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How Weather Modeling Gets Better
Dr_Ish writes: Bob Henson over at Weather Underground has posted a fascinating discussion of the recent improvements made to the major weather models that are used to forecast hurricanes and the like. The post also included interesting links that explain more about the models. Quoting: "The latest version of the ECMWF model, introduced in May, has significant changes to model physics and the ways in which observations are brought into and used within the model. The overall improvements include better portrayal of clouds and precipitation, including a more accurate depiction of intense rainfall. The main effect of the model upgrade for tropical cyclones is slightly lower central pressure. During the first 3 days of a forecast, the ECMWF has tended to have a slight weak bias on tropical cyclones; the new version is closer to the mark."
Weather often varies dramatically over small distances. It may be sunny at the studio and raining 1/2 a mile away where you are. Rain predictions are not 50% chance that a given spot will get an inch of rain. The prediction is that 50% of a large area will get a inch of rain. Big difference between those.
Yes, but it's not that simple.
The partial differential equations you're referring to are the Navier-Stokes equations, which have no known analytical solution. Instead, they're solved numerically with atmospheric data on a three dimensional grid. There are still a few problems here:
1) Although dx, dy, dz, and dt are pretty small these days, an order of magnitude lower than a couple of decades ago, we don't have in situ observations every dx, dy, and dz. You might have a few grid points in each county of the US now, perhaps more depending on the model. You probably don't have that many observations in most cases, and certainly not over the oceans where such observations are quite sparse. There are efforts to better assimilate observations into the models than what's been used in the past. For the most part, this has been a trend away from schemes such as a two pass Barnes Analysis and toward more complex and stochastic schemes such as the Ensemble Kalman Filter. Regardless, the first guess in any of these schemes is a forecast from a previous run of the model, which may or may not be a good approximation of the state of the atmosphere. The atmosphere is a chaotic system, so small errors in the initial state will grow greatly with time. Lewis Fry Richardson, one of the fathers of numerical weather prediction, put the theoretical limit on numerical weather forecasting with any skill at around three weeks.
2) There are processes that aren't directly simulated the model. These include surface processes like evapotranspiration and conduction of heat from the surface downward or into the lowest layer of air. Radiative transfer is another key process and it's affected by aerosols in the atmosphere. There are atmospheric circulations that occur on scales smaller than dx, dy, and dz such as subgrid turbulence and circulations in the lowest part of the atmosphere, the planetary boundary layer. Many of the global models such as the ECMWF, GFS, and UkMet have a coarse enough grid spacing that they can't resolve things like a thunderstorm. Microphysics, the types of hydrometeors like warm rain, ice crystals, snow, and graupel can't be directly simulated though the model dynamics, either. However, all of these things are very important to producing anything accurately resembling an accurate forecast. These are parameterized in the model instead of being explicitly resolved. The parameterizations have improved but they're still a somewhat coarse approximation.
There's a whole lot more involved than solving a few partial differential equations. If only numerical weather prediction were that simple...