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**1 - 3**of**3**### Assimilation of Stratospheric Chemical Tracer Observations Using a Kalman Filter. Part I: Formulation

, 1999

"... The first part of this two-part article describes the formulation of a Kalman filter system for assimilating limb-sounding observations of stratospheric chemical constituents into a tracer transport model. The system is based on a two-dimensional isentropic approximation, permitting a full Kalman fi ..."

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The first part of this two-part article describes the formulation of a Kalman filter system for assimilating limb-sounding observations of stratospheric chemical constituents into a tracer transport model. The system is based on a two-dimensional isentropic approximation, permitting a full Kalman filter implementation and a thorough study of its behavior in a real-data environment. Datasets from two instruments on the Upper Atmosphere Research Satellite with very different viewing geometries are used in the assimilation experiments. A robust chi-squared diagnostic, which compares statistics of the observed-minus-forecast residuals with those calculated by the filter algorithm, is used to help formulate the statistical inputs to the filter, as well as to tune covariance parameters and to validate the assimilation results. Two significant departures from the standard (discrete) Kalman filter formulation were found to be important in this study. First, it was discovered that the standard Kalman filter covariance propagation is highly inaccurate for this problem. Spurious and rapid loss of variance and increase of correlation length scales occur as a result of diffusion of the small-scale structures inherent in tracer error covariance fields. A new formulation based on well-understood properties of the continuum error covariance propagation was therefore introduced. Second, validation diagnostics suggested that the initial error, model error, and representativeness error are all more appropriately assumed to be relative than absolute in this problem. A filter formulation for relative errors was therefore devised. With these two modifications, this Kalman filter assimilation system has only three tunable variance parameters and one tunable correlation length-scale parameter. 1.

### Environmental Prediction global model

, 2004

"... Assessing a local ensemble Kalman filter: perfect model ..."

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### experiments with the National Centers for Environmental Prediction global model

, 2004

"... The accuracy and computational efficiency of the recently proposed local ensemble Kalman filter (LEKF) data assimilation scheme is investigated on a state-of-the-art operational numerical weather prediction model using simulated observations. The model selected for this purpose is the T62 horizontal ..."

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The accuracy and computational efficiency of the recently proposed local ensemble Kalman filter (LEKF) data assimilation scheme is investigated on a state-of-the-art operational numerical weather prediction model using simulated observations. The model selected for this purpose is the T62 horizontal- and 28-level vertical-resolution version of the Global Forecast System (GFS) of the National Center for Environmental Prediction. The performance of the data assimilation system is assessed for different configurations of the LEKF scheme. It is shown that a modest size (40-member) ensemble is sufficient to track the evolution of the atmospheric state with high accuracy. For this ensemble size, the computational time per analysis is less than 9 min on a cluster of PCs. The analyses are extremely accurate in the mid-latitude storm track regions. The largest analysis errors, which are typically much smaller than the observational errors, occur where parametrized physical processes play important roles. Because these are also the regions where model errors are expected to be the largest, limitations of a real-data implementation of the ensemble-based Kalman