Numerical Weather Prediction models, or computer models for short, form the backbone of modern weather forecasting. They assimilate a diverse mix of observations collected all around the globe by satellites, weather stations, aircraft, radars, and other instruments, form a coherent analysis of the atmosphere, and integrate forward to produce a forecast.
How the hell do they do it? We'll focus here on two aspects of computer modeling, discretization
Today's computer models begin with a set of partial differential equations, known as the primitive equations
, that describe fluid motion and are based on conservation of mass, conservation of momentum, conservation of energy and the ideal gas law. The primitive equations can be used to describe the flow and behavior of fluids in a variety of contexts, including ocean circulations.
Unfortunately, computers can't solve these types of equations directly. The primitive equations must be converted into algebraic equations to be solved on a computer. There are a variety of steps and techniques for doing this, which is known as discretization.
Discretization requires approximations and compromises. One aspect of the discretization process that most weather hobbyists are aware of is resolution. For grid cell models, this is commonly expressed as a distance. For example, the NAM has a horizontal grid spacing of about 12-km. Often, these grid cells are conceptualized as rectangles, but other shapes can be used. For example, the Model for Prediction Across Scales (MPAS), being developed by the National Center for Atmospheric Research uses hexagons, with the occasional pentagon or septagon, to cover the sphere.
Not all models are based on this grid cell concept. For example, the GFS is a spectral model which, instead of using grid cells, represents the atmosphere as a combination of waves with differing wavelengths.
The National Weather Service is currently developing a new modeling system that will replace the GFS, known as the FV3. It is based on a third approach, known as finite volume (the "FV" in FV3). More info at https://www.gfdl.noaa.gov/fv3/
The primitive equations describe fluid motion, but a computer model also needs what meteorologists call "physics" — for example, radiation, clouds, precipitation, and interactions with the land surface. This is really where the rubber hits the road, as in general we can't simulate these things directly. For example, we can't simulate the evolution of every cloud drop in a cloud. There's simply too many of them. As a result, we need to take shortcuts and make simplifications, known as parameterizations.
In the case of the cloud, since we can't simulate every cloud drop, we might instead simulate how much total cloud water is in each grid box, and then specify how that water is spread across small, medium, and large droplets. Similar shortcuts are made in how we deal with other physical processes.
In some cases, we have a good understanding of the physical processes and the parameterizations, while a shortcut, are quite accurate. In others, understanding is weaker (in some cases much weaker), and we are using educated guesses and tuning to get something that looks reasonable.
All Models Are Wrong, But Some Are Useful
That famous George Box quote is a good one to keep in mind when using numerical weather prediction models. Really, modern day numerical weather prediction is a remarkable scientific achievement, and the forecasts are getting better every day. There's every reason to expect them to improve in the future, as knowledge and techniques advance, provided we continue to invest in our global and regional observing systems. A perfect model will give you a lousy forecast if it doesn't start with a good analysis of the atmosphere, as well as land, sea, ice, and lake conditions. But that's a subject for another post.