# Data assimilation

Every day the Met Office receives around half a million observations recording the atmospheric conditions around the world. However, even with this many observations we do not have enough information to tell us what the atmosphere is doing at all points on and above the Earth's surface.

There are large areas of ocean, inaccessible regions on land and remote levels in the atmosphere where we have very few, or no, observations. To fill in the 'gaps' we can combine what observations we do have with forecasts of what we expect the conditions in the atmosphere to be. This is a process called data assimilation and gives us our best estimate of the current state of the atmosphere — the first step in producing a weather forecast.

Without data assimilation, any attempt to produce reliable forecasts is almost certain to end in failure.

## How does data assimilation work?

Assimilating data into our supercomputers requires sophisticated mathematics, but the example below explains the basic principles.

In practice a data assimilation system has to do much more than this. Globally we need to use measurements of all the major atmospheric properties (pressure, temperature, wind, humidity), whereas locally we may need to use rainfall and visibility measurements as well.

We have to be able to include observations made at different times and of varying quality, and to use our understanding of the processes at work in the atmosphere to ensure that our final estimate is really the best we can achieve.

## Forecasting for a specific site — a large field

We want to be able to estimate what the temperature is at any given point in the large field. Some recent observations have been made at a few locations at the site and plotted (as blue circles, Fig. 1) on a map of the area.

Fig. 1

By calculating and plotting contours (the blue lines, Fig. 2), we can make a first guess at what the temperature is in the areas of the field where we don't have measurements. Obviously the more observations we have to do this the greater the confidence we will have in our prediction.

Fig. 2

We can improve on this first guess by using another source of information — a previous temperature forecast for the site. Plotting this forecast (the red lines, Fig. 3) on top of our observation-only estimate we find that they agree quite closely in some areas, less so in others. What is important, however, is that the forecast predicts the temperature over the whole field, giving us more of an idea as to what may be happening in the areas where we have fewer observations.

Fig. 3

To decide what the best estimate for the temperature will be we use data assimilation. This combines both sources of information, the observations and the forecast (taking into account the accuracy of each), to produce the best overall guess (the black lines, Fig. 4) of the temperature at all locations in the field.

Fig. 4