Climate change, and its effects on our weather, is important, controversial and is possibly going to affect all of our lives over the next fifty years. The understanding and analysis of climate change is an area where mathematicians, scientists, policy makers (such as members of parliament) and anyone involved in health, insurance or agriculture, meet to try to interpret the current evidence and to make predictions for the future. It is truly an area where mathematics is making a very big difference to the way that people think about the future.
But why should we bother? Predictions made by the IPCC (Intergovernmental Panel for Climate Change) that we might have a three-degree (Celsius) rise in mean temperature over the next 50 years or so don't on the face of it seem very scary. However, we are seeing a lot of extreme weather events at the moment, such as the extensive flooding just before Christmas. These cost billions of pounds and can lead to great hardship and even loss of life for those affected. If these extreme events are just what you would expect from random weather variations, then we can just about live with them. If instead they are part of a series of events due to climate change, then we need to be worried indeed. It is the job of the mathematician to help to sort this out.
Evidence for climate change
There are at least five indicators that make us think that climate change is occurring. The first of these is the rise in the Earth's temperature. The chart below shows the measured temperature (relative to a reference temperature) over the last 150 years. You can see that the average temperature is showing a steady rise over this time, with 2015 looking like being the warmest year on record. On top of this rise is what appears to be a random variation. This variation causes a lot of discussion in the climate science debate.The second indicator is the loss of the Arctic sea ice. It is an undisputable fact that the amount of this ice has been decreasing dramatically in recent years, with an annual loss in area of about the size of Scotland. The chart below shows the measured values. If you fit a straight line to this data using the statistical methods taught in A level maths, then the prediction is that all of the Arctic ice will have vanished by the end of this century. (Interestingly the amount of Antarctic sea ice is currently increasing slowly, again leading to many discussions. However the evidence is that the Antarctic land ice is also decreasing.)The three other main indicators are: the increase in mean sea level over the last 100 years, the increase in the number of extreme rainfall events, and the year-on-year rise in the level of carbon dioxide in the atmosphere, with measured values now above 400 parts per million (twice the level before the industrial revolution).
The climate change debate
Most scientists (and this includes mathematicians) believe that climate change is occurring, but this is certainly not a universally held opinion. One reason for this is that predicting the climate is genuinely hard. As the great scientist Niels Bohr famously remarked, "It is difficult to make predictions, especially about the future." There are a number of (mathematical) reasons why this is the case for climate.
Firstly, as we have seen from the temperature measurements, there is a lot of statistical variation and uncertainty in the data that is being measured, so long-term trends can be hard to determine. Secondly, the equations for the climate are nonlinear. This means that they can have solutions which are chaotic, showing a lot of variability and therefore being hard to predict. We can see this in the weather, which is basically impossible to predict with any accuracy much more than a week into the future. It is often argued that if we can't predict the weather, we can't hope to be able to predict the climate for 100 years ahead. But this argument is not really valid: climate is much more about finding general trends rather than day-to-day variations and therefore easier to forecast (climate is what you expect and weather is what you get).Mathematicians can help a great deal to clarify the issues in this debate, using and extending the mathematics taught at A level. Firstly, they can look at past variations in climate (such as the sequence of ice ages in the last million years) and find mathematical models which explain these. Then they can use these (and other) models, combined with a lot of statistics and probability theory, to make sense of the data that we are currently measuring about the weather and climate, so that we can distinguish between cause and effect. Finally, they can combine all of this knowledge to produce models which can predict what the climate might do in the next 100 years or so. These results are used to inform policy makers such as the IPCC. It is very important to say that these models, and the data which informs them, are far from perfect. A vital part of all of this analysis is identifying and then quantifying the level of uncertainty in all of these predictions. In short, never trust any prediction unless you can estimate how uncertain it is!
Mathematicians around the world are heavily involved with constructing, studying and solving, models for the future climate. Many of these work in climate centres, such as the Met Office's Hadley Centre in Exeter, UK. The basis of all of these models are mathematical equations.
To simulate the climate, one starts with these equations and then adds more for a variety of other effects, such as the movement of ice, ocean currents, the carbon cycle, vegetation changes, etc. The sets of equations are too hard to solve by hand, so instead we find approximate solutions on a (super-)computer. To do this, the computer has to solve billions of different problems, as well as incorporating as much data about the system as possible, such as measurements of the air and ocean temperatures and velocities.
In the chart below, we show the predictions of the future mean temperature from various climate centres around the world. Note that these predictions are not all the same. This is because the models make different assumptions about the level of carbon dioxide and other factors. However, they are all predicting a significant temperature rise by the end of the 21st Century.What can a mathematician do next?
There are many ways in which a mathematician can help in the climate debate, from making and analysing climate models, and better understanding of data, to a more informed presentation to policy makers of the nature of the issues involved. But the moral of this article is that you should always use your mathematical judgment to test whatever is said, in the media and otherwise, about weather and climate.
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What are the main ideas of the passage
1. Climate change is important, controversial, and will likely affect everyone's lives in the next fifty years.
2. Mathematics plays a significant role in understanding and analyzing climate change.
3. The evidence for climate change includes rising temperatures, decreasing Arctic sea ice, rising sea levels, increased extreme rainfall events, and rising levels of carbon dioxide in the atmosphere.
4. The climate change debate includes skeptics and challenges in predicting long-term climate trends due to statistical variation, nonlinear equations, and chaotic solutions.
5. Mathematicians contribute to the debate by studying past climate variations, developing mathematical models, analyzing data, and making predictions for future climate trends.
6. Climate models, based on mathematical equations, are used to simulate climate on supercomputers and provide predictions for future mean temperatures. There may be variations in predictions based on different assumptions and factors.
7. Mathematicians can further contribute by analyzing climate models, improving data understanding, and presenting informed information to policymakers.
8. It is important to critically evaluate and use mathematical judgment when interpreting information about weather and climate in the media.