Weather models are computer simulations of the atmosphere for weather research and forecasting

Weather forecasting is hard. To make accurate forecasts, meteorologists use weather data from the present, and from the past, to predict the future state of the atmosphere and its impact on weather patterns. But what weather data is needed to make an accurate forecast? Meteorologists collect weather observations on temperature, air pressure, humidity, precipitation, wind speed, and more, from weather stations, weather satellites, and weather balloons all over the world. As these weather conditions continue to change over time, this results in a massive amount of data.

Turning this data into an accurate weather forecast requires modelling the interactions between thousands or even millions of variables that are in a constant state of flux—a computation that, in mathematics, is known as a “hydrodynamic differential equation.” These mathematical equations are so complex and involve so much data, they are generally run on supercomputers.

Weather forecasting based on these equations is called numerical weather prediction, and the computer programs that run them are called weather models.

Weather models are computer simulations of the atmosphere.

The Earth's atmosphere is a layer of air roughly sixty miles high, in which the air—a fluid—moves from one place to another as a result of complex chemical, thermodynamic and fluid dynamics. In theory, these flows of air can be calculated using laws of physics and mathematics—if one has enough data, computing power, and an equation that can accurately describe the interplay between the different elements.

These are the three integral parts of any weather forecasting model: weather data, computing power, and a mathematical equation that simulates the interactions of different weather conditions in the atmosphere.

For a computer program to output predictions about the future state of the atmosphere, first it needs the input of current weather data for the region that will be described by the model. Generally, weather models come in two types—local models, focused on a specific location, and global models, which aim to give accurate forecasts of weather across the planet.

Both types of models use a similar process; the difference is scale. Weather observations are made with weather stations, weather balloons, buoys, radar, weather satellites and more, and data is collected on precipitation and thunderstorms, wind speed and direction, air temperature and pressure, and so on. These initial data, taken from one snapshot of time, are called the “initial conditions” of the model. This initial data is updated periodically, in regular recurring time steps.

The data from these initial conditions are arrayed into a grid—a three-dimensional set of points that cover the region of the model and extend upward into the atmosphere. The grid points are not the points where weather observations were made; rather, they are a computer-generated set of locations, spatially equidistant and running in horizontal and vertical directions. At each grid point, the computer program executes a model run to generate a numerical forecast for that location, and the process is repeated for each grid point until calculations have been made for the entire grid.

From these initial conditions, the model can then make incremental time steps forward to begin predicting the flows of the atmosphere and the weather conditions that may result.

The number of grid points and the space between each grid point affect the accuracy of the forecast model: a model with a high number of grid points is called “high resolution” and has improved accuracy, but higher-resolution grids also require more computational power.^{1}

Even the simplest forecast models make use of complicated mathematical equations, and the more data a model uses, the more computing power it requires. The most sophisticated and accurate forecast models in the world—like the ECMWF or the High-Resolution Rapid Refresh (HRRR) used by NOAA—run on supercomputers that can perform 12 quadrillion calculations each second.^{2} But simpler weather models with fewer data points need less computing power, and don't need to be run on supercomputers.^{3}

Weather is what is known as a chaotic system: because it involves so many interrelated variables, small variances in initial conditions—say, the difference between a wind speed measured at 4mph versus 4.2mph—can multiply quickly and have large effects on the rest of the system, making its behaviors challenging to predict over time.

Because of the number of variables and unknowns involved in a weather system, meteorologists often rely on what is called an "ensemble forecast." In ensemble forecasts, multiple model runs are performed, each with different parameters, to account for uncertainties. The complete set of these forecasts—the ensemble—can be used to model the range of possible future states of the atmosphere and provide a probabilistic forecast of future weather.^{4}

No model can forecast every weather event with high accuracy. Instead, meteorologists make choices about what they want to predict and design the model to have high accuracy for that kind of result. One kind of accuracy may come at the expense of other kinds. For example, models are designed to have high accuracy for either short-range forecasts (up to 3 days ahead), medium-range forecasts (3-15 days ahead), or long-range forecasts (10 days to 2 years ahead), and each type requires different choices. A meteorologist seeking a short-term forecast might choose to use a mesoscale model, which incorporates weather data collected from points as high as 1000km up in the atmosphere, because this mesoscale data produces more accurate short-term forecasts. For a more reliable long-range forecast, a meteorologist might prefer a non-mesoscale model—one that excludes weather observations from the high-altitude atmosphere.

Meteorologists are always looking to improve on existing weather models and might create new computer models for weather research and forecasting. Because the mathematical equations of the model are meant to be simulations of the atmosphere, meteorologists test and adjust algorithms to see which ones result the most accurate weather forecasting. Some of these formulas are open source and others are proprietary.

The GFS updates four times per day and forecasts out to sixteen days. The ECMWF updates only twice a day and generates a 10-day forecast, but is higher resolution than the GFS and has, historically, generated more accurate forecasts.

Another well-known forecast model is the North American Mesoscale Model (NAM), a short-range regional model that covers all of North America and generates forecasts 61 hours out. NAM is built upon the Weather Research and Forecasting (WRF) model, an open-source forecast model that also powers two widely used models run by the National Oceanic and Atmospheric Administration (NOAA): the Rapid Refresh (RR or RAP) model and the High Resolution Rapid Refresh (HRRR).

There are other weather models: the Canadian Meteorological Centre (CMC) model, UK Met Office model, German Weather Service (DWD) model, Australian Bureau of Meteorology (BoM) model, and many more. Each different model is designed to make accurate forecasts that focus on different things, incorporate different data, and calculate with different mathematical equations to produce the best desired kind of accuracy. Each has its own strengths and its own limitations.

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* ^{1 }Weather Models*, National Oceanic and Atmospheric Administration, May 18, 2023. (link resides ouside ibm.com)