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Data assimilation (DA) methods for convective‐scale numerical weather prediction at operational centres are surveyed. The operational methods include variational methods (3D‐Var and 4D‐Var), ensemble methods (LETKF) and hybrids between variational and ensemble methods (3DEnVar and 4DEnVar). At several operational centres, other assimilation algorithms, like latent heat nudging, are additionally applied to improve the model initial state, with emphasis on convective scales. It is demonstrated that the quality of forecasts based on initial data from convective‐scale DA is significantly better than the quality of forecasts from simple downscaling of larger‐scale initial data. However, the duration of positive impact depends on the weather situation, the size of the computational domain and the data that are assimilated. Furthermore it is shown that more advanced methods applied at convective scales provide improvements over simpler methods. This motivates continued research and development in convective‐scale DA. Challenges in research and development for improvements of convective‐scale DA are also reviewed and discussed. The difficulty of handling the wide range of spatial and temporal scales makes development of multi‐scale assimilation methods and space–time covariance localization techniques important. Improved utilization of observations is also important. In order to extract more information from existing observing systems of convective‐scale phenomena (e.g. weather radar data and satellite image data), it is necessary to provide improved statistical descriptions of the observation errors associated with these observations.

Abstract. Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examples and in operational numerical weather prediction models. A simple law is derived to relate model error to likely shadowing performance (how long the model can stay close to the observations). Imperfect model experiments are used to contrast the performance of truncated models relative to a high resolution run, and the operational model relative to the analysis. In both cases the component of forecast error due to state-dependent model error tends to grow as the square-root of forecast time, and provides a major source of error out to three days. These initial results suggest that model error plays a major role and calls for further research in quantifying both the local model drift and expected shadowing times.

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Abstract. Climate proxy data provide noisy, and spatially incomplete information on some aspects of past climate states, whereas palaeosimulations with climate models provide global, multi-variable states, which may however differ from the true states due to unpredictable internal variability not related to climate forcings, as well as due to model deficiencies. Using data assimilation for combining the empirical information from proxy data with the physical understanding of the climate system represented by the equations in a climate model is in principle a promising way to obtain better estimates for the climate of the past.Data assimilation has been used for a long time in weather forecasting and atmospheric analyses to control the states in atmospheric General Circulation Models such that they are in agreement with observation from surface, upper air, and satellite measurements. Here we discuss the similarities and the differences between the data assimilation problem in palaeoclimatology and in weather forecasting, and present and conceptually compare three data assimilation methods that have been developed in recent years for applications in palaeoclimatology. All three methods (selection of ensemble members, Forcing Singular Vectors, and Pattern Nudging) are illustrated by examples that are related to climate variability over the extratropical Northern Hemisphere during the last millennium. In particular it is shown that all three methods suggest that the cold period Correspondence to: M. Widmann (m.widmann@bham.ac.uk) over Scandinavia during 1790-1820 is linked to anomalous northerly or easterly atmospheric flow, which in turn is related to a pressure anomaly that resembles a negative state of the Northern Annular Mode.