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We present a non‐Gaussian ensemble data assimilation method based on the maximum‐likelihood ensemble filter, which allows for any combination of Gaussian, lognormal, and reverse lognormal errors in both the background and the observations. The technique is fully nonlinear, does not require a tangent linear model, and uses a Hessian preconditioner to minimise the cost function efficiently in ensemble space. When the Gaussian assumption is relaxed, the results show significant improvements in the analysis skill within two atmospheric toy models, and the performance of data assimilation systems for (semi)bounded variables is expected to improve.more » « less
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Van_Loon, Senne; Thompson, David_W J (, Geophysical Research Letters)Abstract We compare insights provided by local and large‐scale perspectives of extreme heat events in ERA5 near‐surface temperature data. Heat waves where temperatures exceed four standard deviations about the climatological‐mean are expected less than once a century locally but occur roughly once every 10 days somewhere in the Northern Hemisphere midlatitudes. The high frequency of occurrence indicated by the hemispheric perspective is not well represented by normal statistics because it strongly depends on the shapes of the local temperature distributions. The large effective sample size afforded by the hemispheric perspective provides robust evidence of trends in the frequency of occurrence of extreme heat events integrated over the Northern Hemisphere. It also confirms that trends in heat events summed over the hemisphere can be explained by changes in mean temperature alone.more » « less
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