Lesson video

Hello, there, my name is Dr.

Ronson, and, in today's lesson, we're going to be looking at some really interesting stuff.

I hope you find it useful.

So let's get started.

Welcome to today's lesson from the unit of "Maths And The Environment".

This lesson is called "Predicting The Weather", and, by the end of today's lesson, we will be able to use a simple model to predict the weather.

The lesson make use of two previous keywords.

One of them is forecast.

A forecast is a prediction of a future event occurring which is based on data.

The other is extrapolation.

Extrapolation is a process of estimating unknown values that are outside the range of existing data.

The lesson is broken into two learning cycles, and we're going to start by looking at rainfall forecasting.

Weather reports can include a lot of information about the rain.

For example, it might include the type of rain we should expect, the chance of rainfall, and also the amount of rainfall which is usually measured in millimetres.

Here we have Andeep.

He says, "What does all that information mean, though? Surely the prediction is either it will rain, or it won't rain?" (teacher humming) Well, there are different types of rainfall.

Let's take a look at some.

One is rain showers.

Rain showers are caused by individual clouds.

Rain showers can affect small areas whilst leaving nearby areas dry.

Think of it as little pockets of rain.

Another type of rain is just rain.

Rain is caused by large grey skies rather than individual small clouds.

Rain lasts longer than rain showers, and can result in more rainfall.

Another is heavy rain.

Heavy rain is also caused by large grey skies.

However, the amount of rain that falls each second is a lot heavier.

Heavy rain can last as long as normal rain, or it can last longer than normal rain instead.

The amount of rain we predict will fall will differ depending on the type of rainfall predicted.

For example, if we are forecasting rain showers, we might only predict one millimetre of rainfall, because the rain just occurs in small pockets for short periods of time.

For rain, though, we might expect something a bit more like 2.

8 millimetres, because it's raining for a longer period of time.

But for heavy rain, where there is more rain occurring per second than just rain, we may predict a lot more.

So five millimetres might be our prediction.

We might now be thinking, how big are these numbers in the context of rainfall? And that's what Andeep says.

He says, "Is one millimetre of rainfall a lot? How much rain actually falls if the weather report says, 'One millimetre of rain'?" Let's take a look.

If a rainfall event is predicted to produce one millimetre of rain, then on any flat land affected by the rainfall, the rainwater would be one millimetre high.

One millimetre of rainfall also means that every one square metre of area will have one litre of water fall on top of it.

Let's take a look at what we mean by that.

Here we have a patio.

The patio is two metres by four metres, and we split it up now into one metre squares.

We can see that there are eight of them.

If one millimetre of rain was predicted to fall, how much water would fall onto this patio area? Well, we would predict that there'll be one litre in each of these squares, so, altogether, we could predict that eight litres of water would land on this patio.

So let's check what we've learned with this weather report.

At 10:00 AM, this weather report is released showing the weather for the rest of the day.

According to the weather report, how much rain is predicted to fall later on in the day per one square metre of area? Pause the video while you write down something, and press Play when you are ready to see what the answer is.

Well, we can see that there is no rainfall predicted for 6:00 PM, so we're really looking at this box here.

This box says there is 6.

5 millimetres of rain predicted, which means there'd be 6.

5 litres of rain, or 6,500 millilitres of rain, in one square metre.

Here, we have a water butt, and this water butt has an open top to collect the rainfall.

The area of its open top is 0.

8 square metres.

How many litres of water will be collected by today's predicted rainfall? And you can use a ratio table to help you if you like.

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

Well, the weather report says that there would be 6.

5 millimetres of rain, which suggests there'll be 6.

5 litres of rain per one square metre.

We have 0.

8 square metres, so we could use multipliers, and the multiplier is 0.

8, to predict that we should get 5.

2 litres of rainfall in that space.

So let's take a look at this weather report now.

It says, at 12 o'clock, it's predicted to be rain showers with an 80% chance of rainfall, and two millimetres of predicted rainfall.

And here we have Andeep.

He says, "So if I see this weather report, then it's guaranteed that there will be a rain shower, and two millimetres of rain will fall?" (teacher humming) It's got a question mark in that which makes me think that he's not quite sure about it.

A weather forecast is a prediction of something that might happen in the future, but it's just a prediction, and there are a lot of factors that go into a weather prediction such as the size of a cloud, wind direction, wind speed, pressure fronts, and so on.

Quite complex.

Therefore, because these factors, some predictions about rainfall will be more or less accurate than others.

The greater the chance of rainfall percentage, the more likely it is that rain will fall in that area around that period of time.

In this case, it says 80%.

Andeep says, "80% is pretty big.

That means it's definitely going to rain." Is Andeep correct? (teacher humming) Well, Laura says, "I don't think so.

Any percentage less than 100% means it isn't guaranteed to rain." So 100% represents the probability that is certain.

Let's now take a look at the weather report for more of this day.

We can now see five times during this day, and, at each of those times, the chance of rainfall is 80%.

Would you expect rain at one of these times in the day? Well, 80% is equivalent to four fifths, and four fifths suggests that if there are five periods of time, each with an 80% chance of rainfall, then it is expected, and I wanna stress the word expected, not guaranteed, it's expected that, in four of those periods of time, it will actually rain.

Four out of five.

So for example, it could look something a bit like this.

Four out of those five periods of time, it's raining, and one of them, it isn't.

However, just because we expect four out of five periods of time to result in rain, that doesn't necessarily mean there will be exactly four periods of rainfall.

For example, when you flip a coin, say 10 times, you might expect to get heads five times, and a tails five times, but that doesn't necessarily mean it will happen.

You might get head six times, or four times, or so on.

We are more likely to see around four of those five periods of time result in rainfall, but it is possible for any amount of rain to fall, including no rainfall at all.

This is just a very unlikely, extreme outcome, though, based on the prediction we have here.

For example, imagine rolling a dice five times.

It is possible for the dice to land on the number six each and every time.

However, this outcome is very unlikely.

Let's model this now with a visual representation to see how the reality may differ from predicted weather forecasts.

For example, 20 days in a row, each have a predicted 80% chance of rainfall, and this timeline shows whether or not the rain actually fell.

On day one, it rained.

We can see that here with a spot on line with Day With Rain above the number one on that number line.

So that means, after one day, there is one day that rained, one out of one is 100%.

100% of days had rainfall, not 80%.

However, on day two, it didn't rain.

So it means, after two days, there is one day that rained.

One out of two is 50%, which means 50% of days had rainfall, not the 80% we might predict based on the percentage chance of rainfall.

After 10 days, there are nine days that rained, and nine tenths is equivalent to 90%, which means 90% of these days had rainfall rather than 80%.

After 20 days, there are 15 days that rained.

15 twentieths is 75%.

We're getting closer to 80%, but not quite.

Whilst at no point did exactly 80% of the days have rainfall as predicted, the percentage was usually in the range of numbers close to 80%.

This became more and more true, the greater the number of days that were analysed.

So let's check what we've learned.

Here, you've got a weather report.

The weather forecast for the next week predicts five days each with the same chance of rainfall.

From this weather forecast, on how many days should you expect rain to fall? Pause while you write something down, and press Play for an answer.

Well, 40% is equivalent to two fifths, so we expect two out of five days, which will be two days.

Well, it turns out it rained actually in all five of these days.

So let's take a look at some statements here from Aisha, Izzy, and Jun.

Which of those statements is guaranteed to be correct? Pause while you write something down, and press Play for answer.

Aisha and Izzy's statements are guaranteed to be correct.

Aisha said, "The weather prediction was incorrect", which we can see it was.

And Izzy said, "Reality can differ from even accurate predictions." What about Jun's statement? Well, Jun's assumption may not be correct.

Just because a weather forecast prediction over five days does not come true does not mean the model used to predict the weather is inaccurate.

Five days is not a large enough sample size to make this judgement fairly.

The model may be more accurate across several months or years.

Okay, it's over to you for task A.

This task has three questions, and here is question one.

Pause while you do it, and press Play for question two.

And here is question two.

Pause while you do this, and press Play for question three.

And here is question three.

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

Okay, let's take a look at some answers.

For question 1A, you should have five millimetres for Monday, 1.

6 millimetres for Tuesday, 0.

7 millimetres for Wednesday, and 8.

5 millimetres for Thursday.

For 1B, the weather prediction for any one day may not always be correct even if the model used to predict the weather is accurate.

Because remember it's just a prediction, it's mostly think about probability.

Also, a 90% chance does not mean rain is guaranteed.

It only means that it's very likely.

On one in every 10 days, with a 90% chance of rain, it is expected it will not rain.

And for part 1C, it may be hard to predict whether the group of clouds that are modelled to form will be rain clouds resulting in showers, or clouds that won't produce rain.

So this is especially true since a lot of contributing factors could change between Saturday, the time the forecast is made, and Wednesday.

And for question two, for part A, you should have 7.

5 litres, and for part B, you should have 13,500 litres.

Then for part C, there is only a 73% chance that it'll rain on Sunday.

This means that there is a 27% chance that no rain will fall onto the field.

Even if it does rain, the amount of rainfall is also only a prediction.

It could rain more or less than two millimetres on the Sunday.

And then with question three, part A, 35% of 20 is 7, so that means we'd expect around seven days of rain out of those 20, might be fewer, might be more.

B, we had to complete a table based on the information presented in the graph for the first five days.

We can see that there are three days with rain out those first five days, which means the percentage of days with rain was 60%.

And for part C, we can see that four out of the first 10 days had rain, and four tenths is equivalent to 40%.

40% of the first 10 days had rain.

And then for part D, the graph shows greater than the 35% of the days had rain, and this is because 9 out 20 days, which is 45%, had rain, not the seven days that was predicted.

You're doing great so far.

Let's now move on to the next part of this lesson where we're going to use historical data to predict the weather.

It is possible to use patterns or trends from historical data in order to predict future weather forecasts.

Historical data can be plotted on a time-series graph, and trends from the graph can then be extrapolated to predict what the graph will look like in future years.

For example, here we have a time-series graph.

The graph shows the mean night-time temperature in November each year from 2009 to 2022 in Oakfield.

We can see that there is a bit of variety in the temperatures when comparing one year to the next.

It goes up, and it goes down.

This can make spotting long-term trends quite tricky.

It is important not to focus on patterns between only two or three data points.

If you are trying to get a sense of whether the temperatures are generally going up, or generally going down, it's hard to see that by comparing one point with the next one, 'cause sometimes it goes up, sometimes it goes down.

It goes up and down from one year to the next.

But if you wanna see generally what it does over time, then a trend line of the data can be used to identify that the temperatures are increasing over a longer period of time even if the temperatures may fluctuate from one year to the next.

When predicting future weather forecasts, we can extrapolate predictions using the trends seen in the historical times-series graph.

A basic way of predicting future temperatures is by extending the trend line.

A bit like what you can see here.

We can look at a particular year that is beyond the data that we have, for example, 2023, and use that to predict what the temperature will be.

Using this method, we've extrapolated the mean night-time temperature in November 2023 will be nine degrees Celsius.

However, extrapolation is unreliable when trying to make accurate predictions.

We can see from the historical data that the temperatures fluctuate each year, so it's uncertain whether the trend in the future will continue in the same trend line, or it might begin to change like this.

So rather than using a trend line, a broader range of the trend can be used instead.

And that might look something a bit more like this.

It could be extrapolated, and then we could use it to make predictions.

For example, 2023, one prediction is just above eight degrees Celsius, maybe a little bit below 9.

5 degrees Celsius, and another prediction using the top trend line would be just below 10 degrees Celsius.

So what does it mean? Well, that gives us a range for our prediction.

This range can then be used as a prediction of likely temperatures.

We can say, using this method, we extrapolated for the mean night-time temperature in November 2023 will be likely be between 8.

3 and 9.

6 degrees Celsius.

This predicted range of temperatures may then be modified and improved using other data, such as measurements of current weather conditions in Oakfield or elsewhere.

This current data is then analysed to see what influence it might have on the results extrapolated from the historical data.

Like so.

Let's check what we've learned.

Here we have a graph that shows data from the Met office on the mean daily maximum temperatures in April each year from 1957 to 2022 in Heathrow.

Which of these statements is correct about this data? Pause while you choose, and press Play for an answer.

Well, we have two statements here that are correct.

B, that is the trend of the temperatures over time shows an increase.

We can see that with a trend line just gradually increasing, or we can even say it's got a positive gradient.

And that's what it says for statement D.

The trend line is extended to extrapolate and predict temperatures in the future.

Write down an estimate for the predicted mean daily maximum temperature in April 2023.

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

The answer is 15.

8 degrees Celsius.

So which of these statements is correct about the extrapolated trend line? Pause while choose, and press Play for an answer.

The answer is B.

It is difficult to predict whether the trend of the data will continue in the same way as previously observed.

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

This task has just one question, but it's split into parts A to G.

Here are parts A and B.

Pause while you do this, and press Play for more of the question.

Here are parts C to F.

Pause while you do this, and press Play for the final part.

And here is part G.

Pause while you do this, and press Play when you're ready for some answers.

Okay, let's go through some answers.

In question one, part A, you have to write a sentence explaining what the trend line is suggesting about the total amount of monthly rainfall each March.

Well, the trend line is suggesting that the amount of rainfall each March is increasing over long periods of time.

This does not mean that the amount of rainfall each March will always be greater than the previous year, though, just generally over time, it may increase and decrease from one March the next, but generally, over time, it'll increase.

In part B, Izzy says, "The amount of rainfall in March 2022 is lower than in March 2021.

This means the amount of rainfall in March 2023 will be even lower." Explain why Izzy's assumption may not be correct.

Well, the trend line is suggesting the opposite thing.

It is important to look at longer-term trends rather than the fluctuations between only two consecutive years.

Remember, it goes up and down from one year to the next.

We wanna look at the trend over a long period of time.

For part C, you have to extend the trend line beyond 2022.

It might look something a bit like what you can see on the screen here.

And then part D, you have to use it to make a prediction for the total amount of rainfall in March 2024.

If you do that, and with this trend line the way it's been extended here, we can see approximately 120 millimetres of rainfall.

And part E, you had to explain why your prediction in part D may not be accurate.

Well, there is a lot of variation in March rainfall from one year to the next.

Future rainfall may not follow the same long-term trend as previous years.

And part F, suggests a suitable range of likely predictions by considering a broader trend in the data.

So that means you could draw two trend lines, one towards the top of the data and one towards the bottom of the data, and make some readings based on those.

You should get approximately between 75 millimetres and 165 millimetres.

Then for part G, you've got a weather report, and you had to imagine if this was the weather forecast for March 2024 in Stornoway, based on weather conditions at the end of February 2024, explain how this might affect your prediction for part C.

Well, the weather report suggests that March 2024 will be a sunny month with little significant rainfall.

This may mean that there is less rainfall than what the trend line suggests from the previous Marches, and this means that the prediction of 120 millimetres might be too high.

As we commented on earlier, the amount of rainfall from one year to the next increases and decreases.

When we look at the graph, some of the points are below the trend line, and some are above the trend line.

So maybe, based on this weather report, this year is a year that would be below the trend line if we plotted it.

So is it helpful to consider the current weather data, such as weather conditions from the previous month, to modify and improve predictions based on historical data.

Fantastic work today.

Now let's summarise what we've learned.

There are different types of rainfall based on the different types of rain clouds.

Each type of rainfall may produce different quantities of rain.

If the chance of rainfall is less than 100%, then there is a chance that the rain will not fall at a certain location even if rainfall is predicted.

And that does not mean that the model used to predict the rainfall is wrong.

Remember it's based on probabilities.

Predictions about the weather can be based on longer-term trends in historical data.

Predictions using historical data may not be accurate as there is no guarantee future data will follow the trends of the past.

This is especially true if historical data fluctuates significantly from one year to the next.

Well done today.

Have a great day.