Numerical climate models, also called climate system models, are tools that use math to show how important parts of Earth's climate work together. These parts include the atmosphere, oceans, land, and ice. Scientists use these models to study how the climate changes over time and to predict future climate conditions. Some climate models are not based on numbers but instead describe possible future situations in words.
These models consider energy coming from the Sun and energy leaving Earth. When more energy comes in than goes out, Earth's temperature changes. Energy from the Sun is mostly visible light and short-wave infrared. Energy leaving Earth is long-wave infrared. These processes are part of the greenhouse effect.
Climate models can be simple or very complex. A basic model might treat Earth as a single point and average energy leaving the planet. More detailed models divide Earth into layers and sections. The most complex models include the atmosphere, oceans, and sea ice and use full equations to describe how mass, energy, and radiation move. Other models can connect different systems, like including how land is used and how that use changes over time. This helps scientists study how climate and ecosystems affect each other.
Climate models use math equations based on physics, how fluids move, and chemistry. Scientists divide Earth into a 3D grid and apply these equations to each part. Models for the atmosphere calculate wind, heat, radiation, humidity, and water movement in each grid section and how these parts interact. These models are linked with ocean models to study climate changes caused by ocean currents and the ocean's ability to store heat. Scientists can also add models for ice sheets to better understand long-term effects, like rising sea levels.
Uses
Climate models help scientists study extreme weather events, such as heatwaves or heavy storms. This process, called extreme event attribution, shows how human-caused climate change affects how often these events happen, how strong they are, and their effects. Scientists use this method to find out if these events are caused by human activities that increase global warming or if they are just part of natural weather patterns.
Climate models are created and used in three main types of organizations:
– National weather services: These usually have a section that studies climate patterns.
– Universities: Departments like atmospheric sciences, meteorology, climatology, and geography work on climate models.
– Research labs: Examples include the National Center for Atmospheric Research (NCAR) in the United States, the Geophysical Fluid Dynamics Laboratory (GFDL) in the United States, Los Alamos National Laboratory, the Hadley Centre in the United Kingdom, the Max Planck Institute for Meteorology in Germany, and the Laboratoire des Sciences du Climat et de l'Environnement (LSCE) in France.
Large climate models are important tools, but they are not perfect. Scientists must also study real-world observations, such as data from satellites, to understand what is happening. These models help combine all observations into detailed analyses, which can then be used to make predictions. Smaller models are sometimes used, but they often leave out important parts, like the water cycle, and are not as reliable for accurate predictions.
General circulation models (GCMs)
A general circulation model (GCM) is a type of climate model. It uses mathematical equations to describe how air and water move in the atmosphere or ocean of a planet. These equations include the Navier–Stokes equations, which are used on a rotating sphere and include terms for heat-related factors like radiation and latent heat. These equations form the basis for computer programs that simulate Earth’s atmosphere or oceans. Atmospheric and oceanic GCMs (AGCM and OGCM) are important parts of climate models, along with components that represent sea ice and land surfaces.
GCMs and global climate models are used for weather forecasting, studying climate patterns, and predicting future climate changes.
Atmospheric GCMs (AGCMs) focus on modeling the atmosphere and use sea surface temperatures as fixed conditions. Coupled atmosphere-ocean GCMs (AOGCMs), such as HadCM3, EdGCM, GFDL CM2.X, and ARPEGE-Climat, combine models of the atmosphere and ocean. The first GCM that included both ocean and atmospheric processes was developed in the late 1960s at the NOAA Geophysical Fluid Dynamics Laboratory. AOGCMs are the most complex type of climate model and include as many natural processes as possible. However, these models are still being improved, and some uncertainty remains. They can also be linked to models of other processes, like the carbon cycle, to better understand how different systems interact. These combined models are sometimes called "earth system models" or "global climate models."
Versions of these models designed for studying climate changes over decades to centuries were created by Syukuro Manabe and Kirk Bryan at the Geophysical Fluid Dynamics Laboratory (GFDL) in Princeton, New Jersey. These models use combinations of equations related to fluid movement, chemistry, and sometimes biology.
Energy balance models (EBMs)
Before the 1960s, it was not possible to simulate the climate system in full 3-D space and time because large computers were not available. To begin understanding factors that may have changed Earth's past climate conditions, scientists needed to simplify the system's complexity. A simple model that balanced incoming and outgoing energy was first created for the atmosphere in the late 1800s. Other Energy Balance Models (EBMs) also aim to describe surface temperatures by applying the rule that energy must be conserved to individual columns of the Earth-atmosphere system.
Key features of EBMs include their simplicity and ability to sometimes provide clear solutions. Some models account for effects of oceans, land, or ice on the surface energy balance. Others include interactions with parts of the water cycle or carbon cycle. Many of these simplified models are helpful for specific tasks that support more detailed models called General Circulation Models (GCMs), especially when linking simulations to understanding.
Zero-dimensional models treat Earth as a single point in space, similar to the image of Earth taken by Voyager 1 or how astronomers view distant objects. This simplified view, though limited, is still useful because physics rules apply broadly to unknown objects or in a grouped way if major properties are known. For example, astronomers know that most planets in our solar system have a solid or liquid surface covered by a gaseous atmosphere.
A very simple model of Earth's radiative balance is:
– The left side shows the total incoming shortwave energy from the Sun (in Watts).
– The right side shows the total outgoing longwave energy from Earth, calculated using the Stefan–Boltzmann law.
Constant values include:
– S: the solar constant, which is the incoming solar radiation per unit area (about 1367 W·m²).
– r: Earth's radius (about 6.371 million meters).
– π: a mathematical constant (3.141…).
– σ: the Stefan–Boltzmann constant (about 5.67×10⁻⁸ J·K⁻⁴·m⁻²·s⁻¹).
The term πr² can be removed, leaving a zero-dimensional equation for equilibrium:
– The left side shows the incoming shortwave energy flux from the Sun (in W·m²).
– The right side shows the outgoing longwave energy flux from Earth (in W·m²).
Variables specific to Earth include:
– a: Earth's average albedo (about 0.3).
– T: Earth's average surface temperature (about 288 K as of 2020).
– ϵ: Earth's effective emissivity (about 0.61), which represents how well Earth emits energy compared to a perfect emitter.
This model helps explain how Earth's temperature changes with variations in the solar constant, albedo, or emissivity. The emissivity also reflects the strength of the greenhouse effect, as it compares the energy escaping to space with the energy emitted from Earth's surface.
Calculated emissivity can be compared to real data. Earth's surface emissivity is usually between 0.96 and 0.99 (except for some deserts, which may be as low as 0.7). Clouds, which cover about half Earth's surface, have an average emissivity of about 0.5. When all factors are considered, Earth's effective emissivity is about 0.64 (with an average temperature of 285 K).
Models without dimensions have also been built with distinct atmospheric layers. The simplest is the zero-dimensional, one-layer model, which can be expanded to include more layers. Each layer has a temperature and emissivity, but no thickness. Using radiative equilibrium at the boundaries between layers creates equations that can be solved.
These multi-layered EBMs are examples of models with separate sections. They can estimate average temperatures closer to those observed on Earth's surface and in the troposphere. They also help explain the heat transfer processes that cause the greenhouse effect. A version of the one-layer model was first used by Svante Arrhenius in 1896 to study this phenomenon.
Water vapor strongly affects Earth's atmospheric emissivity. It influences radiation flows and is affected by heat movement through air and vapor in a way that depends on elevation (like humidity levels). This was studied by improving the zero-dimensional model into a one-dimensional radiative-convective model, which considers two processes:
– Upward and downward movement of radiation through atmospheric layers that absorb and emit infrared light.
– Heat movement through air and vapor convection, which is especially important near Earth's surface.
Radiative-convective models use a detailed representation of the atmosphere based on elevation. This is better than simplified models and helps create more complex models. These models can estimate both surface temperatures and temperature changes with elevation more accurately. They also simulate how adding small amounts of non-condensing greenhouse gases, like carbon dioxide, affects atmospheric temperatures.
Other factors are sometimes added to simulate effects in different areas and explain how energy moves across Earth. For example, the impact of ice-albedo feedback on global climate sensitivity has been studied using a one-dimensional radiative-convective model.
The zero-dimensional model can be expanded to include horizontal energy movement in the atmosphere. This model might average conditions across zones. It allows local albedo and emissivity to depend on temperature, such as icy poles and warm equators, but horizontal energy movement must be specified directly.
Early examples include work by Mikhail Budyko and William D.
Earth systems models of intermediate complexity (EMICs)
There are different types of models used to study climate, depending on the questions being asked and the time periods involved. On one end, there are simple models that focus on general patterns and ideas. On the other end, there are complex models that use the most detailed data available for both space and time. Models with medium complexity fall between these two extremes. An example is the Climber-3 model. Its atmosphere is a 2.5-dimensional model that uses statistics and dynamics, with a grid size of 7.5° × 22.5° and a time step of half a day. Its ocean is based on the Modular Ocean Model (MOM-3), which uses a grid size of 3.75° × 3.75° and has 24 layers vertically.
Box models
Box models are simplified versions of complex systems, showing them as boxes connected by flows. Each box holds a reservoir, which is a collection of matter and energy that is evenly mixed. The concentration of any substance inside a box is the same throughout the box at any time. However, the amount of a substance in a box can change over time because of incoming or outgoing flows, or because the substance is created, used up, or changed inside the box.
Simple box models, which have a small number of boxes and do not change in size over time, are often helpful for creating formulas that describe how substances behave in a system. These formulas, called governing equations, are based on rules like the conservation of energy and the conservation of mass. More complex models, which involve many substances and equations, are studied using numerical methods to understand how the system works.
Box models are widely used to study environmental systems and ecosystems. In 1961, Henry Stommel created the first simple 2-box model to examine the stability of large-scale ocean currents. Another model has been used to study how ocean currents interact with the carbon cycle.
Networked data models
The study of complex networks has become an important area of science that helps scientists better understand complex systems. Using network theory in climate science is a new and growing field. To find and study patterns in the global climate, scientists create models that represent climate data as complex networks.
In most real-world networks, the points (called nodes) and connections (called edges) are clearly defined. However, in climate networks, nodes are points in a grid that covers the Earth's climate data. This grid can be shown at different levels of detail. An edge connects two nodes if the data from those points is statistically similar, which may indicate a relationship. This method helps scientists learn more about how the climate system changes over time and across different areas of the world.
History
In 1956, Norman Phillips created a mathematical model that showed monthly and seasonal changes in the troposphere. This was the first successful climate model. Soon after, several groups started working to build general circulation models. The first general circulation climate model combined ocean and air processes. It was developed in the late 1960s at the Geophysical Fluid Dynamics Laboratory, which is part of the U.S. National Oceanic and Atmospheric Administration.
By 1975, Manabe and Wetherald had created a three-dimensional global climate model that gave a rough but accurate picture of Earth’s current climate. When the model’s atmosphere had twice as much CO₂ as usual, the global temperature rose by about 2 °C. Other computer models also showed similar results: it was not possible to create a model that matched real climate patterns without showing higher temperatures when CO₂ levels increased.
By the early 1980s, the U.S. National Center for Atmospheric Research developed the Community Atmosphere Model (CAM). This model can be used alone or as part of the Community Climate System Model. The latest version of the standalone CAM (version 3.1) was released on February 1, 2006. In 1986, scientists began modeling soil and plant types, which improved the accuracy of forecasts. Coupled ocean-atmosphere climate models, like the Hadley Centre’s HadCM3 model, are now used in climate change studies. Reviews of past climate models show they were generally accurate, but they often predicted less warming than actually occurred.
The Coupled Model Intercomparison Project (CMIP) has helped improve global climate models and climate change understanding since 1995.
In 2010, the IPCC said it has more confidence in predictions made by climate models.
Coordination of research
The World Climate Research Programme (WCRP), which is managed by the World Meteorological Organization (WMO), helps organize climate modeling research around the world.
A 2012 report by the U.S. National Research Council explained how the large and varied U.S. climate modeling efforts could become more unified. The report suggested that saving time and resources could be achieved by creating a shared computer system for all U.S. climate researchers and by holding a yearly meeting for climate modelers.
Issues
Cloud-resolving climate models are now run on powerful supercomputers that use a lot of energy and produce carbon dioxide emissions. These models need exascale computing, which means performing a quintillion calculations each second. For example, the Frontier supercomputer uses 29 megawatts of power and can simulate one year of climate data at cloud-resolving scales in just one day.
Ways to save energy include reducing the precision of calculations, using machine learning to skip unnecessary steps, and creating new, efficient numerical methods that increase the amount of climate data simulated each day.
Parametrization in atmospheric models (such as weather or climate models) is a method used to simplify processes that are too small or complex to be directly included in the model. This is different from processes, like large-scale air movement, that are directly calculated in models. Parametrization involves using specific values, or parameters, to represent simplified processes. Examples include the speed at which raindrops fall, the formation of convective clouds, simplified calculations of how radiation moves through the atmosphere, and how clouds form. Radiative parametrization is important for both weather and ocean models. Emissions from sources like factories or vehicles within specific areas of a model also need to be simplified to study their effects on air quality.