Numerical weather prediction has gotten pretty darn good over the past few decades, but it wasn't always that way. But taking this class has made me realize how incredible numerical weather prediction really is. I mean, c'mon now... we take a whole bunch of numbers, put them through these crazy equations that I am only beginning to understand, and we magically get these pretty accurate forecasts of what's going to happen. It's like looking into the future. It's weird. It's also 11:45 p.m., and I've got a long way to go.
First, we've got three "prognostic equations" - one for T, one for u, and one for v, that we use for weather modeling. Here they are.
We will let the atmosphere be adiabatic, frictionless, and dry, so H=0, a=0, and T_v = T. The flow will be geostrophic (for simplicity purposes).
In this case, the state of a sample of air is described by six dependent variables: T, rho, Z, u, v, and omega. Each dependent variable has a value at each point (x, y, p, t). These points are in a grid in the atmosphere called the "model domain."
Because we have six unknowns, we need three more equations. We already have these.
These are called the diagnostic equations because they don't contain time derivatives and don't have any prognostic value. Therefore, they allow us to find rho, Z, and omega from the predicted variables T, u, and v.
Why do weather predictions suck?
Well first off, they don't, thank you very much. But they've got one big thing working against them, and that is that the atmosphere is a chaotic system; it is one whose future states are sensitive to its initial state. That's kind of the nature of the beast itself.
There are four other main points that Professor Houze brought up in his lectures that talk about some of the reasons models aren't as accurate as they could be. Here they are:
1.) Input data are incomplete
- this is especially true over oceans, deserts, polar ice caps, Siberia, the Congo, etc. Certainly not over Oklahoma City.
2.) Small scale processes are not observed (you can't get in between every grid point)
3.) Observational errors - some people are dumb, but nobody's perfect
4.) Errors with friction and heating in the mathematical representations of the equations.