# Data Assimilation

Data assimilation creates the starting values ​​(weather situation) for a numerical prediction model. It is one of the most important components of a forecast system.

Data assimilation in meteorology is about using different types of weather observations to find out how the weather is at one particular time. What is generally meant by weather is characterized by a variety of atmospheric properties, such as air temperature, wind and cloudiness.

There is a large amount of available weather observations. Some observations are ground-based while others are made from space with satellite-based measuring instruments.

One problem is that the observations are geographically unevenly distributed and in some areas there are no observations of all or some characteristics that characterize the weather. To solve this problem, weather information from the observations is combined with the information from a computer-based weather forecast, valid at the time of observation.

Through this procedure one can, through the forecast, get complete information about the weather even in areas where observations are missing.

## Combination of information

In areas where we have weather observations, we find out how the weather is through a combination of observed atmospheric properties and the predicted properties. This is because weather observations as well as weather forecasts may contain errors. Calculating how to combine the information is an important part of meteorological data assimilation.

To get a complete picture of how the weather is at a certain time is interesting in itself, but the weather condition obtained by data assimilationis also used as the starting state for the computer-based weather forecast. The forecast quality is highly dependent on a correct starting field because the atmosphere is designed so that errors in the initial state can rapidly grow and result in major undesirable errors in weather forecasts.

## Different methods

There are a variety of methods for atmospheric data assimilation. At SMHI we use variational data assimilation for the atmosphere. This is formulated as optimization problems where we define a penalty function that is minimized. The penalty function consists of a part that depends on the reliability of the observations and a part that depends on the reliability of the computer-based weather forecast at the time of observation. Reliability is based on estimated typical errors for different weather observations and also for computer-based weather forecasts. The minimization of the penalty is numerically achieved by an iterative procedure and the atmospheric state that minimizes penalty function is the best consistent with observations as well as computer-based prediction.