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. This operation carried out for hundreds of points on a weather chart allows a new weather map for several days ahead to be constructed.
The keystone of this process, however, is getting the initial description of the atmosphere correct, a description based on weather observations flowing in continually from every corner of the world. These come from thousands of ships, land stations, ocean buoys, satellites and weather-balloons, all from different places, 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 adjusts itself accordingly.
There is a danger, of course, that a new observation may be inaccurate, or even wrong. To cope with this eventuality, three-dimensional variation analysis carries the above process a step further. When the computer receives an observation that might require it to revise its first ideas, 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 directions. If it appears consistent, the model makes the appropriate adjustments: if not, the observation is discarded.
Recently, however, meteorologists have succeeded in introducing into the process the fourth dimension, time. With four-dimensional variational analysis or 4DVAR for short, 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 the new observation seems consistent, the model can then revise its picture of the atmosphere as it was at that former time, incorporates this change into its current "snapshot" of the weather map, and then proceeds to do its calculations step by step into the future.
4DVAR in conceptual terms is analogous to the action of the forecaster who, armed with later information, redraws his previous charts, thereby acquiring a better insight into the present condition of the atmosphere. In a different sense, it represents another step towards the ultimate goal of capturing the entire atmosphere in a silicon chip; a post-modern interpretation of the vision of the poet William Blake: "To see the world in a grain of sand . . ."