Skip to main content
U.S. flag

An official website of the United States government

Dot Gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Estimation of Analysis and Forecast Error Variances


Accurate estimates of error variances in numerical analyses and forecasts (i.e. difference between analysis or forecast fields and nature on the resolved scales) are critical for the evaluation of forecasting systems, the tuning of data assimilation (DA) systems and the proper initialisation of ensemble forecasts. Errors in observations and the difficulty in their estimation, the fact that estimates of analysis errors derived via DA schemes, are influenced by the same assumptions as those used to create the analysis fields themselves, and the presumed but unknown correlation between analysis and forecast errors make the problem difficult. In this paper, an approach is introduced for the unbiased estimation of analysis and forecast errors. The method is independent of any assumption or tuning parameter used in DA schemes. The method combines information from differences between forecast and analysis fields (‘perceived forecast errors’) with prior knowledge regarding the time evolution of (1) forecast error variance and (2) correlation between errors in analyses and forecasts. The quality of the error estimates, given the validity of the prior relationships, depends on the sample size of independent measurements of perceived errors. In a simulated forecast environment, the method is demonstrated to reproduce the true analysis and forecast error within predicted error bounds. The method is then applied to forecasts from four leading numerical weather prediction centres to assess the performance of their corresponding DA and modelling systems. Error variance estimates are qualitatively consistent with earlier studies regarding the performance of the forecast systems compared. The estimated correlation between forecast and analysis errors is found to be a useful diagnostic of the performance of observing and DA systems. In case of significant model-related errors, a methodology to decompose initial value and model-related forecast errors is also proposed and successfully demonstrated.

Article / Publication Data
Available Metadata
Accepted On
September 30, 2014
Fiscal Year
Peer Reviewed
Publication Name
Tellus A: Dynamic Meteorology and Oceanography
Published On
November 24, 2014
Publisher Name
Taylor & Francis Online
Print Volume
Print Number
Page Range
Submitted On
June 17, 2013


Authors who have authored or contributed to this publication.