FOUR dimensional variational analysis, or 4DVAR for short, is all the rage in weather circles nowadays. The forecaster to whom 4DVAR is not available, must languish in "grim visag'd comfortless despair": it is the haute chic of modern meteorology.
Forecasting by computer is based on a mathematical model of the atmosphere. Given values of pressure, temperature and humidity at a certain spot, the model calculates the expected values of these elements in the same place at a future time. When this operation is carried out for hundreds of points, on a weather chart, a new weather map for some days ahead can be constructed.
The keystone of this entire process, however, is getting the initial description of the atmosphere correct - a description based on weather observations flowing in continually from all parts of the world. These include reports from a huge number of ships, land stations, ocean buoys, satellites, aircraft and weather balloons - all from different locations, relating to different times and having widely varying degrees of accuracy.
The objective is achieved by means of "variational analysis". When a new observation comes to hand, the computer checks to see how much it varies from the value already estimated by the model for that time and place: if the variation is significant, the model makes the appropriate adjustment.
There is a danger, of course, that the new observation may be inaccurate, or even totally wrong. Three dimensional variation analysis, therefore, carries the above process a step further. When the computer model receives an observation that might require it to revise its first thoughts significantly, it first compares the new information to other reports available from both above and below the point in question, and for several hundred miles in all direction. If it appears consistent, the model makes the appropriate adjustments: if not, the observation is discarded.
Time is the fourth dimension used in 4DVAR. With this technique the computer not only relates new data to, information already available for the same time in the same general locality - but also to neighbouring observations for, say, 12 hours previously.
If necessary, the model then revises its picture of the atmosphere as it was at that former time, incorporates this change into its current "snapshot" of the weather map - and their proceeds to do its calculations step by step into the future.
The situation is analogous to that of the forecaster who, armed with later information, redraws his previous charts, thereby acquiring a better insight into the current condition of the atmosphere.