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Abstract

The largest errors in weather and climate predictions are generally associated with near bound variables such as aerosols, clouds and precipitation. These variables are "near-bound" in the sense that they are non-negative (bounded at zero) and that the error standard deviation of their observations and forecasts is not that different from the distance of their true value from the bound. Typically, the observation error standard deviation decreases as the true value of the variable approaches the bound and is typically specified by a relative standard deviation rather than an absolute standard deviation. The associated uncertainty distributions for both forecasts and observations of these variables are typically highly skewed and non-Gaussian. Sometimes the observed variables are non-linear functions of the underlying model variables. In this paper, we will show how well-known data assimilation frameworks such as Serial Ensemble Kalman Filters that assimilate observations in batches, Ensemble Kalman Filters that assimilate observations all at the same time (e.g. ETKF), and variational schemes such as 3DVar and 4DVar, can all be adjusted to greatly improve their ability to accommodate these bounded variables. The new theory will be explained and illustrated with simple examples in which the new method profoundly outperforms methods that attempt to treat these variables in the same way as other (Gaussian) variables.