 1940, and in that second period of time, which Aisha has highlighted, we can see that at the mean global temperatures are between 0 and 0.

55 degrees warmer than pre-industrial conditions.

So what happens after 1970? Well, Sam says, "I can see an upward trend in the mean global temperatures from around 1970 onwards." It still goes up and down, you can see that because the line is still wiggling as it goes between those years, but from 1970 onwards, it generally seems to go up more than it goes down.

And here we have Izzy, who has looked at the data in a slightly different way.

She's paid particular attention to the horizontal axis, which is in line with zero on the vertical axis.

Now any data points that are around that line, around zero, suggests that the annual global mean temperatures for those years are similar to what they were in pre-industrial conditions.

Data points that are below it suggest that they are colder years, and data points that are above that line suggest that those years are warmer than pre-industrial conditions.

Now Izzy says that the meaning global temperatures have been higher than they were during pre-industrial conditions for nearly every year after 1935.

And we can see that from the graph because most of the data points after 1935 are above zero on that vertical axis, suggesting that those years were warmer than pre-industrial conditions.

So there are lots of different ways we can draw interpretations from this graph and different things we can conclude from it.

Let's now think about trends in the data and how they might be able to help us make predictions for the future.

If we look at the graph now, we can see that there are two dashed lines in it.

Those lines don't have to be dashed, but let's think about what those lines are showing us.

If we look at the data from 1970 onwards, we can see that the data generally tends to increase and decrease again and again over time.

And we can see that by the way the line is wiggling up and down constantly.

One of those dashed lines tries to capture where all the peaks are in the data, and the other dashed line, the bottom one, is trying to capture roughly where all the troughs are in that data.

And the two of them together show us generally what the trend is doing, but it's generally going up more than it's going down.

So if we continue those dashed lines onwards to the year 2050, we are assuming that the data will continue to change in that similar sort of way.

So we can use those dashed lines to make a prediction of what range of values we could expect in 2050 by looking at the horizontal axis at each of those two lines.

And by doing so, we could expect that the mean global temperatures will be between 1.

6 and 2 degrees higher than they were during pre-industrial conditions.

How about if we predict a bit further into the future such as 1970? Well, we can do the same thing again, just need to extend that dashed line further on.

And if we do the same thing, we can see that we would expect the mean global temperatures to be between 2 and 2.

45 degrees Celsius higher than they were during pre-industrial conditions.

However, how confident can we be about these predictions? Perhaps pause video while you think about this.

If you think we can be confident, think about why.

If you think we cannot be confident, think about why as well.

And then press Play when you're ready to continue together.

Well, those predictions are made based on the assumption that the trend which we saw from 1970 to 2024 would continue in the same way into the future.

But trends in data can be affected by events or actions.

Something might happen in the future that may cause that trend to change.

So the further we predict into the future, the less confident we may be about that particular prediction.

So let's check what we've learned.

Here, we have a graph that shows data from the Met Office and the OSI SAF about sea ice in the Antarctic for each November from 1980 to 2014.

It's based on the same data we saw in a first part lesson, but rather than showing every single month, it's only showing the Novembers of each year.

Now the horizontal axis shows us the year that that November was in, and the vertical axis shows us the Antarctic sea ice extent for November expressed as a difference from the 1981 to 2010 average for each of those Novembers, and it's in millions of square kilometres.

Basically, the higher up a data point is on the graph, the more sea ice was recorded in that particular month.

So let's make an interpretation.

True or false? The extent of sea ice increases and decreases from one year to the next.

Is that true or is that false? And explain your answer.

Pause while you do it and press Play for an answer.

The answer is true, and one way you can explain it is by saying, "The values differ each year.

Sometimes there's increase, and sometimes there's a decrease." So true or false? Despite changes between years, the extent of sea ice remained within a similar range of values for most years between 1980 and 2010.

Pause while you write something down and press Play for an answer.

The answer here could be argued to be true.

And the way you could argue that is by saying that apart from 1986, which you can see is a particularly low point in the data, and 2010, which is a particularly high point in the data, all the values are between -0.

5 and +0.

5.

They're all within a similar range.

Here we have Jacob, who notices a slight upward trend in the data.

He draws a pair of lines to predict what data we might expect to observe in the year 2030.

Based on Jacob's lines, we could expect to observe values between blank and blank.

Fill in the blanks.

Pause video while you do that and press Play for an answer.

We could expect to observe values between 0.

3 and 1.

2.

So that means Jacob predicts that the extent of sea ice in the year 2030 will be between 0.

3 and 1.

2 million square kilometres greater than the 1981 to 2010 average for each November.

Could you please explain why might this prediction not come true? Pause video while you write something down and press Play for an answer.

Now, you might have wondered, "Why does the data on this graph stop at around the year 2014?" Well, there was more data in this dataset.

We just haven't shown it yet on this graph.

And the reason why is to illustrate this next point I'm about to make.

Here, Jacob has detected a trend in the data, but trends may change.

For example, the graph now includes the data from 2015 to the year 2024, and what we can see is it doesn't follow the same trend as it did in the earlier data.

So that's the reason why prediction may not come true.

Trends can change.

Okay, it's over to you now for task B.

This task has two questions, and each question has a part A and a part B.

Here is question one part A.

Pause video while you do it and press Play when you're ready for part B.

And here is part B.

Pause video while you do this and press Play for question two.

Here is question two part A.

Pause while you do this and press Play for part B.

And here is part B.

Pause while you do this and press Play for some answers.

Okay, let's go through some answers.

In question one, the graph shows you data about sea-surface temperatures, and in part A, you had to write down at least two observations that you make about trends in the data.

Now, there are all sorts of things you can say.

Let's take a look at a few examples.

One example could be to say that the global mean Sea-surface temperatures remain relatively stable between 1850 and 1930.

You could also say that there's an upward trend from 1920 to 1945.

The global mean sea-surface temperatures then remain relatively stable between 1945 and around 1980.

But then, from 1980 onwards, there is a clear upward trend.

If you wrote any of those things, be well done.

In part B, assuming that the trend in the mean global sea-surface temperatures continues in the same wave that has done since 1970, you have to write down what range of data we could expect to observe in the following years.

Well, we could do that by drawing on a pair of lines that tried to capture the peaks and troughs of the majority of those data points from 1970 onwards, extend those lines into the future, and use them to make the predictions.

If you do so, you may have some predictions a bit like these.

If yours are slightly different to these, don't worry.

It depends very much on where you draw those lines and how you draw them.

It's an interpretation of the data.

So your answers may differ ever so slightly from the ones given here.

But hopefully, you've got something similar.

Then question two, the graph shows you data about sea ice in the Arctic from 1980 to 2024, and it's for each January, and you have to write down at least one observation that you made about trends in data.

Well, there are different things you could say, but here are some examples.

You may say that overall, there's been a downward trend from 1980 onwards.

You could also say that the trend possibly changes from around the year 2006 onwards to something slightly more stable.

And in part B, you had to assume that the trend in the extent of Arctic sea ice would continue in the same way that has done since 1980, and predict what range of data we could expect in each of those years.

Could do it in the same way we did in question one by drawing on a pair of lines that captured at peaks and troughs, generally other the data, and use that to get these three ranges here.

Once again, your answers are slightly different to these, don't worry too much about it.

Hopefully, you got something similar.

Next, I'll summarise what we've learned.

The effects of climate change can be observed through data.

And a dataset can be represented in multiple different ways.

We've seen a couple of different ways today.

Comparisons can be made between different periods of time and trends can also be interpreted.

And by analysing how the northern or southern polar ice caps have changed, predictions can be made for the future.

Well done today.

Have a great day.