Influence-matrix diagnostic of a data assimilation system

The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

Conditioning of incremental variational data assimilation, with application to the Met Office system

Implementations of incremental variational data assimilation require the iterative minimization of a series of linear least-squares cost functions. The accuracy and speed with which these linear minimization problems can be solved is determined by the condition number of the Hessian of the problem. In this study, we examine how different components of the assimilation system influence this condition number. Theoretical bounds on the condition number for a single parameter system are presented and used to predict how the condition number is affected by the observation distribution and accuracy and by the specified lengthscales in the background error covariance matrix. The theoretical results are verified in the Met Office variational data assimilation system, using both pseudo-observations and real data.

A new floating model level scheme for the assimilation of boundary layer top inversions: the univariate assimilation of temperature.

The assimilation of observations with a forecast is often heavily influenced by the description of the error covariances associated with the forecast. When a temperature inversion is present at the top of the boundary layer (BL), a significant part of the forecast error may be described as a vertical positional error (as opposed to amplitude error normally dealt with in data assimilation). In these cases, failing to account for positional error explicitly is shown t o r esult in an analysis for which the inversion structure is erroneously weakened and degraded. In this article, a new assimilation scheme is proposed to explicitly include the positional error associated with an inversion. This is done through the introduction of an extra control variable to allow position errors in the a priori to be treated simultaneously with the usual amplitude errors. This new scheme, referred to as the ‘floating BL scheme’, is applied to the one-dimensional (vertical) variational assimilation of temperature. The floating BL scheme is tested with a series of idealised experiments a nd with real data from radiosondes. For each idealised experiment, the floating BL scheme gives an analysis which has the inversion structure and position in agreement with the truth, and outperforms the a ssimilation which accounts only for forecast a mplitude error. When the floating BL scheme is used to assimilate a l arge sample of radiosonde data, its ability to give an analysis with an inversion height in better agreement with that observed is confirmed. However, it is found that the use of Gaussian statistics is an inappropriate description o f t he error statistics o f t he extra c ontrol variable. This problem is alleviated by incorporating a non-Gaussian description of the new control variable in the new scheme. Anticipated challenges in implementing the scheme operationally are discussed towards the end of the article.