Data Assimilation

Data assimilation is how a forecast model learns the present: it blends millions of scattered, imperfect observations with a short prior forecast to produce the best estimate of the atmosphere's current state.

Definition

Data assimilation is the process of combining observations with a model-based prior estimate, weighted by their respective uncertainties, to produce an optimal analysis of the atmospheric state used to initialize a forecast.

Scope

This topic covers the methods used to estimate the atmospheric initial state for forecasting, including optimal interpolation, three- and four-dimensional variational assimilation, the Kalman filter and ensemble Kalman filter, the treatment of observation and background errors, and the assimilation of satellite and other indirect observations.

Core questions

• How are observations and a prior model forecast combined into a best estimate?
• What roles do observation error and background error play?
• How do variational and ensemble Kalman filter methods differ?
• How are indirect observations such as satellite radiances assimilated?

Key theories

Bayesian state estimation

Data assimilation casts the analysis as a Bayesian estimation problem, combining a prior forecast and new observations weighted by their error covariances to minimize the expected error in the resulting state estimate.

Ensemble Kalman filtering

An ensemble of forecasts is used to estimate the flow-dependent background-error covariances, allowing the filter to update the analysis in a way that reflects the day's uncertainty rather than a fixed statistical model.

Mechanisms

Assimilation starts from a background, a short forecast valid at the analysis time, and corrects it toward incoming observations. The correction weights observations against the background according to their error covariances, so more accurate data and uncertain regions of the background receive more influence. Variational methods minimize a cost function measuring departures from both the background and the observations, optionally over a time window, while ensemble methods estimate the background-error statistics from the spread of an ensemble of forecasts. Observation operators map model variables to observed quantities such as satellite radiances.

Clinical relevance

Because forecast quality depends critically on the initial conditions, data assimilation is central to operational prediction; advances in assimilating satellite observations are widely credited as a leading driver of the steady improvement in global forecast skill over recent decades.

History

Early objective analysis used hand and statistical interpolation of observations onto grids; optimal interpolation formalized the use of error statistics in the 1960s and 1970s. Variational methods, building on Kalman's filtering theory, came to dominate operational centers in the 1990s, and ensemble Kalman filters introduced by Evensen and others added flow-dependent error estimates that now underpin many hybrid assimilation systems.

Key figures

• Rudolf Kalman
• Geir Evensen
• Andrew Lorenc
• Eugenia Kalnay

Seminal works

• kalnay2003
• evensen1994

Frequently asked questions

Why not just start a forecast from the observations themselves?

Observations are scattered, unevenly spaced, and noisy, and they do not measure every model variable everywhere; assimilation spreads their information sensibly across the grid by combining them with a physically consistent prior forecast.

What is the background in data assimilation?

The background, or first guess, is a short-range forecast valid at the analysis time; assimilation adjusts it toward new observations, so each analysis carries forward information from earlier ones.