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Geopotential in 500 hPa (solid, black lines) and Vorticity advection in 10⁵/(s*6h) (colored lines)

Tarife:

The two types of vorticity advection are positive (PVA) and negative vorticity advection (NVA). The closed circles in the figure show the 500 hPa absolute vorticity lines, the others the 500 hPa height lines. When an air parcel is moving from an area higher vorticity to an area lower vorticity this is called: PVA (red color). The other way around is called: NVA (blue color). PVA is associated with upper-air divergence, i.e. upward vertical motion. NVA is associated with down ward vertical motion. Therefore, PVA  at 500 hPa is strongest above a surface low, while NVA at 500 hPa is strongest above a surface high.
In operational meteorology Vorticity advection maps are used to identify areas with vertical air motion to see where clouds, precipitation or clear conditions are likely to occur. Keep in mind, however, that PVA is not the same as upward vertical motion. Here temperature advection is important too.

Spaghetti plots:

are a method of viewing data from an ensemble forecast.
A meteorological variable e.g. pressure, temperature is drawn on a chart for a number of slightly different model runs from an ensemble. The model can then be stepped forward in time and the results compared and be used to gauge the amount of uncertainty in the forecast.
If there is good agreement and the contours follow a recognisable pattern through the sequence then the confidence in the forecast can be high, conversely if the pattern is chaotic i.e resembling a plate of spaghetti then confidence will be low. Ensemble members will generally diverge over time and spaghetti plots are quick way to see when this happens.

Spaghetti plot. (2009, July 7). In Wikipedia, The Free Encyclopedia. Retrieved 20:22, February 9, 2010, from http://en.wikipedia.org/w/index.php?title=Spaghetti_plot&oldid=300824682

NWP:

Numerical weather prediction uses current weather conditions as input into mathematical models of the atmosphere to predict the weather. Although the first efforts to accomplish this were done in the 1920s, it wasn't until the advent of the computer and computer simulation that it was feasible to do in real-time. Manipulating the huge datasets and performing the complex calculations necessary to do this on a resolution fine enough to make the results useful requires the use of some of the most powerful supercomputers in the world. A number of forecast models, both global and regional in scale, are run to help create forecasts for nations worldwide. Use of model ensemble forecasts helps to define the forecast uncertainty and extend weather forecasting farther into the future than would otherwise be possible.

Wikipedia, Numerical weather prediction, http://en.wikipedia.org/wiki/Numerical_weather_prediction(as of Feb. 9, 2010, 20:50 UTC).