Climate models

If the atmosphere is chaotic, how can we trust climate models?

Before they can understand how our planet’s climate is changing, scientists must first understand the basic principles of this complex system – the gears that turn Earth’s climate. You can create simple models with simple interactions, and that’s what happened in the first part of the 20th century. But from the 1950s and 1960s, researchers began to integrate more and more complex components into their models, using the ever-increasing computing power.

But the more researchers looked at the climate (and the atmosphere, in particular), the more they understood that not everything is clean and orderly. Many things are predictable – if you know the state of the system today, you can calculate what it will be like tomorrow with perfect accuracy. But some components are seemingly chaotic.

chaos theory studies these well-defined systems and attempts to describe their inner workings and patterns. Chaos theory asserts that behind the apparent randomness of such systems there are interconnected mechanisms and self-organization that can be studied. The so-called chaotic systems are very sensitive to their initial conditions. In mathematics (and especially in dynamical systems), initial conditions are the “seed” values ​​that describe a system. Even very small variations in conditions today can have major consequences in the future.

That’s a lot to understand, but if you really want to study the planet’s climate, this is where you need to come in.

Butterfly Effect

Edward Lorenz and Ellen Fetter are two of the pioneers of chaos theory. These “chaos heroes” used a big, noisy computer called the LGP-30 to develop what we now call chaos theory.

Lorenz used the computer to run a weather simulation. After a while he wanted to run the results again, but he just wanted half of the results, so he started the calculations using the results from the previous run as the initial condition. The computer ran everything with six digits, but the printed results were rounded to 3 digits. After the calculations were completed, the result was completely different from the previous one.

This incident led to enormous changes in the fields of meteorology, social sciences and even pandemic strategies. A famous expression often used to describe this type of situation is the “butterfly effect”. You may know the idea: “A butterfly flapping its wings in Brazil can trigger a tornado in Texas”. This sums up the whole idea behind the small change in initial conditions, and how small changes in seemingly chaotic systems can lead to big changes.

Simulation of the Lorenz attractor of a chaotic system. Wikimedia Commons.

To get the idea, Lorenz then constructed a diagram that depicts this chaos. It’s called the Lorenz attractor, and basically it displays the trajectory of a particle described by a simple set of equations. The particle starts from a point and spirals around a critical point – a chaotic system is not cyclic, so it never returns to the point of origin. After a while, it goes beyond a certain distance and begins to spiral around another critical point, forming the shape of a butterfly.

Why is it chaotic?

If the atmosphere is chaotic, how can we predict it? First, let’s clarify two things. Predicting the weather is totally different from predicting the climate. Climate is a long period of atmospheric events, on the scale of decades, centuries, or even more. Time is what we experience in hours, days or weeks.

Weather forecasts are based on forecast models that focus on predicting conditions for a few days. To make a forecast for tomorrow, models need today’s observations as an initial condition. The observations are not perfect due to small deviations from reality, but have improved considerably due to the increase in computing power and satellites.

However, the fluctuations contribute to making things harder to predict because of the chaos. There is a limit to when the forecasts are accurate – usually no more than a few days. Anything longer makes predictions unreliable.

Fortunately, our knowledge of the atmosphere and advances in technology makes better predictions than 30 years ago. Unfortunately, there are still uncertainties due to the chaotic behavior of the atmosphere. This is illustrated in the image below, the efficiency of the model is compared between the ranges of the day. The 3-day forecast is always more accurate, compared to the 5-10 day forecast.

The evolution of weather predictability. Credits: Shapiro et al. (ADM).

This image also shows an interesting social issue. The northern hemisphere has always been better at predicting the weather than the south.

This happens because this region contains a greater number of wealthier countries that developed advanced science and technology earlier than countries in the South, and have more monitoring stations in operation. Therefore, they had far more resources to observe the weather than poorer countries. Without these observations, you have no initial conditions to use for comparison and modeling. That started to change in the late 1990s and early 2000s when space agencies launched weather satellites that observe more of the planet.

Predict the climate

Predicting the climate is a different challenge and in some ways is surprisingly easier than predicting the weather. A longer period means more statistical predictability added to the problem. Take a game of chance, for example. If you roll the dice once and try to guess what you will get, the odds are stacked against you. But roll a dice a million times and you have a pretty good idea of ​​what you’ll get. Similarly, when it comes to climate, a bunch of events are linked on average to long-term conditions and, taken together, can be easier to predict.

In terms of models, there are many different aspects of weather and climate models. Weather models can predict where and when an atmospheric event occurs. Climate models don’t focus on where exactly something will happen, but they care about how many events occur on average over a specific time period.

With respect to climate, the Lorenz attractor is the average of the conditions of the underlying system – the wings of the butterfly as a whole. Scientists use a set of smaller models to “fill the butterfly” with possibilities that represent on average a possible outcome, and determine how the system as a whole is likely to evolve. This is why the predictions and projections of climate models like those of the IPCC are extremely reliable, even when dealing with a complex and seemingly chaotic system.

Compare models

Today, climatologists have the computing power to average a bunch of models trying to predict the same climate pattern, further refining the results. They can also run simulations with the same model, changing the initial conditions slightly and averaging the results. This provides a good indicator of what might happen for each outcome. Even further than that, there is a comparative workforce between the scientific community to show that independent models from independent scientific groups agree on the effects of the climate crisis.

Organized in 1995, the Coupled Model Intercomparison Project (CMIP) is a way to analyze different models. This workforce ensures that scientists compare the same scenario but with different details in the calculations. With many results pointing to a similar result, the simulations are even more reliable.

Changes in global surface temperature over the past 170 years (black line) relative to 1850-1900 and annual mean, compared to CMIP6 climate model simulations of temperature response to human and natural factors (red) and only natural factors (solar and volcanic activity, green). Solid colored lines indicate the multi-model mean and colored shades indicate the (“very likely”) range of the simulations. Source: IPCC AR6 WGI>

Ultimately, predicting the climate is not like we are going to predict if it will rain on January 27, 2122. Climate predictions focus on the average conditions that a particular season of an oscillatory event will look like. Despite the chaotic nature of the atmosphere, thanks to the duration of the climate and its statistical predictability, long-term climate predictions can be made reliably.