# Assimilation of time-averaged observations in a quasi-geostrophic atmospheric jet model

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## Abstract

The problem of reconstructing past climates from a sparse network of noisy time-averaged observations is considered with a novel ensemble Kalman filter approach. Results for a sparse network of 100 idealized observations for a quasi-geostrophic model of a jet interacting with a mountain reveal that, for a wide range of observation averaging times, analysis errors are reduced by about 50% relative to the control case without assimilation. Results are robust to changes to observational error, the number of observations, and an imperfect model. Specifically, analysis errors are reduced relative to the control case for observations having errors up to three times the climatological variance for a fixed 100-station network, and for networks consisting of ten or more stations when observational errors are fixed at one-third the climatological variance. In the limit of small numbers of observations, station location becomes critically important, motivating an optimally determined network. A network of fifteen optimally determined observations reduces analysis errors by 30% relative to the control, as compared to 50% for a randomly chosen network of 100 observations.

## Keywords

Data assimilation Paleoclimate Ensemble Kalman filter Atmospheric modeling## Notes

### Acknowledgments

We thank Ryan Torn for discussions on ensemble filtering, Jeff Anderson for helpful comments on an earlier version of the manuscript, and Angie Pendergrass for discussions on literature related to paleoclimate state estimation and for reviewing an earlier version of the paper. We also thank two anonymous reviewers, whose comments have made this a better paper. The first author was supported in part by a National Science Foundation VIGRE grant and the second author was supported by the following grants: National Oceanic and Atmospheric Administration CSTAR Grant NA17RJ1232, Office of Naval Research Grant N00014-06-1-0510, and National Science Foundation grants 0552004 and 0902500, awarded to the University of Washington.

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