Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

Poetry on Pre-Raphaelite principles: science, nature and knowledge in William Michael Rossetti’s 'Fancies at Leisure' and 'Mrs. Holmes Grey'

This article demonstrates how early Pre-Raphaelite poetry worked according to the principle that art should be modelled on science theorised by the Pre-Raphaelites in their early essays. As the main theorists (rather than practitioners) of Pre-Raphaelite art, F. G. Stephens and William Michael Rossetti defined the Pre-Raphaelite project in terms of observation, investigation, experiment, the “adherence to fact” and the “search after truth”. In the hands of the early Pre-Raphaelite poets, and particularly Rossetti himself, poetry too becomes a mode of scientific enquiry into the natural world, the nature of observation, human psychology and medical practice.

Persia and kingship in William Cartwright's The Royall Slave (1636)

The recent reorientation of early modern studies draws attention to the Renaissance stage as a site of exploration of images of the Islamic world. This article examines the use of ancient and contemporary Persia in William Cartwright’s The Royall Slave (1636), in which Persia figures as a convenient space through which to examine political issues relevant to the audience at home in England. Assessing the construction of idealized societies and rulers in the play, The Royall Slave is a contemporary Court and academic drama that demonstrates its importance as one of a number of synchronous texts that represent Persia.