Climate Math

How do we know Earth is getting warmer?

Scientists are confident that the Earth is getting hotter. But how do they know this?

Image - Text Version

Shown are various kinds of thermometers. At the top is a digital thermometer that reads 14°C. In the middle is a mercury and glass thermometer. The red liquid in this thermometer is almost reaching the top of the glass, indicating a warm temperature. At the bottom is a dial showing a temperature of 60°F.

 

For one, scientists get temperature data from thousands of weather stations around the world. Some of these stations record the temperature every couple of minutes. Think about how many numbers that is!

In Canada, observations of temperature are stored in the National Climate Data and Information Archive. These observations come from organizations, such as Aviation Weather Services and the Department of National Defense. The map below shows locations where data has been collected in the past and where it is collected today. There are 508 locations with an active station and records from before 1990 (blue dots). There are 53 locations with an active station and records starting from 1990 (green dots). There are 219 locations with closed stations but with more than 30 years of data (red dots).

Imagine if scientists put all that temperature data into a massive list. Do you think that they would be able to easily understand how the climate is changing? Probably not! Scientists need to organize the data so that they can look for patternspatterns and trendstrends.

Seasonal Variation

One way to help us see trends is by creating graphsgraphs. However, even when we graph temperature data, it can still be hard to see long-term trends. This is because in many locations temperature varies a lot over the year.

For example, look at the line graph below for Toronto, Ontario. What are the lines showing?

The top red line is the average maximum temperature for each month. The bottom blue line is the average minimum temperature for each month.

Graphing monthly average temperatures helps us to understand seasonal changes. It can also help predict seasonal patterns from year to year.

But what if we wanted to know what the maximum and minimum temperatures were for more than one year? We would need more data!

Image - Text Version

Shown is an illustration of the same tree through the four seasons. The illustration for each season appears as a card resembling a Polaroid photo. The tree in winter does not have any leaves. It's base is surrounded by snow. The tree in spring has buds just beginning to form on the branches and the snow around the base is almost completely gone. The tree in summer is covered in green leaves and the base is surrounded by green grass. The tree in autumn has orange leaves which are beginning to fall off. Surrounding the tree is brown grass and fallen leaves.

 

Here is another graph. It shows average temperatures in Toronto for every year between 1840 and 2015. Look at the lines of this graph. What does each line represent?

The top red line is the average temperature for July. The bottom blue line is the average temperature for January. Now what patterns or trends do you see?

It is pretty hard to see patterns and trends with a graph like this. Luckily, scientists have thought of a way to look at the data differently.

Temperature Anomaly

Scientists looking at climate data often calculate temperature anomalies. A temperature anomaly is the difference between a temperature and an average temperature. The average temperature is often called the baseline temperature.

The baseline temperature is usually the average of 30 or more years of temperature data. For example, we often use 1961-1990 as the baseline period in Canada.

Image - Text Version

Shown is an illustration beside the definition of a temperature anomaly. A vertical doubled-headed arrow is between the phrases "Today's Temperature" and "Baseline Temperature".

 

A temperature anomaly can tell us how this December is different from past Decembers. It can also show us how the temperature at a place has changed over time. It is pretty easy to calculate a temperature anomaly. All you need is simple subtraction. Let’s give it a try.

Example 1: Winnipeg

Take a look at this temperature data from Winnipeg. Let’s calculate the temperature anomaly for July 2021.

Average Temperature - Baseline Temperature = Temperature Anomaly

22.7 °C - 19.8°C = 2.9°C

This means that the temperature anomaly for July 2021 in Winnipeg is 2.9°C. July 2021 was 2.9°C warmer than an average July.

Now you give it a try:

Both of those temperature anomalies were positive. Positive temperature anomalies mean that an observed temperature was warmer than average. Negative temperature anomalies mean that an observed temperature is colder than average.

Visualizing Temperature Anomalies

Just like we can graph actual temperatures and average temperatures, we can also graph temperature anomalies.

The scatterplotscatterplot below shows yearly temperature anomalies in Ontario from 1900 to 2018. The temperature anomaly for each year is represented by a green dot.

Visualizing temperature anomalies is much more helpful than looking at absolute temperatures. It is much easier to see trends when we look at temperature anomalies. Can you see a trend here? Probably not.

To look for a trend, you can draw a trend line. A trend line, also known as a line of best fit, shows the relationship between two variablesvariables. In this case, the relationship between temperature and year. A line of best fit is a straight line drawn on a scatter plot that best represents the trend of the data. The line of best fit is as close as possible to all of the points on a scatter plot. This usually means that approximately half of the points are above the line and half are below the line. If the line slopes up to the right, the slopeslope is positive. If the line slopes down the right, the slope is negative.

Finding a line of best fit by eye alone can be tricky. This is why a statistical tool called regression analysis is used to calculate an accurate line of best fit.

The red line is the line of best fit for the data in the scatterplot. How close was your line?

We can take a similar look at global temperature anomalies. The graph below shows the change in global surface temperatures relative to 1951 -1980 average temperatures. Instead of a straight line of best fit, it takes all of the points and creates a curved line of best fit.

It is clear that temperature anomalies continue to increase. This means that temperatures are becoming warmer than past average temperatures. Even small increases in global temperatures can have a big impact on our planet. 

Did you know?

Nineteen of the warmest years since 1880 have happened since 2000.

Temperature anomalies address other issues that scientists run into when analyzing temperature data. For example, weather stations are sometimes moved or data is missing from the record. These changes can impact average temperature data. However, temperature anomalies are much less affected by these types of problems.

Other ways of visualizing data provide new ways of thinking about temperature trends. For example, maps can help us look at temperature trends in many locations at once.

The map below shows how local temperatures in 2020 have increased relative to 1951-1980 average temperatures. 

Other creative visualizations allow us to understand climate change in a whole different way. For example, Ed Hawkins’ Warming Stripes shows temperature anomalies from 1850-2020. Visit the website to see Warming Stripes for Canadian provinces and territories.

Similar to the map above, the darker the shade of blue, the larger the negative temperature anomaly. The darker the shade of red, the larger the positive temperature anomaly.

Image - Text Version

Shown is a visual representation of temperature anomalies from 1850-2020 called Warming Stripes. The image is made up of vertical stripes of blue and red. Each stripe indicates the temperature anomaly for one year. Blue stripes indicate negative temperature anomalies. Red stripes indicate positive temperature anomalies. Darker shades indicate an anomaly that is further away from zero. The earlier stripes on the left side of the image are primarily dark blue. As you move further right, the stripes become lighter blues and then lighter reds. The most recent stripes are primarily dark reds, indicating increasing temperatures.

 

Similarly, the Prairie Climate Centre created a warming stripes image for Canada.

Temperature trends and other indicators show us that the climate is warming. This warming is already having large impacts on the world as we know it. We humans will need to make choices that keep temperatures from continuing to go up. You can make a big difference by taking action now. Sharing thought-provoking data visualizations is one way that we can address climate change. We need people like you who can use data to explain how we know the climate is changing. Understanding these trends helps us tackle this problem together.