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I. M. Moroz

Abstract

A coupled pair of envelope equations is derived which describe the nonlinear evolution of slowly varying wave packets in a three-layer model of baroclinic instability on a βplane. The equations are identical in form to those obtained by Pedlosky (1972) to study wave-packet evolution in a two-layer model. They are transformable to the Self-Induced Transparency equations of nonlinear optics for complex wave amplitude, and to the sine-Gordon equation for real wave amplitude. Both are known to possess solution solutions, with associated highly predictable behavior.

The three-layer model therefore is another example of a mathematical model of baroclinic instability to exhibit solution behavior. The significance of such solutions to meteorology and oceanography is discussed.

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H. M. Christensen, I. M. Moroz, and T. N. Palmer

Abstract

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and a number of different techniques have been proposed for this purpose. This paper presents new perturbed parameter schemes for use in the European Centre for Medium-Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parameterization scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are varied between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, stochastically perturbed parameterization tendencies (SPPT), and to a model that does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parameterization in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skillful representations of model uncertainty owing to convection parameterization.

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